Subgroups — C₂×#22574724 #31763167

Order 17152.

8122 conjugacy classes of subgroups.

The subgroup lattice has 1416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574724	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864142	C₂	1	2	yes	maximal, complemented
3	C₂×#16864138	C₂	1	2	yes	maximal, complemented
4	C₂×#16864131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864129	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864058	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16864056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16864043	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16864039	C₂	1	2	yes	maximal, complemented
10	C₂×#16864037	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16864037	C₂	1	2	yes	maximal, complemented
12	C₂×D₄×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16864030	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16864020	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16863985	C₂	1	2	yes	maximal, complemented
16	C₂×#16863985	C₂	1	2	yes	maximal, complemented
17	C₂×#16863982	C₂	1	2	yes	maximal, complemented
18	C₂×#16863965	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16863964	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16863957	C₂	1	2	yes	maximal, complemented
21	C₂×#16863947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863924	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#124×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761629	C₂²	1	2	yes	complemented
26	C₂²×#11761629	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#11761628	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
30	C₂³×D₂₆₈	C₂²	1	2	yes	complemented
31	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic
32	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
33	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
34	#16864142	C₂²	1	32	yes	complemented
35	#16864138	C₂²	1	32	yes	complemented
36	#16864131	C₂²	1	16	yes	complemented
37	#16864129	C₂²	1	16	yes	complemented
38	#16864058	C₂²	1	16	yes	complemented
39	#16864056	C₂²	1	16	yes	complemented
40	#16864043	C₂²	1	16	yes	complemented
41	#16864039	C₂²	1	32	yes	complemented
42	#16864037	C₂²	1	16	yes	complemented
43	#16864037	C₂²	1	32	yes	complemented
44	D₄×D₂₆₈	C₂²	1	16	yes	complemented
45	#16864030	C₂²	1	16	yes	complemented
46	#16864020	C₂²	1	16	yes	complemented
47	#16863985	C₂²	1	32	yes	complemented
48	#16863985	C₂²	1	32	yes	complemented
49	#16863982	C₂²	1	32	yes	complemented
50	#16863965	C₂²	1	16	yes	complemented
51	#16863964	C₂²	1	16	yes	complemented
52	#16863957	C₂²	1	32	yes	complemented
53	#16863947	C₂²	1	16	yes	complemented
54	C₂×#14524040	C₂²	1	1	yes	characteristic
55	C₂×#14524040	C₂²	1	1	yes	characteristic, complemented
56	C₂×#14524039	C₂²	1	1	yes	characteristic
57	#16863924	C₂²	1	16	yes	complemented
58	C₂×#14524038	C₂²	1	2	yes	complemented
59	C₂×#14524038	C₂²	1	1	yes	characteristic, complemented
60	C₂×#14524036	C₂²	1	1	yes	characteristic, complemented
61	C₂×#14524033	C₂²	1	1	yes	characteristic, complemented
62	C₂×#14524032	C₂²	1	2	yes	complemented
63	C₂×#14524032	C₂²	1	1	yes	characteristic, complemented
64	C₂×#14524032	C₂²	1	1	yes	characteristic, complemented
65	C₂×#14524032	C₂²	1	2	yes	complemented
66	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
67	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
68	C₂×#14524031	C₂²	1	2	yes	complemented
69	C₂×#14524031	C₂²	1	2	yes	complemented
70	C₂×#14524030	C₂²	1	1	yes	characteristic, complemented
71	C₂×#14524029	C₂²	1	2	yes	complemented
72	C₂×#14524029	C₂²	1	2	yes	complemented
73	C₂×#14524029	C₂²	1	2	yes	complemented
74	C₂×#14524029	C₂²	1	1	yes	characteristic, complemented
75	C₂×#14524029	C₂²	1	2	yes	complemented
76	#124×D₆₇	C₂²	1	16	yes	complemented
77	C₂×#14524028	C₂²	1	2	yes	complemented
78	C₂×#14524028	C₂²	1	1	yes	characteristic, complemented
79	C₂×#14524028	C₂²	1	2	yes	complemented
80	C₂×#14524028	C₂²	1	2	yes	complemented
81	C₂×#14524028	C₂²	1	2	yes	complemented
82	C₂×#14524026	C₂²	1	2	yes	complemented
83	C₂×#14524025	C₂²	1	1	yes	characteristic, complemented
84	C₂×#14524025	C₂²	1	2	yes	complemented
85	C₂×#14524025	C₂²	1	2	yes	complemented
86	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
87	C₂×#14524023	C₂²	1	2	yes	complemented
88	C₂×#14524021	C₂²	1	2	yes	complemented
89	C₂×#14524021	C₂²	1	1	yes	characteristic, complemented
90	C₂×#14524019	C₂²	1	2	yes	complemented
91	C₂×#14524018	C₂²	1	1	yes	characteristic
92	C₂×#14524018	C₂²	1	1	yes	characteristic, complemented
93	C₂×#14524018	C₂²	1	1	yes	characteristic, complemented
94	C₂×#14524018	C₂²	1	2	yes	complemented
95	C₂×#14524018	C₂²	1	2	yes	complemented
96	C₂×#14524018	C₂²	1	2	yes	complemented
97	C₂×#14524018	C₂²	1	2	yes	complemented
98	C₂×#14524018	C₂²	1	2	yes	complemented
99	C₂×#14524017	C₂²	1	2	yes	complemented
100	C₂×#14524016	C₂²	1	1	yes	characteristic
101	C₂×#14524016	C₂²	1	2	yes	complemented
102	C₂×#14524016	C₂²	1	2	yes	complemented
103	C₂×#14524016	C₂²	1	2	yes	complemented
104	C₂×#14524016	C₂²	1	2	yes	complemented
105	C₂×#14524014	C₂²	1	2	yes	complemented
106	C₂×#14524013	C₂²	1	2	yes	complemented
107	C₂×#14524013	C₂²	1	2	yes	complemented
108	C₂×#14524013	C₂²	1	2	yes	complemented
109	C₂×#14524013	C₂²	1	2	yes	complemented
110	C₂×#14524013	C₂²	1	2	yes	complemented
111	C₂×#14524013	C₂²	1	2	yes	complemented
112	C₂×#14524013	C₂²	1	2	yes	complemented
113	C₂×#14524013	C₂²	1	2	yes	complemented
114	C₂×#14524011	C₂²	1	2	yes	complemented
115	C₂×#14524011	C₂²	1	2	yes	complemented
116	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
117	C₂×#14524008	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
120	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
121	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
122	C₂×#14524005	C₂²	1	2	yes	complemented
123	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
124	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
125	C₂×#14524005	C₂²	1	2	yes	complemented
126	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
129	C₂×#14524000	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
131	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
132	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
134	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
135	#542×C₆₇	C₂²	1	16	yes	complemented
136	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
138	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
139	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
140	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
141	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
143	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
144	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
146	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₆₇	C₂³	1	2	yes	—
148	C₂⁴×D₆₇	C₂³	1	2	yes	—
149	C₂⁴×D₆₇	C₂³	1	2	yes	—
150	C₂×#11761629	—	4	4	no	—
151	C₂×#11761629	—	4	8	no	—
152	C₂×#11761629	C₂³	1	16	yes	complemented
153	C₂×#11761629	C₂³	1	8	yes	complemented
154	C₂×#11761628	—	4	4	no	—
155	C₂×#11761628	C₂³	1	8	yes	complemented
156	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
157	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
158	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
159	C₂×Q₈×D₆₇	—	4	4	no	—
160	C₂×Q₈×D₆₇	C₂³	1	8	yes	complemented
161	C₂²×D₂₆₈	—	4	4	no	—
162	C₂²×D₂₆₈	—	4	8	no	—
163	C₂²×D₂₆₈	C₂³	1	2	yes	—
164	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
165	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
166	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
167	C₂²×D₂₆₈	C₂³	1	2	yes	—
168	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
169	C₂²×D₂₆₈	C₂³	1	2	yes	—
170	C₂²×D₂₆₈	C₂³	1	2	yes	—
171	C₂²×D₂₆₈	C₂³	1	2	yes	—
172	C₂²×D₂₆₈	C₂³	1	2	yes	—
173	C₂²×D₂₆₈	C₂³	1	2	yes	—
174	C₂²×D₂₆₈	C₂³	1	2	yes	—
175	C₂²×D₂₆₈	C₂³	1	2	yes	—
176	C₂²×D₂₆₈	C₂³	1	8	yes	complemented
177	C₂²×D₂₆₈	C₂³	1	16	yes	complemented
178	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
179	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
181	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
182	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
183	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
184	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
185	C₂×D₄×D₆₇	—	4	4	no	—
186	C₂×D₄×D₆₇	—	4	4	no	—
187	C₂×D₄×D₆₇	—	4	8	no	—
188	C₂×D₄×D₆₇	C₂³	1	8	yes	—
189	C₂×D₄×D₆₇	C₂³	1	16	yes	complemented
190	C₂×D₄×D₆₇	C₂³	1	8	yes	complemented
191	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
196	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
197	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
198	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
199	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
200	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
201	#14524040	C₂³	1	8	yes	—
202	#14524040	C₂³	1	8	yes	complemented
203	#14524039	C₂³	1	8	yes	—
204	#14524038	C₂³	1	16	yes	complemented
205	#14524038	C₂³	1	8	yes	complemented
206	#14524036	C₂³	1	8	yes	complemented
207	#14524033	C₂³	1	8	yes	complemented
208	#14524032	C₂³	1	16	yes	complemented
209	#14524032	C₂³	1	8	yes	complemented
210	#14524032	C₂³	1	8	yes	complemented
211	#14524032	C₂³	1	16	yes	complemented
212	#14524031	C₂³	1	8	yes	complemented
213	#14524031	C₂³	1	8	yes	complemented
214	#14524031	C₂³	1	16	yes	complemented
215	#14524031	C₂³	1	16	yes	complemented
216	#14524030	C₂³	1	8	yes	complemented
217	#14524029	C₂³	1	16	yes	complemented
218	#14524029	C₂³	1	16	yes	complemented
219	#14524029	C₂³	1	8	yes	complemented
220	#14524029	C₂³	1	16	yes	complemented
221	#14524029	C₂³	1	16	yes	complemented
222	#14524028	C₂³	1	16	yes	complemented
223	#14524028	C₂³	1	8	yes	complemented
224	#14524028	C₂³	1	16	yes	complemented
225	#14524028	C₂³	1	16	yes	complemented
226	#14524028	C₂³	1	16	yes	complemented
227	#14524026	C₂³	1	16	yes	complemented
228	#14524025	C₂³	1	8	yes	complemented
229	#14524025	C₂³	1	16	yes	complemented
230	#14524025	C₂³	1	16	yes	complemented
231	#14524023	C₂³	1	8	yes	complemented
232	#14524023	C₂³	1	16	yes	complemented
233	#14524021	C₂³	1	16	yes	complemented
234	#14524021	C₂³	1	8	yes	complemented
235	#14524019	C₂³	1	16	yes	complemented
236	#14524018	C₂³	1	8	yes	—
237	#14524018	C₂³	1	8	yes	complemented
238	#14524018	C₂³	1	8	yes	complemented
239	#14524018	C₂³	1	16	yes	complemented
240	#14524018	C₂³	1	16	yes	complemented
241	#14524018	C₂³	1	16	yes	complemented
242	#14524018	C₂³	1	16	yes	complemented
243	#14524018	C₂³	1	16	yes	complemented
244	#14524017	C₂³	1	16	yes	complemented
245	#14524016	C₂³	1	8	yes	—
246	#14524016	C₂³	1	16	yes	complemented
247	#14524016	C₂³	1	16	yes	complemented
248	#14524016	C₂³	1	16	yes	complemented
249	#14524016	C₂³	1	16	yes	complemented
250	#14524014	C₂³	1	16	yes	complemented
251	#14524013	C₂³	1	16	yes	complemented
252	#14524013	C₂³	1	16	yes	complemented
253	#14524013	C₂³	1	16	yes	complemented
254	#14524013	C₂³	1	16	yes	complemented
255	#14524013	C₂³	1	16	yes	complemented
256	#14524013	C₂³	1	16	yes	complemented
257	#14524013	C₂³	1	16	yes	complemented
258	#14524013	C₂³	1	16	yes	complemented
259	#14524011	C₂³	1	16	yes	complemented
260	#14524011	C₂³	1	16	yes	complemented
261	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
262	#14524008	C₂³	1	8	yes	complemented
263	C₄×D₂₆₈	C₂³	1	8	yes	complemented
264	C₄×D₂₆₈	C₂³	1	16	yes	complemented
265	C₄×D₂₆₈	C₂³	1	16	yes	complemented
266	#14524005	C₂³	1	8	yes	complemented
267	#14524005	C₂³	1	16	yes	complemented
268	#14524005	C₂³	1	8	yes	complemented
269	#14524005	C₂³	1	8	yes	complemented
270	#14524005	C₂³	1	16	yes	complemented
271	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
272	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
273	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
274	#14524000	C₂³	1	8	yes	complemented
275	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
277	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
278	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
284	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
287	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
288	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
289	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
291	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
292	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
293	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
294	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
295	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
296	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
300	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
301	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
302	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
303	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
304	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
305	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
306	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
307	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
308	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
309	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
310	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
311	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
312	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
313	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
314	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
315	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
316	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
317	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
318	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
319	C₄²×D₆₇	C₂³	1	8	yes	complemented
320	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
321	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
322	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
324	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
325	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
326	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
327	#126×C₆₇	C₂³	1	16	yes	complemented
328	#124×C₆₇	C₂³	1	16	yes	complemented
329	#124×C₆₇	C₂³	1	8	yes	complemented
330	#123×C₆₇	C₂³	1	16	yes	complemented
331	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
332	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
333	#121×C₆₇	C₂³	1	8	yes	—
334	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
335	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
336	#117×C₆₇	C₂³	1	8	yes	complemented
337	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
342	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
343	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
344	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
347	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
348	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
349	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
350	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
351	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
353	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
354	C₂³×D₆₇	—	2	8	no	—
355	C₂³×D₆₇	—	4	4	no	—
356	C₂³×D₆₇	—	4	4	no	—
357	C₂³×D₆₇	—	4	4	no	—
358	C₂³×D₆₇	—	4	4	no	—
359	C₂³×D₆₇	—	4	4	no	—
360	C₂³×D₆₇	—	4	4	no	—
361	C₂³×D₆₇	—	4	4	no	—
362	C₂³×D₆₇	—	4	4	no	—
363	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
364	C₂³×D₆₇	C₂⁴	1	2	yes	—
365	C₂³×D₆₇	C₂⁴	1	2	yes	—
366	C₂³×D₆₇	C₂⁴	1	2	yes	—
367	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
368	C₂³×D₆₇	C₂⁴	1	8	yes	—
369	C₂³×D₆₇	C₂⁴	1	8	yes	—
370	C₂³×D₆₇	C₂⁴	1	8	yes	—
371	#11761629	—	4	32	no	—
372	#11761629	—	4	16	no	—
373	#11761628	—	4	16	no	—
374	C₂×Dic₁₃₄	—	2	4	no	—
375	C₂×Dic₁₃₄	—	4	4	no	—
376	C₂×Dic₁₃₄	—	4	2	no	—
377	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
378	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
379	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
380	Q₈×D₆₇	—	4	16	no	—
381	C₂×D₂₆₈	—	2	8	no	—
382	C₂×D₂₆₈	—	2	4	no	—
383	C₂×D₂₆₈	—	2	8	no	—
384	C₂×D₂₆₈	—	2	4	no	—
385	C₂×D₂₆₈	—	2	4	no	—
386	C₂×D₂₆₈	—	2	4	no	—
387	C₂×D₂₆₈	—	4	16	no	—
388	C₂×D₂₆₈	—	4	32	no	—
389	C₂×D₂₆₈	—	4	4	no	—
390	C₂×D₂₆₈	—	4	4	no	—
391	C₂×D₂₆₈	—	4	4	no	—
392	C₂×D₂₆₈	—	4	4	no	—
393	C₂×D₂₆₈	—	4	4	no	—
394	C₂×D₂₆₈	—	4	4	no	—
395	C₂×D₂₆₈	—	4	4	no	—
396	C₂×D₂₆₈	C₂⁴	1	8	yes	—
397	C₂×D₂₆₈	C₂⁴	1	4	yes	—
398	C₂×D₂₆₈	C₂⁴	1	4	yes	—
399	C₂×D₂₆₈	C₂⁴	1	4	yes	—
400	C₂×D₂₆₈	C₂⁴	1	8	yes	—
401	C₂×D₂₆₈	C₂⁴	1	4	yes	—
402	C₂×D₂₆₈	C₂⁴	1	8	yes	—
403	C₂×D₂₆₈	C₂⁴	1	8	yes	—
404	C₂×D₂₆₈	C₂⁴	1	8	yes	—
405	C₂×D₂₆₈	C₂⁴	1	8	yes	—
406	C₂×D₂₆₈	C₂⁴	1	8	yes	—
407	C₂×D₂₆₈	C₂⁴	1	8	yes	—
408	C₂×D₂₆₈	C₂⁴	1	8	yes	—
409	C₂×C₂²⋊D₆₇	—	2	4	no	—
410	C₂×C₂²⋊D₆₇	—	4	4	no	—
411	C₂×C₂²⋊D₆₇	—	4	4	no	—
412	C₂×C₂²⋊D₆₇	—	4	4	no	—
413	C₂×C₂²⋊D₆₇	—	4	2	no	—
414	C₂×C₂²⋊D₆₇	—	4	4	no	—
415	C₂×C₂²⋊D₆₇	—	4	4	no	—
416	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
417	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
418	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
419	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
420	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
421	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
422	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
423	D₄×D₆₇	—	4	16	no	—
424	D₄×D₆₇	—	4	16	no	—
425	D₄×D₆₇	—	4	32	no	—
426	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
428	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
429	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
430	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
431	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
432	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
433	C₂×C₄×D₆₇	—	2	4	no	—
434	C₂×C₄×D₆₇	—	2	4	no	—
435	C₂×C₄×D₆₇	—	2	4	no	—
436	C₂×C₄×D₆₇	—	4	2	no	—
437	C₂×C₄×D₆₇	—	4	4	no	—
438	C₂×C₄×D₆₇	—	4	4	no	—
439	C₂×C₄×D₆₇	—	4	4	no	—
440	C₂×C₄×D₆₇	—	4	4	no	—
441	C₂×C₄×D₆₇	—	4	4	no	—
442	C₂×C₄×D₆₇	—	4	4	no	—
443	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
444	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
445	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
446	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
447	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
448	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
449	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
450	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
451	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
452	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
453	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
454	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
455	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
456	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
457	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
458	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
459	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
460	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
461	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
462	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
463	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
464	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
465	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
466	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
467	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
468	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
469	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
470	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
471	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
472	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
473	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
474	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
475	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
476	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	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	4	yes	—
485	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
486	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
487	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	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	8	yes	—
493	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
494	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
495	C₂×Q₈×C₆₇	—	2	4	no	—
496	C₂×Q₈×C₆₇	—	4	4	no	—
497	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
498	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
499	C₂×D₄×C₆₇	—	2	4	no	—
500	C₂×D₄×C₆₇	—	4	4	no	—
501	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
502	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
503	C₂²×C₄×C₆₇	—	2	4	no	—
504	C₂²×C₄×C₆₇	—	4	4	no	—
505	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
507	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
508	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
510	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
511	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
512	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
513	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
514	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
515	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
516	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
517	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
518	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
519	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
520	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
521	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
522	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
523	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
524	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
525	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
526	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
527	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
528	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
529	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
530	C₄²×C₆₇	C₂⁴	1	4	yes	—
531	C₄²×C₆₇	C₂⁴	1	4	yes	—
532	C₄²×C₆₇	C₂⁴	1	8	yes	—
533	C₂³×C₆₇	—	2	2	no	—
534	C₂³×C₆₇	—	2	4	no	—
535	C₂³×C₆₇	—	2	4	no	—
536	C₂³×C₆₇	—	2	2	no	—
537	C₂³×C₆₇	—	2	4	no	—
538	C₂³×C₆₇	—	2	2	no	—
539	C₂³×C₆₇	C₂⁵	1	2	yes	—
540	C₂³×C₆₇	C₂⁵	1	4	yes	—
541	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
542	C₂²×D₆₇	—	2	2	no	—
543	C₂²×D₆₇	—	2	2	no	—
544	C₂²×D₆₇	—	2	2	no	—
545	C₂²×D₆₇	—	2	4	no	—
546	C₂²×D₆₇	—	2	4	no	—
547	C₂²×D₆₇	—	2	4	no	—
548	C₂²×D₆₇	—	2	4	no	—
549	C₂²×D₆₇	—	2	4	no	—
550	C₂²×D₆₇	—	2	4	no	—
551	C₂²×D₆₇	—	2	2	no	—
552	C₂²×D₆₇	—	2	4	no	—
553	C₂²×D₆₇	—	2	2	no	—
554	C₂²×D₆₇	—	2	4	no	—
555	C₂²×D₆₇	—	2	4	no	—
556	C₂²×D₆₇	—	2	16	no	—
557	C₂²×D₆₇	—	4	8	no	—
558	C₂²×D₆₇	—	4	8	no	—
559	C₂²×D₆₇	—	4	8	no	—
560	C₂²×D₆₇	—	4	8	no	—
561	C₂²×D₆₇	—	4	8	no	—
562	C₂²×D₆₇	—	4	8	no	—
563	C₂²×D₆₇	—	4	8	no	—
564	C₂²×D₆₇	—	4	8	no	—
565	C₂²×D₆₇	—	8	16	no	—
566	C₂²×D₆₇	—	8	16	no	—
567	C₂²×D₆₇	—	8	16	no	—
568	C₂²×D₆₇	H(5,𝔽₂)	1	4	yes	—
569	C₂²×D₆₇	C₂⁵	1	2	yes	—
570	C₂²×D₆₇	C₂⁵	1	4	yes	—
571	C₂²×D₆₇	C₂⁵	1	4	yes	—
572	C₂²×D₆₇	C₂⁵	1	4	yes	—
573	C₂²×D₆₇	C₂⁵	1	2	yes	—
574	Q₈×C₆₇	—	2	8	no	—
575	Q₈×C₆₇	—	4	8	no	—
576	D₄×C₆₇	—	2	8	no	—
577	D₄×C₆₇	—	4	8	no	—
578	C₂×C₄×C₆₇	—	2	2	no	—
579	C₂×C₄×C₆₇	—	2	2	no	—
580	C₂×C₄×C₆₇	—	2	4	no	—
581	C₂×C₄×C₆₇	—	2	4	no	—
582	C₂×C₄×C₆₇	—	2	4	no	—
583	C₂×C₄×C₆₇	—	2	2	no	—
584	C₂×C₄×C₆₇	—	2	2	no	—
585	C₂×C₄×C₆₇	—	2	2	no	—
586	C₂×C₄×C₆₇	—	2	8	no	—
587	C₂×C₄×C₆₇	—	4	8	no	—
588	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
589	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
590	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
591	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
592	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
593	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
594	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
595	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
596	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
597	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
598	C₂²⋊D₆₇	—	2	8	no	—
599	C₂²⋊D₆₇	—	4	8	no	—
600	C₂²⋊D₆₇	—	4	8	no	—
601	C₂²⋊D₆₇	—	4	8	no	—
602	C₂²⋊D₆₇	—	4	4	no	—
603	C₂²⋊D₆₇	—	4	8	no	—
604	C₂²⋊D₆₇	—	4	8	no	—
605	C₂×Dic₆₇	—	2	2	no	—
606	C₂×Dic₆₇	—	2	2	no	—
607	C₂×Dic₆₇	—	2	2	no	—
608	C₂×Dic₆₇	—	2	2	no	—
609	C₂×Dic₆₇	—	2	4	no	—
610	C₂×Dic₆₇	—	2	2	no	—
611	C₂×Dic₆₇	—	2	2	no	—
612	C₂×Dic₆₇	C₂⁵	1	2	yes	—
613	C₂×Dic₆₇	C₂⁵	1	2	yes	—
614	C₂×Dic₆₇	C₂⁵	1	2	yes	—
615	C₂×Dic₆₇	C₂⁵	1	2	yes	—
616	C₂×Dic₆₇	C₂⁵	1	4	yes	—
617	C₂×Dic₆₇	C₂⁵	1	2	yes	—
618	C₂×Dic₆₇	C₂⁵	1	2	yes	—
619	D₂₆₈	—	2	16	no	—
620	D₂₆₈	—	2	8	no	—
621	D₂₆₈	—	2	16	no	—
622	D₂₆₈	—	2	8	no	—
623	D₂₆₈	—	2	8	no	—
624	D₂₆₈	—	2	8	no	—
625	D₂₆₈	—	4	8	no	—
626	D₂₆₈	—	4	8	no	—
627	D₂₆₈	—	4	8	no	—
628	D₂₆₈	—	4	8	no	—
629	D₂₆₈	—	4	8	no	—
630	D₂₆₈	—	4	8	no	—
631	D₂₆₈	—	4	8	no	—
632	C₄×D₆₇	—	2	8	no	—
633	C₄×D₆₇	—	2	8	no	—
634	C₄×D₆₇	—	2	8	no	—
635	C₄×D₆₇	—	4	4	no	—
636	C₄×D₆₇	—	4	8	no	—
637	C₄×D₆₇	—	4	8	no	—
638	C₄×D₆₇	—	4	8	no	—
639	C₄×D₆₇	—	4	8	no	—
640	C₄×D₆₇	—	4	8	no	—
641	C₄×D₆₇	—	4	8	no	—
642	Dic₁₃₄	—	2	8	no	—
643	Dic₁₃₄	—	4	8	no	—
644	Dic₁₃₄	—	4	4	no	—
645	C₂²×C₆₇	—	2	2	no	—
646	C₂²×C₆₇	—	2	2	no	—
647	C₂²×C₆₇	—	2	4	no	—
648	C₂²×C₆₇	—	2	4	no	—
649	C₂²×C₆₇	—	2	4	no	—
650	C₂²×C₆₇	—	2	2	no	—
651	C₂²×C₆₇	—	4	8	no	—
652	C₂²×C₆₇	—	4	4	no	—
653	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
654	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
655	C₂²×C₆₇	#585	1	2	yes	—
656	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
657	C₂×D₆₇	—	2	2	no	—
658	C₂×D₆₇	—	2	2	no	—
659	C₂×D₆₇	—	2	8	no	—
660	C₂×D₆₇	—	2	2	no	—
661	C₂×D₆₇	—	2	4	no	—
662	C₂×D₆₇	—	2	4	no	—
663	C₂×D₆₇	—	2	4	no	—
664	C₂×D₆₇	—	2	4	no	—
665	C₂×D₆₇	—	2	4	no	—
666	C₂×D₆₇	—	2	2	no	—
667	C₂×D₆₇	—	2	4	no	—
668	C₂×D₆₇	—	2	4	no	—
669	C₂×D₆₇	—	2	4	no	—
670	C₂×D₆₇	—	2	4	no	—
671	C₂×D₆₇	—	2	2	no	—
672	C₂×D₆₇	—	4	8	no	—
673	C₂×D₆₇	—	4	8	no	—
674	C₂×D₆₇	—	4	4	no	—
675	C₂×D₆₇	—	4	8	no	—
676	C₂×D₆₇	—	8	16	no	—
677	C₂×D₆₇	—	8	16	no	—
678	C₂×D₆₇	—	8	16	no	—
679	C₂×D₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
680	C₄×C₆₇	—	2	4	no	—
681	C₄×C₆₇	—	2	2	no	—
682	C₄×C₆₇	—	2	4	no	—
683	C₄×C₆₇	—	2	2	no	—
684	C₄×C₆₇	—	2	4	no	—
685	C₄×C₆₇	—	2	2	no	—
686	C₄×C₆₇	—	2	2	no	—
687	C₄×C₆₇	—	2	2	no	—
688	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
689	Dic₆₇	—	2	4	no	—
690	Dic₆₇	—	2	2	no	—
691	Dic₆₇	—	2	2	no	—
692	Dic₆₇	—	2	2	no	—
693	Dic₆₇	—	2	2	no	—
694	Dic₆₇	—	2	2	no	—
695	Dic₆₇	—	2	2	no	—
696	C₂×#3558	—	67	1	no	maximal, Sylow
697	C₂×C₆₇	—	4	4	no	—
698	C₂×C₆₇	—	4	2	no	—
699	C₂×C₆₇	#3558	1	4	yes	complemented
700	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
703	D₆₇	—	2	4	no	—
704	D₆₇	—	4	4	no	—
705	D₆₇	—	4	4	no	—
706	D₆₇	—	4	2	no	—
707	D₆₇	—	4	4	no	—
708	#3558	—	67	32	no	—
709	C₂×#562	—	67	2	no	—
710	C₂×H(3,𝔽₄)	—	67	2	no	—
711	C₂×#559	—	67	1	no	—
712	C₂×#559	—	67	1	no	—
713	C₂×#548	—	67	1	no	—
714	C₂×#548	—	67	1	no	—
715	C₂×#546	—	67	2	no	—
716	C₂×#546	—	67	2	no	—
717	C₂×#546	—	67	1	no	—
718	C₂×#546	—	67	1	no	—
719	C₂×D₄²	—	67	1	no	—
720	C₂×D₄²	—	67	1	no	—
721	C₂×#542	—	67	1	no	—
722	C₂×#542	D₆₇	1	1	yes	characteristic, complemented
723	C₂×#538	—	67	2	no	—
724	C₂×#538	—	67	2	no	—
725	C₂×#538	—	67	2	no	—
726	C₂×#535	—	67	1	no	—
727	C₂×#535	—	67	1	no	—
728	C₂×#534	—	67	2	no	—
729	C₂×#532	—	67	1	no	—
730	C₂×#529	—	67	1	no	—
731	C₂²×#124	—	67	1	no	—
732	C₆₇	C₂×#3558	1	1	yes	characteristic, complemented, Sylow
733	C₂²×#41	—	67	2	no	—
734	C₂²×#41	—	67	1	no	—
735	C₂²×#41	—	67	1	no	—
736	C₂³×Q₈	—	67	1	no	—
737	C₂³×D₄	—	67	1	no	—
738	C₂³×D₄	—	67	2	no	—
739	C₂³×D₄	—	67	1	no	—
740	C₂³×D₄	—	67	2	no	—
741	C₂³×D₄	—	67	1	no	—
742	#562	—	67	32	no	—
743	H(3,𝔽₄)	—	67	32	no	—
744	#559	—	67	16	no	—
745	#559	—	67	16	no	—
746	#548	—	67	16	no	—
747	#548	—	67	16	no	—
748	#546	—	67	32	no	—
749	#546	—	67	32	no	—
750	#546	—	67	16	no	—
751	#546	—	67	16	no	—
752	D₄²	—	67	16	no	—
753	D₄²	—	67	16	no	—
754	#542	—	67	16	no	—
755	#542	C₂×D₆₇	1	16	yes	complemented
756	#538	—	67	32	no	—
757	#538	—	67	32	no	—
758	#538	—	67	32	no	—
759	#535	—	67	16	no	—
760	#535	—	67	16	no	—
761	#534	—	67	32	no	—
762	#532	—	67	16	no	—
763	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
764	C₂×#127	—	67	1	no	—
765	C₂×#127	—	67	1	no	—
766	C₂×#127	—	67	1	no	—
767	#529	—	67	16	no	—
768	C₂×#126	—	67	1	no	—
769	C₂×#126	—	67	2	no	—
770	C₂×#126	—	67	1	no	—
771	C₂×#126	C₂×D₆₇	1	2	yes	complemented
772	C₂×#125	—	67	1	no	—
773	C₂×#124	—	67	1	no	—
774	C₂×#124	—	67	2	no	—
775	C₂×#124	—	67	1	no	—
776	C₂×#124	—	67	2	no	—
777	C₂×#124	—	67	1	no	—
778	C₂×#124	—	67	16	no	—
779	C₂×#124	—	67	2	no	—
780	C₂×#124	—	67	2	no	—
781	C₂×#124	—	67	1	no	—
782	C₂×#124	—	67	2	no	—
783	C₂×#124	—	67	2	no	—
784	C₂×#124	—	67	1	no	—
785	C₂×#124	—	67	1	no	—
786	C₂×#124	—	67	2	no	—
787	C₂×#124	—	67	2	no	—
788	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
789	C₂×#124	C₂×D₆₇	1	2	yes	complemented
790	C₂×#123	—	67	2	no	—
791	C₂×#123	—	67	1	no	—
792	C₂×#123	—	67	2	no	—
793	C₂×#123	—	67	2	no	—
794	C₂×#123	—	67	2	no	—
795	C₂×#123	—	67	2	no	—
796	C₂×#123	—	67	1	no	—
797	C₂×#123	—	67	2	no	—
798	C₂×#123	—	67	2	no	—
799	C₂×#123	C₂×D₆₇	1	2	yes	complemented
800	C₂×C₂²⋊Q₈	—	67	2	no	—
801	C₂×C₂²⋊Q₈	—	67	1	no	—
802	C₂×C₂²⋊Q₈	—	67	2	no	—
803	C₂×C₂²⋊Q₈	—	67	2	no	—
804	C₂×C₂²⋊Q₈	—	67	1	no	—
805	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
806	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
807	C₂×#121	—	67	2	no	—
808	C₂×#121	—	67	2	no	—
809	C₂×#121	—	67	2	no	—
810	C₂×#121	—	67	1	no	—
811	C₂×#121	—	67	1	no	—
812	C₂×#121	—	67	2	no	—
813	C₂×#121	—	67	2	no	—
814	C₂×#121	—	67	2	no	—
815	C₂×#121	—	67	2	no	—
816	C₂×#121	—	67	1	no	—
817	C₂×#121	—	67	1	no	—
818	C₂×#121	—	67	2	no	—
819	C₂×#121	—	67	2	no	—
820	C₂×#121	—	67	2	no	—
821	C₂×#121	—	67	2	no	—
822	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
823	C₂×#120	—	67	2	no	—
824	C₂×#120	—	67	2	no	—
825	C₂×#120	—	67	2	no	—
826	C₂×#120	—	67	2	no	—
827	C₂×#120	—	67	2	no	—
828	C₂×#120	—	67	2	no	—
829	C₂×#120	—	67	2	no	—
830	C₂×#120	—	67	2	no	—
831	C₂×#120	—	67	2	no	—
832	C₂×#120	—	67	2	no	—
833	C₂×C₄×Q₈	—	67	1	no	—
834	C₂×C₄×Q₈	—	67	1	no	—
835	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
836	C₂×C₄×D₄	—	67	1	no	—
837	C₂×C₄×D₄	—	67	1	no	—
838	C₂×C₄×D₄	—	67	2	no	—
839	C₂×C₄×D₄	—	67	2	no	—
840	C₂×C₄×D₄	—	67	1	no	—
841	C₂×C₄×D₄	—	67	1	no	—
842	C₂×C₄×D₄	—	67	2	no	—
843	C₂×C₄×D₄	—	67	1	no	—
844	C₂×C₄×D₄	—	67	1	no	—
845	C₂×C₄×D₄	—	67	2	no	—
846	C₂×C₄×D₄	—	67	2	no	—
847	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
848	C₂×#117	—	67	1	no	—
849	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
850	C₂²×C₂²⋊C₄	—	67	2	no	—
851	C₂²×C₂²⋊C₄	—	67	2	no	—
852	C₂²×C₂²⋊C₄	—	67	2	no	—
853	C₂²×C₂²⋊C₄	—	67	2	no	—
854	C₂²×C₄²	—	67	1	no	—
855	C₂⁵	—	67	2	no	—
856	C₂⁵	—	67	2	no	—
857	C₂⁵	—	67	2	no	—
858	C₂×#41	—	268	4	no	—
859	C₂×#41	—	268	4	no	—
860	C₂×#41	—	268	8	no	—
861	C₂×#41	—	67	16	no	—
862	C₂×#41	—	67	8	no	—
863	C₂×#41	—	67	8	no	—
864	C₂²×Q₈	—	268	4	no	—
865	C₂²×Q₈	—	67	8	no	—
866	C₂²×Q₈	—	67	1	no	—
867	C₂²×Q₈	—	67	2	no	—
868	C₂²×Q₈	—	67	1	no	—
869	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
870	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
871	C₂²×D₄	—	268	4	no	—
872	C₂²×D₄	—	268	8	no	—
873	C₂²×D₄	—	268	8	no	—
874	C₂²×D₄	—	268	4	no	—
875	C₂²×D₄	—	268	4	no	—
876	C₂²×D₄	—	67	1	no	—
877	C₂²×D₄	—	67	2	no	—
878	C₂²×D₄	—	67	2	no	—
879	C₂²×D₄	—	67	2	no	—
880	C₂²×D₄	—	67	2	no	—
881	C₂²×D₄	—	67	2	no	—
882	C₂²×D₄	—	67	8	no	—
883	C₂²×D₄	—	67	16	no	—
884	C₂²×D₄	—	67	8	no	—
885	C₂²×D₄	—	67	1	no	—
886	C₂²×D₄	—	67	2	no	—
887	C₂²×D₄	—	67	2	no	—
888	C₂²×D₄	—	67	2	no	—
889	C₂²×D₄	—	67	2	no	—
890	C₂²×D₄	—	67	2	no	—
891	C₂²×D₄	—	67	2	no	—
892	C₂²×D₄	—	67	2	no	—
893	C₂²×D₄	—	67	16	no	—
894	C₂²×D₄	—	67	8	no	—
895	C₂²×D₄	—	67	2	no	—
896	C₂²×D₄	—	67	2	no	—
897	C₂²×D₄	—	67	1	no	—
898	C₂²×D₄	—	67	1	no	—
899	C₂²×D₄	—	67	1	no	—
900	C₂²×D₄	—	67	1	no	—
901	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
902	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
903	C₂³×C₄	—	67	2	no	—
904	C₂³×C₄	—	67	1	no	—
905	C₂³×C₄	—	67	2	no	—
906	C₂³×C₄	—	67	2	no	—
907	C₂³×C₄	—	67	2	no	—
908	C₂³×C₄	—	67	2	no	—
909	C₂³×C₄	—	67	2	no	—
910	C₂³×C₄	—	67	1	no	—
911	C₂³×C₄	—	67	1	no	—
912	C₂³×C₄	—	67	1	no	—
913	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
914	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
915	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
916	#127	—	67	8	no	—
917	#127	—	67	8	no	—
918	#127	—	67	8	no	—
919	#126	—	67	8	no	—
920	#126	—	67	16	no	—
921	#126	—	67	8	no	—
922	#126	C₂²×D₆₇	1	16	yes	complemented
923	#125	—	67	8	no	—
924	#124	—	67	8	no	—
925	#124	—	67	16	no	—
926	#124	—	67	8	no	—
927	#124	—	67	16	no	—
928	#124	—	67	8	no	—
929	#124	—	67	16	no	—
930	#124	—	67	16	no	—
931	#124	—	67	8	no	—
932	#124	—	67	16	no	—
933	#124	—	67	16	no	—
934	#124	—	67	8	no	—
935	#124	—	67	8	no	—
936	#124	—	67	16	no	—
937	#124	—	67	16	no	—
938	#124	C₂²×D₆₇	1	8	yes	complemented
939	#124	C₂²×D₆₇	1	16	yes	complemented
940	#123	—	67	16	no	—
941	#123	—	67	8	no	—
942	#123	—	67	16	no	—
943	#123	—	67	16	no	—
944	#123	—	67	16	no	—
945	#123	—	67	16	no	—
946	#123	—	67	8	no	—
947	#123	—	67	16	no	—
948	#123	—	67	16	no	—
949	#123	C₂²×D₆₇	1	16	yes	complemented
950	C₂²⋊Q₈	—	67	16	no	—
951	C₂²⋊Q₈	—	67	8	no	—
952	C₂²⋊Q₈	—	67	16	no	—
953	C₂²⋊Q₈	—	67	16	no	—
954	C₂²⋊Q₈	—	67	8	no	—
955	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
956	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
957	#121	—	67	16	no	—
958	#121	—	67	16	no	—
959	#121	—	67	16	no	—
960	#121	—	67	8	no	—
961	#121	—	67	8	no	—
962	#121	—	67	16	no	—
963	#121	—	67	16	no	—
964	#121	—	67	16	no	—
965	#121	—	67	16	no	—
966	#121	—	67	8	no	—
967	#121	—	67	8	no	—
968	#121	—	67	16	no	—
969	#121	—	67	16	no	—
970	#121	—	67	16	no	—
971	#121	—	67	16	no	—
972	#121	C₂²×D₆₇	1	8	yes	—
973	#120	—	67	16	no	—
974	#120	—	67	16	no	—
975	#120	—	67	16	no	—
976	#120	—	67	16	no	—
977	#120	—	67	16	no	—
978	#120	—	67	16	no	—
979	#120	—	67	16	no	—
980	#120	—	67	16	no	—
981	#120	—	67	16	no	—
982	#120	—	67	16	no	—
983	C₄×Q₈	—	67	8	no	—
984	C₄×Q₈	—	67	8	no	—
985	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
986	C₄×D₄	—	67	8	no	—
987	C₄×D₄	—	67	8	no	—
988	C₄×D₄	—	67	16	no	—
989	C₄×D₄	—	67	16	no	—
990	C₄×D₄	—	67	8	no	—
991	C₄×D₄	—	67	8	no	—
992	C₄×D₄	—	67	16	no	—
993	C₄×D₄	—	67	8	no	—
994	C₄×D₄	—	67	8	no	—
995	C₄×D₄	—	67	16	no	—
996	C₄×D₄	—	67	16	no	—
997	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
998	#117	—	67	8	no	—
999	#117	C₂²×D₆₇	1	8	yes	complemented
1000	C₂×C₄⋊C₄	—	67	1	no	—
1001	C₂×C₄⋊C₄	—	67	1	no	—
1002	C₂×C₄⋊C₄	—	67	1	no	—
1003	C₂×C₄⋊C₄	—	67	1	no	—
1004	C₂×C₄⋊C₄	—	67	1	no	—
1005	C₂×C₄⋊C₄	—	67	1	no	—
1006	C₂×C₄⋊C₄	—	67	2	no	—
1007	C₂×C₄⋊C₄	—	67	1	no	—
1008	C₂×C₄⋊C₄	—	67	2	no	—
1009	C₂×C₄⋊C₄	—	67	1	no	—
1010	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1014	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
1015	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
1016	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
1017	C₂×C₂²⋊C₄	—	67	1	no	—
1018	C₂×C₂²⋊C₄	—	67	2	no	—
1019	C₂×C₂²⋊C₄	—	67	2	no	—
1020	C₂×C₂²⋊C₄	—	67	1	no	—
1021	C₂×C₂²⋊C₄	—	67	1	no	—
1022	C₂×C₂²⋊C₄	—	67	2	no	—
1023	C₂×C₂²⋊C₄	—	67	2	no	—
1024	C₂×C₂²⋊C₄	—	67	2	no	—
1025	C₂×C₂²⋊C₄	—	67	2	no	—
1026	C₂×C₂²⋊C₄	—	67	2	no	—
1027	C₂×C₂²⋊C₄	—	67	2	no	—
1028	C₂×C₂²⋊C₄	—	67	1	no	—
1029	C₂×C₂²⋊C₄	—	67	1	no	—
1030	C₂×C₂²⋊C₄	—	67	1	no	—
1031	C₂×C₂²⋊C₄	—	67	1	no	—
1032	C₂×C₂²⋊C₄	—	67	2	no	—
1033	C₂×C₂²⋊C₄	—	67	1	no	—
1034	C₂×C₂²⋊C₄	—	67	2	no	—
1035	C₂×C₂²⋊C₄	—	67	2	no	—
1036	C₂×C₂²⋊C₄	—	67	2	no	—
1037	C₂×C₂²⋊C₄	—	67	2	no	—
1038	C₂×C₂²⋊C₄	—	67	2	no	—
1039	C₂×C₂²⋊C₄	—	67	2	no	—
1040	C₂×C₂²⋊C₄	—	67	2	no	—
1041	C₂×C₂²⋊C₄	—	67	2	no	—
1042	C₂×C₂²⋊C₄	—	67	16	no	—
1043	C₂×C₂²⋊C₄	—	67	16	no	—
1044	C₂×C₂²⋊C₄	—	67	16	no	—
1045	C₂×C₂²⋊C₄	—	67	16	no	—
1046	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1047	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1048	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1049	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1050	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1053	C₂×C₄²	—	67	1	no	—
1054	C₂×C₄²	—	67	1	no	—
1055	C₂×C₄²	—	67	2	no	—
1056	C₂×C₄²	—	67	1	no	—
1057	C₂×C₄²	—	67	1	no	—
1058	C₂×C₄²	—	67	8	no	—
1059	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1060	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1061	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1062	C₂⁴	—	268	4	no	—
1063	C₂⁴	—	268	4	no	—
1064	C₂⁴	—	268	4	no	—
1065	C₂⁴	—	268	4	no	—
1066	C₂⁴	—	268	4	no	—
1067	C₂⁴	—	268	4	no	—
1068	C₂⁴	—	268	4	no	—
1069	C₂⁴	—	268	4	no	—
1070	C₂⁴	—	67	8	no	—
1071	C₂⁴	—	67	8	no	—
1072	C₂⁴	—	67	8	no	—
1073	C₂⁴	—	67	1	no	—
1074	C₂⁴	—	67	2	no	—
1075	C₂⁴	—	67	1	no	—
1076	C₂⁴	—	67	2	no	—
1077	C₂⁴	—	67	2	no	—
1078	C₂⁴	—	134	8	no	—
1079	C₂⁴	C₂³×D₆₇	1	2	yes	—
1080	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1081	#41	—	268	16	no	—
1082	#41	—	268	16	no	—
1083	#41	—	268	32	no	—
1084	C₂×Q₈	—	2	4	no	—
1085	C₂×Q₈	—	4	4	no	—
1086	C₂×Q₈	—	268	4	no	—
1087	C₂×Q₈	—	268	2	no	—
1088	C₂×Q₈	—	268	16	no	—
1089	C₂×Q₈	—	67	4	no	—
1090	C₂×Q₈	—	67	8	no	—
1091	C₂×Q₈	—	67	4	no	—
1092	C₂×Q₈	—	134	4	no	—
1093	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1094	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
1095	C₂×D₄	—	2	4	no	—
1096	C₂×D₄	—	4	4	no	—
1097	C₂×D₄	—	268	4	no	—
1098	C₂×D₄	—	268	4	no	—
1099	C₂×D₄	—	268	4	no	—
1100	C₂×D₄	—	268	4	no	—
1101	C₂×D₄	—	268	4	no	—
1102	C₂×D₄	—	268	4	no	—
1103	C₂×D₄	—	268	4	no	—
1104	C₂×D₄	—	268	16	no	—
1105	C₂×D₄	—	268	32	no	—
1106	C₂×D₄	—	268	32	no	—
1107	C₂×D₄	—	268	16	no	—
1108	C₂×D₄	—	268	16	no	—
1109	C₂×D₄	—	268	4	no	—
1110	C₂×D₄	—	268	4	no	—
1111	C₂×D₄	—	268	4	no	—
1112	C₂×D₄	—	268	4	no	—
1113	C₂×D₄	—	268	2	no	—
1114	C₂×D₄	—	268	4	no	—
1115	C₂×D₄	—	67	4	no	—
1116	C₂×D₄	—	67	8	no	—
1117	C₂×D₄	—	67	8	no	—
1118	C₂×D₄	—	67	8	no	—
1119	C₂×D₄	—	67	8	no	—
1120	C₂×D₄	—	67	8	no	—
1121	C₂×D₄	—	67	4	no	—
1122	C₂×D₄	—	67	8	no	—
1123	C₂×D₄	—	67	8	no	—
1124	C₂×D₄	—	67	8	no	—
1125	C₂×D₄	—	67	8	no	—
1126	C₂×D₄	—	67	8	no	—
1127	C₂×D₄	—	67	8	no	—
1128	C₂×D₄	—	67	8	no	—
1129	C₂×D₄	—	67	8	no	—
1130	C₂×D₄	—	67	8	no	—
1131	C₂×D₄	—	67	4	no	—
1132	C₂×D₄	—	67	4	no	—
1133	C₂×D₄	—	67	4	no	—
1134	C₂×D₄	—	67	4	no	—
1135	C₂×D₄	—	134	4	no	—
1136	C₂×D₄	—	134	8	no	—
1137	C₂×D₄	—	134	8	no	—
1138	C₂×D₄	—	134	4	no	—
1139	C₂×D₄	—	134	4	no	—
1140	C₂×D₄	—	134	4	no	—
1141	C₂×D₄	—	134	4	no	—
1142	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1143	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1144	C₂²×C₄	—	2	4	no	—
1145	C₂²×C₄	—	4	4	no	—
1146	C₂²×C₄	—	268	4	no	—
1147	C₂²×C₄	—	268	4	no	—
1148	C₂²×C₄	—	268	4	no	—
1149	C₂²×C₄	—	268	4	no	—
1150	C₂²×C₄	—	268	4	no	—
1151	C₂²×C₄	—	268	4	no	—
1152	C₂²×C₄	—	268	2	no	—
1153	C₂²×C₄	—	67	4	no	—
1154	C₂²×C₄	—	67	8	no	—
1155	C₂²×C₄	—	67	8	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	1	no	—
1161	C₂²×C₄	—	67	1	no	—
1162	C₂²×C₄	—	67	1	no	—
1163	C₂²×C₄	—	67	1	no	—
1164	C₂²×C₄	—	67	2	no	—
1165	C₂²×C₄	—	67	1	no	—
1166	C₂²×C₄	—	67	1	no	—
1167	C₂²×C₄	—	67	4	no	—
1168	C₂²×C₄	—	67	4	no	—
1169	C₂²×C₄	—	67	4	no	—
1170	C₂²×C₄	—	134	4	no	—
1171	C₂²×C₄	—	134	4	no	—
1172	C₂²×C₄	—	134	4	no	—
1173	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1174	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1175	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1176	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1177	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1178	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1179	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1180	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1181	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1182	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1183	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1184	C₄⋊C₄	—	67	4	no	—
1185	C₄⋊C₄	—	67	4	no	—
1186	C₄⋊C₄	—	67	4	no	—
1187	C₄⋊C₄	—	67	4	no	—
1188	C₄⋊C₄	—	67	4	no	—
1189	C₄⋊C₄	—	67	4	no	—
1190	C₄⋊C₄	—	67	8	no	—
1191	C₄⋊C₄	—	67	4	no	—
1192	C₄⋊C₄	—	67	8	no	—
1193	C₄⋊C₄	—	67	4	no	—
1194	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1195	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1196	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1197	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1198	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1199	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1200	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1201	C₂²⋊C₄	—	67	4	no	—
1202	C₂²⋊C₄	—	67	8	no	—
1203	C₂²⋊C₄	—	67	8	no	—
1204	C₂²⋊C₄	—	67	4	no	—
1205	C₂²⋊C₄	—	67	4	no	—
1206	C₂²⋊C₄	—	67	8	no	—
1207	C₂²⋊C₄	—	67	8	no	—
1208	C₂²⋊C₄	—	67	8	no	—
1209	C₂²⋊C₄	—	67	8	no	—
1210	C₂²⋊C₄	—	67	8	no	—
1211	C₂²⋊C₄	—	67	8	no	—
1212	C₂²⋊C₄	—	67	4	no	—
1213	C₂²⋊C₄	—	67	4	no	—
1214	C₂²⋊C₄	—	67	4	no	—
1215	C₂²⋊C₄	—	67	4	no	—
1216	C₂²⋊C₄	—	67	8	no	—
1217	C₂²⋊C₄	—	67	4	no	—
1218	C₂²⋊C₄	—	67	8	no	—
1219	C₂²⋊C₄	—	67	8	no	—
1220	C₂²⋊C₄	—	67	8	no	—
1221	C₂²⋊C₄	—	67	8	no	—
1222	C₂²⋊C₄	—	67	8	no	—
1223	C₂²⋊C₄	—	67	8	no	—
1224	C₂²⋊C₄	—	67	8	no	—
1225	C₂²⋊C₄	—	67	8	no	—
1226	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1227	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1228	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1229	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1230	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1231	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1232	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1233	C₄²	—	67	4	no	—
1234	C₄²	—	67	4	no	—
1235	C₄²	—	67	4	no	—
1236	C₄²	—	67	4	no	—
1237	C₄²	—	67	8	no	—
1238	C₄²	C₂³×D₆₇	1	4	yes	—
1239	C₄²	C₂³×D₆₇	1	4	yes	—
1240	C₄²	C₂³×D₆₇	1	8	yes	—
1241	C₂³	—	2	4	no	—
1242	C₂³	—	2	2	no	—
1243	C₂³	—	2	2	no	—
1244	C₂³	—	2	4	no	—
1245	C₂³	—	2	4	no	—
1246	C₂³	—	2	2	no	—
1247	C₂³	—	268	8	no	—
1248	C₂³	—	268	8	no	—
1249	C₂³	—	268	8	no	—
1250	C₂³	—	268	8	no	—
1251	C₂³	—	268	8	no	—
1252	C₂³	—	268	8	no	—
1253	C₂³	—	268	8	no	—
1254	C₂³	—	268	8	no	—
1255	C₂³	—	536	16	no	—
1256	C₂³	—	536	16	no	—
1257	C₂³	—	536	16	no	—
1258	C₂³	—	67	4	no	—
1259	C₂³	—	67	2	no	—
1260	C₂³	—	67	4	no	—
1261	C₂³	—	67	2	no	—
1262	C₂³	—	67	4	no	—
1263	C₂³	—	67	4	no	—
1264	C₂³	—	134	16	no	—
1265	C₂³	—	134	4	no	—
1266	C₂³	—	134	4	no	—
1267	C₂³	—	134	4	no	—
1268	C₂³	—	134	2	no	—
1269	C₂³	—	134	4	no	—
1270	C₂³	—	134	4	no	—
1271	C₂³	—	134	2	no	—
1272	C₂³	—	134	4	no	—
1273	C₂³	—	134	4	no	—
1274	C₂³	—	134	4	no	—
1275	C₂³	—	134	4	no	—
1276	C₂³	—	134	2	no	—
1277	C₂³	—	134	2	no	—
1278	C₂³	—	134	2	no	—
1279	C₂³	C₂⁴×D₆₇	1	4	yes	—
1280	C₂³	C₂⁴×D₆₇	1	2	yes	—
1281	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1282	Q₈	—	2	8	no	—
1283	Q₈	—	4	8	no	—
1284	Q₈	—	268	8	no	—
1285	Q₈	—	268	4	no	—
1286	Q₈	—	134	8	no	—
1287	D₄	—	2	8	no	—
1288	D₄	—	4	8	no	—
1289	D₄	—	268	8	no	—
1290	D₄	—	268	8	no	—
1291	D₄	—	268	8	no	—
1292	D₄	—	268	8	no	—
1293	D₄	—	268	8	no	—
1294	D₄	—	268	8	no	—
1295	D₄	—	268	8	no	—
1296	D₄	—	268	8	no	—
1297	D₄	—	268	8	no	—
1298	D₄	—	268	8	no	—
1299	D₄	—	268	8	no	—
1300	D₄	—	268	4	no	—
1301	D₄	—	268	8	no	—
1302	D₄	—	134	8	no	—
1303	D₄	—	134	16	no	—
1304	D₄	—	134	16	no	—
1305	D₄	—	134	8	no	—
1306	D₄	—	134	8	no	—
1307	D₄	—	134	8	no	—
1308	D₄	—	134	8	no	—
1309	C₂×C₄	—	2	2	no	—
1310	C₂×C₄	—	2	4	no	—
1311	C₂×C₄	—	2	4	no	—
1312	C₂×C₄	—	2	2	no	—
1313	C₂×C₄	—	2	2	no	—
1314	C₂×C₄	—	2	4	no	—
1315	C₂×C₄	—	2	2	no	—
1316	C₂×C₄	—	2	2	no	—
1317	C₂×C₄	—	2	8	no	—
1318	C₂×C₄	—	4	8	no	—
1319	C₂×C₄	—	268	8	no	—
1320	C₂×C₄	—	268	8	no	—
1321	C₂×C₄	—	268	8	no	—
1322	C₂×C₄	—	268	8	no	—
1323	C₂×C₄	—	268	8	no	—
1324	C₂×C₄	—	268	8	no	—
1325	C₂×C₄	—	268	4	no	—
1326	C₂×C₄	—	67	2	no	—
1327	C₂×C₄	—	67	2	no	—
1328	C₂×C₄	—	67	2	no	—
1329	C₂×C₄	—	67	2	no	—
1330	C₂×C₄	—	67	4	no	—
1331	C₂×C₄	—	67	2	no	—
1332	C₂×C₄	—	67	2	no	—
1333	C₂×C₄	—	134	8	no	—
1334	C₂×C₄	—	134	2	no	—
1335	C₂×C₄	—	134	2	no	—
1336	C₂×C₄	—	134	2	no	—
1337	C₂×C₄	—	134	4	no	—
1338	C₂×C₄	—	134	2	no	—
1339	C₂×C₄	—	134	2	no	—
1340	C₂×C₄	—	134	2	no	—
1341	C₂×C₄	—	134	8	no	—
1342	C₂×C₄	—	134	8	no	—
1343	C₂×C₄	#14524089	1	4	yes	—
1344	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1345	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1346	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1347	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1348	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1349	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1350	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1351	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1352	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1353	C₂²	—	2	4	no	—
1354	C₂²	—	2	2	no	—
1355	C₂²	—	2	2	no	—
1356	C₂²	—	2	4	no	—
1357	C₂²	—	2	4	no	—
1358	C₂²	—	2	2	no	—
1359	C₂²	—	4	8	no	—
1360	C₂²	—	4	4	no	—
1361	C₂²	—	268	4	no	—
1362	C₂²	—	268	8	no	—
1363	C₂²	—	268	8	no	—
1364	C₂²	—	268	8	no	—
1365	C₂²	—	536	16	no	—
1366	C₂²	—	536	16	no	—
1367	C₂²	—	536	16	no	—
1368	C₂²	—	67	4	no	—
1369	C₂²	—	134	4	no	—
1370	C₂²	—	134	4	no	—
1371	C₂²	—	134	4	no	—
1372	C₂²	—	134	2	no	—
1373	C₂²	—	134	4	no	—
1374	C₂²	—	134	4	no	—
1375	C₂²	—	134	2	no	—
1376	C₂²	—	134	4	no	—
1377	C₂²	—	134	4	no	—
1378	C₂²	—	134	4	no	—
1379	C₂²	—	134	4	no	—
1380	C₂²	—	134	2	no	—
1381	C₂²	—	134	8	no	—
1382	C₂²	—	134	2	no	—
1383	C₂²	—	134	2	no	—
1384	C₂²	H(5,𝔽₂)×D₆₇	1	2	yes	—
1385	C₂²	C₂×#14524089	1	2	yes	—
1386	C₂²	#16864233	1	2	yes	—
1387	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1388	C₄	—	2	2	no	—
1389	C₄	—	2	4	no	—
1390	C₄	—	2	4	no	—
1391	C₄	—	2	2	no	—
1392	C₄	—	2	2	no	—
1393	C₄	—	2	4	no	—
1394	C₄	—	2	2	no	—
1395	C₄	—	2	2	no	—
1396	C₄	—	134	2	no	—
1397	C₄	—	134	2	no	—
1398	C₄	—	134	2	no	—
1399	C₄	—	134	4	no	—
1400	C₄	—	134	2	no	—
1401	C₄	—	134	2	no	—
1402	C₄	—	134	2	no	—
1403	C₄	C₂×#14524089	1	4	yes	—
1404	C₂	—	4	4	no	—
1405	C₂	—	4	2	no	—
1406	C₂	—	268	2	no	—
1407	C₂	—	268	4	no	—
1408	C₂	—	268	4	no	—
1409	C₂	—	268	4	no	—
1410	C₂	—	134	4	no	—
1411	C₂	#22574724	1	4	yes	direct product factor
1412	C₂	C₂×H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1413	C₂	C₂²×#14524089	1	1	yes	characteristic
1414	C₂	C₂×#16864233	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#542×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#542	D₆₇
hypocenter	C₆₇	C₂×#3558
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

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

N	H ≅ G/N	type
1. #22574724	C₂	direct (N × H)
2. C₂×#16864142	C₂	semidirect
3. C₂×#16864138	C₂	semidirect
4. C₂×#16864131	C₂	semidirect
5. C₂×#16864129	C₂	semidirect
6. C₂×#16864058	C₂	semidirect
7. C₂×#16864056	C₂	semidirect
8. C₂×#16864043	C₂	semidirect
9. C₂×#16864039	C₂	semidirect
10. C₂×#16864037	C₂	semidirect
11. C₂×#16864037	C₂	semidirect
12. C₂×D₄×D₂₆₈	C₂	semidirect
13. C₂×#16864030	C₂	semidirect
14. C₂×#16864020	C₂	semidirect
15. C₂×#16863985	C₂	semidirect
16. C₂×#16863985	C₂	semidirect
17. C₂×#16863982	C₂	semidirect
18. C₂×#16863965	C₂	semidirect
19. C₂×#16863964	C₂	semidirect
20. C₂×#16863957	C₂	semidirect
21. C₂×#16863947	C₂	semidirect
22. C₂×#16863924	C₂	semidirect
23. C₂×#124×D₆₇	C₂	semidirect
24. C₂×#542×C₆₇	C₂	semidirect
25. C₂²×#11761629	C₂²	semidirect
26. C₂²×#11761629	C₂²	semidirect
27. C₂²×#11761628	C₂²	semidirect
28. C₂²×Q₈×D₆₇	C₂²	semidirect
29. C₂³×D₂₆₈	C₂²	semidirect
30. C₂³×D₂₆₈	C₂²	semidirect
32. C₂²×D₄×D₆₇	C₂²	semidirect
33. C₂²×D₄×D₆₇	C₂²	semidirect
34. #16864142	C₂²	semidirect
35. #16864138	C₂²	semidirect
36. #16864131	C₂²	semidirect
37. #16864129	C₂²	semidirect
38. #16864058	C₂²	semidirect
39. #16864056	C₂²	semidirect
40. #16864043	C₂²	semidirect
41. #16864039	C₂²	semidirect
42. #16864037	C₂²	semidirect
43. #16864037	C₂²	semidirect
44. D₄×D₂₆₈	C₂²	semidirect
45. #16864030	C₂²	semidirect
46. #16864020	C₂²	semidirect
47. #16863985	C₂²	semidirect
48. #16863985	C₂²	semidirect
49. #16863982	C₂²	semidirect
50. #16863965	C₂²	semidirect
51. #16863964	C₂²	semidirect
52. #16863957	C₂²	semidirect
53. #16863947	C₂²	semidirect
55. C₂×#14524040	C₂²	semidirect
57. #16863924	C₂²	semidirect
58. C₂×#14524038	C₂²	semidirect
59. C₂×#14524038	C₂²	semidirect
60. C₂×#14524036	C₂²	semidirect
61. C₂×#14524033	C₂²	semidirect
62. C₂×#14524032	C₂²	semidirect
63. C₂×#14524032	C₂²	semidirect
64. C₂×#14524032	C₂²	semidirect
65. C₂×#14524032	C₂²	semidirect
66. C₂×#14524031	C₂²	semidirect
67. C₂×#14524031	C₂²	semidirect
68. C₂×#14524031	C₂²	semidirect
69. C₂×#14524031	C₂²	semidirect
70. C₂×#14524030	C₂²	semidirect
71. C₂×#14524029	C₂²	semidirect
72. C₂×#14524029	C₂²	semidirect
73. C₂×#14524029	C₂²	semidirect
74. C₂×#14524029	C₂²	semidirect
75. C₂×#14524029	C₂²	semidirect
76. #124×D₆₇	C₂²	semidirect
77. C₂×#14524028	C₂²	semidirect
78. C₂×#14524028	C₂²	semidirect
79. C₂×#14524028	C₂²	semidirect
80. C₂×#14524028	C₂²	semidirect
81. C₂×#14524028	C₂²	semidirect
82. C₂×#14524026	C₂²	semidirect
83. C₂×#14524025	C₂²	semidirect
84. C₂×#14524025	C₂²	semidirect
85. C₂×#14524025	C₂²	semidirect
86. C₂×#14524023	C₂²	semidirect
87. C₂×#14524023	C₂²	semidirect
88. C₂×#14524021	C₂²	semidirect
89. C₂×#14524021	C₂²	semidirect
90. C₂×#14524019	C₂²	semidirect
92. C₂×#14524018	C₂²	semidirect
93. C₂×#14524018	C₂²	semidirect
94. C₂×#14524018	C₂²	semidirect
95. C₂×#14524018	C₂²	semidirect
96. C₂×#14524018	C₂²	semidirect
97. C₂×#14524018	C₂²	semidirect
98. C₂×#14524018	C₂²	semidirect
99. C₂×#14524017	C₂²	semidirect
101. C₂×#14524016	C₂²	semidirect
102. C₂×#14524016	C₂²	semidirect
103. C₂×#14524016	C₂²	semidirect
104. C₂×#14524016	C₂²	semidirect
105. C₂×#14524014	C₂²	semidirect
106. C₂×#14524013	C₂²	semidirect
107. C₂×#14524013	C₂²	semidirect
108. C₂×#14524013	C₂²	semidirect
109. C₂×#14524013	C₂²	semidirect
110. C₂×#14524013	C₂²	semidirect
111. C₂×#14524013	C₂²	semidirect
112. C₂×#14524013	C₂²	semidirect
113. C₂×#14524013	C₂²	semidirect
114. C₂×#14524011	C₂²	semidirect
115. C₂×#14524011	C₂²	semidirect
116. C₂×C₄×Dic₁₃₄	C₂²	semidirect
117. C₂×#14524008	C₂²	semidirect
118. C₂×C₄×D₂₆₈	C₂²	semidirect
119. C₂×C₄×D₂₆₈	C₂²	semidirect
120. C₂×C₄×D₂₆₈	C₂²	semidirect
121. C₂×#14524005	C₂²	semidirect
122. C₂×#14524005	C₂²	semidirect
123. C₂×#14524005	C₂²	semidirect
124. C₂×#14524005	C₂²	semidirect
125. C₂×#14524005	C₂²	semidirect
126. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
127. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
128. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
129. C₂×#14524000	C₂²	semidirect
130. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
131. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
132. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
133. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
134. C₂×C₄²×D₆₇	C₂²	semidirect
135. #542×C₆₇	C₂²	semidirect
136. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
137. C₂×#126×C₆₇	C₂²	semidirect
138. C₂×#124×C₆₇	C₂²	semidirect
139. C₂×#124×C₆₇	C₂²	semidirect
140. C₂×#123×C₆₇	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
142. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
144. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
145. C₂×C₄×D₄×C₆₇	C₂²	semidirect
146. C₂×#117×C₆₇	C₂²	semidirect
152. C₂×#11761629	C₂³	semidirect
153. C₂×#11761629	C₂³	semidirect
155. C₂×#11761628	C₂³	semidirect
160. C₂×Q₈×D₆₇	C₂³	semidirect
176. C₂²×D₂₆₈	C₂³	semidirect
177. C₂²×D₂₆₈	C₂³	semidirect
189. C₂×D₄×D₆₇	C₂³	semidirect
190. C₂×D₄×D₆₇	C₂³	semidirect
202. #14524040	C₂³	semidirect
204. #14524038	C₂³	semidirect
205. #14524038	C₂³	semidirect
206. #14524036	C₂³	semidirect
207. #14524033	C₂³	semidirect
208. #14524032	C₂³	semidirect
209. #14524032	C₂³	semidirect
210. #14524032	C₂³	semidirect
211. #14524032	C₂³	semidirect
212. #14524031	C₂³	semidirect
213. #14524031	C₂³	semidirect
214. #14524031	C₂³	semidirect
215. #14524031	C₂³	semidirect
216. #14524030	C₂³	semidirect
217. #14524029	C₂³	semidirect
218. #14524029	C₂³	semidirect
219. #14524029	C₂³	semidirect
220. #14524029	C₂³	semidirect
221. #14524029	C₂³	semidirect
222. #14524028	C₂³	semidirect
223. #14524028	C₂³	semidirect
224. #14524028	C₂³	semidirect
225. #14524028	C₂³	semidirect
226. #14524028	C₂³	semidirect
227. #14524026	C₂³	semidirect
228. #14524025	C₂³	semidirect
229. #14524025	C₂³	semidirect
230. #14524025	C₂³	semidirect
231. #14524023	C₂³	semidirect
232. #14524023	C₂³	semidirect
233. #14524021	C₂³	semidirect
234. #14524021	C₂³	semidirect
235. #14524019	C₂³	semidirect
237. #14524018	C₂³	semidirect
238. #14524018	C₂³	semidirect
239. #14524018	C₂³	semidirect
240. #14524018	C₂³	semidirect
241. #14524018	C₂³	semidirect
242. #14524018	C₂³	semidirect
243. #14524018	C₂³	semidirect
244. #14524017	C₂³	semidirect
246. #14524016	C₂³	semidirect
247. #14524016	C₂³	semidirect
248. #14524016	C₂³	semidirect
249. #14524016	C₂³	semidirect
250. #14524014	C₂³	semidirect
251. #14524013	C₂³	semidirect
252. #14524013	C₂³	semidirect
253. #14524013	C₂³	semidirect
254. #14524013	C₂³	semidirect
255. #14524013	C₂³	semidirect
256. #14524013	C₂³	semidirect
257. #14524013	C₂³	semidirect
258. #14524013	C₂³	semidirect
259. #14524011	C₂³	semidirect
260. #14524011	C₂³	semidirect
261. C₄×Dic₁₃₄	C₂³	semidirect
262. #14524008	C₂³	semidirect
263. C₄×D₂₆₈	C₂³	semidirect
264. C₄×D₂₆₈	C₂³	semidirect
265. C₄×D₂₆₈	C₂³	semidirect
266. #14524005	C₂³	semidirect
267. #14524005	C₂³	semidirect
268. #14524005	C₂³	semidirect
269. #14524005	C₂³	semidirect
270. #14524005	C₂³	semidirect
271. C₄×C₂²⋊D₆₇	C₂³	semidirect
272. C₄×C₂²⋊D₆₇	C₂³	semidirect
273. C₄×C₂²⋊D₆₇	C₂³	semidirect
274. #14524000	C₂³	semidirect
310. C₂²⋊C₄×D₆₇	C₂³	semidirect
311. C₂²⋊C₄×D₆₇	C₂³	semidirect
312. C₂²⋊C₄×D₆₇	C₂³	semidirect
313. C₂²⋊C₄×D₆₇	C₂³	semidirect
319. C₄²×D₆₇	C₂³	semidirect
326. C₄⋊Q₈×C₆₇	C₂³	semidirect
327. #126×C₆₇	C₂³	semidirect
328. #124×C₆₇	C₂³	semidirect
329. #124×C₆₇	C₂³	semidirect
330. #123×C₆₇	C₂³	semidirect
331. C₂²⋊Q₈×C₆₇	C₂³	semidirect
332. C₂²⋊Q₈×C₆₇	C₂³	semidirect
334. C₄×Q₈×C₆₇	C₂³	semidirect
335. C₄×D₄×C₆₇	C₂³	semidirect
336. #117×C₆₇	C₂³	semidirect
699. C₂×C₆₇	#3558	semidirect
722. C₂×#542	D₆₇	semidirect
732. C₆₇	C₂×#3558	semidirect
755. #542	C₂×D₆₇	semidirect
763. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
771. C₂×#126	C₂×D₆₇	semidirect
788. C₂×#124	C₂×D₆₇	semidirect
789. C₂×#124	C₂×D₆₇	semidirect
799. C₂×#123	C₂×D₆₇	semidirect
805. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
806. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
835. C₂×C₄×Q₈	C₂×D₆₇	semidirect
847. C₂×C₄×D₄	C₂×D₆₇	semidirect
849. C₂×#117	C₂×D₆₇	semidirect
915. C₄⋊Q₈	C₂²×D₆₇	semidirect
922. #126	C₂²×D₆₇	semidirect
938. #124	C₂²×D₆₇	semidirect
939. #124	C₂²×D₆₇	semidirect
949. #123	C₂²×D₆₇	semidirect
955. C₂²⋊Q₈	C₂²×D₆₇	semidirect
956. C₂²⋊Q₈	C₂²×D₆₇	semidirect
985. C₄×Q₈	C₂²×D₆₇	semidirect
997. C₄×D₄	C₂²×D₆₇	semidirect
999. #117	C₂²×D₆₇	semidirect
1411. C₂	#22574724	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574724	2
C₂×#16864142	2
C₂×#16864138	2
C₂×#16864131	2
C₂×#16864129	2
C₂×#16864058	2
C₂×#16864056	2
C₂×#16864043	2
C₂×#16864039	2
C₂×#16864037	2
C₂×D₄×D₂₆₈	2
C₂×#16864030	2
C₂×#16864020	2
C₂×#16863985	2
C₂×#16863982	2
C₂×#16863965	2
C₂×#16863964	2
C₂×#16863957	2
C₂×#16863947	2
C₂×#16863924	2
C₂×#124×D₆₇	2
C₂×#542×C₆₇	2
C₂×#3558	67

Subgroups — C2×#22574724 #31763167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574724 #31763167