Subgroups — C₂×#22574905 #31763263

Order 17152.

6726 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574905	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864150	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864150	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864146	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864138	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864118	C₂	1	2	yes	maximal, complemented
7	C₂×#16864114	C₂	1	2	yes	maximal, complemented
8	C₂×#16864113	C₂	1	2	yes	maximal, complemented
9	C₂×#16864075	C₂	1	2	yes	maximal, complemented
10	C₂×#16864071	C₂	1	2	yes	maximal, complemented
11	C₂×#16864070	C₂	1	2	yes	maximal, complemented
12	C₂×#16864016	C₂	1	2	yes	maximal, complemented
13	C₂×#16864014	C₂	1	2	yes	maximal, complemented
14	C₂×#16864011	C₂	1	2	yes	maximal, complemented
15	C₂×#16863982	C₂	1	2	yes	maximal, complemented
16	C₂×#16863979	C₂	1	2	yes	maximal, complemented
17	C₂×#16863978	C₂	1	2	yes	maximal, complemented
18	C₂×#16863930	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16863930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	#16864150	C₂²	1	16	yes	complemented
22	#16864150	C₂²	1	16	yes	complemented
23	#16864146	C₂²	1	16	yes	complemented
24	#16864138	C₂²	1	16	yes	complemented
25	#16864118	C₂²	1	32	yes	complemented
26	#16864114	C₂²	1	32	yes	complemented
27	#16864113	C₂²	1	32	yes	complemented
28	#16864075	C₂²	1	32	yes	complemented
29	#16864071	C₂²	1	32	yes	complemented
30	#16864070	C₂²	1	32	yes	complemented
31	#16864016	C₂²	1	32	yes	complemented
32	#16864014	C₂²	1	32	yes	complemented
33	#16864011	C₂²	1	32	yes	complemented
34	#16863982	C₂²	1	32	yes	complemented
35	#16863979	C₂²	1	32	yes	complemented
36	#16863978	C₂²	1	32	yes	complemented
37	C₂×#14524042	C₂²	1	2	yes	complemented
38	C₂×#14524042	C₂²	1	2	yes	complemented
39	C₂×#14524041	C₂²	1	2	yes	complemented
40	#16863930	C₂²	1	16	yes	complemented
41	#16863930	C₂²	1	16	yes	complemented
42	C₂×#14524038	C₂²	1	2	yes	complemented
43	C₂×#14524038	C₂²	1	2	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×#14524037	C₂²	1	2	yes	complemented
50	C₂×#14524036	C₂²	1	2	yes	complemented
51	C₂×#14524036	C₂²	1	2	yes	complemented
52	C₂×#14524036	C₂²	1	2	yes	complemented
53	C₂×#14524036	C₂²	1	2	yes	complemented
54	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
55	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
56	C₂×#14524032	C₂²	1	2	yes	—
57	C₂×#14524031	C₂²	1	1	yes	characteristic
58	C₂×#14524031	C₂²	1	1	yes	characteristic
59	C₂×#14524031	C₂²	1	2	yes	—
60	C₂×#14524030	C₂²	1	2	yes	complemented
61	C₂×#14524029	C₂²	1	2	yes	—
62	C₂×#14524029	C₂²	1	2	yes	—
63	C₂×#14524029	C₂²	1	2	yes	—
64	C₂×#14524029	C₂²	1	2	yes	—
65	C₂×#14524029	C₂²	1	2	yes	complemented
66	C₂×#14524029	C₂²	1	2	yes	complemented
67	C₂×#14524028	C₂²	1	2	yes	—
68	C₂×#14524028	C₂²	1	2	yes	—
69	C₂×#14524028	C₂²	1	2	yes	—
70	C₂×#14524026	C₂²	1	2	yes	—
71	C₂×#14524026	C₂²	1	2	yes	complemented
72	C₂×#14524026	C₂²	1	2	yes	complemented
73	C₂×#14524025	C₂²	1	2	yes	—
74	C₂×#14524024	C₂²	1	2	yes	—
75	C₂×#14524023	C₂²	1	2	yes	complemented
76	C₂×#14524023	C₂²	1	2	yes	complemented
77	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
78	C₂×#14524022	C₂²	1	2	yes	complemented
79	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
80	C₂×#14524021	C₂²	1	2	yes	complemented
81	C₂×#14524021	C₂²	1	2	yes	complemented
82	C₂×#14524021	C₂²	1	2	yes	complemented
83	C₂×#14524021	C₂²	1	2	yes	complemented
84	C₂×#14524020	C₂²	1	2	yes	complemented
85	C₂×#14524020	C₂²	1	2	yes	complemented
86	C₂×#14524017	C₂²	1	1	yes	characteristic
87	C₂×#14524017	C₂²	1	1	yes	characteristic
88	C₂×#14524016	C₂²	1	2	yes	—
89	C₂×#14524015	C₂²	1	2	yes	—
90	C₂×#14524014	C₂²	1	2	yes	—
91	C₂×#14524013	C₂²	1	2	yes	—
92	C₂×#14524013	C₂²	1	2	yes	—
93	C₂×#14524011	C₂²	1	2	yes	—
94	C₂×#14524011	C₂²	1	2	yes	complemented
95	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
96	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
98	C₂×#14524008	C₂²	1	2	yes	complemented
99	C₂×#14524008	C₂²	1	2	yes	complemented
100	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
101	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
102	C₂×#14524005	C₂²	1	2	yes	—
103	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
104	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
105	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
106	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
107	C₂×#14524001	C₂²	1	2	yes	complemented
108	C₂×#14524000	C₂²	1	2	yes	complemented
109	C₂×#14524000	C₂²	1	2	yes	complemented
110	C₂×#14524000	C₂²	1	2	yes	complemented
111	C₂×#14523999	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
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	1	yes	characteristic
124	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	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	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
129	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
130	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
132	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
133	C₂²×D₂₆₈	C₂³	1	2	yes	—
134	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
135	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
136	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
137	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
138	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
139	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
140	C₂³×Dic₆₇	C₂³	1	2	yes	—
141	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
142	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
143	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
144	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
145	#14524042	C₂³	1	16	yes	complemented
146	#14524042	C₂³	1	16	yes	complemented
147	#14524041	C₂³	1	16	yes	complemented
148	#14524038	C₂³	1	16	yes	complemented
149	#14524038	C₂³	1	16	yes	complemented
150	#14524038	C₂³	1	16	yes	complemented
151	#14524038	C₂³	1	16	yes	complemented
152	#14524038	C₂³	1	16	yes	complemented
153	#14524037	C₂³	1	16	yes	complemented
154	#14524037	C₂³	1	16	yes	complemented
155	#14524037	C₂³	1	16	yes	complemented
156	#14524036	C₂³	1	16	yes	complemented
157	#14524036	C₂³	1	16	yes	complemented
158	#14524036	C₂³	1	16	yes	complemented
159	#14524036	C₂³	1	16	yes	complemented
160	#14524035	C₂³	1	8	yes	complemented
161	#14524035	C₂³	1	8	yes	complemented
162	#14524032	C₂³	1	16	yes	—
163	#14524031	C₂³	1	16	yes	—
164	#14524031	C₂³	1	8	yes	—
165	#14524031	C₂³	1	8	yes	—
166	#14524030	C₂³	1	16	yes	complemented
167	#14524029	C₂³	1	16	yes	—
168	#14524029	C₂³	1	16	yes	—
169	#14524029	C₂³	1	16	yes	—
170	#14524029	C₂³	1	16	yes	—
171	#14524029	C₂³	1	16	yes	complemented
172	#14524029	C₂³	1	16	yes	complemented
173	#14524028	C₂³	1	16	yes	—
174	#14524028	C₂³	1	16	yes	—
175	#14524028	C₂³	1	16	yes	—
176	#14524026	C₂³	1	16	yes	—
177	#14524026	C₂³	1	16	yes	complemented
178	#14524026	C₂³	1	16	yes	complemented
179	#14524025	C₂³	1	16	yes	—
180	#14524024	C₂³	1	16	yes	—
181	#14524023	C₂³	1	16	yes	complemented
182	#14524023	C₂³	1	16	yes	complemented
183	#14524022	C₂³	1	8	yes	complemented
184	#14524022	C₂³	1	16	yes	complemented
185	#14524022	C₂³	1	8	yes	complemented
186	#14524021	C₂³	1	16	yes	complemented
187	#14524021	C₂³	1	16	yes	complemented
188	#14524021	C₂³	1	16	yes	complemented
189	#14524021	C₂³	1	16	yes	complemented
190	#14524020	C₂³	1	16	yes	complemented
191	#14524020	C₂³	1	16	yes	complemented
192	#14524017	C₂³	1	8	yes	—
193	#14524017	C₂³	1	8	yes	—
194	#14524016	C₂³	1	16	yes	—
195	#14524015	C₂³	1	16	yes	—
196	#14524014	C₂³	1	16	yes	—
197	#14524013	C₂³	1	16	yes	—
198	#14524013	C₂³	1	16	yes	—
199	#14524011	C₂³	1	16	yes	—
200	#14524011	C₂³	1	16	yes	complemented
201	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
202	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
203	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
204	#14524008	C₂³	1	16	yes	complemented
205	#14524008	C₂³	1	16	yes	complemented
206	C₄×D₂₆₈	C₂³	1	8	yes	—
207	C₄×D₂₆₈	C₂³	1	8	yes	—
208	#14524005	C₂³	1	16	yes	—
209	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
210	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
211	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
212	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	—
213	#14524001	C₂³	1	16	yes	complemented
214	#14524000	C₂³	1	16	yes	complemented
215	#14524000	C₂³	1	16	yes	complemented
216	#14524000	C₂³	1	16	yes	complemented
217	#14523999	C₂³	1	16	yes	complemented
218	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
219	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
222	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
224	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
225	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
226	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
227	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
228	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
229	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
230	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
231	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
237	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
238	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
239	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
240	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
241	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
242	C₂×(C₂×D₆₇)⋊C₄	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	16	yes	complemented
259	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
260	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
261	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
262	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
263	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
264	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
265	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
266	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
267	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
268	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
269	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
270	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
271	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
272	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
273	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
274	#126×C₆₇	C₂³	1	16	yes	complemented
275	#125×C₆₇	C₂³	1	8	yes	complemented
276	#124×C₆₇	C₂³	1	8	yes	—
277	#123×C₆₇	C₂³	1	16	yes	complemented
278	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
279	#121×C₆₇	C₂³	1	8	yes	—
280	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
281	C₄×D₄×C₆₇	C₂³	1	8	yes	—
282	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
283	#117×C₆₇	C₂³	1	16	yes	complemented
284	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
285	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
286	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
290	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
291	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
292	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
293	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
295	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
300	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
301	C₂³×D₆₇	—	4	4	no	—
302	C₂³×D₆₇	—	4	4	no	—
303	C₂³×D₆₇	—	4	4	no	—
304	C₂³×D₆₇	C₂⁴	1	2	yes	—
305	C₂³×D₆₇	C₂⁴	1	2	yes	—
306	C₂³×D₆₇	C₂⁴	1	8	yes	—
307	C₂×Dic₁₃₄	—	4	4	no	—
308	C₂×Dic₁₃₄	—	4	4	no	—
309	C₂×Dic₁₃₄	—	4	4	no	—
310	C₂×Dic₁₃₄	—	4	2	no	—
311	C₂×Dic₁₃₄	—	4	2	no	—
312	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
313	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
314	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
315	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
316	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
317	C₂×D₂₆₈	—	4	2	no	—
318	C₂×D₂₆₈	—	4	2	no	—
319	C₂×D₂₆₈	—	4	4	no	—
320	C₂×D₂₆₈	C₂⁴	1	8	yes	—
321	C₂×D₂₆₈	C₂⁴	1	4	yes	—
322	C₂×D₂₆₈	C₂⁴	1	4	yes	—
323	C₂×C₂²⋊D₆₇	—	4	4	no	—
324	C₂×C₂²⋊D₆₇	—	4	4	no	—
325	C₂×C₂²⋊D₆₇	—	4	4	no	—
326	C₂×C₂²⋊D₆₇	—	4	4	no	—
327	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
328	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
329	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
330	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
331	C₂²×Dic₆₇	—	4	4	no	—
332	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
333	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
334	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
335	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
336	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
337	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
338	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
339	C₂×C₄×D₆₇	—	4	4	no	—
340	C₂×C₄×D₆₇	—	4	4	no	—
341	C₂×C₄×D₆₇	—	4	4	no	—
342	C₂×C₄×D₆₇	—	4	4	no	—
343	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
344	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
345	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
346	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
347	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
348	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
349	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
350	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
351	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
352	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
353	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
354	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
355	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
356	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
357	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
358	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
359	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
360	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
361	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
362	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
363	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
364	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
365	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
366	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
367	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
368	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
369	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
370	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
371	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
372	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
373	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
374	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
375	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
376	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
377	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
378	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
379	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
380	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
381	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
382	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
383	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
384	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
385	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
386	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
387	C₄×Dic₆₇	C₂⁴	1	8	yes	—
388	C₄×Dic₆₇	C₂⁴	1	8	yes	—
389	C₄×Dic₆₇	C₂⁴	1	8	yes	—
390	C₄×Dic₆₇	C₂⁴	1	8	yes	—
391	C₄×Dic₆₇	C₂⁴	1	8	yes	—
392	C₄×Dic₆₇	C₂⁴	1	8	yes	—
393	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
394	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×Q₈×C₆₇	—	4	2	no	—
396	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
397	C₂×D₄×C₆₇	—	4	2	no	—
398	C₂×D₄×C₆₇	—	4	4	no	—
399	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
400	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
401	C₂²×C₄×C₆₇	—	4	4	no	—
402	C₂²×C₄×C₆₇	—	4	2	no	—
403	C₂²×C₄×C₆₇	—	4	2	no	—
404	C₂²×C₄×C₆₇	—	4	2	no	—
405	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
412	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
413	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
414	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
415	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
416	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
417	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
418	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
419	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
420	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
421	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
422	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
423	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
424	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
425	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
426	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
427	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
428	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
429	C₄²×C₆₇	C₂⁴	1	4	yes	—
430	C₄²×C₆₇	C₂⁴	1	4	yes	—
431	C₄²×C₆₇	C₂⁴	1	4	yes	—
432	C₄²×C₆₇	C₂⁴	1	4	yes	—
433	C₄²×C₆₇	C₂⁴	1	8	yes	—
434	C₂³×C₆₇	—	2	2	no	—
435	C₂³×C₆₇	—	2	2	no	—
436	C₂³×C₆₇	—	2	2	no	—
437	C₂³×C₆₇	—	2	4	no	—
438	C₂³×C₆₇	—	2	4	no	—
439	C₂³×C₆₇	—	2	4	no	—
440	C₂³×C₆₇	C₂⁵	1	4	yes	—
441	C₂³×C₆₇	C₂⁵	1	2	yes	—
442	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
443	C₂²×D₆₇	—	2	4	no	—
444	C₂²×D₆₇	—	2	4	no	—
445	C₂²×D₆₇	—	2	4	no	—
446	C₂²×D₆₇	—	2	4	no	—
447	C₂²×D₆₇	—	2	4	no	—
448	C₂²×D₆₇	—	2	4	no	—
449	C₂²×D₆₇	—	4	8	no	—
450	C₂²×D₆₇	—	4	8	no	—
451	C₂²×D₆₇	—	4	8	no	—
452	C₂²×D₆₇	—	8	16	no	—
453	C₂²×D₆₇	C₂⁵	1	4	yes	—
454	C₂²×D₆₇	C₂⁵	1	4	yes	—
455	Q₈×C₆₇	—	4	4	no	—
456	D₄×C₆₇	—	4	8	no	—
457	D₄×C₆₇	—	4	4	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	2	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	4	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	2	4	no	—
466	C₂×C₄×C₆₇	—	2	4	no	—
467	C₂×C₄×C₆₇	—	4	8	no	—
468	C₂×C₄×C₆₇	—	4	4	no	—
469	C₂×C₄×C₆₇	—	4	4	no	—
470	C₂×C₄×C₆₇	—	4	4	no	—
471	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
472	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
473	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
474	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
475	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
476	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
477	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
478	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
479	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
480	C₂²⋊D₆₇	—	4	8	no	—
481	C₂²⋊D₆₇	—	4	8	no	—
482	C₂²⋊D₆₇	—	4	8	no	—
483	C₂²⋊D₆₇	—	4	8	no	—
484	C₂×Dic₆₇	—	2	4	no	—
485	C₂×Dic₆₇	—	2	4	no	—
486	C₂×Dic₆₇	—	2	4	no	—
487	C₂×Dic₆₇	—	2	4	no	—
488	C₂×Dic₆₇	—	2	4	no	—
489	C₂×Dic₆₇	—	2	4	no	—
490	C₂×Dic₆₇	—	4	8	no	—
491	C₂×Dic₆₇	C₂⁵	1	4	yes	—
492	C₂×Dic₆₇	C₂⁵	1	4	yes	—
493	C₂×Dic₆₇	C₂⁵	1	4	yes	—
494	C₂×Dic₆₇	C₂⁵	1	4	yes	—
495	C₂×Dic₆₇	C₂⁵	1	4	yes	—
496	C₂×Dic₆₇	C₂⁵	1	4	yes	—
497	D₂₆₈	—	4	4	no	—
498	D₂₆₈	—	4	4	no	—
499	D₂₆₈	—	4	8	no	—
500	C₄×D₆₇	—	4	8	no	—
501	C₄×D₆₇	—	4	8	no	—
502	C₄×D₆₇	—	4	8	no	—
503	C₄×D₆₇	—	4	8	no	—
504	Dic₁₃₄	—	4	4	no	—
505	Dic₁₃₄	—	4	4	no	—
506	Dic₁₃₄	—	4	8	no	—
507	Dic₁₃₄	—	4	8	no	—
508	Dic₁₃₄	—	4	8	no	—
509	C₂²×C₆₇	—	2	4	no	—
510	C₂²×C₆₇	—	2	2	no	—
511	C₂²×C₆₇	—	2	2	no	—
512	C₂²×C₆₇	—	2	4	no	—
513	C₂²×C₆₇	—	2	4	no	—
514	C₂²×C₆₇	—	2	2	no	—
515	C₂²×C₆₇	—	4	8	no	—
516	C₂²×C₆₇	—	4	4	no	—
517	C₂²×C₆₇	#585	1	2	yes	—
518	C₂²×C₆₇	#585	1	2	yes	—
519	C₂²×C₆₇	#585	1	2	yes	—
520	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
521	C₂×D₆₇	—	2	4	no	—
522	C₂×D₆₇	—	2	4	no	—
523	C₂×D₆₇	—	2	4	no	—
524	C₂×D₆₇	—	2	4	no	—
525	C₂×D₆₇	—	2	4	no	—
526	C₂×D₆₇	—	2	4	no	—
527	C₂×D₆₇	—	4	8	no	—
528	C₂×D₆₇	—	4	8	no	—
529	C₂×D₆₇	—	8	16	no	—
530	C₄×C₆₇	—	2	4	no	—
531	C₄×C₆₇	—	2	4	no	—
532	C₄×C₆₇	—	2	2	no	—
533	C₄×C₆₇	—	2	2	no	—
534	C₄×C₆₇	—	2	4	no	—
535	C₄×C₆₇	—	2	2	no	—
536	C₄×C₆₇	—	2	2	no	—
537	C₄×C₆₇	—	2	2	no	—
538	C₄×C₆₇	—	2	2	no	—
539	Dic₆₇	—	2	4	no	—
540	Dic₆₇	—	2	4	no	—
541	Dic₆₇	—	2	4	no	—
542	Dic₆₇	—	2	4	no	—
543	Dic₆₇	—	2	4	no	—
544	Dic₆₇	—	2	4	no	—
545	C₂×#3568	—	67	1	no	maximal, Sylow
546	C₂×C₆₇	—	4	4	no	—
547	C₂×C₆₇	—	4	2	no	—
548	C₂×C₆₇	#3568	1	4	yes	complemented
549	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
550	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
551	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
552	D₆₇	—	4	4	no	—
553	D₆₇	—	4	4	no	—
554	#3568	—	67	32	no	—
555	C₂×#563	—	67	1	no	—
556	C₂×#563	—	67	1	no	—
557	C₂×#563	—	67	1	no	—
558	C₂×H(3,𝔽₄)	—	67	1	no	—
559	C₂×#556	—	67	2	no	—
560	C₂×#556	—	67	2	no	—
561	C₂×#556	—	67	2	no	—
562	C₂×#551	—	67	2	no	—
563	C₂×#551	—	67	2	no	—
564	C₂×#551	—	67	2	no	—
565	C₂×#542	—	67	2	no	—
566	C₂×#542	—	67	2	no	—
567	C₂×#542	—	67	2	no	—
568	C₂×#538	—	67	2	no	—
569	C₂×#538	—	67	2	no	—
570	C₂×#538	—	67	2	no	—
571	C₂×#529	—	67	1	no	—
572	C₂×#529	—	67	1	no	—
573	C₂×#529	D₆₇	1	1	yes	characteristic, complemented
574	C₆₇	C₂×#3568	1	1	yes	characteristic, complemented, Sylow
575	#563	—	67	16	no	—
576	#563	—	67	16	no	—
577	#563	—	67	16	no	—
578	H(3,𝔽₄)	—	67	16	no	—
579	#556	—	67	32	no	—
580	#556	—	67	32	no	—
581	#556	—	67	32	no	—
582	#551	—	67	32	no	—
583	#551	—	67	32	no	—
584	#551	—	67	32	no	—
585	#542	—	67	32	no	—
586	#542	—	67	32	no	—
587	#542	—	67	32	no	—
588	#538	—	67	32	no	—
589	#538	—	67	32	no	—
590	#538	—	67	32	no	—
591	C₂×C₄⋊Q₈	—	67	2	no	—
592	C₂×C₄⋊Q₈	—	67	2	no	—
593	C₂×C₄⋊Q₈	—	67	2	no	—
594	#529	—	67	16	no	—
595	#529	—	67	16	no	—
596	#529	C₂×D₆₇	1	16	yes	complemented
597	C₂×#126	—	67	2	no	—
598	C₂×#126	—	67	2	no	—
599	C₂×#126	—	67	2	no	—
600	C₂×#126	—	67	2	no	—
601	C₂×#126	—	67	2	no	—
602	C₂×#126	—	67	2	no	—
603	C₂×#126	—	67	2	no	—
604	C₂×#126	—	67	2	no	—
605	C₂×#126	—	67	2	no	—
606	C₂×#126	—	67	2	no	—
607	C₂×#126	—	67	2	no	—
608	C₂×#126	—	67	2	no	—
609	C₂×#126	C₂×D₆₇	1	2	yes	complemented
610	C₂×#125	—	67	1	no	—
611	C₂×#125	—	67	1	no	—
612	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
613	C₂×#124	—	67	2	no	—
614	C₂×#124	—	67	2	no	—
615	C₂×#124	—	67	2	no	—
616	C₂×#124	—	67	2	no	—
617	C₂×#124	—	67	2	no	—
618	C₂×#124	—	67	2	no	—
619	C₂×#124	—	67	2	no	—
620	C₂×#124	—	67	2	no	—
621	C₂×#124	—	67	1	no	—
622	C₂×#124	—	67	1	no	—
623	C₂×#124	—	67	2	no	—
624	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
625	C₂×#123	—	67	2	no	—
626	C₂×#123	—	67	2	no	—
627	C₂×#123	—	67	2	no	—
628	C₂×#123	—	67	2	no	—
629	C₂×#123	—	67	2	no	—
630	C₂×#123	—	67	2	no	—
631	C₂×#123	—	67	2	no	—
632	C₂×#123	—	67	2	no	—
633	C₂×#123	C₂×D₆₇	1	2	yes	complemented
634	C₂×C₂²⋊Q₈	—	67	1	no	—
635	C₂×C₂²⋊Q₈	—	67	1	no	—
636	C₂×C₂²⋊Q₈	—	67	2	no	—
637	C₂×C₂²⋊Q₈	—	67	2	no	—
638	C₂×C₂²⋊Q₈	—	67	2	no	—
639	C₂×C₂²⋊Q₈	—	67	2	no	—
640	C₂×C₂²⋊Q₈	—	67	2	no	—
641	C₂×C₂²⋊Q₈	—	67	2	no	—
642	C₂×C₂²⋊Q₈	—	67	2	no	—
643	C₂×C₂²⋊Q₈	—	67	2	no	—
644	C₂×C₂²⋊Q₈	—	67	2	no	—
645	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
646	C₂×#121	—	67	2	no	—
647	C₂×#121	—	67	2	no	—
648	C₂×#121	—	67	1	no	—
649	C₂×#121	—	67	1	no	—
650	C₂×#121	—	67	2	no	—
651	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
652	C₂×#120	—	67	2	no	—
653	C₂×#120	—	67	2	no	—
654	C₂×#120	—	67	2	no	—
655	C₂×#120	—	67	2	no	—
656	C₂×C₄×Q₈	—	67	2	no	—
657	C₂×C₄×Q₈	—	67	2	no	—
658	C₂×C₄×Q₈	—	67	1	no	—
659	C₂×C₄×Q₈	—	67	1	no	—
660	C₂×C₄×Q₈	—	67	2	no	—
661	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
662	C₂×C₄×D₄	—	67	2	no	—
663	C₂×C₄×D₄	—	67	2	no	—
664	C₂×C₄×D₄	—	67	2	no	—
665	C₂×C₄×D₄	—	67	2	no	—
666	C₂×C₄×D₄	—	67	2	no	—
667	C₂×C₄×D₄	—	67	1	no	—
668	C₂×C₄×D₄	—	67	1	no	—
669	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
670	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
671	C₂×#117	—	67	2	no	—
672	C₂×#117	—	67	2	no	—
673	C₂×#117	—	67	2	no	—
674	C₂×#117	—	67	2	no	—
675	C₂×#117	—	67	2	no	—
676	C₂×#117	C₂×D₆₇	1	2	yes	complemented
677	C₂²×C₂²⋊C₄	—	67	2	no	—
678	C₂²×C₂²⋊C₄	—	67	2	no	—
679	C₂²×C₂²⋊C₄	—	67	2	no	—
680	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
681	C₂⁵	—	67	2	no	—
682	C₂²×Q₈	—	67	2	no	—
683	C₂²×Q₈	—	67	2	no	—
684	C₂²×Q₈	—	67	2	no	—
685	C₂²×Q₈	—	67	1	no	—
686	C₂²×Q₈	—	67	1	no	—
687	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
688	C₂²×D₄	—	67	2	no	—
689	C₂²×D₄	—	67	2	no	—
690	C₂²×D₄	—	67	2	no	—
691	C₂²×D₄	—	67	2	no	—
692	C₂²×D₄	—	67	1	no	—
693	C₂²×D₄	—	67	1	no	—
694	C₂²×D₄	—	67	2	no	—
695	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
696	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
697	C₂³×C₄	—	67	2	no	—
698	C₂³×C₄	—	67	2	no	—
699	C₂³×C₄	—	67	2	no	—
700	C₂³×C₄	—	67	2	no	—
701	C₂³×C₄	—	67	2	no	—
702	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
703	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
704	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
705	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
706	C₄⋊Q₈	—	67	16	no	—
707	C₄⋊Q₈	—	67	16	no	—
708	C₄⋊Q₈	—	67	16	no	—
709	#126	—	67	16	no	—
710	#126	—	67	16	no	—
711	#126	—	67	16	no	—
712	#126	—	67	16	no	—
713	#126	—	67	16	no	—
714	#126	—	67	16	no	—
715	#126	—	67	16	no	—
716	#126	—	67	16	no	—
717	#126	—	67	16	no	—
718	#126	—	67	16	no	—
719	#126	—	67	16	no	—
720	#126	—	67	16	no	—
721	#126	C₂²×D₆₇	1	16	yes	complemented
722	#125	—	67	8	no	—
723	#125	—	67	8	no	—
724	#125	C₂²×D₆₇	1	8	yes	complemented
725	#124	—	67	16	no	—
726	#124	—	67	16	no	—
727	#124	—	67	16	no	—
728	#124	—	67	16	no	—
729	#124	—	67	16	no	—
730	#124	—	67	16	no	—
731	#124	—	67	16	no	—
732	#124	—	67	16	no	—
733	#124	—	67	8	no	—
734	#124	—	67	8	no	—
735	#124	—	67	16	no	—
736	#124	C₂²×D₆₇	1	8	yes	—
737	#123	—	67	16	no	—
738	#123	—	67	16	no	—
739	#123	—	67	16	no	—
740	#123	—	67	16	no	—
741	#123	—	67	16	no	—
742	#123	—	67	16	no	—
743	#123	—	67	16	no	—
744	#123	—	67	16	no	—
745	#123	C₂²×D₆₇	1	16	yes	complemented
746	C₂²⋊Q₈	—	67	8	no	—
747	C₂²⋊Q₈	—	67	8	no	—
748	C₂²⋊Q₈	—	67	16	no	—
749	C₂²⋊Q₈	—	67	16	no	—
750	C₂²⋊Q₈	—	67	16	no	—
751	C₂²⋊Q₈	—	67	16	no	—
752	C₂²⋊Q₈	—	67	16	no	—
753	C₂²⋊Q₈	—	67	16	no	—
754	C₂²⋊Q₈	—	67	16	no	—
755	C₂²⋊Q₈	—	67	16	no	—
756	C₂²⋊Q₈	—	67	16	no	—
757	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
758	#121	—	67	16	no	—
759	#121	—	67	16	no	—
760	#121	—	67	8	no	—
761	#121	—	67	8	no	—
762	#121	—	67	16	no	—
763	#121	C₂²×D₆₇	1	8	yes	—
764	#120	—	67	16	no	—
765	#120	—	67	16	no	—
766	#120	—	67	16	no	—
767	#120	—	67	16	no	—
768	C₄×Q₈	—	67	16	no	—
769	C₄×Q₈	—	67	16	no	—
770	C₄×Q₈	—	67	8	no	—
771	C₄×Q₈	—	67	8	no	—
772	C₄×Q₈	—	67	16	no	—
773	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
774	C₄×D₄	—	67	16	no	—
775	C₄×D₄	—	67	16	no	—
776	C₄×D₄	—	67	16	no	—
777	C₄×D₄	—	67	16	no	—
778	C₄×D₄	—	67	16	no	—
779	C₄×D₄	—	67	8	no	—
780	C₄×D₄	—	67	8	no	—
781	C₄×D₄	C₂²×D₆₇	1	8	yes	—
782	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
783	#117	—	67	16	no	—
784	#117	—	67	16	no	—
785	#117	—	67	16	no	—
786	#117	—	67	16	no	—
787	#117	—	67	16	no	—
788	#117	C₂²×D₆₇	1	16	yes	complemented
789	C₂×C₄⋊C₄	—	67	2	no	—
790	C₂×C₄⋊C₄	—	67	2	no	—
791	C₂×C₄⋊C₄	—	67	2	no	—
792	C₂×C₄⋊C₄	—	67	2	no	—
793	C₂×C₄⋊C₄	—	67	2	no	—
794	C₂×C₄⋊C₄	—	67	2	no	—
795	C₂×C₄⋊C₄	—	67	2	no	—
796	C₂×C₄⋊C₄	—	67	2	no	—
797	C₂×C₄⋊C₄	—	67	2	no	—
798	C₂×C₄⋊C₄	—	67	1	no	—
799	C₂×C₄⋊C₄	—	67	1	no	—
800	C₂×C₄⋊C₄	—	67	2	no	—
801	C₂×C₄⋊C₄	—	67	2	no	—
802	C₂×C₄⋊C₄	—	67	1	no	—
803	C₂×C₄⋊C₄	—	67	1	no	—
804	C₂×C₄⋊C₄	—	67	2	no	—
805	C₂×C₄⋊C₄	—	67	2	no	—
806	C₂×C₄⋊C₄	—	67	2	no	—
807	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
808	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
809	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
810	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
811	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
812	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
813	C₂×C₂²⋊C₄	—	67	2	no	—
814	C₂×C₂²⋊C₄	—	67	2	no	—
815	C₂×C₂²⋊C₄	—	67	2	no	—
816	C₂×C₂²⋊C₄	—	67	2	no	—
817	C₂×C₂²⋊C₄	—	67	2	no	—
818	C₂×C₂²⋊C₄	—	67	2	no	—
819	C₂×C₂²⋊C₄	—	67	2	no	—
820	C₂×C₂²⋊C₄	—	67	2	no	—
821	C₂×C₂²⋊C₄	—	67	2	no	—
822	C₂×C₂²⋊C₄	—	67	2	no	—
823	C₂×C₂²⋊C₄	—	67	2	no	—
824	C₂×C₂²⋊C₄	—	67	2	no	—
825	C₂×C₂²⋊C₄	—	67	2	no	—
826	C₂×C₂²⋊C₄	—	67	2	no	—
827	C₂×C₂²⋊C₄	—	67	16	no	—
828	C₂×C₂²⋊C₄	—	67	2	no	—
829	C₂×C₂²⋊C₄	—	67	2	no	—
830	C₂×C₂²⋊C₄	—	67	2	no	—
831	C₂×C₂²⋊C₄	—	67	2	no	—
832	C₂×C₂²⋊C₄	—	67	2	no	—
833	C₂×C₂²⋊C₄	—	67	2	no	—
834	C₂×C₂²⋊C₄	—	67	2	no	—
835	C₂×C₂²⋊C₄	—	67	2	no	—
836	C₂×C₂²⋊C₄	—	67	16	no	—
837	C₂×C₂²⋊C₄	—	67	16	no	—
838	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
839	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
840	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
841	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
843	C₂×C₄²	—	67	2	no	—
844	C₂×C₄²	—	67	2	no	—
845	C₂×C₄²	—	67	2	no	—
846	C₂×C₄²	—	67	2	no	—
847	C₂×C₄²	—	67	2	no	—
848	C₂×C₄²	—	67	2	no	—
849	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
850	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
851	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
852	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
853	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
854	C₂×C₄²	C₂²×D₆₇	1	8	yes	complemented
855	C₂⁴	—	268	4	no	—
856	C₂⁴	—	268	4	no	—
857	C₂⁴	—	268	4	no	—
858	C₂⁴	—	67	8	no	—
859	C₂⁴	—	67	2	no	—
860	C₂⁴	—	67	2	no	—
861	C₂⁴	C₂³×D₆₇	1	2	yes	—
862	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
863	C₂×Q₈	—	4	2	no	—
864	C₂×Q₈	—	268	4	no	—
865	C₂×Q₈	—	268	2	no	—
866	C₂×Q₈	—	268	2	no	—
867	C₂×Q₈	—	268	4	no	—
868	C₂×Q₈	—	268	4	no	—
869	C₂×Q₈	—	67	8	no	—
870	C₂×Q₈	—	67	8	no	—
871	C₂×Q₈	—	67	8	no	—
872	C₂×Q₈	—	67	4	no	—
873	C₂×Q₈	—	67	4	no	—
874	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
875	C₂×D₄	—	4	2	no	—
876	C₂×D₄	—	4	4	no	—
877	C₂×D₄	—	268	2	no	—
878	C₂×D₄	—	268	2	no	—
879	C₂×D₄	—	268	4	no	—
880	C₂×D₄	—	268	4	no	—
881	C₂×D₄	—	268	4	no	—
882	C₂×D₄	—	268	4	no	—
883	C₂×D₄	—	268	4	no	—
884	C₂×D₄	—	67	8	no	—
885	C₂×D₄	—	67	8	no	—
886	C₂×D₄	—	67	8	no	—
887	C₂×D₄	—	67	8	no	—
888	C₂×D₄	—	67	4	no	—
889	C₂×D₄	—	67	4	no	—
890	C₂×D₄	—	67	8	no	—
891	C₂×D₄	C₂³×D₆₇	1	4	yes	—
892	C₂×D₄	C₂³×D₆₇	1	8	yes	—
893	C₂²×C₄	—	4	4	no	—
894	C₂²×C₄	—	4	2	no	—
895	C₂²×C₄	—	4	2	no	—
896	C₂²×C₄	—	4	2	no	—
897	C₂²×C₄	—	268	4	no	—
898	C₂²×C₄	—	268	4	no	—
899	C₂²×C₄	—	268	4	no	—
900	C₂²×C₄	—	268	4	no	—
901	C₂²×C₄	—	268	4	no	—
902	C₂²×C₄	—	67	8	no	—
903	C₂²×C₄	—	67	8	no	—
904	C₂²×C₄	—	67	8	no	—
905	C₂²×C₄	—	67	8	no	—
906	C₂²×C₄	—	67	8	no	—
907	C₂²×C₄	—	67	2	no	—
908	C₂²×C₄	—	67	2	no	—
909	C₂²×C₄	—	67	2	no	—
910	C₂²×C₄	—	67	2	no	—
911	C₂²×C₄	—	67	2	no	—
912	C₂²×C₄	—	67	2	no	—
913	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
914	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
915	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
916	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
917	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
918	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
919	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
920	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
921	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
922	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
923	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
924	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
925	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
926	C₄⋊C₄	—	67	8	no	—
927	C₄⋊C₄	—	67	8	no	—
928	C₄⋊C₄	—	67	8	no	—
929	C₄⋊C₄	—	67	8	no	—
930	C₄⋊C₄	—	67	8	no	—
931	C₄⋊C₄	—	67	8	no	—
932	C₄⋊C₄	—	67	8	no	—
933	C₄⋊C₄	—	67	8	no	—
934	C₄⋊C₄	—	67	8	no	—
935	C₄⋊C₄	—	67	4	no	—
936	C₄⋊C₄	—	67	4	no	—
937	C₄⋊C₄	—	67	8	no	—
938	C₄⋊C₄	—	67	8	no	—
939	C₄⋊C₄	—	67	4	no	—
940	C₄⋊C₄	—	67	4	no	—
941	C₄⋊C₄	—	67	8	no	—
942	C₄⋊C₄	—	67	8	no	—
943	C₄⋊C₄	—	67	8	no	—
944	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
945	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
946	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
947	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
948	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
949	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
950	C₂²⋊C₄	—	67	8	no	—
951	C₂²⋊C₄	—	67	8	no	—
952	C₂²⋊C₄	—	67	8	no	—
953	C₂²⋊C₄	—	67	8	no	—
954	C₂²⋊C₄	—	67	8	no	—
955	C₂²⋊C₄	—	67	8	no	—
956	C₂²⋊C₄	—	67	8	no	—
957	C₂²⋊C₄	—	67	8	no	—
958	C₂²⋊C₄	—	67	8	no	—
959	C₂²⋊C₄	—	67	8	no	—
960	C₂²⋊C₄	—	67	8	no	—
961	C₂²⋊C₄	—	67	8	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	8	no	—
970	C₂²⋊C₄	—	67	8	no	—
971	C₂²⋊C₄	—	67	8	no	—
972	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
973	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
974	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
975	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
976	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
977	C₄²	—	67	8	no	—
978	C₄²	—	67	8	no	—
979	C₄²	—	67	8	no	—
980	C₄²	—	67	8	no	—
981	C₄²	—	67	8	no	—
982	C₄²	—	67	8	no	—
983	C₄²	C₂³×D₆₇	1	4	yes	—
984	C₄²	C₂³×D₆₇	1	4	yes	—
985	C₄²	C₂³×D₆₇	1	4	yes	—
986	C₄²	C₂³×D₆₇	1	4	yes	—
987	C₄²	C₂³×D₆₇	1	8	yes	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	2	no	—
991	C₂³	—	2	4	no	—
992	C₂³	—	2	4	no	—
993	C₂³	—	2	4	no	—
994	C₂³	—	268	8	no	—
995	C₂³	—	268	8	no	—
996	C₂³	—	268	8	no	—
997	C₂³	—	536	16	no	—
998	C₂³	—	67	4	no	—
999	C₂³	—	67	4	no	—
1000	C₂³	—	134	4	no	—
1001	C₂³	—	134	4	no	—
1002	C₂³	—	134	4	no	—
1003	C₂³	—	134	4	no	—
1004	C₂³	—	134	4	no	—
1005	C₂³	—	134	4	no	—
1006	C₂³	C₂⁴×D₆₇	1	4	yes	—
1007	C₂³	C₂⁴×D₆₇	1	2	yes	—
1008	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1009	Q₈	—	4	4	no	—
1010	Q₈	—	268	8	no	—
1011	Q₈	—	268	4	no	—
1012	Q₈	—	268	4	no	—
1013	Q₈	—	268	8	no	—
1014	Q₈	—	268	8	no	—
1015	D₄	—	4	4	no	—
1016	D₄	—	4	8	no	—
1017	D₄	—	268	4	no	—
1018	D₄	—	268	4	no	—
1019	D₄	—	268	8	no	—
1020	D₄	—	268	8	no	—
1021	D₄	—	268	8	no	—
1022	D₄	—	268	8	no	—
1023	D₄	—	268	8	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	4	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	4	no	—
1032	C₂×C₄	—	2	4	no	—
1033	C₂×C₄	—	4	8	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	4	4	no	—
1037	C₂×C₄	—	268	8	no	—
1038	C₂×C₄	—	268	8	no	—
1039	C₂×C₄	—	268	8	no	—
1040	C₂×C₄	—	268	8	no	—
1041	C₂×C₄	—	268	8	no	—
1042	C₂×C₄	—	67	4	no	—
1043	C₂×C₄	—	67	4	no	—
1044	C₂×C₄	—	67	4	no	—
1045	C₂×C₄	—	67	4	no	—
1046	C₂×C₄	—	67	4	no	—
1047	C₂×C₄	—	67	4	no	—
1048	C₂×C₄	—	134	4	no	—
1049	C₂×C₄	—	134	4	no	—
1050	C₂×C₄	—	134	4	no	—
1051	C₂×C₄	—	134	4	no	—
1052	C₂×C₄	—	134	4	no	—
1053	C₂×C₄	—	134	4	no	—
1054	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1055	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1056	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1057	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1058	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1059	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1060	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1061	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1062	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	4	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	4	no	—
1069	C₂²	—	4	8	no	—
1070	C₂²	—	4	4	no	—
1071	C₂²	—	268	8	no	—
1072	C₂²	—	268	8	no	—
1073	C₂²	—	536	16	no	—
1074	C₂²	—	134	4	no	—
1075	C₂²	—	134	4	no	—
1076	C₂²	—	134	4	no	—
1077	C₂²	—	134	4	no	—
1078	C₂²	—	134	4	no	—
1079	C₂²	—	134	4	no	—
1080	C₂²	#16864232	1	2	yes	—
1081	C₂²	#16864232	1	2	yes	—
1082	C₂²	#16864232	1	2	yes	—
1083	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	4	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	4	no	—
1092	C₄	—	2	4	no	—
1093	C₄	—	134	4	no	—
1094	C₄	—	134	4	no	—
1095	C₄	—	134	4	no	—
1096	C₄	—	134	4	no	—
1097	C₄	—	134	4	no	—
1098	C₄	—	134	4	no	—
1099	C₂	—	4	4	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	268	4	no	—
1102	C₂	—	268	4	no	—
1103	C₂	#22574905	1	4	yes	direct product factor
1104	C₂	C₂×#16864232	1	1	yes	characteristic
1105	C₂	C₂×#16864232	1	1	yes	characteristic
1106	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×#3568
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. #22574905	C₂	direct (N × H)
2. C₂×#16864150	C₂	semidirect
3. C₂×#16864150	C₂	semidirect
4. C₂×#16864146	C₂	semidirect
5. C₂×#16864138	C₂	semidirect
6. C₂×#16864118	C₂	semidirect
7. C₂×#16864114	C₂	semidirect
8. C₂×#16864113	C₂	semidirect
9. C₂×#16864075	C₂	semidirect
10. C₂×#16864071	C₂	semidirect
11. C₂×#16864070	C₂	semidirect
12. C₂×#16864016	C₂	semidirect
13. C₂×#16864014	C₂	semidirect
14. C₂×#16864011	C₂	semidirect
15. C₂×#16863982	C₂	semidirect
16. C₂×#16863979	C₂	semidirect
17. C₂×#16863978	C₂	semidirect
18. C₂×#16863930	C₂	semidirect
19. C₂×#16863930	C₂	semidirect
20. C₂×#529×C₆₇	C₂	semidirect
21. #16864150	C₂²	semidirect
22. #16864150	C₂²	semidirect
23. #16864146	C₂²	semidirect
24. #16864138	C₂²	semidirect
25. #16864118	C₂²	semidirect
26. #16864114	C₂²	semidirect
27. #16864113	C₂²	semidirect
28. #16864075	C₂²	semidirect
29. #16864071	C₂²	semidirect
30. #16864070	C₂²	semidirect
31. #16864016	C₂²	semidirect
32. #16864014	C₂²	semidirect
33. #16864011	C₂²	semidirect
34. #16863982	C₂²	semidirect
35. #16863979	C₂²	semidirect
36. #16863978	C₂²	semidirect
37. C₂×#14524042	C₂²	semidirect
38. C₂×#14524042	C₂²	semidirect
39. C₂×#14524041	C₂²	semidirect
40. #16863930	C₂²	semidirect
41. #16863930	C₂²	semidirect
42. C₂×#14524038	C₂²	semidirect
43. C₂×#14524038	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×#14524037	C₂²	semidirect
50. C₂×#14524036	C₂²	semidirect
51. C₂×#14524036	C₂²	semidirect
52. C₂×#14524036	C₂²	semidirect
53. C₂×#14524036	C₂²	semidirect
54. C₂×#14524035	C₂²	semidirect
55. C₂×#14524035	C₂²	semidirect
60. C₂×#14524030	C₂²	semidirect
65. C₂×#14524029	C₂²	semidirect
66. C₂×#14524029	C₂²	semidirect
71. C₂×#14524026	C₂²	semidirect
72. C₂×#14524026	C₂²	semidirect
75. C₂×#14524023	C₂²	semidirect
76. C₂×#14524023	C₂²	semidirect
77. C₂×#14524022	C₂²	semidirect
78. C₂×#14524022	C₂²	semidirect
79. C₂×#14524022	C₂²	semidirect
80. C₂×#14524021	C₂²	semidirect
81. C₂×#14524021	C₂²	semidirect
82. C₂×#14524021	C₂²	semidirect
83. C₂×#14524021	C₂²	semidirect
84. C₂×#14524020	C₂²	semidirect
85. C₂×#14524020	C₂²	semidirect
94. C₂×#14524011	C₂²	semidirect
95. C₂×C₄×Dic₁₃₄	C₂²	semidirect
96. C₂×C₄×Dic₁₃₄	C₂²	semidirect
97. C₂×C₄×Dic₁₃₄	C₂²	semidirect
98. C₂×#14524008	C₂²	semidirect
99. C₂×#14524008	C₂²	semidirect
104. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
105. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
107. C₂×#14524001	C₂²	semidirect
108. C₂×#14524000	C₂²	semidirect
109. C₂×#14524000	C₂²	semidirect
110. C₂×#14524000	C₂²	semidirect
111. C₂×#14523999	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
119. C₂×#123×C₆₇	C₂²	semidirect
120. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
122. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
124. C₂×C₄×D₄×C₆₇	C₂²	semidirect
125. C₂×#117×C₆₇	C₂²	semidirect
126. C₂²×C₄²×C₆₇	C₂²	semidirect
145. #14524042	C₂³	semidirect
146. #14524042	C₂³	semidirect
147. #14524041	C₂³	semidirect
148. #14524038	C₂³	semidirect
149. #14524038	C₂³	semidirect
150. #14524038	C₂³	semidirect
151. #14524038	C₂³	semidirect
152. #14524038	C₂³	semidirect
153. #14524037	C₂³	semidirect
154. #14524037	C₂³	semidirect
155. #14524037	C₂³	semidirect
156. #14524036	C₂³	semidirect
157. #14524036	C₂³	semidirect
158. #14524036	C₂³	semidirect
159. #14524036	C₂³	semidirect
160. #14524035	C₂³	semidirect
161. #14524035	C₂³	semidirect
166. #14524030	C₂³	semidirect
171. #14524029	C₂³	semidirect
172. #14524029	C₂³	semidirect
177. #14524026	C₂³	semidirect
178. #14524026	C₂³	semidirect
181. #14524023	C₂³	semidirect
182. #14524023	C₂³	semidirect
183. #14524022	C₂³	semidirect
184. #14524022	C₂³	semidirect
185. #14524022	C₂³	semidirect
186. #14524021	C₂³	semidirect
187. #14524021	C₂³	semidirect
188. #14524021	C₂³	semidirect
189. #14524021	C₂³	semidirect
190. #14524020	C₂³	semidirect
191. #14524020	C₂³	semidirect
200. #14524011	C₂³	semidirect
201. C₄×Dic₁₃₄	C₂³	semidirect
202. C₄×Dic₁₃₄	C₂³	semidirect
203. C₄×Dic₁₃₄	C₂³	semidirect
204. #14524008	C₂³	semidirect
205. #14524008	C₂³	semidirect
210. C₄×C₂²⋊D₆₇	C₂³	semidirect
211. C₄×C₂²⋊D₆₇	C₂³	semidirect
213. #14524001	C₂³	semidirect
214. #14524000	C₂³	semidirect
215. #14524000	C₂³	semidirect
216. #14524000	C₂³	semidirect
217. #14523999	C₂³	semidirect
258. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
259. C₂²⋊C₄×D₆₇	C₂³	semidirect
260. C₂²⋊C₄×D₆₇	C₂³	semidirect
274. #126×C₆₇	C₂³	semidirect
275. #125×C₆₇	C₂³	semidirect
277. #123×C₆₇	C₂³	semidirect
278. C₂²⋊Q₈×C₆₇	C₂³	semidirect
280. C₄×Q₈×C₆₇	C₂³	semidirect
282. C₄×D₄×C₆₇	C₂³	semidirect
283. #117×C₆₇	C₂³	semidirect
300. C₂×C₄²×C₆₇	C₂³	semidirect
548. C₂×C₆₇	#3568	semidirect
573. C₂×#529	D₆₇	semidirect
574. C₆₇	C₂×#3568	semidirect
596. #529	C₂×D₆₇	semidirect
609. C₂×#126	C₂×D₆₇	semidirect
612. C₂×#125	C₂×D₆₇	semidirect
633. C₂×#123	C₂×D₆₇	semidirect
645. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
661. C₂×C₄×Q₈	C₂×D₆₇	semidirect
670. C₂×C₄×D₄	C₂×D₆₇	semidirect
676. C₂×#117	C₂×D₆₇	semidirect
680. C₂²×C₄²	C₂×D₆₇	semidirect
721. #126	C₂²×D₆₇	semidirect
724. #125	C₂²×D₆₇	semidirect
745. #123	C₂²×D₆₇	semidirect
757. C₂²⋊Q₈	C₂²×D₆₇	semidirect
773. C₄×Q₈	C₂²×D₆₇	semidirect
782. C₄×D₄	C₂²×D₆₇	semidirect
788. #117	C₂²×D₆₇	semidirect
854. C₂×C₄²	C₂²×D₆₇	semidirect
1103. C₂	#22574905	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574905	2
C₂×#16864150	2
C₂×#16864146	2
C₂×#16864138	2
C₂×#16864118	2
C₂×#16864114	2
C₂×#16864113	2
C₂×#16864075	2
C₂×#16864071	2
C₂×#16864070	2
C₂×#16864016	2
C₂×#16864014	2
C₂×#16864011	2
C₂×#16863982	2
C₂×#16863979	2
C₂×#16863978	2
C₂×#16863930	2
C₂×#529×C₆₇	2
C₂×#3568	67

Subgroups — C2×#22574905 #31763263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574905 #31763263