Subgroups — #22574822

Order 8576.

936 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864150	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864148	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864147	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864145	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864119	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864114	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864107	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864102	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864087	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864084	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864082	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864078	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864073	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864071	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864071	C₂	1	1	yes	maximal, characteristic, complemented
16	#16864070	C₂	1	1	yes	maximal, characteristic, complemented
17	#16864026	C₂	1	1	yes	maximal, characteristic, complemented
18	#16864021	C₂	1	1	yes	maximal, characteristic, complemented
19	#16864018	C₂	1	1	yes	maximal, characteristic, complemented
20	#16864012	C₂	1	1	yes	maximal, characteristic, complemented
21	#16864005	C₂	1	1	yes	maximal, characteristic, complemented
22	#16864005	C₂	1	1	yes	maximal, characteristic, complemented
23	#16864003	C₂	1	1	yes	maximal, characteristic, complemented
24	#16863994	C₂	1	1	yes	maximal, characteristic, complemented
25	#16863994	C₂	1	1	yes	maximal, characteristic, complemented
26	#16863992	C₂	1	1	yes	maximal, characteristic, complemented
27	#16863985	C₂	1	1	yes	maximal, characteristic
28	#16863950	C₂	1	1	yes	maximal, characteristic, complemented
29	#16863931	C₂	1	1	yes	maximal, characteristic, complemented
30	#126×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
31	#541×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
32	#14524043	C₂²	1	1	yes	characteristic, complemented
33	#14524042	C₂²	1	1	yes	characteristic, complemented
34	#14524042	C₂²	1	1	yes	characteristic, complemented
35	#14524042	C₂²	1	1	yes	characteristic, complemented
36	#14524042	C₂²	1	1	yes	characteristic, complemented
37	#14524042	C₂²	1	1	yes	characteristic, complemented
38	#14524041	C₂²	1	1	yes	characteristic, complemented
39	#14524038	C₂²	1	1	yes	characteristic
40	#14524038	C₂²	1	1	yes	characteristic
41	#14524038	C₂²	1	1	yes	characteristic
42	#14524038	C₂²	1	1	yes	characteristic
43	#14524038	C₂²	1	1	yes	characteristic
44	#14524038	C₂²	1	1	yes	characteristic
45	#14524038	C₂²	1	1	yes	characteristic
46	#14524038	C₂²	1	1	yes	characteristic, complemented
47	#14524038	C₂²	1	1	yes	characteristic, complemented
48	#14524038	C₂²	1	1	yes	characteristic, complemented
49	#14524038	C₂²	1	1	yes	characteristic, complemented
50	#14524038	C₂²	1	1	yes	characteristic, complemented
51	#14524037	C₂²	1	1	yes	characteristic
52	#14524037	C₂²	1	1	yes	characteristic
53	#14524037	C₂²	1	1	yes	characteristic, complemented
54	#14524037	C₂²	1	1	yes	characteristic, complemented
55	#14524037	C₂²	1	1	yes	characteristic, complemented
56	#14524036	C₂²	1	1	yes	characteristic
57	#14524036	C₂²	1	1	yes	characteristic
58	#14524036	C₂²	1	1	yes	characteristic
59	#14524036	C₂²	1	1	yes	characteristic
60	#14524036	C₂²	1	1	yes	characteristic
61	#14524035	C₂²	1	1	yes	characteristic, complemented
62	#14524034	C₂²	1	1	yes	characteristic, complemented
63	#14524034	C₂²	1	1	yes	characteristic, complemented
64	#14524034	C₂²	1	1	yes	characteristic, complemented
65	#14524034	C₂²	1	1	yes	characteristic, complemented
66	#14524033	C₂²	1	1	yes	characteristic, complemented
67	#14524033	C₂²	1	1	yes	characteristic, complemented
68	#14524033	C₂²	1	1	yes	characteristic, complemented
69	#14524033	C₂²	1	1	yes	characteristic, complemented
70	#14524033	C₂²	1	1	yes	characteristic, complemented
71	#14524033	C₂²	1	1	yes	characteristic, complemented
72	#14524033	C₂²	1	1	yes	characteristic, complemented
73	#14524033	C₂²	1	1	yes	characteristic, complemented
74	#14524033	C₂²	1	1	yes	characteristic, complemented
75	#14524032	C₂²	1	1	yes	characteristic
76	#14524031	C₂²	1	1	yes	characteristic
77	#14524031	C₂²	1	1	yes	characteristic
78	#14524031	C₂²	1	1	yes	characteristic, complemented
79	#14524029	C₂²	1	1	yes	characteristic
80	#14524029	C₂²	1	1	yes	characteristic
81	#14524029	C₂²	1	1	yes	characteristic
82	#14524028	C₂²	1	1	yes	characteristic
83	#14524028	C₂²	1	1	yes	characteristic
84	#14524028	C₂²	1	1	yes	characteristic
85	#14524028	C₂²	1	1	yes	characteristic
86	#14524028	C₂²	1	1	yes	characteristic
87	#14524028	C₂²	1	1	yes	characteristic
88	#14524028	C₂²	1	1	yes	characteristic
89	#14524028	C₂²	1	1	yes	characteristic
90	#14524028	C₂²	1	1	yes	characteristic
91	#14524028	C₂²	1	1	yes	characteristic, complemented
92	#14524028	C₂²	1	1	yes	characteristic, complemented
93	#14524027	C₂²	1	1	yes	characteristic
94	#14524026	C₂²	1	1	yes	characteristic
95	#14524025	C₂²	1	1	yes	characteristic
96	#14524025	C₂²	1	1	yes	characteristic
97	#14524025	C₂²	1	1	yes	characteristic
98	#14524023	C₂²	1	1	yes	characteristic
99	#14524023	C₂²	1	1	yes	characteristic
100	#14524023	C₂²	1	1	yes	characteristic
101	#14524023	C₂²	1	1	yes	characteristic
102	#14524023	C₂²	1	1	yes	characteristic, complemented
103	#14524023	C₂²	1	1	yes	characteristic, complemented
104	#14524023	C₂²	1	1	yes	characteristic, complemented
105	#14524022	C₂²	1	1	yes	characteristic
106	#14524021	C₂²	1	1	yes	characteristic
107	#14524021	C₂²	1	1	yes	characteristic
108	#14524021	C₂²	1	1	yes	characteristic
109	#14524021	C₂²	1	1	yes	characteristic
110	#14524021	C₂²	1	1	yes	characteristic
111	#14524021	C₂²	1	1	yes	characteristic
112	#14524021	C₂²	1	1	yes	characteristic
113	#14524021	C₂²	1	1	yes	characteristic
114	#14524021	C₂²	1	1	yes	characteristic, complemented
115	#14524021	C₂²	1	1	yes	characteristic, complemented
116	#14524021	C₂²	1	1	yes	characteristic, complemented
117	#14524021	C₂²	1	1	yes	characteristic, complemented
118	#14524020	C₂²	1	1	yes	characteristic
119	#14524020	C₂²	1	1	yes	characteristic
120	#14524020	C₂²	1	1	yes	characteristic
121	#14524019	C₂²	1	1	yes	characteristic
122	#14524019	C₂²	1	1	yes	characteristic
123	#14524019	C₂²	1	1	yes	characteristic
124	#14524019	C₂²	1	1	yes	characteristic, complemented
125	#14524019	C₂²	1	1	yes	characteristic, complemented
126	#14524019	C₂²	1	1	yes	characteristic, complemented
127	#14524018	C₂²	1	1	yes	characteristic
128	#14524018	C₂²	1	1	yes	characteristic
129	#14524016	C₂²	1	1	yes	characteristic
130	#14524013	C₂²	1	1	yes	characteristic
131	#14524013	C₂²	1	1	yes	characteristic
132	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
133	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
134	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
135	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
136	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
137	#14524008	C₂²	1	1	yes	characteristic, complemented
138	#14524008	C₂²	1	1	yes	characteristic, complemented
139	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
140	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
141	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
142	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
143	#14524005	C₂²	1	1	yes	characteristic
144	#14524005	C₂²	1	1	yes	characteristic
145	#14524005	C₂²	1	1	yes	characteristic
146	#14524005	C₂²	1	1	yes	characteristic
147	#14524005	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
149	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
150	#14524001	C₂²	1	1	yes	characteristic
151	#14524001	C₂²	1	1	yes	characteristic
152	#14524001	C₂²	1	1	yes	characteristic
153	#14524001	C₂²	1	1	yes	characteristic, complemented
154	#14524001	C₂²	1	1	yes	characteristic, complemented
155	#14524001	C₂²	1	1	yes	characteristic, complemented
156	#14524000	C₂²	1	1	yes	characteristic
157	#14524000	C₂²	1	1	yes	characteristic
158	#14524000	C₂²	1	1	yes	characteristic
159	#14524000	C₂²	1	1	yes	characteristic, complemented
160	#14523999	C₂²	1	1	yes	characteristic
161	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
162	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
163	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
164	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
165	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
166	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
171	C₄²×D₆₇	C₂²	1	1	yes	characteristic
172	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
173	#126×C₆₇	C₂²	1	1	yes	characteristic
174	#126×C₆₇	C₂²	1	1	yes	characteristic
175	#126×C₆₇	C₂²	1	1	yes	characteristic
176	#126×C₆₇	C₂²	1	1	yes	characteristic
177	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
178	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
179	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
180	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
181	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
183	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
184	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
185	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
186	#117×C₆₇	C₂²	1	1	yes	characteristic
187	C₂³×D₆₇	C₂³	1	1	yes	characteristic
188	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
189	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
190	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
191	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
192	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
193	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
194	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
195	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
196	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
197	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
198	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
199	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
202	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
231	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
232	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
233	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
234	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
263	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
264	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
265	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
266	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
267	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
268	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
269	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
270	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
271	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
272	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
273	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
274	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
295	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
296	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
297	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
298	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
299	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
300	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
301	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
302	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
303	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
304	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
305	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
306	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
307	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
308	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
310	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
311	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
312	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
313	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
314	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
315	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
316	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
317	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₄²×C₆₇	C₂³	1	1	yes	characteristic
337	C₄²×C₆₇	C₂³	1	1	yes	characteristic
338	C₄²×C₆₇	C₂³	1	1	yes	characteristic
339	C₄²×C₆₇	C₂³	1	1	yes	characteristic
340	C₄²×C₆₇	C₂³	1	1	yes	characteristic
341	C₄²×C₆₇	C₂³	1	1	yes	characteristic
342	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂²×D₆₇	—	2	2	no	—
344	C₂²×D₆₇	—	4	1	no	—
345	C₂²×D₆₇	—	4	1	no	—
346	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
347	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
348	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
349	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
350	Q₈×C₆₇	—	4	1	no	—
351	Q₈×C₆₇	—	4	1	no	—
352	C₂×C₄×C₆₇	—	4	1	no	—
353	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
363	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
364	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂²⋊D₆₇	—	4	1	no	—
368	C₂²⋊D₆₇	—	4	1	no	—
369	C₂×Dic₆₇	—	4	1	no	—
370	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
371	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
372	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
373	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
374	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
376	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
382	D₂₆₈	—	2	2	no	—
383	D₂₆₈	—	2	2	no	—
384	D₂₆₈	—	4	1	no	—
385	D₂₆₈	—	4	1	no	—
386	D₂₆₈	—	4	1	no	—
387	C₄×D₆₇	—	2	2	no	—
388	C₄×D₆₇	—	2	2	no	—
389	C₄×D₆₇	—	4	1	no	—
390	C₄×D₆₇	—	4	1	no	—
391	C₄×D₆₇	—	4	1	no	—
392	C₄×D₆₇	—	4	1	no	—
393	C₄×D₆₇	—	4	1	no	—
394	C₄×D₆₇	—	4	1	no	—
395	C₄×D₆₇	—	4	1	no	—
396	C₄×D₆₇	—	4	1	no	—
397	C₄×D₆₇	—	4	1	no	—
398	C₄×D₆₇	—	4	1	no	—
399	C₄×D₆₇	—	4	1	no	—
400	C₄×D₆₇	—	4	1	no	—
401	Dic₁₃₄	—	4	1	no	—
402	Dic₁₃₄	—	4	1	no	—
403	Dic₁₃₄	—	4	1	no	—
404	Dic₁₃₄	—	4	1	no	—
405	Dic₁₃₄	—	4	1	no	—
406	Dic₁₃₄	—	4	1	no	—
407	Dic₁₃₄	—	4	1	no	—
408	C₂²×C₆₇	—	2	1	no	—
409	C₂²×C₆₇	—	2	1	no	—
410	C₂²×C₆₇	—	2	1	no	—
411	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
412	C₂×D₆₇	—	2	1	no	—
413	C₂×D₆₇	—	2	1	no	—
414	C₂×D₆₇	—	2	1	no	—
415	C₂×D₆₇	—	2	1	no	—
416	C₂×D₆₇	—	2	1	no	—
417	C₂×D₆₇	—	2	1	no	—
418	C₂×D₆₇	—	2	1	no	—
419	C₂×D₆₇	—	2	1	no	—
420	C₂×D₆₇	—	2	1	no	—
421	C₂×D₆₇	—	2	1	no	—
422	C₂×D₆₇	—	2	1	no	—
423	C₂×D₆₇	—	8	2	no	—
424	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
425	C₄×C₆₇	—	2	1	no	—
426	C₄×C₆₇	—	2	1	no	—
427	C₄×C₆₇	—	2	1	no	—
428	C₄×C₆₇	—	2	1	no	—
429	C₄×C₆₇	—	2	1	no	—
430	C₄×C₆₇	—	2	1	no	—
431	C₄×C₆₇	—	2	1	no	—
432	C₄×C₆₇	—	2	1	no	—
433	C₄×C₆₇	—	2	1	no	—
434	C₄×C₆₇	—	2	1	no	—
435	C₄×C₆₇	—	2	1	no	—
436	C₄×C₆₇	—	2	1	no	—
437	C₄×C₆₇	—	2	1	no	—
438	C₄×C₆₇	—	2	1	no	—
439	Dic₆₇	—	2	1	no	—
440	Dic₆₇	—	2	1	no	—
441	Dic₆₇	—	2	1	no	—
442	Dic₆₇	—	2	1	no	—
443	Dic₆₇	—	2	1	no	—
444	Dic₆₇	—	2	1	no	—
445	Dic₆₇	—	2	1	no	—
446	Dic₆₇	—	2	1	no	—
447	Dic₆₇	—	2	1	no	—
448	Dic₆₇	—	2	1	no	—
449	Dic₆₇	—	2	1	no	—
450	Dic₆₇	—	2	1	no	—
451	C₂×C₆₇	—	4	1	no	—
452	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
453	C₂×C₆₇	#585	1	1	yes	characteristic
454	C₂×C₆₇	#585	1	1	yes	characteristic
455	D₆₇	—	2	2	no	—
456	D₆₇	—	4	1	no	—
457	D₆₇	—	4	1	no	—
458	D₆₇	—	4	1	no	—
459	#3564	—	67	1	no	maximal, Sylow
460	C₆₇	#3564	1	1	yes	characteristic, complemented, Sylow
461	#563	—	67	1	no	—
462	#563	—	67	1	no	—
463	#563	—	67	1	no	—
464	#563	—	67	1	no	—
465	#556	—	67	1	no	—
466	#556	—	67	1	no	—
467	#554	—	67	1	no	—
468	#554	—	67	1	no	—
469	#552	—	67	1	no	—
470	#552	—	67	1	no	—
471	#552	—	67	1	no	—
472	#552	—	67	1	no	—
473	#551	—	67	1	no	—
474	#551	—	67	1	no	—
475	#551	—	67	1	no	—
476	#551	—	67	1	no	—
477	#544	—	67	1	no	—
478	#543	—	67	1	no	—
479	#542	—	67	1	no	—
480	#542	—	67	1	no	—
481	#541	—	67	1	no	—
482	#541	—	67	1	no	—
483	#541	—	67	1	no	—
484	#541	D₆₇	1	1	yes	characteristic, complemented
485	#539	—	67	1	no	—
486	#539	—	67	1	no	—
487	#539	—	67	1	no	—
488	#538	—	67	1	no	—
489	#533	—	67	1	no	—
490	#529	—	67	1	no	—
491	C₂×#126	—	67	1	no	—
492	C₄⋊Q₈	—	67	1	no	—
493	C₄⋊Q₈	—	67	1	no	—
494	C₄⋊Q₈	—	67	1	no	—
495	C₄⋊Q₈	—	67	1	no	—
496	C₄⋊Q₈	—	67	1	no	—
497	C₄⋊Q₈	—	67	1	no	—
498	C₄⋊Q₈	—	67	1	no	—
499	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
500	#126	—	67	1	no	—
501	#126	—	67	1	no	—
502	#126	—	67	1	no	—
503	#126	—	67	1	no	—
504	#126	—	67	1	no	—
505	#126	—	67	1	no	—
506	#126	—	67	1	no	—
507	#126	—	67	1	no	—
508	#126	—	67	1	no	—
509	#126	—	67	1	no	—
510	#126	—	67	1	no	—
511	#126	—	67	1	no	—
512	#126	—	67	1	no	—
513	#126	—	67	1	no	—
514	#126	—	67	1	no	—
515	#126	—	67	1	no	—
516	#126	—	67	1	no	—
517	#126	—	67	1	no	—
518	#126	—	67	1	no	—
519	#126	—	67	1	no	—
520	#126	—	67	1	no	—
521	#126	—	67	1	no	—
522	#126	C₂×D₆₇	1	1	yes	characteristic
523	#126	C₂×D₆₇	1	1	yes	characteristic
524	#126	C₂×D₆₇	1	1	yes	characteristic
525	#126	C₂×D₆₇	1	1	yes	characteristic
526	#125	—	67	1	no	—
527	#125	—	67	1	no	—
528	#125	—	67	1	no	—
529	#125	—	67	1	no	—
530	#125	—	67	1	no	—
531	#125	—	67	1	no	—
532	#125	—	67	1	no	—
533	#125	—	67	1	no	—
534	#125	—	67	1	no	—
535	#125	—	67	1	no	—
536	#125	—	67	1	no	—
537	#125	—	67	1	no	—
538	#125	—	67	1	no	—
539	#125	—	67	1	no	—
540	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
541	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
542	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
543	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
544	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
545	#124	—	67	1	no	—
546	#124	—	67	1	no	—
547	#124	—	67	1	no	—
548	#124	—	67	1	no	—
549	#124	—	67	1	no	—
550	#124	—	67	1	no	—
551	#124	—	67	1	no	—
552	#123	—	67	1	no	—
553	#123	—	67	1	no	—
554	#123	—	67	1	no	—
555	#123	—	67	1	no	—
556	#123	—	67	1	no	—
557	#123	—	67	1	no	—
558	#123	—	67	1	no	—
559	#123	—	67	1	no	—
560	#123	—	67	1	no	—
561	#123	—	67	1	no	—
562	#123	—	67	1	no	—
563	#123	—	67	1	no	—
564	#123	—	67	1	no	—
565	#123	—	67	1	no	—
566	#123	—	67	1	no	—
567	#123	—	67	1	no	—
568	C₂²⋊Q₈	—	67	1	no	—
569	C₂²⋊Q₈	—	67	1	no	—
570	C₂²⋊Q₈	—	67	1	no	—
571	C₂²⋊Q₈	—	67	1	no	—
572	C₂²⋊Q₈	—	67	1	no	—
573	C₂²⋊Q₈	—	67	1	no	—
574	C₂²⋊Q₈	—	67	1	no	—
575	C₂²⋊Q₈	—	67	1	no	—
576	C₂²⋊Q₈	—	67	1	no	—
577	C₂²⋊Q₈	—	67	1	no	—
578	C₂²⋊Q₈	—	67	1	no	—
579	C₂²⋊Q₈	—	67	1	no	—
580	C₂²⋊Q₈	—	67	1	no	—
581	C₂²⋊Q₈	—	67	1	no	—
582	C₂²⋊Q₈	—	67	1	no	—
583	C₂²⋊Q₈	—	67	1	no	—
584	C₂²⋊Q₈	—	67	1	no	—
585	C₂²⋊Q₈	—	67	1	no	—
586	C₂²⋊Q₈	—	67	1	no	—
587	C₂²⋊Q₈	—	67	1	no	—
588	C₂²⋊Q₈	—	67	1	no	—
589	C₂²⋊Q₈	—	67	1	no	—
590	C₂²⋊Q₈	—	67	1	no	—
591	C₂²⋊Q₈	—	67	1	no	—
592	C₂²⋊Q₈	—	67	1	no	—
593	C₂²⋊Q₈	—	67	1	no	—
594	C₂²⋊Q₈	—	67	1	no	—
595	C₂²⋊Q₈	—	67	1	no	—
596	C₂²⋊Q₈	—	67	1	no	—
597	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
598	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
599	#121	—	67	1	no	—
600	#121	—	67	1	no	—
601	#121	—	67	1	no	—
602	#120	—	67	1	no	—
603	#120	—	67	1	no	—
604	C₄×Q₈	—	67	1	no	—
605	C₄×Q₈	—	67	1	no	—
606	C₄×Q₈	—	67	1	no	—
607	C₄×Q₈	—	67	1	no	—
608	C₄×Q₈	—	67	1	no	—
609	C₄×Q₈	—	67	1	no	—
610	C₄×Q₈	—	67	1	no	—
611	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
612	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
613	C₄×D₄	—	67	1	no	—
614	C₄×D₄	—	67	1	no	—
615	C₄×D₄	—	67	1	no	—
616	C₄×D₄	—	67	1	no	—
617	C₄×D₄	—	67	1	no	—
618	C₄×D₄	—	67	1	no	—
619	C₄×D₄	—	67	1	no	—
620	C₄×D₄	—	67	1	no	—
621	C₄×D₄	—	67	1	no	—
622	C₄×D₄	—	67	1	no	—
623	C₄×D₄	—	67	1	no	—
624	#117	—	67	1	no	—
625	#117	—	67	1	no	—
626	#117	—	67	1	no	—
627	#117	—	67	1	no	—
628	#117	—	67	1	no	—
629	#117	—	67	1	no	—
630	#117	—	67	1	no	—
631	#117	—	67	1	no	—
632	#117	—	67	1	no	—
633	#117	—	67	1	no	—
634	#117	—	67	1	no	—
635	#117	C₂×D₆₇	1	1	yes	characteristic
636	C₂×C₄⋊C₄	—	67	1	no	—
637	C₂×C₄⋊C₄	—	67	1	no	—
638	C₂×C₄⋊C₄	—	67	1	no	—
639	C₂×C₄⋊C₄	—	67	1	no	—
640	C₂×C₄⋊C₄	—	67	1	no	—
641	C₂×C₂²⋊C₄	—	67	1	no	—
642	C₂×C₂²⋊C₄	—	67	1	no	—
643	C₂×C₂²⋊C₄	—	67	1	no	—
644	C₂×C₂²⋊C₄	—	67	1	no	—
645	C₂×C₂²⋊C₄	—	67	1	no	—
646	C₂×C₄²	—	67	1	no	—
647	C₂⁴	—	67	1	no	—
648	C₂×Q₈	—	67	1	no	—
649	C₂×Q₈	—	67	1	no	—
650	C₂×Q₈	—	67	1	no	—
651	C₂×Q₈	—	67	1	no	—
652	C₂×Q₈	—	67	1	no	—
653	C₂×Q₈	—	67	1	no	—
654	C₂×Q₈	—	67	1	no	—
655	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
656	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
657	C₂×D₄	—	67	1	no	—
658	C₂×D₄	—	67	1	no	—
659	C₂×D₄	—	67	1	no	—
660	C₂×D₄	—	67	1	no	—
661	C₂×D₄	—	67	1	no	—
662	C₂×D₄	—	67	1	no	—
663	C₂×D₄	—	67	1	no	—
664	C₂²×C₄	—	67	1	no	—
665	C₂²×C₄	—	67	1	no	—
666	C₂²×C₄	—	67	1	no	—
667	C₂²×C₄	—	67	1	no	—
668	C₂²×C₄	—	67	1	no	—
669	C₂²×C₄	—	67	1	no	—
670	C₂²×C₄	—	67	1	no	—
671	C₂²×C₄	—	67	1	no	—
672	C₂²×C₄	—	67	1	no	—
673	C₂²×C₄	—	67	1	no	—
674	C₂²×C₄	—	67	1	no	—
675	C₂²×C₄	—	67	1	no	—
676	C₂²×C₄	—	67	1	no	—
677	C₂²×C₄	—	67	1	no	—
678	C₂²×C₄	—	67	1	no	—
679	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
680	C₄⋊C₄	—	67	1	no	—
681	C₄⋊C₄	—	67	1	no	—
682	C₄⋊C₄	—	67	1	no	—
683	C₄⋊C₄	—	67	1	no	—
684	C₄⋊C₄	—	67	1	no	—
685	C₄⋊C₄	—	67	1	no	—
686	C₄⋊C₄	—	67	1	no	—
687	C₄⋊C₄	—	67	1	no	—
688	C₄⋊C₄	—	67	1	no	—
689	C₄⋊C₄	—	67	1	no	—
690	C₄⋊C₄	—	67	1	no	—
691	C₄⋊C₄	—	67	1	no	—
692	C₄⋊C₄	—	67	1	no	—
693	C₄⋊C₄	—	67	1	no	—
694	C₄⋊C₄	—	67	1	no	—
695	C₄⋊C₄	—	67	1	no	—
696	C₄⋊C₄	—	67	1	no	—
697	C₄⋊C₄	—	67	1	no	—
698	C₄⋊C₄	—	67	1	no	—
699	C₄⋊C₄	—	67	1	no	—
700	C₄⋊C₄	—	67	1	no	—
701	C₄⋊C₄	—	67	1	no	—
702	C₄⋊C₄	—	67	1	no	—
703	C₄⋊C₄	—	67	1	no	—
704	C₄⋊C₄	—	67	1	no	—
705	C₄⋊C₄	—	67	1	no	—
706	C₄⋊C₄	—	67	1	no	—
707	C₄⋊C₄	—	67	1	no	—
708	C₄⋊C₄	—	67	1	no	—
709	C₄⋊C₄	—	67	1	no	—
710	C₄⋊C₄	—	67	1	no	—
711	C₄⋊C₄	—	67	1	no	—
712	C₄⋊C₄	—	67	1	no	—
713	C₄⋊C₄	—	67	1	no	—
714	C₄⋊C₄	—	67	1	no	—
715	C₄⋊C₄	—	67	1	no	—
716	C₄⋊C₄	—	67	1	no	—
717	C₄⋊C₄	—	67	1	no	—
718	C₄⋊C₄	—	67	1	no	—
719	C₄⋊C₄	—	67	1	no	—
720	C₄⋊C₄	—	67	1	no	—
721	C₄⋊C₄	—	67	1	no	—
722	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
723	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
724	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
725	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
731	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
732	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
733	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
734	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
742	C₂²⋊C₄	—	67	1	no	—
743	C₂²⋊C₄	—	67	1	no	—
744	C₂²⋊C₄	—	67	1	no	—
745	C₂²⋊C₄	—	67	1	no	—
746	C₂²⋊C₄	—	67	1	no	—
747	C₂²⋊C₄	—	67	1	no	—
748	C₂²⋊C₄	—	67	1	no	—
749	C₂²⋊C₄	—	67	1	no	—
750	C₂²⋊C₄	—	67	1	no	—
751	C₂²⋊C₄	—	67	1	no	—
752	C₂²⋊C₄	—	67	1	no	—
753	C₂²⋊C₄	—	67	1	no	—
754	C₂²⋊C₄	—	67	1	no	—
755	C₂²⋊C₄	—	67	1	no	—
756	C₂²⋊C₄	—	67	1	no	—
757	C₂²⋊C₄	—	67	1	no	—
758	C₂²⋊C₄	—	67	1	no	—
759	C₂²⋊C₄	—	67	1	no	—
760	C₂²⋊C₄	—	67	1	no	—
761	C₂²⋊C₄	—	67	1	no	—
762	C₂²⋊C₄	—	67	1	no	—
763	C₂²⋊C₄	—	67	1	no	—
764	C₂²⋊C₄	—	67	1	no	—
765	C₂²⋊C₄	—	67	1	no	—
766	C₂²⋊C₄	—	67	1	no	—
767	C₂²⋊C₄	—	67	1	no	—
768	C₂²⋊C₄	—	67	1	no	—
769	C₂²⋊C₄	—	67	1	no	—
770	C₂²⋊C₄	—	67	1	no	—
771	C₂²⋊C₄	—	67	1	no	—
772	C₂²⋊C₄	—	67	1	no	—
773	C₂²⋊C₄	—	67	1	no	—
774	C₂²⋊C₄	—	67	1	no	—
775	C₂²⋊C₄	—	67	1	no	—
776	C₂²⋊C₄	—	67	1	no	—
777	C₂²⋊C₄	—	67	1	no	—
778	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
779	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
780	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
781	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
782	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
784	C₄²	—	67	1	no	—
785	C₄²	—	67	1	no	—
786	C₄²	—	67	1	no	—
787	C₄²	—	67	1	no	—
788	C₄²	—	67	1	no	—
789	C₄²	—	67	1	no	—
790	C₄²	—	67	1	no	—
791	C₄²	—	67	1	no	—
792	C₄²	—	67	1	no	—
793	C₄²	—	67	1	no	—
794	C₄²	—	67	1	no	—
795	C₄²	—	67	1	no	—
796	C₄²	C₂²×D₆₇	1	1	yes	characteristic
797	C₄²	C₂²×D₆₇	1	1	yes	characteristic
798	C₄²	C₂²×D₆₇	1	1	yes	characteristic
799	C₄²	C₂²×D₆₇	1	1	yes	characteristic
800	C₄²	C₂²×D₆₇	1	1	yes	characteristic
801	C₄²	C₂²×D₆₇	1	1	yes	characteristic
802	C₂³	—	268	1	no	—
803	C₂³	—	268	1	no	—
804	C₂³	—	67	1	no	—
805	C₂³	—	67	1	no	—
806	C₂³	—	67	1	no	—
807	C₂³	—	67	1	no	—
808	C₂³	—	134	2	no	—
809	C₂³	C₂³×D₆₇	1	1	yes	characteristic
810	Q₈	—	4	1	no	—
811	Q₈	—	4	1	no	—
812	Q₈	—	268	1	no	—
813	Q₈	—	268	1	no	—
814	Q₈	—	268	1	no	—
815	Q₈	—	268	1	no	—
816	Q₈	—	268	1	no	—
817	Q₈	—	268	1	no	—
818	Q₈	—	268	1	no	—
819	D₄	—	268	1	no	—
820	D₄	—	268	1	no	—
821	D₄	—	268	1	no	—
822	D₄	—	268	1	no	—
823	D₄	—	268	1	no	—
824	D₄	—	134	2	no	—
825	D₄	—	134	2	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	268	1	no	—
828	C₂×C₄	—	268	1	no	—
829	C₂×C₄	—	268	1	no	—
830	C₂×C₄	—	268	1	no	—
831	C₂×C₄	—	268	1	no	—
832	C₂×C₄	—	268	1	no	—
833	C₂×C₄	—	268	1	no	—
834	C₂×C₄	—	268	1	no	—
835	C₂×C₄	—	268	1	no	—
836	C₂×C₄	—	268	1	no	—
837	C₂×C₄	—	268	1	no	—
838	C₂×C₄	—	268	1	no	—
839	C₂×C₄	—	268	1	no	—
840	C₂×C₄	—	67	1	no	—
841	C₂×C₄	—	67	1	no	—
842	C₂×C₄	—	67	1	no	—
843	C₂×C₄	—	67	1	no	—
844	C₂×C₄	—	67	1	no	—
845	C₂×C₄	—	67	1	no	—
846	C₂×C₄	—	67	1	no	—
847	C₂×C₄	—	67	1	no	—
848	C₂×C₄	—	67	1	no	—
849	C₂×C₄	—	67	1	no	—
850	C₂×C₄	—	67	1	no	—
851	C₂×C₄	—	67	1	no	—
852	C₂×C₄	—	134	2	no	—
853	C₂×C₄	—	134	2	no	—
854	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
855	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
857	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
858	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
859	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
860	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
861	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
862	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
863	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
864	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
865	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
866	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
867	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	536	2	no	—
872	C₂²	—	67	2	no	—
873	C₂²	—	134	1	no	—
874	C₂²	—	134	1	no	—
875	C₂²	—	134	1	no	—
876	C₂²	—	134	1	no	—
877	C₂²	—	134	1	no	—
878	C₂²	—	134	1	no	—
879	C₂²	—	134	1	no	—
880	C₂²	—	134	1	no	—
881	C₂²	—	134	1	no	—
882	C₂²	—	134	1	no	—
883	C₂²	—	134	1	no	—
884	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	2	1	no	—
899	C₄	—	134	1	no	—
900	C₄	—	134	1	no	—
901	C₄	—	134	1	no	—
902	C₄	—	134	1	no	—
903	C₄	—	134	1	no	—
904	C₄	—	134	1	no	—
905	C₄	—	134	1	no	—
906	C₄	—	134	1	no	—
907	C₄	—	134	1	no	—
908	C₄	—	134	1	no	—
909	C₄	—	134	1	no	—
910	C₄	—	134	1	no	—
911	C₂	—	4	1	no	—
912	C₂	—	268	1	no	—
913	C₂	—	268	1	no	—
914	C₂	—	268	1	no	—
915	C₂	—	134	2	no	—
916	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
917	C₂	#16864232	1	1	yes	characteristic
918	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#541×C₆₇	C₂
hypercenter	#541	D₆₇
hypocenter	C₆₇	#3564
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #16864150	C₂	semidirect
2. #16864148	C₂	semidirect
3. #16864147	C₂	semidirect
4. #16864145	C₂	semidirect
5. #16864119	C₂	semidirect
6. #16864114	C₂	semidirect
7. #16864107	C₂	semidirect
8. #16864102	C₂	semidirect
9. #16864087	C₂	semidirect
10. #16864084	C₂	semidirect
11. #16864082	C₂	semidirect
12. #16864078	C₂	semidirect
13. #16864073	C₂	semidirect
14. #16864071	C₂	semidirect
15. #16864071	C₂	semidirect
16. #16864070	C₂	semidirect
17. #16864026	C₂	semidirect
18. #16864021	C₂	semidirect
19. #16864018	C₂	semidirect
20. #16864012	C₂	semidirect
21. #16864005	C₂	semidirect
22. #16864005	C₂	semidirect
23. #16864003	C₂	semidirect
24. #16863994	C₂	semidirect
25. #16863994	C₂	semidirect
26. #16863992	C₂	semidirect
28. #16863950	C₂	semidirect
29. #16863931	C₂	semidirect
30. #126×D₆₇	C₂	semidirect
31. #541×C₆₇	C₂	semidirect
32. #14524043	C₂²	semidirect
33. #14524042	C₂²	semidirect
34. #14524042	C₂²	semidirect
35. #14524042	C₂²	semidirect
36. #14524042	C₂²	semidirect
37. #14524042	C₂²	semidirect
38. #14524041	C₂²	semidirect
46. #14524038	C₂²	semidirect
47. #14524038	C₂²	semidirect
48. #14524038	C₂²	semidirect
49. #14524038	C₂²	semidirect
50. #14524038	C₂²	semidirect
53. #14524037	C₂²	semidirect
54. #14524037	C₂²	semidirect
55. #14524037	C₂²	semidirect
61. #14524035	C₂²	semidirect
62. #14524034	C₂²	semidirect
63. #14524034	C₂²	semidirect
64. #14524034	C₂²	semidirect
65. #14524034	C₂²	semidirect
66. #14524033	C₂²	semidirect
67. #14524033	C₂²	semidirect
68. #14524033	C₂²	semidirect
69. #14524033	C₂²	semidirect
70. #14524033	C₂²	semidirect
71. #14524033	C₂²	semidirect
72. #14524033	C₂²	semidirect
73. #14524033	C₂²	semidirect
74. #14524033	C₂²	semidirect
78. #14524031	C₂²	semidirect
91. #14524028	C₂²	semidirect
92. #14524028	C₂²	semidirect
102. #14524023	C₂²	semidirect
103. #14524023	C₂²	semidirect
104. #14524023	C₂²	semidirect
114. #14524021	C₂²	semidirect
115. #14524021	C₂²	semidirect
116. #14524021	C₂²	semidirect
117. #14524021	C₂²	semidirect
124. #14524019	C₂²	semidirect
125. #14524019	C₂²	semidirect
126. #14524019	C₂²	semidirect
132. C₄×Dic₁₃₄	C₂²	semidirect
133. C₄×Dic₁₃₄	C₂²	semidirect
134. C₄×Dic₁₃₄	C₂²	semidirect
135. C₄×Dic₁₃₄	C₂²	semidirect
136. C₄×Dic₁₃₄	C₂²	semidirect
137. #14524008	C₂²	semidirect
138. #14524008	C₂²	semidirect
147. #14524005	C₂²	semidirect
153. #14524001	C₂²	semidirect
154. #14524001	C₂²	semidirect
155. #14524001	C₂²	semidirect
159. #14524000	C₂²	semidirect
164. C₄⋊C₄×D₆₇	C₂²	semidirect
165. C₄⋊C₄×D₆₇	C₂²	semidirect
172. C₄⋊Q₈×C₆₇	C₂²	semidirect
177. #125×C₆₇	C₂²	semidirect
178. #125×C₆₇	C₂²	semidirect
179. #125×C₆₇	C₂²	semidirect
180. #125×C₆₇	C₂²	semidirect
181. #125×C₆₇	C₂²	semidirect
184. C₄×Q₈×C₆₇	C₂²	semidirect
185. C₄×Q₈×C₆₇	C₂²	semidirect
460. C₆₇	#3564	semidirect
484. #541	D₆₇	semidirect
499. C₄⋊Q₈	C₂×D₆₇	semidirect
540. #125	C₂×D₆₇	semidirect
541. #125	C₂×D₆₇	semidirect
542. #125	C₂×D₆₇	semidirect
543. #125	C₂×D₆₇	semidirect
544. #125	C₂×D₆₇	semidirect
611. C₄×Q₈	C₂×D₆₇	semidirect
612. C₄×Q₈	C₂×D₆₇	semidirect