Subgroups — C₂×#22574271 #31763955

Order 17152.

7314 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574271	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864115	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864096	C₂	1	2	yes	maximal, complemented
6	C₂×#16864093	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16864085	C₂	1	2	yes	maximal, complemented
8	C₂×#16864084	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16864075	C₂	1	2	yes	maximal, complemented
10	C₂×#16864070	C₂	1	2	yes	maximal, complemented
11	C₂×#16864048	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16864043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16864039	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16864011	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16864004	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16863989	C₂	1	2	yes	maximal, complemented
17	C₂×#16863982	C₂	1	2	yes	maximal, complemented
18	C₂×#16863930	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16863929	C₂	1	2	yes	maximal, complemented
20	C₂×#126×D₆₇	C₂	1	2	yes	maximal, complemented
21	C₂×#16863878	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863868	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×#11761628	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761629	C₂²	1	1	yes	characteristic
26	C₂²×#11761628	C₂²	1	1	yes	characteristic
27	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic
28	#16864117	C₂²	1	16	yes	complemented
29	#16864115	C₂²	1	16	yes	complemented
30	#16864102	C₂²	1	16	yes	complemented
31	#16864096	C₂²	1	32	yes	complemented
32	#16864093	C₂²	1	16	yes	complemented
33	#16864085	C₂²	1	32	yes	complemented
34	#16864084	C₂²	1	16	yes	complemented
35	#16864075	C₂²	1	32	yes	complemented
36	#16864070	C₂²	1	32	yes	complemented
37	#16864048	C₂²	1	16	yes	complemented
38	#16864043	C₂²	1	16	yes	complemented
39	#16864039	C₂²	1	16	yes	complemented
40	#16864011	C₂²	1	16	yes	complemented
41	#16864004	C₂²	1	16	yes	complemented
42	#16863989	C₂²	1	32	yes	complemented
43	#16863982	C₂²	1	32	yes	complemented
44	C₂×#14524042	C₂²	1	1	yes	characteristic, complemented
45	C₂×#14524041	C₂²	1	1	yes	characteristic, complemented
46	#16863930	C₂²	1	16	yes	complemented
47	#16863929	C₂²	1	32	yes	complemented
48	C₂×#14524038	C₂²	1	2	yes	—
49	C₂×#14524038	C₂²	1	2	yes	—
50	C₂×#14524038	C₂²	1	2	yes	—
51	C₂×#14524037	C₂²	1	2	yes	—
52	C₂×#14524037	C₂²	1	1	yes	characteristic
53	C₂×#14524037	C₂²	1	1	yes	characteristic, complemented
54	C₂×#14524036	C₂²	1	2	yes	complemented
55	C₂×#14524036	C₂²	1	2	yes	complemented
56	C₂×#14524036	C₂²	1	2	yes	complemented
57	C₂×#14524036	C₂²	1	2	yes	complemented
58	C₂×#14524036	C₂²	1	2	yes	complemented
59	#126×D₆₇	C₂²	1	32	yes	complemented
60	C₂×#14524035	C₂²	1	2	yes	complemented
61	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
62	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
63	C₂×#14524034	C₂²	1	2	yes	complemented
64	C₂×#14524033	C₂²	1	2	yes	complemented
65	C₂×#14524031	C₂²	1	1	yes	characteristic
66	C₂×#14524030	C₂²	1	1	yes	characteristic
67	C₂×#14524029	C₂²	1	2	yes	—
68	C₂×#14524029	C₂²	1	2	yes	complemented
69	C₂×#14524028	C₂²	1	2	yes	—
70	C₂×#14524028	C₂²	1	2	yes	complemented
71	C₂×#14524026	C₂²	1	1	yes	characteristic
72	C₂×#14524026	C₂²	1	2	yes	complemented
73	C₂×#14524026	C₂²	1	1	yes	characteristic, complemented
74	C₂×#14524025	C₂²	1	2	yes	—
75	C₂×#14524025	C₂²	1	2	yes	—
76	C₂×#14524025	C₂²	1	2	yes	complemented
77	C₂×#14524024	C₂²	1	2	yes	complemented
78	C₂×#14524023	C₂²	1	1	yes	characteristic
79	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
80	C₂×#14524023	C₂²	1	2	yes	complemented
81	C₂×#14524022	C₂²	1	2	yes	complemented
82	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
83	C₂×#14524021	C₂²	1	2	yes	complemented
84	C₂×#14524021	C₂²	1	2	yes	complemented
85	C₂×#14524020	C₂²	1	2	yes	complemented
86	C₂×#14524019	C₂²	1	1	yes	characteristic
87	C₂×#14524017	C₂²	1	1	yes	characteristic
88	C₂×#14524016	C₂²	1	2	yes	—
89	C₂×#14524016	C₂²	1	2	yes	complemented
90	C₂×#14524014	C₂²	1	1	yes	characteristic
91	C₂×#14524014	C₂²	1	2	yes	—
92	C₂×#14524014	C₂²	1	2	yes	complemented
93	C₂×#14524013	C₂²	1	2	yes	—
94	C₂×#14524011	C₂²	1	2	yes	—
95	#16863878	C₂²	1	16	yes	complemented
96	#16863868	C₂²	1	16	yes	complemented
97	C₄×#11761628	C₂²	1	16	yes	complemented
98	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
102	C₂×#14524008	C₂²	1	2	yes	complemented
103	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
104	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
105	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
106	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
107	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
108	C₂×#14524005	C₂²	1	1	yes	characteristic
109	C₂×#14524005	C₂²	1	1	yes	characteristic
110	C₂×#14524005	C₂²	1	2	yes	complemented
111	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
112	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
113	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
114	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
115	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
117	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
118	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
119	C₂×#14524001	C₂²	1	1	yes	characteristic
120	C₂×#14524001	C₂²	1	2	yes	complemented
121	C₂×#14524000	C₂²	1	1	yes	characteristic
122	C₂×#14524000	C₂²	1	1	yes	characteristic, complemented
123	C₂×#14524000	C₂²	1	2	yes	complemented
124	C₂×#14524000	C₂²	1	2	yes	complemented
125	C₂×#14523999	C₂²	1	2	yes	complemented
126	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
127	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
129	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
130	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
131	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
132	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
133	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
134	C₂×C₄²×D₆₇	C₂²	1	2	yes	complemented
135	#529×C₆₇	C₂²	1	16	yes	complemented
136	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
137	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
138	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
139	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
140	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
141	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
142	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
144	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
145	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
146	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₆₇	C₂³	1	2	yes	—
148	C₂×#11761629	—	2	8	no	—
149	C₂×#11761629	C₂³	1	8	yes	—
150	C₂×#11761628	—	2	8	no	—
151	C₂×#11761628	C₂³	1	8	yes	—
152	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
153	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
154	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
155	C₂²×D₂₆₈	C₂³	1	2	yes	—
156	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
157	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
158	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
159	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
160	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
161	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
162	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
163	C₂×D₄×D₆₇	—	2	8	no	—
164	C₂×D₄×D₆₇	C₂³	1	8	yes	—
165	C₂³×Dic₆₇	C₂³	1	2	yes	—
166	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
167	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
168	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
169	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
170	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
171	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
172	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
173	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
174	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
175	#14524042	C₂³	1	8	yes	complemented
176	#14524041	C₂³	1	8	yes	complemented
177	#14524038	C₂³	1	16	yes	—
178	#14524038	C₂³	1	16	yes	—
179	#14524038	C₂³	1	16	yes	—
180	#14524037	C₂³	1	16	yes	—
181	#14524037	C₂³	1	8	yes	—
182	#14524037	C₂³	1	8	yes	complemented
183	#14524036	C₂³	1	16	yes	complemented
184	#14524036	C₂³	1	16	yes	complemented
185	#14524036	C₂³	1	16	yes	complemented
186	#14524036	C₂³	1	16	yes	complemented
187	#14524036	C₂³	1	16	yes	complemented
188	#14524035	C₂³	1	16	yes	complemented
189	#14524035	C₂³	1	8	yes	complemented
190	#14524034	C₂³	1	8	yes	complemented
191	#14524034	C₂³	1	16	yes	complemented
192	#14524033	C₂³	1	16	yes	complemented
193	#14524031	C₂³	1	8	yes	—
194	#14524030	C₂³	1	8	yes	—
195	#14524029	C₂³	1	16	yes	—
196	#14524029	C₂³	1	16	yes	complemented
197	#14524028	C₂³	1	16	yes	—
198	#14524028	C₂³	1	16	yes	complemented
199	#14524026	C₂³	1	8	yes	—
200	#14524026	C₂³	1	16	yes	complemented
201	#14524026	C₂³	1	8	yes	complemented
202	#14524025	C₂³	1	16	yes	—
203	#14524025	C₂³	1	16	yes	—
204	#14524025	C₂³	1	16	yes	complemented
205	#14524024	C₂³	1	16	yes	complemented
206	#14524023	C₂³	1	8	yes	—
207	#14524023	C₂³	1	8	yes	complemented
208	#14524023	C₂³	1	16	yes	complemented
209	#14524022	C₂³	1	16	yes	complemented
210	#14524022	C₂³	1	8	yes	complemented
211	#14524021	C₂³	1	16	yes	complemented
212	#14524021	C₂³	1	16	yes	complemented
213	#14524020	C₂³	1	16	yes	complemented
214	#14524019	C₂³	1	8	yes	—
215	#14524017	C₂³	1	8	yes	—
216	#14524016	C₂³	1	16	yes	—
217	#14524016	C₂³	1	16	yes	complemented
218	#14524014	C₂³	1	8	yes	—
219	#14524014	C₂³	1	16	yes	—
220	#14524014	C₂³	1	16	yes	complemented
221	#14524013	C₂³	1	16	yes	—
222	#14524011	C₂³	1	16	yes	—
223	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
224	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
225	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
226	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
227	#14524008	C₂³	1	16	yes	complemented
228	C₄×D₂₆₈	C₂³	1	8	yes	—
229	C₄×D₂₆₈	C₂³	1	8	yes	—
230	C₄×D₂₆₈	C₂³	1	8	yes	—
231	C₄×D₂₆₈	C₂³	1	16	yes	complemented
232	D₄×Dic₆₇	C₂³	1	8	yes	—
233	#14524005	C₂³	1	8	yes	—
234	#14524005	C₂³	1	8	yes	—
235	#14524005	C₂³	1	16	yes	complemented
236	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
237	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
238	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
239	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
240	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
241	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	—
242	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
243	#14524002	C₂³	1	8	yes	complemented
244	#14524001	C₂³	1	8	yes	—
245	#14524001	C₂³	1	16	yes	complemented
246	#14524000	C₂³	1	8	yes	—
247	#14524000	C₂³	1	8	yes	complemented
248	#14524000	C₂³	1	16	yes	complemented
249	#14524000	C₂³	1	16	yes	complemented
250	#14523999	C₂³	1	16	yes	complemented
251	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
253	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
254	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
255	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
256	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
259	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
261	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
264	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
265	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
267	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
271	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
272	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
273	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
275	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
276	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
277	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
278	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
279	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
280	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
281	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
282	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
283	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
284	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
286	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	—
287	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
291	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
292	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
293	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
295	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
296	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
297	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
298	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
301	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
302	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
303	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
304	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
305	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
306	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
307	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
308	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
309	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
310	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
313	C₄²×D₆₇	C₂³	1	16	yes	complemented
314	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
316	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
317	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
321	#126×C₆₇	C₂³	1	16	yes	complemented
322	#125×C₆₇	C₂³	1	8	yes	complemented
323	#124×C₆₇	C₂³	1	8	yes	—
324	#123×C₆₇	C₂³	1	16	yes	complemented
325	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
326	#121×C₆₇	C₂³	1	8	yes	—
327	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
328	C₄×D₄×C₆₇	C₂³	1	8	yes	—
329	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
330	#117×C₆₇	C₂³	1	16	yes	complemented
331	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
332	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
333	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
335	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
337	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
338	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
339	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
340	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
341	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
342	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
347	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
348	C₂³×D₆₇	—	2	8	no	—
349	C₂³×D₆₇	—	4	4	no	—
350	C₂³×D₆₇	—	4	4	no	—
351	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
352	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
353	C₂³×D₆₇	C₂⁴	1	2	yes	—
354	C₂³×D₆₇	C₂⁴	1	8	yes	—
355	#11761629	—	2	32	no	—
356	#11761628	—	2	32	no	—
357	C₂×Dic₁₃₄	—	2	4	no	—
358	C₂×Dic₁₃₄	—	4	2	no	—
359	C₂×Dic₁₃₄	—	4	4	no	—
360	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
361	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
362	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
363	C₂×D₂₆₈	—	2	8	no	—
364	C₂×D₂₆₈	—	4	2	no	—
365	C₂×D₂₆₈	#41	1	8	yes	—
366	C₂×D₂₆₈	C₂⁴	1	8	yes	—
367	C₂×D₂₆₈	C₂⁴	1	4	yes	—
368	C₂×D₂₆₈	C₂⁴	1	4	yes	—
369	C₂×C₂²⋊D₆₇	—	2	8	no	—
370	C₂×C₂²⋊D₆₇	—	2	8	no	—
371	C₂×C₂²⋊D₆₇	—	4	2	no	—
372	C₂×C₂²⋊D₆₇	—	4	4	no	—
373	C₂×C₂²⋊D₆₇	—	4	2	no	—
374	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
375	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
376	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
377	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
378	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
379	D₄×D₆₇	—	2	32	no	—
380	C₂²×Dic₆₇	—	4	4	no	—
381	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
382	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
383	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
384	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
385	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
391	C₂×C₄×D₆₇	—	2	8	no	—
392	C₂×C₄×D₆₇	—	2	8	no	—
393	C₂×C₄×D₆₇	—	2	4	no	—
394	C₂×C₄×D₆₇	—	2	4	no	—
395	C₂×C₄×D₆₇	—	4	4	no	—
396	C₂×C₄×D₆₇	—	4	4	no	—
397	C₂×C₄×D₆₇	—	4	4	no	—
398	C₂×C₄×D₆₇	—	4	4	no	—
399	C₂×C₄×D₆₇	—	4	4	no	—
400	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
401	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
402	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
403	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
404	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
405	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
406	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
407	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
408	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
409	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
410	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
411	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
412	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
413	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
414	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
415	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
416	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
417	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
418	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
419	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
420	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
421	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
422	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
423	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
424	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
425	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
426	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
427	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
428	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
429	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
430	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
431	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
432	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
433	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
434	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
435	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
436	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
437	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
438	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
439	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
440	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
441	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
442	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
443	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
444	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
445	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
446	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
447	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
448	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
449	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
450	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
451	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
452	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
453	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
454	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
455	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
456	C₄×Dic₆₇	C₂⁴	1	8	yes	—
457	C₄×Dic₆₇	C₂⁴	1	8	yes	—
458	C₄×Dic₆₇	C₂⁴	1	8	yes	—
459	C₄×Dic₆₇	C₂⁴	1	8	yes	—
460	C₄×Dic₆₇	C₂⁴	1	4	yes	—
461	C₄×Dic₆₇	C₂⁴	1	4	yes	—
462	C₄×Dic₆₇	C₂⁴	1	8	yes	—
463	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
464	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
465	C₂×Q₈×C₆₇	—	2	4	no	—
466	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
467	C₂×D₄×C₆₇	—	2	4	no	—
468	C₂×D₄×C₆₇	—	4	4	no	—
469	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
470	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
471	C₂²×C₄×C₆₇	—	2	4	no	—
472	C₂²×C₄×C₆₇	—	4	2	no	—
473	C₂²×C₄×C₆₇	—	4	4	no	—
474	C₂²×C₄×C₆₇	—	4	2	no	—
475	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
476	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
478	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
479	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
481	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
482	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
483	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
484	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
485	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
486	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
487	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
488	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
489	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
490	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
491	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
492	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
493	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
494	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
495	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
496	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
497	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
498	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
499	C₄²×C₆₇	C₂⁴	1	4	yes	—
500	C₄²×C₆₇	C₂⁴	1	4	yes	—
501	C₄²×C₆₇	C₂⁴	1	4	yes	—
502	C₄²×C₆₇	C₂⁴	1	4	yes	—
503	C₄²×C₆₇	C₂⁴	1	8	yes	—
504	C₂³×C₆₇	—	2	2	no	—
505	C₂³×C₆₇	—	2	4	no	—
506	C₂³×C₆₇	—	2	2	no	—
507	C₂³×C₆₇	—	2	2	no	—
508	C₂³×C₆₇	—	2	4	no	—
509	C₂³×C₆₇	—	2	4	no	—
510	C₂³×C₆₇	C₂⁵	1	4	yes	—
511	C₂³×C₆₇	C₂⁵	1	2	yes	—
512	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
513	C₂²×D₆₇	—	2	4	no	—
514	C₂²×D₆₇	—	2	4	no	—
515	C₂²×D₆₇	—	2	2	no	—
516	C₂²×D₆₇	—	2	2	no	—
517	C₂²×D₆₇	—	2	2	no	—
518	C₂²×D₆₇	—	2	2	no	—
519	C₂²×D₆₇	—	2	2	no	—
520	C₂²×D₆₇	—	2	2	no	—
521	C₂²×D₆₇	—	2	16	no	—
522	C₂²×D₆₇	—	4	8	no	—
523	C₂²×D₆₇	—	4	8	no	—
524	C₂²×D₆₇	—	8	16	no	—
525	C₂²×D₆₇	C₂×#41	1	8	yes	—
526	C₂²×D₆₇	C₂⁵	1	2	yes	—
527	C₂²×D₆₇	C₂⁵	1	2	yes	—
528	C₂²×D₆₇	C₂⁵	1	4	yes	—
529	Q₈×C₆₇	—	2	8	no	—
530	D₄×C₆₇	—	2	8	no	—
531	D₄×C₆₇	—	4	8	no	—
532	C₂×C₄×C₆₇	—	2	2	no	—
533	C₂×C₄×C₆₇	—	2	4	no	—
534	C₂×C₄×C₆₇	—	2	2	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	2	no	—
537	C₂×C₄×C₆₇	—	2	4	no	—
538	C₂×C₄×C₆₇	—	2	2	no	—
539	C₂×C₄×C₆₇	—	2	4	no	—
540	C₂×C₄×C₆₇	—	2	8	no	—
541	C₂×C₄×C₆₇	—	4	8	no	—
542	C₂×C₄×C₆₇	—	4	4	no	—
543	C₂×C₄×C₆₇	—	4	4	no	—
544	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
545	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
546	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
547	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
548	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
549	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
550	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
551	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
552	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
553	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
554	C₂²⋊D₆₇	—	2	16	no	—
555	C₂²⋊D₆₇	—	2	16	no	—
556	C₂²⋊D₆₇	—	4	4	no	—
557	C₂²⋊D₆₇	—	4	8	no	—
558	C₂²⋊D₆₇	—	4	4	no	—
559	C₂×Dic₆₇	—	2	2	no	—
560	C₂×Dic₆₇	—	2	2	no	—
561	C₂×Dic₆₇	—	2	4	no	—
562	C₂×Dic₆₇	—	2	4	no	—
563	C₂×Dic₆₇	—	2	2	no	—
564	C₂×Dic₆₇	—	2	2	no	—
565	C₂×Dic₆₇	—	2	4	no	—
566	C₂×Dic₆₇	—	2	2	no	—
567	C₂×Dic₆₇	—	2	2	no	—
568	C₂×Dic₆₇	—	4	8	no	—
569	C₂×Dic₆₇	C₂⁵	1	4	yes	—
570	C₂×Dic₆₇	C₂⁵	1	2	yes	—
571	C₂×Dic₆₇	C₂⁵	1	4	yes	—
572	C₂×Dic₆₇	C₂⁵	1	4	yes	—
573	C₂×Dic₆₇	C₂⁵	1	2	yes	—
574	C₂×Dic₆₇	C₂⁵	1	2	yes	—
575	C₂×Dic₆₇	C₂⁵	1	2	yes	—
576	C₂×Dic₆₇	C₂⁵	1	2	yes	—
577	C₂×Dic₆₇	C₂⁵	1	2	yes	—
578	D₂₆₈	—	2	16	no	—
579	D₂₆₈	—	4	4	no	—
580	D₂₆₈	C₂×#41	1	16	yes	—
581	C₄×D₆₇	—	2	16	no	—
582	C₄×D₆₇	—	2	16	no	—
583	C₄×D₆₇	—	2	8	no	—
584	C₄×D₆₇	—	2	8	no	—
585	C₄×D₆₇	—	4	8	no	—
586	C₄×D₆₇	—	4	8	no	—
587	C₄×D₆₇	—	4	8	no	—
588	C₄×D₆₇	—	4	8	no	—
589	C₄×D₆₇	—	4	8	no	—
590	Dic₁₃₄	—	2	8	no	—
591	Dic₁₃₄	—	4	8	no	—
592	Dic₁₃₄	—	4	4	no	—
593	C₂²×C₆₇	—	2	2	no	—
594	C₂²×C₆₇	—	2	4	no	—
595	C₂²×C₆₇	—	2	4	no	—
596	C₂²×C₆₇	—	2	2	no	—
597	C₂²×C₆₇	—	2	4	no	—
598	C₂²×C₆₇	—	2	2	no	—
599	C₂²×C₆₇	—	4	8	no	—
600	C₂²×C₆₇	—	4	4	no	—
601	C₂²×C₆₇	C₂²×#41	1	2	yes	—
602	C₂²×C₆₇	#585	1	2	yes	—
603	C₂²×C₆₇	#585	1	2	yes	—
604	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
605	C₂×D₆₇	—	2	4	no	—
606	C₂×D₆₇	—	2	4	no	—
607	C₂×D₆₇	—	2	16	no	—
608	C₂×D₆₇	—	2	2	no	—
609	C₂×D₆₇	—	2	2	no	—
610	C₂×D₆₇	—	2	2	no	—
611	C₂×D₆₇	—	2	2	no	—
612	C₂×D₆₇	—	2	2	no	—
613	C₂×D₆₇	—	2	2	no	—
614	C₂×D₆₇	—	4	4	no	—
615	C₂×D₆₇	—	4	4	no	—
616	C₂×D₆₇	—	8	16	no	—
617	C₂×D₆₇	C₂²×#41	1	8	yes	—
618	C₄×C₆₇	—	2	2	no	—
619	C₄×C₆₇	—	2	4	no	—
620	C₄×C₆₇	—	2	4	no	—
621	C₄×C₆₇	—	2	2	no	—
622	C₄×C₆₇	—	2	2	no	—
623	C₄×C₆₇	—	2	2	no	—
624	C₄×C₆₇	—	2	4	no	—
625	C₄×C₆₇	—	2	2	no	—
626	C₄×C₆₇	C₂²×#41	1	4	yes	—
627	Dic₆₇	—	2	4	no	—
628	Dic₆₇	—	2	2	no	—
629	Dic₆₇	—	2	2	no	—
630	Dic₆₇	—	2	2	no	—
631	Dic₆₇	—	2	2	no	—
632	Dic₆₇	—	2	4	no	—
633	Dic₆₇	—	2	2	no	—
634	Dic₆₇	—	2	4	no	—
635	Dic₆₇	—	2	2	no	—
636	C₂×#3521	—	67	1	no	maximal, Sylow
637	C₂×C₆₇	—	4	4	no	—
638	C₂×C₆₇	—	4	2	no	—
639	C₂×C₆₇	#3521	1	4	yes	complemented
640	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
641	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
642	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
643	D₆₇	—	2	8	no	—
644	D₆₇	—	4	2	no	—
645	D₆₇	—	4	2	no	—
646	#3521	—	67	32	no	—
647	C₂×#556	—	67	1	no	—
648	C₂×#556	—	67	1	no	—
649	C₂×#554	—	67	1	no	—
650	C₂×#553	—	67	1	no	—
651	C₂×#553	—	67	2	no	—
652	C₂×#552	—	67	1	no	—
653	C₂×#552	—	67	2	no	—
654	C₂×#551	—	67	2	no	—
655	C₂×#551	—	67	2	no	—
656	C₂×#547	—	67	1	no	—
657	C₂×#546	—	67	1	no	—
658	C₂×#546	—	67	1	no	—
659	C₂×#542	—	67	1	no	—
660	C₂×#541	—	67	1	no	—
661	C₂×#539	—	67	2	no	—
662	C₂×#538	—	67	2	no	—
663	C₂×#529	—	67	1	no	—
664	C₂×#529	—	67	2	no	—
665	C₂×#529	D₆₇	1	1	yes	characteristic, complemented
666	C₂²×#126	—	67	2	no	—
667	C₂×#520	—	67	1	no	—
668	C₂×#518	—	67	1	no	—
669	C₂×C₄×#41	—	67	1	no	—
670	C₆₇	C₂×#3521	1	1	yes	characteristic, complemented, Sylow
671	C₂²×#41	—	67	1	no	—
672	C₂²×#41	—	67	1	no	—
673	C₂³×D₄	—	67	1	no	—
674	#556	—	67	16	no	—
675	#556	—	67	16	no	—
676	#554	—	67	16	no	—
677	#553	—	67	16	no	—
678	#553	—	67	32	no	—
679	#552	—	67	16	no	—
680	#552	—	67	32	no	—
681	#551	—	67	32	no	—
682	#551	—	67	32	no	—
683	#547	—	67	16	no	—
684	#546	—	67	16	no	—
685	#546	—	67	16	no	—
686	#542	—	67	16	no	—
687	#541	—	67	16	no	—
688	#539	—	67	32	no	—
689	#538	—	67	32	no	—
690	C₂×C₄⋊Q₈	—	67	1	no	—
691	C₂×C₄⋊Q₈	—	67	1	no	—
692	#529	—	67	32	no	—
693	#529	—	67	16	no	—
694	#529	C₂×D₆₇	1	16	yes	complemented
695	C₂×#126	—	67	32	no	—
696	C₂×#126	—	67	2	no	—
697	C₂×#126	—	67	2	no	—
698	C₂×#126	—	67	2	no	—
699	C₂×#126	—	67	2	no	—
700	C₂×#126	—	67	2	no	—
701	C₂×#126	—	67	2	no	—
702	C₂×#126	—	67	2	no	—
703	C₂×#126	—	67	2	no	—
704	C₂×#126	—	67	1	no	—
705	C₂×#126	—	67	1	no	—
706	C₂×#126	—	67	2	no	—
707	C₂×#126	C₂×D₆₇	1	2	yes	complemented
708	C₂×#125	—	67	2	no	—
709	C₂×#125	—	67	2	no	—
710	C₂×#125	—	67	1	no	—
711	C₂×#125	—	67	1	no	—
712	C₂×#125	—	67	2	no	—
713	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
714	C₂×#124	—	67	1	no	—
715	C₂×#124	—	67	2	no	—
716	C₂×#124	—	67	2	no	—
717	C₂×#124	—	67	1	no	—
718	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
719	C₂×#123	—	67	2	no	—
720	C₂×#123	—	67	1	no	—
721	C₂×#123	—	67	1	no	—
722	C₂×#123	—	67	2	no	—
723	C₂×#123	—	67	2	no	—
724	C₂×#123	—	67	2	no	—
725	C₂×#123	—	67	2	no	—
726	C₂×#123	—	67	2	no	—
727	C₂×#123	—	67	2	no	—
728	C₂×#123	C₂×D₆₇	1	2	yes	complemented
729	C₂×C₂²⋊Q₈	—	67	1	no	—
730	C₂×C₂²⋊Q₈	—	67	1	no	—
731	C₂×C₂²⋊Q₈	—	67	2	no	—
732	C₂×C₂²⋊Q₈	—	67	2	no	—
733	C₂×C₂²⋊Q₈	—	67	2	no	—
734	C₂×C₂²⋊Q₈	—	67	2	no	—
735	C₂×C₂²⋊Q₈	—	67	1	no	—
736	C₂×C₂²⋊Q₈	—	67	1	no	—
737	C₂×C₂²⋊Q₈	—	67	2	no	—
738	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
739	C₂×#121	—	67	2	no	—
740	C₂×#121	—	67	2	no	—
741	C₂×#121	—	67	1	no	—
742	C₂×#121	—	67	1	no	—
743	C₂×#121	—	67	2	no	—
744	C₂×#121	—	67	2	no	—
745	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
746	C₂×#120	—	67	2	no	—
747	C₂×#120	—	67	2	no	—
748	#520	—	67	16	no	—
749	#518	—	67	16	no	—
750	C₄×#41	—	67	16	no	—
751	C₂×C₄×Q₈	—	67	1	no	—
752	C₂×C₄×Q₈	—	67	2	no	—
753	C₂×C₄×Q₈	—	67	1	no	—
754	C₂×C₄×Q₈	—	67	1	no	—
755	C₂×C₄×Q₈	—	67	1	no	—
756	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
757	C₂×C₄×D₄	—	67	1	no	—
758	C₂×C₄×D₄	—	67	2	no	—
759	C₂×C₄×D₄	—	67	2	no	—
760	C₂×C₄×D₄	—	67	2	no	—
761	C₂×C₄×D₄	—	67	1	no	—
762	C₂×C₄×D₄	—	67	1	no	—
763	C₂×C₄×D₄	—	67	1	no	—
764	C₂×C₄×D₄	—	67	2	no	—
765	C₂×C₄×D₄	—	67	1	no	—
766	C₂×C₄×D₄	—	67	2	no	—
767	C₂×C₄×D₄	—	67	2	no	—
768	C₂×C₄×D₄	—	67	1	no	—
769	C₂×C₄×D₄	—	67	1	no	—
770	C₂×C₄×D₄	—	67	2	no	—
771	C₂×C₄×D₄	—	67	1	no	—
772	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
773	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
774	C₂×#117	—	67	1	no	—
775	C₂×#117	—	67	1	no	—
776	C₂×#117	—	67	2	no	—
777	C₂×#117	—	67	2	no	—
778	C₂×#117	—	67	2	no	—
779	C₂×#117	—	67	1	no	—
780	C₂×#117	—	67	1	no	—
781	C₂×#117	—	67	2	no	—
782	C₂×#117	C₂×D₆₇	1	2	yes	complemented
783	C₂²×C₄⋊C₄	—	67	2	no	—
784	C₂²×C₄⋊C₄	—	67	1	no	—
785	C₂²×C₄⋊C₄	—	67	2	no	—
786	C₂²×C₄⋊C₄	—	67	2	no	—
787	C₂²×C₂²⋊C₄	—	67	2	no	—
788	C₂²×C₂²⋊C₄	—	67	2	no	—
789	C₂²×C₂²⋊C₄	—	67	2	no	—
790	C₂²×C₂²⋊C₄	—	67	2	no	—
791	C₂²×C₄²	—	67	2	no	—
792	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
793	C₂⁵	—	67	2	no	—
794	C₂×#41	—	67	8	no	—
795	C₂×#41	—	67	8	no	—
796	C₂×#41	—	134	8	no	—
797	C₂×#41	—	134	8	no	—
798	C₂²×Q₈	—	67	1	no	—
799	C₂²×Q₈	—	67	2	no	—
800	C₂²×Q₈	—	67	1	no	—
801	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
802	C₂²×D₄	—	67	1	no	—
803	C₂²×D₄	—	67	2	no	—
804	C₂²×D₄	—	67	1	no	—
805	C₂²×D₄	—	67	2	no	—
806	C₂²×D₄	—	67	2	no	—
807	C₂²×D₄	—	67	8	no	—
808	C₂²×D₄	—	67	1	no	—
809	C₂²×D₄	—	67	1	no	—
810	C₂²×D₄	—	67	2	no	—
811	C₂²×D₄	—	134	8	no	—
812	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
813	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
814	C₂³×C₄	—	67	2	no	—
815	C₂³×C₄	—	67	2	no	—
816	C₂³×C₄	—	67	2	no	—
817	C₂³×C₄	—	67	2	no	—
818	C₂³×C₄	—	67	2	no	—
819	C₂³×C₄	—	67	2	no	—
820	C₂³×C₄	—	67	2	no	—
821	C₂³×C₄	—	67	2	no	—
822	C₂³×C₄	—	67	1	no	—
823	C₂³×C₄	—	67	1	no	—
824	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
825	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
826	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
827	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
828	C₄⋊Q₈	—	67	8	no	—
829	C₄⋊Q₈	—	67	8	no	—
830	#126	—	67	16	no	—
831	#126	—	67	16	no	—
832	#126	—	67	16	no	—
833	#126	—	67	16	no	—
834	#126	—	67	16	no	—
835	#126	—	67	16	no	—
836	#126	—	67	16	no	—
837	#126	—	67	16	no	—
838	#126	—	67	8	no	—
839	#126	—	67	8	no	—
840	#126	—	67	16	no	—
841	#126	C₂²×D₆₇	1	16	yes	complemented
842	#125	—	67	16	no	—
843	#125	—	67	16	no	—
844	#125	—	67	8	no	—
845	#125	—	67	8	no	—
846	#125	—	67	16	no	—
847	#125	C₂²×D₆₇	1	8	yes	complemented
848	#124	—	67	8	no	—
849	#124	—	67	16	no	—
850	#124	—	67	16	no	—
851	#124	—	67	8	no	—
852	#124	C₂²×D₆₇	1	8	yes	—
853	#123	—	67	16	no	—
854	#123	—	67	8	no	—
855	#123	—	67	8	no	—
856	#123	—	67	16	no	—
857	#123	—	67	16	no	—
858	#123	—	67	16	no	—
859	#123	—	67	16	no	—
860	#123	—	67	16	no	—
861	#123	—	67	16	no	—
862	#123	C₂²×D₆₇	1	16	yes	complemented
863	C₂²⋊Q₈	—	67	8	no	—
864	C₂²⋊Q₈	—	67	8	no	—
865	C₂²⋊Q₈	—	67	16	no	—
866	C₂²⋊Q₈	—	67	16	no	—
867	C₂²⋊Q₈	—	67	16	no	—
868	C₂²⋊Q₈	—	67	16	no	—
869	C₂²⋊Q₈	—	67	8	no	—
870	C₂²⋊Q₈	—	67	8	no	—
871	C₂²⋊Q₈	—	67	16	no	—
872	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
873	#121	—	67	16	no	—
874	#121	—	67	16	no	—
875	#121	—	67	8	no	—
876	#121	—	67	8	no	—
877	#121	—	67	16	no	—
878	#121	—	67	16	no	—
879	#121	C₂²×D₆₇	1	8	yes	—
880	#120	—	67	16	no	—
881	#120	—	67	16	no	—
882	C₄×Q₈	—	67	8	no	—
883	C₄×Q₈	—	67	16	no	—
884	C₄×Q₈	—	67	8	no	—
885	C₄×Q₈	—	67	8	no	—
886	C₄×Q₈	—	67	8	no	—
887	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
888	C₄×D₄	—	67	8	no	—
889	C₄×D₄	—	67	16	no	—
890	C₄×D₄	—	67	16	no	—
891	C₄×D₄	—	67	16	no	—
892	C₄×D₄	—	67	8	no	—
893	C₄×D₄	—	67	8	no	—
894	C₄×D₄	—	67	8	no	—
895	C₄×D₄	—	67	16	no	—
896	C₄×D₄	—	67	8	no	—
897	C₄×D₄	—	67	16	no	—
898	C₄×D₄	—	67	16	no	—
899	C₄×D₄	—	67	8	no	—
900	C₄×D₄	—	67	8	no	—
901	C₄×D₄	—	67	16	no	—
902	C₄×D₄	—	67	8	no	—
903	C₄×D₄	C₂²×D₆₇	1	8	yes	—
904	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
905	#117	—	67	8	no	—
906	#117	—	67	8	no	—
907	#117	—	67	16	no	—
908	#117	—	67	16	no	—
909	#117	—	67	16	no	—
910	#117	—	67	8	no	—
911	#117	—	67	8	no	—
912	#117	—	67	16	no	—
913	#117	C₂²×D₆₇	1	16	yes	complemented
914	C₂×C₄⋊C₄	—	67	1	no	—
915	C₂×C₄⋊C₄	—	67	2	no	—
916	C₂×C₄⋊C₄	—	67	1	no	—
917	C₂×C₄⋊C₄	—	67	1	no	—
918	C₂×C₄⋊C₄	—	67	1	no	—
919	C₂×C₄⋊C₄	—	67	2	no	—
920	C₂×C₄⋊C₄	—	67	2	no	—
921	C₂×C₄⋊C₄	—	67	2	no	—
922	C₂×C₄⋊C₄	—	67	2	no	—
923	C₂×C₄⋊C₄	—	67	2	no	—
924	C₂×C₄⋊C₄	—	67	1	no	—
925	C₂×C₄⋊C₄	—	67	1	no	—
926	C₂×C₄⋊C₄	—	67	1	no	—
927	C₂×C₄⋊C₄	—	67	1	no	—
928	C₂×C₄⋊C₄	—	67	1	no	—
929	C₂×C₄⋊C₄	—	67	2	no	—
930	C₂×C₄⋊C₄	—	67	2	no	—
931	C₂×C₄⋊C₄	—	67	2	no	—
932	C₂×C₄⋊C₄	—	67	2	no	—
933	C₂×C₄⋊C₄	—	67	1	no	—
934	C₂×C₄⋊C₄	—	67	2	no	—
935	C₂×C₄⋊C₄	—	67	1	no	—
936	C₂×C₄⋊C₄	—	67	1	no	—
937	C₂×C₄⋊C₄	—	67	2	no	—
938	C₂×C₄⋊C₄	—	67	16	no	—
939	C₂×C₄⋊C₄	—	67	8	no	—
940	C₂×C₄⋊C₄	—	67	16	no	—
941	C₂×C₄⋊C₄	—	67	16	no	—
942	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
943	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
944	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
946	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
948	C₂×C₂²⋊C₄	—	67	2	no	—
949	C₂×C₂²⋊C₄	—	67	2	no	—
950	C₂×C₂²⋊C₄	—	67	2	no	—
951	C₂×C₂²⋊C₄	—	67	2	no	—
952	C₂×C₂²⋊C₄	—	67	2	no	—
953	C₂×C₂²⋊C₄	—	67	1	no	—
954	C₂×C₂²⋊C₄	—	67	1	no	—
955	C₂×C₂²⋊C₄	—	67	1	no	—
956	C₂×C₂²⋊C₄	—	67	2	no	—
957	C₂×C₂²⋊C₄	—	67	1	no	—
958	C₂×C₂²⋊C₄	—	67	1	no	—
959	C₂×C₂²⋊C₄	—	67	1	no	—
960	C₂×C₂²⋊C₄	—	67	2	no	—
961	C₂×C₂²⋊C₄	—	67	2	no	—
962	C₂×C₂²⋊C₄	—	67	16	no	—
963	C₂×C₂²⋊C₄	—	67	2	no	—
964	C₂×C₂²⋊C₄	—	67	2	no	—
965	C₂×C₂²⋊C₄	—	67	1	no	—
966	C₂×C₂²⋊C₄	—	67	2	no	—
967	C₂×C₂²⋊C₄	—	67	2	no	—
968	C₂×C₂²⋊C₄	—	67	1	no	—
969	C₂×C₂²⋊C₄	—	67	1	no	—
970	C₂×C₂²⋊C₄	—	67	2	no	—
971	C₂×C₂²⋊C₄	—	67	1	no	—
972	C₂×C₂²⋊C₄	—	67	16	no	—
973	C₂×C₂²⋊C₄	—	67	16	no	—
974	C₂×C₂²⋊C₄	—	67	16	no	—
975	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
976	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
977	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
978	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
979	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
980	C₂×C₄²	—	67	2	no	—
981	C₂×C₄²	—	67	2	no	—
982	C₂×C₄²	—	67	2	no	—
983	C₂×C₄²	—	67	2	no	—
984	C₂×C₄²	—	67	1	no	—
985	C₂×C₄²	—	67	1	no	—
986	C₂×C₄²	—	67	2	no	—
987	C₂×C₄²	—	67	16	no	—
988	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
989	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
990	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
991	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
992	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
993	C₂×C₄²	C₂²×D₆₇	1	8	yes	complemented
994	C₂⁴	—	268	4	no	—
995	C₂⁴	—	268	4	no	—
996	C₂⁴	—	67	8	no	—
997	C₂⁴	—	67	2	no	—
998	C₂⁴	—	67	1	no	—
999	C₂⁴	—	67	1	no	—
1000	C₂⁴	—	134	8	no	—
1001	C₂⁴	C₂³×D₆₇	1	2	yes	—
1002	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1003	#41	—	134	32	no	—
1004	#41	—	134	32	no	—
1005	C₂×Q₈	—	2	4	no	—
1006	C₂×Q₈	—	268	4	no	—
1007	C₂×Q₈	—	268	2	no	—
1008	C₂×Q₈	—	67	4	no	—
1009	C₂×Q₈	—	67	8	no	—
1010	C₂×Q₈	—	67	4	no	—
1011	C₂×Q₈	—	134	4	no	—
1012	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1013	C₂×D₄	—	2	4	no	—
1014	C₂×D₄	—	4	4	no	—
1015	C₂×D₄	—	268	2	no	—
1016	C₂×D₄	—	268	2	no	—
1017	C₂×D₄	—	268	4	no	—
1018	C₂×D₄	—	268	2	no	—
1019	C₂×D₄	—	67	4	no	—
1020	C₂×D₄	—	67	8	no	—
1021	C₂×D₄	—	67	4	no	—
1022	C₂×D₄	—	67	8	no	—
1023	C₂×D₄	—	67	8	no	—
1024	C₂×D₄	—	67	8	no	—
1025	C₂×D₄	—	67	4	no	—
1026	C₂×D₄	—	67	4	no	—
1027	C₂×D₄	—	67	8	no	—
1028	C₂×D₄	—	134	8	no	—
1029	C₂×D₄	—	134	32	no	—
1030	C₂×D₄	—	134	8	no	—
1031	C₂×D₄	—	134	8	no	—
1032	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1033	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1034	C₂²×C₄	—	2	4	no	—
1035	C₂²×C₄	—	4	2	no	—
1036	C₂²×C₄	—	4	4	no	—
1037	C₂²×C₄	—	4	2	no	—
1038	C₂²×C₄	—	268	4	no	—
1039	C₂²×C₄	—	268	4	no	—
1040	C₂²×C₄	—	268	4	no	—
1041	C₂²×C₄	—	268	4	no	—
1042	C₂²×C₄	—	268	4	no	—
1043	C₂²×C₄	—	268	4	no	—
1044	C₂²×C₄	—	67	8	no	—
1045	C₂²×C₄	—	67	8	no	—
1046	C₂²×C₄	—	67	8	no	—
1047	C₂²×C₄	—	67	8	no	—
1048	C₂²×C₄	—	67	8	no	—
1049	C₂²×C₄	—	67	8	no	—
1050	C₂²×C₄	—	67	2	no	—
1051	C₂²×C₄	—	67	1	no	—
1052	C₂²×C₄	—	67	2	no	—
1053	C₂²×C₄	—	67	2	no	—
1054	C₂²×C₄	—	67	1	no	—
1055	C₂²×C₄	—	67	1	no	—
1056	C₂²×C₄	—	67	1	no	—
1057	C₂²×C₄	—	67	1	no	—
1058	C₂²×C₄	—	67	1	no	—
1059	C₂²×C₄	—	67	8	no	—
1060	C₂²×C₄	—	67	8	no	—
1061	C₂²×C₄	—	67	4	no	—
1062	C₂²×C₄	—	67	4	no	—
1063	C₂²×C₄	—	134	8	no	—
1064	C₂²×C₄	—	134	8	no	—
1065	C₂²×C₄	—	134	4	no	—
1066	C₂²×C₄	—	134	4	no	—
1067	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1068	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1069	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1070	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1071	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1072	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1073	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1074	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1075	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1076	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1077	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1078	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1079	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1080	C₄⋊C₄	—	67	4	no	—
1081	C₄⋊C₄	—	67	8	no	—
1082	C₄⋊C₄	—	67	4	no	—
1083	C₄⋊C₄	—	67	4	no	—
1084	C₄⋊C₄	—	67	4	no	—
1085	C₄⋊C₄	—	67	8	no	—
1086	C₄⋊C₄	—	67	8	no	—
1087	C₄⋊C₄	—	67	8	no	—
1088	C₄⋊C₄	—	67	8	no	—
1089	C₄⋊C₄	—	67	8	no	—
1090	C₄⋊C₄	—	67	4	no	—
1091	C₄⋊C₄	—	67	4	no	—
1092	C₄⋊C₄	—	67	4	no	—
1093	C₄⋊C₄	—	67	4	no	—
1094	C₄⋊C₄	—	67	4	no	—
1095	C₄⋊C₄	—	67	8	no	—
1096	C₄⋊C₄	—	67	8	no	—
1097	C₄⋊C₄	—	67	8	no	—
1098	C₄⋊C₄	—	67	8	no	—
1099	C₄⋊C₄	—	67	4	no	—
1100	C₄⋊C₄	—	67	8	no	—
1101	C₄⋊C₄	—	67	4	no	—
1102	C₄⋊C₄	—	67	4	no	—
1103	C₄⋊C₄	—	67	8	no	—
1104	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1105	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1106	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1107	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1108	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1109	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1110	C₂²⋊C₄	—	67	8	no	—
1111	C₂²⋊C₄	—	67	8	no	—
1112	C₂²⋊C₄	—	67	8	no	—
1113	C₂²⋊C₄	—	67	8	no	—
1114	C₂²⋊C₄	—	67	8	no	—
1115	C₂²⋊C₄	—	67	4	no	—
1116	C₂²⋊C₄	—	67	4	no	—
1117	C₂²⋊C₄	—	67	4	no	—
1118	C₂²⋊C₄	—	67	8	no	—
1119	C₂²⋊C₄	—	67	4	no	—
1120	C₂²⋊C₄	—	67	4	no	—
1121	C₂²⋊C₄	—	67	4	no	—
1122	C₂²⋊C₄	—	67	8	no	—
1123	C₂²⋊C₄	—	67	8	no	—
1124	C₂²⋊C₄	—	67	8	no	—
1125	C₂²⋊C₄	—	67	8	no	—
1126	C₂²⋊C₄	—	67	4	no	—
1127	C₂²⋊C₄	—	67	8	no	—
1128	C₂²⋊C₄	—	67	8	no	—
1129	C₂²⋊C₄	—	67	4	no	—
1130	C₂²⋊C₄	—	67	4	no	—
1131	C₂²⋊C₄	—	67	8	no	—
1132	C₂²⋊C₄	—	67	4	no	—
1133	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1134	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1135	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1136	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1137	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1138	C₄²	—	67	8	no	—
1139	C₄²	—	67	8	no	—
1140	C₄²	—	67	8	no	—
1141	C₄²	—	67	8	no	—
1142	C₄²	—	67	8	no	—
1143	C₄²	—	67	4	no	—
1144	C₄²	—	67	4	no	—
1145	C₄²	C₂³×D₆₇	1	4	yes	—
1146	C₄²	C₂³×D₆₇	1	4	yes	—
1147	C₄²	C₂³×D₆₇	1	4	yes	—
1148	C₄²	C₂³×D₆₇	1	4	yes	—
1149	C₄²	C₂³×D₆₇	1	8	yes	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	4	no	—
1152	C₂³	—	2	2	no	—
1153	C₂³	—	2	2	no	—
1154	C₂³	—	2	4	no	—
1155	C₂³	—	2	4	no	—
1156	C₂³	—	268	8	no	—
1157	C₂³	—	268	8	no	—
1158	C₂³	—	536	16	no	—
1159	C₂³	—	67	8	no	—
1160	C₂³	—	67	4	no	—
1161	C₂³	—	67	2	no	—
1162	C₂³	—	67	2	no	—
1163	C₂³	—	134	16	no	—
1164	C₂³	—	134	2	no	—
1165	C₂³	—	134	2	no	—
1166	C₂³	—	134	2	no	—
1167	C₂³	—	134	2	no	—
1168	C₂³	—	134	2	no	—
1169	C₂³	—	134	2	no	—
1170	C₂³	—	134	4	no	—
1171	C₂³	—	134	4	no	—
1172	C₂³	C₂⁴×D₆₇	1	4	yes	—
1173	C₂³	C₂⁴×D₆₇	1	2	yes	—
1174	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1175	Q₈	—	2	8	no	—
1176	Q₈	—	268	8	no	—
1177	Q₈	—	268	4	no	—
1178	Q₈	—	134	8	no	—
1179	D₄	—	2	8	no	—
1180	D₄	—	4	8	no	—
1181	D₄	—	268	4	no	—
1182	D₄	—	268	4	no	—
1183	D₄	—	268	8	no	—
1184	D₄	—	268	4	no	—
1185	D₄	—	67	16	no	—
1186	D₄	—	134	16	no	—
1187	D₄	—	134	16	no	—
1188	D₄	—	134	16	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	4	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	4	no	—
1195	C₂×C₄	—	2	2	no	—
1196	C₂×C₄	—	2	4	no	—
1197	C₂×C₄	—	2	8	no	—
1198	C₂×C₄	—	4	4	no	—
1199	C₂×C₄	—	4	8	no	—
1200	C₂×C₄	—	4	4	no	—
1201	C₂×C₄	—	268	8	no	—
1202	C₂×C₄	—	268	8	no	—
1203	C₂×C₄	—	268	8	no	—
1204	C₂×C₄	—	268	8	no	—
1205	C₂×C₄	—	268	8	no	—
1206	C₂×C₄	—	268	8	no	—
1207	C₂×C₄	—	67	4	no	—
1208	C₂×C₄	—	67	2	no	—
1209	C₂×C₄	—	67	4	no	—
1210	C₂×C₄	—	67	4	no	—
1211	C₂×C₄	—	67	2	no	—
1212	C₂×C₄	—	67	2	no	—
1213	C₂×C₄	—	67	2	no	—
1214	C₂×C₄	—	67	2	no	—
1215	C₂×C₄	—	67	2	no	—
1216	C₂×C₄	—	134	16	no	—
1217	C₂×C₄	—	134	16	no	—
1218	C₂×C₄	—	134	2	no	—
1219	C₂×C₄	—	134	2	no	—
1220	C₂×C₄	—	134	4	no	—
1221	C₂×C₄	—	134	4	no	—
1222	C₂×C₄	—	134	2	no	—
1223	C₂×C₄	—	134	2	no	—
1224	C₂×C₄	—	134	2	no	—
1225	C₂×C₄	—	134	4	no	—
1226	C₂×C₄	—	134	2	no	—
1227	C₂×C₄	—	134	8	no	—
1228	C₂×C₄	—	134	8	no	—
1229	C₂×C₄	#41×D₆₇	1	4	yes	—
1230	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1231	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1232	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1233	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1234	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1235	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1236	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1237	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1238	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1239	C₂²	—	2	2	no	—
1240	C₂²	—	2	4	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	2	no	—
1243	C₂²	—	2	4	no	—
1244	C₂²	—	2	4	no	—
1245	C₂²	—	4	8	no	—
1246	C₂²	—	4	4	no	—
1247	C₂²	—	268	4	no	—
1248	C₂²	—	268	4	no	—
1249	C₂²	—	536	16	no	—
1250	C₂²	—	67	8	no	—
1251	C₂²	—	134	2	no	—
1252	C₂²	—	134	2	no	—
1253	C₂²	—	134	2	no	—
1254	C₂²	—	134	2	no	—
1255	C₂²	—	134	2	no	—
1256	C₂²	—	134	2	no	—
1257	C₂²	—	134	4	no	—
1258	C₂²	—	134	4	no	—
1259	C₂²	—	134	16	no	—
1260	C₂²	C₂×#41×D₆₇	1	2	yes	—
1261	C₂²	#16864232	1	2	yes	—
1262	C₂²	#16864232	1	2	yes	—
1263	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1264	C₄	—	2	2	no	—
1265	C₄	—	2	4	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	2	2	no	—
1268	C₄	—	2	2	no	—
1269	C₄	—	2	4	no	—
1270	C₄	—	2	2	no	—
1271	C₄	—	2	4	no	—
1272	C₄	—	134	2	no	—
1273	C₄	—	134	2	no	—
1274	C₄	—	134	4	no	—
1275	C₄	—	134	4	no	—
1276	C₄	—	134	2	no	—
1277	C₄	—	134	2	no	—
1278	C₄	—	134	2	no	—
1279	C₄	—	134	4	no	—
1280	C₄	—	134	2	no	—
1281	C₄	C₂×#41×D₆₇	1	4	yes	—
1282	C₂	—	4	4	no	—
1283	C₂	—	4	2	no	—
1284	C₂	—	268	2	no	—
1285	C₂	—	268	2	no	—
1286	C₂	—	134	8	no	—
1287	C₂	#22574271	1	4	yes	direct product factor
1288	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1289	C₂	C₂×#16864232	1	1	yes	characteristic
1290	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×#3521
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. #22574271	C₂	direct (N × H)
2. C₂×#16864117	C₂	semidirect
3. C₂×#16864115	C₂	semidirect
4. C₂×#16864102	C₂	semidirect
5. C₂×#16864096	C₂	semidirect
6. C₂×#16864093	C₂	semidirect
7. C₂×#16864085	C₂	semidirect
8. C₂×#16864084	C₂	semidirect
9. C₂×#16864075	C₂	semidirect
10. C₂×#16864070	C₂	semidirect
11. C₂×#16864048	C₂	semidirect
12. C₂×#16864043	C₂	semidirect
13. C₂×#16864039	C₂	semidirect
14. C₂×#16864011	C₂	semidirect
15. C₂×#16864004	C₂	semidirect
16. C₂×#16863989	C₂	semidirect
17. C₂×#16863982	C₂	semidirect
18. C₂×#16863930	C₂	semidirect
19. C₂×#16863929	C₂	semidirect
20. C₂×#126×D₆₇	C₂	semidirect
21. C₂×#16863878	C₂	semidirect
22. C₂×#16863868	C₂	semidirect
23. C₂×C₄×#11761628	C₂	semidirect
24. C₂×#529×C₆₇	C₂	semidirect
28. #16864117	C₂²	semidirect
29. #16864115	C₂²	semidirect
30. #16864102	C₂²	semidirect
31. #16864096	C₂²	semidirect
32. #16864093	C₂²	semidirect
33. #16864085	C₂²	semidirect
34. #16864084	C₂²	semidirect
35. #16864075	C₂²	semidirect
36. #16864070	C₂²	semidirect
37. #16864048	C₂²	semidirect
38. #16864043	C₂²	semidirect
39. #16864039	C₂²	semidirect
40. #16864011	C₂²	semidirect
41. #16864004	C₂²	semidirect
42. #16863989	C₂²	semidirect
43. #16863982	C₂²	semidirect
44. C₂×#14524042	C₂²	semidirect
45. C₂×#14524041	C₂²	semidirect
46. #16863930	C₂²	semidirect
47. #16863929	C₂²	semidirect
53. C₂×#14524037	C₂²	semidirect
54. C₂×#14524036	C₂²	semidirect
55. C₂×#14524036	C₂²	semidirect
56. C₂×#14524036	C₂²	semidirect
57. C₂×#14524036	C₂²	semidirect
58. C₂×#14524036	C₂²	semidirect
59. #126×D₆₇	C₂²	semidirect
60. C₂×#14524035	C₂²	semidirect
61. C₂×#14524035	C₂²	semidirect
62. C₂×#14524034	C₂²	semidirect
63. C₂×#14524034	C₂²	semidirect
64. C₂×#14524033	C₂²	semidirect
68. C₂×#14524029	C₂²	semidirect
70. C₂×#14524028	C₂²	semidirect
72. C₂×#14524026	C₂²	semidirect
73. C₂×#14524026	C₂²	semidirect
76. C₂×#14524025	C₂²	semidirect
77. C₂×#14524024	C₂²	semidirect
79. C₂×#14524023	C₂²	semidirect
80. C₂×#14524023	C₂²	semidirect
81. C₂×#14524022	C₂²	semidirect
82. C₂×#14524022	C₂²	semidirect
83. C₂×#14524021	C₂²	semidirect
84. C₂×#14524021	C₂²	semidirect
85. C₂×#14524020	C₂²	semidirect
89. C₂×#14524016	C₂²	semidirect
92. C₂×#14524014	C₂²	semidirect
95. #16863878	C₂²	semidirect
96. #16863868	C₂²	semidirect
97. C₄×#11761628	C₂²	semidirect
98. C₂×Q₈×Dic₆₇	C₂²	semidirect
99. C₂×C₄×Dic₁₃₄	C₂²	semidirect
100. C₂×C₄×Dic₁₃₄	C₂²	semidirect
101. C₂×C₄×Dic₁₃₄	C₂²	semidirect
102. C₂×#14524008	C₂²	semidirect
106. C₂×C₄×D₂₆₈	C₂²	semidirect
110. C₂×#14524005	C₂²	semidirect
113. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
114. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
115. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
117. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
118. C₂×#14524002	C₂²	semidirect
120. C₂×#14524001	C₂²	semidirect
122. C₂×#14524000	C₂²	semidirect
123. C₂×#14524000	C₂²	semidirect
124. C₂×#14524000	C₂²	semidirect
125. C₂×#14523999	C₂²	semidirect
126. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
127. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
128. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
129. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
134. C₂×C₄²×D₆₇	C₂²	semidirect
135. #529×C₆₇	C₂²	semidirect
136. C₂×#126×C₆₇	C₂²	semidirect
137. C₂×#125×C₆₇	C₂²	semidirect
139. C₂×#123×C₆₇	C₂²	semidirect
140. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
142. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
144. C₂×C₄×D₄×C₆₇	C₂²	semidirect
145. C₂×#117×C₆₇	C₂²	semidirect
146. C₂²×C₄²×C₆₇	C₂²	semidirect
175. #14524042	C₂³	semidirect
176. #14524041	C₂³	semidirect
182. #14524037	C₂³	semidirect
183. #14524036	C₂³	semidirect
184. #14524036	C₂³	semidirect
185. #14524036	C₂³	semidirect
186. #14524036	C₂³	semidirect
187. #14524036	C₂³	semidirect
188. #14524035	C₂³	semidirect
189. #14524035	C₂³	semidirect
190. #14524034	C₂³	semidirect
191. #14524034	C₂³	semidirect
192. #14524033	C₂³	semidirect
196. #14524029	C₂³	semidirect
198. #14524028	C₂³	semidirect
200. #14524026	C₂³	semidirect
201. #14524026	C₂³	semidirect
204. #14524025	C₂³	semidirect
205. #14524024	C₂³	semidirect
207. #14524023	C₂³	semidirect
208. #14524023	C₂³	semidirect
209. #14524022	C₂³	semidirect
210. #14524022	C₂³	semidirect
211. #14524021	C₂³	semidirect
212. #14524021	C₂³	semidirect
213. #14524020	C₂³	semidirect
217. #14524016	C₂³	semidirect
220. #14524014	C₂³	semidirect
223. Q₈×Dic₆₇	C₂³	semidirect
224. C₄×Dic₁₃₄	C₂³	semidirect
225. C₄×Dic₁₃₄	C₂³	semidirect
226. C₄×Dic₁₃₄	C₂³	semidirect
227. #14524008	C₂³	semidirect
231. C₄×D₂₆₈	C₂³	semidirect
235. #14524005	C₂³	semidirect
238. C₄×C₂²⋊D₆₇	C₂³	semidirect
239. C₄×C₂²⋊D₆₇	C₂³	semidirect
240. C₄×C₂²⋊D₆₇	C₂³	semidirect
242. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
243. #14524002	C₂³	semidirect
245. #14524001	C₂³	semidirect
247. #14524000	C₂³	semidirect
248. #14524000	C₂³	semidirect
249. #14524000	C₂³	semidirect
250. #14523999	C₂³	semidirect
275. C₄⋊C₄×D₆₇	C₂³	semidirect
276. C₄⋊C₄×D₆₇	C₂³	semidirect
277. C₄⋊C₄×D₆₇	C₂³	semidirect
278. C₄⋊C₄×D₆₇	C₂³	semidirect
313. C₄²×D₆₇	C₂³	semidirect
321. #126×C₆₇	C₂³	semidirect
322. #125×C₆₇	C₂³	semidirect
324. #123×C₆₇	C₂³	semidirect
325. C₂²⋊Q₈×C₆₇	C₂³	semidirect
327. C₄×Q₈×C₆₇	C₂³	semidirect
329. C₄×D₄×C₆₇	C₂³	semidirect
330. #117×C₆₇	C₂³	semidirect
347. C₂×C₄²×C₆₇	C₂³	semidirect
639. C₂×C₆₇	#3521	semidirect
665. C₂×#529	D₆₇	semidirect
670. C₆₇	C₂×#3521	semidirect
694. #529	C₂×D₆₇	semidirect
707. C₂×#126	C₂×D₆₇	semidirect
713. C₂×#125	C₂×D₆₇	semidirect
728. C₂×#123	C₂×D₆₇	semidirect
738. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
756. C₂×C₄×Q₈	C₂×D₆₇	semidirect
773. C₂×C₄×D₄	C₂×D₆₇	semidirect
782. C₂×#117	C₂×D₆₇	semidirect
792. C₂²×C₄²	C₂×D₆₇	semidirect
841. #126	C₂²×D₆₇	semidirect
847. #125	C₂²×D₆₇	semidirect
862. #123	C₂²×D₆₇	semidirect
872. C₂²⋊Q₈	C₂²×D₆₇	semidirect
887. C₄×Q₈	C₂²×D₆₇	semidirect
904. C₄×D₄	C₂²×D₆₇	semidirect
913. #117	C₂²×D₆₇	semidirect
993. C₂×C₄²	C₂²×D₆₇	semidirect
1287. C₂	#22574271	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574271	2
C₂×#16864117	2
C₂×#16864115	2
C₂×#16864102	2
C₂×#16864096	2
C₂×#16864093	2
C₂×#16864085	2
C₂×#16864084	2
C₂×#16864075	2
C₂×#16864070	2
C₂×#16864048	2
C₂×#16864043	2
C₂×#16864039	2
C₂×#16864011	2
C₂×#16864004	2
C₂×#16863989	2
C₂×#16863982	2
C₂×#16863930	2
C₂×#16863929	2
C₂×#126×D₆₇	2
C₂×#16863878	2
C₂×#16863868	2
C₂×C₄×#11761628	2
C₂×#529×C₆₇	2
C₂×#3521	67

Subgroups — C2×#22574271 #31763955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574271 #31763955