Subgroups — C₂×#22574561 #31763585

Order 17152.

7430 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574561	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864150	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864144	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864140	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864138	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864109	C₂	1	2	yes	maximal, complemented
7	C₂×#16864075	C₂	1	2	yes	maximal, complemented
8	C₂×#16864073	C₂	1	2	yes	maximal, complemented
9	C₂×#16864070	C₂	1	2	yes	maximal, complemented
10	C₂×#16864041	C₂	1	2	yes	maximal, complemented
11	C₂×#16864035	C₂	1	2	yes	maximal, complemented
12	C₂×#16864018	C₂	1	2	yes	maximal, complemented
13	C₂×#16864012	C₂	1	2	yes	maximal, complemented
14	C₂×#16863985	C₂	1	2	yes	maximal, complemented
15	C₂×#16863979	C₂	1	2	yes	maximal, complemented
16	C₂×#16863968	C₂	1	2	yes	maximal, complemented
17	C₂×#16863957	C₂	1	2	yes	maximal, complemented
18	C₂×#16863930	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#14524031	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#11761627	C₂²	1	2	yes	—
22	C₂³×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
24	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
25	#16864150	C₂²	1	16	yes	complemented
26	#16864144	C₂²	1	16	yes	complemented
27	#16864140	C₂²	1	16	yes	complemented
28	#16864138	C₂²	1	16	yes	complemented
29	#16864109	C₂²	1	32	yes	complemented
30	#16864075	C₂²	1	32	yes	complemented
31	#16864073	C₂²	1	32	yes	complemented
32	#16864070	C₂²	1	32	yes	complemented
33	#16864041	C₂²	1	32	yes	complemented
34	#16864035	C₂²	1	32	yes	complemented
35	#16864018	C₂²	1	32	yes	complemented
36	#16864012	C₂²	1	32	yes	complemented
37	#16863985	C₂²	1	32	yes	complemented
38	#16863979	C₂²	1	32	yes	complemented
39	#16863968	C₂²	1	32	yes	complemented
40	#16863957	C₂²	1	32	yes	complemented
41	C₂×#14524042	C₂²	1	2	yes	complemented
42	C₂×#14524042	C₂²	1	2	yes	complemented
43	#16863930	C₂²	1	16	yes	complemented
44	C₂×#14524038	C₂²	1	2	yes	complemented
45	C₂×#14524038	C₂²	1	2	yes	complemented
46	C₂×#14524038	C₂²	1	2	yes	complemented
47	C₂×#14524037	C₂²	1	2	yes	complemented
48	C₂×#14524037	C₂²	1	2	yes	complemented
49	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
50	C₂×#14524032	C₂²	1	2	yes	complemented
51	C₂×#14524031	C₂²	1	1	yes	characteristic
52	C₂×#14524031	C₂²	1	1	yes	characteristic
53	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
54	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
55	C₂×#14524031	C₂²	1	2	yes	complemented
56	C₂×#14524031	C₂²	1	2	yes	complemented
57	C₂×#14524031	C₂²	1	2	yes	complemented
58	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
59	C₂×#14524031	C₂²	1	16	yes	complemented
60	C₂×#14524029	C₂²	1	2	yes	complemented
61	C₂×#14524029	C₂²	1	2	yes	complemented
62	C₂×#14524029	C₂²	1	2	yes	complemented
63	C₂×#14524029	C₂²	1	2	yes	complemented
64	C₂×#14524028	C₂²	1	2	yes	—
65	C₂×#14524028	C₂²	1	2	yes	complemented
66	C₂×#14524028	C₂²	1	2	yes	complemented
67	C₂×#14524028	C₂²	1	2	yes	complemented
68	C₂×#14524028	C₂²	1	2	yes	complemented
69	C₂×#14524027	C₂²	1	2	yes	complemented
70	C₂×#14524027	C₂²	1	2	yes	complemented
71	C₂×#14524026	C₂²	1	2	yes	complemented
72	C₂×#14524026	C₂²	1	2	yes	complemented
73	C₂×#14524025	C₂²	1	2	yes	complemented
74	C₂×#14524024	C₂²	1	2	yes	complemented
75	C₂×#14524023	C₂²	1	2	yes	complemented
76	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
77	C₂×#14524021	C₂²	1	2	yes	complemented
78	C₂×#14524021	C₂²	1	2	yes	complemented
79	C₂×#14524021	C₂²	1	2	yes	complemented
80	C₂×#14524021	C₂²	1	2	yes	complemented
81	C₂×#14524020	C₂²	1	2	yes	complemented
82	C₂×#14524020	C₂²	1	2	yes	complemented
83	C₂×#14524019	C₂²	1	2	yes	complemented
84	C₂×#14524018	C₂²	1	2	yes	—
85	C₂×#14524018	C₂²	1	2	yes	complemented
86	C₂×#14524018	C₂²	1	2	yes	complemented
87	C₂×#14524017	C₂²	1	1	yes	characteristic
88	C₂×#14524017	C₂²	1	2	yes	complemented
89	C₂×#14524016	C₂²	1	2	yes	—
90	C₂×#14524016	C₂²	1	2	yes	complemented
91	C₂×#14524016	C₂²	1	2	yes	complemented
92	C₂×#14524015	C₂²	1	2	yes	complemented
93	C₂×#14524013	C₂²	1	2	yes	—
94	C₂×#14524013	C₂²	1	2	yes	—
95	C₂×#14524013	C₂²	1	2	yes	complemented
96	C₂×#14524013	C₂²	1	2	yes	complemented
97	C₂×#14524011	C₂²	1	2	yes	—
98	C₂×#14524011	C₂²	1	2	yes	complemented
99	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
101	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
102	C₂×#14524005	C₂²	1	2	yes	complemented
103	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
104	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
105	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
106	C₂×#14524001	C₂²	1	2	yes	complemented
107	C₂×#14524000	C₂²	1	2	yes	complemented
108	C₂×#14524000	C₂²	1	2	yes	complemented
109	C₂×#14523999	C₂²	1	2	yes	complemented
110	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
111	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
112	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
113	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
114	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
115	#529×C₆₇	C₂²	1	16	yes	complemented
116	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
117	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
120	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
124	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
126	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₂⁴×D₆₇	C₂³	1	2	yes	—
128	C₂⁴×D₆₇	C₂³	1	2	yes	—
129	C₂×#11761627	—	4	8	no	—
130	C₂×#11761627	C₂³	1	16	yes	—
131	C₂²×Dic₁₃₄	—	4	4	no	—
132	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
134	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
135	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
136	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₃₄	C₂³	1	8	yes	complemented
138	C₂²×D₂₆₈	—	4	4	no	—
139	C₂²×D₂₆₈	C₂³	1	2	yes	—
140	C₂²×D₂₆₈	C₂³	1	2	yes	—
141	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
142	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
143	C₂²×D₂₆₈	C₂³	1	2	yes	—
144	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
145	C₂²×D₂₆₈	C₂³	1	2	yes	—
146	C₂²×D₂₆₈	C₂³	1	8	yes	—
147	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
148	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
149	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
150	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
151	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
152	C₂×D₄×D₆₇	—	4	8	no	—
153	C₂×D₄×D₆₇	C₂³	1	16	yes	complemented
154	C₂³×Dic₆₇	C₂³	1	2	yes	—
155	C₂³×Dic₆₇	C₂³	1	2	yes	—
156	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
157	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
158	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
159	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
160	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
161	#14524042	C₂³	1	16	yes	complemented
162	#14524042	C₂³	1	16	yes	complemented
163	#14524038	C₂³	1	16	yes	complemented
164	#14524038	C₂³	1	16	yes	complemented
165	#14524038	C₂³	1	16	yes	complemented
166	#14524037	C₂³	1	16	yes	complemented
167	#14524037	C₂³	1	16	yes	complemented
168	#14524035	C₂³	1	8	yes	complemented
169	#14524032	C₂³	1	16	yes	complemented
170	#14524031	C₂³	1	8	yes	—
171	#14524031	C₂³	1	8	yes	—
172	#14524031	C₂³	1	16	yes	complemented
173	#14524031	C₂³	1	16	yes	complemented
174	#14524031	C₂³	1	16	yes	complemented
175	#14524031	C₂³	1	8	yes	complemented
176	#14524031	C₂³	1	8	yes	complemented
177	#14524031	C₂³	1	8	yes	complemented
178	#14524029	C₂³	1	16	yes	complemented
179	#14524029	C₂³	1	16	yes	complemented
180	#14524029	C₂³	1	16	yes	complemented
181	#14524029	C₂³	1	16	yes	complemented
182	#14524028	C₂³	1	16	yes	—
183	#14524028	C₂³	1	16	yes	complemented
184	#14524028	C₂³	1	16	yes	complemented
185	#14524028	C₂³	1	16	yes	complemented
186	#14524028	C₂³	1	16	yes	complemented
187	#14524027	C₂³	1	16	yes	complemented
188	#14524027	C₂³	1	16	yes	complemented
189	#14524026	C₂³	1	16	yes	complemented
190	#14524026	C₂³	1	16	yes	complemented
191	#14524025	C₂³	1	16	yes	complemented
192	#14524024	C₂³	1	16	yes	complemented
193	#14524023	C₂³	1	16	yes	complemented
194	#14524022	C₂³	1	8	yes	complemented
195	#14524021	C₂³	1	16	yes	complemented
196	#14524021	C₂³	1	16	yes	complemented
197	#14524021	C₂³	1	16	yes	complemented
198	#14524021	C₂³	1	16	yes	complemented
199	#14524020	C₂³	1	16	yes	complemented
200	#14524020	C₂³	1	16	yes	complemented
201	#14524019	C₂³	1	16	yes	complemented
202	#14524018	C₂³	1	16	yes	—
203	#14524018	C₂³	1	16	yes	complemented
204	#14524018	C₂³	1	16	yes	complemented
205	#14524017	C₂³	1	8	yes	—
206	#14524017	C₂³	1	16	yes	complemented
207	#14524016	C₂³	1	16	yes	—
208	#14524016	C₂³	1	16	yes	complemented
209	#14524016	C₂³	1	16	yes	complemented
210	#14524015	C₂³	1	16	yes	complemented
211	#14524013	C₂³	1	16	yes	—
212	#14524013	C₂³	1	16	yes	—
213	#14524013	C₂³	1	16	yes	complemented
214	#14524013	C₂³	1	16	yes	complemented
215	#14524011	C₂³	1	16	yes	—
216	#14524011	C₂³	1	16	yes	complemented
217	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
218	C₄×D₂₆₈	C₂³	1	16	yes	complemented
219	C₄×D₂₆₈	C₂³	1	8	yes	complemented
220	#14524005	C₂³	1	16	yes	complemented
221	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
222	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
223	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
224	#14524001	C₂³	1	16	yes	complemented
225	#14524000	C₂³	1	16	yes	complemented
226	#14524000	C₂³	1	16	yes	complemented
227	#14523999	C₂³	1	16	yes	complemented
228	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
229	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
230	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
232	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
233	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
234	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
235	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
236	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
237	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
238	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
239	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
240	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
241	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
242	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
243	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
244	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
245	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
246	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
247	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
248	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
249	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
250	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
251	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
252	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
253	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
254	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
255	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
256	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
257	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
258	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
259	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
260	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
261	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
262	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
263	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
264	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
265	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
266	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
267	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
268	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
269	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
270	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
271	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
272	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
273	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
274	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
275	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
276	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
277	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
278	#126×C₆₇	C₂³	1	16	yes	complemented
279	#125×C₆₇	C₂³	1	8	yes	complemented
280	#124×C₆₇	C₂³	1	8	yes	complemented
281	#123×C₆₇	C₂³	1	16	yes	complemented
282	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
283	#121×C₆₇	C₂³	1	8	yes	—
284	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
285	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
286	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
287	#117×C₆₇	C₂³	1	16	yes	complemented
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
292	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
295	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
296	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
297	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
298	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
299	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
304	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
305	C₂³×D₆₇	—	2	8	no	—
306	C₂³×D₆₇	—	4	4	no	—
307	C₂³×D₆₇	—	4	4	no	—
308	C₂³×D₆₇	—	4	4	no	—
309	C₂³×D₆₇	—	4	4	no	—
310	C₂³×D₆₇	—	4	4	no	—
311	C₂³×D₆₇	C₂⁴	1	2	yes	—
312	C₂³×D₆₇	C₂⁴	1	2	yes	—
313	C₂³×D₆₇	C₂⁴	1	2	yes	—
314	C₂³×D₆₇	C₂⁴	1	8	yes	—
315	C₂³×D₆₇	C₂⁴	1	8	yes	—
316	#11761627	—	4	32	no	—
317	C₂×Dic₁₃₄	—	4	2	no	—
318	C₂×Dic₁₃₄	—	4	4	no	—
319	C₂×Dic₁₃₄	—	4	2	no	—
320	C₂×Dic₁₃₄	—	4	16	no	—
321	C₂×Dic₁₃₄	—	4	2	no	—
322	C₂×Dic₁₃₄	—	4	4	no	—
323	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
324	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
325	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
326	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
327	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
328	C₂×D₂₆₈	—	4	4	no	—
329	C₂×D₂₆₈	—	4	2	no	—
330	C₂×D₂₆₈	—	4	4	no	—
331	C₂×D₂₆₈	—	4	2	no	—
332	C₂×D₂₆₈	—	4	16	no	—
333	C₂×D₂₆₈	—	4	4	no	—
334	C₂×D₂₆₈	—	4	2	no	—
335	C₂×D₂₆₈	—	4	4	no	—
336	C₂×D₂₆₈	C₂⁴	1	8	yes	—
337	C₂×D₂₆₈	C₂⁴	1	8	yes	—
338	C₂×D₂₆₈	C₂⁴	1	4	yes	—
339	C₂×D₂₆₈	C₂⁴	1	4	yes	—
340	C₂×D₂₆₈	C₂⁴	1	8	yes	—
341	C₂×D₂₆₈	C₂⁴	1	4	yes	—
342	C₂×D₂₆₈	C₂⁴	1	8	yes	—
343	C₂×C₂²⋊D₆₇	—	2	8	no	—
344	C₂×C₂²⋊D₆₇	—	4	4	no	—
345	C₂×C₂²⋊D₆₇	—	4	4	no	—
346	C₂×C₂²⋊D₆₇	—	4	4	no	—
347	C₂×C₂²⋊D₆₇	—	4	4	no	—
348	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
349	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
350	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
351	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
352	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
353	D₄×D₆₇	—	4	32	no	—
354	C₂²×Dic₆₇	—	2	8	no	—
355	C₂²×Dic₆₇	—	4	4	no	—
356	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
357	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
358	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
359	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
360	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
361	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
362	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
363	C₂×C₄×D₆₇	—	4	4	no	—
364	C₂×C₄×D₆₇	—	4	4	no	—
365	C₂×C₄×D₆₇	—	4	4	no	—
366	C₂×C₄×D₆₇	—	4	4	no	—
367	C₂×C₄×D₆₇	—	4	4	no	—
368	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
369	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
370	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
371	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
372	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
373	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
374	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
375	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
376	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
377	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
378	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
379	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
380	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
381	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
382	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
383	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
384	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
385	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
386	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
387	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
388	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
389	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
390	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
391	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
392	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
393	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
394	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
395	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
396	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
397	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
398	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
399	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
400	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
401	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
402	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
403	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
404	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
405	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
406	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
407	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
408	C₄×Dic₆₇	C₂⁴	1	8	yes	—
409	C₄×Dic₆₇	C₂⁴	1	8	yes	—
410	C₄×Dic₆₇	C₂⁴	1	8	yes	—
411	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
412	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂×Q₈×C₆₇	—	4	2	no	—
414	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
415	C₂×D₄×C₆₇	—	2	8	no	—
416	C₂×D₄×C₆₇	—	4	2	no	—
417	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
418	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
419	C₂²×C₄×C₆₇	—	2	4	no	—
420	C₂²×C₄×C₆₇	—	4	4	no	—
421	C₂²×C₄×C₆₇	—	4	2	no	—
422	C₂²×C₄×C₆₇	—	4	2	no	—
423	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
430	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
431	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
432	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
433	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
434	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
435	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
436	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
437	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
438	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
439	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
440	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
441	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
442	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
443	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
444	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
445	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
446	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
447	C₄²×C₆₇	C₂⁴	1	4	yes	—
448	C₄²×C₆₇	C₂⁴	1	4	yes	—
449	C₄²×C₆₇	C₂⁴	1	4	yes	—
450	C₄²×C₆₇	C₂⁴	1	4	yes	—
451	C₄²×C₆₇	C₂⁴	1	8	yes	—
452	C₂³×C₆₇	—	2	2	no	—
453	C₂³×C₆₇	—	2	2	no	—
454	C₂³×C₆₇	—	2	4	no	—
455	C₂³×C₆₇	—	2	4	no	—
456	C₂³×C₆₇	—	2	4	no	—
457	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
458	C₂³×C₆₇	C₂⁵	1	4	yes	—
459	C₂³×C₆₇	C₂⁵	1	2	yes	—
460	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
461	C₂²×D₆₇	—	2	4	no	—
462	C₂²×D₆₇	—	2	4	no	—
463	C₂²×D₆₇	—	2	4	no	—
464	C₂²×D₆₇	—	2	4	no	—
465	C₂²×D₆₇	—	2	4	no	—
466	C₂²×D₆₇	—	2	4	no	—
467	C₂²×D₆₇	—	2	4	no	—
468	C₂²×D₆₇	—	2	4	no	—
469	C₂²×D₆₇	—	2	4	no	—
470	C₂²×D₆₇	—	2	16	no	—
471	C₂²×D₆₇	—	4	8	no	—
472	C₂²×D₆₇	—	4	8	no	—
473	C₂²×D₆₇	—	4	8	no	—
474	C₂²×D₆₇	—	4	8	no	—
475	C₂²×D₆₇	—	4	8	no	—
476	C₂²×D₆₇	—	8	16	no	—
477	C₂²×D₆₇	—	8	16	no	—
478	C₂²×D₆₇	C₂⁵	1	4	yes	—
479	C₂²×D₆₇	C₂⁵	1	4	yes	—
480	C₂²×D₆₇	C₂⁵	1	4	yes	—
481	Q₈×C₆₇	—	4	4	no	—
482	D₄×C₆₇	—	2	16	no	—
483	D₄×C₆₇	—	4	4	no	—
484	C₂×C₄×C₆₇	—	2	8	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	4	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	2	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	4	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	4	no	—
494	C₂×C₄×C₆₇	—	4	4	no	—
495	C₂×C₄×C₆₇	—	4	4	no	—
496	C₂×C₄×C₆₇	—	4	8	no	—
497	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
498	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
499	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
500	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
501	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
502	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
503	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
504	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
505	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
506	C₂²⋊D₆₇	—	2	16	no	—
507	C₂²⋊D₆₇	—	4	8	no	—
508	C₂²⋊D₆₇	—	4	8	no	—
509	C₂²⋊D₆₇	—	4	8	no	—
510	C₂²⋊D₆₇	—	4	8	no	—
511	C₂×Dic₆₇	—	2	4	no	—
512	C₂×Dic₆₇	—	2	4	no	—
513	C₂×Dic₆₇	—	2	4	no	—
514	C₂×Dic₆₇	—	2	16	no	—
515	C₂×Dic₆₇	—	2	4	no	—
516	C₂×Dic₆₇	—	2	4	no	—
517	C₂×Dic₆₇	—	4	8	no	—
518	C₂×Dic₆₇	C₂⁵	1	4	yes	—
519	C₂×Dic₆₇	C₂⁵	1	4	yes	—
520	C₂×Dic₆₇	C₂⁵	1	4	yes	—
521	C₂×Dic₆₇	C₂⁵	1	4	yes	—
522	C₂×Dic₆₇	C₂⁵	1	4	yes	—
523	D₂₆₈	—	4	8	no	—
524	D₂₆₈	—	4	4	no	—
525	D₂₆₈	—	4	8	no	—
526	D₂₆₈	—	4	4	no	—
527	D₂₆₈	—	4	4	no	—
528	D₂₆₈	—	4	8	no	—
529	D₂₆₈	—	4	8	no	—
530	C₄×D₆₇	—	4	8	no	—
531	C₄×D₆₇	—	4	8	no	—
532	C₄×D₆₇	—	4	8	no	—
533	C₄×D₆₇	—	4	8	no	—
534	C₄×D₆₇	—	4	8	no	—
535	Dic₁₃₄	—	4	4	no	—
536	Dic₁₃₄	—	4	8	no	—
537	Dic₁₃₄	—	4	4	no	—
538	Dic₁₃₄	—	4	4	no	—
539	Dic₁₃₄	—	4	8	no	—
540	C₂²×C₆₇	—	2	2	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	2	8	no	—
543	C₂²×C₆₇	—	2	4	no	—
544	C₂²×C₆₇	—	2	4	no	—
545	C₂²×C₆₇	—	2	4	no	—
546	C₂²×C₆₇	—	4	8	no	—
547	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
548	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
549	C₂²×C₆₇	#585	1	2	yes	—
550	C₂²×C₆₇	#585	1	2	yes	—
551	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
552	C₂×D₆₇	—	2	4	no	—
553	C₂×D₆₇	—	2	4	no	—
554	C₂×D₆₇	—	2	4	no	—
555	C₂×D₆₇	—	2	4	no	—
556	C₂×D₆₇	—	2	4	no	—
557	C₂×D₆₇	—	2	4	no	—
558	C₂×D₆₇	—	2	4	no	—
559	C₂×D₆₇	—	2	4	no	—
560	C₂×D₆₇	—	2	4	no	—
561	C₂×D₆₇	—	4	8	no	—
562	C₂×D₆₇	—	4	8	no	—
563	C₂×D₆₇	—	4	8	no	—
564	C₂×D₆₇	—	8	16	no	—
565	C₂×D₆₇	—	8	16	no	—
566	C₄×C₆₇	—	2	2	no	—
567	C₄×C₆₇	—	2	2	no	—
568	C₄×C₆₇	—	2	4	no	—
569	C₄×C₆₇	—	2	2	no	—
570	C₄×C₆₇	—	2	2	no	—
571	C₄×C₆₇	—	2	4	no	—
572	C₄×C₆₇	—	2	4	no	—
573	C₄×C₆₇	—	2	2	no	—
574	C₄×C₆₇	—	2	2	no	—
575	Dic₆₇	—	2	4	no	—
576	Dic₆₇	—	2	4	no	—
577	Dic₆₇	—	2	4	no	—
578	Dic₆₇	—	2	4	no	—
579	Dic₆₇	—	2	4	no	—
580	C₂×#3545	—	67	1	no	maximal, Sylow
581	C₂×C₆₇	—	2	4	no	—
582	C₂×C₆₇	—	4	4	no	—
583	C₂×C₆₇	#3545	1	4	yes	complemented
584	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
586	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
587	D₆₇	—	4	4	no	—
588	D₆₇	—	4	4	no	—
589	D₆₇	—	4	4	no	—
590	#3545	—	67	32	no	—
591	C₂×#563	—	67	1	no	—
592	C₂×#562	—	67	1	no	—
593	C₂×#562	—	67	1	no	—
594	C₂×H(3,𝔽₄)	—	67	1	no	—
595	C₂×#555	—	67	2	no	—
596	C₂×#551	—	67	2	no	—
597	C₂×#551	—	67	2	no	—
598	C₂×#551	—	67	2	no	—
599	C₂×#546	—	67	2	no	—
600	C₂×#546	—	67	2	no	—
601	C₂×#542	—	67	2	no	—
602	C₂×#542	—	67	2	no	—
603	C₂×#538	—	67	2	no	—
604	C₂×#538	—	67	2	no	—
605	C₂×#536	—	67	2	no	—
606	C₂×#534	—	67	2	no	—
607	C₂×#529	—	67	1	no	—
608	C₂×#529	D₆₇	1	1	yes	characteristic, complemented
609	C₂²×#124	—	67	1	no	—
610	C₆₇	C₂×#3545	1	1	yes	characteristic, complemented, Sylow
611	C₂²×#41	—	67	2	no	—
612	C₂³×Q₈	—	67	1	no	—
613	C₂³×D₄	—	67	2	no	—
614	C₂³×D₄	—	67	1	no	—
615	#563	—	67	16	no	—
616	#562	—	67	16	no	—
617	#562	—	67	16	no	—
618	H(3,𝔽₄)	—	67	16	no	—
619	#555	—	67	32	no	—
620	#551	—	67	32	no	—
621	#551	—	67	32	no	—
622	#551	—	67	32	no	—
623	#546	—	67	32	no	—
624	#546	—	67	32	no	—
625	#542	—	67	32	no	—
626	#542	—	67	32	no	—
627	#538	—	67	32	no	—
628	#538	—	67	32	no	—
629	#536	—	67	32	no	—
630	#534	—	67	32	no	—
631	C₂×C₄⋊Q₈	—	67	2	no	—
632	C₂×C₄⋊Q₈	—	67	2	no	—
633	#529	—	67	16	no	—
634	#529	C₂×D₆₇	1	16	yes	complemented
635	C₂×#126	—	67	2	no	—
636	C₂×#126	—	67	2	no	—
637	C₂×#126	—	67	2	no	—
638	C₂×#126	—	67	2	no	—
639	C₂×#126	—	67	2	no	—
640	C₂×#126	C₂×D₆₇	1	2	yes	complemented
641	C₂×#125	—	67	1	no	—
642	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
643	C₂×#124	—	67	2	no	—
644	C₂×#124	—	67	2	no	—
645	C₂×#124	—	67	2	no	—
646	C₂×#124	—	67	2	no	—
647	C₂×#124	—	67	2	no	—
648	C₂×#124	—	67	2	no	—
649	C₂×#124	—	67	2	no	—
650	C₂×#124	—	67	1	no	—
651	C₂×#124	—	67	1	no	—
652	C₂×#124	—	67	1	no	—
653	C₂×#124	—	67	1	no	—
654	C₂×#124	—	67	1	no	—
655	C₂×#124	—	67	2	no	—
656	C₂×#124	—	67	16	no	—
657	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
658	C₂×#123	—	67	2	no	—
659	C₂×#123	—	67	2	no	—
660	C₂×#123	—	67	2	no	—
661	C₂×#123	—	67	2	no	—
662	C₂×#123	—	67	2	no	—
663	C₂×#123	—	67	2	no	—
664	C₂×#123	—	67	2	no	—
665	C₂×#123	—	67	2	no	—
666	C₂×#123	—	67	2	no	—
667	C₂×#123	—	67	2	no	—
668	C₂×#123	—	67	2	no	—
669	C₂×#123	C₂×D₆₇	1	2	yes	complemented
670	C₂×C₂²⋊Q₈	—	67	2	no	—
671	C₂×C₂²⋊Q₈	—	67	1	no	—
672	C₂×C₂²⋊Q₈	—	67	2	no	—
673	C₂×C₂²⋊Q₈	—	67	2	no	—
674	C₂×C₂²⋊Q₈	—	67	2	no	—
675	C₂×C₂²⋊Q₈	—	67	2	no	—
676	C₂×C₂²⋊Q₈	—	67	2	no	—
677	C₂×C₂²⋊Q₈	—	67	2	no	—
678	C₂×C₂²⋊Q₈	—	67	2	no	—
679	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
680	C₂×#121	—	67	2	no	—
681	C₂×#121	—	67	1	no	—
682	C₂×#121	—	67	2	no	—
683	C₂×#121	—	67	2	no	—
684	C₂×#121	—	67	2	no	—
685	C₂×#121	—	67	2	no	—
686	C₂×#121	—	67	2	no	—
687	C₂×#121	—	67	2	no	—
688	C₂×#121	—	67	2	no	—
689	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
690	C₂×#120	—	67	2	no	—
691	C₂×#120	—	67	2	no	—
692	C₂×#120	—	67	2	no	—
693	C₂×#120	—	67	2	no	—
694	C₂×#120	—	67	2	no	—
695	C₂×#120	—	67	2	no	—
696	C₂×C₄×Q₈	—	67	1	no	—
697	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
698	C₂×C₄×D₄	—	67	2	no	—
699	C₂×C₄×D₄	—	67	2	no	—
700	C₂×C₄×D₄	—	67	2	no	—
701	C₂×C₄×D₄	—	67	2	no	—
702	C₂×C₄×D₄	—	67	1	no	—
703	C₂×C₄×D₄	—	67	2	no	—
704	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
705	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
706	C₂×#117	—	67	2	no	—
707	C₂×#117	—	67	2	no	—
708	C₂×#117	—	67	2	no	—
709	C₂×#117	—	67	2	no	—
710	C₂×#117	C₂×D₆₇	1	2	yes	complemented
711	C₂²×C₂²⋊C₄	—	67	2	no	—
712	C₂²×C₂²⋊C₄	—	67	2	no	—
713	C₂²×C₂²⋊C₄	—	67	2	no	—
714	C₂²×C₂²⋊C₄	—	67	2	no	—
715	C₂²×C₂²⋊C₄	—	67	2	no	—
716	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
717	C₂⁵	—	67	2	no	—
718	C₂⁵	—	67	2	no	—
719	C₂×#41	—	268	8	no	—
720	C₂×#41	—	67	16	no	—
721	C₂²×Q₈	—	268	4	no	—
722	C₂²×Q₈	—	67	1	no	—
723	C₂²×Q₈	—	67	1	no	—
724	C₂²×Q₈	—	67	2	no	—
725	C₂²×Q₈	—	67	2	no	—
726	C₂²×Q₈	—	67	1	no	—
727	C₂²×Q₈	—	67	8	no	—
728	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
729	C₂²×D₄	—	268	4	no	—
730	C₂²×D₄	—	268	8	no	—
731	C₂²×D₄	—	67	2	no	—
732	C₂²×D₄	—	67	2	no	—
733	C₂²×D₄	—	67	2	no	—
734	C₂²×D₄	—	67	2	no	—
735	C₂²×D₄	—	67	16	no	—
736	C₂²×D₄	—	67	2	no	—
737	C₂²×D₄	—	67	2	no	—
738	C₂²×D₄	—	67	2	no	—
739	C₂²×D₄	—	67	1	no	—
740	C₂²×D₄	—	67	1	no	—
741	C₂²×D₄	—	67	2	no	—
742	C₂²×D₄	—	67	2	no	—
743	C₂²×D₄	—	67	1	no	—
744	C₂²×D₄	—	67	8	no	—
745	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
746	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
747	C₂³×C₄	—	67	2	no	—
748	C₂³×C₄	—	67	2	no	—
749	C₂³×C₄	—	67	2	no	—
750	C₂³×C₄	—	67	2	no	—
751	C₂³×C₄	—	67	2	no	—
752	C₂³×C₄	—	67	2	no	—
753	C₂³×C₄	—	67	2	no	—
754	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
755	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
756	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
757	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
758	C₄⋊Q₈	—	67	16	no	—
759	C₄⋊Q₈	—	67	16	no	—
760	#126	—	67	16	no	—
761	#126	—	67	16	no	—
762	#126	—	67	16	no	—
763	#126	—	67	16	no	—
764	#126	—	67	16	no	—
765	#126	C₂²×D₆₇	1	16	yes	complemented
766	#125	—	67	8	no	—
767	#125	C₂²×D₆₇	1	8	yes	complemented
768	#124	—	67	16	no	—
769	#124	—	67	16	no	—
770	#124	—	67	16	no	—
771	#124	—	67	16	no	—
772	#124	—	67	16	no	—
773	#124	—	67	16	no	—
774	#124	—	67	16	no	—
775	#124	—	67	8	no	—
776	#124	—	67	8	no	—
777	#124	—	67	8	no	—
778	#124	—	67	8	no	—
779	#124	—	67	8	no	—
780	#124	—	67	16	no	—
781	#124	C₂²×D₆₇	1	8	yes	complemented
782	#123	—	67	16	no	—
783	#123	—	67	16	no	—
784	#123	—	67	16	no	—
785	#123	—	67	16	no	—
786	#123	—	67	16	no	—
787	#123	—	67	16	no	—
788	#123	—	67	16	no	—
789	#123	—	67	16	no	—
790	#123	—	67	16	no	—
791	#123	—	67	16	no	—
792	#123	—	67	16	no	—
793	#123	C₂²×D₆₇	1	16	yes	complemented
794	C₂²⋊Q₈	—	67	16	no	—
795	C₂²⋊Q₈	—	67	8	no	—
796	C₂²⋊Q₈	—	67	16	no	—
797	C₂²⋊Q₈	—	67	16	no	—
798	C₂²⋊Q₈	—	67	16	no	—
799	C₂²⋊Q₈	—	67	16	no	—
800	C₂²⋊Q₈	—	67	16	no	—
801	C₂²⋊Q₈	—	67	16	no	—
802	C₂²⋊Q₈	—	67	16	no	—
803	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
804	#121	—	67	16	no	—
805	#121	—	67	8	no	—
806	#121	—	67	16	no	—
807	#121	—	67	16	no	—
808	#121	—	67	16	no	—
809	#121	—	67	16	no	—
810	#121	—	67	16	no	—
811	#121	—	67	16	no	—
812	#121	—	67	16	no	—
813	#121	C₂²×D₆₇	1	8	yes	—
814	#120	—	67	16	no	—
815	#120	—	67	16	no	—
816	#120	—	67	16	no	—
817	#120	—	67	16	no	—
818	#120	—	67	16	no	—
819	#120	—	67	16	no	—
820	C₄×Q₈	—	67	8	no	—
821	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
822	C₄×D₄	—	67	16	no	—
823	C₄×D₄	—	67	16	no	—
824	C₄×D₄	—	67	16	no	—
825	C₄×D₄	—	67	16	no	—
826	C₄×D₄	—	67	8	no	—
827	C₄×D₄	—	67	16	no	—
828	C₄×D₄	C₂²×D₆₇	1	8	yes	complemented
829	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
830	#117	—	67	16	no	—
831	#117	—	67	16	no	—
832	#117	—	67	16	no	—
833	#117	—	67	16	no	—
834	#117	C₂²×D₆₇	1	16	yes	complemented
835	C₂×C₄⋊C₄	—	67	2	no	—
836	C₂×C₄⋊C₄	—	67	2	no	—
837	C₂×C₄⋊C₄	—	67	2	no	—
838	C₂×C₄⋊C₄	—	67	2	no	—
839	C₂×C₄⋊C₄	—	67	2	no	—
840	C₂×C₄⋊C₄	—	67	2	no	—
841	C₂×C₄⋊C₄	—	67	2	no	—
842	C₂×C₄⋊C₄	—	67	2	no	—
843	C₂×C₄⋊C₄	—	67	2	no	—
844	C₂×C₄⋊C₄	—	67	1	no	—
845	C₂×C₄⋊C₄	—	67	1	no	—
846	C₂×C₄⋊C₄	—	67	2	no	—
847	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
848	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
849	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
850	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
852	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
853	C₂×C₂²⋊C₄	—	67	2	no	—
854	C₂×C₂²⋊C₄	—	67	2	no	—
855	C₂×C₂²⋊C₄	—	67	2	no	—
856	C₂×C₂²⋊C₄	—	67	2	no	—
857	C₂×C₂²⋊C₄	—	67	2	no	—
858	C₂×C₂²⋊C₄	—	67	2	no	—
859	C₂×C₂²⋊C₄	—	67	2	no	—
860	C₂×C₂²⋊C₄	—	67	2	no	—
861	C₂×C₂²⋊C₄	—	67	2	no	—
862	C₂×C₂²⋊C₄	—	67	2	no	—
863	C₂×C₂²⋊C₄	—	67	2	no	—
864	C₂×C₂²⋊C₄	—	67	2	no	—
865	C₂×C₂²⋊C₄	—	67	2	no	—
866	C₂×C₂²⋊C₄	—	67	2	no	—
867	C₂×C₂²⋊C₄	—	67	2	no	—
868	C₂×C₂²⋊C₄	—	67	2	no	—
869	C₂×C₂²⋊C₄	—	67	2	no	—
870	C₂×C₂²⋊C₄	—	67	16	no	—
871	C₂×C₂²⋊C₄	—	67	16	no	—
872	C₂×C₂²⋊C₄	—	67	16	no	—
873	C₂×C₂²⋊C₄	—	67	2	no	—
874	C₂×C₂²⋊C₄	—	67	2	no	—
875	C₂×C₂²⋊C₄	—	67	2	no	—
876	C₂×C₂²⋊C₄	—	67	2	no	—
877	C₂×C₂²⋊C₄	—	67	2	no	—
878	C₂×C₂²⋊C₄	—	67	2	no	—
879	C₂×C₂²⋊C₄	—	67	16	no	—
880	C₂×C₂²⋊C₄	—	67	16	no	—
881	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
882	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
883	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
884	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
885	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
886	C₂×C₄²	—	67	2	no	—
887	C₂×C₄²	—	67	2	no	—
888	C₂×C₄²	—	67	2	no	—
889	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
890	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
891	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
892	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
893	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
894	C₂×C₄²	C₂²×D₆₇	1	8	yes	complemented
895	C₂⁴	—	268	4	no	—
896	C₂⁴	—	268	4	no	—
897	C₂⁴	—	268	4	no	—
898	C₂⁴	—	268	4	no	—
899	C₂⁴	—	268	4	no	—
900	C₂⁴	—	67	8	no	—
901	C₂⁴	—	67	8	no	—
902	C₂⁴	—	67	2	no	—
903	C₂⁴	—	67	2	no	—
904	C₂⁴	—	67	2	no	—
905	C₂⁴	—	134	8	no	—
906	C₂⁴	C₂³×D₆₇	1	2	yes	—
907	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
908	#41	—	268	32	no	—
909	C₂×Q₈	—	4	2	no	—
910	C₂×Q₈	—	268	2	no	—
911	C₂×Q₈	—	268	4	no	—
912	C₂×Q₈	—	268	2	no	—
913	C₂×Q₈	—	268	16	no	—
914	C₂×Q₈	—	268	4	no	—
915	C₂×Q₈	—	268	2	no	—
916	C₂×Q₈	—	67	4	no	—
917	C₂×Q₈	—	67	4	no	—
918	C₂×Q₈	—	67	8	no	—
919	C₂×Q₈	—	67	8	no	—
920	C₂×Q₈	—	67	4	no	—
921	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
922	C₂×D₄	—	2	8	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	268	2	no	—
925	C₂×D₄	—	268	4	no	—
926	C₂×D₄	—	268	2	no	—
927	C₂×D₄	—	268	16	no	—
928	C₂×D₄	—	268	4	no	—
929	C₂×D₄	—	268	4	no	—
930	C₂×D₄	—	268	2	no	—
931	C₂×D₄	—	268	4	no	—
932	C₂×D₄	—	268	32	no	—
933	C₂×D₄	—	268	4	no	—
934	C₂×D₄	—	268	4	no	—
935	C₂×D₄	—	268	4	no	—
936	C₂×D₄	—	268	4	no	—
937	C₂×D₄	—	67	8	no	—
938	C₂×D₄	—	67	8	no	—
939	C₂×D₄	—	67	8	no	—
940	C₂×D₄	—	67	8	no	—
941	C₂×D₄	—	67	8	no	—
942	C₂×D₄	—	67	8	no	—
943	C₂×D₄	—	67	8	no	—
944	C₂×D₄	—	67	4	no	—
945	C₂×D₄	—	67	4	no	—
946	C₂×D₄	—	67	8	no	—
947	C₂×D₄	—	67	8	no	—
948	C₂×D₄	—	67	4	no	—
949	C₂×D₄	—	134	8	no	—
950	C₂×D₄	C₂³×D₆₇	1	8	yes	—
951	C₂×D₄	C₂³×D₆₇	1	4	yes	—
952	C₂²×C₄	—	2	4	no	—
953	C₂²×C₄	—	4	4	no	—
954	C₂²×C₄	—	4	2	no	—
955	C₂²×C₄	—	4	2	no	—
956	C₂²×C₄	—	268	4	no	—
957	C₂²×C₄	—	268	4	no	—
958	C₂²×C₄	—	268	4	no	—
959	C₂²×C₄	—	268	4	no	—
960	C₂²×C₄	—	268	4	no	—
961	C₂²×C₄	—	268	4	no	—
962	C₂²×C₄	—	67	8	no	—
963	C₂²×C₄	—	67	8	no	—
964	C₂²×C₄	—	67	8	no	—
965	C₂²×C₄	—	67	8	no	—
966	C₂²×C₄	—	67	8	no	—
967	C₂²×C₄	—	67	8	no	—
968	C₂²×C₄	—	67	8	no	—
969	C₂²×C₄	—	67	2	no	—
970	C₂²×C₄	—	67	2	no	—
971	C₂²×C₄	—	67	2	no	—
972	C₂²×C₄	—	67	2	no	—
973	C₂²×C₄	—	67	2	no	—
974	C₂²×C₄	—	134	8	no	—
975	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
976	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
977	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
978	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
979	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
980	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
981	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
982	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
983	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
984	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
985	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
986	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
987	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
988	C₄⋊C₄	—	67	8	no	—
989	C₄⋊C₄	—	67	8	no	—
990	C₄⋊C₄	—	67	8	no	—
991	C₄⋊C₄	—	67	8	no	—
992	C₄⋊C₄	—	67	8	no	—
993	C₄⋊C₄	—	67	8	no	—
994	C₄⋊C₄	—	67	8	no	—
995	C₄⋊C₄	—	67	8	no	—
996	C₄⋊C₄	—	67	8	no	—
997	C₄⋊C₄	—	67	4	no	—
998	C₄⋊C₄	—	67	4	no	—
999	C₄⋊C₄	—	67	8	no	—
1000	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1001	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1002	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1003	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1004	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1005	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1006	C₂²⋊C₄	—	67	8	no	—
1007	C₂²⋊C₄	—	67	8	no	—
1008	C₂²⋊C₄	—	67	8	no	—
1009	C₂²⋊C₄	—	67	8	no	—
1010	C₂²⋊C₄	—	67	8	no	—
1011	C₂²⋊C₄	—	67	8	no	—
1012	C₂²⋊C₄	—	67	8	no	—
1013	C₂²⋊C₄	—	67	8	no	—
1014	C₂²⋊C₄	—	67	8	no	—
1015	C₂²⋊C₄	—	67	8	no	—
1016	C₂²⋊C₄	—	67	8	no	—
1017	C₂²⋊C₄	—	67	8	no	—
1018	C₂²⋊C₄	—	67	8	no	—
1019	C₂²⋊C₄	—	67	8	no	—
1020	C₂²⋊C₄	—	67	8	no	—
1021	C₂²⋊C₄	—	67	8	no	—
1022	C₂²⋊C₄	—	67	8	no	—
1023	C₂²⋊C₄	—	67	8	no	—
1024	C₂²⋊C₄	—	67	8	no	—
1025	C₂²⋊C₄	—	67	8	no	—
1026	C₂²⋊C₄	—	67	8	no	—
1027	C₂²⋊C₄	—	67	8	no	—
1028	C₂²⋊C₄	—	67	8	no	—
1029	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1030	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1031	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1032	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1033	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1034	C₄²	—	67	8	no	—
1035	C₄²	—	67	8	no	—
1036	C₄²	—	67	8	no	—
1037	C₄²	C₂³×D₆₇	1	4	yes	—
1038	C₄²	C₂³×D₆₇	1	4	yes	—
1039	C₄²	C₂³×D₆₇	1	4	yes	—
1040	C₄²	C₂³×D₆₇	1	4	yes	—
1041	C₄²	C₂³×D₆₇	1	8	yes	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	4	no	—
1045	C₂³	—	2	4	no	—
1046	C₂³	—	2	4	no	—
1047	C₂³	—	268	8	no	—
1048	C₂³	—	268	8	no	—
1049	C₂³	—	268	8	no	—
1050	C₂³	—	268	8	no	—
1051	C₂³	—	268	8	no	—
1052	C₂³	—	536	16	no	—
1053	C₂³	—	536	16	no	—
1054	C₂³	—	67	4	no	—
1055	C₂³	—	67	4	no	—
1056	C₂³	—	67	4	no	—
1057	C₂³	—	134	4	no	—
1058	C₂³	—	134	4	no	—
1059	C₂³	—	134	4	no	—
1060	C₂³	—	134	4	no	—
1061	C₂³	—	134	4	no	—
1062	C₂³	—	134	4	no	—
1063	C₂³	—	134	4	no	—
1064	C₂³	—	134	4	no	—
1065	C₂³	—	134	4	no	—
1066	C₂³	—	134	16	no	—
1067	C₂³	#14524089	1	4	yes	—
1068	C₂³	C₂⁴×D₆₇	1	4	yes	—
1069	C₂³	C₂⁴×D₆₇	1	2	yes	—
1070	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1071	Q₈	—	4	4	no	—
1072	Q₈	—	268	4	no	—
1073	Q₈	—	268	8	no	—
1074	Q₈	—	268	4	no	—
1075	Q₈	—	268	8	no	—
1076	Q₈	—	268	4	no	—
1077	D₄	—	2	16	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	268	4	no	—
1080	D₄	—	268	8	no	—
1081	D₄	—	268	4	no	—
1082	D₄	—	268	8	no	—
1083	D₄	—	268	8	no	—
1084	D₄	—	268	4	no	—
1085	D₄	—	268	8	no	—
1086	D₄	—	268	8	no	—
1087	D₄	—	268	8	no	—
1088	D₄	—	268	8	no	—
1089	D₄	—	268	8	no	—
1090	D₄	—	134	16	no	—
1091	C₂×C₄	—	2	8	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	4	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	4	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	4	no	—
1101	C₂×C₄	—	4	8	no	—
1102	C₂×C₄	—	4	4	no	—
1103	C₂×C₄	—	4	4	no	—
1104	C₂×C₄	—	268	8	no	—
1105	C₂×C₄	—	268	8	no	—
1106	C₂×C₄	—	268	8	no	—
1107	C₂×C₄	—	268	8	no	—
1108	C₂×C₄	—	268	8	no	—
1109	C₂×C₄	—	268	8	no	—
1110	C₂×C₄	—	67	4	no	—
1111	C₂×C₄	—	67	4	no	—
1112	C₂×C₄	—	67	4	no	—
1113	C₂×C₄	—	67	4	no	—
1114	C₂×C₄	—	67	4	no	—
1115	C₂×C₄	—	134	4	no	—
1116	C₂×C₄	—	134	4	no	—
1117	C₂×C₄	—	134	4	no	—
1118	C₂×C₄	—	134	16	no	—
1119	C₂×C₄	—	134	4	no	—
1120	C₂×C₄	—	134	4	no	—
1121	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1122	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1123	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1124	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1125	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1126	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1127	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1128	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1129	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	8	no	—
1133	C₂²	—	2	4	no	—
1134	C₂²	—	2	4	no	—
1135	C₂²	—	2	4	no	—
1136	C₂²	—	4	8	no	—
1137	C₂²	—	268	8	no	—
1138	C₂²	—	268	8	no	—
1139	C₂²	—	268	8	no	—
1140	C₂²	—	536	16	no	—
1141	C₂²	—	536	16	no	—
1142	C₂²	—	134	4	no	—
1143	C₂²	—	134	4	no	—
1144	C₂²	—	134	4	no	—
1145	C₂²	—	134	4	no	—
1146	C₂²	—	134	4	no	—
1147	C₂²	—	134	4	no	—
1148	C₂²	—	134	4	no	—
1149	C₂²	—	134	4	no	—
1150	C₂²	—	134	4	no	—
1151	C₂²	C₂×#14524089	1	4	yes	—
1152	C₂²	C₂×#14524089	1	2	yes	—
1153	C₂²	#16864232	1	2	yes	—
1154	C₂²	#16864232	1	2	yes	—
1155	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1156	C₄	—	2	2	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	4	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	4	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	4	no	—
1165	C₄	—	134	4	no	—
1166	C₄	—	134	4	no	—
1167	C₄	—	134	4	no	—
1168	C₄	—	134	4	no	—
1169	C₄	—	134	4	no	—
1170	C₂	—	2	4	no	—
1171	C₂	—	4	4	no	—
1172	C₂	—	268	4	no	—
1173	C₂	—	268	4	no	—
1174	C₂	—	268	4	no	—
1175	C₂	#22574561	1	4	yes	direct product factor
1176	C₂	C₂²×#14524089	1	1	yes	characteristic
1177	C₂	C₂×#16864232	1	1	yes	characteristic
1178	C₂	C₂×#16864232	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#529×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#529	D₆₇
hypocenter	C₆₇	C₂×#3545
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #22574561	C₂	direct (N × H)
2. C₂×#16864150	C₂	semidirect
3. C₂×#16864144	C₂	semidirect
4. C₂×#16864140	C₂	semidirect
5. C₂×#16864138	C₂	semidirect
6. C₂×#16864109	C₂	semidirect
7. C₂×#16864075	C₂	semidirect
8. C₂×#16864073	C₂	semidirect
9. C₂×#16864070	C₂	semidirect
10. C₂×#16864041	C₂	semidirect
11. C₂×#16864035	C₂	semidirect
12. C₂×#16864018	C₂	semidirect
13. C₂×#16864012	C₂	semidirect
14. C₂×#16863985	C₂	semidirect
15. C₂×#16863979	C₂	semidirect
16. C₂×#16863968	C₂	semidirect
17. C₂×#16863957	C₂	semidirect
18. C₂×#16863930	C₂	semidirect
19. C₂²×#14524031	C₂	semidirect
20. C₂×#529×C₆₇	C₂	semidirect
22. C₂³×Dic₁₃₄	C₂²	semidirect
24. C₂²×D₄×D₆₇	C₂²	semidirect
25. #16864150	C₂²	semidirect
26. #16864144	C₂²	semidirect
27. #16864140	C₂²	semidirect
28. #16864138	C₂²	semidirect
29. #16864109	C₂²	semidirect
30. #16864075	C₂²	semidirect
31. #16864073	C₂²	semidirect
32. #16864070	C₂²	semidirect
33. #16864041	C₂²	semidirect
34. #16864035	C₂²	semidirect
35. #16864018	C₂²	semidirect
36. #16864012	C₂²	semidirect
37. #16863985	C₂²	semidirect
38. #16863979	C₂²	semidirect
39. #16863968	C₂²	semidirect
40. #16863957	C₂²	semidirect
41. C₂×#14524042	C₂²	semidirect
42. C₂×#14524042	C₂²	semidirect
43. #16863930	C₂²	semidirect
44. C₂×#14524038	C₂²	semidirect
45. C₂×#14524038	C₂²	semidirect
46. C₂×#14524038	C₂²	semidirect
47. C₂×#14524037	C₂²	semidirect
48. C₂×#14524037	C₂²	semidirect
49. C₂×#14524035	C₂²	semidirect
50. C₂×#14524032	C₂²	semidirect
53. C₂×#14524031	C₂²	semidirect
54. C₂×#14524031	C₂²	semidirect
55. C₂×#14524031	C₂²	semidirect
56. C₂×#14524031	C₂²	semidirect
57. C₂×#14524031	C₂²	semidirect
58. C₂×#14524031	C₂²	semidirect
59. C₂×#14524031	C₂²	semidirect
60. C₂×#14524029	C₂²	semidirect
61. C₂×#14524029	C₂²	semidirect
62. C₂×#14524029	C₂²	semidirect
63. C₂×#14524029	C₂²	semidirect
65. C₂×#14524028	C₂²	semidirect
66. C₂×#14524028	C₂²	semidirect
67. C₂×#14524028	C₂²	semidirect
68. C₂×#14524028	C₂²	semidirect
69. C₂×#14524027	C₂²	semidirect
70. C₂×#14524027	C₂²	semidirect
71. C₂×#14524026	C₂²	semidirect
72. C₂×#14524026	C₂²	semidirect
73. C₂×#14524025	C₂²	semidirect
74. C₂×#14524024	C₂²	semidirect
75. C₂×#14524023	C₂²	semidirect
76. C₂×#14524022	C₂²	semidirect
77. C₂×#14524021	C₂²	semidirect
78. C₂×#14524021	C₂²	semidirect
79. C₂×#14524021	C₂²	semidirect
80. C₂×#14524021	C₂²	semidirect
81. C₂×#14524020	C₂²	semidirect
82. C₂×#14524020	C₂²	semidirect
83. C₂×#14524019	C₂²	semidirect
85. C₂×#14524018	C₂²	semidirect
86. C₂×#14524018	C₂²	semidirect
88. C₂×#14524017	C₂²	semidirect
90. C₂×#14524016	C₂²	semidirect
91. C₂×#14524016	C₂²	semidirect
92. C₂×#14524015	C₂²	semidirect
95. C₂×#14524013	C₂²	semidirect
96. C₂×#14524013	C₂²	semidirect
98. C₂×#14524011	C₂²	semidirect
99. C₂×C₄×Dic₁₃₄	C₂²	semidirect
100. C₂×C₄×D₂₆₈	C₂²	semidirect
101. C₂×C₄×D₂₆₈	C₂²	semidirect
102. C₂×#14524005	C₂²	semidirect
103. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
104. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
105. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
106. C₂×#14524001	C₂²	semidirect
107. C₂×#14524000	C₂²	semidirect
108. C₂×#14524000	C₂²	semidirect
109. C₂×#14523999	C₂²	semidirect
110. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
111. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
112. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
113. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
114. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
115. #529×C₆₇	C₂²	semidirect
116. C₂×#126×C₆₇	C₂²	semidirect
117. C₂×#125×C₆₇	C₂²	semidirect
118. C₂×#124×C₆₇	C₂²	semidirect
119. C₂×#123×C₆₇	C₂²	semidirect
120. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
122. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
123. C₂×C₄×D₄×C₆₇	C₂²	semidirect
124. C₂×C₄×D₄×C₆₇	C₂²	semidirect
125. C₂×#117×C₆₇	C₂²	semidirect
126. C₂²×C₄²×C₆₇	C₂²	semidirect
137. C₂²×Dic₁₃₄	C₂³	semidirect
153. C₂×D₄×D₆₇	C₂³	semidirect
161. #14524042	C₂³	semidirect
162. #14524042	C₂³	semidirect
163. #14524038	C₂³	semidirect
164. #14524038	C₂³	semidirect
165. #14524038	C₂³	semidirect
166. #14524037	C₂³	semidirect
167. #14524037	C₂³	semidirect
168. #14524035	C₂³	semidirect
169. #14524032	C₂³	semidirect
172. #14524031	C₂³	semidirect
173. #14524031	C₂³	semidirect
174. #14524031	C₂³	semidirect
175. #14524031	C₂³	semidirect
176. #14524031	C₂³	semidirect
177. #14524031	C₂³	semidirect
178. #14524029	C₂³	semidirect
179. #14524029	C₂³	semidirect
180. #14524029	C₂³	semidirect
181. #14524029	C₂³	semidirect
183. #14524028	C₂³	semidirect
184. #14524028	C₂³	semidirect
185. #14524028	C₂³	semidirect
186. #14524028	C₂³	semidirect
187. #14524027	C₂³	semidirect
188. #14524027	C₂³	semidirect
189. #14524026	C₂³	semidirect
190. #14524026	C₂³	semidirect
191. #14524025	C₂³	semidirect
192. #14524024	C₂³	semidirect
193. #14524023	C₂³	semidirect
194. #14524022	C₂³	semidirect
195. #14524021	C₂³	semidirect
196. #14524021	C₂³	semidirect
197. #14524021	C₂³	semidirect
198. #14524021	C₂³	semidirect
199. #14524020	C₂³	semidirect
200. #14524020	C₂³	semidirect
201. #14524019	C₂³	semidirect
203. #14524018	C₂³	semidirect
204. #14524018	C₂³	semidirect
206. #14524017	C₂³	semidirect
208. #14524016	C₂³	semidirect
209. #14524016	C₂³	semidirect
210. #14524015	C₂³	semidirect
213. #14524013	C₂³	semidirect
214. #14524013	C₂³	semidirect
216. #14524011	C₂³	semidirect
217. C₄×Dic₁₃₄	C₂³	semidirect
218. C₄×D₂₆₈	C₂³	semidirect
219. C₄×D₂₆₈	C₂³	semidirect
220. #14524005	C₂³	semidirect
221. C₄×C₂²⋊D₆₇	C₂³	semidirect
222. C₄×C₂²⋊D₆₇	C₂³	semidirect
223. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
224. #14524001	C₂³	semidirect
225. #14524000	C₂³	semidirect
226. #14524000	C₂³	semidirect
227. #14523999	C₂³	semidirect
263. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
264. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
265. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
266. C₂²⋊C₄×D₆₇	C₂³	semidirect
267. C₂²⋊C₄×D₆₇	C₂³	semidirect
278. #126×C₆₇	C₂³	semidirect
279. #125×C₆₇	C₂³	semidirect
280. #124×C₆₇	C₂³	semidirect
281. #123×C₆₇	C₂³	semidirect
282. C₂²⋊Q₈×C₆₇	C₂³	semidirect
284. C₄×Q₈×C₆₇	C₂³	semidirect
285. C₄×D₄×C₆₇	C₂³	semidirect
286. C₄×D₄×C₆₇	C₂³	semidirect
287. #117×C₆₇	C₂³	semidirect
304. C₂×C₄²×C₆₇	C₂³	semidirect
583. C₂×C₆₇	#3545	semidirect
608. C₂×#529	D₆₇	semidirect
610. C₆₇	C₂×#3545	semidirect
634. #529	C₂×D₆₇	semidirect
640. C₂×#126	C₂×D₆₇	semidirect
642. C₂×#125	C₂×D₆₇	semidirect
657. C₂×#124	C₂×D₆₇	semidirect
669. C₂×#123	C₂×D₆₇	semidirect
679. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
697. C₂×C₄×Q₈	C₂×D₆₇	semidirect
704. C₂×C₄×D₄	C₂×D₆₇	semidirect
705. C₂×C₄×D₄	C₂×D₆₇	semidirect
710. C₂×#117	C₂×D₆₇	semidirect
716. C₂²×C₄²	C₂×D₆₇	semidirect
765. #126	C₂²×D₆₇	semidirect
767. #125	C₂²×D₆₇	semidirect
781. #124	C₂²×D₆₇	semidirect
793. #123	C₂²×D₆₇	semidirect
803. C₂²⋊Q₈	C₂²×D₆₇	semidirect
821. C₄×Q₈	C₂²×D₆₇	semidirect
828. C₄×D₄	C₂²×D₆₇	semidirect
829. C₄×D₄	C₂²×D₆₇	semidirect
834. #117	C₂²×D₆₇	semidirect
894. C₂×C₄²	C₂²×D₆₇	semidirect
1175. C₂	#22574561	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574561	2
C₂×#16864150	2
C₂×#16864144	2
C₂×#16864140	2
C₂×#16864138	2
C₂×#16864109	2
C₂×#16864075	2
C₂×#16864073	2
C₂×#16864070	2
C₂×#16864041	2
C₂×#16864035	2
C₂×#16864018	2
C₂×#16864012	2
C₂×#16863985	2
C₂×#16863979	2
C₂×#16863968	2
C₂×#16863957	2
C₂×#16863930	2
C₂²×#14524031	2
C₂×#529×C₆₇	2
C₂×#3545	67

Subgroups — C2×#22574561 #31763585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574561 #31763585