Subgroups — #3543×D₆₇ #31763414

Order 17152.

8814 conjugacy classes of subgroups.

The subgroup lattice has 1672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574543	C₂	1	1	yes	maximal, characteristic, complemented
2	#22574542	C₂	1	1	yes	maximal, characteristic, complemented
3	#22574541	C₂	1	4	yes	maximal, complemented
4	#22574540	C₂	1	1	yes	maximal, characteristic, complemented
5	#22574539	C₂	1	2	yes	maximal, complemented
6	#22574538	C₂	1	4	yes	maximal, complemented
7	#22574537	C₂	1	4	yes	maximal, complemented
8	#22574536	C₂	1	4	yes	maximal, complemented
9	#22574535	C₂	1	4	yes	maximal, complemented
10	#22574534	C₂	1	4	yes	maximal, complemented
11	#22574533	C₂	1	2	yes	maximal, complemented
12	#560×D₆₇	C₂	1	4	yes	maximal, complemented
13	#559×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#550×D₆₇	C₂	1	2	yes	maximal, complemented
15	#546×D₆₇	C₂	1	4	yes	maximal, complemented
16	D₄²×D₆₇	C₂	1	4	yes	maximal, complemented
17	D₄²×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#540×D₆₇	C₂	1	4	yes	maximal, complemented
19	#535×D₆₇	C₂	1	4	yes	maximal, complemented
20	#534×D₆₇	C₂	1	4	yes	maximal, complemented
21	C₂×#127×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#529×D₆₇	C₂	1	2	yes	maximal, complemented
23	C₆₇×#3543	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×D₆₇	C₂²	1	4	yes	complemented
25	C₂²×D₄×D₆₇	C₂²	1	4	yes	complemented
26	C₂²×D₄×D₆₇	C₂²	1	4	yes	complemented
27	C₂²×D₄×D₆₇	C₂²	1	4	yes	complemented
28	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
29	#16864137	C₂²	1	8	yes	complemented
30	#16864136	C₂²	1	4	yes	complemented
31	#16864136	C₂²	1	8	yes	complemented
32	#16864135	C₂²	1	8	yes	complemented
33	#16864135	C₂²	1	4	yes	complemented
34	#16864134	C₂²	1	8	yes	complemented
35	#16864134	C₂²	1	8	yes	complemented
36	#16864134	C₂²	1	8	yes	complemented
37	#16864133	C₂²	1	4	yes	complemented
38	#16864132	C₂²	1	1	yes	characteristic, complemented
39	#16864131	C₂²	1	2	yes	complemented
40	#16864130	C₂²	1	4	yes	complemented
41	#16864129	C₂²	1	4	yes	complemented
42	#16864128	C₂²	1	4	yes	complemented
43	#16864068	C₂²	1	2	yes	complemented
44	#16864067	C₂²	1	4	yes	complemented
45	#16864067	C₂²	1	2	yes	complemented
46	#16864066	C₂²	1	2	yes	complemented
47	#16864066	C₂²	1	4	yes	complemented
48	#16864065	C₂²	1	4	yes	complemented
49	#16864064	C₂²	1	4	yes	complemented
50	#16864064	C₂²	1	8	yes	complemented
51	#16864043	C₂²	1	4	yes	complemented
52	#16864042	C₂²	1	4	yes	complemented
53	#16864041	C₂²	1	4	yes	complemented
54	#16864040	C₂²	1	4	yes	complemented
55	#16864039	C₂²	1	4	yes	complemented
56	#16864038	C₂²	1	8	yes	complemented
57	#16864037	C₂²	1	4	yes	complemented
58	#16864036	C₂²	1	8	yes	complemented
59	#16864035	C₂²	1	8	yes	complemented
60	#16864034	C₂²	1	4	yes	complemented
61	#16864033	C₂²	1	8	yes	complemented
62	D₄×D₂₆₈	C₂²	1	4	yes	complemented
63	D₄×D₂₆₈	C₂²	1	4	yes	complemented
64	D₄×D₂₆₈	C₂²	1	2	yes	complemented
65	#16864031	C₂²	1	1	yes	characteristic, complemented
66	#16864031	C₂²	1	4	yes	complemented
67	#16864030	C₂²	1	4	yes	complemented
68	#16864030	C₂²	1	8	yes	complemented
69	#16864030	C₂²	1	4	yes	complemented
70	#16864030	C₂²	1	4	yes	complemented
71	D₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
72	D₄×C₂²⋊D₆₇	C₂²	1	8	yes	complemented
73	D₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
74	D₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
75	#16864028	C₂²	1	8	yes	complemented
76	#16864028	C₂²	1	8	yes	complemented
77	#16864028	C₂²	1	4	yes	complemented
78	#16864002	C₂²	1	4	yes	complemented
79	#16864001	C₂²	1	4	yes	complemented
80	#16864000	C₂²	1	4	yes	complemented
81	#16863999	C₂²	1	4	yes	complemented
82	#16863999	C₂²	1	4	yes	complemented
83	#16863998	C₂²	1	8	yes	complemented
84	#16863998	C₂²	1	8	yes	complemented
85	#16863997	C₂²	1	4	yes	complemented
86	#16863997	C₂²	1	4	yes	complemented
87	#16863996	C₂²	1	8	yes	complemented
88	#16863996	C₂²	1	8	yes	complemented
89	#16863965	C₂²	1	4	yes	complemented
90	#16863964	C₂²	1	4	yes	complemented
91	#16863964	C₂²	1	4	yes	complemented
92	#16863963	C₂²	1	4	yes	complemented
93	#16863962	C₂²	1	8	yes	complemented
94	#16863962	C₂²	1	8	yes	complemented
95	#16863961	C₂²	1	8	yes	complemented
96	#16863961	C₂²	1	8	yes	complemented
97	#16863960	C₂²	1	4	yes	complemented
98	#16863959	C₂²	1	4	yes	complemented
99	#16863959	C₂²	1	4	yes	complemented
100	#16863958	C₂²	1	4	yes	complemented
101	#16863957	C₂²	1	8	yes	complemented
102	#16863957	C₂²	1	4	yes	complemented
103	#16863957	C₂²	1	4	yes	complemented
104	#16863956	C₂²	1	8	yes	complemented
105	#16863956	C₂²	1	4	yes	complemented
106	#16863956	C₂²	1	4	yes	complemented
107	#16863955	C₂²	1	4	yes	complemented
108	#16863955	C₂²	1	4	yes	complemented
109	#16863954	C₂²	1	8	yes	complemented
110	#16863954	C₂²	1	8	yes	complemented
111	C₂×#14524040	C₂²	1	1	yes	characteristic, complemented
112	C₂×#14524039	C₂²	1	4	yes	complemented
113	C₂×#14524039	C₂²	1	2	yes	complemented
114	#127×D₆₇	C₂²	1	1	yes	characteristic
115	#127×D₆₇	C₂²	1	1	yes	characteristic, complemented
116	#127×D₆₇	C₂²	1	4	yes	complemented
117	#127×D₆₇	C₂²	1	1	yes	characteristic, complemented
118	#127×D₆₇	C₂²	1	4	yes	complemented
119	#127×D₆₇	C₂²	1	2	yes	complemented
120	#127×D₆₇	C₂²	1	4	yes	complemented
121	#127×D₆₇	C₂²	1	2	yes	complemented
122	#127×D₆₇	C₂²	1	1	yes	characteristic, complemented
123	#16863933	C₂²	1	2	yes	complemented
124	#16863932	C₂²	1	2	yes	complemented
125	#16863931	C₂²	1	2	yes	complemented
126	#16863930	C₂²	1	2	yes	complemented
127	#16863929	C₂²	1	4	yes	complemented
128	#16863928	C₂²	1	2	yes	complemented
129	#16863927	C₂²	1	2	yes	complemented
130	#16863926	C₂²	1	4	yes	complemented
131	#16863925	C₂²	1	2	yes	complemented
132	#16863924	C₂²	1	4	yes	complemented
133	#16863923	C₂²	1	4	yes	complemented
134	#126×D₆₇	C₂²	1	4	yes	complemented
135	#125×D₆₇	C₂²	1	2	yes	complemented
136	#124×D₆₇	C₂²	1	4	yes	complemented
137	#124×D₆₇	C₂²	1	2	yes	complemented
138	#123×D₆₇	C₂²	1	8	yes	complemented
139	#123×D₆₇	C₂²	1	4	yes	complemented
140	#123×D₆₇	C₂²	1	4	yes	complemented
141	#123×D₆₇	C₂²	1	4	yes	complemented
142	C₂²⋊Q₈×D₆₇	C₂²	1	2	yes	complemented
143	#121×D₆₇	C₂²	1	2	yes	—
144	#121×D₆₇	C₂²	1	4	yes	complemented
145	#121×D₆₇	C₂²	1	4	yes	complemented
146	#121×D₆₇	C₂²	1	8	yes	complemented
147	#121×D₆₇	C₂²	1	8	yes	complemented
148	#121×D₆₇	C₂²	1	8	yes	complemented
149	#121×D₆₇	C₂²	1	8	yes	complemented
150	#120×D₆₇	C₂²	1	8	yes	complemented
151	#120×D₆₇	C₂²	1	4	yes	complemented
152	#120×D₆₇	C₂²	1	8	yes	complemented
153	#120×D₆₇	C₂²	1	4	yes	complemented
154	C₄×Q₈×D₆₇	C₂²	1	2	yes	complemented
155	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
156	C₄×D₄×D₆₇	C₂²	1	2	yes	complemented
157	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
158	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
159	#117×D₆₇	C₂²	1	4	yes	complemented
160	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
161	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
162	#560×C₆₇	C₂²	1	4	yes	complemented
163	#559×C₆₇	C₂²	1	1	yes	characteristic, complemented
164	#550×C₆₇	C₂²	1	2	yes	complemented
165	#546×C₆₇	C₂²	1	4	yes	complemented
166	D₄²×C₆₇	C₂²	1	4	yes	complemented
167	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
168	#540×C₆₇	C₂²	1	4	yes	complemented
169	#535×C₆₇	C₂²	1	4	yes	complemented
170	#534×C₆₇	C₂²	1	4	yes	complemented
171	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
172	#529×C₆₇	C₂²	1	2	yes	complemented
173	C₂⁴×D₆₇	C₂³	1	4	yes	—
174	C₂⁴×D₆₇	C₂³	1	4	yes	—
175	C₂×#11761629	C₂³	1	4	yes	complemented
176	C₂×#11761628	C₂³	1	8	yes	complemented
177	C₂×#11761628	C₂³	1	4	yes	complemented
178	C₂×#11761627	C₂³	1	8	yes	complemented
179	C₂×#11761627	C₂³	1	4	yes	complemented
180	#41×D₆₇	—	4	16	no	—
181	C₂×Q₈×D₆₇	C₂³	1	2	yes	—
182	C₂²×D₂₆₈	C₂³	1	4	yes	complemented
183	C₂²×D₂₆₈	C₂³	1	4	yes	complemented
184	C₂²×D₂₆₈	C₂³	1	4	yes	complemented
185	C₂²×D₂₆₈	C₂³	1	2	yes	complemented
186	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
187	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
188	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
189	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
190	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
191	C₂×D₄×D₆₇	—	4	16	no	—
192	C₂×D₄×D₆₇	—	4	16	no	—
193	C₂×D₄×D₆₇	—	4	8	no	—
194	C₂×D₄×D₆₇	—	4	16	no	—
195	C₂×D₄×D₆₇	C₂³	1	4	yes	—
196	C₂×D₄×D₆₇	C₂³	1	2	yes	—
197	C₂×D₄×D₆₇	C₂³	1	4	yes	—
198	C₂×D₄×D₆₇	C₂³	1	4	yes	—
199	C₂×D₄×D₆₇	C₂³	1	8	yes	—
200	C₂×D₄×D₆₇	C₂³	1	8	yes	—
201	C₂×D₄×D₆₇	C₂³	1	2	yes	—
202	C₂×D₄×D₆₇	C₂³	1	8	yes	—
203	C₂×D₄×D₆₇	C₂³	1	8	yes	—
204	C₂×D₄×D₆₇	C₂³	1	4	yes	—
205	C₂×D₄×D₆₇	C₂³	1	2	yes	—
206	C₂×D₄×D₆₇	C₂³	1	8	yes	complemented
207	C₂×D₄×D₆₇	C₂³	1	8	yes	complemented
208	C₂×D₄×D₆₇	C₂³	1	8	yes	complemented
209	C₂×D₄×D₆₇	C₂³	1	8	yes	complemented
210	C₂×D₄×D₆₇	C₂³	1	4	yes	complemented
211	C₂×D₄×D₆₇	C₂³	1	4	yes	complemented
212	C₂×D₄×D₆₇	C₂³	1	4	yes	complemented
213	C₂×D₄×D₆₇	C₂³	1	4	yes	complemented
214	C₂×D₄×D₆₇	C₂³	1	2	yes	complemented
215	C₂×D₄×D₆₇	C₂³	1	4	yes	complemented
216	C₂×D₄×D₆₇	C₂³	1	2	yes	complemented
217	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
218	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
219	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
220	C₂²×C₄×D₆₇	C₂³	1	8	yes	—
221	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
222	#14524040	C₂³	1	1	yes	characteristic
223	#14524040	C₂³	1	4	yes	complemented
224	#14524040	C₂³	1	4	yes	complemented
225	#14524040	C₂³	1	1	yes	characteristic, complemented
226	#14524040	C₂³	1	2	yes	complemented
227	#14524039	C₂³	1	2	yes	—
228	#14524039	C₂³	1	4	yes	—
229	#14524039	C₂³	1	8	yes	complemented
230	#14524039	C₂³	1	8	yes	complemented
231	#14524039	C₂³	1	4	yes	complemented
232	#14524039	C₂³	1	4	yes	complemented
233	#14524039	C₂³	1	2	yes	complemented
234	#14524039	C₂³	1	4	yes	complemented
235	#14524039	C₂³	1	2	yes	complemented
236	#14524039	C₂³	1	8	yes	complemented
237	#14524039	C₂³	1	2	yes	complemented
238	#14524039	C₂³	1	4	yes	complemented
239	#14524039	C₂³	1	8	yes	complemented
240	#14524039	C₂³	1	8	yes	complemented
241	#14524039	C₂³	1	4	yes	complemented
242	#14524038	C₂³	1	4	yes	complemented
243	#14524038	C₂³	1	4	yes	complemented
244	#14524038	C₂³	1	4	yes	complemented
245	#14524037	C₂³	1	4	yes	complemented
246	#14524036	C₂³	1	4	yes	complemented
247	#14524036	C₂³	1	4	yes	complemented
248	#14524036	C₂³	1	4	yes	complemented
249	#14524035	C₂³	1	2	yes	complemented
250	#14524034	C₂³	1	2	yes	complemented
251	#14524034	C₂³	1	2	yes	complemented
252	#14524033	C₂³	1	4	yes	complemented
253	#14524033	C₂³	1	4	yes	complemented
254	#14524032	C₂³	1	4	yes	complemented
255	#14524032	C₂³	1	2	yes	complemented
256	#14524031	C₂³	1	4	yes	complemented
257	#14524031	C₂³	1	2	yes	complemented
258	#14524030	C₂³	1	4	yes	complemented
259	#14524030	C₂³	1	2	yes	complemented
260	#14524029	C₂³	1	8	yes	complemented
261	#14524029	C₂³	1	8	yes	complemented
262	#14524029	C₂³	1	4	yes	complemented
263	#14524029	C₂³	1	4	yes	complemented
264	#14524028	C₂³	1	8	yes	complemented
265	#14524028	C₂³	1	8	yes	complemented
266	#14524028	C₂³	1	8	yes	complemented
267	#14524028	C₂³	1	8	yes	complemented
268	#14524028	C₂³	1	4	yes	complemented
269	#14524028	C₂³	1	4	yes	complemented
270	#14524027	C₂³	1	8	yes	complemented
271	#14524027	C₂³	1	4	yes	complemented
272	#14524027	C₂³	1	4	yes	complemented
273	#14524027	C₂³	1	4	yes	complemented
274	#14524026	C₂³	1	8	yes	complemented
275	#14524026	C₂³	1	4	yes	complemented
276	#14524026	C₂³	1	4	yes	complemented
277	#14524026	C₂³	1	4	yes	complemented
278	#14524025	C₂³	1	8	yes	complemented
279	#14524025	C₂³	1	8	yes	complemented
280	#14524025	C₂³	1	8	yes	complemented
281	#14524025	C₂³	1	4	yes	complemented
282	#14524025	C₂³	1	4	yes	complemented
283	#14524025	C₂³	1	8	yes	complemented
284	#14524024	C₂³	1	4	yes	complemented
285	#14524024	C₂³	1	8	yes	complemented
286	#14524024	C₂³	1	4	yes	complemented
287	#14524024	C₂³	1	4	yes	complemented
288	#14524023	C₂³	1	2	yes	complemented
289	#14524022	C₂³	1	2	yes	complemented
290	#14524021	C₂³	1	4	yes	complemented
291	#14524020	C₂³	1	4	yes	complemented
292	#14524019	C₂³	1	2	yes	complemented
293	#14524018	C₂³	1	2	yes	—
294	#14524018	C₂³	1	4	yes	complemented
295	#14524018	C₂³	1	4	yes	complemented
296	#14524018	C₂³	1	8	yes	complemented
297	#14524018	C₂³	1	8	yes	complemented
298	#14524018	C₂³	1	8	yes	complemented
299	#14524018	C₂³	1	8	yes	complemented
300	#14524017	C₂³	1	2	yes	—
301	#14524017	C₂³	1	4	yes	complemented
302	#14524017	C₂³	1	4	yes	complemented
303	#14524017	C₂³	1	8	yes	complemented
304	#14524017	C₂³	1	8	yes	complemented
305	#14524017	C₂³	1	8	yes	complemented
306	#14524017	C₂³	1	8	yes	complemented
307	#14524016	C₂³	1	4	yes	—
308	#14524016	C₂³	1	8	yes	complemented
309	#14524016	C₂³	1	8	yes	complemented
310	#14524016	C₂³	1	8	yes	complemented
311	#14524016	C₂³	1	8	yes	complemented
312	#14524016	C₂³	1	8	yes	complemented
313	#14524016	C₂³	1	8	yes	complemented
314	#14524016	C₂³	1	8	yes	complemented
315	#14524016	C₂³	1	8	yes	complemented
316	#14524016	C₂³	1	8	yes	complemented
317	#14524016	C₂³	1	8	yes	complemented
318	#14524015	C₂³	1	4	yes	—
319	#14524015	C₂³	1	8	yes	complemented
320	#14524015	C₂³	1	8	yes	complemented
321	#14524015	C₂³	1	8	yes	complemented
322	#14524015	C₂³	1	8	yes	complemented
323	#14524015	C₂³	1	8	yes	complemented
324	#14524015	C₂³	1	8	yes	complemented
325	#14524015	C₂³	1	8	yes	complemented
326	#14524015	C₂³	1	8	yes	complemented
327	#14524015	C₂³	1	8	yes	complemented
328	#14524015	C₂³	1	8	yes	complemented
329	#14524014	C₂³	1	2	yes	—
330	#14524014	C₂³	1	4	yes	complemented
331	#14524014	C₂³	1	4	yes	complemented
332	#14524014	C₂³	1	8	yes	complemented
333	#14524014	C₂³	1	8	yes	complemented
334	#14524014	C₂³	1	8	yes	complemented
335	#14524014	C₂³	1	8	yes	complemented
336	#14524013	C₂³	1	8	yes	complemented
337	#14524013	C₂³	1	8	yes	complemented
338	#14524013	C₂³	1	8	yes	complemented
339	#14524013	C₂³	1	8	yes	complemented
340	#14524013	C₂³	1	8	yes	complemented
341	#14524013	C₂³	1	8	yes	complemented
342	#14524013	C₂³	1	8	yes	complemented
343	#14524013	C₂³	1	4	yes	complemented
344	#14524013	C₂³	1	8	yes	complemented
345	#14524013	C₂³	1	4	yes	complemented
346	#14524012	C₂³	1	8	yes	complemented
347	#14524012	C₂³	1	4	yes	complemented
348	#14524012	C₂³	1	8	yes	complemented
349	#14524012	C₂³	1	4	yes	complemented
350	#14524011	C₂³	1	8	yes	complemented
351	#14524011	C₂³	1	4	yes	complemented
352	#14524011	C₂³	1	8	yes	complemented
353	#14524011	C₂³	1	8	yes	complemented
354	#14524011	C₂³	1	8	yes	complemented
355	#14524011	C₂³	1	8	yes	complemented
356	#14524011	C₂³	1	8	yes	complemented
357	#14524011	C₂³	1	8	yes	complemented
358	#14524011	C₂³	1	8	yes	complemented
359	#14524011	C₂³	1	4	yes	complemented
360	Q₈×Dic₆₇	C₂³	1	2	yes	complemented
361	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
362	C₄×Dic₁₃₄	C₂³	1	2	yes	complemented
363	#14524008	C₂³	1	2	yes	complemented
364	#14524008	C₂³	1	4	yes	complemented
365	C₄×D₂₆₈	C₂³	1	4	yes	complemented
366	C₄×D₂₆₈	C₂³	1	4	yes	complemented
367	C₄×D₂₆₈	C₂³	1	4	yes	complemented
368	C₄×D₂₆₈	C₂³	1	2	yes	complemented
369	D₄×Dic₆₇	C₂³	1	4	yes	complemented
370	D₄×Dic₆₇	C₂³	1	4	yes	complemented
371	D₄×Dic₆₇	C₂³	1	4	yes	complemented
372	D₄×Dic₆₇	C₂³	1	2	yes	complemented
373	#14524005	C₂³	1	4	yes	complemented
374	#14524005	C₂³	1	4	yes	complemented
375	#14524005	C₂³	1	4	yes	complemented
376	#14524005	C₂³	1	2	yes	complemented
377	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
378	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
379	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
380	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
381	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
382	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	complemented
383	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	complemented
384	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	complemented
385	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
386	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
387	#14524002	C₂³	1	4	yes	complemented
388	#14524001	C₂³	1	4	yes	complemented
389	#14524001	C₂³	1	4	yes	complemented
390	#14524000	C₂³	1	4	yes	complemented
391	#14524000	C₂³	1	4	yes	complemented
392	#14523999	C₂³	1	4	yes	complemented
393	#14523999	C₂³	1	4	yes	complemented
394	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
395	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
396	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
397	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
398	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
399	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
400	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	complemented
401	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
402	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
403	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
404	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
405	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
406	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
407	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
408	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
409	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
410	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
411	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
412	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	complemented
413	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	complemented
414	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic, complemented
415	C₂×C₄×Dic₆₇	C₂³	1	2	yes	complemented
416	C₄²×D₆₇	C₂³	1	2	yes	—
417	C₄²×D₆₇	C₂³	1	1	yes	characteristic
418	C₄²×D₆₇	C₂³	1	1	yes	characteristic
419	C₄²×D₆₇	C₂³	1	4	yes	—
420	C₄²×D₆₇	C₂³	1	2	yes	complemented
421	C₄²×D₆₇	C₂³	1	1	yes	characteristic, complemented
422	C₄²×D₆₇	C₂³	1	1	yes	characteristic, complemented
423	C₂×#41×C₆₇	C₂³	1	4	yes	complemented
424	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
425	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
426	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
427	C₂²×D₄×C₆₇	C₂³	1	2	yes	complemented
428	#127×C₆₇	C₂³	1	1	yes	characteristic
429	#127×C₆₇	C₂³	1	4	yes	complemented
430	#127×C₆₇	C₂³	1	4	yes	complemented
431	#127×C₆₇	C₂³	1	1	yes	characteristic, complemented
432	#127×C₆₇	C₂³	1	2	yes	complemented
433	#126×C₆₇	C₂³	1	4	yes	complemented
434	#125×C₆₇	C₂³	1	2	yes	complemented
435	#124×C₆₇	C₂³	1	4	yes	complemented
436	#124×C₆₇	C₂³	1	2	yes	complemented
437	#123×C₆₇	C₂³	1	8	yes	complemented
438	#123×C₆₇	C₂³	1	4	yes	complemented
439	#123×C₆₇	C₂³	1	4	yes	complemented
440	#123×C₆₇	C₂³	1	4	yes	complemented
441	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
442	#121×C₆₇	C₂³	1	2	yes	—
443	#121×C₆₇	C₂³	1	4	yes	complemented
444	#121×C₆₇	C₂³	1	4	yes	complemented
445	#121×C₆₇	C₂³	1	8	yes	complemented
446	#121×C₆₇	C₂³	1	8	yes	complemented
447	#121×C₆₇	C₂³	1	8	yes	complemented
448	#121×C₆₇	C₂³	1	8	yes	complemented
449	#120×C₆₇	C₂³	1	8	yes	complemented
450	#120×C₆₇	C₂³	1	4	yes	complemented
451	#120×C₆₇	C₂³	1	8	yes	complemented
452	#120×C₆₇	C₂³	1	4	yes	complemented
453	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
454	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
455	C₄×D₄×C₆₇	C₂³	1	2	yes	complemented
456	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
457	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
458	#117×C₆₇	C₂³	1	4	yes	complemented
459	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	complemented
460	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic, complemented
461	C₂³×D₆₇	—	2	16	no	—
462	C₂³×D₆₇	—	4	16	no	—
463	C₂³×D₆₇	—	4	16	no	—
464	C₂³×D₆₇	—	4	8	no	—
465	C₂³×D₆₇	C₂⁴	1	4	yes	—
466	C₂³×D₆₇	C₂⁴	1	4	yes	—
467	C₂³×D₆₇	C₂⁴	1	4	yes	—
468	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
469	C₂³×D₆₇	C₂⁴	1	4	yes	—
470	C₂³×D₆₇	C₂⁴	1	4	yes	—
471	C₂³×D₆₇	C₂⁴	1	4	yes	—
472	C₂³×D₆₇	C₂⁴	1	4	yes	—
473	C₂³×D₆₇	C₂⁴	1	8	yes	—
474	#11761629	—	4	8	no	—
475	#11761628	—	4	16	no	—
476	#11761628	—	4	8	no	—
477	#11761627	—	4	8	no	—
478	#11761627	—	4	16	no	—
479	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
480	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
481	Q₈×D₆₇	—	2	8	no	—
482	C₂×D₂₆₈	—	4	8	no	—
483	C₂×D₂₆₈	—	4	8	no	—
484	C₂×D₂₆₈	—	4	8	no	—
485	C₂×D₂₆₈	—	4	4	no	—
486	C₂×D₂₆₈	C₂⁴	1	4	yes	—
487	C₂×D₂₆₈	C₂⁴	1	2	yes	—
488	C₂×D₂₆₈	C₂⁴	1	4	yes	—
489	C₂×D₂₆₈	C₂⁴	1	4	yes	—
490	C₂×D₂₆₈	C₂⁴	1	8	yes	—
491	C₂×D₂₆₈	C₂⁴	1	8	yes	—
492	C₂×D₂₆₈	C₂⁴	1	2	yes	—
493	C₂×D₂₆₈	C₂⁴	1	8	yes	—
494	C₂×D₂₆₈	C₂⁴	1	8	yes	—
495	C₂×D₂₆₈	C₂⁴	1	4	yes	—
496	C₂×D₂₆₈	C₂⁴	1	2	yes	—
497	C₂×C₂²⋊D₆₇	—	4	16	no	—
498	C₂×C₂²⋊D₆₇	—	4	16	no	—
499	C₂×C₂²⋊D₆₇	—	4	8	no	—
500	C₂×C₂²⋊D₆₇	—	4	8	no	—
501	C₂×C₂²⋊D₆₇	—	4	8	no	—
502	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
503	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
504	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
505	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
506	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
507	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
508	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
509	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
510	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
511	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
512	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
513	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
514	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
515	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
516	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
517	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
518	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
519	D₄×D₆₇	—	2	16	no	—
520	D₄×D₆₇	—	2	8	no	—
521	D₄×D₆₇	—	2	16	no	—
522	D₄×D₆₇	—	2	16	no	—
523	D₄×D₆₇	—	4	8	no	—
524	D₄×D₆₇	—	4	8	no	—
525	D₄×D₆₇	—	4	8	no	—
526	D₄×D₆₇	—	4	8	no	—
527	D₄×D₆₇	—	4	16	no	—
528	D₄×D₆₇	—	4	16	no	—
529	D₄×D₆₇	—	4	16	no	—
530	D₄×D₆₇	—	4	16	no	—
531	D₄×D₆₇	—	4	4	no	—
532	D₄×D₆₇	—	4	8	no	—
533	D₄×D₆₇	—	4	4	no	—
534	D₄×D₆₇	—	4	16	no	—
535	D₄×D₆₇	—	4	4	no	—
536	D₄×D₆₇	—	4	8	no	—
537	D₄×D₆₇	—	4	4	no	—
538	D₄×D₆₇	—	4	16	no	—
539	D₄×D₆₇	—	4	16	no	—
540	D₄×D₆₇	—	4	16	no	—
541	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
542	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
543	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
544	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
545	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
546	C₂×C₄×D₆₇	—	2	4	no	—
547	C₂×C₄×D₆₇	—	2	8	no	—
548	C₂×C₄×D₆₇	—	2	16	no	—
549	C₂×C₄×D₆₇	—	4	8	no	—
550	C₂×C₄×D₆₇	—	4	16	no	—
551	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
552	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
553	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
554	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
555	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
556	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
557	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
558	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
559	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
560	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
561	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
562	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
563	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
564	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
565	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
566	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
567	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
568	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
569	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
570	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
571	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
572	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
573	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
574	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
575	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
576	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
577	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
578	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
579	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
580	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
581	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
582	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
583	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
584	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
585	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
586	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
587	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
588	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
589	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
590	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
591	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
592	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
593	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
594	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
595	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
596	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
597	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
598	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
599	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
600	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
601	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
602	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
603	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
604	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
605	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
606	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
607	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
608	C₄×Dic₆₇	C₂⁴	1	2	yes	—
609	C₄×Dic₆₇	C₂⁴	1	2	yes	—
610	C₄×Dic₆₇	C₂⁴	1	2	yes	—
611	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
612	C₄×Dic₆₇	C₂⁴	1	2	yes	—
613	C₄×Dic₆₇	C₂⁴	1	2	yes	—
614	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
615	C₄×Dic₆₇	C₂⁴	1	4	yes	—
616	C₄×Dic₆₇	C₂⁴	1	4	yes	—
617	C₄×Dic₆₇	C₂⁴	1	4	yes	—
618	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
619	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
620	#41×C₆₇	—	4	8	no	—
621	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
622	C₂×D₄×C₆₇	—	4	8	no	—
623	C₂×D₄×C₆₇	—	4	8	no	—
624	C₂×D₄×C₆₇	—	4	4	no	—
625	C₂×D₄×C₆₇	—	4	8	no	—
626	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
627	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
628	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
629	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
630	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
631	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
632	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
633	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
634	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
635	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
636	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
637	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
638	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
639	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
640	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
641	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
642	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
643	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
644	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
645	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
646	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
647	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
648	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
649	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
650	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
651	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
652	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
653	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
654	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
655	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
656	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
657	C₄²×C₆₇	C₂⁴	1	2	yes	—
658	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
659	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
660	C₄²×C₆₇	C₂⁴	1	4	yes	—
661	C₂³×C₆₇	—	2	8	no	—
662	C₂³×C₆₇	—	4	8	no	—
663	C₂³×C₆₇	—	4	8	no	—
664	C₂³×C₆₇	—	4	4	no	—
665	C₂³×C₆₇	C₂⁵	1	4	yes	—
666	C₂³×C₆₇	C₂⁵	1	4	yes	—
667	C₂³×C₆₇	C₂⁵	1	4	yes	—
668	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
669	C₂²×D₆₇	—	2	4	no	—
670	C₂²×D₆₇	—	2	8	no	—
671	C₂²×D₆₇	—	2	8	no	—
672	C₂²×D₆₇	—	2	16	no	—
673	C₂²×D₆₇	—	2	8	no	—
674	C₂²×D₆₇	—	2	8	no	—
675	C₂²×D₆₇	—	2	8	no	—
676	C₂²×D₆₇	—	2	16	no	—
677	C₂²×D₆₇	—	2	8	no	—
678	C₂²×D₆₇	—	2	8	no	—
679	C₂²×D₆₇	—	2	8	no	—
680	C₂²×D₆₇	—	4	8	no	—
681	C₂²×D₆₇	—	4	8	no	—
682	C₂²×D₆₇	—	4	8	no	—
683	C₂²×D₆₇	—	4	8	no	—
684	C₂²×D₆₇	—	4	8	no	—
685	C₂²×D₆₇	—	4	8	no	—
686	C₂²×D₆₇	—	4	8	no	—
687	C₂²×D₆₇	—	4	4	no	—
688	C₂²×D₆₇	—	8	32	no	—
689	C₂²×D₆₇	—	8	32	no	—
690	C₂²×D₆₇	H(5,𝔽₂)	1	4	yes	—
691	C₂²×D₆₇	C₂⁵	1	4	yes	—
692	C₂²×D₆₇	C₂⁵	1	4	yes	—
693	C₂²×D₆₇	C₂⁵	1	4	yes	—
694	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
695	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
696	Q₈×C₆₇	—	2	4	no	—
697	D₄×C₆₇	—	2	8	no	—
698	D₄×C₆₇	—	2	4	no	—
699	D₄×C₆₇	—	2	8	no	—
700	D₄×C₆₇	—	2	8	no	—
701	D₄×C₆₇	—	4	8	no	—
702	D₄×C₆₇	—	4	8	no	—
703	D₄×C₆₇	—	4	2	no	—
704	D₄×C₆₇	—	4	4	no	—
705	D₄×C₆₇	—	4	2	no	—
706	D₄×C₆₇	—	4	8	no	—
707	D₄×C₆₇	—	4	8	no	—
708	C₂×C₄×C₆₇	—	2	2	no	—
709	C₂×C₄×C₆₇	—	2	4	no	—
710	C₂×C₄×C₆₇	—	2	8	no	—
711	C₂×C₄×C₆₇	—	4	4	no	—
712	C₂×C₄×C₆₇	—	4	8	no	—
713	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
714	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
715	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
716	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
717	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
718	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
719	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
720	C₂²⋊D₆₇	—	2	8	no	—
721	C₂²⋊D₆₇	—	2	8	no	—
722	C₂²⋊D₆₇	—	2	8	no	—
723	C₂²⋊D₆₇	—	2	16	no	—
724	C₂²⋊D₆₇	—	2	16	no	—
725	C₂²⋊D₆₇	—	4	8	no	—
726	C₂²⋊D₆₇	—	4	8	no	—
727	C₂²⋊D₆₇	—	4	8	no	—
728	C₂²⋊D₆₇	—	4	4	no	—
729	C₂²⋊D₆₇	—	4	4	no	—
730	C₂²⋊D₆₇	—	4	8	no	—
731	C₂²⋊D₆₇	—	4	4	no	—
732	C₂²⋊D₆₇	—	4	4	no	—
733	C₂²⋊D₆₇	—	4	8	no	—
734	C₂²⋊D₆₇	—	4	8	no	—
735	C₂²⋊D₆₇	—	4	8	no	—
736	C₂²⋊D₆₇	—	4	8	no	—
737	C₂×Dic₆₇	—	2	2	no	—
738	C₂×Dic₆₇	—	2	4	no	—
739	C₂×Dic₆₇	—	2	8	no	—
740	C₂×Dic₆₇	—	4	4	no	—
741	C₂×Dic₆₇	—	4	8	no	—
742	C₂×Dic₆₇	C₂⁵	1	1	yes	characteristic
743	C₂×Dic₆₇	C₂⁵	1	2	yes	—
744	C₂×Dic₆₇	C₂⁵	1	1	yes	characteristic
745	C₂×Dic₆₇	C₂⁵	1	4	yes	—
746	C₂×Dic₆₇	C₂⁵	1	4	yes	—
747	C₂×Dic₆₇	C₂⁵	1	4	yes	—
748	C₂×Dic₆₇	C₂⁵	1	2	yes	—
749	D₂₆₈	—	2	8	no	—
750	D₂₆₈	—	2	4	no	—
751	D₂₆₈	—	2	8	no	—
752	D₂₆₈	—	2	8	no	—
753	D₂₆₈	—	4	8	no	—
754	D₂₆₈	—	4	8	no	—
755	D₂₆₈	—	4	2	no	—
756	D₂₆₈	—	4	4	no	—
757	D₂₆₈	—	4	2	no	—
758	D₂₆₈	—	4	8	no	—
759	D₂₆₈	—	4	8	no	—
760	C₄×D₆₇	—	2	8	no	—
761	C₄×D₆₇	—	2	2	no	—
762	C₄×D₆₇	—	2	2	no	—
763	C₄×D₆₇	—	2	2	no	—
764	C₄×D₆₇	—	2	2	no	—
765	C₄×D₆₇	—	2	4	no	—
766	C₄×D₆₇	—	2	8	no	—
767	C₄×D₆₇	—	2	8	no	—
768	C₄×D₆₇	—	2	4	no	—
769	C₄×D₆₇	—	2	8	no	—
770	C₄×D₆₇	—	2	4	no	—
771	C₄×D₆₇	—	2	8	no	—
772	C₄×D₆₇	—	4	8	no	—
773	C₄×D₆₇	—	4	8	no	—
774	C₄×D₆₇	—	4	8	no	—
775	C₄×D₆₇	H(5,𝔽₂)	1	8	yes	—
776	Dic₁₃₄	—	2	4	no	—
777	Dic₁₃₄	—	2	8	no	—
778	C₂²×C₆₇	—	2	2	no	—
779	C₂²×C₆₇	—	2	4	no	—
780	C₂²×C₆₇	—	2	8	no	—
781	C₂²×C₆₇	—	2	4	no	—
782	C₂²×C₆₇	—	2	4	no	—
783	C₂²×C₆₇	—	2	8	no	—
784	C₂²×C₆₇	—	2	4	no	—
785	C₂²×C₆₇	—	2	4	no	—
786	C₂²×C₆₇	—	8	8	no	—
787	C₂²×C₆₇	—	8	8	no	—
788	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
789	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
790	C₂×D₆₇	—	2	2	no	—
791	C₂×D₆₇	—	2	8	no	—
792	C₂×D₆₇	—	2	4	no	—
793	C₂×D₆₇	—	2	8	no	—
794	C₂×D₆₇	—	2	4	no	—
795	C₂×D₆₇	—	2	4	no	—
796	C₂×D₆₇	—	2	4	no	—
797	C₂×D₆₇	—	2	8	no	—
798	C₂×D₆₇	—	2	4	no	—
799	C₂×D₆₇	—	4	16	no	—
800	C₂×D₆₇	—	4	16	no	—
801	C₂×D₆₇	—	4	16	no	—
802	C₂×D₆₇	—	8	8	no	—
803	C₂×D₆₇	—	8	8	no	—
804	C₂×D₆₇	—	8	8	no	—
805	C₂×D₆₇	—	8	8	no	—
806	C₂×D₆₇	—	8	16	no	—
807	C₂×D₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
808	C₂×D₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
809	C₂×D₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
810	C₄×C₆₇	—	2	4	no	—
811	C₄×C₆₇	—	2	4	no	—
812	C₄×C₆₇	—	2	1	no	—
813	C₄×C₆₇	—	2	1	no	—
814	C₄×C₆₇	—	2	2	no	—
815	C₄×C₆₇	—	2	4	no	—
816	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
817	Dic₆₇	—	2	4	no	—
818	Dic₆₇	—	2	4	no	—
819	Dic₆₇	—	2	1	no	—
820	Dic₆₇	—	2	1	no	—
821	Dic₆₇	—	2	2	no	—
822	Dic₆₇	—	2	4	no	—
823	Dic₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
824	C₂×#3543	—	67	1	no	maximal, Sylow
825	C₂×C₆₇	—	2	2	no	—
826	C₂×C₆₇	—	4	4	no	—
827	C₂×C₆₇	—	4	4	no	—
828	C₂×C₆₇	—	4	4	no	—
829	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	2	yes	—
831	D₆₇	—	2	2	no	—
832	D₆₇	—	4	4	no	—
833	D₆₇	—	4	4	no	—
834	D₆₇	—	4	4	no	—
835	D₆₇	#3543	1	4	yes	direct product factor
836	#3543	—	67	4	no	—
837	#3543	—	67	1	no	—
838	#3543	—	67	2	no	—
839	#3543	—	67	4	no	—
840	#3543	—	67	4	no	—
841	#3543	—	67	1	no	—
842	#3543	—	67	4	no	—
843	#3543	—	67	4	no	—
844	#3543	—	67	4	no	—
845	#3543	—	67	1	no	—
846	#3543	—	67	2	no	—
847	#3543	D₆₇	1	1	yes	characteristic, direct product factor
848	C₂×#560	—	67	4	no	—
849	C₂×#559	—	67	1	no	—
850	C₂×#550	—	67	2	no	—
851	C₂×#546	—	67	4	no	—
852	C₂×D₄²	—	67	4	no	—
853	C₂×D₄²	—	67	1	no	—
854	C₂×#540	—	67	4	no	—
855	C₂×#535	—	67	4	no	—
856	C₂×#534	—	67	4	no	—
857	C₂²×#127	—	67	1	no	—
858	C₂×#529	—	67	2	no	—
859	C₆₇	C₂×#3543	1	1	yes	characteristic, complemented, Sylow
860	C₂²×#41	—	67	4	no	—
861	C₂³×D₄	—	67	2	no	—
862	C₂³×D₄	—	67	4	no	—
863	C₂³×D₄	—	67	4	no	—
864	C₂³×D₄	—	67	4	no	—
865	#560	—	67	4	no	—
866	#560	—	67	8	no	—
867	#560	—	67	4	no	—
868	#560	—	67	8	no	—
869	#560	—	67	8	no	—
870	#560	—	67	8	no	—
871	#560	—	67	8	no	—
872	#560	—	67	8	no	—
873	#560	—	67	4	no	—
874	#560	C₂×D₆₇	1	4	yes	complemented
875	#559	—	67	1	no	—
876	#559	—	67	4	no	—
877	#559	—	67	4	no	—
878	#559	—	67	2	no	—
879	#559	—	67	4	no	—
880	#559	C₂×D₆₇	1	1	yes	characteristic, complemented
881	#550	—	67	4	no	—
882	#550	—	67	4	no	—
883	#550	—	67	2	no	—
884	#550	—	67	4	no	—
885	#550	—	67	8	no	—
886	#550	—	67	2	no	—
887	#550	—	67	4	no	—
888	#550	—	67	2	no	—
889	#550	C₂×D₆₇	1	2	yes	complemented
890	#546	—	67	4	no	—
891	#546	—	67	4	no	—
892	#546	—	67	4	no	—
893	#546	—	67	8	no	—
894	#546	—	67	4	no	—
895	#546	—	67	8	no	—
896	#546	—	67	4	no	—
897	#546	—	67	8	no	—
898	#546	—	67	4	no	—
899	#546	—	67	4	no	—
900	#546	—	67	8	no	—
901	#546	C₂×D₆₇	1	4	yes	complemented
902	D₄²	—	67	8	no	—
903	D₄²	—	67	4	no	—
904	D₄²	—	67	4	no	—
905	D₄²	—	67	4	no	—
906	D₄²	—	67	1	no	—
907	D₄²	—	67	4	no	—
908	D₄²	—	67	4	no	—
909	D₄²	—	67	4	no	—
910	D₄²	—	67	4	no	—
911	D₄²	—	67	8	no	—
912	D₄²	—	67	8	no	—
913	D₄²	—	67	8	no	—
914	D₄²	—	67	4	no	—
915	D₄²	—	67	4	no	—
916	D₄²	—	67	2	no	—
917	D₄²	—	67	4	no	—
918	D₄²	C₂×D₆₇	1	4	yes	complemented
919	D₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
920	#540	—	67	4	no	—
921	#540	—	67	4	no	—
922	#540	—	67	8	no	—
923	#540	—	67	8	no	—
924	#540	—	67	8	no	—
925	#540	—	67	8	no	—
926	#540	—	67	4	no	—
927	#540	—	67	4	no	—
928	#540	—	67	4	no	—
929	#540	—	67	4	no	—
930	#540	—	67	4	no	—
931	#540	C₂×D₆₇	1	4	yes	complemented
932	#535	—	67	4	no	—
933	#535	—	67	4	no	—
934	#535	—	67	4	no	—
935	#535	—	67	4	no	—
936	#535	—	67	4	no	—
937	#535	—	67	4	no	—
938	#535	—	67	8	no	—
939	#535	—	67	8	no	—
940	#535	—	67	8	no	—
941	#535	—	67	8	no	—
942	#535	—	67	4	no	—
943	#535	C₂×D₆₇	1	4	yes	complemented
944	#534	—	67	4	no	—
945	#534	—	67	4	no	—
946	#534	—	67	4	no	—
947	#534	—	67	8	no	—
948	#534	—	67	4	no	—
949	#534	—	67	8	no	—
950	#534	—	67	8	no	—
951	#534	—	67	4	no	—
952	#534	—	67	8	no	—
953	#534	—	67	4	no	—
954	#534	—	67	4	no	—
955	#534	C₂×D₆₇	1	4	yes	complemented
956	C₂×#127	—	67	4	no	—
957	C₂×#127	—	67	2	no	—
958	C₂×#127	—	67	1	no	—
959	C₂×#127	—	67	1	no	—
960	C₂×#127	—	67	4	no	—
961	C₂×#127	—	67	1	no	—
962	C₂×#127	—	67	2	no	—
963	C₂×#127	—	67	2	no	—
964	C₂×#127	—	67	1	no	—
965	C₂×#127	—	67	4	no	—
966	C₂×#127	—	67	4	no	—
967	C₂×#127	—	67	1	no	—
968	C₂×#127	C₂×D₆₇	1	1	yes	characteristic, complemented
969	#529	—	67	4	no	—
970	#529	—	67	2	no	—
971	#529	—	67	2	no	—
972	#529	—	67	4	no	—
973	#529	—	67	2	no	—
974	#529	—	67	2	no	—
975	#529	—	67	2	no	—
976	#529	—	67	4	no	—
977	#529	—	67	2	no	—
978	#529	—	67	4	no	—
979	#529	—	67	2	no	—
980	#529	C₂×D₆₇	1	2	yes	complemented
981	C₂×#126	—	67	4	no	—
982	C₂×#125	—	67	2	no	—
983	C₂×#124	—	67	2	no	—
984	C₂×#124	—	67	4	no	—
985	C₂×#123	—	67	4	no	—
986	C₂×#123	—	67	4	no	—
987	C₂×#123	—	67	4	no	—
988	C₂×#123	—	67	8	no	—
989	C₂×C₂²⋊Q₈	—	67	2	no	—
990	C₂×#121	—	67	2	no	—
991	C₂×#121	—	67	8	no	—
992	C₂×#121	—	67	8	no	—
993	C₂×#121	—	67	8	no	—
994	C₂×#121	—	67	4	no	—
995	C₂×#121	—	67	4	no	—
996	C₂×#121	—	67	8	no	—
997	C₂×#120	—	67	4	no	—
998	C₂×#120	—	67	8	no	—
999	C₂×#120	—	67	4	no	—
1000	C₂×#120	—	67	8	no	—
1001	C₂×C₄×Q₈	—	67	2	no	—
1002	C₂×C₄×D₄	—	67	4	no	—
1003	C₂×C₄×D₄	—	67	2	no	—
1004	C₂×C₄×D₄	—	67	4	no	—
1005	C₂×C₄×D₄	—	67	4	no	—
1006	C₂×#117	—	67	4	no	—
1007	C₂²×C₂²⋊C₄	—	67	4	no	—
1008	C₂²×C₄²	—	67	1	no	—
1009	C₂⁵	—	67	4	no	—
1010	C₂⁵	—	67	4	no	—
1011	C₂×#41	—	268	16	no	—
1012	C₂×#41	—	67	4	no	—
1013	C₂×#41	—	67	4	no	—
1014	C₂×#41	—	67	8	no	—
1015	C₂×#41	—	67	4	no	—
1016	C₂×#41	—	67	8	no	—
1017	C₂×#41	C₂²×D₆₇	1	4	yes	complemented
1018	C₂²×Q₈	—	67	2	no	—
1019	C₂²×D₄	—	268	16	no	—
1020	C₂²×D₄	—	268	8	no	—
1021	C₂²×D₄	—	268	16	no	—
1022	C₂²×D₄	—	268	16	no	—
1023	C₂²×D₄	—	67	4	no	—
1024	C₂²×D₄	—	67	8	no	—
1025	C₂²×D₄	—	67	4	no	—
1026	C₂²×D₄	—	67	4	no	—
1027	C₂²×D₄	—	67	8	no	—
1028	C₂²×D₄	—	67	8	no	—
1029	C₂²×D₄	—	67	8	no	—
1030	C₂²×D₄	—	67	2	no	—
1031	C₂²×D₄	—	67	8	no	—
1032	C₂²×D₄	—	67	4	no	—
1033	C₂²×D₄	—	67	8	no	—
1034	C₂²×D₄	—	67	2	no	—
1035	C₂²×D₄	—	67	4	no	—
1036	C₂²×D₄	—	67	2	no	—
1037	C₂²×D₄	—	67	2	no	—
1038	C₂²×D₄	—	67	4	no	—
1039	C₂²×D₄	—	67	4	no	—
1040	C₂²×D₄	—	67	8	no	—
1041	C₂²×D₄	—	67	8	no	—
1042	C₂²×D₄	—	67	8	no	—
1043	C₂²×D₄	—	67	4	no	—
1044	C₂²×D₄	—	67	4	no	—
1045	C₂²×D₄	—	67	8	no	—
1046	C₂²×D₄	—	67	4	no	—
1047	C₂²×D₄	—	67	2	no	—
1048	C₂²×D₄	—	67	4	no	—
1049	C₂²×D₄	—	67	4	no	—
1050	C₂²×D₄	—	67	2	no	—
1051	C₂²×D₄	—	67	4	no	—
1052	C₂²×D₄	—	67	4	no	—
1053	C₂²×D₄	—	67	4	no	—
1054	C₂²×D₄	C₂²×D₆₇	1	2	yes	complemented
1055	C₂²×D₄	C₂²×D₆₇	1	4	yes	complemented
1056	C₂²×D₄	C₂²×D₆₇	1	4	yes	complemented
1057	C₂²×D₄	C₂²×D₆₇	1	4	yes	complemented
1058	C₂³×C₄	—	67	8	no	—
1059	C₂³×C₄	—	67	4	no	—
1060	C₂³×C₄	—	67	4	no	—
1061	C₂³×C₄	—	67	2	no	—
1062	C₂³×C₄	—	67	1	no	—
1063	#127	—	67	4	no	—
1064	#127	—	67	4	no	—
1065	#127	—	67	8	no	—
1066	#127	—	67	8	no	—
1067	#127	—	67	4	no	—
1068	#127	—	67	2	no	—
1069	#127	—	67	4	no	—
1070	#127	—	67	2	no	—
1071	#127	—	67	8	no	—
1072	#127	—	67	2	no	—
1073	#127	—	67	2	no	—
1074	#127	—	67	4	no	—
1075	#127	—	67	4	no	—
1076	#127	—	67	8	no	—
1077	#127	—	67	8	no	—
1078	#127	—	67	4	no	—
1079	#127	—	67	1	no	—
1080	#127	—	67	1	no	—
1081	#127	—	67	2	no	—
1082	#127	—	67	4	no	—
1083	#127	C₂²×D₆₇	1	1	yes	characteristic
1084	#127	C₂²×D₆₇	1	4	yes	complemented
1085	#127	C₂²×D₆₇	1	1	yes	characteristic, complemented
1086	#127	C₂²×D₆₇	1	2	yes	complemented
1087	#127	C₂²×D₆₇	1	4	yes	complemented
1088	#126	—	67	4	no	—
1089	#126	—	67	4	no	—
1090	#126	—	67	4	no	—
1091	#126	—	67	4	no	—
1092	#126	—	67	4	no	—
1093	#126	—	67	4	no	—
1094	#126	—	67	4	no	—
1095	#126	C₂²×D₆₇	1	4	yes	complemented
1096	#125	—	67	4	no	—
1097	#125	—	67	4	no	—
1098	#125	—	67	2	no	—
1099	#125	—	67	2	no	—
1100	#125	—	67	2	no	—
1101	#125	C₂²×D₆₇	1	2	yes	complemented
1102	#124	—	67	2	no	—
1103	#124	—	67	4	no	—
1104	#124	—	67	2	no	—
1105	#124	—	67	4	no	—
1106	#124	—	67	4	no	—
1107	#124	—	67	4	no	—
1108	#124	—	67	8	no	—
1109	#124	—	67	8	no	—
1110	#124	—	67	2	no	—
1111	#124	—	67	4	no	—
1112	#124	C₂²×D₆₇	1	2	yes	complemented
1113	#124	C₂²×D₆₇	1	4	yes	complemented
1114	#123	—	67	4	no	—
1115	#123	—	67	4	no	—
1116	#123	—	67	4	no	—
1117	#123	—	67	8	no	—
1118	#123	—	67	4	no	—
1119	#123	—	67	4	no	—
1120	#123	—	67	4	no	—
1121	#123	—	67	8	no	—
1122	#123	—	67	4	no	—
1123	#123	—	67	4	no	—
1124	#123	—	67	8	no	—
1125	#123	—	67	8	no	—
1126	#123	—	67	8	no	—
1127	#123	—	67	8	no	—
1128	#123	—	67	4	no	—
1129	#123	—	67	4	no	—
1130	#123	—	67	4	no	—
1131	#123	—	67	8	no	—
1132	#123	—	67	4	no	—
1133	#123	—	67	8	no	—
1134	#123	—	67	4	no	—
1135	#123	—	67	8	no	—
1136	#123	—	67	8	no	—
1137	#123	—	67	8	no	—
1138	#123	C₂²×D₆₇	1	4	yes	complemented
1139	#123	C₂²×D₆₇	1	4	yes	complemented
1140	#123	C₂²×D₆₇	1	4	yes	complemented
1141	#123	C₂²×D₆₇	1	8	yes	complemented
1142	C₂²⋊Q₈	—	67	2	no	—
1143	C₂²⋊Q₈	—	67	2	no	—
1144	C₂²⋊Q₈	—	67	4	no	—
1145	C₂²⋊Q₈	—	67	2	no	—
1146	C₂²⋊Q₈	—	67	4	no	—
1147	C₂²⋊Q₈	C₂²×D₆₇	1	2	yes	complemented
1148	#121	—	67	2	no	—
1149	#121	—	67	4	no	—
1150	#121	—	67	8	no	—
1151	#121	—	67	8	no	—
1152	#121	—	67	8	no	—
1153	#121	—	67	8	no	—
1154	#121	—	67	8	no	—
1155	#121	—	67	8	no	—
1156	#121	—	67	8	no	—
1157	#121	—	67	8	no	—
1158	#121	—	67	8	no	—
1159	#121	—	67	4	no	—
1160	#121	—	67	8	no	—
1161	#121	—	67	4	no	—
1162	#121	—	67	8	no	—
1163	#121	—	67	8	no	—
1164	#121	—	67	8	no	—
1165	#121	—	67	8	no	—
1166	#121	—	67	2	no	—
1167	#121	—	67	8	no	—
1168	#121	—	67	8	no	—
1169	#121	—	67	8	no	—
1170	#121	—	67	4	no	—
1171	#121	—	67	4	no	—
1172	#121	—	67	8	no	—
1173	#121	—	67	2	no	—
1174	#121	—	67	8	no	—
1175	#121	—	67	8	no	—
1176	#121	—	67	8	no	—
1177	#121	—	67	4	no	—
1178	#121	—	67	4	no	—
1179	#121	—	67	8	no	—
1180	#121	—	67	4	no	—
1181	#121	—	67	8	no	—
1182	#121	—	67	8	no	—
1183	#121	—	67	8	no	—
1184	#121	—	67	8	no	—
1185	#121	—	67	8	no	—
1186	#121	—	67	8	no	—
1187	#121	—	67	8	no	—
1188	#121	—	67	8	no	—
1189	#121	—	67	8	no	—
1190	#121	—	67	8	no	—
1191	#121	C₂²×D₆₇	1	2	yes	—
1192	#121	C₂²×D₆₇	1	8	yes	complemented
1193	#121	C₂²×D₆₇	1	8	yes	complemented
1194	#121	C₂²×D₆₇	1	8	yes	complemented
1195	#121	C₂²×D₆₇	1	4	yes	complemented
1196	#121	C₂²×D₆₇	1	4	yes	complemented
1197	#121	C₂²×D₆₇	1	8	yes	complemented
1198	#120	—	67	4	no	—
1199	#120	—	67	8	no	—
1200	#120	—	67	4	no	—
1201	#120	—	67	8	no	—
1202	#120	—	67	4	no	—
1203	#120	—	67	8	no	—
1204	#120	—	67	8	no	—
1205	#120	—	67	8	no	—
1206	#120	—	67	8	no	—
1207	#120	—	67	4	no	—
1208	#120	—	67	8	no	—
1209	#120	—	67	8	no	—
1210	#120	—	67	8	no	—
1211	#120	—	67	8	no	—
1212	#120	—	67	8	no	—
1213	#120	—	67	4	no	—
1214	#120	—	67	8	no	—
1215	#120	—	67	8	no	—
1216	#120	—	67	8	no	—
1217	#120	—	67	8	no	—
1218	#120	—	67	4	no	—
1219	#120	—	67	8	no	—
1220	#120	—	67	8	no	—
1221	#120	—	67	8	no	—
1222	#120	C₂²×D₆₇	1	4	yes	complemented
1223	#120	C₂²×D₆₇	1	8	yes	complemented
1224	#120	C₂²×D₆₇	1	4	yes	complemented
1225	#120	C₂²×D₆₇	1	8	yes	complemented
1226	C₄×Q₈	—	67	2	no	—
1227	C₄×Q₈	—	67	4	no	—
1228	C₄×Q₈	—	67	2	no	—
1229	C₄×Q₈	—	67	4	no	—
1230	C₄×Q₈	—	67	2	no	—
1231	C₄×Q₈	C₂²×D₆₇	1	2	yes	complemented
1232	C₄×D₄	—	67	4	no	—
1233	C₄×D₄	—	67	2	no	—
1234	C₄×D₄	—	67	4	no	—
1235	C₄×D₄	—	67	4	no	—
1236	C₄×D₄	—	67	4	no	—
1237	C₄×D₄	—	67	4	no	—
1238	C₄×D₄	—	67	4	no	—
1239	C₄×D₄	—	67	8	no	—
1240	C₄×D₄	—	67	8	no	—
1241	C₄×D₄	—	67	4	no	—
1242	C₄×D₄	—	67	2	no	—
1243	C₄×D₄	—	67	4	no	—
1244	C₄×D₄	—	67	4	no	—
1245	C₄×D₄	—	67	4	no	—
1246	C₄×D₄	—	67	4	no	—
1247	C₄×D₄	—	67	4	no	—
1248	C₄×D₄	—	67	8	no	—
1249	C₄×D₄	—	67	8	no	—
1250	C₄×D₄	—	67	4	no	—
1251	C₄×D₄	—	67	2	no	—
1252	C₄×D₄	—	67	4	no	—
1253	C₄×D₄	—	67	4	no	—
1254	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1255	C₄×D₄	C₂²×D₆₇	1	2	yes	complemented
1256	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1257	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1258	#117	—	67	4	no	—
1259	#117	—	67	4	no	—
1260	#117	—	67	4	no	—
1261	#117	—	67	4	no	—
1262	#117	—	67	4	no	—
1263	#117	—	67	4	no	—
1264	#117	—	67	4	no	—
1265	#117	C₂²×D₆₇	1	4	yes	complemented
1266	C₂×C₄⋊C₄	—	67	4	no	—
1267	C₂×C₄⋊C₄	—	67	4	no	—
1268	C₂×C₄⋊C₄	—	67	2	no	—
1269	C₂×C₄⋊C₄	—	67	2	no	—
1270	C₂×C₄⋊C₄	—	67	4	no	—
1271	C₂×C₄⋊C₄	—	67	4	no	—
1272	C₂×C₂²⋊C₄	—	67	4	no	—
1273	C₂×C₂²⋊C₄	—	67	8	no	—
1274	C₂×C₂²⋊C₄	—	67	4	no	—
1275	C₂×C₂²⋊C₄	—	67	4	no	—
1276	C₂×C₂²⋊C₄	—	67	4	no	—
1277	C₂×C₂²⋊C₄	—	67	8	no	—
1278	C₂×C₂²⋊C₄	—	67	4	no	—
1279	C₂×C₂²⋊C₄	—	67	4	no	—
1280	C₂×C₂²⋊C₄	—	67	4	no	—
1281	C₂×C₂²⋊C₄	—	67	4	no	—
1282	C₂×C₂²⋊C₄	—	67	4	no	—
1283	C₂×C₂²⋊C₄	—	67	4	no	—
1284	C₂×C₂²⋊C₄	—	67	8	no	—
1285	C₂×C₂²⋊C₄	—	67	8	no	—
1286	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	complemented
1287	C₂×C₄²	—	67	1	no	—
1288	C₂×C₄²	—	67	2	no	—
1289	C₂×C₄²	—	67	2	no	—
1290	C₂×C₄²	—	67	4	no	—
1291	C₂×C₄²	—	67	1	no	—
1292	C₂×C₄²	—	67	1	no	—
1293	C₂×C₄²	—	67	1	no	—
1294	C₂×C₄²	—	67	1	no	—
1295	C₂×C₄²	—	67	2	no	—
1296	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic, complemented
1297	C₂⁴	—	268	8	no	—
1298	C₂⁴	—	268	16	no	—
1299	C₂⁴	—	268	16	no	—
1300	C₂⁴	—	67	4	no	—
1301	C₂⁴	—	67	8	no	—
1302	C₂⁴	—	67	4	no	—
1303	C₂⁴	—	67	4	no	—
1304	C₂⁴	—	67	4	no	—
1305	C₂⁴	—	67	1	no	—
1306	C₂⁴	—	67	4	no	—
1307	C₂⁴	—	67	4	no	—
1308	C₂⁴	—	67	4	no	—
1309	C₂⁴	—	134	16	no	—
1310	C₂⁴	C₂³×D₆₇	1	4	yes	—
1311	C₂⁴	C₂³×D₆₇	1	4	yes	—
1312	#41	—	4	8	no	—
1313	#41	—	268	8	no	—
1314	#41	—	268	16	no	—
1315	#41	—	268	8	no	—
1316	#41	—	268	16	no	—
1317	#41	—	268	8	no	—
1318	C₂×Q₈	—	67	4	no	—
1319	C₂×Q₈	—	67	2	no	—
1320	C₂×Q₈	—	134	8	no	—
1321	C₂×Q₈	C₂³×D₆₇	1	2	yes	—
1322	C₂×D₄	—	4	8	no	—
1323	C₂×D₄	—	4	8	no	—
1324	C₂×D₄	—	4	4	no	—
1325	C₂×D₄	—	4	8	no	—
1326	C₂×D₄	—	268	4	no	—
1327	C₂×D₄	—	268	8	no	—
1328	C₂×D₄	—	268	8	no	—
1329	C₂×D₄	—	268	8	no	—
1330	C₂×D₄	—	268	16	no	—
1331	C₂×D₄	—	268	16	no	—
1332	C₂×D₄	—	268	8	no	—
1333	C₂×D₄	—	268	8	no	—
1334	C₂×D₄	—	268	8	no	—
1335	C₂×D₄	—	268	8	no	—
1336	C₂×D₄	—	268	8	no	—
1337	C₂×D₄	—	268	8	no	—
1338	C₂×D₄	—	268	16	no	—
1339	C₂×D₄	—	268	16	no	—
1340	C₂×D₄	—	268	16	no	—
1341	C₂×D₄	—	268	4	no	—
1342	C₂×D₄	—	268	8	no	—
1343	C₂×D₄	—	268	4	no	—
1344	C₂×D₄	—	268	4	no	—
1345	C₂×D₄	—	268	8	no	—
1346	C₂×D₄	—	268	4	no	—
1347	C₂×D₄	—	268	16	no	—
1348	C₂×D₄	—	268	16	no	—
1349	C₂×D₄	—	268	16	no	—
1350	C₂×D₄	—	268	8	no	—
1351	C₂×D₄	—	268	16	no	—
1352	C₂×D₄	—	268	16	no	—
1353	C₂×D₄	—	67	8	no	—
1354	C₂×D₄	—	67	8	no	—
1355	C₂×D₄	—	67	8	no	—
1356	C₂×D₄	—	67	8	no	—
1357	C₂×D₄	—	67	4	no	—
1358	C₂×D₄	—	67	8	no	—
1359	C₂×D₄	—	67	8	no	—
1360	C₂×D₄	—	67	4	no	—
1361	C₂×D₄	—	67	8	no	—
1362	C₂×D₄	—	67	4	no	—
1363	C₂×D₄	—	67	8	no	—
1364	C₂×D₄	—	67	4	no	—
1365	C₂×D₄	—	67	4	no	—
1366	C₂×D₄	—	67	4	no	—
1367	C₂×D₄	—	67	4	no	—
1368	C₂×D₄	—	67	8	no	—
1369	C₂×D₄	—	67	8	no	—
1370	C₂×D₄	—	67	8	no	—
1371	C₂×D₄	—	67	8	no	—
1372	C₂×D₄	—	67	2	no	—
1373	C₂×D₄	—	67	8	no	—
1374	C₂×D₄	—	67	4	no	—
1375	C₂×D₄	—	67	8	no	—
1376	C₂×D₄	—	67	2	no	—
1377	C₂×D₄	—	67	4	no	—
1378	C₂×D₄	—	67	2	no	—
1379	C₂×D₄	—	67	4	no	—
1380	C₂×D₄	—	67	4	no	—
1381	C₂×D₄	—	134	8	no	—
1382	C₂×D₄	—	134	16	no	—
1383	C₂×D₄	—	134	16	no	—
1384	C₂×D₄	—	134	16	no	—
1385	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1386	C₂×D₄	C₂³×D₆₇	1	2	yes	—
1387	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1388	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1389	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1390	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1391	C₂×D₄	C₂³×D₆₇	1	2	yes	—
1392	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1393	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1394	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1395	C₂×D₄	C₂³×D₆₇	1	2	yes	—
1396	C₂²×C₄	—	268	8	no	—
1397	C₂²×C₄	—	268	16	no	—
1398	C₂²×C₄	—	67	8	no	—
1399	C₂²×C₄	—	67	4	no	—
1400	C₂²×C₄	—	67	8	no	—
1401	C₂²×C₄	—	67	8	no	—
1402	C₂²×C₄	—	67	8	no	—
1403	C₂²×C₄	—	67	2	no	—
1404	C₂²×C₄	—	67	2	no	—
1405	C₂²×C₄	—	67	1	no	—
1406	C₂²×C₄	—	67	4	no	—
1407	C₂²×C₄	—	67	1	no	—
1408	C₂²×C₄	—	67	2	no	—
1409	C₂²×C₄	—	67	1	no	—
1410	C₂²×C₄	—	67	2	no	—
1411	C₂²×C₄	—	67	2	no	—
1412	C₂²×C₄	—	67	1	no	—
1413	C₂²×C₄	—	67	1	no	—
1414	C₂²×C₄	—	67	4	no	—
1415	C₂²×C₄	—	67	4	no	—
1416	C₂²×C₄	—	67	4	no	—
1417	C₂²×C₄	—	67	4	no	—
1418	C₂²×C₄	—	67	4	no	—
1419	C₂²×C₄	—	134	8	no	—
1420	C₂²×C₄	—	134	16	no	—
1421	C₂²×C₄	—	134	4	no	—
1422	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1423	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1424	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1425	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1426	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1427	C₄⋊C₄	—	67	4	no	—
1428	C₄⋊C₄	—	67	4	no	—
1429	C₄⋊C₄	—	67	4	no	—
1430	C₄⋊C₄	—	67	4	no	—
1431	C₄⋊C₄	—	67	4	no	—
1432	C₄⋊C₄	—	67	4	no	—
1433	C₄⋊C₄	—	67	4	no	—
1434	C₄⋊C₄	—	67	2	no	—
1435	C₄⋊C₄	—	67	4	no	—
1436	C₄⋊C₄	—	67	2	no	—
1437	C₄⋊C₄	—	67	4	no	—
1438	C₄⋊C₄	—	67	4	no	—
1439	C₄⋊C₄	—	67	4	no	—
1440	C₄⋊C₄	—	67	4	no	—
1441	C₄⋊C₄	—	67	4	no	—
1442	C₄⋊C₄	—	67	4	no	—
1443	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1444	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1445	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
1446	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
1447	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1448	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1449	C₂²⋊C₄	—	67	4	no	—
1450	C₂²⋊C₄	—	67	4	no	—
1451	C₂²⋊C₄	—	67	4	no	—
1452	C₂²⋊C₄	—	67	4	no	—
1453	C₂²⋊C₄	—	67	4	no	—
1454	C₂²⋊C₄	—	67	4	no	—
1455	C₂²⋊C₄	—	67	4	no	—
1456	C₂²⋊C₄	—	67	8	no	—
1457	C₂²⋊C₄	—	67	8	no	—
1458	C₂²⋊C₄	—	67	4	no	—
1459	C₂²⋊C₄	—	67	4	no	—
1460	C₂²⋊C₄	—	67	8	no	—
1461	C₂²⋊C₄	—	67	8	no	—
1462	C₂²⋊C₄	—	67	4	no	—
1463	C₂²⋊C₄	—	67	4	no	—
1464	C₂²⋊C₄	—	67	4	no	—
1465	C₂²⋊C₄	—	67	4	no	—
1466	C₂²⋊C₄	—	67	4	no	—
1467	C₂²⋊C₄	—	67	4	no	—
1468	C₂²⋊C₄	—	67	4	no	—
1469	C₂²⋊C₄	—	67	4	no	—
1470	C₂²⋊C₄	—	67	8	no	—
1471	C₂²⋊C₄	—	67	8	no	—
1472	C₂²⋊C₄	—	67	8	no	—
1473	C₂²⋊C₄	—	67	8	no	—
1474	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1475	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1476	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1477	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1478	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1479	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1480	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1481	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1482	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1483	C₄²	—	67	2	no	—
1484	C₄²	—	67	2	no	—
1485	C₄²	—	67	2	no	—
1486	C₄²	—	67	1	no	—
1487	C₄²	—	67	2	no	—
1488	C₄²	—	67	1	no	—
1489	C₄²	—	67	2	no	—
1490	C₄²	—	67	4	no	—
1491	C₄²	—	67	4	no	—
1492	C₄²	—	67	4	no	—
1493	C₄²	C₂³×D₆₇	1	2	yes	—
1494	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1495	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1496	C₄²	C₂³×D₆₇	1	4	yes	—
1497	C₂³	—	2	8	no	—
1498	C₂³	—	4	8	no	—
1499	C₂³	—	4	8	no	—
1500	C₂³	—	4	4	no	—
1501	C₂³	—	268	8	no	—
1502	C₂³	—	268	8	no	—
1503	C₂³	—	268	8	no	—
1504	C₂³	—	268	4	no	—
1505	C₂³	—	268	8	no	—
1506	C₂³	—	268	8	no	—
1507	C₂³	—	268	8	no	—
1508	C₂³	—	268	8	no	—
1509	C₂³	—	536	32	no	—
1510	C₂³	—	536	32	no	—
1511	C₂³	—	67	1	no	—
1512	C₂³	—	67	4	no	—
1513	C₂³	—	67	1	no	—
1514	C₂³	—	67	4	no	—
1515	C₂³	—	67	4	no	—
1516	C₂³	—	67	4	no	—
1517	C₂³	—	134	16	no	—
1518	C₂³	—	134	8	no	—
1519	C₂³	—	134	8	no	—
1520	C₂³	—	134	8	no	—
1521	C₂³	—	134	8	no	—
1522	C₂³	—	134	16	no	—
1523	C₂³	—	134	8	no	—
1524	C₂³	—	134	8	no	—
1525	C₂³	—	134	8	no	—
1526	C₂³	—	134	4	no	—
1527	C₂³	—	134	8	no	—
1528	C₂³	C₂⁴×D₆₇	1	4	yes	—
1529	C₂³	C₂⁴×D₆₇	1	4	yes	—
1530	C₂³	C₂⁴×D₆₇	1	4	yes	—
1531	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1532	Q₈	—	2	4	no	—
1533	Q₈	—	134	8	no	—
1534	Q₈	—	134	4	no	—
1535	D₄	—	2	8	no	—
1536	D₄	—	2	4	no	—
1537	D₄	—	2	8	no	—
1538	D₄	—	2	8	no	—
1539	D₄	—	4	8	no	—
1540	D₄	—	4	8	no	—
1541	D₄	—	4	2	no	—
1542	D₄	—	4	4	no	—
1543	D₄	—	4	2	no	—
1544	D₄	—	4	8	no	—
1545	D₄	—	4	8	no	—
1546	D₄	—	268	8	no	—
1547	D₄	—	268	8	no	—
1548	D₄	—	268	2	no	—
1549	D₄	—	268	4	no	—
1550	D₄	—	268	2	no	—
1551	D₄	—	268	8	no	—
1552	D₄	—	268	8	no	—
1553	D₄	—	268	8	no	—
1554	D₄	—	268	8	no	—
1555	D₄	—	268	8	no	—
1556	D₄	—	268	8	no	—
1557	D₄	—	268	8	no	—
1558	D₄	—	268	4	no	—
1559	D₄	—	268	4	no	—
1560	D₄	—	268	8	no	—
1561	D₄	—	268	4	no	—
1562	D₄	—	268	4	no	—
1563	D₄	—	268	8	no	—
1564	D₄	—	268	8	no	—
1565	D₄	—	134	8	no	—
1566	D₄	—	134	16	no	—
1567	D₄	—	134	8	no	—
1568	D₄	—	134	16	no	—
1569	D₄	—	134	8	no	—
1570	D₄	—	134	8	no	—
1571	D₄	—	134	8	no	—
1572	D₄	—	134	4	no	—
1573	D₄	—	134	8	no	—
1574	C₂×C₄	—	2	2	no	—
1575	C₂×C₄	—	2	4	no	—
1576	C₂×C₄	—	2	8	no	—
1577	C₂×C₄	—	4	4	no	—
1578	C₂×C₄	—	4	8	no	—
1579	C₂×C₄	—	268	8	no	—
1580	C₂×C₄	—	268	8	no	—
1581	C₂×C₄	—	268	8	no	—
1582	C₂×C₄	—	268	4	no	—
1583	C₂×C₄	—	268	8	no	—
1584	C₂×C₄	—	67	2	no	—
1585	C₂×C₄	—	67	8	no	—
1586	C₂×C₄	—	67	1	no	—
1587	C₂×C₄	—	67	2	no	—
1588	C₂×C₄	—	67	1	no	—
1589	C₂×C₄	—	67	4	no	—
1590	C₂×C₄	—	67	4	no	—
1591	C₂×C₄	—	67	4	no	—
1592	C₂×C₄	—	134	4	no	—
1593	C₂×C₄	—	134	8	no	—
1594	C₂×C₄	—	134	8	no	—
1595	C₂×C₄	—	134	8	no	—
1596	C₂×C₄	—	134	8	no	—
1597	C₂×C₄	—	134	4	no	—
1598	C₂×C₄	—	134	2	no	—
1599	C₂×C₄	—	134	2	no	—
1600	C₂×C₄	—	134	2	no	—
1601	C₂×C₄	—	134	2	no	—
1602	C₂×C₄	—	134	4	no	—
1603	C₂×C₄	—	134	8	no	—
1604	C₂×C₄	—	134	2	no	—
1605	C₂×C₄	—	134	4	no	—
1606	C₂×C₄	—	134	8	no	—
1607	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1608	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1609	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1610	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1611	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1612	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1613	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1614	C₂²	—	2	2	no	—
1615	C₂²	—	2	4	no	—
1616	C₂²	—	2	8	no	—
1617	C₂²	—	2	4	no	—
1618	C₂²	—	2	4	no	—
1619	C₂²	—	2	4	no	—
1620	C₂²	—	2	8	no	—
1621	C₂²	—	2	4	no	—
1622	C₂²	—	8	8	no	—
1623	C₂²	—	8	8	no	—
1624	C₂²	—	268	16	no	—
1625	C₂²	—	268	16	no	—
1626	C₂²	—	268	16	no	—
1627	C₂²	—	536	8	no	—
1628	C₂²	—	536	16	no	—
1629	C₂²	—	536	8	no	—
1630	C₂²	—	536	8	no	—
1631	C₂²	—	536	8	no	—
1632	C₂²	—	67	4	no	—
1633	C₂²	—	67	2	no	—
1634	C₂²	—	67	2	no	—
1635	C₂²	—	134	8	no	—
1636	C₂²	—	134	8	no	—
1637	C₂²	—	134	4	no	—
1638	C₂²	—	134	4	no	—
1639	C₂²	—	134	4	no	—
1640	C₂²	—	134	4	no	—
1641	C₂²	—	134	8	no	—
1642	C₂²	—	134	4	no	—
1643	C₂²	—	134	2	no	—
1644	C₂²	H(5,𝔽₂)×D₆₇	1	2	yes	—
1645	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1646	C₄	—	2	4	no	—
1647	C₄	—	2	1	no	—
1648	C₄	—	2	1	no	—
1649	C₄	—	2	2	no	—
1650	C₄	—	2	4	no	—
1651	C₄	—	2	4	no	—
1652	C₄	—	67	4	no	—
1653	C₄	—	134	4	no	—
1654	C₄	—	134	4	no	—
1655	C₄	—	134	4	no	—
1656	C₄	—	134	1	no	—
1657	C₄	—	134	1	no	—
1658	C₄	—	134	2	no	—
1659	C₄	H(5,𝔽₂)×D₆₇	1	4	yes	—
1660	C₂	—	2	2	no	—
1661	C₂	—	4	4	no	—
1662	C₂	—	4	4	no	—
1663	C₂	—	4	4	no	—
1664	C₂	—	268	4	no	—
1665	C₂	—	268	4	no	—
1666	C₂	—	268	4	no	—
1667	C₂	—	67	4	no	—
1668	C₂	—	134	2	no	—
1669	C₂	C₂×H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1670	C₂	C₂×H(5,𝔽₂)×D₆₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Fitting	C₆₇×#3543	C₂
hypercenter	#3543	D₆₇
hypocenter	C₆₇	C₂×#3543
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #3543

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #22574543	C₂	semidirect
2. #22574542	C₂	semidirect
3. #22574541	C₂	semidirect
4. #22574540	C₂	semidirect
5. #22574539	C₂	semidirect
6. #22574538	C₂	semidirect
7. #22574537	C₂	semidirect
8. #22574536	C₂	semidirect
9. #22574535	C₂	semidirect
10. #22574534	C₂	semidirect
11. #22574533	C₂	semidirect
12. #560×D₆₇	C₂	semidirect
13. #559×D₆₇	C₂	semidirect
14. #550×D₆₇	C₂	semidirect
15. #546×D₆₇	C₂	semidirect
16. D₄²×D₆₇	C₂	semidirect
17. D₄²×D₆₇	C₂	semidirect
18. #540×D₆₇	C₂	semidirect
19. #535×D₆₇	C₂	semidirect
20. #534×D₆₇	C₂	semidirect
21. C₂×#127×D₆₇	C₂	semidirect
22. #529×D₆₇	C₂	semidirect
23. C₆₇×#3543	C₂	semidirect
24. C₂×#41×D₆₇	C₂²	semidirect
25. C₂²×D₄×D₆₇	C₂²	semidirect
26. C₂²×D₄×D₆₇	C₂²	semidirect
27. C₂²×D₄×D₆₇	C₂²	semidirect
28. C₂²×D₄×D₆₇	C₂²	semidirect
29. #16864137	C₂²	semidirect
30. #16864136	C₂²	semidirect
31. #16864136	C₂²	semidirect
32. #16864135	C₂²	semidirect
33. #16864135	C₂²	semidirect
34. #16864134	C₂²	semidirect
35. #16864134	C₂²	semidirect
36. #16864134	C₂²	semidirect
37. #16864133	C₂²	semidirect
38. #16864132	C₂²	semidirect
39. #16864131	C₂²	semidirect
40. #16864130	C₂²	semidirect
41. #16864129	C₂²	semidirect
42. #16864128	C₂²	semidirect
43. #16864068	C₂²	semidirect
44. #16864067	C₂²	semidirect
45. #16864067	C₂²	semidirect
46. #16864066	C₂²	semidirect
47. #16864066	C₂²	semidirect
48. #16864065	C₂²	semidirect
49. #16864064	C₂²	semidirect
50. #16864064	C₂²	semidirect
51. #16864043	C₂²	semidirect
52. #16864042	C₂²	semidirect
53. #16864041	C₂²	semidirect
54. #16864040	C₂²	semidirect
55. #16864039	C₂²	semidirect
56. #16864038	C₂²	semidirect
57. #16864037	C₂²	semidirect
58. #16864036	C₂²	semidirect
59. #16864035	C₂²	semidirect
60. #16864034	C₂²	semidirect
61. #16864033	C₂²	semidirect
62. D₄×D₂₆₈	C₂²	semidirect
63. D₄×D₂₆₈	C₂²	semidirect
64. D₄×D₂₆₈	C₂²	semidirect
65. #16864031	C₂²	semidirect
66. #16864031	C₂²	semidirect
67. #16864030	C₂²	semidirect
68. #16864030	C₂²	semidirect
69. #16864030	C₂²	semidirect
70. #16864030	C₂²	semidirect
71. D₄×C₂²⋊D₆₇	C₂²	semidirect
72. D₄×C₂²⋊D₆₇	C₂²	semidirect
73. D₄×C₂²⋊D₆₇	C₂²	semidirect
74. D₄×C₂²⋊D₆₇	C₂²	semidirect
75. #16864028	C₂²	semidirect
76. #16864028	C₂²	semidirect
77. #16864028	C₂²	semidirect
78. #16864002	C₂²	semidirect
79. #16864001	C₂²	semidirect
80. #16864000	C₂²	semidirect
81. #16863999	C₂²	semidirect
82. #16863999	C₂²	semidirect
83. #16863998	C₂²	semidirect
84. #16863998	C₂²	semidirect
85. #16863997	C₂²	semidirect
86. #16863997	C₂²	semidirect
87. #16863996	C₂²	semidirect
88. #16863996	C₂²	semidirect
89. #16863965	C₂²	semidirect
90. #16863964	C₂²	semidirect
91. #16863964	C₂²	semidirect
92. #16863963	C₂²	semidirect
93. #16863962	C₂²	semidirect
94. #16863962	C₂²	semidirect
95. #16863961	C₂²	semidirect
96. #16863961	C₂²	semidirect
97. #16863960	C₂²	semidirect
98. #16863959	C₂²	semidirect
99. #16863959	C₂²	semidirect
100. #16863958	C₂²	semidirect
101. #16863957	C₂²	semidirect
102. #16863957	C₂²	semidirect
103. #16863957	C₂²	semidirect
104. #16863956	C₂²	semidirect
105. #16863956	C₂²	semidirect
106. #16863956	C₂²	semidirect
107. #16863955	C₂²	semidirect
108. #16863955	C₂²	semidirect
109. #16863954	C₂²	semidirect
110. #16863954	C₂²	semidirect
111. C₂×#14524040	C₂²	semidirect
112. C₂×#14524039	C₂²	semidirect
113. C₂×#14524039	C₂²	semidirect
115. #127×D₆₇	C₂²	semidirect
116. #127×D₆₇	C₂²	semidirect
117. #127×D₆₇	C₂²	semidirect
118. #127×D₆₇	C₂²	semidirect
119. #127×D₆₇	C₂²	semidirect
120. #127×D₆₇	C₂²	semidirect
121. #127×D₆₇	C₂²	semidirect
122. #127×D₆₇	C₂²	semidirect
123. #16863933	C₂²	semidirect
124. #16863932	C₂²	semidirect
125. #16863931	C₂²	semidirect
126. #16863930	C₂²	semidirect
127. #16863929	C₂²	semidirect
128. #16863928	C₂²	semidirect
129. #16863927	C₂²	semidirect
130. #16863926	C₂²	semidirect
131. #16863925	C₂²	semidirect
132. #16863924	C₂²	semidirect
133. #16863923	C₂²	semidirect
134. #126×D₆₇	C₂²	semidirect
135. #125×D₆₇	C₂²	semidirect
136. #124×D₆₇	C₂²	semidirect
137. #124×D₆₇	C₂²	semidirect
138. #123×D₆₇	C₂²	semidirect
139. #123×D₆₇	C₂²	semidirect
140. #123×D₆₇	C₂²	semidirect
141. #123×D₆₇	C₂²	semidirect
142. C₂²⋊Q₈×D₆₇	C₂²	semidirect
144. #121×D₆₇	C₂²	semidirect
145. #121×D₆₇	C₂²	semidirect
146. #121×D₆₇	C₂²	semidirect
147. #121×D₆₇	C₂²	semidirect
148. #121×D₆₇	C₂²	semidirect
149. #121×D₆₇	C₂²	semidirect
150. #120×D₆₇	C₂²	semidirect
151. #120×D₆₇	C₂²	semidirect
152. #120×D₆₇	C₂²	semidirect
153. #120×D₆₇	C₂²	semidirect
154. C₄×Q₈×D₆₇	C₂²	semidirect
155. C₄×D₄×D₆₇	C₂²	semidirect
156. C₄×D₄×D₆₇	C₂²	semidirect
157. C₄×D₄×D₆₇	C₂²	semidirect
158. C₄×D₄×D₆₇	C₂²	semidirect
159. #117×D₆₇	C₂²	semidirect
160. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
161. C₂×C₄²×D₆₇	C₂²	semidirect
162. #560×C₆₇	C₂²	semidirect
163. #559×C₆₇	C₂²	semidirect
164. #550×C₆₇	C₂²	semidirect
165. #546×C₆₇	C₂²	semidirect
166. D₄²×C₆₇	C₂²	semidirect
167. D₄²×C₆₇	C₂²	semidirect
168. #540×C₆₇	C₂²	semidirect
169. #535×C₆₇	C₂²	semidirect
170. #534×C₆₇	C₂²	semidirect
171. C₂×#127×C₆₇	C₂²	semidirect
172. #529×C₆₇	C₂²	semidirect
175. C₂×#11761629	C₂³	semidirect
176. C₂×#11761628	C₂³	semidirect
177. C₂×#11761628	C₂³	semidirect
178. C₂×#11761627	C₂³	semidirect
179. C₂×#11761627	C₂³	semidirect
182. C₂²×D₂₆₈	C₂³	semidirect
183. C₂²×D₂₆₈	C₂³	semidirect
184. C₂²×D₂₆₈	C₂³	semidirect
185. C₂²×D₂₆₈	C₂³	semidirect
186. C₂²×C₂²⋊D₆₇	C₂³	semidirect
187. C₂²×C₂²⋊D₆₇	C₂³	semidirect
188. C₂²×C₂²⋊D₆₇	C₂³	semidirect
189. C₂²×C₂²⋊D₆₇	C₂³	semidirect
190. C₂²×C₂²⋊D₆₇	C₂³	semidirect
206. C₂×D₄×D₆₇	C₂³	semidirect
207. C₂×D₄×D₆₇	C₂³	semidirect
208. C₂×D₄×D₆₇	C₂³	semidirect
209. C₂×D₄×D₆₇	C₂³	semidirect
210. C₂×D₄×D₆₇	C₂³	semidirect
211. C₂×D₄×D₆₇	C₂³	semidirect
212. C₂×D₄×D₆₇	C₂³	semidirect
213. C₂×D₄×D₆₇	C₂³	semidirect
214. C₂×D₄×D₆₇	C₂³	semidirect
215. C₂×D₄×D₆₇	C₂³	semidirect
216. C₂×D₄×D₆₇	C₂³	semidirect
223. #14524040	C₂³	semidirect
224. #14524040	C₂³	semidirect
225. #14524040	C₂³	semidirect
226. #14524040	C₂³	semidirect
229. #14524039	C₂³	semidirect
230. #14524039	C₂³	semidirect
231. #14524039	C₂³	semidirect
232. #14524039	C₂³	semidirect
233. #14524039	C₂³	semidirect
234. #14524039	C₂³	semidirect
235. #14524039	C₂³	semidirect
236. #14524039	C₂³	semidirect
237. #14524039	C₂³	semidirect
238. #14524039	C₂³	semidirect
239. #14524039	C₂³	semidirect
240. #14524039	C₂³	semidirect
241. #14524039	C₂³	semidirect
242. #14524038	C₂³	semidirect
243. #14524038	C₂³	semidirect
244. #14524038	C₂³	semidirect
245. #14524037	C₂³	semidirect
246. #14524036	C₂³	semidirect
247. #14524036	C₂³	semidirect
248. #14524036	C₂³	semidirect
249. #14524035	C₂³	semidirect
250. #14524034	C₂³	semidirect
251. #14524034	C₂³	semidirect
252. #14524033	C₂³	semidirect
253. #14524033	C₂³	semidirect
254. #14524032	C₂³	semidirect
255. #14524032	C₂³	semidirect
256. #14524031	C₂³	semidirect
257. #14524031	C₂³	semidirect
258. #14524030	C₂³	semidirect
259. #14524030	C₂³	semidirect
260. #14524029	C₂³	semidirect
261. #14524029	C₂³	semidirect
262. #14524029	C₂³	semidirect
263. #14524029	C₂³	semidirect
264. #14524028	C₂³	semidirect
265. #14524028	C₂³	semidirect
266. #14524028	C₂³	semidirect
267. #14524028	C₂³	semidirect
268. #14524028	C₂³	semidirect
269. #14524028	C₂³	semidirect
270. #14524027	C₂³	semidirect
271. #14524027	C₂³	semidirect
272. #14524027	C₂³	semidirect
273. #14524027	C₂³	semidirect
274. #14524026	C₂³	semidirect
275. #14524026	C₂³	semidirect
276. #14524026	C₂³	semidirect
277. #14524026	C₂³	semidirect
278. #14524025	C₂³	semidirect
279. #14524025	C₂³	semidirect
280. #14524025	C₂³	semidirect
281. #14524025	C₂³	semidirect
282. #14524025	C₂³	semidirect
283. #14524025	C₂³	semidirect
284. #14524024	C₂³	semidirect
285. #14524024	C₂³	semidirect
286. #14524024	C₂³	semidirect
287. #14524024	C₂³	semidirect
288. #14524023	C₂³	semidirect
289. #14524022	C₂³	semidirect
290. #14524021	C₂³	semidirect
291. #14524020	C₂³	semidirect
292. #14524019	C₂³	semidirect
294. #14524018	C₂³	semidirect
295. #14524018	C₂³	semidirect
296. #14524018	C₂³	semidirect
297. #14524018	C₂³	semidirect
298. #14524018	C₂³	semidirect
299. #14524018	C₂³	semidirect
301. #14524017	C₂³	semidirect
302. #14524017	C₂³	semidirect
303. #14524017	C₂³	semidirect
304. #14524017	C₂³	semidirect
305. #14524017	C₂³	semidirect
306. #14524017	C₂³	semidirect
308. #14524016	C₂³	semidirect
309. #14524016	C₂³	semidirect
310. #14524016	C₂³	semidirect
311. #14524016	C₂³	semidirect
312. #14524016	C₂³	semidirect
313. #14524016	C₂³	semidirect
314. #14524016	C₂³	semidirect
315. #14524016	C₂³	semidirect
316. #14524016	C₂³	semidirect
317. #14524016	C₂³	semidirect
319. #14524015	C₂³	semidirect
320. #14524015	C₂³	semidirect
321. #14524015	C₂³	semidirect
322. #14524015	C₂³	semidirect
323. #14524015	C₂³	semidirect
324. #14524015	C₂³	semidirect
325. #14524015	C₂³	semidirect
326. #14524015	C₂³	semidirect
327. #14524015	C₂³	semidirect
328. #14524015	C₂³	semidirect
330. #14524014	C₂³	semidirect
331. #14524014	C₂³	semidirect
332. #14524014	C₂³	semidirect
333. #14524014	C₂³	semidirect
334. #14524014	C₂³	semidirect
335. #14524014	C₂³	semidirect
336. #14524013	C₂³	semidirect
337. #14524013	C₂³	semidirect
338. #14524013	C₂³	semidirect
339. #14524013	C₂³	semidirect
340. #14524013	C₂³	semidirect
341. #14524013	C₂³	semidirect
342. #14524013	C₂³	semidirect
343. #14524013	C₂³	semidirect
344. #14524013	C₂³	semidirect
345. #14524013	C₂³	semidirect
346. #14524012	C₂³	semidirect
347. #14524012	C₂³	semidirect
348. #14524012	C₂³	semidirect
349. #14524012	C₂³	semidirect
350. #14524011	C₂³	semidirect
351. #14524011	C₂³	semidirect
352. #14524011	C₂³	semidirect
353. #14524011	C₂³	semidirect
354. #14524011	C₂³	semidirect
355. #14524011	C₂³	semidirect
356. #14524011	C₂³	semidirect
357. #14524011	C₂³	semidirect
358. #14524011	C₂³	semidirect
359. #14524011	C₂³	semidirect
360. Q₈×Dic₆₇	C₂³	semidirect
361. C₄×Dic₁₃₄	C₂³	semidirect
362. C₄×Dic₁₃₄	C₂³	semidirect
363. #14524008	C₂³	semidirect
364. #14524008	C₂³	semidirect
365. C₄×D₂₆₈	C₂³	semidirect
366. C₄×D₂₆₈	C₂³	semidirect
367. C₄×D₂₆₈	C₂³	semidirect
368. C₄×D₂₆₈	C₂³	semidirect
369. D₄×Dic₆₇	C₂³	semidirect
370. D₄×Dic₆₇	C₂³	semidirect
371. D₄×Dic₆₇	C₂³	semidirect
372. D₄×Dic₆₇	C₂³	semidirect
373. #14524005	C₂³	semidirect
374. #14524005	C₂³	semidirect
375. #14524005	C₂³	semidirect
376. #14524005	C₂³	semidirect
377. C₄×C₂²⋊D₆₇	C₂³	semidirect
378. C₄×C₂²⋊D₆₇	C₂³	semidirect
379. C₄×C₂²⋊D₆₇	C₂³	semidirect
380. C₄×C₂²⋊D₆₇	C₂³	semidirect
381. C₄×C₂²⋊D₆₇	C₂³	semidirect
382. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
383. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
384. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
385. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
386. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
387. #14524002	C₂³	semidirect
388. #14524001	C₂³	semidirect
389. #14524001	C₂³	semidirect
390. #14524000	C₂³	semidirect
391. #14524000	C₂³	semidirect
392. #14523999	C₂³	semidirect
393. #14523999	C₂³	semidirect
400. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
401. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
411. C₂²⋊C₄×D₆₇	C₂³	semidirect
412. C₂²⋊C₄×D₆₇	C₂³	semidirect
413. C₂²⋊C₄×D₆₇	C₂³	semidirect
414. C₂×C₄×Dic₆₇	C₂³	semidirect
415. C₂×C₄×Dic₆₇	C₂³	semidirect
420. C₄²×D₆₇	C₂³	semidirect
421. C₄²×D₆₇	C₂³	semidirect
422. C₄²×D₆₇	C₂³	semidirect
423. C₂×#41×C₆₇	C₂³	semidirect
424. C₂²×D₄×C₆₇	C₂³	semidirect
425. C₂²×D₄×C₆₇	C₂³	semidirect
426. C₂²×D₄×C₆₇	C₂³	semidirect
427. C₂²×D₄×C₆₇	C₂³	semidirect
429. #127×C₆₇	C₂³	semidirect
430. #127×C₆₇	C₂³	semidirect
431. #127×C₆₇	C₂³	semidirect
432. #127×C₆₇	C₂³	semidirect
433. #126×C₆₇	C₂³	semidirect
434. #125×C₆₇	C₂³	semidirect
435. #124×C₆₇	C₂³	semidirect
436. #124×C₆₇	C₂³	semidirect
437. #123×C₆₇	C₂³	semidirect
438. #123×C₆₇	C₂³	semidirect
439. #123×C₆₇	C₂³	semidirect
440. #123×C₆₇	C₂³	semidirect
441. C₂²⋊Q₈×C₆₇	C₂³	semidirect
443. #121×C₆₇	C₂³	semidirect
444. #121×C₆₇	C₂³	semidirect
445. #121×C₆₇	C₂³	semidirect
446. #121×C₆₇	C₂³	semidirect
447. #121×C₆₇	C₂³	semidirect
448. #121×C₆₇	C₂³	semidirect
449. #120×C₆₇	C₂³	semidirect
450. #120×C₆₇	C₂³	semidirect
451. #120×C₆₇	C₂³	semidirect
452. #120×C₆₇	C₂³	semidirect
453. C₄×Q₈×C₆₇	C₂³	semidirect
454. C₄×D₄×C₆₇	C₂³	semidirect
455. C₄×D₄×C₆₇	C₂³	semidirect
456. C₄×D₄×C₆₇	C₂³	semidirect
457. C₄×D₄×C₆₇	C₂³	semidirect
458. #117×C₆₇	C₂³	semidirect
459. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
460. C₂×C₄²×C₆₇	C₂³	semidirect
835. D₆₇	#3543	direct (N × H)
847. #3543	D₆₇	direct (N × H)
859. C₆₇	C₂×#3543	semidirect
874. #560	C₂×D₆₇	semidirect
880. #559	C₂×D₆₇	semidirect
889. #550	C₂×D₆₇	semidirect
901. #546	C₂×D₆₇	semidirect
918. D₄²	C₂×D₆₇	semidirect
919. D₄²	C₂×D₆₇	semidirect
931. #540	C₂×D₆₇	semidirect
943. #535	C₂×D₆₇	semidirect
955. #534	C₂×D₆₇	semidirect
968. C₂×#127	C₂×D₆₇	semidirect
980. #529	C₂×D₆₇	semidirect
1017. C₂×#41	C₂²×D₆₇	semidirect
1054. C₂²×D₄	C₂²×D₆₇	semidirect
1055. C₂²×D₄	C₂²×D₆₇	semidirect
1056. C₂²×D₄	C₂²×D₆₇	semidirect
1057. C₂²×D₄	C₂²×D₆₇	semidirect
1084. #127	C₂²×D₆₇	semidirect
1085. #127	C₂²×D₆₇	semidirect
1086. #127	C₂²×D₆₇	semidirect
1087. #127	C₂²×D₆₇	semidirect
1095. #126	C₂²×D₆₇	semidirect
1101. #125	C₂²×D₆₇	semidirect
1112. #124	C₂²×D₆₇	semidirect
1113. #124	C₂²×D₆₇	semidirect
1138. #123	C₂²×D₆₇	semidirect
1139. #123	C₂²×D₆₇	semidirect
1140. #123	C₂²×D₆₇	semidirect
1141. #123	C₂²×D₆₇	semidirect
1147. C₂²⋊Q₈	C₂²×D₆₇	semidirect
1192. #121	C₂²×D₆₇	semidirect
1193. #121	C₂²×D₆₇	semidirect
1194. #121	C₂²×D₆₇	semidirect
1195. #121	C₂²×D₆₇	semidirect
1196. #121	C₂²×D₆₇	semidirect
1197. #121	C₂²×D₆₇	semidirect
1222. #120	C₂²×D₆₇	semidirect
1223. #120	C₂²×D₆₇	semidirect
1224. #120	C₂²×D₆₇	semidirect
1225. #120	C₂²×D₆₇	semidirect
1231. C₄×Q₈	C₂²×D₆₇	semidirect
1254. C₄×D₄	C₂²×D₆₇	semidirect
1255. C₄×D₄	C₂²×D₆₇	semidirect
1256. C₄×D₄	C₂²×D₆₇	semidirect
1257. C₄×D₄	C₂²×D₆₇	semidirect
1265. #117	C₂²×D₆₇	semidirect
1286. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
1296. C₂×C₄²	C₂²×D₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22574543	2
#22574542	2
#22574541	2
#22574540	2
#22574539	2
#22574538	2
#22574537	2
#22574536	2
#22574535	2
#22574534	2
#22574533	2
#560×D₆₇	2
#559×D₆₇	2
#550×D₆₇	2
#546×D₆₇	2
D₄²×D₆₇	2
#540×D₆₇	2
#535×D₆₇	2
#534×D₆₇	2
C₂×#127×D₆₇	2
#529×D₆₇	2
C₆₇×#3543	2
C₂×#3543	67

Subgroups — #3543×D67 #31763414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3543×D₆₇ #31763414