Subgroups — C₂×#22574563 #31763588

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	#22574563	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864145	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864142	C₂	1	2	yes	maximal, complemented
4	C₂×#16864138	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864112	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864108	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16864073	C₂	1	2	yes	maximal, complemented
8	C₂×#16864070	C₂	1	2	yes	maximal, complemented
9	C₂×#16864069	C₂	1	2	yes	maximal, complemented
10	C₂×#16864038	C₂	1	2	yes	maximal, complemented
11	C₂×#16864034	C₂	1	2	yes	maximal, complemented
12	C₂×#16864020	C₂	1	2	yes	maximal, complemented
13	C₂×#16864016	C₂	1	2	yes	maximal, complemented
14	C₂×#16863986	C₂	1	2	yes	maximal, complemented
15	C₂×#16863980	C₂	1	2	yes	maximal, complemented
16	C₂×#16863970	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16863957	C₂	1	2	yes	maximal, complemented
18	C₂×#16863923	C₂	1	2	yes	maximal, complemented
19	C₂²×#14524032	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#536×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#11761628	C₂²	1	1	yes	characteristic
22	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
23	C₂²×D₄×D₆₇	C₂²	1	2	yes	complemented
24	#16864145	C₂²	1	16	yes	complemented
25	#16864142	C₂²	1	32	yes	complemented
26	#16864138	C₂²	1	16	yes	complemented
27	#16864112	C₂²	1	16	yes	complemented
28	#16864108	C₂²	1	16	yes	complemented
29	#16864073	C₂²	1	32	yes	complemented
30	#16864070	C₂²	1	32	yes	complemented
31	#16864069	C₂²	1	32	yes	complemented
32	#16864038	C₂²	1	32	yes	complemented
33	#16864034	C₂²	1	32	yes	complemented
34	#16864020	C₂²	1	32	yes	complemented
35	#16864016	C₂²	1	32	yes	complemented
36	#16863986	C₂²	1	32	yes	complemented
37	#16863980	C₂²	1	32	yes	complemented
38	#16863970	C₂²	1	16	yes	complemented
39	#16863957	C₂²	1	32	yes	complemented
40	C₂×#14524041	C₂²	1	1	yes	characteristic, complemented
41	C₂×#14524041	C₂²	1	1	yes	characteristic, complemented
42	#16863923	C₂²	1	32	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×#14524036	C₂²	1	2	yes	complemented
49	C₂×#14524033	C₂²	1	2	yes	complemented
50	C₂×#14524032	C₂²	1	1	yes	characteristic
51	C₂×#14524032	C₂²	1	1	yes	characteristic
52	C₂×#14524032	C₂²	1	2	yes	complemented
53	C₂×#14524032	C₂²	1	2	yes	complemented
54	C₂×#14524032	C₂²	1	2	yes	complemented
55	C₂×#14524032	C₂²	1	1	yes	characteristic, complemented
56	C₂×#14524032	C₂²	1	1	yes	characteristic, complemented
57	C₂×#14524032	C₂²	1	1	yes	characteristic, complemented
58	C₂×#14524032	C₂²	1	1	yes	characteristic, complemented
59	C₂×#14524032	C₂²	1	16	yes	complemented
60	C₂×#14524031	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×#14524026	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×#14524023	C₂²	1	2	yes	complemented
75	C₂×#14524021	C₂²	1	2	yes	complemented
76	C₂×#14524021	C₂²	1	2	yes	complemented
77	C₂×#14524020	C₂²	1	2	yes	complemented
78	C₂×#14524019	C₂²	1	2	yes	complemented
79	C₂×#14524019	C₂²	1	2	yes	complemented
80	C₂×#14524019	C₂²	1	2	yes	complemented
81	C₂×#14524018	C₂²	1	2	yes	—
82	C₂×#14524018	C₂²	1	2	yes	complemented
83	C₂×#14524018	C₂²	1	2	yes	complemented
84	C₂×#14524017	C₂²	1	2	yes	complemented
85	C₂×#14524016	C₂²	1	2	yes	—
86	C₂×#14524016	C₂²	1	2	yes	complemented
87	C₂×#14524016	C₂²	1	2	yes	complemented
88	C₂×#14524015	C₂²	1	2	yes	—
89	C₂×#14524015	C₂²	1	2	yes	complemented
90	C₂×#14524013	C₂²	1	2	yes	—
91	C₂×#14524013	C₂²	1	2	yes	—
92	C₂×#14524013	C₂²	1	2	yes	complemented
93	C₂×#14524013	C₂²	1	2	yes	complemented
94	C₂×#14524011	C₂²	1	2	yes	—
95	C₂×#14524011	C₂²	1	2	yes	complemented
96	C₂×#14524008	C₂²	1	2	yes	complemented
97	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
98	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
99	C₂×#14524005	C₂²	1	2	yes	complemented
100	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
101	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
102	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
103	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
104	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
105	C₂×#14524001	C₂²	1	2	yes	complemented
106	C₂×#14524001	C₂²	1	2	yes	complemented
107	C₂×#14524000	C₂²	1	2	yes	complemented
108	C₂×#14523999	C₂²	1	2	yes	complemented
109	C₂²×(C₂×D₆₇)⋊C₄	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	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
113	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
114	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
116	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#536×C₆₇	C₂²	1	16	yes	complemented
118	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
123	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
124	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
125	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
126	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₂⁴×D₆₇	C₂³	1	2	yes	—
128	C₂⁴×D₆₇	C₂³	1	2	yes	—
129	C₂×#11761628	—	4	4	no	—
130	C₂×#11761628	C₂³	1	8	yes	—
131	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
132	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
133	C₂²×D₂₆₈	—	4	4	no	—
134	C₂²×D₂₆₈	C₂³	1	2	yes	—
135	C₂²×D₂₆₈	C₂³	1	2	yes	—
136	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
137	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
138	C₂²×D₂₆₈	C₂³	1	2	yes	—
139	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
140	C₂²×D₂₆₈	C₂³	1	2	yes	—
141	C₂²×D₂₆₈	C₂³	1	8	yes	—
142	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
143	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
144	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
145	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
146	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
147	C₂×D₄×D₆₇	—	4	8	no	—
148	C₂×D₄×D₆₇	C₂³	1	16	yes	complemented
149	C₂³×Dic₆₇	C₂³	1	2	yes	—
150	C₂³×Dic₆₇	C₂³	1	2	yes	—
151	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
152	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
153	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
154	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
155	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
156	#14524041	C₂³	1	8	yes	complemented
157	#14524041	C₂³	1	8	yes	complemented
158	#14524038	C₂³	1	16	yes	complemented
159	#14524038	C₂³	1	16	yes	complemented
160	#14524038	C₂³	1	16	yes	complemented
161	#14524038	C₂³	1	16	yes	complemented
162	#14524037	C₂³	1	16	yes	complemented
163	#14524036	C₂³	1	16	yes	complemented
164	#14524033	C₂³	1	16	yes	complemented
165	#14524032	C₂³	1	8	yes	—
166	#14524032	C₂³	1	8	yes	—
167	#14524032	C₂³	1	16	yes	complemented
168	#14524032	C₂³	1	16	yes	complemented
169	#14524032	C₂³	1	16	yes	complemented
170	#14524032	C₂³	1	8	yes	complemented
171	#14524032	C₂³	1	8	yes	complemented
172	#14524032	C₂³	1	8	yes	complemented
173	#14524032	C₂³	1	8	yes	complemented
174	#14524031	C₂³	1	16	yes	complemented
175	#14524029	C₂³	1	16	yes	complemented
176	#14524029	C₂³	1	16	yes	complemented
177	#14524029	C₂³	1	16	yes	complemented
178	#14524028	C₂³	1	16	yes	—
179	#14524028	C₂³	1	16	yes	complemented
180	#14524028	C₂³	1	16	yes	complemented
181	#14524028	C₂³	1	16	yes	complemented
182	#14524028	C₂³	1	16	yes	complemented
183	#14524027	C₂³	1	16	yes	complemented
184	#14524026	C₂³	1	16	yes	complemented
185	#14524026	C₂³	1	16	yes	complemented
186	#14524026	C₂³	1	16	yes	complemented
187	#14524025	C₂³	1	16	yes	complemented
188	#14524023	C₂³	1	16	yes	complemented
189	#14524021	C₂³	1	16	yes	complemented
190	#14524021	C₂³	1	16	yes	complemented
191	#14524020	C₂³	1	16	yes	complemented
192	#14524019	C₂³	1	16	yes	complemented
193	#14524019	C₂³	1	16	yes	complemented
194	#14524019	C₂³	1	16	yes	complemented
195	#14524018	C₂³	1	16	yes	—
196	#14524018	C₂³	1	16	yes	complemented
197	#14524018	C₂³	1	16	yes	complemented
198	#14524017	C₂³	1	16	yes	complemented
199	#14524016	C₂³	1	16	yes	—
200	#14524016	C₂³	1	16	yes	complemented
201	#14524016	C₂³	1	16	yes	complemented
202	#14524015	C₂³	1	16	yes	—
203	#14524015	C₂³	1	16	yes	complemented
204	#14524013	C₂³	1	16	yes	—
205	#14524013	C₂³	1	16	yes	—
206	#14524013	C₂³	1	16	yes	complemented
207	#14524013	C₂³	1	16	yes	complemented
208	#14524011	C₂³	1	16	yes	—
209	#14524011	C₂³	1	16	yes	complemented
210	#14524008	C₂³	1	16	yes	complemented
211	C₄×D₂₆₈	C₂³	1	16	yes	complemented
212	D₄×Dic₆₇	C₂³	1	16	yes	complemented
213	#14524005	C₂³	1	16	yes	complemented
214	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
215	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
216	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
217	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
218	#14524002	C₂³	1	8	yes	complemented
219	#14524001	C₂³	1	16	yes	complemented
220	#14524001	C₂³	1	16	yes	complemented
221	#14524000	C₂³	1	16	yes	complemented
222	#14523999	C₂³	1	16	yes	complemented
223	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
224	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
225	C₂×C₄⋊Dic₆₇	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×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
235	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
236	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
237	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
238	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
239	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
240	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
241	C₂×(C₂×D₆₇)⋊C₄	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	16	yes	complemented
258	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
259	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
260	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
261	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
262	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
264	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
266	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
268	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₆₇	C₂³	1	8	yes	complemented
270	C₂×#41×C₆₇	—	4	4	no	—
271	C₂×#41×C₆₇	C₂³	1	8	yes	—
272	C₂²×Q₈×C₆₇	—	4	4	no	—
273	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
274	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
275	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
276	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
277	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
278	C₂²×Q₈×C₆₇	C₂³	1	8	yes	complemented
279	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
280	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
281	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
282	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
283	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
284	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
285	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
286	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
287	#124×C₆₇	C₂³	1	8	yes	complemented
288	#124×C₆₇	C₂³	1	8	yes	complemented
289	#123×C₆₇	C₂³	1	16	yes	complemented
290	#123×C₆₇	C₂³	1	16	yes	complemented
291	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
292	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
293	#117×C₆₇	C₂³	1	8	yes	complemented
294	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
295	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
296	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
299	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
300	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
301	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
302	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
303	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
304	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
306	C₂³×D₆₇	—	2	8	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	—	4	4	no	—
312	C₂³×D₆₇	C₂⁴	1	2	yes	—
313	C₂³×D₆₇	C₂⁴	1	2	yes	—
314	C₂³×D₆₇	C₂⁴	1	2	yes	—
315	C₂³×D₆₇	C₂⁴	1	8	yes	—
316	C₂³×D₆₇	C₂⁴	1	8	yes	—
317	#11761628	—	4	16	no	—
318	C₂×Dic₁₃₄	—	4	4	no	—
319	C₂×Dic₁₃₄	—	4	2	no	—
320	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
321	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
322	C₂×D₂₆₈	—	4	4	no	—
323	C₂×D₂₆₈	—	4	2	no	—
324	C₂×D₂₆₈	—	4	4	no	—
325	C₂×D₂₆₈	—	4	2	no	—
326	C₂×D₂₆₈	—	4	16	no	—
327	C₂×D₂₆₈	—	4	4	no	—
328	C₂×D₂₆₈	—	4	4	no	—
329	C₂×D₂₆₈	—	4	2	no	—
330	C₂×D₂₆₈	C₂⁴	1	8	yes	—
331	C₂×D₂₆₈	C₂⁴	1	8	yes	—
332	C₂×D₂₆₈	C₂⁴	1	4	yes	—
333	C₂×D₂₆₈	C₂⁴	1	4	yes	—
334	C₂×D₂₆₈	C₂⁴	1	8	yes	—
335	C₂×D₂₆₈	C₂⁴	1	4	yes	—
336	C₂×D₂₆₈	C₂⁴	1	8	yes	—
337	C₂×C₂²⋊D₆₇	—	2	8	no	—
338	C₂×C₂²⋊D₆₇	—	4	4	no	—
339	C₂×C₂²⋊D₆₇	—	4	4	no	—
340	C₂×C₂²⋊D₆₇	—	4	4	no	—
341	C₂×C₂²⋊D₆₇	—	4	4	no	—
342	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
343	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
344	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
345	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
346	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
347	D₄×D₆₇	—	4	32	no	—
348	C₂²×Dic₆₇	—	4	4	no	—
349	C₂²×Dic₆₇	—	4	4	no	—
350	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
351	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
352	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
353	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
354	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
355	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
356	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
357	C₂×C₄×D₆₇	—	4	4	no	—
358	C₂×C₄×D₆₇	—	4	4	no	—
359	C₂×C₄×D₆₇	—	4	4	no	—
360	C₂×C₄×D₆₇	—	4	4	no	—
361	C₂×C₄×D₆₇	—	4	4	no	—
362	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
363	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
364	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
365	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
366	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
367	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
368	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
369	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
370	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
371	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
372	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
373	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
374	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
375	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
376	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
377	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
378	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
379	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
380	C₂²⋊Dic₆₇	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	(C₂×D₆₇)⋊C₄	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	C₄×Dic₆₇	C₂⁴	1	4	yes	—
402	C₄×Dic₆₇	C₂⁴	1	8	yes	—
403	C₄×Dic₆₇	C₂⁴	1	4	yes	—
404	C₄×Dic₆₇	C₂⁴	1	8	yes	—
405	C₄×Dic₆₇	C₂⁴	1	4	yes	—
406	C₄×Dic₆₇	C₂⁴	1	8	yes	—
407	C₄×Dic₆₇	C₂⁴	1	4	yes	—
408	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
409	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
410	#41×C₆₇	—	4	16	no	—
411	C₂×Q₈×C₆₇	—	4	2	no	—
412	C₂×Q₈×C₆₇	—	4	2	no	—
413	C₂×Q₈×C₆₇	—	4	2	no	—
414	C₂×Q₈×C₆₇	—	4	2	no	—
415	C₂×Q₈×C₆₇	—	4	16	no	—
416	C₂×Q₈×C₆₇	—	4	2	no	—
417	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
418	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
419	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
420	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
421	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
422	C₂×D₄×C₆₇	—	2	8	no	—
423	C₂×D₄×C₆₇	—	4	2	no	—
424	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
425	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
426	C₂²×C₄×C₆₇	—	2	4	no	—
427	C₂²×C₄×C₆₇	—	2	4	no	—
428	C₂²×C₄×C₆₇	—	2	4	no	—
429	C₂²×C₄×C₆₇	—	4	4	no	—
430	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
432	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
433	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
438	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
440	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
441	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
442	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
443	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
444	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
445	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
446	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
447	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
448	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
449	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
451	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
452	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
453	C₄²×C₆₇	C₂⁴	1	4	yes	—
454	C₄²×C₆₇	C₂⁴	1	4	yes	—
455	C₂³×C₆₇	—	2	4	no	—
456	C₂³×C₆₇	—	2	4	no	—
457	C₂³×C₆₇	—	2	4	no	—
458	C₂³×C₆₇	—	2	4	no	—
459	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
460	C₂³×C₆₇	C₂⁵	1	4	yes	—
461	C₂³×C₆₇	C₂⁵	1	2	yes	—
462	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
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	4	no	—
471	C₂²×D₆₇	—	2	4	no	—
472	C₂²×D₆₇	—	2	16	no	—
473	C₂²×D₆₇	—	4	8	no	—
474	C₂²×D₆₇	—	4	8	no	—
475	C₂²×D₆₇	—	4	8	no	—
476	C₂²×D₆₇	—	4	8	no	—
477	C₂²×D₆₇	—	4	8	no	—
478	C₂²×D₆₇	—	8	16	no	—
479	C₂²×D₆₇	—	8	16	no	—
480	C₂²×D₆₇	C₂⁵	1	4	yes	—
481	C₂²×D₆₇	C₂⁵	1	4	yes	—
482	C₂²×D₆₇	C₂⁵	1	4	yes	—
483	Q₈×C₆₇	—	4	4	no	—
484	Q₈×C₆₇	—	4	4	no	—
485	Q₈×C₆₇	—	4	4	no	—
486	Q₈×C₆₇	—	4	4	no	—
487	Q₈×C₆₇	—	4	4	no	—
488	D₄×C₆₇	—	2	16	no	—
489	D₄×C₆₇	—	4	4	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	2	no	—
492	C₂×C₄×C₆₇	—	2	8	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	8	no	—
495	C₂×C₄×C₆₇	—	2	2	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	8	no	—
499	C₂×C₄×C₆₇	—	2	4	no	—
500	C₂×C₄×C₆₇	—	2	4	no	—
501	C₂×C₄×C₆₇	—	2	4	no	—
502	C₂×C₄×C₆₇	—	4	8	no	—
503	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
504	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
505	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
506	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
507	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
508	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
509	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
510	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
511	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
512	C₂²⋊D₆₇	—	2	16	no	—
513	C₂²⋊D₆₇	—	4	8	no	—
514	C₂²⋊D₆₇	—	4	8	no	—
515	C₂²⋊D₆₇	—	4	8	no	—
516	C₂²⋊D₆₇	—	4	8	no	—
517	C₂×Dic₆₇	—	2	4	no	—
518	C₂×Dic₆₇	—	2	4	no	—
519	C₂×Dic₆₇	—	2	4	no	—
520	C₂×Dic₆₇	—	2	4	no	—
521	C₂×Dic₆₇	—	2	4	no	—
522	C₂×Dic₆₇	—	4	8	no	—
523	C₂×Dic₆₇	—	4	8	no	—
524	C₂×Dic₆₇	C₂⁵	1	4	yes	—
525	C₂×Dic₆₇	C₂⁵	1	4	yes	—
526	C₂×Dic₆₇	C₂⁵	1	4	yes	—
527	C₂×Dic₆₇	C₂⁵	1	4	yes	—
528	C₂×Dic₆₇	C₂⁵	1	4	yes	—
529	D₂₆₈	—	4	8	no	—
530	D₂₆₈	—	4	4	no	—
531	D₂₆₈	—	4	8	no	—
532	D₂₆₈	—	4	4	no	—
533	D₂₆₈	—	4	8	no	—
534	D₂₆₈	—	4	8	no	—
535	D₂₆₈	—	4	4	no	—
536	C₄×D₆₇	—	4	8	no	—
537	C₄×D₆₇	—	4	8	no	—
538	C₄×D₆₇	—	4	8	no	—
539	C₄×D₆₇	—	4	8	no	—
540	C₄×D₆₇	—	4	8	no	—
541	Dic₁₃₄	—	4	8	no	—
542	Dic₁₃₄	—	4	4	no	—
543	C₂²×C₆₇	—	2	4	no	—
544	C₂²×C₆₇	—	2	8	no	—
545	C₂²×C₆₇	—	2	4	no	—
546	C₂²×C₆₇	—	2	4	no	—
547	C₂²×C₆₇	—	2	4	no	—
548	C₂²×C₆₇	—	4	8	no	—
549	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
550	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
551	C₂²×C₆₇	#585	1	4	yes	—
552	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
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	—	2	4	no	—
562	C₂×D₆₇	—	4	8	no	—
563	C₂×D₆₇	—	4	8	no	—
564	C₂×D₆₇	—	4	8	no	—
565	C₂×D₆₇	—	8	16	no	—
566	C₂×D₆₇	—	8	16	no	—
567	C₄×C₆₇	—	2	2	no	—
568	C₄×C₆₇	—	2	2	no	—
569	C₄×C₆₇	—	2	4	no	—
570	C₄×C₆₇	—	2	2	no	—
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	2	2	no	—
574	C₄×C₆₇	—	2	4	no	—
575	C₄×C₆₇	—	2	4	no	—
576	Dic₆₇	—	2	4	no	—
577	Dic₆₇	—	2	4	no	—
578	Dic₆₇	—	2	4	no	—
579	Dic₆₇	—	2	4	no	—
580	Dic₆₇	—	2	4	no	—
581	C₂×#3545	—	67	1	no	maximal, Sylow
582	C₂×C₆₇	—	2	4	no	—
583	C₂×C₆₇	—	4	4	no	—
584	C₂×C₆₇	#3545	1	4	yes	complemented
585	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂×C₆₇	C₂×#585	1	2	yes	—
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	2	no	—
593	C₂×H(3,𝔽₄)	—	67	1	no	—
594	C₂×#555	—	67	1	no	—
595	C₂×#555	—	67	1	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	1	no	—
606	C₂×#536	D₆₇	1	1	yes	characteristic, complemented
607	C₂×#534	—	67	2	no	—
608	C₂×#529	—	67	2	no	—
609	C₂²×#124	—	67	1	no	—
610	C₆₇	C₂×#3545	1	1	yes	characteristic, complemented, Sylow
611	C₂²×#41	—	67	1	no	—
612	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
613	C₂³×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
614	C₂³×D₄	—	67	2	no	—
615	C₂³×D₄	—	67	1	no	—
616	#563	—	67	16	no	—
617	#562	—	67	32	no	—
618	H(3,𝔽₄)	—	67	16	no	—
619	#555	—	67	16	no	—
620	#555	—	67	16	no	—
621	#551	—	67	32	no	—
622	#551	—	67	32	no	—
623	#551	—	67	32	no	—
624	#546	—	67	32	no	—
625	#546	—	67	32	no	—
626	#542	—	67	32	no	—
627	#542	—	67	32	no	—
628	#538	—	67	32	no	—
629	#538	—	67	32	no	—
630	#536	—	67	16	no	—
631	#536	C₂×D₆₇	1	16	yes	complemented
632	#534	—	67	32	no	—
633	C₂×C₄⋊Q₈	—	67	1	no	—
634	C₂×C₄⋊Q₈	—	67	1	no	—
635	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
636	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
637	#529	—	67	32	no	—
638	C₂×#126	—	67	2	no	—
639	C₂×#126	—	67	2	no	—
640	C₂×#126	—	67	2	no	—
641	C₂×#126	—	67	2	no	—
642	C₂×#126	—	67	2	no	—
643	C₂×#126	—	67	2	no	—
644	C₂×#125	—	67	2	no	—
645	C₂×#124	—	67	2	no	—
646	C₂×#124	—	67	2	no	—
647	C₂×#124	—	67	1	no	—
648	C₂×#124	—	67	1	no	—
649	C₂×#124	—	67	1	no	—
650	C₂×#124	—	67	1	no	—
651	C₂×#124	—	67	1	no	—
652	C₂×#124	—	67	1	no	—
653	C₂×#124	—	67	2	no	—
654	C₂×#124	—	67	16	no	—
655	C₂×#124	—	67	2	no	—
656	C₂×#124	—	67	2	no	—
657	C₂×#124	—	67	2	no	—
658	C₂×#124	—	67	2	no	—
659	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
660	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
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	—	67	2	no	—
670	C₂×#123	—	67	2	no	—
671	C₂×#123	C₂×D₆₇	1	2	yes	complemented
672	C₂×#123	C₂×D₆₇	1	2	yes	complemented
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	—	67	2	no	—
680	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
681	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
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	—	67	2	no	—
690	C₂×#121	—	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×#120	—	67	2	no	—
697	C₂×C₄×Q₈	—	67	2	no	—
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	2	no	—
703	C₂×C₄×D₄	—	67	2	no	—
704	C₂×C₄×D₄	—	67	2	no	—
705	C₂×#117	—	67	1	no	—
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	1	yes	characteristic, 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	—	67	1	no	—
717	C₂⁵	—	67	2	no	—
718	C₂⁵	—	67	2	no	—
719	C₂×#41	—	4	4	no	—
720	C₂×#41	—	268	4	no	—
721	C₂×#41	—	67	8	no	—
722	C₂×#41	C₂²×D₆₇	1	8	yes	—
723	C₂²×Q₈	—	4	4	no	—
724	C₂²×Q₈	—	67	2	no	—
725	C₂²×Q₈	—	67	1	no	—
726	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
727	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
728	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
729	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
730	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
731	C₂²×Q₈	C₂²×D₆₇	1	8	yes	complemented
732	C₂²×D₄	—	268	4	no	—
733	C₂²×D₄	—	268	8	no	—
734	C₂²×D₄	—	67	2	no	—
735	C₂²×D₄	—	67	2	no	—
736	C₂²×D₄	—	67	2	no	—
737	C₂²×D₄	—	67	2	no	—
738	C₂²×D₄	—	67	16	no	—
739	C₂²×D₄	—	67	2	no	—
740	C₂²×D₄	—	67	2	no	—
741	C₂²×D₄	—	67	2	no	—
742	C₂²×D₄	—	67	1	no	—
743	C₂²×D₄	—	67	1	no	—
744	C₂²×D₄	—	67	2	no	—
745	C₂²×D₄	—	67	2	no	—
746	C₂²×D₄	—	67	1	no	—
747	C₂²×D₄	—	67	8	no	—
748	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
749	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
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	—	67	2	no	—
755	C₂³×C₄	—	67	2	no	—
756	C₂³×C₄	—	67	2	no	—
757	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
758	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
759	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
760	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
761	C₄⋊Q₈	—	67	8	no	—
762	C₄⋊Q₈	—	67	8	no	—
763	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
764	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
765	#126	—	67	16	no	—
766	#126	—	67	16	no	—
767	#126	—	67	16	no	—
768	#126	—	67	16	no	—
769	#126	—	67	16	no	—
770	#126	—	67	16	no	—
771	#125	—	67	16	no	—
772	#124	—	67	16	no	—
773	#124	—	67	16	no	—
774	#124	—	67	8	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	—	67	16	no	—
782	#124	—	67	16	no	—
783	#124	—	67	16	no	—
784	#124	—	67	16	no	—
785	#124	C₂²×D₆₇	1	8	yes	complemented
786	#124	C₂²×D₆₇	1	8	yes	complemented
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	—	67	16	no	—
794	#123	—	67	16	no	—
795	#123	—	67	16	no	—
796	#123	—	67	16	no	—
797	#123	C₂²×D₆₇	1	16	yes	complemented
798	#123	C₂²×D₆₇	1	16	yes	complemented
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	—	67	16	no	—
804	C₂²⋊Q₈	—	67	16	no	—
805	C₂²⋊Q₈	—	67	16	no	—
806	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
807	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
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	—	67	16	no	—
814	#121	—	67	16	no	—
815	#121	—	67	16	no	—
816	#121	—	67	16	no	—
817	#120	—	67	16	no	—
818	#120	—	67	16	no	—
819	#120	—	67	16	no	—
820	#120	—	67	16	no	—
821	#120	—	67	16	no	—
822	#120	—	67	16	no	—
823	C₄×Q₈	—	67	16	no	—
824	C₄×D₄	—	67	16	no	—
825	C₄×D₄	—	67	16	no	—
826	C₄×D₄	—	67	16	no	—
827	C₄×D₄	—	67	16	no	—
828	C₄×D₄	—	67	16	no	—
829	C₄×D₄	—	67	16	no	—
830	C₄×D₄	—	67	16	no	—
831	#117	—	67	8	no	—
832	#117	—	67	16	no	—
833	#117	—	67	16	no	—
834	#117	—	67	16	no	—
835	#117	—	67	16	no	—
836	#117	C₂²×D₆₇	1	8	yes	complemented
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	2	no	—
845	C₂×C₄⋊C₄	—	67	2	no	—
846	C₂×C₄⋊C₄	—	67	2	no	—
847	C₂×C₄⋊C₄	—	67	2	no	—
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	2	yes	—
851	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
852	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
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	1	no	—
887	C₂×C₄²	—	67	1	no	—
888	C₂×C₄²	—	67	2	no	—
889	C₂×C₄²	—	67	2	no	—
890	C₂×C₄²	—	67	1	no	—
891	C₂×C₄²	—	67	2	no	—
892	C₂×C₄²	—	67	1	no	—
893	C₂×C₄²	—	67	8	no	—
894	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
895	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
896	C₂⁴	—	268	4	no	—
897	C₂⁴	—	268	4	no	—
898	C₂⁴	—	268	4	no	—
899	C₂⁴	—	268	4	no	—
900	C₂⁴	—	268	4	no	—
901	C₂⁴	—	67	8	no	—
902	C₂⁴	—	67	8	no	—
903	C₂⁴	—	67	2	no	—
904	C₂⁴	—	67	2	no	—
905	C₂⁴	—	67	2	no	—
906	C₂⁴	—	134	8	no	—
907	C₂⁴	C₂³×D₆₇	1	2	yes	—
908	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
909	#41	—	4	16	no	—
910	#41	—	268	16	no	—
911	C₂×Q₈	—	4	2	no	—
912	C₂×Q₈	—	4	2	no	—
913	C₂×Q₈	—	4	2	no	—
914	C₂×Q₈	—	4	2	no	—
915	C₂×Q₈	—	4	16	no	—
916	C₂×Q₈	—	4	2	no	—
917	C₂×Q₈	—	268	2	no	—
918	C₂×Q₈	—	268	4	no	—
919	C₂×Q₈	—	67	8	no	—
920	C₂×Q₈	—	67	4	no	—
921	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
922	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
923	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
924	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
925	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
926	C₂×D₄	—	2	8	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	268	2	no	—
929	C₂×D₄	—	268	4	no	—
930	C₂×D₄	—	268	2	no	—
931	C₂×D₄	—	268	16	no	—
932	C₂×D₄	—	268	4	no	—
933	C₂×D₄	—	268	2	no	—
934	C₂×D₄	—	268	4	no	—
935	C₂×D₄	—	268	4	no	—
936	C₂×D₄	—	268	32	no	—
937	C₂×D₄	—	268	4	no	—
938	C₂×D₄	—	268	4	no	—
939	C₂×D₄	—	268	4	no	—
940	C₂×D₄	—	268	4	no	—
941	C₂×D₄	—	67	8	no	—
942	C₂×D₄	—	67	8	no	—
943	C₂×D₄	—	67	8	no	—
944	C₂×D₄	—	67	8	no	—
945	C₂×D₄	—	67	8	no	—
946	C₂×D₄	—	67	8	no	—
947	C₂×D₄	—	67	8	no	—
948	C₂×D₄	—	67	4	no	—
949	C₂×D₄	—	67	4	no	—
950	C₂×D₄	—	67	8	no	—
951	C₂×D₄	—	67	8	no	—
952	C₂×D₄	—	67	4	no	—
953	C₂×D₄	—	134	8	no	—
954	C₂×D₄	C₂³×D₆₇	1	8	yes	—
955	C₂×D₄	C₂³×D₆₇	1	4	yes	—
956	C₂²×C₄	—	2	4	no	—
957	C₂²×C₄	—	2	4	no	—
958	C₂²×C₄	—	2	4	no	—
959	C₂²×C₄	—	4	4	no	—
960	C₂²×C₄	—	268	4	no	—
961	C₂²×C₄	—	268	4	no	—
962	C₂²×C₄	—	268	4	no	—
963	C₂²×C₄	—	268	4	no	—
964	C₂²×C₄	—	268	4	no	—
965	C₂²×C₄	—	268	4	no	—
966	C₂²×C₄	—	268	4	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	—	67	8	no	—
973	C₂²×C₄	—	67	8	no	—
974	C₂²×C₄	—	67	2	no	—
975	C₂²×C₄	—	67	2	no	—
976	C₂²×C₄	—	67	2	no	—
977	C₂²×C₄	—	67	2	no	—
978	C₂²×C₄	—	67	2	no	—
979	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
980	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
981	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
982	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
983	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
984	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
985	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
986	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
987	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
988	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
989	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
990	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
991	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
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	8	no	—
998	C₄⋊C₄	—	67	8	no	—
999	C₄⋊C₄	—	67	8	no	—
1000	C₄⋊C₄	—	67	8	no	—
1001	C₄⋊C₄	—	67	8	no	—
1002	C₄⋊C₄	—	67	8	no	—
1003	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1004	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1005	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1006	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1007	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
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	—	67	8	no	—
1030	C₂²⋊C₄	—	67	8	no	—
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	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1035	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1036	C₄²	—	67	4	no	—
1037	C₄²	—	67	8	no	—
1038	C₄²	—	67	4	no	—
1039	C₄²	—	67	4	no	—
1040	C₄²	—	67	8	no	—
1041	C₄²	—	67	8	no	—
1042	C₄²	—	67	4	no	—
1043	C₄²	C₂³×D₆₇	1	4	yes	—
1044	C₄²	C₂³×D₆₇	1	4	yes	—
1045	C₂³	—	2	4	no	—
1046	C₂³	—	2	4	no	—
1047	C₂³	—	2	4	no	—
1048	C₂³	—	2	4	no	—
1049	C₂³	—	268	8	no	—
1050	C₂³	—	268	8	no	—
1051	C₂³	—	268	8	no	—
1052	C₂³	—	268	8	no	—
1053	C₂³	—	268	8	no	—
1054	C₂³	—	536	16	no	—
1055	C₂³	—	536	16	no	—
1056	C₂³	—	67	4	no	—
1057	C₂³	—	67	4	no	—
1058	C₂³	—	67	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	4	no	—
1067	C₂³	—	134	4	no	—
1068	C₂³	—	134	16	no	—
1069	C₂³	#14524088	1	4	yes	—
1070	C₂³	C₂⁴×D₆₇	1	4	yes	—
1071	C₂³	C₂⁴×D₆₇	1	2	yes	—
1072	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1073	Q₈	—	4	4	no	—
1074	Q₈	—	4	4	no	—
1075	Q₈	—	4	4	no	—
1076	Q₈	—	4	4	no	—
1077	Q₈	—	4	4	no	—
1078	Q₈	—	268	4	no	—
1079	Q₈	—	268	8	no	—
1080	D₄	—	2	16	no	—
1081	D₄	—	4	4	no	—
1082	D₄	—	268	4	no	—
1083	D₄	—	268	8	no	—
1084	D₄	—	268	4	no	—
1085	D₄	—	268	8	no	—
1086	D₄	—	268	4	no	—
1087	D₄	—	268	8	no	—
1088	D₄	—	268	8	no	—
1089	D₄	—	268	8	no	—
1090	D₄	—	268	8	no	—
1091	D₄	—	268	8	no	—
1092	D₄	—	268	8	no	—
1093	D₄	—	134	16	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	8	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	8	no	—
1102	C₂×C₄	—	2	8	no	—
1103	C₂×C₄	—	2	4	no	—
1104	C₂×C₄	—	2	4	no	—
1105	C₂×C₄	—	2	4	no	—
1106	C₂×C₄	—	4	8	no	—
1107	C₂×C₄	—	268	8	no	—
1108	C₂×C₄	—	268	8	no	—
1109	C₂×C₄	—	268	8	no	—
1110	C₂×C₄	—	268	8	no	—
1111	C₂×C₄	—	268	8	no	—
1112	C₂×C₄	—	268	8	no	—
1113	C₂×C₄	—	268	8	no	—
1114	C₂×C₄	—	67	4	no	—
1115	C₂×C₄	—	67	4	no	—
1116	C₂×C₄	—	67	4	no	—
1117	C₂×C₄	—	67	4	no	—
1118	C₂×C₄	—	67	4	no	—
1119	C₂×C₄	—	134	4	no	—
1120	C₂×C₄	—	134	4	no	—
1121	C₂×C₄	—	134	4	no	—
1122	C₂×C₄	—	134	4	no	—
1123	C₂×C₄	—	134	4	no	—
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	4	yes	—
1128	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1129	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1130	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1131	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1132	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1133	C₂²	—	2	4	no	—
1134	C₂²	—	2	8	no	—
1135	C₂²	—	2	4	no	—
1136	C₂²	—	2	4	no	—
1137	C₂²	—	2	4	no	—
1138	C₂²	—	4	8	no	—
1139	C₂²	—	268	8	no	—
1140	C₂²	—	268	8	no	—
1141	C₂²	—	268	8	no	—
1142	C₂²	—	536	16	no	—
1143	C₂²	—	536	16	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	—	134	4	no	—
1152	C₂²	—	134	4	no	—
1153	C₂²	C₂×#14524088	1	4	yes	—
1154	C₂²	C₂×#14524088	1	2	yes	—
1155	C₂²	#16864233	1	4	yes	—
1156	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1157	C₄	—	2	2	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	4	no	—
1164	C₄	—	2	4	no	—
1165	C₄	—	2	4	no	—
1166	C₄	—	134	4	no	—
1167	C₄	—	134	4	no	—
1168	C₄	—	134	4	no	—
1169	C₄	—	134	4	no	—
1170	C₄	—	134	4	no	—
1171	C₂	—	2	4	no	—
1172	C₂	—	4	4	no	—
1173	C₂	—	268	4	no	—
1174	C₂	—	268	4	no	—
1175	C₂	—	268	4	no	—
1176	C₂	#22574563	1	4	yes	direct product factor
1177	C₂	C₂²×#14524088	1	1	yes	characteristic
1178	C₂	C₂×#16864233	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#536×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#536	D₆₇
hypocenter	C₆₇	C₂×#3545
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#536

Complements

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

N	H ≅ G/N	type
1. #22574563	C₂	direct (N × H)
2. C₂×#16864145	C₂	semidirect
3. C₂×#16864142	C₂	semidirect
4. C₂×#16864138	C₂	semidirect
5. C₂×#16864112	C₂	semidirect
6. C₂×#16864108	C₂	semidirect
7. C₂×#16864073	C₂	semidirect
8. C₂×#16864070	C₂	semidirect
9. C₂×#16864069	C₂	semidirect
10. C₂×#16864038	C₂	semidirect
11. C₂×#16864034	C₂	semidirect
12. C₂×#16864020	C₂	semidirect
13. C₂×#16864016	C₂	semidirect
14. C₂×#16863986	C₂	semidirect
15. C₂×#16863980	C₂	semidirect
16. C₂×#16863970	C₂	semidirect
17. C₂×#16863957	C₂	semidirect
18. C₂×#16863923	C₂	semidirect
19. C₂²×#14524032	C₂	semidirect
20. C₂×#536×C₆₇	C₂	semidirect
23. C₂²×D₄×D₆₇	C₂²	semidirect
24. #16864145	C₂²	semidirect
25. #16864142	C₂²	semidirect
26. #16864138	C₂²	semidirect
27. #16864112	C₂²	semidirect
28. #16864108	C₂²	semidirect
29. #16864073	C₂²	semidirect
30. #16864070	C₂²	semidirect
31. #16864069	C₂²	semidirect
32. #16864038	C₂²	semidirect
33. #16864034	C₂²	semidirect
34. #16864020	C₂²	semidirect
35. #16864016	C₂²	semidirect
36. #16863986	C₂²	semidirect
37. #16863980	C₂²	semidirect
38. #16863970	C₂²	semidirect
39. #16863957	C₂²	semidirect
40. C₂×#14524041	C₂²	semidirect
41. C₂×#14524041	C₂²	semidirect
42. #16863923	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×#14524036	C₂²	semidirect
49. C₂×#14524033	C₂²	semidirect
52. C₂×#14524032	C₂²	semidirect
53. C₂×#14524032	C₂²	semidirect
54. C₂×#14524032	C₂²	semidirect
55. C₂×#14524032	C₂²	semidirect
56. C₂×#14524032	C₂²	semidirect
57. C₂×#14524032	C₂²	semidirect
58. C₂×#14524032	C₂²	semidirect
59. C₂×#14524032	C₂²	semidirect
60. C₂×#14524031	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×#14524026	C₂²	semidirect
71. C₂×#14524026	C₂²	semidirect
72. C₂×#14524026	C₂²	semidirect
73. C₂×#14524025	C₂²	semidirect
74. C₂×#14524023	C₂²	semidirect
75. C₂×#14524021	C₂²	semidirect
76. C₂×#14524021	C₂²	semidirect
77. C₂×#14524020	C₂²	semidirect
78. C₂×#14524019	C₂²	semidirect
79. C₂×#14524019	C₂²	semidirect
80. C₂×#14524019	C₂²	semidirect
82. C₂×#14524018	C₂²	semidirect
83. C₂×#14524018	C₂²	semidirect
84. C₂×#14524017	C₂²	semidirect
86. C₂×#14524016	C₂²	semidirect
87. C₂×#14524016	C₂²	semidirect
89. C₂×#14524015	C₂²	semidirect
92. C₂×#14524013	C₂²	semidirect
93. C₂×#14524013	C₂²	semidirect
95. C₂×#14524011	C₂²	semidirect
96. C₂×#14524008	C₂²	semidirect
97. C₂×C₄×D₂₆₈	C₂²	semidirect
98. C₂×D₄×Dic₆₇	C₂²	semidirect
99. C₂×#14524005	C₂²	semidirect
100. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
101. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
102. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
103. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
104. C₂×#14524002	C₂²	semidirect
105. C₂×#14524001	C₂²	semidirect
106. C₂×#14524001	C₂²	semidirect
107. C₂×#14524000	C₂²	semidirect
108. C₂×#14523999	C₂²	semidirect
109. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
110. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
111. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
112. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
113. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
114. C₂²×C₄×Dic₆₇	C₂²	semidirect
116. C₂³×Q₈×C₆₇	C₂²	semidirect
117. #536×C₆₇	C₂²	semidirect
118. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
119. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
120. C₂×#124×C₆₇	C₂²	semidirect
121. C₂×#124×C₆₇	C₂²	semidirect
122. C₂×#123×C₆₇	C₂²	semidirect
123. C₂×#123×C₆₇	C₂²	semidirect
124. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
125. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
126. C₂×#117×C₆₇	C₂²	semidirect
148. C₂×D₄×D₆₇	C₂³	semidirect
156. #14524041	C₂³	semidirect
157. #14524041	C₂³	semidirect
158. #14524038	C₂³	semidirect
159. #14524038	C₂³	semidirect
160. #14524038	C₂³	semidirect
161. #14524038	C₂³	semidirect
162. #14524037	C₂³	semidirect
163. #14524036	C₂³	semidirect
164. #14524033	C₂³	semidirect
167. #14524032	C₂³	semidirect
168. #14524032	C₂³	semidirect
169. #14524032	C₂³	semidirect
170. #14524032	C₂³	semidirect
171. #14524032	C₂³	semidirect
172. #14524032	C₂³	semidirect
173. #14524032	C₂³	semidirect
174. #14524031	C₂³	semidirect
175. #14524029	C₂³	semidirect
176. #14524029	C₂³	semidirect
177. #14524029	C₂³	semidirect
179. #14524028	C₂³	semidirect
180. #14524028	C₂³	semidirect
181. #14524028	C₂³	semidirect
182. #14524028	C₂³	semidirect
183. #14524027	C₂³	semidirect
184. #14524026	C₂³	semidirect
185. #14524026	C₂³	semidirect
186. #14524026	C₂³	semidirect
187. #14524025	C₂³	semidirect
188. #14524023	C₂³	semidirect
189. #14524021	C₂³	semidirect
190. #14524021	C₂³	semidirect
191. #14524020	C₂³	semidirect
192. #14524019	C₂³	semidirect
193. #14524019	C₂³	semidirect
194. #14524019	C₂³	semidirect
196. #14524018	C₂³	semidirect
197. #14524018	C₂³	semidirect
198. #14524017	C₂³	semidirect
200. #14524016	C₂³	semidirect
201. #14524016	C₂³	semidirect
203. #14524015	C₂³	semidirect
206. #14524013	C₂³	semidirect
207. #14524013	C₂³	semidirect
209. #14524011	C₂³	semidirect
210. #14524008	C₂³	semidirect
211. C₄×D₂₆₈	C₂³	semidirect
212. D₄×Dic₆₇	C₂³	semidirect
213. #14524005	C₂³	semidirect
214. C₄×C₂²⋊D₆₇	C₂³	semidirect
215. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
216. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
217. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
218. #14524002	C₂³	semidirect
219. #14524001	C₂³	semidirect
220. #14524001	C₂³	semidirect
221. #14524000	C₂³	semidirect
222. #14523999	C₂³	semidirect
257. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
258. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
259. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
260. C₂²⋊C₄×D₆₇	C₂³	semidirect
261. C₂²⋊C₄×D₆₇	C₂³	semidirect
269. C₂×C₄×Dic₆₇	C₂³	semidirect
278. C₂²×Q₈×C₆₇	C₂³	semidirect
285. C₄⋊Q₈×C₆₇	C₂³	semidirect
286. C₄⋊Q₈×C₆₇	C₂³	semidirect
287. #124×C₆₇	C₂³	semidirect
288. #124×C₆₇	C₂³	semidirect
289. #123×C₆₇	C₂³	semidirect
290. #123×C₆₇	C₂³	semidirect
291. C₂²⋊Q₈×C₆₇	C₂³	semidirect
292. C₂²⋊Q₈×C₆₇	C₂³	semidirect
293. #117×C₆₇	C₂³	semidirect
584. C₂×C₆₇	#3545	semidirect
606. C₂×#536	D₆₇	semidirect
610. C₆₇	C₂×#3545	semidirect
613. C₂³×Q₈	C₂×D₆₇	semidirect
631. #536	C₂×D₆₇	semidirect
635. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
636. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
659. C₂×#124	C₂×D₆₇	semidirect
660. C₂×#124	C₂×D₆₇	semidirect
671. C₂×#123	C₂×D₆₇	semidirect
672. C₂×#123	C₂×D₆₇	semidirect
680. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
681. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
710. C₂×#117	C₂×D₆₇	semidirect
731. C₂²×Q₈	C₂²×D₆₇	semidirect
763. C₄⋊Q₈	C₂²×D₆₇	semidirect
764. C₄⋊Q₈	C₂²×D₆₇	semidirect
785. #124	C₂²×D₆₇	semidirect
786. #124	C₂²×D₆₇	semidirect
797. #123	C₂²×D₆₇	semidirect
798. #123	C₂²×D₆₇	semidirect
806. C₂²⋊Q₈	C₂²×D₆₇	semidirect
807. C₂²⋊Q₈	C₂²×D₆₇	semidirect
836. #117	C₂²×D₆₇	semidirect
1176. C₂	#22574563	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574563	2
C₂×#16864145	2
C₂×#16864142	2
C₂×#16864138	2
C₂×#16864112	2
C₂×#16864108	2
C₂×#16864073	2
C₂×#16864070	2
C₂×#16864069	2
C₂×#16864038	2
C₂×#16864034	2
C₂×#16864020	2
C₂×#16864016	2
C₂×#16863986	2
C₂×#16863980	2
C₂×#16863970	2
C₂×#16863957	2
C₂×#16863923	2
C₂²×#14524032	2
C₂×#536×C₆₇	2
C₂×#3545	67

Subgroups — C2×#22574563 #31763588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574563 #31763588