Subgroups — #3491×D₆₇ #31763877

Order 17152.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573908	C₂	1	1	yes	maximal, characteristic, complemented
2	#22573907	C₂	1	1	yes	maximal, characteristic, complemented
3	#22573906	C₂	1	1	yes	maximal, characteristic, complemented
4	#22573905	C₂	1	2	yes	maximal, complemented
5	#22573904	C₂	1	8	yes	maximal, complemented
6	#22573903	C₂	1	4	yes	maximal, complemented
7	#22573902	C₂	1	2	yes	maximal, complemented
8	#22573901	C₂	1	4	yes	maximal, complemented
9	#22573900	C₂	1	8	yes	maximal, complemented
10	#552×D₆₇	C₂	1	8	yes	maximal, complemented
11	#551×D₆₇	C₂	1	8	yes	maximal, complemented
12	#543×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#539×D₆₇	C₂	1	4	yes	maximal, complemented
14	#534×D₆₇	C₂	1	1	yes	maximal, characteristic
15	#529×D₆₇	C₂	1	4	yes	maximal, complemented
16	C₂×#123×D₆₇	C₂	1	2	yes	maximal, complemented
17	#518×D₆₇	C₂	1	2	yes	maximal, complemented
18	C₂×#117×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3491	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×D₄×D₆₇	C₂²	1	2	yes	—
21	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic
22	#16864088	C₂²	1	8	yes	complemented
23	#16864087	C₂²	1	8	yes	complemented
24	#16864086	C₂²	1	8	yes	complemented
25	#16864085	C₂²	1	8	yes	complemented
26	#16864084	C₂²	1	8	yes	complemented
27	#16864083	C₂²	1	8	yes	complemented
28	#16864083	C₂²	1	8	yes	complemented
29	#16864082	C₂²	1	8	yes	complemented
30	#16864082	C₂²	1	8	yes	complemented
31	#16864081	C₂²	1	8	yes	complemented
32	#16864080	C₂²	1	8	yes	complemented
33	#16864079	C₂²	1	8	yes	complemented
34	#16864079	C₂²	1	8	yes	complemented
35	#16864078	C₂²	1	8	yes	complemented
36	#16864078	C₂²	1	8	yes	complemented
37	#16864077	C₂²	1	8	yes	complemented
38	#16864076	C₂²	1	8	yes	complemented
39	#16864075	C₂²	1	8	yes	complemented
40	#16864075	C₂²	1	8	yes	complemented
41	#16864074	C₂²	1	8	yes	complemented
42	#16864073	C₂²	1	8	yes	complemented
43	#16864073	C₂²	1	8	yes	complemented
44	#16864072	C₂²	1	8	yes	complemented
45	#16864072	C₂²	1	8	yes	complemented
46	#16864071	C₂²	1	8	yes	complemented
47	#16864071	C₂²	1	8	yes	complemented
48	#16864070	C₂²	1	8	yes	complemented
49	#16864070	C₂²	1	8	yes	complemented
50	#16864069	C₂²	1	8	yes	complemented
51	#16864069	C₂²	1	8	yes	complemented
52	#16864022	C₂²	1	2	yes	complemented
53	#16864022	C₂²	1	1	yes	characteristic, complemented
54	#16864021	C₂²	1	8	yes	complemented
55	#16864021	C₂²	1	4	yes	complemented
56	#16863995	C₂²	1	4	yes	complemented
57	#16863994	C₂²	1	8	yes	complemented
58	#16863993	C₂²	1	4	yes	complemented
59	#16863992	C₂²	1	8	yes	complemented
60	#16863991	C₂²	1	4	yes	complemented
61	#16863990	C₂²	1	8	yes	complemented
62	#16863989	C₂²	1	8	yes	complemented
63	#16863988	C₂²	1	8	yes	complemented
64	#16863987	C₂²	1	8	yes	complemented
65	#16863958	C₂²	1	1	yes	characteristic
66	#16863957	C₂²	1	4	yes	—
67	#16863956	C₂²	1	4	yes	—
68	#16863955	C₂²	1	2	yes	—
69	#16863954	C₂²	1	4	yes	—
70	#16863933	C₂²	1	4	yes	complemented
71	#16863932	C₂²	1	4	yes	complemented
72	#16863931	C₂²	1	4	yes	complemented
73	#16863930	C₂²	1	4	yes	complemented
74	#16863929	C₂²	1	8	yes	complemented
75	#16863928	C₂²	1	4	yes	complemented
76	#16863927	C₂²	1	4	yes	complemented
77	#16863926	C₂²	1	8	yes	complemented
78	#16863925	C₂²	1	4	yes	complemented
79	#16863924	C₂²	1	8	yes	complemented
80	#16863923	C₂²	1	8	yes	complemented
81	#126×D₆₇	C₂²	1	8	yes	complemented
82	#126×D₆₇	C₂²	1	8	yes	complemented
83	#125×D₆₇	C₂²	1	4	yes	complemented
84	#125×D₆₇	C₂²	1	8	yes	complemented
85	#124×D₆₇	C₂²	1	4	yes	complemented
86	C₂×#14524028	C₂²	1	4	yes	complemented
87	C₂×#14524027	C₂²	1	2	yes	complemented
88	C₂×#14524026	C₂²	1	2	yes	complemented
89	C₂×#14524025	C₂²	1	4	yes	complemented
90	C₂×#14524024	C₂²	1	2	yes	complemented
91	#123×D₆₇	C₂²	1	8	yes	—
92	#123×D₆₇	C₂²	1	4	yes	—
93	#123×D₆₇	C₂²	1	8	yes	complemented
94	#123×D₆₇	C₂²	1	4	yes	complemented
95	#123×D₆₇	C₂²	1	4	yes	complemented
96	#123×D₆₇	C₂²	1	8	yes	complemented
97	#123×D₆₇	C₂²	1	4	yes	complemented
98	#123×D₆₇	C₂²	1	4	yes	complemented
99	C₂²⋊Q₈×D₆₇	C₂²	1	8	yes	complemented
100	C₂²⋊Q₈×D₆₇	C₂²	1	4	yes	complemented
101	C₂²⋊Q₈×D₆₇	C₂²	1	8	yes	complemented
102	#121×D₆₇	C₂²	1	4	yes	—
103	#120×D₆₇	C₂²	1	4	yes	—
104	#16863871	C₂²	1	2	yes	complemented
105	#16863870	C₂²	1	4	yes	complemented
106	#16863869	C₂²	1	2	yes	complemented
107	#16863869	C₂²	1	2	yes	complemented
108	#16863869	C₂²	1	4	yes	complemented
109	#16863868	C₂²	1	8	yes	complemented
110	#16863868	C₂²	1	8	yes	complemented
111	C₄×Q₈×D₆₇	C₂²	1	4	yes	complemented
112	C₄×D₄×D₆₇	C₂²	1	8	yes	—
113	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
114	C₄×D₄×D₆₇	C₂²	1	4	yes	complemented
115	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
116	C₂×#14524001	C₂²	1	2	yes	complemented
117	C₂×#14524000	C₂²	1	2	yes	complemented
118	C₂×#14523999	C₂²	1	1	yes	characteristic, complemented
119	C₂×#14523999	C₂²	1	1	yes	characteristic, complemented
120	#117×D₆₇	C₂²	1	8	yes	complemented
121	#117×D₆₇	C₂²	1	4	yes	complemented
122	#117×D₆₇	C₂²	1	8	yes	complemented
123	#117×D₆₇	C₂²	1	8	yes	complemented
124	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₄×D₆₇	C₂²	1	4	yes	complemented
126	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
128	C₂×C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
130	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
131	C₂×C₄²×D₆₇	C₂²	1	2	yes	complemented
132	#552×C₆₇	C₂²	1	8	yes	complemented
133	#551×C₆₇	C₂²	1	8	yes	complemented
134	#543×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#539×C₆₇	C₂²	1	4	yes	complemented
136	#534×C₆₇	C₂²	1	1	yes	characteristic
137	#529×C₆₇	C₂²	1	4	yes	complemented
138	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
139	#518×C₆₇	C₂²	1	2	yes	complemented
140	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
141	C₂⁴×D₆₇	C₂³	1	2	yes	—
142	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
143	C₂×Q₈×D₆₇	C₂³	1	4	yes	—
144	C₂²×D₂₆₈	C₂³	1	2	yes	—
145	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
146	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
147	C₂×D₄×D₆₇	—	2	16	no	—
148	C₂×D₄×D₆₇	C₂³	1	4	yes	—
149	C₂×D₄×D₆₇	C₂³	1	4	yes	—
150	C₂×D₄×D₆₇	C₂³	1	4	yes	—
151	C₂×D₄×D₆₇	C₂³	1	4	yes	—
152	C₂×D₄×D₆₇	C₂³	1	4	yes	—
153	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
154	C₂²×C₄×D₆₇	—	2	8	no	—
155	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
156	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
157	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
158	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
159	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
160	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
161	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
162	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
163	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
164	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
165	C₂²×C₄×D₆₇	C₂³	1	8	yes	—
166	#14524038	C₂³	1	8	yes	complemented
167	#14524038	C₂³	1	8	yes	complemented
168	#14524038	C₂³	1	8	yes	complemented
169	#14524038	C₂³	1	8	yes	complemented
170	#14524038	C₂³	1	8	yes	complemented
171	#14524038	C₂³	1	8	yes	complemented
172	#14524037	C₂³	1	8	yes	complemented
173	#14524037	C₂³	1	8	yes	complemented
174	#14524036	C₂³	1	8	yes	complemented
175	#14524036	C₂³	1	8	yes	complemented
176	#14524036	C₂³	1	8	yes	complemented
177	#14524036	C₂³	1	8	yes	complemented
178	#14524036	C₂³	1	8	yes	complemented
179	#14524036	C₂³	1	8	yes	complemented
180	#14524035	C₂³	1	4	yes	complemented
181	#14524035	C₂³	1	8	yes	complemented
182	#14524034	C₂³	1	8	yes	complemented
183	#14524034	C₂³	1	4	yes	complemented
184	#14524034	C₂³	1	8	yes	complemented
185	#14524034	C₂³	1	4	yes	complemented
186	#14524033	C₂³	1	8	yes	complemented
187	#14524033	C₂³	1	8	yes	complemented
188	#14524033	C₂³	1	8	yes	complemented
189	#14524033	C₂³	1	8	yes	complemented
190	#14524033	C₂³	1	8	yes	complemented
191	#14524033	C₂³	1	8	yes	complemented
192	#14524032	C₂³	1	4	yes	complemented
193	#14524031	C₂³	1	4	yes	complemented
194	#14524030	C₂³	1	4	yes	complemented
195	#14524029	C₂³	1	8	yes	complemented
196	#14524029	C₂³	1	8	yes	complemented
197	#14524028	C₂³	1	8	yes	—
198	#14524028	C₂³	1	8	yes	—
199	#14524028	C₂³	1	8	yes	—
200	#14524028	C₂³	1	8	yes	complemented
201	#14524028	C₂³	1	8	yes	complemented
202	#14524028	C₂³	1	8	yes	complemented
203	#14524028	C₂³	1	8	yes	complemented
204	#14524027	C₂³	1	8	yes	—
205	#14524027	C₂³	1	4	yes	—
206	#14524027	C₂³	1	8	yes	complemented
207	#14524027	C₂³	1	4	yes	complemented
208	#14524027	C₂³	1	4	yes	complemented
209	#14524026	C₂³	1	8	yes	—
210	#14524026	C₂³	1	4	yes	—
211	#14524026	C₂³	1	8	yes	complemented
212	#14524026	C₂³	1	4	yes	complemented
213	#14524026	C₂³	1	4	yes	complemented
214	#14524025	C₂³	1	8	yes	—
215	#14524025	C₂³	1	8	yes	—
216	#14524025	C₂³	1	8	yes	—
217	#14524025	C₂³	1	8	yes	complemented
218	#14524025	C₂³	1	8	yes	complemented
219	#14524025	C₂³	1	8	yes	complemented
220	#14524025	C₂³	1	8	yes	complemented
221	#14524024	C₂³	1	8	yes	—
222	#14524024	C₂³	1	4	yes	—
223	#14524024	C₂³	1	8	yes	complemented
224	#14524024	C₂³	1	4	yes	complemented
225	#14524024	C₂³	1	4	yes	complemented
226	#14524023	C₂³	1	8	yes	complemented
227	#14524023	C₂³	1	4	yes	complemented
228	#14524023	C₂³	1	8	yes	complemented
229	#14524022	C₂³	1	8	yes	complemented
230	#14524022	C₂³	1	4	yes	complemented
231	#14524022	C₂³	1	8	yes	complemented
232	#14524021	C₂³	1	8	yes	complemented
233	#14524021	C₂³	1	8	yes	complemented
234	#14524021	C₂³	1	8	yes	complemented
235	#14524021	C₂³	1	8	yes	complemented
236	#14524021	C₂³	1	8	yes	complemented
237	#14524020	C₂³	1	8	yes	complemented
238	#14524020	C₂³	1	8	yes	complemented
239	#14524020	C₂³	1	8	yes	complemented
240	#14524020	C₂³	1	8	yes	complemented
241	#14524020	C₂³	1	8	yes	complemented
242	#14524019	C₂³	1	8	yes	complemented
243	#14524019	C₂³	1	4	yes	complemented
244	#14524019	C₂³	1	8	yes	complemented
245	#14524018	C₂³	1	4	yes	—
246	#14524017	C₂³	1	4	yes	—
247	#14524016	C₂³	1	8	yes	—
248	#14524015	C₂³	1	8	yes	—
249	#14524014	C₂³	1	4	yes	—
250	#14524013	C₂³	1	4	yes	—
251	#14524013	C₂³	1	8	yes	—
252	#14524012	C₂³	1	4	yes	—
253	#14524011	C₂³	1	4	yes	—
254	#14524011	C₂³	1	8	yes	—
255	Q₈×Dic₆₇	C₂³	1	4	yes	complemented
256	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
257	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
258	#14524008	C₂³	1	4	yes	complemented
259	#14524008	C₂³	1	8	yes	complemented
260	C₄×D₂₆₈	C₂³	1	8	yes	—
261	C₄×D₂₆₈	C₂³	1	4	yes	complemented
262	C₄×D₂₆₈	C₂³	1	8	yes	complemented
263	D₄×Dic₆₇	C₂³	1	8	yes	—
264	D₄×Dic₆₇	C₂³	1	4	yes	complemented
265	D₄×Dic₆₇	C₂³	1	8	yes	complemented
266	#14524005	C₂³	1	8	yes	—
267	#14524005	C₂³	1	4	yes	complemented
268	#14524005	C₂³	1	8	yes	complemented
269	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
270	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
271	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
272	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
273	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
274	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
275	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
276	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
277	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
278	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
279	#14524002	C₂³	1	8	yes	complemented
280	#14524002	C₂³	1	8	yes	complemented
281	#14524002	C₂³	1	4	yes	complemented
282	#14524001	C₂³	1	8	yes	complemented
283	#14524001	C₂³	1	8	yes	complemented
284	#14524001	C₂³	1	8	yes	complemented
285	#14524001	C₂³	1	8	yes	complemented
286	#14524001	C₂³	1	8	yes	complemented
287	#14524000	C₂³	1	8	yes	complemented
288	#14524000	C₂³	1	8	yes	complemented
289	#14524000	C₂³	1	8	yes	complemented
290	#14524000	C₂³	1	8	yes	complemented
291	#14524000	C₂³	1	8	yes	complemented
292	#14523999	C₂³	1	8	yes	complemented
293	#14523999	C₂³	1	8	yes	complemented
294	#14523999	C₂³	1	8	yes	complemented
295	#14523999	C₂³	1	8	yes	complemented
296	#14523999	C₂³	1	4	yes	complemented
297	#14523999	C₂³	1	4	yes	complemented
298	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	complemented
299	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	complemented
300	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	complemented
301	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	complemented
302	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	complemented
303	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	complemented
304	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
305	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
306	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
307	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
308	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
309	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
310	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
311	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
312	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
313	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
314	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
316	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	complemented
318	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	complemented
319	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
320	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
321	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
322	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	complemented
323	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
324	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	complemented
325	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
326	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
327	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
328	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
329	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
330	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
331	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
332	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
333	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
334	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
335	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
336	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
337	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	complemented
338	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
339	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	complemented
340	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
341	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	complemented
342	C₂×C₄×Dic₆₇	C₂³	1	2	yes	complemented
343	C₂×C₄×Dic₆₇	C₂³	1	2	yes	complemented
344	C₂×C₄×Dic₆₇	C₂³	1	2	yes	complemented
345	C₄²×D₆₇	C₂³	1	4	yes	—
346	C₄²×D₆₇	C₂³	1	4	yes	—
347	C₄²×D₆₇	C₂³	1	8	yes	—
348	C₄²×D₆₇	C₂³	1	4	yes	complemented
349	C₄²×D₆₇	C₂³	1	4	yes	complemented
350	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
351	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
352	#126×C₆₇	C₂³	1	8	yes	complemented
353	#126×C₆₇	C₂³	1	8	yes	complemented
354	#125×C₆₇	C₂³	1	4	yes	complemented
355	#125×C₆₇	C₂³	1	8	yes	complemented
356	#124×C₆₇	C₂³	1	4	yes	complemented
357	#123×C₆₇	C₂³	1	8	yes	—
358	#123×C₆₇	C₂³	1	4	yes	—
359	#123×C₆₇	C₂³	1	8	yes	complemented
360	#123×C₆₇	C₂³	1	4	yes	complemented
361	#123×C₆₇	C₂³	1	4	yes	complemented
362	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
363	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
364	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
365	#121×C₆₇	C₂³	1	4	yes	—
366	#120×C₆₇	C₂³	1	4	yes	—
367	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
368	C₄×D₄×C₆₇	C₂³	1	8	yes	—
369	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
370	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
371	#117×C₆₇	C₂³	1	8	yes	complemented
372	#117×C₆₇	C₂³	1	4	yes	complemented
373	#117×C₆₇	C₂³	1	8	yes	complemented
374	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	complemented
375	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
376	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
377	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
378	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
379	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	complemented
380	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	complemented
381	C₂×C₄²×C₆₇	C₂³	1	2	yes	complemented
382	C₂³×D₆₇	—	2	8	no	—
383	C₂³×D₆₇	—	4	4	no	—
384	C₂³×D₆₇	—	4	8	no	—
385	C₂³×D₆₇	#41	1	8	yes	—
386	C₂³×D₆₇	C₂⁴	1	4	yes	—
387	C₂³×D₆₇	C₂⁴	1	2	yes	—
388	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
389	C₂³×D₆₇	C₂⁴	1	4	yes	—
390	C₂³×D₆₇	C₂⁴	1	2	yes	—
391	C₂³×D₆₇	C₂⁴	1	2	yes	—
392	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
394	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
395	Q₈×D₆₇	—	4	8	no	—
396	C₂×D₂₆₈	—	2	8	no	—
397	C₂×D₂₆₈	C₂⁴	1	4	yes	—
398	C₂×D₂₆₈	C₂⁴	1	4	yes	—
399	C₂×D₂₆₈	C₂⁴	1	4	yes	—
400	C₂×C₂²⋊D₆₇	—	2	8	no	—
401	C₂×C₂²⋊D₆₇	—	2	8	no	—
402	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
403	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
404	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
405	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
406	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
407	D₄×D₆₇	—	2	16	no	—
408	D₄×D₆₇	—	2	16	no	—
409	D₄×D₆₇	—	2	16	no	—
410	D₄×D₆₇	—	2	16	no	—
411	D₄×D₆₇	—	4	8	no	—
412	C₂²×Dic₆₇	—	2	4	no	—
413	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
415	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
417	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
418	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
419	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
420	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
421	C₂×C₄×D₆₇	—	2	16	no	—
422	C₂×C₄×D₆₇	—	2	4	no	—
423	C₂×C₄×D₆₇	—	2	4	no	—
424	C₂×C₄×D₆₇	—	2	4	no	—
425	C₂×C₄×D₆₇	—	2	4	no	—
426	C₂×C₄×D₆₇	—	2	16	no	—
427	C₂×C₄×D₆₇	—	2	8	no	—
428	C₂×C₄×D₆₇	—	4	4	no	—
429	C₂×C₄×D₆₇	—	4	16	no	—
430	C₂×C₄×D₆₇	—	4	8	no	—
431	C₂×C₄×D₆₇	—	4	4	no	—
432	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
433	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
434	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
435	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
436	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
437	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
438	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
439	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
440	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
441	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
442	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
443	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
444	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
445	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
446	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
447	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
448	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
449	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
450	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
451	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
452	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
453	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
454	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
455	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
456	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
457	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
458	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
459	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
460	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
461	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
462	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
463	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
464	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
465	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
466	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
467	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
468	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
469	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
470	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
471	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
472	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
473	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
474	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
475	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
476	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
477	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
478	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
479	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
480	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
481	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
482	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
483	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
484	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
485	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
486	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
487	C₄×Dic₆₇	C₂⁴	1	4	yes	—
488	C₄×Dic₆₇	C₂⁴	1	4	yes	—
489	C₄×Dic₆₇	C₂⁴	1	4	yes	—
490	C₄×Dic₆₇	C₂⁴	1	4	yes	—
491	C₄×Dic₆₇	C₂⁴	1	4	yes	—
492	C₄×Dic₆₇	C₂⁴	1	4	yes	—
493	C₄×Dic₆₇	C₂⁴	1	8	yes	—
494	C₄×Dic₆₇	C₂⁴	1	8	yes	—
495	C₄×Dic₆₇	C₂⁴	1	8	yes	—
496	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
497	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
499	C₂×D₄×C₆₇	—	2	8	no	—
500	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
501	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
502	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
503	C₂²×C₄×C₆₇	—	2	4	no	—
504	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
506	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
507	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
509	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
510	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
511	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
512	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
513	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
514	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
515	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
516	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
517	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
518	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
519	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
520	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
521	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
522	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
523	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
524	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
525	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
526	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
527	C₄²×C₆₇	C₂⁴	1	4	yes	—
528	C₄²×C₆₇	C₂⁴	1	4	yes	—
529	C₄²×C₆₇	C₂⁴	1	8	yes	—
530	C₂³×C₆₇	—	2	4	no	—
531	C₂³×C₆₇	—	4	2	no	—
532	C₂³×C₆₇	—	4	4	no	—
533	C₂³×C₆₇	C₂×#41	1	4	yes	—
534	C₂³×C₆₇	C₂⁵	1	4	yes	—
535	C₂³×C₆₇	C₂⁵	1	2	yes	—
536	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
537	C₂²×D₆₇	—	2	4	no	—
538	C₂²×D₆₇	—	2	8	no	—
539	C₂²×D₆₇	—	2	4	no	—
540	C₂²×D₆₇	—	2	8	no	—
541	C₂²×D₆₇	—	2	16	no	—
542	C₂²×D₆₇	—	2	8	no	—
543	C₂²×D₆₇	—	4	16	no	—
544	C₂²×D₆₇	—	4	4	no	—
545	C₂²×D₆₇	—	4	2	no	—
546	C₂²×D₆₇	—	4	8	no	—
547	C₂²×D₆₇	—	4	4	no	—
548	C₂²×D₆₇	—	8	16	no	—
549	C₂²×D₆₇	C₂×#41	1	8	yes	—
550	C₂²×D₆₇	C₂×#41	1	4	yes	—
551	C₂²×D₆₇	C₂×#41	1	4	yes	—
552	C₂²×D₆₇	C₂×#41	1	8	yes	—
553	C₂²×D₆₇	C₂⁵	1	4	yes	—
554	C₂²×D₆₇	C₂⁵	1	2	yes	—
555	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
556	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
557	Q₈×C₆₇	—	4	4	no	—
558	D₄×C₆₇	—	2	8	no	—
559	D₄×C₆₇	—	2	8	no	—
560	D₄×C₆₇	—	4	4	no	—
561	C₂×C₄×C₆₇	—	2	8	no	—
562	C₂×C₄×C₆₇	—	2	2	no	—
563	C₂×C₄×C₆₇	—	2	2	no	—
564	C₂×C₄×C₆₇	—	2	4	no	—
565	C₂×C₄×C₆₇	—	4	4	no	—
566	C₂×C₄×C₆₇	—	4	8	no	—
567	C₂×C₄×C₆₇	—	4	2	no	—
568	C₂×C₄×C₆₇	—	4	2	no	—
569	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
570	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
571	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
572	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
573	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
574	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
575	C₂²⋊D₆₇	—	2	8	no	—
576	C₂²⋊D₆₇	—	2	8	no	—
577	C₂²⋊D₆₇	—	2	8	no	—
578	C₂²⋊D₆₇	—	2	8	no	—
579	C₂²⋊D₆₇	—	4	8	no	—
580	C₂×Dic₆₇	—	2	8	no	—
581	C₂×Dic₆₇	—	2	2	no	—
582	C₂×Dic₆₇	—	2	2	no	—
583	C₂×Dic₆₇	—	2	4	no	—
584	C₂×Dic₆₇	—	4	4	no	—
585	C₂×Dic₆₇	—	4	8	no	—
586	C₂×Dic₆₇	—	4	2	no	—
587	C₂×Dic₆₇	—	4	2	no	—
588	C₂×Dic₆₇	C₂⁵	1	2	yes	—
589	C₂×Dic₆₇	C₂⁵	1	4	yes	—
590	C₂×Dic₆₇	C₂⁵	1	4	yes	—
591	C₂×Dic₆₇	C₂⁵	1	4	yes	—
592	C₂×Dic₆₇	C₂⁵	1	8	yes	—
593	C₂×Dic₆₇	C₂⁵	1	2	yes	—
594	D₂₆₈	—	2	8	no	—
595	D₂₆₈	—	2	8	no	—
596	D₂₆₈	—	4	4	no	—
597	C₄×D₆₇	—	2	8	no	—
598	C₄×D₆₇	—	2	8	no	—
599	C₄×D₆₇	—	2	4	no	—
600	C₄×D₆₇	—	2	4	no	—
601	C₄×D₆₇	—	2	4	no	—
602	C₄×D₆₇	—	2	4	no	—
603	C₄×D₆₇	—	2	8	no	—
604	C₄×D₆₇	—	2	8	no	—
605	C₄×D₆₇	—	2	8	no	—
606	C₄×D₆₇	—	2	16	no	—
607	C₄×D₆₇	—	2	8	no	—
608	C₄×D₆₇	—	4	8	no	—
609	C₄×D₆₇	—	4	8	no	—
610	C₄×D₆₇	—	4	4	no	—
611	C₄×D₆₇	—	4	8	no	—
612	C₄×D₆₇	—	4	4	no	—
613	Dic₁₃₄	—	4	4	no	—
614	Dic₁₃₄	—	4	8	no	—
615	C₂²×C₆₇	—	2	2	no	—
616	C₂²×C₆₇	—	2	4	no	—
617	C₂²×C₆₇	—	2	4	no	—
618	C₂²×C₆₇	—	2	8	no	—
619	C₂²×C₆₇	—	4	4	no	—
620	C₂²×C₆₇	—	8	4	no	—
621	C₂²×C₆₇	C₂²×#41	1	4	yes	—
622	C₂²×C₆₇	C₂²×#41	1	2	yes	—
623	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
624	C₂×D₆₇	—	2	2	no	—
625	C₂×D₆₇	—	2	4	no	—
626	C₂×D₆₇	—	2	16	no	—
627	C₂×D₆₇	—	2	8	no	—
628	C₂×D₆₇	—	2	4	no	—
629	C₂×D₆₇	—	2	8	no	—
630	C₂×D₆₇	—	4	4	no	—
631	C₂×D₆₇	—	4	8	no	—
632	C₂×D₆₇	—	4	16	no	—
633	C₂×D₆₇	—	8	8	no	—
634	C₂×D₆₇	—	8	4	no	—
635	C₂×D₆₇	C₂²×#41	1	4	yes	—
636	C₂×D₆₇	C₂²×#41	1	2	yes	—
637	C₂×D₆₇	C₂²×#41	1	2	yes	—
638	C₂×D₆₇	#585	1	4	yes	—
639	C₄×C₆₇	—	2	2	no	—
640	C₄×C₆₇	—	2	2	no	—
641	C₄×C₆₇	—	2	4	no	—
642	C₄×C₆₇	—	2	8	no	—
643	C₄×C₆₇	—	2	4	no	—
644	C₄×C₆₇	—	2	4	no	—
645	Dic₆₇	—	2	2	no	—
646	Dic₆₇	—	2	2	no	—
647	Dic₆₇	—	2	4	no	—
648	Dic₆₇	—	2	8	no	—
649	Dic₆₇	—	2	4	no	—
650	Dic₆₇	—	2	4	no	—
651	C₂×#3491	—	67	1	no	maximal, Sylow
652	C₂×C₆₇	—	2	4	no	—
653	C₂×C₆₇	—	2	2	no	—
654	C₂×C₆₇	—	4	4	no	—
655	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
656	C₂×C₆₇	C₂×#585	1	2	yes	—
657	D₆₇	—	2	4	no	—
658	D₆₇	—	2	2	no	—
659	D₆₇	—	4	4	no	—
660	D₆₇	#3491	1	4	yes	direct product factor
661	#3491	—	67	8	no	—
662	#3491	—	67	8	no	—
663	#3491	—	67	1	no	—
664	#3491	—	67	4	no	—
665	#3491	—	67	1	no	—
666	#3491	—	67	4	no	—
667	#3491	—	67	2	no	—
668	#3491	—	67	2	no	—
669	#3491	—	67	1	no	—
670	#3491	D₆₇	1	1	yes	characteristic, direct product factor
671	C₂×#552	—	67	8	no	—
672	C₂×#551	—	67	8	no	—
673	C₂×#543	—	67	1	no	—
674	C₂×#539	—	67	4	no	—
675	C₂×#534	—	67	1	no	—
676	C₂×#529	—	67	4	no	—
677	C₂²×#123	—	67	2	no	—
678	C₂×#518	—	67	2	no	—
679	C₂²×#117	—	67	1	no	—
680	C₆₇	C₂×#3491	1	1	yes	characteristic, complemented, Sylow
681	C₂³×D₄	—	67	2	no	—
682	C₂⁴×C₄	—	67	1	no	—
683	#552	—	67	8	no	—
684	#552	—	67	8	no	—
685	#552	—	67	8	no	—
686	#552	—	67	8	no	—
687	#552	—	67	8	no	—
688	#552	—	67	8	no	—
689	#552	—	67	8	no	—
690	#552	—	67	8	no	—
691	#552	—	67	8	no	—
692	#552	—	67	8	no	—
693	#552	—	67	8	no	—
694	#552	—	67	8	no	—
695	#552	—	67	8	no	—
696	#552	—	67	8	no	—
697	#552	—	67	8	no	—
698	#552	C₂×D₆₇	1	8	yes	complemented
699	#551	—	67	8	no	—
700	#551	—	67	8	no	—
701	#551	—	67	8	no	—
702	#551	—	67	8	no	—
703	#551	—	67	8	no	—
704	#551	—	67	8	no	—
705	#551	—	67	8	no	—
706	#551	—	67	8	no	—
707	#551	—	67	8	no	—
708	#551	—	67	8	no	—
709	#551	—	67	8	no	—
710	#551	—	67	8	no	—
711	#551	—	67	8	no	—
712	#551	—	67	8	no	—
713	#551	—	67	8	no	—
714	#551	C₂×D₆₇	1	8	yes	complemented
715	#543	—	67	4	no	—
716	#543	—	67	8	no	—
717	#543	—	67	2	no	—
718	#543	—	67	1	no	—
719	#543	C₂×D₆₇	1	1	yes	characteristic, complemented
720	#539	—	67	8	no	—
721	#539	—	67	8	no	—
722	#539	—	67	8	no	—
723	#539	—	67	8	no	—
724	#539	—	67	8	no	—
725	#539	—	67	4	no	—
726	#539	—	67	4	no	—
727	#539	—	67	8	no	—
728	#539	—	67	4	no	—
729	#539	C₂×D₆₇	1	4	yes	complemented
730	#534	—	67	2	no	—
731	#534	—	67	4	no	—
732	#534	—	67	4	no	—
733	#534	—	67	4	no	—
734	#534	—	67	1	no	—
735	#534	C₂×D₆₇	1	1	yes	characteristic
736	#529	—	67	8	no	—
737	#529	—	67	4	no	—
738	#529	—	67	4	no	—
739	#529	—	67	8	no	—
740	#529	—	67	4	no	—
741	#529	—	67	4	no	—
742	#529	—	67	4	no	—
743	#529	—	67	8	no	—
744	#529	—	67	4	no	—
745	#529	—	67	8	no	—
746	#529	—	67	4	no	—
747	#529	C₂×D₆₇	1	4	yes	complemented
748	C₂×#126	—	67	8	no	—
749	C₂×#126	—	67	8	no	—
750	C₂×#125	—	67	4	no	—
751	C₂×#125	—	67	8	no	—
752	C₂×#124	—	67	4	no	—
753	C₂×#123	—	67	2	no	—
754	C₂×#123	—	67	2	no	—
755	C₂×#123	—	67	8	no	—
756	C₂×#123	—	67	8	no	—
757	C₂×#123	—	67	4	no	—
758	C₂×#123	—	67	4	no	—
759	C₂×#123	—	67	4	no	—
760	C₂×#123	—	67	4	no	—
761	C₂×#123	—	67	4	no	—
762	C₂×#123	—	67	8	no	—
763	C₂×#123	—	67	4	no	—
764	C₂×#123	—	67	2	no	—
765	C₂×#123	—	67	4	no	—
766	C₂×#123	C₂×D₆₇	1	2	yes	complemented
767	C₂×C₂²⋊Q₈	—	67	4	no	—
768	C₂×C₂²⋊Q₈	—	67	8	no	—
769	C₂×C₂²⋊Q₈	—	67	8	no	—
770	C₂×#121	—	67	4	no	—
771	C₂×#120	—	67	4	no	—
772	#518	—	67	2	no	—
773	#518	—	67	8	no	—
774	#518	—	67	8	no	—
775	#518	—	67	4	no	—
776	#518	—	67	2	no	—
777	#518	—	67	2	no	—
778	#518	—	67	4	no	—
779	#518	C₂×D₆₇	1	2	yes	complemented
780	C₂×C₄×Q₈	—	67	4	no	—
781	C₂×C₄×D₄	—	67	8	no	—
782	C₂×C₄×D₄	—	67	8	no	—
783	C₂×C₄×D₄	—	67	4	no	—
784	C₂×#117	—	67	1	no	—
785	C₂×#117	—	67	8	no	—
786	C₂×#117	—	67	8	no	—
787	C₂×#117	—	67	4	no	—
788	C₂×#117	—	67	8	no	—
789	C₂×#117	—	67	2	no	—
790	C₂×#117	—	67	1	no	—
791	C₂×#117	—	67	1	no	—
792	C₂×#117	—	67	2	no	—
793	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
794	C₂²×C₄⋊C₄	—	67	2	no	—
795	C₂²×C₄⋊C₄	—	67	4	no	—
796	C₂²×C₂²⋊C₄	—	67	1	no	—
797	C₂²×C₂²⋊C₄	—	67	1	no	—
798	C₂²×C₂²⋊C₄	—	67	2	no	—
799	C₂²×C₂²⋊C₄	—	67	4	no	—
800	C₂²×C₂²⋊C₄	—	67	4	no	—
801	C₂²×C₄²	—	67	2	no	—
802	C₂⁵	—	67	1	no	—
803	C₂⁵	—	67	2	no	—
804	C₂²×Q₈	—	67	4	no	—
805	C₂²×D₄	—	67	4	no	—
806	C₂²×D₄	—	67	2	no	—
807	C₂²×D₄	—	67	2	no	—
808	C₂²×D₄	—	67	4	no	—
809	C₂²×D₄	—	67	4	no	—
810	C₂²×D₄	—	67	4	no	—
811	C₂²×D₄	—	67	4	no	—
812	C₂²×D₄	—	67	2	no	—
813	C₂²×D₄	—	134	16	no	—
814	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
815	C₂³×C₄	—	67	4	no	—
816	C₂³×C₄	—	67	2	no	—
817	C₂³×C₄	—	67	2	no	—
818	C₂³×C₄	—	67	8	no	—
819	C₂³×C₄	—	67	1	no	—
820	C₂³×C₄	—	67	4	no	—
821	C₂³×C₄	—	67	2	no	—
822	C₂³×C₄	—	67	1	no	—
823	C₂³×C₄	—	67	1	no	—
824	C₂³×C₄	—	67	4	no	—
825	C₂³×C₄	—	67	1	no	—
826	C₂³×C₄	—	67	1	no	—
827	C₂³×C₄	—	134	8	no	—
828	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
829	#126	—	67	8	no	—
830	#126	—	67	8	no	—
831	#126	—	67	8	no	—
832	#126	—	67	8	no	—
833	#126	—	67	8	no	—
834	#126	—	67	8	no	—
835	#126	—	67	8	no	—
836	#126	—	67	8	no	—
837	#126	—	67	8	no	—
838	#126	—	67	8	no	—
839	#126	—	67	8	no	—
840	#126	—	67	8	no	—
841	#126	—	67	8	no	—
842	#126	—	67	8	no	—
843	#126	C₂²×D₆₇	1	8	yes	complemented
844	#126	C₂²×D₆₇	1	8	yes	complemented
845	#125	—	67	8	no	—
846	#125	—	67	8	no	—
847	#125	—	67	4	no	—
848	#125	—	67	4	no	—
849	#125	—	67	8	no	—
850	#125	—	67	8	no	—
851	#125	—	67	8	no	—
852	#125	—	67	8	no	—
853	#125	—	67	8	no	—
854	#125	—	67	8	no	—
855	#125	—	67	4	no	—
856	#125	—	67	8	no	—
857	#125	C₂²×D₆₇	1	4	yes	complemented
858	#125	C₂²×D₆₇	1	8	yes	complemented
859	#124	—	67	4	no	—
860	#124	—	67	4	no	—
861	#124	—	67	8	no	—
862	#124	—	67	8	no	—
863	#124	—	67	4	no	—
864	#124	C₂²×D₆₇	1	4	yes	complemented
865	#123	—	67	4	no	—
866	#123	—	67	4	no	—
867	#123	—	67	8	no	—
868	#123	—	67	4	no	—
869	#123	—	67	8	no	—
870	#123	—	67	4	no	—
871	#123	—	67	4	no	—
872	#123	—	67	8	no	—
873	#123	—	67	4	no	—
874	#123	—	67	8	no	—
875	#123	—	67	8	no	—
876	#123	—	67	8	no	—
877	#123	—	67	8	no	—
878	#123	—	67	8	no	—
879	#123	—	67	8	no	—
880	#123	—	67	8	no	—
881	#123	—	67	8	no	—
882	#123	—	67	8	no	—
883	#123	—	67	4	no	—
884	#123	—	67	8	no	—
885	#123	—	67	4	no	—
886	#123	—	67	8	no	—
887	#123	—	67	8	no	—
888	#123	—	67	8	no	—
889	#123	—	67	8	no	—
890	#123	—	67	4	no	—
891	#123	—	67	8	no	—
892	#123	—	67	8	no	—
893	#123	—	67	8	no	—
894	#123	C₂²×D₆₇	1	8	yes	—
895	#123	C₂²×D₆₇	1	4	yes	—
896	#123	C₂²×D₆₇	1	4	yes	complemented
897	#123	C₂²×D₆₇	1	4	yes	complemented
898	#123	C₂²×D₆₇	1	8	yes	complemented
899	C₂²⋊Q₈	—	67	4	no	—
900	C₂²⋊Q₈	—	67	8	no	—
901	C₂²⋊Q₈	—	67	8	no	—
902	C₂²⋊Q₈	—	67	4	no	—
903	C₂²⋊Q₈	—	67	8	no	—
904	C₂²⋊Q₈	—	67	8	no	—
905	C₂²⋊Q₈	—	67	8	no	—
906	C₂²⋊Q₈	—	67	4	no	—
907	C₂²⋊Q₈	—	67	8	no	—
908	C₂²⋊Q₈	—	67	8	no	—
909	C₂²⋊Q₈	—	67	8	no	—
910	C₂²⋊Q₈	—	67	8	no	—
911	C₂²⋊Q₈	—	67	8	no	—
912	C₂²⋊Q₈	—	67	8	no	—
913	C₂²⋊Q₈	—	67	8	no	—
914	C₂²⋊Q₈	—	67	8	no	—
915	C₂²⋊Q₈	—	67	8	no	—
916	C₂²⋊Q₈	—	67	8	no	—
917	C₂²⋊Q₈	—	67	8	no	—
918	C₂²⋊Q₈	C₂²×D₆₇	1	4	yes	complemented
919	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
920	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
921	#121	—	67	4	no	—
922	#121	—	67	8	no	—
923	#121	—	67	4	no	—
924	#121	—	67	4	no	—
925	#121	—	67	8	no	—
926	#121	C₂²×D₆₇	1	4	yes	—
927	#120	—	67	4	no	—
928	#120	—	67	4	no	—
929	#120	—	67	8	no	—
930	#120	—	67	8	no	—
931	#120	—	67	4	no	—
932	#120	C₂²×D₆₇	1	4	yes	—
933	C₄×Q₈	—	67	4	no	—
934	C₄×Q₈	—	67	4	no	—
935	C₄×Q₈	—	67	8	no	—
936	C₄×Q₈	—	67	8	no	—
937	C₄×Q₈	—	67	4	no	—
938	C₄×Q₈	C₂²×D₆₇	1	4	yes	complemented
939	C₄×D₄	—	67	8	no	—
940	C₄×D₄	—	67	8	no	—
941	C₄×D₄	—	67	4	no	—
942	C₄×D₄	—	67	8	no	—
943	C₄×D₄	—	67	8	no	—
944	C₄×D₄	—	67	8	no	—
945	C₄×D₄	—	67	8	no	—
946	C₄×D₄	—	67	8	no	—
947	C₄×D₄	—	67	8	no	—
948	C₄×D₄	—	67	8	no	—
949	C₄×D₄	—	67	4	no	—
950	C₄×D₄	—	67	8	no	—
951	C₄×D₄	—	67	8	no	—
952	C₄×D₄	—	67	8	no	—
953	C₄×D₄	—	67	8	no	—
954	C₄×D₄	—	67	8	no	—
955	C₄×D₄	—	67	8	no	—
956	C₄×D₄	—	67	8	no	—
957	C₄×D₄	—	67	4	no	—
958	C₄×D₄	C₂²×D₆₇	1	8	yes	—
959	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
960	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
961	#117	—	67	8	no	—
962	#117	—	67	4	no	—
963	#117	—	67	8	no	—
964	#117	—	67	8	no	—
965	#117	—	67	8	no	—
966	#117	—	67	8	no	—
967	#117	—	67	8	no	—
968	#117	—	67	8	no	—
969	#117	—	67	8	no	—
970	#117	—	67	8	no	—
971	#117	—	67	4	no	—
972	#117	—	67	4	no	—
973	#117	—	67	8	no	—
974	#117	—	67	8	no	—
975	#117	—	67	8	no	—
976	#117	—	67	8	no	—
977	#117	—	67	8	no	—
978	#117	—	67	8	no	—
979	#117	—	67	8	no	—
980	#117	C₂²×D₆₇	1	8	yes	complemented
981	#117	C₂²×D₆₇	1	4	yes	complemented
982	#117	C₂²×D₆₇	1	8	yes	complemented
983	C₂×C₄⋊C₄	—	67	2	no	—
984	C₂×C₄⋊C₄	—	67	2	no	—
985	C₂×C₄⋊C₄	—	67	2	no	—
986	C₂×C₄⋊C₄	—	67	4	no	—
987	C₂×C₄⋊C₄	—	67	4	no	—
988	C₂×C₄⋊C₄	—	67	4	no	—
989	C₂×C₄⋊C₄	—	67	8	no	—
990	C₂×C₄⋊C₄	—	67	8	no	—
991	C₂×C₄⋊C₄	—	67	8	no	—
992	C₂×C₄⋊C₄	—	67	8	no	—
993	C₂×C₄⋊C₄	—	67	8	no	—
994	C₂×C₄⋊C₄	—	67	8	no	—
995	C₂×C₄⋊C₄	—	67	8	no	—
996	C₂×C₄⋊C₄	—	67	8	no	—
997	C₂×C₄⋊C₄	—	67	4	no	—
998	C₂×C₄⋊C₄	—	67	4	no	—
999	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	complemented
1000	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	complemented
1001	C₂×C₂²⋊C₄	—	67	1	no	—
1002	C₂×C₂²⋊C₄	—	67	1	no	—
1003	C₂×C₂²⋊C₄	—	67	2	no	—
1004	C₂×C₂²⋊C₄	—	67	4	no	—
1005	C₂×C₂²⋊C₄	—	67	4	no	—
1006	C₂×C₂²⋊C₄	—	67	2	no	—
1007	C₂×C₂²⋊C₄	—	67	2	no	—
1008	C₂×C₂²⋊C₄	—	67	4	no	—
1009	C₂×C₂²⋊C₄	—	67	8	no	—
1010	C₂×C₂²⋊C₄	—	67	4	no	—
1011	C₂×C₂²⋊C₄	—	67	4	no	—
1012	C₂×C₂²⋊C₄	—	67	4	no	—
1013	C₂×C₂²⋊C₄	—	67	4	no	—
1014	C₂×C₂²⋊C₄	—	67	4	no	—
1015	C₂×C₂²⋊C₄	—	67	4	no	—
1016	C₂×C₂²⋊C₄	—	67	4	no	—
1017	C₂×C₂²⋊C₄	—	67	8	no	—
1018	C₂×C₂²⋊C₄	—	67	4	no	—
1019	C₂×C₂²⋊C₄	—	67	8	no	—
1020	C₂×C₂²⋊C₄	—	67	4	no	—
1021	C₂×C₂²⋊C₄	—	67	4	no	—
1022	C₂×C₂²⋊C₄	—	67	4	no	—
1023	C₂×C₂²⋊C₄	—	67	4	no	—
1024	C₂×C₂²⋊C₄	—	67	8	no	—
1025	C₂×C₂²⋊C₄	—	67	8	no	—
1026	C₂×C₂²⋊C₄	—	67	8	no	—
1027	C₂×C₂²⋊C₄	—	67	8	no	—
1028	C₂×C₂²⋊C₄	—	67	8	no	—
1029	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1032	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	complemented
1033	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	complemented
1034	C₂×C₄²	—	67	2	no	—
1035	C₂×C₄²	—	67	2	no	—
1036	C₂×C₄²	—	67	2	no	—
1037	C₂×C₄²	—	67	4	no	—
1038	C₂×C₄²	—	67	8	no	—
1039	C₂×C₄²	—	67	4	no	—
1040	C₂×C₄²	—	67	4	no	—
1041	C₂×C₄²	—	67	4	no	—
1042	C₂×C₄²	C₂²×D₆₇	1	2	yes	complemented
1043	C₂⁴	—	268	4	no	—
1044	C₂⁴	—	268	8	no	—
1045	C₂⁴	—	67	8	no	—
1046	C₂⁴	—	67	1	no	—
1047	C₂⁴	—	67	2	no	—
1048	C₂⁴	—	67	4	no	—
1049	C₂⁴	—	67	2	no	—
1050	C₂⁴	—	67	2	no	—
1051	C₂⁴	—	67	1	no	—
1052	C₂⁴	—	67	4	no	—
1053	C₂⁴	—	134	8	no	—
1054	C₂⁴	C₂³×D₆₇	1	2	yes	—
1055	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1056	C₂×Q₈	—	268	8	no	—
1057	C₂×Q₈	—	67	8	no	—
1058	C₂×Q₈	—	67	4	no	—
1059	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1060	C₂×D₄	—	2	8	no	—
1061	C₂×D₄	—	268	8	no	—
1062	C₂×D₄	—	67	8	no	—
1063	C₂×D₄	—	67	4	no	—
1064	C₂×D₄	—	67	4	no	—
1065	C₂×D₄	—	67	4	no	—
1066	C₂×D₄	—	67	4	no	—
1067	C₂×D₄	—	67	4	no	—
1068	C₂×D₄	—	67	4	no	—
1069	C₂×D₄	—	67	4	no	—
1070	C₂×D₄	—	134	8	no	—
1071	C₂×D₄	—	134	16	no	—
1072	C₂×D₄	—	134	16	no	—
1073	C₂×D₄	—	134	16	no	—
1074	C₂×D₄	—	134	16	no	—
1075	C₂×D₄	—	134	8	no	—
1076	C₂×D₄	—	134	8	no	—
1077	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1078	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1079	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1080	C₂²×C₄	—	2	4	no	—
1081	C₂²×C₄	—	268	4	no	—
1082	C₂²×C₄	—	268	16	no	—
1083	C₂²×C₄	—	268	8	no	—
1084	C₂²×C₄	—	268	4	no	—
1085	C₂²×C₄	—	67	2	no	—
1086	C₂²×C₄	—	67	2	no	—
1087	C₂²×C₄	—	67	4	no	—
1088	C₂²×C₄	—	67	8	no	—
1089	C₂²×C₄	—	67	4	no	—
1090	C₂²×C₄	—	67	4	no	—
1091	C₂²×C₄	—	67	8	no	—
1092	C₂²×C₄	—	67	8	no	—
1093	C₂²×C₄	—	67	8	no	—
1094	C₂²×C₄	—	67	1	no	—
1095	C₂²×C₄	—	67	4	no	—
1096	C₂²×C₄	—	67	2	no	—
1097	C₂²×C₄	—	67	1	no	—
1098	C₂²×C₄	—	67	4	no	—
1099	C₂²×C₄	—	67	2	no	—
1100	C₂²×C₄	—	67	2	no	—
1101	C₂²×C₄	—	67	4	no	—
1102	C₂²×C₄	—	67	4	no	—
1103	C₂²×C₄	—	67	8	no	—
1104	C₂²×C₄	—	67	2	no	—
1105	C₂²×C₄	—	67	4	no	—
1106	C₂²×C₄	—	67	4	no	—
1107	C₂²×C₄	—	67	4	no	—
1108	C₂²×C₄	—	67	2	no	—
1109	C₂²×C₄	—	134	16	no	—
1110	C₂²×C₄	—	134	4	no	—
1111	C₂²×C₄	—	134	4	no	—
1112	C₂²×C₄	—	134	16	no	—
1113	C₂²×C₄	—	134	4	no	—
1114	C₂²×C₄	—	134	4	no	—
1115	C₂²×C₄	—	134	8	no	—
1116	C₂²×C₄	—	134	4	no	—
1117	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1118	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1119	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1120	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1121	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1122	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1123	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1124	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1125	C₄⋊C₄	—	67	8	no	—
1126	C₄⋊C₄	—	67	8	no	—
1127	C₄⋊C₄	—	67	8	no	—
1128	C₄⋊C₄	—	67	8	no	—
1129	C₄⋊C₄	—	67	8	no	—
1130	C₄⋊C₄	—	67	8	no	—
1131	C₄⋊C₄	—	67	8	no	—
1132	C₄⋊C₄	—	67	8	no	—
1133	C₄⋊C₄	—	67	8	no	—
1134	C₄⋊C₄	—	67	8	no	—
1135	C₄⋊C₄	—	67	8	no	—
1136	C₄⋊C₄	—	67	8	no	—
1137	C₄⋊C₄	—	67	8	no	—
1138	C₄⋊C₄	—	67	8	no	—
1139	C₄⋊C₄	—	67	8	no	—
1140	C₄⋊C₄	—	67	8	no	—
1141	C₄⋊C₄	—	67	4	no	—
1142	C₄⋊C₄	—	67	8	no	—
1143	C₄⋊C₄	—	67	4	no	—
1144	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1145	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1146	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1147	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1148	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1149	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1150	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1151	C₂²⋊C₄	—	67	4	no	—
1152	C₂²⋊C₄	—	67	4	no	—
1153	C₂²⋊C₄	—	67	4	no	—
1154	C₂²⋊C₄	—	67	8	no	—
1155	C₂²⋊C₄	—	67	4	no	—
1156	C₂²⋊C₄	—	67	8	no	—
1157	C₂²⋊C₄	—	67	8	no	—
1158	C₂²⋊C₄	—	67	8	no	—
1159	C₂²⋊C₄	—	67	8	no	—
1160	C₂²⋊C₄	—	67	8	no	—
1161	C₂²⋊C₄	—	67	8	no	—
1162	C₂²⋊C₄	—	67	8	no	—
1163	C₂²⋊C₄	—	67	8	no	—
1164	C₂²⋊C₄	—	67	8	no	—
1165	C₂²⋊C₄	—	67	8	no	—
1166	C₂²⋊C₄	—	67	8	no	—
1167	C₂²⋊C₄	—	67	8	no	—
1168	C₂²⋊C₄	—	67	8	no	—
1169	C₂²⋊C₄	—	67	8	no	—
1170	C₂²⋊C₄	—	67	8	no	—
1171	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1172	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1173	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1174	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1175	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1176	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1177	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1178	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1179	C₄²	—	67	4	no	—
1180	C₄²	—	67	4	no	—
1181	C₄²	—	67	4	no	—
1182	C₄²	—	67	4	no	—
1183	C₄²	—	67	4	no	—
1184	C₄²	—	67	4	no	—
1185	C₄²	—	67	8	no	—
1186	C₄²	—	67	8	no	—
1187	C₄²	—	67	8	no	—
1188	C₄²	C₂³×D₆₇	1	4	yes	—
1189	C₄²	C₂³×D₆₇	1	4	yes	—
1190	C₄²	C₂³×D₆₇	1	8	yes	—
1191	C₂³	—	2	4	no	—
1192	C₂³	—	4	2	no	—
1193	C₂³	—	4	4	no	—
1194	C₂³	—	268	2	no	—
1195	C₂³	—	268	4	no	—
1196	C₂³	—	268	4	no	—
1197	C₂³	—	268	8	no	—
1198	C₂³	—	268	16	no	—
1199	C₂³	—	536	16	no	—
1200	C₂³	—	67	4	no	—
1201	C₂³	—	67	8	no	—
1202	C₂³	—	67	1	no	—
1203	C₂³	—	67	8	no	—
1204	C₂³	—	67	4	no	—
1205	C₂³	—	67	2	no	—
1206	C₂³	—	67	1	no	—
1207	C₂³	—	67	4	no	—
1208	C₂³	—	134	16	no	—
1209	C₂³	—	134	8	no	—
1210	C₂³	—	134	8	no	—
1211	C₂³	—	134	4	no	—
1212	C₂³	—	134	8	no	—
1213	C₂³	—	134	4	no	—
1214	C₂³	#41×D₆₇	1	4	yes	—
1215	C₂³	C₂⁴×D₆₇	1	4	yes	—
1216	C₂³	C₂⁴×D₆₇	1	2	yes	—
1217	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1218	Q₈	—	4	4	no	—
1219	Q₈	—	268	8	no	—
1220	Q₈	—	268	4	no	—
1221	D₄	—	2	8	no	—
1222	D₄	—	2	8	no	—
1223	D₄	—	4	4	no	—
1224	D₄	—	268	4	no	—
1225	D₄	—	268	8	no	—
1226	D₄	—	134	8	no	—
1227	D₄	—	134	8	no	—
1228	D₄	—	134	8	no	—
1229	D₄	—	134	8	no	—
1230	D₄	—	134	8	no	—
1231	D₄	—	134	8	no	—
1232	C₂×C₄	—	2	8	no	—
1233	C₂×C₄	—	2	2	no	—
1234	C₂×C₄	—	2	2	no	—
1235	C₂×C₄	—	2	4	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	4	8	no	—
1238	C₂×C₄	—	4	4	no	—
1239	C₂×C₄	—	4	2	no	—
1240	C₂×C₄	—	268	4	no	—
1241	C₂×C₄	—	268	8	no	—
1242	C₂×C₄	—	268	8	no	—
1243	C₂×C₄	—	268	8	no	—
1244	C₂×C₄	—	268	4	no	—
1245	C₂×C₄	—	268	2	no	—
1246	C₂×C₄	—	268	8	no	—
1247	C₂×C₄	—	268	4	no	—
1248	C₂×C₄	—	268	2	no	—
1249	C₂×C₄	—	67	2	no	—
1250	C₂×C₄	—	67	4	no	—
1251	C₂×C₄	—	67	4	no	—
1252	C₂×C₄	—	67	4	no	—
1253	C₂×C₄	—	67	8	no	—
1254	C₂×C₄	—	67	2	no	—
1255	C₂×C₄	—	134	8	no	—
1256	C₂×C₄	—	134	16	no	—
1257	C₂×C₄	—	134	8	no	—
1258	C₂×C₄	—	134	4	no	—
1259	C₂×C₄	—	134	4	no	—
1260	C₂×C₄	—	134	8	no	—
1261	C₂×C₄	—	134	8	no	—
1262	C₂×C₄	—	134	4	no	—
1263	C₂×C₄	—	134	4	no	—
1264	C₂×C₄	—	134	8	no	—
1265	C₂×C₄	—	134	8	no	—
1266	C₂×C₄	—	134	8	no	—
1267	C₂×C₄	—	134	2	no	—
1268	C₂×C₄	—	134	2	no	—
1269	C₂×C₄	—	134	4	no	—
1270	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1271	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1272	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1273	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1274	C₂×C₄	C₂⁴×D₆₇	1	8	yes	—
1275	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	2	4	no	—
1278	C₂²	—	2	4	no	—
1279	C₂²	—	2	8	no	—
1280	C₂²	—	4	4	no	—
1281	C₂²	—	8	4	no	—
1282	C₂²	—	268	8	no	—
1283	C₂²	—	268	4	no	—
1284	C₂²	—	268	16	no	—
1285	C₂²	—	536	4	no	—
1286	C₂²	—	536	8	no	—
1287	C₂²	—	67	2	no	—
1288	C₂²	—	67	4	no	—
1289	C₂²	—	67	4	no	—
1290	C₂²	—	67	2	no	—
1291	C₂²	—	134	16	no	—
1292	C₂²	—	134	8	no	—
1293	C₂²	—	134	4	no	—
1294	C₂²	—	134	8	no	—
1295	C₂²	—	134	2	no	—
1296	C₂²	—	134	4	no	—
1297	C₂²	C₂×#41×D₆₇	1	4	yes	—
1298	C₂²	C₂×#41×D₆₇	1	2	yes	—
1299	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1300	C₄	—	2	2	no	—
1301	C₄	—	2	2	no	—
1302	C₄	—	2	4	no	—
1303	C₄	—	2	4	no	—
1304	C₄	—	2	8	no	—
1305	C₄	—	2	4	no	—
1306	C₄	—	134	2	no	—
1307	C₄	—	134	2	no	—
1308	C₄	—	134	4	no	—
1309	C₄	—	134	4	no	—
1310	C₄	—	134	8	no	—
1311	C₄	—	134	4	no	—
1312	C₂	—	2	4	no	—
1313	C₂	—	2	2	no	—
1314	C₂	—	4	4	no	—
1315	C₂	—	268	4	no	—
1316	C₂	—	67	4	no	—
1317	C₂	—	134	4	no	—
1318	C₂	—	134	2	no	—
1319	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1320	C₂	#585×D₆₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Fitting	C₆₇×#3491	C₂
prime radical	#534×D₆₇	C₂
hypercenter	#3491	D₆₇
hypocenter	C₆₇	C₂×#3491
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #3491

Complements

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

N	H ≅ G/N	type
1. #22573908	C₂	semidirect
2. #22573907	C₂	semidirect
3. #22573906	C₂	semidirect
4. #22573905	C₂	semidirect
5. #22573904	C₂	semidirect
6. #22573903	C₂	semidirect
7. #22573902	C₂	semidirect
8. #22573901	C₂	semidirect
9. #22573900	C₂	semidirect
10. #552×D₆₇	C₂	semidirect
11. #551×D₆₇	C₂	semidirect
12. #543×D₆₇	C₂	semidirect
13. #539×D₆₇	C₂	semidirect
15. #529×D₆₇	C₂	semidirect
16. C₂×#123×D₆₇	C₂	semidirect
17. #518×D₆₇	C₂	semidirect
18. C₂×#117×D₆₇	C₂	semidirect
19. C₆₇×#3491	C₂	semidirect
22. #16864088	C₂²	semidirect
23. #16864087	C₂²	semidirect
24. #16864086	C₂²	semidirect
25. #16864085	C₂²	semidirect
26. #16864084	C₂²	semidirect
27. #16864083	C₂²	semidirect
28. #16864083	C₂²	semidirect
29. #16864082	C₂²	semidirect
30. #16864082	C₂²	semidirect
31. #16864081	C₂²	semidirect
32. #16864080	C₂²	semidirect
33. #16864079	C₂²	semidirect
34. #16864079	C₂²	semidirect
35. #16864078	C₂²	semidirect
36. #16864078	C₂²	semidirect
37. #16864077	C₂²	semidirect
38. #16864076	C₂²	semidirect
39. #16864075	C₂²	semidirect
40. #16864075	C₂²	semidirect
41. #16864074	C₂²	semidirect
42. #16864073	C₂²	semidirect
43. #16864073	C₂²	semidirect
44. #16864072	C₂²	semidirect
45. #16864072	C₂²	semidirect
46. #16864071	C₂²	semidirect
47. #16864071	C₂²	semidirect
48. #16864070	C₂²	semidirect
49. #16864070	C₂²	semidirect
50. #16864069	C₂²	semidirect
51. #16864069	C₂²	semidirect
52. #16864022	C₂²	semidirect
53. #16864022	C₂²	semidirect
54. #16864021	C₂²	semidirect
55. #16864021	C₂²	semidirect
56. #16863995	C₂²	semidirect
57. #16863994	C₂²	semidirect
58. #16863993	C₂²	semidirect
59. #16863992	C₂²	semidirect
60. #16863991	C₂²	semidirect
61. #16863990	C₂²	semidirect
62. #16863989	C₂²	semidirect
63. #16863988	C₂²	semidirect
64. #16863987	C₂²	semidirect
70. #16863933	C₂²	semidirect
71. #16863932	C₂²	semidirect
72. #16863931	C₂²	semidirect
73. #16863930	C₂²	semidirect
74. #16863929	C₂²	semidirect
75. #16863928	C₂²	semidirect
76. #16863927	C₂²	semidirect
77. #16863926	C₂²	semidirect
78. #16863925	C₂²	semidirect
79. #16863924	C₂²	semidirect
80. #16863923	C₂²	semidirect
81. #126×D₆₇	C₂²	semidirect
82. #126×D₆₇	C₂²	semidirect
83. #125×D₆₇	C₂²	semidirect
84. #125×D₆₇	C₂²	semidirect
85. #124×D₆₇	C₂²	semidirect
86. C₂×#14524028	C₂²	semidirect
87. C₂×#14524027	C₂²	semidirect
88. C₂×#14524026	C₂²	semidirect
89. C₂×#14524025	C₂²	semidirect
90. C₂×#14524024	C₂²	semidirect
93. #123×D₆₇	C₂²	semidirect
94. #123×D₆₇	C₂²	semidirect
95. #123×D₆₇	C₂²	semidirect
96. #123×D₆₇	C₂²	semidirect
97. #123×D₆₇	C₂²	semidirect
98. #123×D₆₇	C₂²	semidirect
99. C₂²⋊Q₈×D₆₇	C₂²	semidirect
100. C₂²⋊Q₈×D₆₇	C₂²	semidirect
101. C₂²⋊Q₈×D₆₇	C₂²	semidirect
104. #16863871	C₂²	semidirect
105. #16863870	C₂²	semidirect
106. #16863869	C₂²	semidirect
107. #16863869	C₂²	semidirect
108. #16863869	C₂²	semidirect
109. #16863868	C₂²	semidirect
110. #16863868	C₂²	semidirect
111. C₄×Q₈×D₆₇	C₂²	semidirect
113. C₄×D₄×D₆₇	C₂²	semidirect
114. C₄×D₄×D₆₇	C₂²	semidirect
115. C₂×#14524002	C₂²	semidirect
116. C₂×#14524001	C₂²	semidirect
117. C₂×#14524000	C₂²	semidirect
118. C₂×#14523999	C₂²	semidirect
119. C₂×#14523999	C₂²	semidirect
120. #117×D₆₇	C₂²	semidirect
121. #117×D₆₇	C₂²	semidirect
122. #117×D₆₇	C₂²	semidirect
123. #117×D₆₇	C₂²	semidirect
124. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
125. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
129. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
130. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
131. C₂×C₄²×D₆₇	C₂²	semidirect
132. #552×C₆₇	C₂²	semidirect
133. #551×C₆₇	C₂²	semidirect
134. #543×C₆₇	C₂²	semidirect
135. #539×C₆₇	C₂²	semidirect
137. #529×C₆₇	C₂²	semidirect
138. C₂×#123×C₆₇	C₂²	semidirect
139. #518×C₆₇	C₂²	semidirect
140. C₂×#117×C₆₇	C₂²	semidirect
166. #14524038	C₂³	semidirect
167. #14524038	C₂³	semidirect
168. #14524038	C₂³	semidirect
169. #14524038	C₂³	semidirect
170. #14524038	C₂³	semidirect
171. #14524038	C₂³	semidirect
172. #14524037	C₂³	semidirect
173. #14524037	C₂³	semidirect
174. #14524036	C₂³	semidirect
175. #14524036	C₂³	semidirect
176. #14524036	C₂³	semidirect
177. #14524036	C₂³	semidirect
178. #14524036	C₂³	semidirect
179. #14524036	C₂³	semidirect
180. #14524035	C₂³	semidirect
181. #14524035	C₂³	semidirect
182. #14524034	C₂³	semidirect
183. #14524034	C₂³	semidirect
184. #14524034	C₂³	semidirect
185. #14524034	C₂³	semidirect
186. #14524033	C₂³	semidirect
187. #14524033	C₂³	semidirect
188. #14524033	C₂³	semidirect
189. #14524033	C₂³	semidirect
190. #14524033	C₂³	semidirect
191. #14524033	C₂³	semidirect
192. #14524032	C₂³	semidirect
193. #14524031	C₂³	semidirect
194. #14524030	C₂³	semidirect
195. #14524029	C₂³	semidirect
196. #14524029	C₂³	semidirect
200. #14524028	C₂³	semidirect
201. #14524028	C₂³	semidirect
202. #14524028	C₂³	semidirect
203. #14524028	C₂³	semidirect
206. #14524027	C₂³	semidirect
207. #14524027	C₂³	semidirect
208. #14524027	C₂³	semidirect
211. #14524026	C₂³	semidirect
212. #14524026	C₂³	semidirect
213. #14524026	C₂³	semidirect
217. #14524025	C₂³	semidirect
218. #14524025	C₂³	semidirect
219. #14524025	C₂³	semidirect
220. #14524025	C₂³	semidirect
223. #14524024	C₂³	semidirect
224. #14524024	C₂³	semidirect
225. #14524024	C₂³	semidirect
226. #14524023	C₂³	semidirect
227. #14524023	C₂³	semidirect
228. #14524023	C₂³	semidirect
229. #14524022	C₂³	semidirect
230. #14524022	C₂³	semidirect
231. #14524022	C₂³	semidirect
232. #14524021	C₂³	semidirect
233. #14524021	C₂³	semidirect
234. #14524021	C₂³	semidirect
235. #14524021	C₂³	semidirect
236. #14524021	C₂³	semidirect
237. #14524020	C₂³	semidirect
238. #14524020	C₂³	semidirect
239. #14524020	C₂³	semidirect
240. #14524020	C₂³	semidirect
241. #14524020	C₂³	semidirect
242. #14524019	C₂³	semidirect
243. #14524019	C₂³	semidirect
244. #14524019	C₂³	semidirect
255. Q₈×Dic₆₇	C₂³	semidirect
256. C₄×Dic₁₃₄	C₂³	semidirect
257. C₄×Dic₁₃₄	C₂³	semidirect
258. #14524008	C₂³	semidirect
259. #14524008	C₂³	semidirect
261. C₄×D₂₆₈	C₂³	semidirect
262. C₄×D₂₆₈	C₂³	semidirect
264. D₄×Dic₆₇	C₂³	semidirect
265. D₄×Dic₆₇	C₂³	semidirect
267. #14524005	C₂³	semidirect
268. #14524005	C₂³	semidirect
271. C₄×C₂²⋊D₆₇	C₂³	semidirect
272. C₄×C₂²⋊D₆₇	C₂³	semidirect
273. C₄×C₂²⋊D₆₇	C₂³	semidirect
276. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
277. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
278. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
279. #14524002	C₂³	semidirect
280. #14524002	C₂³	semidirect
281. #14524002	C₂³	semidirect
282. #14524001	C₂³	semidirect
283. #14524001	C₂³	semidirect
284. #14524001	C₂³	semidirect
285. #14524001	C₂³	semidirect
286. #14524001	C₂³	semidirect
287. #14524000	C₂³	semidirect
288. #14524000	C₂³	semidirect
289. #14524000	C₂³	semidirect
290. #14524000	C₂³	semidirect
291. #14524000	C₂³	semidirect
292. #14523999	C₂³	semidirect
293. #14523999	C₂³	semidirect
294. #14523999	C₂³	semidirect
295. #14523999	C₂³	semidirect
296. #14523999	C₂³	semidirect
297. #14523999	C₂³	semidirect
298. C₂×C₄⋊Dic₆₇	C₂³	semidirect
299. C₂×C₄⋊Dic₆₇	C₂³	semidirect
300. C₂×Dic₆₇⋊C₄	C₂³	semidirect
301. C₂×Dic₆₇⋊C₄	C₂³	semidirect
302. C₂×Dic₆₇⋊C₄	C₂³	semidirect
303. C₂×Dic₆₇⋊C₄	C₂³	semidirect
311. C₄⋊C₄×D₆₇	C₂³	semidirect
312. C₄⋊C₄×D₆₇	C₂³	semidirect
313. C₄⋊C₄×D₆₇	C₂³	semidirect
317. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
318. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
322. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
323. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
324. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
337. C₂²⋊C₄×D₆₇	C₂³	semidirect
338. C₂²⋊C₄×D₆₇	C₂³	semidirect
339. C₂²⋊C₄×D₆₇	C₂³	semidirect
340. C₂²⋊C₄×D₆₇	C₂³	semidirect
341. C₂²⋊C₄×D₆₇	C₂³	semidirect
342. C₂×C₄×Dic₆₇	C₂³	semidirect
343. C₂×C₄×Dic₆₇	C₂³	semidirect
344. C₂×C₄×Dic₆₇	C₂³	semidirect
348. C₄²×D₆₇	C₂³	semidirect
349. C₄²×D₆₇	C₂³	semidirect
352. #126×C₆₇	C₂³	semidirect
353. #126×C₆₇	C₂³	semidirect
354. #125×C₆₇	C₂³	semidirect
355. #125×C₆₇	C₂³	semidirect
356. #124×C₆₇	C₂³	semidirect
359. #123×C₆₇	C₂³	semidirect
360. #123×C₆₇	C₂³	semidirect
361. #123×C₆₇	C₂³	semidirect
362. C₂²⋊Q₈×C₆₇	C₂³	semidirect
363. C₂²⋊Q₈×C₆₇	C₂³	semidirect
364. C₂²⋊Q₈×C₆₇	C₂³	semidirect
367. C₄×Q₈×C₆₇	C₂³	semidirect
369. C₄×D₄×C₆₇	C₂³	semidirect
370. C₄×D₄×C₆₇	C₂³	semidirect
371. #117×C₆₇	C₂³	semidirect
372. #117×C₆₇	C₂³	semidirect
373. #117×C₆₇	C₂³	semidirect
374. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
375. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
379. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
380. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
381. C₂×C₄²×C₆₇	C₂³	semidirect
660. D₆₇	#3491	direct (N × H)
670. #3491	D₆₇	direct (N × H)
680. C₆₇	C₂×#3491	semidirect
698. #552	C₂×D₆₇	semidirect
714. #551	C₂×D₆₇	semidirect
719. #543	C₂×D₆₇	semidirect
729. #539	C₂×D₆₇	semidirect
747. #529	C₂×D₆₇	semidirect
766. C₂×#123	C₂×D₆₇	semidirect
779. #518	C₂×D₆₇	semidirect
793. C₂×#117	C₂×D₆₇	semidirect
843. #126	C₂²×D₆₇	semidirect
844. #126	C₂²×D₆₇	semidirect
857. #125	C₂²×D₆₇	semidirect
858. #125	C₂²×D₆₇	semidirect
864. #124	C₂²×D₆₇	semidirect
896. #123	C₂²×D₆₇	semidirect
897. #123	C₂²×D₆₇	semidirect
898. #123	C₂²×D₆₇	semidirect
918. C₂²⋊Q₈	C₂²×D₆₇	semidirect
919. C₂²⋊Q₈	C₂²×D₆₇	semidirect
920. C₂²⋊Q₈	C₂²×D₆₇	semidirect
938. C₄×Q₈	C₂²×D₆₇	semidirect
959. C₄×D₄	C₂²×D₆₇	semidirect
960. C₄×D₄	C₂²×D₆₇	semidirect
980. #117	C₂²×D₆₇	semidirect
981. #117	C₂²×D₆₇	semidirect
982. #117	C₂²×D₆₇	semidirect
999. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
1000. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
1032. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
1033. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
1042. 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
#22573908	2
#22573907	2
#22573906	2
#22573905	2
#22573904	2
#22573903	2
#22573902	2
#22573901	2
#22573900	2
#552×D₆₇	2
#551×D₆₇	2
#543×D₆₇	2
#539×D₆₇	2
#534×D₆₇	2
#529×D₆₇	2
C₂×#123×D₆₇	2
#518×D₆₇	2
C₂×#117×D₆₇	2
C₆₇×#3491	2
C₂×#3491	67

Subgroups — #3491×D67 #31763877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3491×D₆₇ #31763877