Subgroups — #3481×D₆₇ #31762907

Order 17152.

8722 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573820	C₂	1	2	yes	maximal, complemented
2	#22573819	C₂	1	2	yes	maximal, complemented
3	#22573818	C₂	1	1	yes	maximal, characteristic, complemented
4	#22573817	C₂	1	1	yes	maximal, characteristic, complemented
5	#22573816	C₂	1	4	yes	maximal, complemented
6	#22573815	C₂	1	4	yes	maximal, complemented
7	#22573814	C₂	1	4	yes	maximal, complemented
8	#22573813	C₂	1	4	yes	maximal, complemented
9	#22573812	C₂	1	4	yes	maximal, complemented
10	#22573811	C₂	1	4	yes	maximal, complemented
11	#22573810	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#554×D₆₇	C₂	1	2	yes	maximal, complemented
14	#553×D₆₇	C₂	1	4	yes	maximal, complemented
15	#551×D₆₇	C₂	1	4	yes	maximal, complemented
16	#546×D₆₇	C₂	1	4	yes	maximal, complemented
17	D₄²×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#532×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	#529×D₆₇	C₂	1	4	yes	maximal, complemented
20	#525×D₆₇	C₂	1	4	yes	maximal, complemented
21	C₄×#41×D₆₇	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×D₄×D₆₇	C₂	1	4	yes	maximal, complemented
23	C₆₇×#3481	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×D₆₇	C₂²	1	2	yes	—
25	C₂×#41×D₆₇	C₂²	1	2	yes	complemented
26	C₂²×D₄×D₆₇	C₂²	1	4	yes	—
27	C₂³×C₄×D₆₇	C₂²	1	4	yes	complemented
28	#16864132	C₂²	1	1	yes	characteristic, complemented
29	#16864131	C₂²	1	2	yes	complemented
30	#16864130	C₂²	1	4	yes	complemented
31	#16864129	C₂²	1	4	yes	complemented
32	#16864128	C₂²	1	4	yes	complemented
33	#16864107	C₂²	1	2	yes	complemented
34	#16864106	C₂²	1	2	yes	complemented
35	#16864105	C₂²	1	4	yes	complemented
36	#16864104	C₂²	1	4	yes	complemented
37	#16864103	C₂²	1	2	yes	complemented
38	#16864102	C₂²	1	4	yes	complemented
39	#16864101	C₂²	1	4	yes	complemented
40	#16864100	C₂²	1	8	yes	complemented
41	#16864099	C₂²	1	4	yes	complemented
42	#16864098	C₂²	1	4	yes	complemented
43	#16864097	C₂²	1	8	yes	complemented
44	#16864096	C₂²	1	4	yes	complemented
45	#16864095	C₂²	1	8	yes	complemented
46	#16864094	C₂²	1	4	yes	complemented
47	#16864093	C₂²	1	4	yes	complemented
48	#16864092	C₂²	1	4	yes	complemented
49	#16864091	C₂²	1	8	yes	complemented
50	#16864090	C₂²	1	4	yes	complemented
51	#16864089	C₂²	1	8	yes	complemented
52	#16864077	C₂²	1	4	yes	complemented
53	#16864076	C₂²	1	4	yes	complemented
54	#16864075	C₂²	1	8	yes	complemented
55	#16864074	C₂²	1	4	yes	complemented
56	#16864073	C₂²	1	8	yes	complemented
57	#16864072	C₂²	1	8	yes	complemented
58	#16864071	C₂²	1	8	yes	complemented
59	#16864070	C₂²	1	8	yes	complemented
60	#16864069	C₂²	1	8	yes	complemented
61	#16864043	C₂²	1	4	yes	complemented
62	#16864042	C₂²	1	4	yes	complemented
63	#16864041	C₂²	1	4	yes	complemented
64	#16864040	C₂²	1	4	yes	complemented
65	#16864039	C₂²	1	4	yes	complemented
66	#16864038	C₂²	1	8	yes	complemented
67	#16864037	C₂²	1	4	yes	complemented
68	#16864036	C₂²	1	8	yes	complemented
69	#16864035	C₂²	1	8	yes	complemented
70	#16864034	C₂²	1	4	yes	complemented
71	#16864033	C₂²	1	8	yes	complemented
72	D₄×D₂₆₈	C₂²	1	2	yes	complemented
73	#16864031	C₂²	1	1	yes	characteristic, complemented
74	#16864030	C₂²	1	4	yes	complemented
75	D₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
76	#16864028	C₂²	1	4	yes	complemented
77	#16863947	C₂²	1	1	yes	characteristic, complemented
78	#16863946	C₂²	1	1	yes	characteristic, complemented
79	#16863945	C₂²	1	2	yes	complemented
80	#16863944	C₂²	1	1	yes	characteristic, complemented
81	#16863943	C₂²	1	4	yes	complemented
82	#16863942	C₂²	1	2	yes	complemented
83	#16863941	C₂²	1	4	yes	complemented
84	C₄⋊Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
85	#127×D₆₇	C₂²	1	1	yes	characteristic
86	#16863933	C₂²	1	4	yes	complemented
87	#16863932	C₂²	1	4	yes	complemented
88	#16863931	C₂²	1	4	yes	complemented
89	#16863930	C₂²	1	4	yes	complemented
90	#16863929	C₂²	1	8	yes	complemented
91	#16863928	C₂²	1	4	yes	complemented
92	#16863927	C₂²	1	4	yes	complemented
93	#16863926	C₂²	1	8	yes	complemented
94	#16863925	C₂²	1	4	yes	complemented
95	#16863924	C₂²	1	8	yes	complemented
96	#16863923	C₂²	1	8	yes	complemented
97	#126×D₆₇	C₂²	1	8	yes	complemented
98	#125×D₆₇	C₂²	1	4	yes	complemented
99	#124×D₆₇	C₂²	1	4	yes	complemented
100	#124×D₆₇	C₂²	1	2	yes	complemented
101	#16863909	C₂²	1	8	yes	complemented
102	#16863908	C₂²	1	4	yes	complemented
103	#16863907	C₂²	1	4	yes	complemented
104	#16863906	C₂²	1	8	yes	complemented
105	#16863905	C₂²	1	8	yes	complemented
106	#16863905	C₂²	1	8	yes	complemented
107	#16863904	C₂²	1	4	yes	complemented
108	#16863904	C₂²	1	4	yes	complemented
109	#16863903	C₂²	1	4	yes	complemented
110	#16863902	C₂²	1	4	yes	complemented
111	#16863902	C₂²	1	4	yes	complemented
112	#123×D₆₇	C₂²	1	8	yes	complemented
113	#123×D₆₇	C₂²	1	4	yes	complemented
114	#123×D₆₇	C₂²	1	4	yes	complemented
115	C₂²⋊Q₈×D₆₇	C₂²	1	4	yes	complemented
116	C₂²⋊Q₈×D₆₇	C₂²	1	8	yes	complemented
117	#121×D₆₇	C₂²	1	4	yes	—
118	#121×D₆₇	C₂²	1	8	yes	complemented
119	#121×D₆₇	C₂²	1	4	yes	complemented
120	#120×D₆₇	C₂²	1	4	yes	—
121	#120×D₆₇	C₂²	1	4	yes	complemented
122	#41×Dic₆₇	C₂²	1	2	yes	complemented
123	C₄×#11761629	C₂²	1	2	yes	complemented
124	C₄×#11761629	C₂²	1	2	yes	complemented
125	C₄×#11761628	C₂²	1	4	yes	complemented
126	C₄×#11761628	C₂²	1	2	yes	complemented
127	#16863864	C₂²	1	4	yes	complemented
128	#16863864	C₂²	1	2	yes	complemented
129	C₄×#11761627	C₂²	1	2	yes	complemented
130	C₄×#11761627	C₂²	1	2	yes	complemented
131	C₄×#11761627	C₂²	1	4	yes	complemented
132	C₄×#11761627	C₂²	1	4	yes	complemented
133	C₄×Q₈×D₆₇	C₂²	1	2	yes	complemented
134	C₄×Q₈×D₆₇	C₂²	1	2	yes	complemented
135	C₂×C₄×D₂₆₈	C₂²	1	4	yes	complemented
136	C₂×D₄×Dic₆₇	C₂²	1	4	yes	complemented
137	C₂×#14524005	C₂²	1	4	yes	complemented
138	C₂×C₄×C₂²⋊D₆₇	C₂²	1	8	yes	complemented
139	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	8	yes	complemented
140	C₄×D₄×D₆₇	C₂²	1	2	yes	—
141	C₄×D₄×D₆₇	C₂²	1	4	yes	—
142	C₄×D₄×D₆₇	C₂²	1	2	yes	—
143	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
144	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
145	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
146	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
147	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
148	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
149	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
150	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
151	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
152	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
153	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
154	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
155	#117×D₆₇	C₂²	1	4	yes	complemented
156	#117×D₆₇	C₂²	1	2	yes	complemented
157	#117×D₆₇	C₂²	1	4	yes	complemented
158	C₂×C₄⋊C₄×D₆₇	C₂²	1	4	yes	complemented
159	C₂×C₂²⋊C₄×D₆₇	C₂²	1	8	yes	complemented
160	C₂×C₄²×D₆₇	C₂²	1	4	yes	complemented
161	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
162	#559×C₆₇	C₂²	1	1	yes	characteristic, complemented
163	#554×C₆₇	C₂²	1	2	yes	complemented
164	#553×C₆₇	C₂²	1	4	yes	complemented
165	#551×C₆₇	C₂²	1	4	yes	complemented
166	#546×C₆₇	C₂²	1	4	yes	complemented
167	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
168	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
169	#529×C₆₇	C₂²	1	4	yes	complemented
170	#525×C₆₇	C₂²	1	4	yes	complemented
171	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
172	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
173	C₂⁴×D₆₇	C₂³	1	4	yes	—
174	C₂×#11761629	C₂³	1	2	yes	—
175	C₂×#11761629	C₂³	1	2	yes	complemented
176	C₂×#11761628	C₂³	1	4	yes	—
177	C₂×#11761628	C₂³	1	2	yes	—
178	C₂×#11761628	C₂³	1	2	yes	complemented
179	C₂×#11761628	C₂³	1	4	yes	complemented
180	C₂×#11761627	C₂³	1	4	yes	—
181	C₂×#11761627	C₂³	1	2	yes	—
182	C₂×#11761627	C₂³	1	2	yes	complemented
183	C₂×#11761627	C₂³	1	4	yes	complemented
184	#41×D₆₇	—	2	16	no	—
185	#41×D₆₇	—	4	8	no	—
186	C₂×Q₈×D₆₇	C₂³	1	2	yes	—
187	C₂×Q₈×D₆₇	C₂³	1	2	yes	—
188	C₂²×D₂₆₈	C₂³	1	4	yes	—
189	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	—
190	C₂×D₄×D₆₇	—	2	32	no	—
191	C₂×D₄×D₆₇	C₂³	1	8	yes	—
192	C₂×D₄×D₆₇	C₂³	1	4	yes	—
193	C₂×D₄×D₆₇	C₂³	1	4	yes	—
194	C₂×D₄×D₆₇	C₂³	1	8	yes	—
195	C₂×D₄×D₆₇	C₂³	1	4	yes	—
196	C₂×D₄×D₆₇	C₂³	1	4	yes	—
197	C₂×D₄×D₆₇	C₂³	1	2	yes	—
198	C₂×D₄×D₆₇	C₂³	1	4	yes	—
199	C₂×D₄×D₆₇	C₂³	1	2	yes	—
200	C₂³×Dic₆₇	C₂³	1	4	yes	complemented
201	C₂²×C₄×D₆₇	—	4	16	no	—
202	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
203	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
204	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
205	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
206	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
208	C₂²×C₄×D₆₇	C₂³	1	8	yes	—
209	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
210	C₂²×C₄×D₆₇	C₂³	1	4	yes	complemented
211	C₂²×C₄×D₆₇	C₂³	1	4	yes	complemented
212	C₂²×C₄×D₆₇	C₂³	1	8	yes	complemented
213	C₂²×C₄×D₆₇	C₂³	1	8	yes	complemented
214	#14524043	C₂³	1	1	yes	characteristic, complemented
215	#14524042	C₂³	1	4	yes	complemented
216	#14524041	C₂³	1	2	yes	complemented
217	#14524040	C₂³	1	1	yes	characteristic
218	#14524039	C₂³	1	2	yes	—
219	#14524039	C₂³	1	4	yes	—
220	#14524038	C₂³	1	8	yes	complemented
221	#14524038	C₂³	1	8	yes	complemented
222	#14524038	C₂³	1	8	yes	complemented
223	#14524037	C₂³	1	8	yes	complemented
224	#14524036	C₂³	1	8	yes	complemented
225	#14524036	C₂³	1	8	yes	complemented
226	#14524036	C₂³	1	8	yes	complemented
227	#14524035	C₂³	1	4	yes	complemented
228	#14524034	C₂³	1	4	yes	complemented
229	#14524034	C₂³	1	4	yes	complemented
230	#14524033	C₂³	1	8	yes	complemented
231	#14524033	C₂³	1	8	yes	complemented
232	#14524032	C₂³	1	4	yes	complemented
233	#14524032	C₂³	1	2	yes	complemented
234	#14524031	C₂³	1	4	yes	complemented
235	#14524031	C₂³	1	2	yes	complemented
236	#14524030	C₂³	1	4	yes	complemented
237	#14524030	C₂³	1	2	yes	complemented
238	#14524029	C₂³	1	8	yes	complemented
239	#14524029	C₂³	1	8	yes	complemented
240	#14524029	C₂³	1	8	yes	complemented
241	#14524028	C₂³	1	8	yes	complemented
242	#14524028	C₂³	1	8	yes	complemented
243	#14524028	C₂³	1	8	yes	complemented
244	#14524028	C₂³	1	8	yes	complemented
245	#14524027	C₂³	1	8	yes	complemented
246	#14524027	C₂³	1	4	yes	complemented
247	#14524027	C₂³	1	4	yes	complemented
248	#14524026	C₂³	1	8	yes	complemented
249	#14524026	C₂³	1	4	yes	complemented
250	#14524026	C₂³	1	4	yes	complemented
251	#14524025	C₂³	1	8	yes	complemented
252	#14524025	C₂³	1	8	yes	complemented
253	#14524025	C₂³	1	8	yes	complemented
254	#14524025	C₂³	1	8	yes	complemented
255	#14524024	C₂³	1	8	yes	complemented
256	#14524024	C₂³	1	4	yes	complemented
257	#14524024	C₂³	1	4	yes	complemented
258	#14524023	C₂³	1	4	yes	complemented
259	#14524023	C₂³	1	8	yes	complemented
260	#14524022	C₂³	1	4	yes	complemented
261	#14524022	C₂³	1	8	yes	complemented
262	#14524021	C₂³	1	8	yes	complemented
263	#14524021	C₂³	1	8	yes	complemented
264	#14524021	C₂³	1	8	yes	complemented
265	#14524020	C₂³	1	8	yes	complemented
266	#14524020	C₂³	1	8	yes	complemented
267	#14524020	C₂³	1	8	yes	complemented
268	#14524019	C₂³	1	4	yes	complemented
269	#14524019	C₂³	1	8	yes	complemented
270	#14524018	C₂³	1	4	yes	—
271	#14524018	C₂³	1	8	yes	complemented
272	#14524018	C₂³	1	4	yes	complemented
273	#14524017	C₂³	1	4	yes	—
274	#14524017	C₂³	1	4	yes	complemented
275	#14524017	C₂³	1	8	yes	complemented
276	#14524016	C₂³	1	8	yes	—
277	#14524016	C₂³	1	8	yes	complemented
278	#14524016	C₂³	1	8	yes	complemented
279	#14524016	C₂³	1	8	yes	complemented
280	#14524015	C₂³	1	8	yes	—
281	#14524015	C₂³	1	8	yes	complemented
282	#14524015	C₂³	1	8	yes	complemented
283	#14524015	C₂³	1	8	yes	complemented
284	#14524014	C₂³	1	4	yes	—
285	#14524014	C₂³	1	8	yes	complemented
286	#14524014	C₂³	1	4	yes	complemented
287	#14524013	C₂³	1	8	yes	—
288	#14524013	C₂³	1	4	yes	—
289	#14524013	C₂³	1	8	yes	complemented
290	#14524013	C₂³	1	4	yes	complemented
291	#14524012	C₂³	1	4	yes	—
292	#14524012	C₂³	1	4	yes	complemented
293	#14524011	C₂³	1	4	yes	—
294	#14524011	C₂³	1	8	yes	—
295	#14524011	C₂³	1	8	yes	complemented
296	#14524011	C₂³	1	4	yes	complemented
297	Q₈×Dic₆₇	C₂³	1	2	yes	complemented
298	Q₈×Dic₆₇	C₂³	1	2	yes	complemented
299	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
300	C₄×Dic₁₃₄	C₂³	1	2	yes	complemented
301	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
302	C₄×Dic₁₃₄	C₂³	1	2	yes	complemented
303	#14524008	C₂³	1	4	yes	complemented
304	#14524008	C₂³	1	2	yes	complemented
305	#14524008	C₂³	1	4	yes	complemented
306	#14524008	C₂³	1	2	yes	complemented
307	C₄×D₂₆₈	C₂³	1	2	yes	—
308	C₄×D₂₆₈	C₂³	1	4	yes	—
309	C₄×D₂₆₈	C₂³	1	2	yes	—
310	C₄×D₂₆₈	C₂³	1	4	yes	complemented
311	C₄×D₂₆₈	C₂³	1	8	yes	complemented
312	C₄×D₂₆₈	C₂³	1	4	yes	complemented
313	C₄×D₂₆₈	C₂³	1	8	yes	complemented
314	C₄×D₂₆₈	C₂³	1	4	yes	complemented
315	C₄×D₂₆₈	C₂³	1	4	yes	complemented
316	D₄×Dic₆₇	C₂³	1	2	yes	—
317	D₄×Dic₆₇	C₂³	1	4	yes	—
318	D₄×Dic₆₇	C₂³	1	2	yes	—
319	D₄×Dic₆₇	C₂³	1	4	yes	complemented
320	D₄×Dic₆₇	C₂³	1	8	yes	complemented
321	D₄×Dic₆₇	C₂³	1	4	yes	complemented
322	D₄×Dic₆₇	C₂³	1	8	yes	complemented
323	D₄×Dic₆₇	C₂³	1	4	yes	complemented
324	D₄×Dic₆₇	C₂³	1	4	yes	complemented
325	#14524005	C₂³	1	2	yes	—
326	#14524005	C₂³	1	4	yes	—
327	#14524005	C₂³	1	2	yes	—
328	#14524005	C₂³	1	4	yes	complemented
329	#14524005	C₂³	1	8	yes	complemented
330	#14524005	C₂³	1	4	yes	complemented
331	#14524005	C₂³	1	8	yes	complemented
332	#14524005	C₂³	1	4	yes	complemented
333	#14524005	C₂³	1	4	yes	complemented
334	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	—
335	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
336	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	—
337	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
338	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
339	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
340	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
341	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
342	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
343	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
344	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
345	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
346	C₄×C₂²⋊D₆₇	C₂³	1	4	yes	complemented
347	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	—
348	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
349	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	—
350	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	complemented
351	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	complemented
352	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
353	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
354	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
355	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
356	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
357	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
358	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	complemented
359	(C₂²⋊D₆₇)⋊C₄	C₂³	1	4	yes	complemented
360	#14524002	C₂³	1	4	yes	complemented
361	#14524002	C₂³	1	2	yes	complemented
362	#14524002	C₂³	1	4	yes	complemented
363	#14524001	C₂³	1	4	yes	complemented
364	#14524001	C₂³	1	4	yes	complemented
365	#14524001	C₂³	1	2	yes	complemented
366	#14524001	C₂³	1	2	yes	complemented
367	#14524001	C₂³	1	8	yes	complemented
368	#14524000	C₂³	1	4	yes	complemented
369	#14524000	C₂³	1	4	yes	complemented
370	#14524000	C₂³	1	4	yes	complemented
371	#14524000	C₂³	1	8	yes	complemented
372	#14523999	C₂³	1	4	yes	complemented
373	#14523999	C₂³	1	4	yes	complemented
374	#14523999	C₂³	1	4	yes	complemented
375	#14523999	C₂³	1	4	yes	complemented
376	#14523999	C₂³	1	4	yes	complemented
377	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	complemented
378	C₂×Dic₆₇⋊C₄	C₂³	1	8	yes	complemented
379	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
380	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
381	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
382	C₄⋊C₄×D₆₇	C₂³	1	2	yes	—
383	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
384	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
385	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
386	C₄⋊C₄×D₆₇	C₂³	1	4	yes	complemented
387	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
388	C₄⋊C₄×D₆₇	C₂³	1	4	yes	complemented
389	C₂×C₂²⋊Dic₆₇	C₂³	1	8	yes	complemented
390	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
391	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
392	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
393	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
394	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
395	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
396	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
397	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
398	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
399	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
400	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
401	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
402	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
403	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
404	C₂×C₄×Dic₆₇	C₂³	1	4	yes	complemented
405	C₂×C₄×Dic₆₇	C₂³	1	4	yes	complemented
406	C₂×C₄×Dic₆₇	C₂³	1	4	yes	complemented
407	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic, complemented
408	C₂×C₄×Dic₆₇	C₂³	1	2	yes	complemented
409	C₄²×D₆₇	C₂³	1	2	yes	—
410	C₄²×D₆₇	C₂³	1	1	yes	characteristic
411	C₄²×D₆₇	C₂³	1	4	yes	—
412	C₄²×D₆₇	C₂³	1	4	yes	—
413	C₄²×D₆₇	C₂³	1	1	yes	characteristic
414	C₄²×D₆₇	C₂³	1	4	yes	—
415	C₄²×D₆₇	C₂³	1	4	yes	complemented
416	C₄²×D₆₇	C₂³	1	4	yes	complemented
417	C₄²×D₆₇	C₂³	1	4	yes	complemented
418	C₄²×D₆₇	C₂³	1	4	yes	complemented
419	C₄²×D₆₇	C₂³	1	1	yes	characteristic, complemented
420	C₄²×D₆₇	C₂³	1	2	yes	complemented
421	C₄²×D₆₇	C₂³	1	1	yes	characteristic, complemented
422	C₂×#41×C₆₇	C₂³	1	2	yes	—
423	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
424	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
425	C₂³×C₄×C₆₇	C₂³	1	4	yes	complemented
426	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
427	#127×C₆₇	C₂³	1	1	yes	characteristic
428	#126×C₆₇	C₂³	1	8	yes	complemented
429	#125×C₆₇	C₂³	1	4	yes	complemented
430	#124×C₆₇	C₂³	1	4	yes	complemented
431	#124×C₆₇	C₂³	1	2	yes	complemented
432	#123×C₆₇	C₂³	1	8	yes	complemented
433	#123×C₆₇	C₂³	1	4	yes	complemented
434	#123×C₆₇	C₂³	1	4	yes	complemented
435	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
436	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
437	#121×C₆₇	C₂³	1	4	yes	—
438	#121×C₆₇	C₂³	1	8	yes	complemented
439	#121×C₆₇	C₂³	1	4	yes	complemented
440	#120×C₆₇	C₂³	1	4	yes	—
441	#120×C₆₇	C₂³	1	4	yes	complemented
442	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
443	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
444	C₄×D₄×C₆₇	C₂³	1	2	yes	—
445	C₄×D₄×C₆₇	C₂³	1	4	yes	—
446	C₄×D₄×C₆₇	C₂³	1	2	yes	—
447	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
448	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
449	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
450	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
451	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
452	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
453	#117×C₆₇	C₂³	1	4	yes	complemented
454	#117×C₆₇	C₂³	1	2	yes	complemented
455	#117×C₆₇	C₂³	1	4	yes	complemented
456	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
457	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
458	C₂×C₄²×C₆₇	C₂³	1	4	yes	complemented
459	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic, complemented
460	C₂³×D₆₇	—	2	32	no	—
461	C₂³×D₆₇	—	4	8	no	—
462	C₂³×D₆₇	C₂⁴	1	4	yes	—
463	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
464	C₂³×D₆₇	C₂⁴	1	4	yes	—
465	C₂³×D₆₇	C₂⁴	1	8	yes	—
466	C₂³×D₆₇	C₂⁴	1	4	yes	—
467	#11761629	—	2	8	no	—
468	#11761629	—	4	4	no	—
469	#11761628	—	2	16	no	—
470	#11761628	—	2	8	no	—
471	#11761628	—	4	4	no	—
472	#11761628	—	4	8	no	—
473	#11761627	—	2	8	no	—
474	#11761627	—	2	16	no	—
475	#11761627	—	4	8	no	—
476	#11761627	—	4	4	no	—
477	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
478	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
479	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
480	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
481	Q₈×D₆₇	—	2	8	no	—
482	Q₈×D₆₇	—	4	4	no	—
483	C₂×D₂₆₈	—	2	16	no	—
484	C₂×D₂₆₈	C₂⁴	1	8	yes	—
485	C₂×D₂₆₈	C₂⁴	1	4	yes	—
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	2	yes	—
490	C₂×C₂²⋊D₆₇	—	2	32	no	—
491	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
492	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
493	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
494	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
495	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
496	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
497	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
498	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
499	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
500	D₄×D₆₇	—	2	32	no	—
501	D₄×D₆₇	—	2	16	no	—
502	D₄×D₆₇	—	2	16	no	—
503	D₄×D₆₇	—	2	32	no	—
504	D₄×D₆₇	—	2	16	no	—
505	D₄×D₆₇	—	2	16	no	—
506	D₄×D₆₇	—	4	8	no	—
507	D₄×D₆₇	—	4	4	no	—
508	D₄×D₆₇	#41	1	16	yes	complemented
509	C₂²×Dic₆₇	—	4	8	no	—
510	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
511	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
512	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
513	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
514	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
515	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
516	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
517	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
518	C₂×C₄×D₆₇	—	2	16	no	—
519	C₂×C₄×D₆₇	—	2	16	no	—
520	C₂×C₄×D₆₇	—	2	8	no	—
521	C₂×C₄×D₆₇	—	2	16	no	—
522	C₂×C₄×D₆₇	—	2	16	no	—
523	C₂×C₄×D₆₇	—	2	4	no	—
524	C₂×C₄×D₆₇	—	4	8	no	—
525	C₂×C₄×D₆₇	—	4	16	no	—
526	C₂×C₄×D₆₇	—	4	8	no	—
527	C₂×C₄×D₆₇	—	4	16	no	—
528	C₂×C₄×D₆₇	—	4	8	no	—
529	C₂×C₄×D₆₇	—	4	16	no	—
530	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
531	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
532	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
533	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
534	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
535	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
536	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
537	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
538	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
539	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
540	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
541	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
542	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
543	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
544	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
545	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
546	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
547	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
548	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
549	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
550	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
551	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
552	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
553	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
554	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
555	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
556	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
557	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
558	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
559	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
560	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
561	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
562	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
563	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
564	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
565	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
566	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
567	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
568	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
569	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
570	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
571	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
572	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
573	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
574	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
575	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
576	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
577	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
578	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
579	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
580	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
581	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
582	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
583	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
584	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
585	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
586	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
587	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
588	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
589	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
590	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
591	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
592	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
593	C₄×Dic₆₇	C₂⁴	1	2	yes	—
594	C₄×Dic₆₇	C₂⁴	1	2	yes	—
595	C₄×Dic₆₇	C₂⁴	1	2	yes	—
596	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
597	C₄×Dic₆₇	C₂⁴	1	2	yes	—
598	C₄×Dic₆₇	C₂⁴	1	4	yes	—
599	C₄×Dic₆₇	C₂⁴	1	4	yes	—
600	C₄×Dic₆₇	C₂⁴	1	4	yes	—
601	C₄×Dic₆₇	C₂⁴	1	4	yes	—
602	C₄×Dic₆₇	C₂⁴	1	4	yes	—
603	C₄×Dic₆₇	C₂⁴	1	4	yes	—
604	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
605	C₄×Dic₆₇	C₂⁴	1	4	yes	—
606	C₄×Dic₆₇	C₂⁴	1	4	yes	—
607	C₄×Dic₆₇	C₂⁴	1	2	yes	—
608	C₄×Dic₆₇	C₂⁴	1	4	yes	—
609	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
610	#41×C₆₇	—	2	8	no	—
611	#41×C₆₇	—	4	4	no	—
612	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
613	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
614	C₂×D₄×C₆₇	—	2	16	no	—
615	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
616	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
617	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
618	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
619	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
620	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
621	C₂²×C₄×C₆₇	—	4	8	no	—
622	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
623	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
624	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
625	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
626	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
627	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
628	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
629	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
630	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
631	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
632	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
633	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
634	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
635	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
636	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
637	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
638	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
639	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
640	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
641	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
642	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
643	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
644	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
645	C₄²×C₆₇	C₂⁴	1	2	yes	—
646	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
647	C₄²×C₆₇	C₂⁴	1	4	yes	—
648	C₄²×C₆₇	C₂⁴	1	4	yes	—
649	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
650	C₄²×C₆₇	C₂⁴	1	4	yes	—
651	C₂³×C₆₇	—	2	16	no	—
652	C₂³×C₆₇	—	4	4	no	—
653	C₂³×C₆₇	C₂⁵	1	4	yes	—
654	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
655	C₂³×C₆₇	C₂⁵	1	4	yes	—
656	C₂²×D₆₇	—	2	8	no	—
657	C₂²×D₆₇	—	2	8	no	—
658	C₂²×D₆₇	—	2	16	no	—
659	C₂²×D₆₇	—	2	4	no	—
660	C₂²×D₆₇	—	2	16	no	—
661	C₂²×D₆₇	—	2	16	no	—
662	C₂²×D₆₇	—	2	16	no	—
663	C₂²×D₆₇	—	2	8	no	—
664	C₂²×D₆₇	—	2	2	no	—
665	C₂²×D₆₇	—	4	4	no	—
666	C₂²×D₆₇	—	4	8	no	—
667	C₂²×D₆₇	—	4	64	no	—
668	C₂²×D₆₇	C₂×#41	1	16	yes	—
669	C₂²×D₆₇	C₂⁵	1	4	yes	—
670	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
671	C₂²×D₆₇	C₂⁵	1	4	yes	—
672	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
673	Q₈×C₆₇	—	2	4	no	—
674	Q₈×C₆₇	—	4	2	no	—
675	D₄×C₆₇	—	2	16	no	—
676	D₄×C₆₇	—	2	8	no	—
677	D₄×C₆₇	—	2	8	no	—
678	D₄×C₆₇	—	4	2	no	—
679	D₄×C₆₇	—	4	4	no	—
680	D₄×C₆₇	C₂×#41	1	8	yes	complemented
681	C₂×C₄×C₆₇	—	2	8	no	—
682	C₂×C₄×C₆₇	—	2	8	no	—
683	C₂×C₄×C₆₇	—	2	4	no	—
684	C₂×C₄×C₆₇	—	2	8	no	—
685	C₂×C₄×C₆₇	—	2	8	no	—
686	C₂×C₄×C₆₇	—	2	2	no	—
687	C₂×C₄×C₆₇	—	4	8	no	—
688	C₂×C₄×C₆₇	—	4	4	no	—
689	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
690	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
691	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
692	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
693	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
694	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
695	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
696	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
697	C₂²⋊D₆₇	—	2	16	no	—
698	C₂²⋊D₆₇	—	2	8	no	—
699	C₂²⋊D₆₇	—	2	16	no	—
700	C₂²⋊D₆₇	—	2	8	no	—
701	C₂²⋊D₆₇	—	2	16	no	—
702	C₂²⋊D₆₇	—	4	4	no	—
703	C₂²⋊D₆₇	—	4	4	no	—
704	C₂²⋊D₆₇	—	4	4	no	—
705	C₂²⋊D₆₇	C₂×#41	1	16	yes	complemented
706	C₂×Dic₆₇	—	2	8	no	—
707	C₂×Dic₆₇	—	2	8	no	—
708	C₂×Dic₆₇	—	2	4	no	—
709	C₂×Dic₆₇	—	2	8	no	—
710	C₂×Dic₆₇	—	2	8	no	—
711	C₂×Dic₆₇	—	2	2	no	—
712	C₂×Dic₆₇	—	4	8	no	—
713	C₂×Dic₆₇	—	4	4	no	—
714	C₂×Dic₆₇	C₂⁵	1	2	yes	—
715	C₂×Dic₆₇	C₂⁵	1	4	yes	—
716	C₂×Dic₆₇	C₂⁵	1	4	yes	—
717	C₂×Dic₆₇	C₂⁵	1	4	yes	—
718	C₂×Dic₆₇	C₂⁵	1	1	yes	characteristic
719	C₂×Dic₆₇	C₂⁵	1	4	yes	—
720	C₂×Dic₆₇	C₂⁵	1	2	yes	—
721	C₂×Dic₆₇	C₂⁵	1	1	yes	characteristic
722	D₂₆₈	—	2	16	no	—
723	D₂₆₈	—	2	8	no	—
724	D₂₆₈	—	2	8	no	—
725	D₂₆₈	—	4	2	no	—
726	D₂₆₈	—	4	4	no	—
727	D₂₆₈	C₂×#41	1	8	yes	complemented
728	C₄×D₆₇	—	2	4	no	—
729	C₄×D₆₇	—	2	8	no	—
730	C₄×D₆₇	—	2	8	no	—
731	C₄×D₆₇	—	2	8	no	—
732	C₄×D₆₇	—	2	8	no	—
733	C₄×D₆₇	—	2	8	no	—
734	C₄×D₆₇	—	2	8	no	—
735	C₄×D₆₇	—	2	2	no	—
736	C₄×D₆₇	—	2	8	no	—
737	C₄×D₆₇	—	2	4	no	—
738	C₄×D₆₇	—	2	8	no	—
739	C₄×D₆₇	—	2	8	no	—
740	C₄×D₆₇	—	2	2	no	—
741	C₄×D₆₇	—	2	8	no	—
742	C₄×D₆₇	—	2	4	no	—
743	C₄×D₆₇	—	2	8	no	—
744	C₄×D₆₇	—	2	8	no	—
745	C₄×D₆₇	—	2	2	no	—
746	C₄×D₆₇	—	4	8	no	—
747	C₄×D₆₇	—	4	8	no	—
748	C₄×D₆₇	—	4	8	no	—
749	C₄×D₆₇	C₂×#41	1	8	yes	—
750	C₄×D₆₇	H(5,𝔽₂)	1	4	yes	—
751	Dic₁₃₄	—	2	4	no	—
752	Dic₁₃₄	—	2	8	no	—
753	Dic₁₃₄	—	4	4	no	—
754	Dic₁₃₄	—	4	2	no	—
755	C₂²×C₆₇	—	2	4	no	—
756	C₂²×C₆₇	—	2	4	no	—
757	C₂²×C₆₇	—	2	2	no	—
758	C₂²×C₆₇	—	2	8	no	—
759	C₂²×C₆₇	—	2	4	no	—
760	C₂²×C₆₇	—	2	1	no	—
761	C₂²×C₆₇	—	4	16	no	—
762	C₂²×C₆₇	C₂²×#41	1	8	yes	—
763	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
764	C₂×D₆₇	—	2	4	no	—
765	C₂×D₆₇	—	2	4	no	—
766	C₂×D₆₇	—	2	32	no	—
767	C₂×D₆₇	—	2	2	no	—
768	C₂×D₆₇	—	2	8	no	—
769	C₂×D₆₇	—	2	4	no	—
770	C₂×D₆₇	—	2	1	no	—
771	C₂×D₆₇	—	4	16	no	—
772	C₂×D₆₇	—	4	32	no	—
773	C₂×D₆₇	—	4	4	no	—
774	C₂×D₆₇	—	4	16	no	—
775	C₂×D₆₇	C₂²×#41	1	8	yes	—
776	C₂×D₆₇	C₂²×#41	1	4	yes	—
777	C₂×D₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
778	C₄×C₆₇	—	2	4	no	—
779	C₄×C₆₇	—	2	2	no	—
780	C₄×C₆₇	—	2	4	no	—
781	C₄×C₆₇	—	2	1	no	—
782	C₄×C₆₇	—	2	4	no	—
783	C₄×C₆₇	—	2	4	no	—
784	C₄×C₆₇	C₂²×#41	1	4	yes	—
785	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
786	Dic₆₇	—	2	4	no	—
787	Dic₆₇	—	2	2	no	—
788	Dic₆₇	—	2	4	no	—
789	Dic₆₇	—	2	1	no	—
790	Dic₆₇	—	2	4	no	—
791	Dic₆₇	—	2	4	no	—
792	Dic₆₇	C₂²×#41	1	4	yes	—
793	Dic₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
794	C₂×#3481	—	67	1	no	maximal, Sylow
795	C₂×C₆₇	—	2	8	no	—
796	C₂×C₆₇	—	4	4	no	—
797	C₂×C₆₇	—	4	1	no	—
798	C₂×C₆₇	C₂³×#41	1	2	yes	—
799	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
800	D₆₇	—	2	8	no	—
801	D₆₇	—	4	1	no	—
802	D₆₇	—	4	4	no	—
803	D₆₇	#3481	1	4	yes	direct product factor
804	#3481	—	67	1	no	—
805	#3481	—	67	2	no	—
806	#3481	—	67	4	no	—
807	#3481	—	67	4	no	—
808	#3481	—	67	4	no	—
809	#3481	—	67	1	no	—
810	#3481	—	67	1	no	—
811	#3481	—	67	4	no	—
812	#3481	—	67	4	no	—
813	#3481	—	67	2	no	—
814	#3481	—	67	4	no	—
815	#3481	D₆₇	1	1	yes	characteristic, direct product factor
816	C₂×#559	—	67	1	no	—
817	C₂×#554	—	67	2	no	—
818	C₂×#553	—	67	4	no	—
819	C₂×#551	—	67	4	no	—
820	C₂×#546	—	67	4	no	—
821	C₂×D₄²	—	67	1	no	—
822	C₂×#532	—	67	1	no	—
823	C₂×#529	—	67	4	no	—
824	C₂×#525	—	67	4	no	—
825	C₂×C₄×#41	—	67	2	no	—
826	C₂²×C₄×D₄	—	67	4	no	—
827	C₆₇	C₂×#3481	1	1	yes	characteristic, complemented, Sylow
828	C₂²×#41	—	67	2	no	—
829	C₂²×#41	—	67	2	no	—
830	C₂³×D₄	—	67	4	no	—
831	C₂⁴×C₄	—	67	4	no	—
832	#559	—	67	1	no	—
833	#559	—	67	4	no	—
834	#559	—	67	4	no	—
835	#559	—	67	2	no	—
836	#559	—	67	4	no	—
837	#559	C₂×D₆₇	1	1	yes	characteristic, complemented
838	#554	—	67	2	no	—
839	#554	—	67	4	no	—
840	#554	—	67	8	no	—
841	#554	—	67	4	no	—
842	#554	—	67	2	no	—
843	#554	—	67	2	no	—
844	#554	—	67	4	no	—
845	#554	—	67	4	no	—
846	#554	C₂×D₆₇	1	2	yes	complemented
847	#553	—	67	8	no	—
848	#553	—	67	4	no	—
849	#553	—	67	8	no	—
850	#553	—	67	4	no	—
851	#553	—	67	8	no	—
852	#553	—	67	4	no	—
853	#553	—	67	4	no	—
854	#553	—	67	8	no	—
855	#553	—	67	4	no	—
856	#553	—	67	4	no	—
857	#553	—	67	4	no	—
858	#553	C₂×D₆₇	1	4	yes	complemented
859	#551	—	67	8	no	—
860	#551	—	67	4	no	—
861	#551	—	67	8	no	—
862	#551	—	67	4	no	—
863	#551	—	67	8	no	—
864	#551	—	67	4	no	—
865	#551	—	67	8	no	—
866	#551	—	67	8	no	—
867	#551	—	67	8	no	—
868	#551	C₂×D₆₇	1	4	yes	complemented
869	#546	—	67	4	no	—
870	#546	—	67	4	no	—
871	#546	—	67	4	no	—
872	#546	—	67	8	no	—
873	#546	—	67	4	no	—
874	#546	—	67	8	no	—
875	#546	—	67	4	no	—
876	#546	—	67	8	no	—
877	#546	—	67	4	no	—
878	#546	—	67	4	no	—
879	#546	—	67	8	no	—
880	#546	C₂×D₆₇	1	4	yes	complemented
881	D₄²	—	67	4	no	—
882	D₄²	—	67	1	no	—
883	D₄²	—	67	4	no	—
884	D₄²	—	67	4	no	—
885	D₄²	—	67	2	no	—
886	D₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
887	#532	—	67	2	no	—
888	#532	—	67	1	no	—
889	#532	—	67	1	no	—
890	#532	—	67	2	no	—
891	#532	—	67	4	no	—
892	#532	—	67	4	no	—
893	#532	—	67	1	no	—
894	#532	C₂×D₆₇	1	1	yes	characteristic, complemented
895	C₂×C₄⋊Q₈	—	67	1	no	—
896	C₂×#127	—	67	1	no	—
897	#529	—	67	8	no	—
898	#529	—	67	4	no	—
899	#529	—	67	4	no	—
900	#529	—	67	8	no	—
901	#529	—	67	4	no	—
902	#529	—	67	4	no	—
903	#529	—	67	4	no	—
904	#529	—	67	8	no	—
905	#529	—	67	4	no	—
906	#529	—	67	8	no	—
907	#529	—	67	4	no	—
908	#529	C₂×D₆₇	1	4	yes	complemented
909	C₂×#126	—	67	8	no	—
910	C₂×#125	—	67	4	no	—
911	C₂×#124	—	67	4	no	—
912	C₂×#124	—	67	2	no	—
913	#525	—	67	4	no	—
914	#525	—	67	4	no	—
915	#525	—	67	4	no	—
916	#525	—	67	4	no	—
917	#525	—	67	8	no	—
918	#525	—	67	8	no	—
919	#525	—	67	4	no	—
920	#525	—	67	4	no	—
921	#525	—	67	8	no	—
922	#525	—	67	8	no	—
923	#525	—	67	4	no	—
924	#525	C₂×D₆₇	1	4	yes	complemented
925	C₂×#123	—	67	4	no	—
926	C₂×#123	—	67	4	no	—
927	C₂×#123	—	67	8	no	—
928	C₂×C₂²⋊Q₈	—	67	8	no	—
929	C₂×C₂²⋊Q₈	—	67	4	no	—
930	C₂×#121	—	67	4	no	—
931	C₂×#121	—	67	8	no	—
932	C₂×#121	—	67	4	no	—
933	C₂×#120	—	67	4	no	—
934	C₂×#120	—	67	4	no	—
935	C₄×#41	—	67	2	no	—
936	C₄×#41	—	67	2	no	—
937	C₄×#41	—	67	2	no	—
938	C₄×#41	—	67	2	no	—
939	C₄×#41	—	67	2	no	—
940	C₄×#41	—	67	4	no	—
941	C₄×#41	—	67	4	no	—
942	C₄×#41	—	67	4	no	—
943	C₄×#41	—	67	2	no	—
944	C₄×#41	—	67	2	no	—
945	C₄×#41	—	67	4	no	—
946	C₄×#41	C₂×D₆₇	1	2	yes	complemented
947	C₂×C₄×Q₈	—	67	2	no	—
948	C₂×C₄×Q₈	—	67	2	no	—
949	C₂×C₄×D₄	—	67	4	no	—
950	C₂×C₄×D₄	—	67	8	no	—
951	C₂×C₄×D₄	—	67	2	no	—
952	C₂×C₄×D₄	—	67	4	no	—
953	C₂×C₄×D₄	—	67	4	no	—
954	C₂×C₄×D₄	—	67	4	no	—
955	C₂×C₄×D₄	—	67	2	no	—
956	C₂×C₄×D₄	—	67	8	no	—
957	C₂×C₄×D₄	—	67	4	no	—
958	C₂×C₄×D₄	—	67	8	no	—
959	C₂×C₄×D₄	—	67	4	no	—
960	C₂×C₄×D₄	—	67	8	no	—
961	C₂×C₄×D₄	—	67	4	no	—
962	C₂×C₄×D₄	—	67	8	no	—
963	C₂×C₄×D₄	—	67	4	no	—
964	C₂×C₄×D₄	—	67	4	no	—
965	C₂×C₄×D₄	—	67	4	no	—
966	C₂×C₄×D₄	—	67	4	no	—
967	C₂×C₄×D₄	—	67	8	no	—
968	C₂×C₄×D₄	—	67	4	no	—
969	C₂×C₄×D₄	C₂×D₆₇	1	4	yes	complemented
970	C₂×#117	—	67	4	no	—
971	C₂×#117	—	67	2	no	—
972	C₂×#117	—	67	4	no	—
973	C₂²×C₄⋊C₄	—	67	4	no	—
974	C₂²×C₂²⋊C₄	—	67	8	no	—
975	C₂²×C₄²	—	67	4	no	—
976	C₂²×C₄²	—	67	1	no	—
977	C₂⁵	—	67	4	no	—
978	C₂×#41	—	268	8	no	—
979	C₂×#41	—	67	2	no	—
980	C₂×#41	—	67	2	no	—
981	C₂×#41	—	67	4	no	—
982	C₂×#41	—	67	2	no	—
983	C₂×#41	—	67	2	no	—
984	C₂×#41	—	67	4	no	—
985	C₂×#41	—	67	4	no	—
986	C₂×#41	—	67	2	no	—
987	C₂×#41	—	67	2	no	—
988	C₂×#41	—	67	4	no	—
989	C₂×#41	—	134	16	no	—
990	C₂×#41	C₂²×D₆₇	1	2	yes	—
991	C₂×#41	C₂²×D₆₇	1	2	yes	complemented
992	C₂²×Q₈	—	67	2	no	—
993	C₂²×Q₈	—	67	2	no	—
994	C₂²×D₄	—	67	2	no	—
995	C₂²×D₄	—	67	4	no	—
996	C₂²×D₄	—	67	2	no	—
997	C₂²×D₄	—	67	8	no	—
998	C₂²×D₄	—	67	4	no	—
999	C₂²×D₄	—	67	8	no	—
1000	C₂²×D₄	—	67	4	no	—
1001	C₂²×D₄	—	67	8	no	—
1002	C₂²×D₄	—	67	4	no	—
1003	C₂²×D₄	—	67	4	no	—
1004	C₂²×D₄	—	67	4	no	—
1005	C₂²×D₄	—	134	32	no	—
1006	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
1007	C₂³×C₄	—	268	16	no	—
1008	C₂³×C₄	—	67	4	no	—
1009	C₂³×C₄	—	67	8	no	—
1010	C₂³×C₄	—	67	4	no	—
1011	C₂³×C₄	—	67	8	no	—
1012	C₂³×C₄	—	67	4	no	—
1013	C₂³×C₄	—	67	4	no	—
1014	C₂³×C₄	—	67	8	no	—
1015	C₂³×C₄	—	67	4	no	—
1016	C₂³×C₄	—	67	4	no	—
1017	C₂³×C₄	—	67	4	no	—
1018	C₂³×C₄	—	67	2	no	—
1019	C₂³×C₄	—	67	4	no	—
1020	C₂³×C₄	—	67	1	no	—
1021	C₂³×C₄	C₂²×D₆₇	1	4	yes	complemented
1022	C₄⋊Q₈	—	67	2	no	—
1023	C₄⋊Q₈	—	67	4	no	—
1024	C₄⋊Q₈	—	67	1	no	—
1025	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic, complemented
1026	#127	—	67	4	no	—
1027	#127	—	67	2	no	—
1028	#127	—	67	1	no	—
1029	#127	C₂²×D₆₇	1	1	yes	characteristic
1030	#126	—	67	8	no	—
1031	#126	—	67	8	no	—
1032	#126	—	67	8	no	—
1033	#126	—	67	8	no	—
1034	#126	—	67	8	no	—
1035	#126	—	67	8	no	—
1036	#126	—	67	8	no	—
1037	#126	C₂²×D₆₇	1	8	yes	complemented
1038	#125	—	67	8	no	—
1039	#125	—	67	8	no	—
1040	#125	—	67	4	no	—
1041	#125	—	67	4	no	—
1042	#125	—	67	4	no	—
1043	#125	C₂²×D₆₇	1	4	yes	complemented
1044	#124	—	67	4	no	—
1045	#124	—	67	2	no	—
1046	#124	—	67	4	no	—
1047	#124	—	67	2	no	—
1048	#124	—	67	8	no	—
1049	#124	—	67	8	no	—
1050	#124	—	67	8	no	—
1051	#124	—	67	4	no	—
1052	#124	—	67	2	no	—
1053	#124	C₂²×D₆₇	1	4	yes	complemented
1054	#124	C₂²×D₆₇	1	2	yes	complemented
1055	#123	—	67	4	no	—
1056	#123	—	67	4	no	—
1057	#123	—	67	8	no	—
1058	#123	—	67	4	no	—
1059	#123	—	67	4	no	—
1060	#123	—	67	8	no	—
1061	#123	—	67	8	no	—
1062	#123	—	67	8	no	—
1063	#123	—	67	8	no	—
1064	#123	—	67	8	no	—
1065	#123	—	67	8	no	—
1066	#123	—	67	4	no	—
1067	#123	—	67	8	no	—
1068	#123	—	67	4	no	—
1069	#123	—	67	8	no	—
1070	#123	—	67	8	no	—
1071	#123	—	67	8	no	—
1072	#123	C₂²×D₆₇	1	4	yes	complemented
1073	#123	C₂²×D₆₇	1	4	yes	complemented
1074	#123	C₂²×D₆₇	1	8	yes	complemented
1075	C₂²⋊Q₈	—	67	8	no	—
1076	C₂²⋊Q₈	—	67	4	no	—
1077	C₂²⋊Q₈	—	67	8	no	—
1078	C₂²⋊Q₈	—	67	4	no	—
1079	C₂²⋊Q₈	—	67	8	no	—
1080	C₂²⋊Q₈	—	67	8	no	—
1081	C₂²⋊Q₈	—	67	8	no	—
1082	C₂²⋊Q₈	—	67	8	no	—
1083	C₂²⋊Q₈	—	67	4	no	—
1084	C₂²⋊Q₈	—	67	8	no	—
1085	C₂²⋊Q₈	—	67	8	no	—
1086	C₂²⋊Q₈	—	67	8	no	—
1087	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
1088	C₂²⋊Q₈	C₂²×D₆₇	1	4	yes	complemented
1089	#121	—	67	8	no	—
1090	#121	—	67	8	no	—
1091	#121	—	67	8	no	—
1092	#121	—	67	4	no	—
1093	#121	—	67	8	no	—
1094	#121	—	67	4	no	—
1095	#121	—	67	8	no	—
1096	#121	—	67	8	no	—
1097	#121	—	67	4	no	—
1098	#121	—	67	4	no	—
1099	#121	—	67	8	no	—
1100	#121	—	67	4	no	—
1101	#121	—	67	4	no	—
1102	#121	—	67	8	no	—
1103	#121	—	67	8	no	—
1104	#121	—	67	8	no	—
1105	#121	—	67	8	no	—
1106	#121	C₂²×D₆₇	1	4	yes	—
1107	#121	C₂²×D₆₇	1	8	yes	complemented
1108	#121	C₂²×D₆₇	1	4	yes	complemented
1109	#120	—	67	4	no	—
1110	#120	—	67	4	no	—
1111	#120	—	67	8	no	—
1112	#120	—	67	4	no	—
1113	#120	—	67	8	no	—
1114	#120	—	67	4	no	—
1115	#120	—	67	4	no	—
1116	#120	—	67	8	no	—
1117	#120	—	67	4	no	—
1118	#120	—	67	8	no	—
1119	#120	C₂²×D₆₇	1	4	yes	—
1120	#120	C₂²×D₆₇	1	4	yes	complemented
1121	C₄×Q₈	—	67	2	no	—
1122	C₄×Q₈	—	67	2	no	—
1123	C₄×Q₈	—	67	4	no	—
1124	C₄×Q₈	—	67	2	no	—
1125	C₄×Q₈	—	67	4	no	—
1126	C₄×Q₈	—	67	2	no	—
1127	C₄×Q₈	—	67	4	no	—
1128	C₄×Q₈	—	67	2	no	—
1129	C₄×Q₈	—	67	2	no	—
1130	C₄×Q₈	—	67	4	no	—
1131	C₄×Q₈	C₂²×D₆₇	1	2	yes	complemented
1132	C₄×Q₈	C₂²×D₆₇	1	2	yes	complemented
1133	C₄×D₄	—	67	2	no	—
1134	C₄×D₄	—	67	8	no	—
1135	C₄×D₄	—	67	4	no	—
1136	C₄×D₄	—	67	4	no	—
1137	C₄×D₄	—	67	8	no	—
1138	C₄×D₄	—	67	4	no	—
1139	C₄×D₄	—	67	4	no	—
1140	C₄×D₄	—	67	2	no	—
1141	C₄×D₄	—	67	4	no	—
1142	C₄×D₄	—	67	4	no	—
1143	C₄×D₄	—	67	8	no	—
1144	C₄×D₄	—	67	8	no	—
1145	C₄×D₄	—	67	8	no	—
1146	C₄×D₄	—	67	8	no	—
1147	C₄×D₄	—	67	8	no	—
1148	C₄×D₄	—	67	8	no	—
1149	C₄×D₄	—	67	8	no	—
1150	C₄×D₄	—	67	4	no	—
1151	C₄×D₄	—	67	4	no	—
1152	C₄×D₄	—	67	4	no	—
1153	C₄×D₄	—	67	4	no	—
1154	C₄×D₄	—	67	4	no	—
1155	C₄×D₄	—	67	2	no	—
1156	C₄×D₄	—	67	8	no	—
1157	C₄×D₄	—	67	4	no	—
1158	C₄×D₄	—	67	4	no	—
1159	C₄×D₄	—	67	8	no	—
1160	C₄×D₄	—	67	4	no	—
1161	C₄×D₄	—	67	4	no	—
1162	C₄×D₄	—	67	2	no	—
1163	C₄×D₄	—	67	4	no	—
1164	C₄×D₄	—	67	4	no	—
1165	C₄×D₄	—	67	8	no	—
1166	C₄×D₄	—	67	8	no	—
1167	C₄×D₄	—	67	8	no	—
1168	C₄×D₄	—	67	8	no	—
1169	C₄×D₄	—	67	8	no	—
1170	C₄×D₄	—	67	8	no	—
1171	C₄×D₄	—	67	8	no	—
1172	C₄×D₄	—	67	4	no	—
1173	C₄×D₄	—	67	4	no	—
1174	C₄×D₄	—	67	4	no	—
1175	C₄×D₄	—	67	4	no	—
1176	C₄×D₄	—	67	4	no	—
1177	C₄×D₄	—	67	2	no	—
1178	C₄×D₄	—	67	8	no	—
1179	C₄×D₄	—	67	4	no	—
1180	C₄×D₄	—	67	4	no	—
1181	C₄×D₄	—	67	8	no	—
1182	C₄×D₄	—	67	4	no	—
1183	C₄×D₄	—	67	4	no	—
1184	C₄×D₄	—	67	2	no	—
1185	C₄×D₄	—	67	4	no	—
1186	C₄×D₄	C₂²×D₆₇	1	2	yes	—
1187	C₄×D₄	C₂²×D₆₇	1	4	yes	—
1188	C₄×D₄	C₂²×D₆₇	1	2	yes	—
1189	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
1190	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1191	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
1192	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1193	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1194	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1195	#117	—	67	4	no	—
1196	#117	—	67	2	no	—
1197	#117	—	67	4	no	—
1198	#117	—	67	4	no	—
1199	#117	—	67	4	no	—
1200	#117	—	67	2	no	—
1201	#117	—	67	2	no	—
1202	#117	—	67	8	no	—
1203	#117	—	67	4	no	—
1204	#117	—	67	4	no	—
1205	#117	—	67	4	no	—
1206	#117	—	67	4	no	—
1207	#117	—	67	4	no	—
1208	#117	—	67	4	no	—
1209	#117	—	67	4	no	—
1210	#117	—	67	4	no	—
1211	#117	—	67	8	no	—
1212	#117	C₂²×D₆₇	1	4	yes	complemented
1213	#117	C₂²×D₆₇	1	2	yes	complemented
1214	#117	C₂²×D₆₇	1	4	yes	complemented
1215	C₂×C₄⋊C₄	—	67	8	no	—
1216	C₂×C₄⋊C₄	—	67	4	no	—
1217	C₂×C₄⋊C₄	—	67	2	no	—
1218	C₂×C₄⋊C₄	—	67	4	no	—
1219	C₂×C₄⋊C₄	—	67	8	no	—
1220	C₂×C₄⋊C₄	—	67	8	no	—
1221	C₂×C₄⋊C₄	—	67	4	no	—
1222	C₂×C₄⋊C₄	—	67	4	no	—
1223	C₂×C₄⋊C₄	—	67	2	no	—
1224	C₂×C₄⋊C₄	—	67	4	no	—
1225	C₂×C₄⋊C₄	—	67	4	no	—
1226	C₂×C₄⋊C₄	—	67	8	no	—
1227	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	complemented
1228	C₂×C₂²⋊C₄	—	67	8	no	—
1229	C₂×C₂²⋊C₄	—	67	8	no	—
1230	C₂×C₂²⋊C₄	—	67	8	no	—
1231	C₂×C₂²⋊C₄	—	67	4	no	—
1232	C₂×C₂²⋊C₄	—	67	8	no	—
1233	C₂×C₂²⋊C₄	—	67	8	no	—
1234	C₂×C₂²⋊C₄	—	67	8	no	—
1235	C₂×C₂²⋊C₄	—	67	8	no	—
1236	C₂×C₂²⋊C₄	—	67	8	no	—
1237	C₂×C₂²⋊C₄	—	67	8	no	—
1238	C₂×C₂²⋊C₄	—	67	8	no	—
1239	C₂×C₂²⋊C₄	—	67	4	no	—
1240	C₂×C₂²⋊C₄	—	67	4	no	—
1241	C₂×C₂²⋊C₄	—	67	4	no	—
1242	C₂×C₂²⋊C₄	—	67	4	no	—
1243	C₂×C₂²⋊C₄	C₂²×D₆₇	1	8	yes	complemented
1244	C₂×C₄²	—	67	4	no	—
1245	C₂×C₄²	—	67	4	no	—
1246	C₂×C₄²	—	67	4	no	—
1247	C₂×C₄²	—	67	2	no	—
1248	C₂×C₄²	—	67	1	no	—
1249	C₂×C₄²	—	67	1	no	—
1250	C₂×C₄²	—	67	4	no	—
1251	C₂×C₄²	—	67	4	no	—
1252	C₂×C₄²	—	67	4	no	—
1253	C₂×C₄²	—	67	2	no	—
1254	C₂×C₄²	—	67	1	no	—
1255	C₂×C₄²	—	67	4	no	—
1256	C₂×C₄²	—	67	4	no	—
1257	C₂×C₄²	—	67	4	no	—
1258	C₂×C₄²	—	67	4	no	—
1259	C₂×C₄²	—	67	1	no	—
1260	C₂×C₄²	—	67	1	no	—
1261	C₂×C₄²	—	67	2	no	—
1262	C₂×C₄²	C₂²×D₆₇	1	4	yes	complemented
1263	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic, complemented
1264	C₂⁴	—	268	8	no	—
1265	C₂⁴	—	67	4	no	—
1266	C₂⁴	—	67	8	no	—
1267	C₂⁴	—	67	4	no	—
1268	C₂⁴	—	67	4	no	—
1269	C₂⁴	—	67	1	no	—
1270	C₂⁴	—	134	32	no	—
1271	C₂⁴	C₂³×D₆₇	1	4	yes	—
1272	#41	—	2	8	no	—
1273	#41	—	4	4	no	—
1274	#41	—	268	8	no	—
1275	#41	—	268	4	no	—
1276	#41	—	268	8	no	—
1277	#41	—	268	4	no	—
1278	#41	—	268	4	no	—
1279	#41	—	134	16	no	—
1280	#41	—	134	8	no	—
1281	#41	—	134	16	no	—
1282	#41	—	134	8	no	—
1283	#41	—	134	8	no	—
1284	C₂×Q₈	—	268	4	no	—
1285	C₂×Q₈	—	67	4	no	—
1286	C₂×Q₈	—	67	2	no	—
1287	C₂×Q₈	—	67	4	no	—
1288	C₂×Q₈	—	67	2	no	—
1289	C₂×Q₈	—	134	8	no	—
1290	C₂×Q₈	C₂³×D₆₇	1	2	yes	—
1291	C₂×Q₈	C₂³×D₆₇	1	2	yes	—
1292	C₂×D₄	—	2	16	no	—
1293	C₂×D₄	—	268	8	no	—
1294	C₂×D₄	—	268	4	no	—
1295	C₂×D₄	—	67	4	no	—
1296	C₂×D₄	—	67	4	no	—
1297	C₂×D₄	—	67	4	no	—
1298	C₂×D₄	—	67	4	no	—
1299	C₂×D₄	—	67	16	no	—
1300	C₂×D₄	—	67	4	no	—
1301	C₂×D₄	—	67	4	no	—
1302	C₂×D₄	—	67	8	no	—
1303	C₂×D₄	—	67	8	no	—
1304	C₂×D₄	—	67	8	no	—
1305	C₂×D₄	—	67	2	no	—
1306	C₂×D₄	—	67	4	no	—
1307	C₂×D₄	—	67	2	no	—
1308	C₂×D₄	—	67	4	no	—
1309	C₂×D₄	—	67	8	no	—
1310	C₂×D₄	—	67	4	no	—
1311	C₂×D₄	—	134	16	no	—
1312	C₂×D₄	—	134	16	no	—
1313	C₂×D₄	—	134	32	no	—
1314	C₂×D₄	—	134	16	no	—
1315	C₂×D₄	—	134	32	no	—
1316	C₂×D₄	—	134	16	no	—
1317	C₂×D₄	—	134	32	no	—
1318	C₂×D₄	—	134	16	no	—
1319	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1320	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1321	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1322	C₂×D₄	C₂³×D₆₇	1	2	yes	—
1323	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1324	C₂×D₄	C₂³×D₆₇	1	2	yes	—
1325	C₂²×C₄	—	4	8	no	—
1326	C₂²×C₄	—	268	16	no	—
1327	C₂²×C₄	—	268	8	no	—
1328	C₂²×C₄	—	268	8	no	—
1329	C₂²×C₄	—	268	16	no	—
1330	C₂²×C₄	—	268	8	no	—
1331	C₂²×C₄	—	268	16	no	—
1332	C₂²×C₄	—	268	8	no	—
1333	C₂²×C₄	—	67	8	no	—
1334	C₂²×C₄	—	67	4	no	—
1335	C₂²×C₄	—	67	8	no	—
1336	C₂²×C₄	—	67	8	no	—
1337	C₂²×C₄	—	67	8	no	—
1338	C₂²×C₄	—	67	2	no	—
1339	C₂²×C₄	—	67	1	no	—
1340	C₂²×C₄	—	67	4	no	—
1341	C₂²×C₄	—	67	4	no	—
1342	C₂²×C₄	—	67	2	no	—
1343	C₂²×C₄	—	67	4	no	—
1344	C₂²×C₄	—	67	1	no	—
1345	C₂²×C₄	—	67	4	no	—
1346	C₂²×C₄	—	67	2	no	—
1347	C₂²×C₄	—	67	4	no	—
1348	C₂²×C₄	—	67	4	no	—
1349	C₂²×C₄	—	67	4	no	—
1350	C₂²×C₄	—	67	1	no	—
1351	C₂²×C₄	—	67	4	no	—
1352	C₂²×C₄	—	67	4	no	—
1353	C₂²×C₄	—	67	4	no	—
1354	C₂²×C₄	—	67	4	no	—
1355	C₂²×C₄	—	67	2	no	—
1356	C₂²×C₄	—	67	2	no	—
1357	C₂²×C₄	—	67	4	no	—
1358	C₂²×C₄	—	67	1	no	—
1359	C₂²×C₄	—	67	4	no	—
1360	C₂²×C₄	—	67	4	no	—
1361	C₂²×C₄	—	67	4	no	—
1362	C₂²×C₄	—	67	1	no	—
1363	C₂²×C₄	—	67	4	no	—
1364	C₂²×C₄	—	134	16	no	—
1365	C₂²×C₄	—	134	16	no	—
1366	C₂²×C₄	—	134	16	no	—
1367	C₂²×C₄	—	134	4	no	—
1368	C₂²×C₄	—	134	8	no	—
1369	C₂²×C₄	—	134	16	no	—
1370	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1371	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1372	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1373	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1374	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1375	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1376	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1377	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1378	C₄⋊C₄	—	67	4	no	—
1379	C₄⋊C₄	—	67	2	no	—
1380	C₄⋊C₄	—	67	8	no	—
1381	C₄⋊C₄	—	67	4	no	—
1382	C₄⋊C₄	—	67	8	no	—
1383	C₄⋊C₄	—	67	8	no	—
1384	C₄⋊C₄	—	67	8	no	—
1385	C₄⋊C₄	—	67	4	no	—
1386	C₄⋊C₄	—	67	2	no	—
1387	C₄⋊C₄	—	67	4	no	—
1388	C₄⋊C₄	—	67	4	no	—
1389	C₄⋊C₄	—	67	4	no	—
1390	C₄⋊C₄	—	67	4	no	—
1391	C₄⋊C₄	—	67	4	no	—
1392	C₄⋊C₄	—	67	4	no	—
1393	C₄⋊C₄	—	67	8	no	—
1394	C₄⋊C₄	—	67	8	no	—
1395	C₄⋊C₄	—	67	8	no	—
1396	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
1397	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1398	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1399	C₄⋊C₄	C₂³×D₆₇	1	2	yes	—
1400	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1401	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1402	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1403	C₂²⋊C₄	—	67	4	no	—
1404	C₂²⋊C₄	—	67	8	no	—
1405	C₂²⋊C₄	—	67	8	no	—
1406	C₂²⋊C₄	—	67	8	no	—
1407	C₂²⋊C₄	—	67	4	no	—
1408	C₂²⋊C₄	—	67	4	no	—
1409	C₂²⋊C₄	—	67	4	no	—
1410	C₂²⋊C₄	—	67	4	no	—
1411	C₂²⋊C₄	—	67	4	no	—
1412	C₂²⋊C₄	—	67	4	no	—
1413	C₂²⋊C₄	—	67	8	no	—
1414	C₂²⋊C₄	—	67	8	no	—
1415	C₂²⋊C₄	—	67	8	no	—
1416	C₂²⋊C₄	—	67	8	no	—
1417	C₂²⋊C₄	—	67	8	no	—
1418	C₂²⋊C₄	—	67	8	no	—
1419	C₂²⋊C₄	—	67	4	no	—
1420	C₂²⋊C₄	—	67	4	no	—
1421	C₂²⋊C₄	—	67	4	no	—
1422	C₂²⋊C₄	—	67	4	no	—
1423	C₂²⋊C₄	—	67	8	no	—
1424	C₂²⋊C₄	—	67	8	no	—
1425	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1426	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1427	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1428	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1429	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1430	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1431	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1432	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1433	C₄²	—	67	2	no	—
1434	C₄²	—	67	2	no	—
1435	C₄²	—	67	1	no	—
1436	C₄²	—	67	2	no	—
1437	C₄²	—	67	4	no	—
1438	C₄²	—	67	4	no	—
1439	C₄²	—	67	4	no	—
1440	C₄²	—	67	4	no	—
1441	C₄²	—	67	4	no	—
1442	C₄²	—	67	4	no	—
1443	C₄²	—	67	4	no	—
1444	C₄²	—	67	4	no	—
1445	C₄²	—	67	1	no	—
1446	C₄²	—	67	2	no	—
1447	C₄²	—	67	2	no	—
1448	C₄²	—	67	4	no	—
1449	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1450	C₄²	C₂³×D₆₇	1	4	yes	—
1451	C₄²	C₂³×D₆₇	1	4	yes	—
1452	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1453	C₄²	C₂³×D₆₇	1	2	yes	—
1454	C₄²	C₂³×D₆₇	1	4	yes	—
1455	C₂³	—	2	16	no	—
1456	C₂³	—	4	4	no	—
1457	C₂³	—	268	8	no	—
1458	C₂³	—	268	4	no	—
1459	C₂³	—	268	64	no	—
1460	C₂³	—	67	1	no	—
1461	C₂³	—	67	16	no	—
1462	C₂³	—	67	4	no	—
1463	C₂³	—	67	4	no	—
1464	C₂³	—	67	1	no	—
1465	C₂³	—	134	8	no	—
1466	C₂³	—	134	2	no	—
1467	C₂³	—	134	4	no	—
1468	C₂³	—	134	16	no	—
1469	C₂³	—	134	16	no	—
1470	C₂³	—	134	16	no	—
1471	C₂³	—	134	8	no	—
1472	C₂³	—	134	8	no	—
1473	C₂³	—	134	16	no	—
1474	C₂³	C₂⁴×D₆₇	1	4	yes	—
1475	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1476	C₂³	C₂⁴×D₆₇	1	4	yes	—
1477	Q₈	—	2	4	no	—
1478	Q₈	—	4	2	no	—
1479	Q₈	—	268	4	no	—
1480	Q₈	—	268	2	no	—
1481	Q₈	—	134	8	no	—
1482	Q₈	—	134	4	no	—
1483	D₄	—	2	16	no	—
1484	D₄	—	2	8	no	—
1485	D₄	—	2	8	no	—
1486	D₄	—	4	4	no	—
1487	D₄	—	4	2	no	—
1488	D₄	—	268	4	no	—
1489	D₄	—	268	2	no	—
1490	D₄	—	268	4	no	—
1491	D₄	—	268	4	no	—
1492	D₄	—	268	4	no	—
1493	D₄	—	67	16	no	—
1494	D₄	—	67	8	no	—
1495	D₄	—	134	16	no	—
1496	D₄	—	134	8	no	—
1497	D₄	—	134	16	no	—
1498	D₄	—	134	16	no	—
1499	D₄	—	134	8	no	—
1500	D₄	—	134	16	no	—
1501	D₄	—	134	8	no	—
1502	D₄	—	134	8	no	—
1503	D₄	#41×D₆₇	1	8	yes	complemented
1504	C₂×C₄	—	2	8	no	—
1505	C₂×C₄	—	2	8	no	—
1506	C₂×C₄	—	2	4	no	—
1507	C₂×C₄	—	2	8	no	—
1508	C₂×C₄	—	2	8	no	—
1509	C₂×C₄	—	2	2	no	—
1510	C₂×C₄	—	4	4	no	—
1511	C₂×C₄	—	4	8	no	—
1512	C₂×C₄	—	268	8	no	—
1513	C₂×C₄	—	268	8	no	—
1514	C₂×C₄	—	268	8	no	—
1515	C₂×C₄	—	268	4	no	—
1516	C₂×C₄	—	268	8	no	—
1517	C₂×C₄	—	67	1	no	—
1518	C₂×C₄	—	67	2	no	—
1519	C₂×C₄	—	67	8	no	—
1520	C₂×C₄	—	67	4	no	—
1521	C₂×C₄	—	67	2	no	—
1522	C₂×C₄	—	67	4	no	—
1523	C₂×C₄	—	67	4	no	—
1524	C₂×C₄	—	67	4	no	—
1525	C₂×C₄	—	67	1	no	—
1526	C₂×C₄	—	67	4	no	—
1527	C₂×C₄	—	134	8	no	—
1528	C₂×C₄	—	134	8	no	—
1529	C₂×C₄	—	134	8	no	—
1530	C₂×C₄	—	134	2	no	—
1531	C₂×C₄	—	134	4	no	—
1532	C₂×C₄	—	134	8	no	—
1533	C₂×C₄	—	134	8	no	—
1534	C₂×C₄	—	134	4	no	—
1535	C₂×C₄	—	134	2	no	—
1536	C₂×C₄	—	134	8	no	—
1537	C₂×C₄	—	134	8	no	—
1538	C₂×C₄	—	134	8	no	—
1539	C₂×C₄	—	134	8	no	—
1540	C₂×C₄	—	134	8	no	—
1541	C₂×C₄	—	134	8	no	—
1542	C₂×C₄	—	134	8	no	—
1543	C₂×C₄	—	134	2	no	—
1544	C₂×C₄	—	134	4	no	—
1545	C₂×C₄	—	134	8	no	—
1546	C₂×C₄	—	134	8	no	—
1547	C₂×C₄	—	134	4	no	—
1548	C₂×C₄	—	134	8	no	—
1549	C₂×C₄	—	134	8	no	—
1550	C₂×C₄	—	134	2	no	—
1551	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1552	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1553	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1554	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1555	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1556	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1557	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1558	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1559	C₂²	—	2	4	no	—
1560	C₂²	—	2	4	no	—
1561	C₂²	—	2	2	no	—
1562	C₂²	—	2	8	no	—
1563	C₂²	—	2	4	no	—
1564	C₂²	—	2	1	no	—
1565	C₂²	—	4	16	no	—
1566	C₂²	—	268	32	no	—
1567	C₂²	—	268	16	no	—
1568	C₂²	—	268	4	no	—
1569	C₂²	—	268	16	no	—
1570	C₂²	—	67	4	no	—
1571	C₂²	—	67	2	no	—
1572	C₂²	—	67	8	no	—
1573	C₂²	—	134	32	no	—
1574	C₂²	—	134	2	no	—
1575	C₂²	—	134	8	no	—
1576	C₂²	—	134	4	no	—
1577	C₂²	—	134	1	no	—
1578	C₂²	—	134	4	no	—
1579	C₂²	—	134	4	no	—
1580	C₂²	C₂×#41×D₆₇	1	8	yes	—
1581	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1582	C₄	—	2	2	no	—
1583	C₄	—	2	4	no	—
1584	C₄	—	2	4	no	—
1585	C₄	—	2	4	no	—
1586	C₄	—	2	4	no	—
1587	C₄	—	2	1	no	—
1588	C₄	—	67	4	no	—
1589	C₄	—	67	2	no	—
1590	C₄	—	134	2	no	—
1591	C₄	—	134	4	no	—
1592	C₄	—	134	4	no	—
1593	C₄	—	134	4	no	—
1594	C₄	—	134	4	no	—
1595	C₄	—	134	1	no	—
1596	C₄	C₂×#41×D₆₇	1	4	yes	—
1597	C₄	H(5,𝔽₂)×D₆₇	1	2	yes	—
1598	C₂	—	2	8	no	—
1599	C₂	—	4	4	no	—
1600	C₂	—	4	1	no	—
1601	C₂	—	268	4	no	—
1602	C₂	—	268	1	no	—
1603	C₂	—	67	4	no	—
1604	C₂	—	134	8	no	—
1605	C₂	C₂²×#41×D₆₇	1	2	yes	—
1606	C₂	C₂×H(5,𝔽₂)×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₆₇×#3481	C₂
hypercenter	#3481	D₆₇
hypocenter	C₆₇	C₂×#3481
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ #3481

Complements

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

N	H ≅ G/N	type
1. #22573820	C₂	semidirect
2. #22573819	C₂	semidirect
3. #22573818	C₂	semidirect
4. #22573817	C₂	semidirect
5. #22573816	C₂	semidirect
6. #22573815	C₂	semidirect
7. #22573814	C₂	semidirect
8. #22573813	C₂	semidirect
9. #22573812	C₂	semidirect
10. #22573811	C₂	semidirect
11. #22573810	C₂	semidirect
12. #559×D₆₇	C₂	semidirect
13. #554×D₆₇	C₂	semidirect
14. #553×D₆₇	C₂	semidirect
15. #551×D₆₇	C₂	semidirect
16. #546×D₆₇	C₂	semidirect
17. D₄²×D₆₇	C₂	semidirect
18. #532×D₆₇	C₂	semidirect
19. #529×D₆₇	C₂	semidirect
20. #525×D₆₇	C₂	semidirect
21. C₄×#41×D₆₇	C₂	semidirect
22. C₂×C₄×D₄×D₆₇	C₂	semidirect
23. C₆₇×#3481	C₂	semidirect
25. C₂×#41×D₆₇	C₂²	semidirect
27. C₂³×C₄×D₆₇	C₂²	semidirect
28. #16864132	C₂²	semidirect
29. #16864131	C₂²	semidirect
30. #16864130	C₂²	semidirect
31. #16864129	C₂²	semidirect
32. #16864128	C₂²	semidirect
33. #16864107	C₂²	semidirect
34. #16864106	C₂²	semidirect
35. #16864105	C₂²	semidirect
36. #16864104	C₂²	semidirect
37. #16864103	C₂²	semidirect
38. #16864102	C₂²	semidirect
39. #16864101	C₂²	semidirect
40. #16864100	C₂²	semidirect
41. #16864099	C₂²	semidirect
42. #16864098	C₂²	semidirect
43. #16864097	C₂²	semidirect
44. #16864096	C₂²	semidirect
45. #16864095	C₂²	semidirect
46. #16864094	C₂²	semidirect
47. #16864093	C₂²	semidirect
48. #16864092	C₂²	semidirect
49. #16864091	C₂²	semidirect
50. #16864090	C₂²	semidirect
51. #16864089	C₂²	semidirect
52. #16864077	C₂²	semidirect
53. #16864076	C₂²	semidirect
54. #16864075	C₂²	semidirect
55. #16864074	C₂²	semidirect
56. #16864073	C₂²	semidirect
57. #16864072	C₂²	semidirect
58. #16864071	C₂²	semidirect
59. #16864070	C₂²	semidirect
60. #16864069	C₂²	semidirect
61. #16864043	C₂²	semidirect
62. #16864042	C₂²	semidirect
63. #16864041	C₂²	semidirect
64. #16864040	C₂²	semidirect
65. #16864039	C₂²	semidirect
66. #16864038	C₂²	semidirect
67. #16864037	C₂²	semidirect
68. #16864036	C₂²	semidirect
69. #16864035	C₂²	semidirect
70. #16864034	C₂²	semidirect
71. #16864033	C₂²	semidirect
72. D₄×D₂₆₈	C₂²	semidirect
73. #16864031	C₂²	semidirect
74. #16864030	C₂²	semidirect
75. D₄×C₂²⋊D₆₇	C₂²	semidirect
76. #16864028	C₂²	semidirect
77. #16863947	C₂²	semidirect
78. #16863946	C₂²	semidirect
79. #16863945	C₂²	semidirect
80. #16863944	C₂²	semidirect
81. #16863943	C₂²	semidirect
82. #16863942	C₂²	semidirect
83. #16863941	C₂²	semidirect
84. C₄⋊Q₈×D₆₇	C₂²	semidirect
86. #16863933	C₂²	semidirect
87. #16863932	C₂²	semidirect
88. #16863931	C₂²	semidirect
89. #16863930	C₂²	semidirect
90. #16863929	C₂²	semidirect
91. #16863928	C₂²	semidirect
92. #16863927	C₂²	semidirect
93. #16863926	C₂²	semidirect
94. #16863925	C₂²	semidirect
95. #16863924	C₂²	semidirect
96. #16863923	C₂²	semidirect
97. #126×D₆₇	C₂²	semidirect
98. #125×D₆₇	C₂²	semidirect
99. #124×D₆₇	C₂²	semidirect
100. #124×D₆₇	C₂²	semidirect
101. #16863909	C₂²	semidirect
102. #16863908	C₂²	semidirect
103. #16863907	C₂²	semidirect
104. #16863906	C₂²	semidirect
105. #16863905	C₂²	semidirect
106. #16863905	C₂²	semidirect
107. #16863904	C₂²	semidirect
108. #16863904	C₂²	semidirect
109. #16863903	C₂²	semidirect
110. #16863902	C₂²	semidirect
111. #16863902	C₂²	semidirect
112. #123×D₆₇	C₂²	semidirect
113. #123×D₆₇	C₂²	semidirect
114. #123×D₆₇	C₂²	semidirect
115. C₂²⋊Q₈×D₆₇	C₂²	semidirect
116. C₂²⋊Q₈×D₆₇	C₂²	semidirect
118. #121×D₆₇	C₂²	semidirect
119. #121×D₆₇	C₂²	semidirect
121. #120×D₆₇	C₂²	semidirect
122. #41×Dic₆₇	C₂²	semidirect
123. C₄×#11761629	C₂²	semidirect
124. C₄×#11761629	C₂²	semidirect
125. C₄×#11761628	C₂²	semidirect
126. C₄×#11761628	C₂²	semidirect
127. #16863864	C₂²	semidirect
128. #16863864	C₂²	semidirect
129. C₄×#11761627	C₂²	semidirect
130. C₄×#11761627	C₂²	semidirect
131. C₄×#11761627	C₂²	semidirect
132. C₄×#11761627	C₂²	semidirect
133. C₄×Q₈×D₆₇	C₂²	semidirect
134. C₄×Q₈×D₆₇	C₂²	semidirect
135. C₂×C₄×D₂₆₈	C₂²	semidirect
136. C₂×D₄×Dic₆₇	C₂²	semidirect
137. C₂×#14524005	C₂²	semidirect
138. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
139. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
143. C₄×D₄×D₆₇	C₂²	semidirect
144. C₄×D₄×D₆₇	C₂²	semidirect
145. C₄×D₄×D₆₇	C₂²	semidirect
146. C₄×D₄×D₆₇	C₂²	semidirect
147. C₄×D₄×D₆₇	C₂²	semidirect
148. C₄×D₄×D₆₇	C₂²	semidirect
149. C₄×D₄×D₆₇	C₂²	semidirect
150. C₄×D₄×D₆₇	C₂²	semidirect
151. C₄×D₄×D₆₇	C₂²	semidirect
152. C₄×D₄×D₆₇	C₂²	semidirect
153. C₄×D₄×D₆₇	C₂²	semidirect
154. C₄×D₄×D₆₇	C₂²	semidirect
155. #117×D₆₇	C₂²	semidirect
156. #117×D₆₇	C₂²	semidirect
157. #117×D₆₇	C₂²	semidirect
158. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
159. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
160. C₂×C₄²×D₆₇	C₂²	semidirect
161. C₂×C₄²×D₆₇	C₂²	semidirect
162. #559×C₆₇	C₂²	semidirect
163. #554×C₆₇	C₂²	semidirect
164. #553×C₆₇	C₂²	semidirect
165. #551×C₆₇	C₂²	semidirect
166. #546×C₆₇	C₂²	semidirect
167. D₄²×C₆₇	C₂²	semidirect
168. #532×C₆₇	C₂²	semidirect
169. #529×C₆₇	C₂²	semidirect
170. #525×C₆₇	C₂²	semidirect
171. C₄×#41×C₆₇	C₂²	semidirect
172. C₂×C₄×D₄×C₆₇	C₂²	semidirect
175. C₂×#11761629	C₂³	semidirect
178. C₂×#11761628	C₂³	semidirect
179. C₂×#11761628	C₂³	semidirect
182. C₂×#11761627	C₂³	semidirect
183. C₂×#11761627	C₂³	semidirect
200. C₂³×Dic₆₇	C₂³	semidirect
210. C₂²×C₄×D₆₇	C₂³	semidirect
211. C₂²×C₄×D₆₇	C₂³	semidirect
212. C₂²×C₄×D₆₇	C₂³	semidirect
213. C₂²×C₄×D₆₇	C₂³	semidirect
214. #14524043	C₂³	semidirect
215. #14524042	C₂³	semidirect
216. #14524041	C₂³	semidirect
220. #14524038	C₂³	semidirect
221. #14524038	C₂³	semidirect
222. #14524038	C₂³	semidirect
223. #14524037	C₂³	semidirect
224. #14524036	C₂³	semidirect
225. #14524036	C₂³	semidirect
226. #14524036	C₂³	semidirect
227. #14524035	C₂³	semidirect
228. #14524034	C₂³	semidirect
229. #14524034	C₂³	semidirect
230. #14524033	C₂³	semidirect
231. #14524033	C₂³	semidirect
232. #14524032	C₂³	semidirect
233. #14524032	C₂³	semidirect
234. #14524031	C₂³	semidirect
235. #14524031	C₂³	semidirect
236. #14524030	C₂³	semidirect
237. #14524030	C₂³	semidirect
238. #14524029	C₂³	semidirect
239. #14524029	C₂³	semidirect
240. #14524029	C₂³	semidirect
241. #14524028	C₂³	semidirect
242. #14524028	C₂³	semidirect
243. #14524028	C₂³	semidirect
244. #14524028	C₂³	semidirect
245. #14524027	C₂³	semidirect
246. #14524027	C₂³	semidirect
247. #14524027	C₂³	semidirect
248. #14524026	C₂³	semidirect
249. #14524026	C₂³	semidirect
250. #14524026	C₂³	semidirect
251. #14524025	C₂³	semidirect
252. #14524025	C₂³	semidirect
253. #14524025	C₂³	semidirect
254. #14524025	C₂³	semidirect
255. #14524024	C₂³	semidirect
256. #14524024	C₂³	semidirect
257. #14524024	C₂³	semidirect
258. #14524023	C₂³	semidirect
259. #14524023	C₂³	semidirect
260. #14524022	C₂³	semidirect
261. #14524022	C₂³	semidirect
262. #14524021	C₂³	semidirect
263. #14524021	C₂³	semidirect
264. #14524021	C₂³	semidirect
265. #14524020	C₂³	semidirect
266. #14524020	C₂³	semidirect
267. #14524020	C₂³	semidirect
268. #14524019	C₂³	semidirect
269. #14524019	C₂³	semidirect
271. #14524018	C₂³	semidirect
272. #14524018	C₂³	semidirect
274. #14524017	C₂³	semidirect
275. #14524017	C₂³	semidirect
277. #14524016	C₂³	semidirect
278. #14524016	C₂³	semidirect
279. #14524016	C₂³	semidirect
281. #14524015	C₂³	semidirect
282. #14524015	C₂³	semidirect
283. #14524015	C₂³	semidirect
285. #14524014	C₂³	semidirect
286. #14524014	C₂³	semidirect
289. #14524013	C₂³	semidirect
290. #14524013	C₂³	semidirect
292. #14524012	C₂³	semidirect
295. #14524011	C₂³	semidirect
296. #14524011	C₂³	semidirect
297. Q₈×Dic₆₇	C₂³	semidirect
298. Q₈×Dic₆₇	C₂³	semidirect
299. C₄×Dic₁₃₄	C₂³	semidirect
300. C₄×Dic₁₃₄	C₂³	semidirect
301. C₄×Dic₁₃₄	C₂³	semidirect
302. C₄×Dic₁₃₄	C₂³	semidirect
303. #14524008	C₂³	semidirect
304. #14524008	C₂³	semidirect
305. #14524008	C₂³	semidirect
306. #14524008	C₂³	semidirect
310. C₄×D₂₆₈	C₂³	semidirect
311. C₄×D₂₆₈	C₂³	semidirect
312. C₄×D₂₆₈	C₂³	semidirect
313. C₄×D₂₆₈	C₂³	semidirect
314. C₄×D₂₆₈	C₂³	semidirect
315. C₄×D₂₆₈	C₂³	semidirect
319. D₄×Dic₆₇	C₂³	semidirect
320. D₄×Dic₆₇	C₂³	semidirect
321. D₄×Dic₆₇	C₂³	semidirect
322. D₄×Dic₆₇	C₂³	semidirect
323. D₄×Dic₆₇	C₂³	semidirect
324. D₄×Dic₆₇	C₂³	semidirect
328. #14524005	C₂³	semidirect
329. #14524005	C₂³	semidirect
330. #14524005	C₂³	semidirect
331. #14524005	C₂³	semidirect
332. #14524005	C₂³	semidirect
333. #14524005	C₂³	semidirect
337. C₄×C₂²⋊D₆₇	C₂³	semidirect
338. C₄×C₂²⋊D₆₇	C₂³	semidirect
339. C₄×C₂²⋊D₆₇	C₂³	semidirect
340. C₄×C₂²⋊D₆₇	C₂³	semidirect
341. C₄×C₂²⋊D₆₇	C₂³	semidirect
342. C₄×C₂²⋊D₆₇	C₂³	semidirect
343. C₄×C₂²⋊D₆₇	C₂³	semidirect
344. C₄×C₂²⋊D₆₇	C₂³	semidirect
345. C₄×C₂²⋊D₆₇	C₂³	semidirect
346. C₄×C₂²⋊D₆₇	C₂³	semidirect
350. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
351. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
352. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
353. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
354. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
355. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
356. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
357. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
358. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
359. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
360. #14524002	C₂³	semidirect
361. #14524002	C₂³	semidirect
362. #14524002	C₂³	semidirect
363. #14524001	C₂³	semidirect
364. #14524001	C₂³	semidirect
365. #14524001	C₂³	semidirect
366. #14524001	C₂³	semidirect
367. #14524001	C₂³	semidirect
368. #14524000	C₂³	semidirect
369. #14524000	C₂³	semidirect
370. #14524000	C₂³	semidirect
371. #14524000	C₂³	semidirect
372. #14523999	C₂³	semidirect
373. #14523999	C₂³	semidirect
374. #14523999	C₂³	semidirect
375. #14523999	C₂³	semidirect
376. #14523999	C₂³	semidirect
377. C₂×C₄⋊Dic₆₇	C₂³	semidirect
378. C₂×Dic₆₇⋊C₄	C₂³	semidirect
386. C₄⋊C₄×D₆₇	C₂³	semidirect
387. C₄⋊C₄×D₆₇	C₂³	semidirect
388. C₄⋊C₄×D₆₇	C₂³	semidirect
389. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
390. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
391. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
400. C₂²⋊C₄×D₆₇	C₂³	semidirect
401. C₂²⋊C₄×D₆₇	C₂³	semidirect
402. C₂²⋊C₄×D₆₇	C₂³	semidirect
403. C₂²⋊C₄×D₆₇	C₂³	semidirect
404. C₂×C₄×Dic₆₇	C₂³	semidirect
405. C₂×C₄×Dic₆₇	C₂³	semidirect
406. C₂×C₄×Dic₆₇	C₂³	semidirect
407. C₂×C₄×Dic₆₇	C₂³	semidirect
408. C₂×C₄×Dic₆₇	C₂³	semidirect
415. C₄²×D₆₇	C₂³	semidirect
416. C₄²×D₆₇	C₂³	semidirect
417. C₄²×D₆₇	C₂³	semidirect
418. C₄²×D₆₇	C₂³	semidirect
419. C₄²×D₆₇	C₂³	semidirect
420. C₄²×D₆₇	C₂³	semidirect
421. C₄²×D₆₇	C₂³	semidirect
423. C₂×#41×C₆₇	C₂³	semidirect
425. C₂³×C₄×C₆₇	C₂³	semidirect
426. C₄⋊Q₈×C₆₇	C₂³	semidirect
428. #126×C₆₇	C₂³	semidirect
429. #125×C₆₇	C₂³	semidirect
430. #124×C₆₇	C₂³	semidirect
431. #124×C₆₇	C₂³	semidirect
432. #123×C₆₇	C₂³	semidirect
433. #123×C₆₇	C₂³	semidirect
434. #123×C₆₇	C₂³	semidirect
435. C₂²⋊Q₈×C₆₇	C₂³	semidirect
436. C₂²⋊Q₈×C₆₇	C₂³	semidirect
438. #121×C₆₇	C₂³	semidirect
439. #121×C₆₇	C₂³	semidirect
441. #120×C₆₇	C₂³	semidirect
442. C₄×Q₈×C₆₇	C₂³	semidirect
443. C₄×Q₈×C₆₇	C₂³	semidirect
447. C₄×D₄×C₆₇	C₂³	semidirect
448. C₄×D₄×C₆₇	C₂³	semidirect
449. C₄×D₄×C₆₇	C₂³	semidirect
450. C₄×D₄×C₆₇	C₂³	semidirect
451. C₄×D₄×C₆₇	C₂³	semidirect
452. C₄×D₄×C₆₇	C₂³	semidirect
453. #117×C₆₇	C₂³	semidirect
454. #117×C₆₇	C₂³	semidirect
455. #117×C₆₇	C₂³	semidirect
456. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
457. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
458. C₂×C₄²×C₆₇	C₂³	semidirect
459. C₂×C₄²×C₆₇	C₂³	semidirect
508. D₄×D₆₇	#41	semidirect
680. D₄×C₆₇	C₂×#41	semidirect
705. C₂²⋊D₆₇	C₂×#41	semidirect
727. D₂₆₈	C₂×#41	semidirect
803. D₆₇	#3481	direct (N × H)
815. #3481	D₆₇	direct (N × H)
827. C₆₇	C₂×#3481	semidirect
837. #559	C₂×D₆₇	semidirect
846. #554	C₂×D₆₇	semidirect
858. #553	C₂×D₆₇	semidirect
868. #551	C₂×D₆₇	semidirect
880. #546	C₂×D₆₇	semidirect
886. D₄²	C₂×D₆₇	semidirect
894. #532	C₂×D₆₇	semidirect
908. #529	C₂×D₆₇	semidirect
924. #525	C₂×D₆₇	semidirect
946. C₄×#41	C₂×D₆₇	semidirect
969. C₂×C₄×D₄	C₂×D₆₇	semidirect
991. C₂×#41	C₂²×D₆₇	semidirect
1021. C₂³×C₄	C₂²×D₆₇	semidirect
1025. C₄⋊Q₈	C₂²×D₆₇	semidirect
1037. #126	C₂²×D₆₇	semidirect
1043. #125	C₂²×D₆₇	semidirect
1053. #124	C₂²×D₆₇	semidirect
1054. #124	C₂²×D₆₇	semidirect
1072. #123	C₂²×D₆₇	semidirect
1073. #123	C₂²×D₆₇	semidirect
1074. #123	C₂²×D₆₇	semidirect
1087. C₂²⋊Q₈	C₂²×D₆₇	semidirect
1088. C₂²⋊Q₈	C₂²×D₆₇	semidirect
1107. #121	C₂²×D₆₇	semidirect
1108. #121	C₂²×D₆₇	semidirect
1120. #120	C₂²×D₆₇	semidirect
1131. C₄×Q₈	C₂²×D₆₇	semidirect
1132. C₄×Q₈	C₂²×D₆₇	semidirect
1189. C₄×D₄	C₂²×D₆₇	semidirect
1190. C₄×D₄	C₂²×D₆₇	semidirect
1191. C₄×D₄	C₂²×D₆₇	semidirect
1192. C₄×D₄	C₂²×D₆₇	semidirect
1193. C₄×D₄	C₂²×D₆₇	semidirect
1194. C₄×D₄	C₂²×D₆₇	semidirect
1212. #117	C₂²×D₆₇	semidirect
1213. #117	C₂²×D₆₇	semidirect
1214. #117	C₂²×D₆₇	semidirect
1227. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
1243. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
1262. C₂×C₄²	C₂²×D₆₇	semidirect
1263. C₂×C₄²	C₂²×D₆₇	semidirect
1503. D₄	#41×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573820	2
#22573819	2
#22573818	2
#22573817	2
#22573816	2
#22573815	2
#22573814	2
#22573813	2
#22573812	2
#22573811	2
#22573810	2
#559×D₆₇	2
#554×D₆₇	2
#553×D₆₇	2
#551×D₆₇	2
#546×D₆₇	2
D₄²×D₆₇	2
#532×D₆₇	2
#529×D₆₇	2
#525×D₆₇	2
C₄×#41×D₆₇	2
C₂×C₄×D₄×D₆₇	2
C₆₇×#3481	2
C₂×#3481	67

Subgroups — #3481×D67 #31762907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3481×D₆₇ #31762907