Subgroups — C₂×#22574154 #31763807

Order 17152.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574154	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864102	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864099	C₂	1	2	yes	maximal, complemented
5	C₂×#16864090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864071	C₂	1	2	yes	maximal, complemented
7	C₂×#16864070	C₂	1	2	yes	maximal, complemented
8	C₂×#16864047	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16864038	C₂	1	2	yes	maximal, complemented
10	C₂×#16864037	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16864037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₄×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16864019	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16864002	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16863994	C₂	1	2	yes	maximal, complemented
16	C₂×#16863985	C₂	1	2	yes	maximal, complemented
17	C₂×#16863932	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16863926	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16863908	C₂	1	2	yes	maximal, complemented
20	C₂×#123×D₆₇	C₂	1	2	yes	maximal, complemented
21	C₂×#16863878	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863870	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂²×#14524005	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761629	C₂²	1	1	yes	characteristic
26	C₂²×#11761628	C₂²	1	2	yes	complemented
27	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
28	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
29	C₂²×D₄×D₆₇	C₂²	1	2	yes	—
30	C₂³×C₄×D₆₇	C₂²	1	2	yes	complemented
31	#16864131	C₂²	1	16	yes	complemented
32	#16864102	C₂²	1	16	yes	complemented
33	#16864099	C₂²	1	32	yes	complemented
34	#16864090	C₂²	1	16	yes	complemented
35	#16864071	C₂²	1	32	yes	complemented
36	#16864070	C₂²	1	32	yes	complemented
37	#16864047	C₂²	1	16	yes	complemented
38	#16864038	C₂²	1	32	yes	complemented
39	#16864037	C₂²	1	16	yes	complemented
40	#16864037	C₂²	1	16	yes	complemented
41	D₄×D₂₆₈	C₂²	1	16	yes	complemented
42	#16864019	C₂²	1	16	yes	complemented
43	#16864002	C₂²	1	16	yes	complemented
44	#16863994	C₂²	1	32	yes	complemented
45	#16863985	C₂²	1	32	yes	complemented
46	C₂×#14524042	C₂²	1	1	yes	characteristic, complemented
47	C₂×#14524040	C₂²	1	1	yes	characteristic
48	#16863932	C₂²	1	16	yes	complemented
49	#16863926	C₂²	1	16	yes	complemented
50	C₂×#14524038	C₂²	1	2	yes	complemented
51	C₂×#14524038	C₂²	1	1	yes	characteristic, complemented
52	C₂×#14524038	C₂²	1	2	yes	complemented
53	C₂×#14524037	C₂²	1	2	yes	complemented
54	C₂×#14524036	C₂²	1	1	yes	characteristic, complemented
55	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
56	C₂×#14524033	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×#14524031	C₂²	1	2	yes	complemented
60	C₂×#14524029	C₂²	1	2	yes	complemented
61	C₂×#14524029	C₂²	1	1	yes	characteristic, complemented
62	#16863908	C₂²	1	32	yes	complemented
63	C₂×#14524028	C₂²	1	2	yes	complemented
64	C₂×#14524028	C₂²	1	2	yes	complemented
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×#14524028	C₂²	1	2	yes	complemented
70	C₂×#14524027	C₂²	1	2	yes	complemented
71	C₂×#14524027	C₂²	1	1	yes	characteristic, complemented
72	C₂×#14524026	C₂²	1	2	yes	complemented
73	C₂×#14524025	C₂²	1	2	yes	complemented
74	C₂×#14524025	C₂²	1	2	yes	complemented
75	C₂×#14524024	C₂²	1	1	yes	characteristic
76	#123×D₆₇	C₂²	1	32	yes	complemented
77	C₂×#14524023	C₂²	1	2	yes	complemented
78	C₂×#14524023	C₂²	1	2	yes	complemented
79	C₂×#14524021	C₂²	1	2	yes	complemented
80	C₂×#14524021	C₂²	1	2	yes	complemented
81	C₂×#14524021	C₂²	1	2	yes	complemented
82	C₂×#14524020	C₂²	1	1	yes	characteristic, complemented
83	C₂×#14524018	C₂²	1	2	yes	—
84	C₂×#14524018	C₂²	1	1	yes	characteristic, complemented
85	C₂×#14524018	C₂²	1	1	yes	characteristic, complemented
86	C₂×#14524018	C₂²	1	2	yes	complemented
87	C₂×#14524018	C₂²	1	2	yes	complemented
88	C₂×#14524018	C₂²	1	2	yes	complemented
89	C₂×#14524018	C₂²	1	2	yes	complemented
90	C₂×#14524017	C₂²	1	1	yes	characteristic
91	C₂×#14524017	C₂²	1	1	yes	characteristic
92	C₂×#14524016	C₂²	1	2	yes	complemented
93	C₂×#14524015	C₂²	1	1	yes	characteristic
94	C₂×#14524013	C₂²	1	2	yes	—
95	C₂×#14524013	C₂²	1	2	yes	—
96	C₂×#14524013	C₂²	1	2	yes	complemented
97	C₂×#14524013	C₂²	1	2	yes	complemented
98	#16863878	C₂²	1	16	yes	complemented
99	#16863870	C₂²	1	16	yes	complemented
100	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
103	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
104	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
105	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
106	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
107	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
108	C₂×#14524005	C₂²	1	1	yes	characteristic
109	C₂×#14524005	C₂²	1	1	yes	characteristic
110	C₂×#14524005	C₂²	1	1	yes	characteristic
111	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
112	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
113	C₂×#14524005	C₂²	1	2	yes	complemented
114	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
115	C₂×#14524005	C₂²	1	2	yes	complemented
116	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
117	C₂×#14524005	C₂²	1	2	yes	complemented
118	C₂×#14524005	C₂²	1	16	yes	complemented
119	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
122	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
123	C₂×#14524001	C₂²	1	2	yes	complemented
124	C₂×#14524000	C₂²	1	1	yes	characteristic, complemented
125	C₂×#14524000	C₂²	1	2	yes	complemented
126	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
128	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
129	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
130	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
131	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
132	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
134	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
135	#552×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×#125×C₆₇	C₂²	1	2	yes	complemented
139	C₂×#123×C₆₇	C₂²	1	2	yes	—
140	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
141	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
144	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
145	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
146	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₆₇	C₂³	1	2	yes	—
148	C₂⁴×D₆₇	C₂³	1	2	yes	—
149	C₂×#11761629	—	2	8	no	—
150	C₂×#11761629	C₂³	1	8	yes	—
151	C₂×#11761628	—	4	8	no	—
152	C₂×#11761628	C₂³	1	16	yes	complemented
153	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
154	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
155	C₂²×D₂₆₈	—	2	8	no	—
156	C₂²×D₂₆₈	—	2	8	no	—
157	C₂²×D₂₆₈	C₂³	1	8	yes	—
158	C₂²×D₂₆₈	C₂³	1	8	yes	—
159	C₂²×D₂₆₈	C₂³	1	2	yes	—
160	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
161	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
162	C₂²×D₂₆₈	C₂³	1	2	yes	—
163	C₂²×D₂₆₈	C₂³	1	2	yes	—
164	C₂²×D₂₆₈	C₂³	1	2	yes	—
165	C₂²×D₂₆₈	C₂³	1	2	yes	—
166	C₂²×D₂₆₈	C₂³	1	2	yes	—
167	C₂²×D₂₆₈	C₂³	1	2	yes	—
168	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
169	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
170	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
171	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
172	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
173	C₂×D₄×D₆₇	—	4	8	no	—
174	C₂×D₄×D₆₇	C₂³	1	16	yes	—
175	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
176	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₆₇	—	4	8	no	—
178	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
179	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
181	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
182	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
183	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
184	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
185	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
186	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
187	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
188	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
189	C₂²×C₄×D₆₇	C₂³	1	16	yes	complemented
190	#14524042	C₂³	1	8	yes	complemented
191	#14524040	C₂³	1	8	yes	—
192	#14524038	C₂³	1	16	yes	complemented
193	#14524038	C₂³	1	8	yes	complemented
194	#14524038	C₂³	1	16	yes	complemented
195	#14524037	C₂³	1	16	yes	complemented
196	#14524036	C₂³	1	8	yes	complemented
197	#14524034	C₂³	1	8	yes	complemented
198	#14524033	C₂³	1	8	yes	complemented
199	#14524032	C₂³	1	8	yes	complemented
200	#14524032	C₂³	1	8	yes	complemented
201	#14524031	C₂³	1	16	yes	complemented
202	#14524029	C₂³	1	16	yes	complemented
203	#14524029	C₂³	1	8	yes	complemented
204	#14524028	C₂³	1	16	yes	complemented
205	#14524028	C₂³	1	16	yes	complemented
206	#14524028	C₂³	1	16	yes	complemented
207	#14524028	C₂³	1	16	yes	complemented
208	#14524028	C₂³	1	16	yes	complemented
209	#14524028	C₂³	1	16	yes	complemented
210	#14524028	C₂³	1	16	yes	complemented
211	#14524027	C₂³	1	16	yes	complemented
212	#14524027	C₂³	1	8	yes	complemented
213	#14524026	C₂³	1	16	yes	complemented
214	#14524025	C₂³	1	16	yes	complemented
215	#14524025	C₂³	1	16	yes	complemented
216	#14524024	C₂³	1	8	yes	—
217	#14524023	C₂³	1	16	yes	complemented
218	#14524023	C₂³	1	16	yes	complemented
219	#14524021	C₂³	1	16	yes	complemented
220	#14524021	C₂³	1	16	yes	complemented
221	#14524021	C₂³	1	16	yes	complemented
222	#14524020	C₂³	1	8	yes	complemented
223	#14524018	C₂³	1	16	yes	—
224	#14524018	C₂³	1	8	yes	complemented
225	#14524018	C₂³	1	8	yes	complemented
226	#14524018	C₂³	1	16	yes	complemented
227	#14524018	C₂³	1	16	yes	complemented
228	#14524018	C₂³	1	16	yes	complemented
229	#14524018	C₂³	1	16	yes	complemented
230	#14524017	C₂³	1	8	yes	—
231	#14524017	C₂³	1	8	yes	—
232	#14524016	C₂³	1	16	yes	complemented
233	#14524015	C₂³	1	8	yes	—
234	#14524013	C₂³	1	16	yes	—
235	#14524013	C₂³	1	16	yes	—
236	#14524013	C₂³	1	16	yes	complemented
237	#14524013	C₂³	1	16	yes	complemented
238	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
239	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
240	C₄×D₂₆₈	C₂³	1	8	yes	—
241	C₄×D₂₆₈	C₂³	1	16	yes	complemented
242	C₄×D₂₆₈	C₂³	1	16	yes	complemented
243	C₄×D₂₆₈	C₂³	1	16	yes	complemented
244	C₄×D₂₆₈	C₂³	1	16	yes	complemented
245	C₄×D₂₆₈	C₂³	1	16	yes	complemented
246	#14524005	C₂³	1	8	yes	—
247	#14524005	C₂³	1	8	yes	—
248	#14524005	C₂³	1	8	yes	—
249	#14524005	C₂³	1	8	yes	complemented
250	#14524005	C₂³	1	8	yes	complemented
251	#14524005	C₂³	1	16	yes	complemented
252	#14524005	C₂³	1	8	yes	complemented
253	#14524005	C₂³	1	16	yes	complemented
254	#14524005	C₂³	1	8	yes	complemented
255	#14524005	C₂³	1	16	yes	complemented
256	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
257	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
258	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
259	#14524002	C₂³	1	8	yes	complemented
260	#14524001	C₂³	1	16	yes	complemented
261	#14524000	C₂³	1	8	yes	complemented
262	#14524000	C₂³	1	16	yes	complemented
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	1	yes	characteristic
268	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
269	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
270	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
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	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
278	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
279	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
280	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
281	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
285	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
286	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
287	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
288	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
289	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
290	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
291	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
292	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
293	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
294	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
295	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
296	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
298	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
300	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
301	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
302	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
303	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
304	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
305	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	complemented
306	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
307	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
308	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
309	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
310	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
313	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
314	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
315	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
316	C₂×C₄×Dic₆₇	C₂³	1	8	yes	complemented
317	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
320	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
322	#126×C₆₇	C₂³	1	16	yes	complemented
323	#125×C₆₇	C₂³	1	8	yes	complemented
324	#125×C₆₇	C₂³	1	16	yes	complemented
325	#123×C₆₇	C₂³	1	16	yes	—
326	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
327	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
328	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
329	C₄×D₄×C₆₇	C₂³	1	8	yes	—
330	#117×C₆₇	C₂³	1	16	yes	complemented
331	#117×C₆₇	C₂³	1	8	yes	complemented
332	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
338	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
340	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
341	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
342	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
343	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
345	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
346	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
348	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
349	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
350	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
351	C₂³×D₆₇	—	2	8	no	—
352	C₂³×D₆₇	—	2	8	no	—
353	C₂³×D₆₇	—	2	8	no	—
354	C₂³×D₆₇	—	4	4	no	—
355	C₂³×D₆₇	—	4	4	no	—
356	C₂³×D₆₇	—	4	4	no	—
357	C₂³×D₆₇	C₂⁴	1	2	yes	—
358	C₂³×D₆₇	C₂⁴	1	2	yes	—
359	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
360	C₂³×D₆₇	C₂⁴	1	8	yes	—
361	C₂³×D₆₇	C₂⁴	1	2	yes	—
362	C₂³×D₆₇	C₂⁴	1	8	yes	—
363	#11761629	—	2	32	no	—
364	#11761628	—	4	32	no	—
365	C₂×Dic₁₃₄	—	4	2	no	—
366	C₂×Dic₁₃₄	—	4	4	no	—
367	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
368	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
369	C₂×D₂₆₈	—	2	8	no	—
370	C₂×D₂₆₈	—	2	8	no	—
371	C₂×D₂₆₈	—	2	8	no	—
372	C₂×D₂₆₈	—	2	4	no	—
373	C₂×D₂₆₈	—	2	4	no	—
374	C₂×D₂₆₈	—	2	32	no	—
375	C₂×D₂₆₈	—	2	32	no	—
376	C₂×D₂₆₈	—	4	4	no	—
377	C₂×D₂₆₈	—	4	4	no	—
378	C₂×D₂₆₈	—	4	4	no	—
379	C₂×D₂₆₈	—	4	4	no	—
380	C₂×D₂₆₈	#41	1	8	yes	complemented
381	C₂×D₂₆₈	C₂⁴	1	8	yes	—
382	C₂×D₂₆₈	C₂⁴	1	4	yes	—
383	C₂×D₂₆₈	C₂⁴	1	4	yes	—
384	C₂×D₂₆₈	C₂⁴	1	8	yes	—
385	C₂×D₂₆₈	C₂⁴	1	8	yes	—
386	C₂×D₂₆₈	C₂⁴	1	8	yes	—
387	C₂×D₂₆₈	C₂⁴	1	8	yes	—
388	C₂×D₂₆₈	C₂⁴	1	8	yes	—
389	C₂×D₂₆₈	C₂⁴	1	8	yes	—
390	C₂×D₂₆₈	C₂⁴	1	4	yes	—
391	C₂×C₂²⋊D₆₇	—	2	8	no	—
392	C₂×C₂²⋊D₆₇	—	2	4	no	—
393	C₂×C₂²⋊D₆₇	—	4	4	no	—
394	C₂×C₂²⋊D₆₇	—	4	2	no	—
395	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
396	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
397	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
398	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
399	D₄×D₆₇	—	4	32	no	—
400	C₂²×Dic₆₇	—	2	4	no	—
401	C₂²×Dic₆₇	—	4	2	no	—
402	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
409	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
410	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
412	C₂×C₄×D₆₇	—	2	8	no	—
413	C₂×C₄×D₆₇	—	2	4	no	—
414	C₂×C₄×D₆₇	—	4	4	no	—
415	C₂×C₄×D₆₇	—	4	4	no	—
416	C₂×C₄×D₆₇	—	4	4	no	—
417	C₂×C₄×D₆₇	—	4	4	no	—
418	C₂×C₄×D₆₇	—	4	32	no	—
419	C₂×C₄×D₆₇	—	4	4	no	—
420	C₂×C₄×D₆₇	—	4	4	no	—
421	C₂×C₄×D₆₇	—	4	4	no	—
422	C₂×C₄×D₆₇	—	4	4	no	—
423	C₂×C₄×D₆₇	—	4	4	no	—
424	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
425	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
426	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
427	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
428	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
429	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
430	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
431	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
432	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
433	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
434	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
435	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
436	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
437	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
438	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
439	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
440	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
441	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
442	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
443	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
444	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
445	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
446	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
447	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
448	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
449	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
450	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
451	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
452	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
453	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
454	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
455	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
456	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
457	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
458	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
459	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
460	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
461	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
462	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
463	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
464	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
465	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
466	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
467	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
468	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
469	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
470	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
471	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
472	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
473	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
474	C₄×Dic₆₇	C₂⁴	1	4	yes	—
475	C₄×Dic₆₇	C₂⁴	1	4	yes	—
476	C₄×Dic₆₇	C₂⁴	1	4	yes	—
477	C₄×Dic₆₇	C₂⁴	1	4	yes	—
478	C₄×Dic₆₇	C₂⁴	1	8	yes	—
479	C₄×Dic₆₇	C₂⁴	1	4	yes	—
480	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
481	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
482	C₂×Q₈×C₆₇	—	2	4	no	—
483	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
484	C₂×D₄×C₆₇	—	2	4	no	—
485	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
486	C₂²×C₄×C₆₇	—	2	8	no	—
487	C₂²×C₄×C₆₇	—	2	4	no	—
488	C₂²×C₄×C₆₇	—	2	4	no	—
489	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
490	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
492	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
493	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
494	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
497	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
498	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
499	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
500	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
502	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
503	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
504	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
505	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
506	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
507	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
508	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
509	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
510	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
511	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
512	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
513	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
514	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
515	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
516	C₄²×C₆₇	C₂⁴	1	8	yes	—
517	C₄²×C₆₇	C₂⁴	1	8	yes	—
518	C₄²×C₆₇	C₂⁴	1	4	yes	—
519	C₂³×C₆₇	—	2	2	no	—
520	C₂³×C₆₇	—	2	2	no	—
521	C₂³×C₆₇	—	2	2	no	—
522	C₂³×C₆₇	—	2	2	no	—
523	C₂³×C₆₇	—	2	2	no	—
524	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
525	C₂³×C₆₇	C₂⁵	1	2	yes	—
526	C₂³×C₆₇	C₂⁵	1	2	yes	—
527	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
528	C₂²×D₆₇	—	2	4	no	—
529	C₂²×D₆₇	—	2	4	no	—
530	C₂²×D₆₇	—	2	2	no	—
531	C₂²×D₆₇	—	2	4	no	—
532	C₂²×D₆₇	—	2	4	no	—
533	C₂²×D₆₇	—	2	16	no	—
534	C₂²×D₆₇	—	2	2	no	—
535	C₂²×D₆₇	—	2	4	no	—
536	C₂²×D₆₇	—	2	4	no	—
537	C₂²×D₆₇	—	2	4	no	—
538	C₂²×D₆₇	—	2	2	no	—
539	C₂²×D₆₇	—	2	4	no	—
540	C₂²×D₆₇	—	2	16	no	—
541	C₂²×D₆₇	—	2	16	no	—
542	C₂²×D₆₇	—	4	8	no	—
543	C₂²×D₆₇	—	4	8	no	—
544	C₂²×D₆₇	—	4	8	no	—
545	C₂²×D₆₇	—	4	32	no	—
546	C₂²×D₆₇	—	8	16	no	—
547	C₂²×D₆₇	C₂×#41	1	8	yes	—
548	C₂²×D₆₇	C₂⁵	1	4	yes	—
549	C₂²×D₆₇	C₂⁵	1	4	yes	—
550	C₂²×D₆₇	C₂⁵	1	2	yes	—
551	C₂²×D₆₇	C₂⁵	1	4	yes	—
552	Q₈×C₆₇	—	2	8	no	—
553	D₄×C₆₇	—	2	8	no	—
554	C₂×C₄×C₆₇	—	2	2	no	—
555	C₂×C₄×C₆₇	—	2	2	no	—
556	C₂×C₄×C₆₇	—	2	4	no	—
557	C₂×C₄×C₆₇	—	2	4	no	—
558	C₂×C₄×C₆₇	—	2	4	no	—
559	C₂×C₄×C₆₇	—	2	16	no	—
560	C₂×C₄×C₆₇	—	2	2	no	—
561	C₂×C₄×C₆₇	—	2	4	no	—
562	C₂×C₄×C₆₇	—	2	2	no	—
563	C₂×C₄×C₆₇	—	2	8	no	—
564	C₂×C₄×C₆₇	—	2	8	no	—
565	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
566	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
567	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
568	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
569	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
570	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
571	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
572	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
573	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
574	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
575	C₂²⋊D₆₇	—	2	16	no	—
576	C₂²⋊D₆₇	—	2	8	no	—
577	C₂²⋊D₆₇	—	4	8	no	—
578	C₂²⋊D₆₇	—	4	4	no	—
579	C₂×Dic₆₇	—	2	2	no	—
580	C₂×Dic₆₇	—	2	8	no	—
581	C₂×Dic₆₇	—	2	2	no	—
582	C₂×Dic₆₇	—	2	2	no	—
583	C₂×Dic₆₇	—	2	4	no	—
584	C₂×Dic₆₇	—	2	2	no	—
585	C₂×Dic₆₇	—	2	2	no	—
586	C₂×Dic₆₇	—	2	2	no	—
587	C₂×Dic₆₇	—	2	2	no	—
588	C₂×Dic₆₇	—	4	4	no	—
589	C₂×Dic₆₇	C₂⁵	1	2	yes	—
590	C₂×Dic₆₇	C₂⁵	1	2	yes	—
591	C₂×Dic₆₇	C₂⁵	1	2	yes	—
592	C₂×Dic₆₇	C₂⁵	1	2	yes	—
593	C₂×Dic₆₇	C₂⁵	1	2	yes	—
594	C₂×Dic₆₇	C₂⁵	1	2	yes	—
595	C₂×Dic₆₇	C₂⁵	1	4	yes	—
596	C₂×Dic₆₇	C₂⁵	1	2	yes	—
597	D₂₆₈	—	2	16	no	—
598	D₂₆₈	—	2	16	no	—
599	D₂₆₈	—	2	16	no	—
600	D₂₆₈	—	2	8	no	—
601	D₂₆₈	—	2	8	no	—
602	D₂₆₈	—	4	8	no	—
603	D₂₆₈	—	4	8	no	—
604	D₂₆₈	—	4	8	no	—
605	D₂₆₈	—	4	8	no	—
606	D₂₆₈	C₂×#41	1	16	yes	complemented
607	C₄×D₆₇	—	2	16	no	—
608	C₄×D₆₇	—	2	8	no	—
609	C₄×D₆₇	—	4	8	no	—
610	C₄×D₆₇	—	4	8	no	—
611	C₄×D₆₇	—	4	8	no	—
612	C₄×D₆₇	—	4	8	no	—
613	C₄×D₆₇	—	4	8	no	—
614	C₄×D₆₇	—	4	8	no	—
615	C₄×D₆₇	—	4	8	no	—
616	C₄×D₆₇	—	4	8	no	—
617	C₄×D₆₇	—	4	8	no	—
618	Dic₁₃₄	—	4	4	no	—
619	Dic₁₃₄	—	4	8	no	—
620	C₂²×C₆₇	—	2	2	no	—
621	C₂²×C₆₇	—	2	2	no	—
622	C₂²×C₆₇	—	2	8	no	—
623	C₂²×C₆₇	—	2	2	no	—
624	C₂²×C₆₇	—	2	2	no	—
625	C₂²×C₆₇	—	2	2	no	—
626	C₂²×C₆₇	—	4	4	no	—
627	C₂²×C₆₇	C₂²×#41	1	2	yes	—
628	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
629	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
630	C₂²×C₆₇	#585	1	2	yes	—
631	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
632	C₂×D₆₇	—	2	4	no	—
633	C₂×D₆₇	—	2	4	no	—
634	C₂×D₆₇	—	2	16	no	—
635	C₂×D₆₇	—	2	2	no	—
636	C₂×D₆₇	—	2	4	no	—
637	C₂×D₆₇	—	2	4	no	—
638	C₂×D₆₇	—	2	2	no	—
639	C₂×D₆₇	—	2	4	no	—
640	C₂×D₆₇	—	2	4	no	—
641	C₂×D₆₇	—	2	4	no	—
642	C₂×D₆₇	—	2	2	no	—
643	C₂×D₆₇	—	2	4	no	—
644	C₂×D₆₇	—	4	32	no	—
645	C₂×D₆₇	—	4	4	no	—
646	C₂×D₆₇	—	4	8	no	—
647	C₂×D₆₇	—	4	8	no	—
648	C₂×D₆₇	—	8	16	no	—
649	C₂×D₆₇	C₂²×#41	1	8	yes	—
650	C₄×C₆₇	—	2	4	no	—
651	C₄×C₆₇	—	2	2	no	—
652	C₄×C₆₇	—	2	2	no	—
653	C₄×C₆₇	—	2	4	no	—
654	C₄×C₆₇	—	2	4	no	—
655	C₄×C₆₇	—	2	2	no	—
656	C₄×C₆₇	—	2	2	no	—
657	C₄×C₆₇	—	2	4	no	—
658	C₄×C₆₇	C₂²×#41	1	4	yes	—
659	Dic₆₇	—	2	2	no	—
660	Dic₆₇	—	2	2	no	—
661	Dic₆₇	—	2	4	no	—
662	Dic₆₇	—	2	2	no	—
663	Dic₆₇	—	2	2	no	—
664	Dic₆₇	—	2	2	no	—
665	Dic₆₇	—	2	2	no	—
666	Dic₆₇	—	2	2	no	—
667	C₂×#3513	—	67	1	no	maximal, Sylow
668	C₂×C₆₇	—	2	4	no	—
669	C₂×C₆₇	—	4	2	no	—
670	C₂×C₆₇	#3513	1	4	yes	complemented
671	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
672	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
674	D₆₇	—	2	8	no	—
675	D₆₇	—	4	2	no	—
676	D₆₇	—	4	4	no	—
677	D₆₇	—	4	4	no	—
678	#3513	—	67	32	no	—
679	C₂×#559	—	67	1	no	—
680	C₂×#554	—	67	1	no	—
681	C₂×#553	—	67	2	no	—
682	C₂×#553	—	67	1	no	—
683	C₂×#552	D₆₇	1	1	yes	characteristic, complemented
684	C₂×#551	—	67	2	no	—
685	C₂×#551	—	67	2	no	—
686	C₂×#547	—	67	1	no	—
687	C₂×#546	—	67	2	no	—
688	C₂×#546	—	67	1	no	—
689	C₂×#546	—	67	1	no	—
690	C₂×D₄²	—	67	1	no	—
691	C₂×#542	—	67	1	no	—
692	C₂×#540	—	67	1	no	—
693	C₂×#539	—	67	2	no	—
694	C₂×#538	—	67	2	no	—
695	C₂×#529	—	67	1	no	—
696	C₂×#529	—	67	1	no	—
697	C₂×#525	—	67	2	no	—
698	C₂²×#123	—	67	2	no	—
699	C₂×#520	—	67	1	no	—
700	C₂×#518	—	67	1	no	—
701	C₂²×C₄×D₄	—	67	1	no	—
702	C₆₇	C₂×#3513	1	1	yes	characteristic, complemented, Sylow
703	C₂²×#41	—	67	1	no	—
704	C₂²×#41	—	67	2	no	—
705	C₂³×D₄	—	67	2	no	—
706	C₂³×D₄	—	67	1	no	—
707	C₂³×D₄	—	67	1	no	—
708	C₂⁴×C₄	—	67	2	no	—
709	#559	—	67	16	no	—
710	#554	—	67	16	no	—
711	#553	—	67	32	no	—
712	#553	—	67	16	no	—
713	#552	C₂×D₆₇	1	16	yes	complemented
714	#551	—	67	32	no	—
715	#551	—	67	32	no	—
716	#547	—	67	16	no	—
717	#546	—	67	32	no	—
718	#546	—	67	16	no	—
719	#546	—	67	16	no	—
720	D₄²	—	67	16	no	—
721	#542	—	67	16	no	—
722	#540	—	67	16	no	—
723	#539	—	67	32	no	—
724	#538	—	67	32	no	—
725	C₂×C₄⋊Q₈	—	67	1	no	—
726	C₂×#127	—	67	1	no	—
727	#529	—	67	16	no	—
728	#529	—	67	16	no	—
729	C₂×#126	—	67	2	no	—
730	C₂×#126	—	67	1	no	—
731	C₂×#126	—	67	2	no	—
732	C₂×#126	—	67	1	no	—
733	C₂×#126	—	67	2	no	—
734	C₂×#126	C₂×D₆₇	1	2	yes	complemented
735	C₂×#125	—	67	1	no	—
736	C₂×#125	—	67	1	no	—
737	C₂×#125	C₂×D₆₇	1	2	yes	complemented
738	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
739	C₂×#124	—	67	1	no	—
740	C₂×#124	—	67	1	no	—
741	C₂×#124	—	67	1	no	—
742	C₂×#124	—	67	2	no	—
743	C₂×#124	—	67	2	no	—
744	#525	—	67	32	no	—
745	C₂×#123	—	67	1	no	—
746	C₂×#123	—	67	2	no	—
747	C₂×#123	—	67	32	no	—
748	C₂×#123	—	67	2	no	—
749	C₂×#123	—	67	2	no	—
750	C₂×#123	—	67	2	no	—
751	C₂×#123	—	67	2	no	—
752	C₂×#123	—	67	2	no	—
753	C₂×#123	—	67	2	no	—
754	C₂×#123	—	67	2	no	—
755	C₂×#123	—	67	2	no	—
756	C₂×#123	—	67	2	no	—
757	C₂×#123	—	67	2	no	—
758	C₂×#123	—	67	1	no	—
759	C₂×#123	C₂×D₆₇	1	2	yes	—
760	C₂×C₂²⋊Q₈	—	67	2	no	—
761	C₂×C₂²⋊Q₈	—	67	2	no	—
762	C₂×C₂²⋊Q₈	—	67	2	no	—
763	C₂×C₂²⋊Q₈	—	67	2	no	—
764	C₂×C₂²⋊Q₈	—	67	2	no	—
765	C₂×C₂²⋊Q₈	—	67	1	no	—
766	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
767	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
768	C₂×#121	—	67	1	no	—
769	C₂×#121	—	67	1	no	—
770	C₂×#121	—	67	1	no	—
771	C₂×#121	—	67	2	no	—
772	C₂×#121	—	67	2	no	—
773	C₂×#121	—	67	2	no	—
774	C₂×#121	—	67	2	no	—
775	C₂×#121	—	67	1	no	—
776	C₂×#121	—	67	2	no	—
777	C₂×#121	—	67	1	no	—
778	C₂×#121	—	67	2	no	—
779	C₂×#120	—	67	2	no	—
780	C₂×#120	—	67	2	no	—
781	C₂×#120	—	67	2	no	—
782	C₂×#120	—	67	2	no	—
783	#520	—	67	16	no	—
784	#518	—	67	16	no	—
785	C₂×C₄×Q₈	—	67	1	no	—
786	C₂×C₄×Q₈	—	67	1	no	—
787	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
788	C₂×C₄×D₄	—	67	1	no	—
789	C₂×C₄×D₄	—	67	1	no	—
790	C₂×C₄×D₄	—	67	1	no	—
791	C₂×C₄×D₄	—	67	1	no	—
792	C₂×C₄×D₄	—	67	2	no	—
793	C₂×C₄×D₄	—	67	1	no	—
794	C₂×C₄×D₄	—	67	2	no	—
795	C₂×C₄×D₄	—	67	1	no	—
796	C₂×C₄×D₄	—	67	1	no	—
797	C₂×C₄×D₄	—	67	1	no	—
798	C₂×C₄×D₄	—	67	1	no	—
799	C₂×C₄×D₄	—	67	2	no	—
800	C₂×C₄×D₄	—	67	16	no	—
801	C₂×C₄×D₄	—	67	2	no	—
802	C₂×C₄×D₄	—	67	2	no	—
803	C₂×C₄×D₄	—	67	2	no	—
804	C₂×C₄×D₄	—	67	2	no	—
805	C₂×C₄×D₄	—	67	1	no	—
806	C₂×C₄×D₄	—	67	2	no	—
807	C₂×C₄×D₄	—	67	2	no	—
808	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
809	C₂×#117	—	67	1	no	—
810	C₂×#117	—	67	2	no	—
811	C₂×#117	—	67	1	no	—
812	C₂×#117	—	67	2	no	—
813	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
814	C₂×#117	C₂×D₆₇	1	2	yes	complemented
815	C₂²×C₄⋊C₄	—	67	2	no	—
816	C₂²×C₄⋊C₄	—	67	1	no	—
817	C₂²×C₄⋊C₄	—	67	2	no	—
818	C₂²×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
819	C₂²×C₂²⋊C₄	—	67	2	no	—
820	C₂²×C₂²⋊C₄	—	67	2	no	—
821	C₂²×C₂²⋊C₄	—	67	2	no	—
822	C₂²×C₂²⋊C₄	—	67	2	no	—
823	C₂²×C₂²⋊C₄	—	67	2	no	—
824	C₂²×C₄²	—	67	1	no	—
825	C₂⁵	—	67	2	no	—
826	C₂⁵	—	67	2	no	—
827	C₂×#41	—	268	8	no	—
828	C₂×#41	—	67	8	no	—
829	C₂×#41	—	67	16	no	—
830	C₂×#41	—	134	8	no	—
831	C₂²×Q₈	—	67	1	no	—
832	C₂²×Q₈	—	67	2	no	—
833	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
834	C₂²×D₄	—	268	8	no	—
835	C₂²×D₄	—	67	1	no	—
836	C₂²×D₄	—	67	2	no	—
837	C₂²×D₄	—	67	16	no	—
838	C₂²×D₄	—	67	1	no	—
839	C₂²×D₄	—	67	2	no	—
840	C₂²×D₄	—	67	2	no	—
841	C₂²×D₄	—	67	2	no	—
842	C₂²×D₄	—	67	2	no	—
843	C₂²×D₄	—	67	2	no	—
844	C₂²×D₄	—	67	1	no	—
845	C₂²×D₄	—	67	2	no	—
846	C₂²×D₄	—	67	2	no	—
847	C₂²×D₄	—	67	2	no	—
848	C₂²×D₄	—	67	1	no	—
849	C₂²×D₄	—	67	1	no	—
850	C₂²×D₄	—	67	8	no	—
851	C₂²×D₄	—	67	8	no	—
852	C₂²×D₄	—	134	8	no	—
853	C₂²×D₄	—	134	8	no	—
854	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
855	C₂³×C₄	—	268	8	no	—
856	C₂³×C₄	—	67	1	no	—
857	C₂³×C₄	—	67	2	no	—
858	C₂³×C₄	—	67	2	no	—
859	C₂³×C₄	—	67	2	no	—
860	C₂³×C₄	—	67	2	no	—
861	C₂³×C₄	—	67	2	no	—
862	C₂³×C₄	—	67	2	no	—
863	C₂³×C₄	—	67	2	no	—
864	C₂³×C₄	—	67	2	no	—
865	C₂³×C₄	—	67	2	no	—
866	C₂³×C₄	—	67	16	no	—
867	C₂³×C₄	—	67	1	no	—
868	C₂³×C₄	—	67	2	no	—
869	C₂³×C₄	—	67	1	no	—
870	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
871	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
872	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
873	C₄⋊Q₈	—	67	8	no	—
874	#127	—	67	8	no	—
875	#126	—	67	16	no	—
876	#126	—	67	8	no	—
877	#126	—	67	16	no	—
878	#126	—	67	8	no	—
879	#126	—	67	16	no	—
880	#126	C₂²×D₆₇	1	16	yes	complemented
881	#125	—	67	8	no	—
882	#125	—	67	8	no	—
883	#125	C₂²×D₆₇	1	16	yes	complemented
884	#125	C₂²×D₆₇	1	8	yes	complemented
885	#124	—	67	8	no	—
886	#124	—	67	8	no	—
887	#124	—	67	8	no	—
888	#124	—	67	16	no	—
889	#124	—	67	16	no	—
890	#123	—	67	8	no	—
891	#123	—	67	16	no	—
892	#123	—	67	16	no	—
893	#123	—	67	16	no	—
894	#123	—	67	16	no	—
895	#123	—	67	16	no	—
896	#123	—	67	16	no	—
897	#123	—	67	16	no	—
898	#123	—	67	16	no	—
899	#123	—	67	16	no	—
900	#123	—	67	16	no	—
901	#123	—	67	16	no	—
902	#123	—	67	8	no	—
903	#123	C₂²×D₆₇	1	16	yes	—
904	C₂²⋊Q₈	—	67	16	no	—
905	C₂²⋊Q₈	—	67	16	no	—
906	C₂²⋊Q₈	—	67	16	no	—
907	C₂²⋊Q₈	—	67	16	no	—
908	C₂²⋊Q₈	—	67	16	no	—
909	C₂²⋊Q₈	—	67	8	no	—
910	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
911	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
912	#121	—	67	8	no	—
913	#121	—	67	8	no	—
914	#121	—	67	8	no	—
915	#121	—	67	16	no	—
916	#121	—	67	16	no	—
917	#121	—	67	16	no	—
918	#121	—	67	16	no	—
919	#121	—	67	8	no	—
920	#121	—	67	16	no	—
921	#121	—	67	8	no	—
922	#121	—	67	16	no	—
923	#120	—	67	16	no	—
924	#120	—	67	16	no	—
925	#120	—	67	16	no	—
926	#120	—	67	16	no	—
927	C₄×Q₈	—	67	8	no	—
928	C₄×Q₈	—	67	8	no	—
929	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
930	C₄×D₄	—	67	8	no	—
931	C₄×D₄	—	67	8	no	—
932	C₄×D₄	—	67	8	no	—
933	C₄×D₄	—	67	16	no	—
934	C₄×D₄	—	67	8	no	—
935	C₄×D₄	—	67	8	no	—
936	C₄×D₄	—	67	16	no	—
937	C₄×D₄	—	67	8	no	—
938	C₄×D₄	—	67	8	no	—
939	C₄×D₄	—	67	8	no	—
940	C₄×D₄	—	67	8	no	—
941	C₄×D₄	—	67	16	no	—
942	C₄×D₄	—	67	16	no	—
943	C₄×D₄	—	67	16	no	—
944	C₄×D₄	—	67	16	no	—
945	C₄×D₄	—	67	16	no	—
946	C₄×D₄	—	67	8	no	—
947	C₄×D₄	—	67	16	no	—
948	C₄×D₄	—	67	16	no	—
949	C₄×D₄	C₂²×D₆₇	1	8	yes	—
950	#117	—	67	8	no	—
951	#117	—	67	16	no	—
952	#117	—	67	8	no	—
953	#117	—	67	16	no	—
954	#117	C₂²×D₆₇	1	8	yes	complemented
955	#117	C₂²×D₆₇	1	16	yes	complemented
956	C₂×C₄⋊C₄	—	67	2	no	—
957	C₂×C₄⋊C₄	—	67	1	no	—
958	C₂×C₄⋊C₄	—	67	1	no	—
959	C₂×C₄⋊C₄	—	67	2	no	—
960	C₂×C₄⋊C₄	—	67	1	no	—
961	C₂×C₄⋊C₄	—	67	2	no	—
962	C₂×C₄⋊C₄	—	67	2	no	—
963	C₂×C₄⋊C₄	—	67	1	no	—
964	C₂×C₄⋊C₄	—	67	1	no	—
965	C₂×C₄⋊C₄	—	67	1	no	—
966	C₂×C₄⋊C₄	—	67	1	no	—
967	C₂×C₄⋊C₄	—	67	2	no	—
968	C₂×C₄⋊C₄	—	67	1	no	—
969	C₂×C₄⋊C₄	—	67	1	no	—
970	C₂×C₄⋊C₄	—	67	1	no	—
971	C₂×C₄⋊C₄	—	67	16	no	—
972	C₂×C₄⋊C₄	—	67	8	no	—
973	C₂×C₄⋊C₄	—	67	16	no	—
974	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
976	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
977	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
978	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
979	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
980	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
981	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
982	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
983	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
984	C₂×C₄⋊C₄	C₂²×D₆₇	1	8	yes	complemented
985	C₂×C₂²⋊C₄	—	67	1	no	—
986	C₂×C₂²⋊C₄	—	67	1	no	—
987	C₂×C₂²⋊C₄	—	67	1	no	—
988	C₂×C₂²⋊C₄	—	67	1	no	—
989	C₂×C₂²⋊C₄	—	67	2	no	—
990	C₂×C₂²⋊C₄	—	67	2	no	—
991	C₂×C₂²⋊C₄	—	67	2	no	—
992	C₂×C₂²⋊C₄	—	67	2	no	—
993	C₂×C₂²⋊C₄	—	67	2	no	—
994	C₂×C₂²⋊C₄	—	67	2	no	—
995	C₂×C₂²⋊C₄	—	67	2	no	—
996	C₂×C₂²⋊C₄	—	67	2	no	—
997	C₂×C₂²⋊C₄	—	67	16	no	—
998	C₂×C₂²⋊C₄	—	67	2	no	—
999	C₂×C₂²⋊C₄	—	67	2	no	—
1000	C₂×C₂²⋊C₄	—	67	2	no	—
1001	C₂×C₂²⋊C₄	—	67	2	no	—
1002	C₂×C₂²⋊C₄	—	67	1	no	—
1003	C₂×C₂²⋊C₄	—	67	1	no	—
1004	C₂×C₂²⋊C₄	—	67	2	no	—
1005	C₂×C₂²⋊C₄	—	67	1	no	—
1006	C₂×C₂²⋊C₄	—	67	2	no	—
1007	C₂×C₂²⋊C₄	—	67	2	no	—
1008	C₂×C₂²⋊C₄	—	67	2	no	—
1009	C₂×C₂²⋊C₄	—	67	1	no	—
1010	C₂×C₂²⋊C₄	—	67	16	no	—
1011	C₂×C₂²⋊C₄	—	67	16	no	—
1012	C₂×C₂²⋊C₄	—	67	16	no	—
1013	C₂×C₂²⋊C₄	—	67	16	no	—
1014	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1015	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1016	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
1017	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1018	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1019	C₂×C₄²	—	67	1	no	—
1020	C₂×C₄²	—	67	2	no	—
1021	C₂×C₄²	—	67	1	no	—
1022	C₂×C₄²	—	67	1	no	—
1023	C₂×C₄²	—	67	1	no	—
1024	C₂×C₄²	—	67	1	no	—
1025	C₂×C₄²	—	67	8	no	—
1026	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1027	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1028	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1029	C₂⁴	—	268	4	no	—
1030	C₂⁴	—	268	4	no	—
1031	C₂⁴	—	268	4	no	—
1032	C₂⁴	—	67	8	no	—
1033	C₂⁴	—	67	8	no	—
1034	C₂⁴	—	67	2	no	—
1035	C₂⁴	—	67	2	no	—
1036	C₂⁴	—	67	2	no	—
1037	C₂⁴	—	67	1	no	—
1038	C₂⁴	—	134	8	no	—
1039	C₂⁴	—	134	8	no	—
1040	C₂⁴	—	134	8	no	—
1041	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1042	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1043	#41	—	268	32	no	—
1044	#41	—	134	32	no	—
1045	C₂×Q₈	—	2	4	no	—
1046	C₂×Q₈	—	268	4	no	—
1047	C₂×Q₈	—	268	2	no	—
1048	C₂×Q₈	—	67	4	no	—
1049	C₂×Q₈	—	67	8	no	—
1050	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1051	C₂×D₄	—	2	4	no	—
1052	C₂×D₄	—	268	4	no	—
1053	C₂×D₄	—	268	4	no	—
1054	C₂×D₄	—	268	4	no	—
1055	C₂×D₄	—	268	4	no	—
1056	C₂×D₄	—	268	32	no	—
1057	C₂×D₄	—	268	4	no	—
1058	C₂×D₄	—	268	2	no	—
1059	C₂×D₄	—	67	4	no	—
1060	C₂×D₄	—	67	8	no	—
1061	C₂×D₄	—	67	4	no	—
1062	C₂×D₄	—	67	8	no	—
1063	C₂×D₄	—	67	8	no	—
1064	C₂×D₄	—	67	8	no	—
1065	C₂×D₄	—	67	8	no	—
1066	C₂×D₄	—	67	8	no	—
1067	C₂×D₄	—	67	8	no	—
1068	C₂×D₄	—	67	4	no	—
1069	C₂×D₄	—	67	8	no	—
1070	C₂×D₄	—	67	8	no	—
1071	C₂×D₄	—	67	8	no	—
1072	C₂×D₄	—	67	4	no	—
1073	C₂×D₄	—	67	4	no	—
1074	C₂×D₄	—	134	32	no	—
1075	C₂×D₄	—	134	32	no	—
1076	C₂×D₄	—	134	8	no	—
1077	C₂×D₄	—	134	8	no	—
1078	C₂×D₄	—	134	8	no	—
1079	C₂×D₄	—	134	8	no	—
1080	C₂×D₄	—	134	4	no	—
1081	C₂×D₄	—	134	4	no	—
1082	C₂×D₄	—	134	4	no	—
1083	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1084	C₂²×C₄	—	2	8	no	—
1085	C₂²×C₄	—	2	4	no	—
1086	C₂²×C₄	—	2	4	no	—
1087	C₂²×C₄	—	268	4	no	—
1088	C₂²×C₄	—	268	4	no	—
1089	C₂²×C₄	—	268	4	no	—
1090	C₂²×C₄	—	268	4	no	—
1091	C₂²×C₄	—	268	32	no	—
1092	C₂²×C₄	—	268	4	no	—
1093	C₂²×C₄	—	268	4	no	—
1094	C₂²×C₄	—	268	4	no	—
1095	C₂²×C₄	—	268	4	no	—
1096	C₂²×C₄	—	268	4	no	—
1097	C₂²×C₄	—	268	2	no	—
1098	C₂²×C₄	—	67	4	no	—
1099	C₂²×C₄	—	67	8	no	—
1100	C₂²×C₄	—	67	8	no	—
1101	C₂²×C₄	—	67	8	no	—
1102	C₂²×C₄	—	67	8	no	—
1103	C₂²×C₄	—	67	8	no	—
1104	C₂²×C₄	—	67	8	no	—
1105	C₂²×C₄	—	67	8	no	—
1106	C₂²×C₄	—	67	8	no	—
1107	C₂²×C₄	—	67	8	no	—
1108	C₂²×C₄	—	67	4	no	—
1109	C₂²×C₄	—	67	1	no	—
1110	C₂²×C₄	—	67	1	no	—
1111	C₂²×C₄	—	67	1	no	—
1112	C₂²×C₄	—	67	1	no	—
1113	C₂²×C₄	—	67	1	no	—
1114	C₂²×C₄	—	67	1	no	—
1115	C₂²×C₄	—	67	2	no	—
1116	C₂²×C₄	—	67	1	no	—
1117	C₂²×C₄	—	67	8	no	—
1118	C₂²×C₄	—	67	4	no	—
1119	C₂²×C₄	—	134	8	no	—
1120	C₂²×C₄	—	134	4	no	—
1121	C₂²×C₄	—	134	4	no	—
1122	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1123	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1124	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1125	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1126	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1127	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1128	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1129	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1130	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1131	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1132	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1133	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1134	C₄⋊C₄	—	67	8	no	—
1135	C₄⋊C₄	—	67	4	no	—
1136	C₄⋊C₄	—	67	4	no	—
1137	C₄⋊C₄	—	67	8	no	—
1138	C₄⋊C₄	—	67	4	no	—
1139	C₄⋊C₄	—	67	8	no	—
1140	C₄⋊C₄	—	67	8	no	—
1141	C₄⋊C₄	—	67	4	no	—
1142	C₄⋊C₄	—	67	4	no	—
1143	C₄⋊C₄	—	67	4	no	—
1144	C₄⋊C₄	—	67	4	no	—
1145	C₄⋊C₄	—	67	8	no	—
1146	C₄⋊C₄	—	67	4	no	—
1147	C₄⋊C₄	—	67	4	no	—
1148	C₄⋊C₄	—	67	4	no	—
1149	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1150	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1151	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1152	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1153	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1154	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1155	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1156	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1157	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1158	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1159	C₂²⋊C₄	—	67	4	no	—
1160	C₂²⋊C₄	—	67	4	no	—
1161	C₂²⋊C₄	—	67	4	no	—
1162	C₂²⋊C₄	—	67	4	no	—
1163	C₂²⋊C₄	—	67	8	no	—
1164	C₂²⋊C₄	—	67	8	no	—
1165	C₂²⋊C₄	—	67	8	no	—
1166	C₂²⋊C₄	—	67	8	no	—
1167	C₂²⋊C₄	—	67	8	no	—
1168	C₂²⋊C₄	—	67	8	no	—
1169	C₂²⋊C₄	—	67	8	no	—
1170	C₂²⋊C₄	—	67	8	no	—
1171	C₂²⋊C₄	—	67	8	no	—
1172	C₂²⋊C₄	—	67	8	no	—
1173	C₂²⋊C₄	—	67	8	no	—
1174	C₂²⋊C₄	—	67	8	no	—
1175	C₂²⋊C₄	—	67	4	no	—
1176	C₂²⋊C₄	—	67	4	no	—
1177	C₂²⋊C₄	—	67	8	no	—
1178	C₂²⋊C₄	—	67	4	no	—
1179	C₂²⋊C₄	—	67	8	no	—
1180	C₂²⋊C₄	—	67	8	no	—
1181	C₂²⋊C₄	—	67	8	no	—
1182	C₂²⋊C₄	—	67	4	no	—
1183	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1184	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1185	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1186	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1187	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1188	C₄²	—	67	4	no	—
1189	C₄²	—	67	4	no	—
1190	C₄²	—	67	4	no	—
1191	C₄²	—	67	4	no	—
1192	C₄²	—	67	8	no	—
1193	C₄²	—	67	4	no	—
1194	C₄²	C₂³×D₆₇	1	8	yes	—
1195	C₄²	C₂³×D₆₇	1	4	yes	—
1196	C₄²	C₂³×D₆₇	1	8	yes	—
1197	C₂³	—	2	2	no	—
1198	C₂³	—	2	2	no	—
1199	C₂³	—	2	2	no	—
1200	C₂³	—	2	2	no	—
1201	C₂³	—	2	2	no	—
1202	C₂³	—	268	32	no	—
1203	C₂³	—	268	8	no	—
1204	C₂³	—	268	8	no	—
1205	C₂³	—	268	8	no	—
1206	C₂³	—	536	16	no	—
1207	C₂³	—	67	8	no	—
1208	C₂³	—	67	4	no	—
1209	C₂³	—	67	4	no	—
1210	C₂³	—	67	4	no	—
1211	C₂³	—	67	2	no	—
1212	C₂³	—	134	16	no	—
1213	C₂³	—	134	16	no	—
1214	C₂³	—	134	2	no	—
1215	C₂³	—	134	4	no	—
1216	C₂³	—	134	4	no	—
1217	C₂³	—	134	2	no	—
1218	C₂³	—	134	16	no	—
1219	C₂³	—	134	4	no	—
1220	C₂³	—	134	4	no	—
1221	C₂³	—	134	4	no	—
1222	C₂³	—	134	2	no	—
1223	C₂³	—	134	4	no	—
1224	C₂³	—	134	4	no	—
1225	C₂³	—	134	4	no	—
1226	C₂³	#14524089	1	4	yes	—
1227	C₂³	C₂⁴×D₆₇	1	2	yes	—
1228	C₂³	C₂⁴×D₆₇	1	2	yes	—
1229	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1230	Q₈	—	2	8	no	—
1231	Q₈	—	268	8	no	—
1232	Q₈	—	268	4	no	—
1233	D₄	—	2	8	no	—
1234	D₄	—	268	8	no	—
1235	D₄	—	268	8	no	—
1236	D₄	—	268	8	no	—
1237	D₄	—	268	8	no	—
1238	D₄	—	268	8	no	—
1239	D₄	—	268	4	no	—
1240	D₄	—	67	16	no	—
1241	D₄	—	134	16	no	—
1242	D₄	—	134	16	no	—
1243	D₄	—	134	16	no	—
1244	D₄	—	134	16	no	—
1245	D₄	—	134	8	no	—
1246	D₄	—	134	8	no	—
1247	D₄	—	134	8	no	—
1248	C₂×C₄	—	2	2	no	—
1249	C₂×C₄	—	2	2	no	—
1250	C₂×C₄	—	2	4	no	—
1251	C₂×C₄	—	2	4	no	—
1252	C₂×C₄	—	2	4	no	—
1253	C₂×C₄	—	2	16	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	4	no	—
1256	C₂×C₄	—	2	2	no	—
1257	C₂×C₄	—	2	8	no	—
1258	C₂×C₄	—	2	8	no	—
1259	C₂×C₄	—	268	8	no	—
1260	C₂×C₄	—	268	8	no	—
1261	C₂×C₄	—	268	8	no	—
1262	C₂×C₄	—	268	8	no	—
1263	C₂×C₄	—	268	8	no	—
1264	C₂×C₄	—	268	8	no	—
1265	C₂×C₄	—	268	8	no	—
1266	C₂×C₄	—	268	8	no	—
1267	C₂×C₄	—	268	8	no	—
1268	C₂×C₄	—	268	4	no	—
1269	C₂×C₄	—	67	2	no	—
1270	C₂×C₄	—	67	2	no	—
1271	C₂×C₄	—	67	2	no	—
1272	C₂×C₄	—	67	2	no	—
1273	C₂×C₄	—	67	2	no	—
1274	C₂×C₄	—	67	2	no	—
1275	C₂×C₄	—	67	4	no	—
1276	C₂×C₄	—	67	2	no	—
1277	C₂×C₄	—	134	16	no	—
1278	C₂×C₄	—	134	2	no	—
1279	C₂×C₄	—	134	8	no	—
1280	C₂×C₄	—	134	2	no	—
1281	C₂×C₄	—	134	2	no	—
1282	C₂×C₄	—	134	4	no	—
1283	C₂×C₄	—	134	2	no	—
1284	C₂×C₄	—	134	2	no	—
1285	C₂×C₄	—	134	2	no	—
1286	C₂×C₄	—	134	2	no	—
1287	C₂×C₄	—	134	8	no	—
1288	C₂×C₄	#41×D₆₇	1	4	yes	—
1289	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1290	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1291	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1292	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1293	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1294	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1295	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1296	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1297	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1298	C₂²	—	2	8	no	—
1299	C₂²	—	2	2	no	—
1300	C₂²	—	2	2	no	—
1301	C₂²	—	2	2	no	—
1302	C₂²	—	2	2	no	—
1303	C₂²	—	2	2	no	—
1304	C₂²	—	4	4	no	—
1305	C₂²	—	268	32	no	—
1306	C₂²	—	268	8	no	—
1307	C₂²	—	268	8	no	—
1308	C₂²	—	268	4	no	—
1309	C₂²	—	536	16	no	—
1310	C₂²	—	67	8	no	—
1311	C₂²	—	134	2	no	—
1312	C₂²	—	134	4	no	—
1313	C₂²	—	134	4	no	—
1314	C₂²	—	134	2	no	—
1315	C₂²	—	134	4	no	—
1316	C₂²	—	134	4	no	—
1317	C₂²	—	134	4	no	—
1318	C₂²	—	134	2	no	—
1319	C₂²	—	134	4	no	—
1320	C₂²	—	134	16	no	—
1321	C₂²	—	134	4	no	—
1322	C₂²	—	134	4	no	—
1323	C₂²	C₂×#41×D₆₇	1	2	yes	—
1324	C₂²	C₂×#14524089	1	4	yes	—
1325	C₂²	C₂×#14524089	1	2	yes	—
1326	C₂²	#16864233	1	2	yes	—
1327	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1328	C₄	—	2	2	no	—
1329	C₄	—	2	2	no	—
1330	C₄	—	2	4	no	—
1331	C₄	—	2	4	no	—
1332	C₄	—	2	4	no	—
1333	C₄	—	2	2	no	—
1334	C₄	—	2	4	no	—
1335	C₄	—	2	2	no	—
1336	C₄	—	134	2	no	—
1337	C₄	—	134	2	no	—
1338	C₄	—	134	2	no	—
1339	C₄	—	134	4	no	—
1340	C₄	—	134	2	no	—
1341	C₄	—	134	2	no	—
1342	C₄	—	134	2	no	—
1343	C₄	—	134	2	no	—
1344	C₄	C₂×#41×D₆₇	1	4	yes	—
1345	C₂	—	2	4	no	—
1346	C₂	—	4	2	no	—
1347	C₂	—	268	4	no	—
1348	C₂	—	268	4	no	—
1349	C₂	—	268	2	no	—
1350	C₂	—	134	8	no	—
1351	C₂	#22574154	1	4	yes	direct product factor
1352	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1353	C₂	C₂²×#14524089	1	1	yes	characteristic
1354	C₂	C₂×#16864233	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#552×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#552	D₆₇
hypocenter	C₆₇	C₂×#3513
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#552

Complements

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

N	H ≅ G/N	type
1. #22574154	C₂	direct (N × H)
2. C₂×#16864131	C₂	semidirect
3. C₂×#16864102	C₂	semidirect
4. C₂×#16864099	C₂	semidirect
5. C₂×#16864090	C₂	semidirect
6. C₂×#16864071	C₂	semidirect
7. C₂×#16864070	C₂	semidirect
8. C₂×#16864047	C₂	semidirect
9. C₂×#16864038	C₂	semidirect
10. C₂×#16864037	C₂	semidirect
11. C₂×#16864037	C₂	semidirect
12. C₂×D₄×D₂₆₈	C₂	semidirect
13. C₂×#16864019	C₂	semidirect
14. C₂×#16864002	C₂	semidirect
15. C₂×#16863994	C₂	semidirect
16. C₂×#16863985	C₂	semidirect
17. C₂×#16863932	C₂	semidirect
18. C₂×#16863926	C₂	semidirect
19. C₂×#16863908	C₂	semidirect
20. C₂×#123×D₆₇	C₂	semidirect
21. C₂×#16863878	C₂	semidirect
22. C₂×#16863870	C₂	semidirect
23. C₂²×#14524005	C₂	semidirect
24. C₂×#552×C₆₇	C₂	semidirect
26. C₂²×#11761628	C₂²	semidirect
30. C₂³×C₄×D₆₇	C₂²	semidirect
31. #16864131	C₂²	semidirect
32. #16864102	C₂²	semidirect
33. #16864099	C₂²	semidirect
34. #16864090	C₂²	semidirect
35. #16864071	C₂²	semidirect
36. #16864070	C₂²	semidirect
37. #16864047	C₂²	semidirect
38. #16864038	C₂²	semidirect
39. #16864037	C₂²	semidirect
40. #16864037	C₂²	semidirect
41. D₄×D₂₆₈	C₂²	semidirect
42. #16864019	C₂²	semidirect
43. #16864002	C₂²	semidirect
44. #16863994	C₂²	semidirect
45. #16863985	C₂²	semidirect
46. C₂×#14524042	C₂²	semidirect
48. #16863932	C₂²	semidirect
49. #16863926	C₂²	semidirect
50. C₂×#14524038	C₂²	semidirect
51. C₂×#14524038	C₂²	semidirect
52. C₂×#14524038	C₂²	semidirect
53. C₂×#14524037	C₂²	semidirect
54. C₂×#14524036	C₂²	semidirect
55. C₂×#14524034	C₂²	semidirect
56. C₂×#14524033	C₂²	semidirect
57. C₂×#14524032	C₂²	semidirect
58. C₂×#14524032	C₂²	semidirect
59. C₂×#14524031	C₂²	semidirect
60. C₂×#14524029	C₂²	semidirect
61. C₂×#14524029	C₂²	semidirect
62. #16863908	C₂²	semidirect
63. C₂×#14524028	C₂²	semidirect
64. C₂×#14524028	C₂²	semidirect
65. C₂×#14524028	C₂²	semidirect
66. C₂×#14524028	C₂²	semidirect
67. C₂×#14524028	C₂²	semidirect
68. C₂×#14524028	C₂²	semidirect
69. C₂×#14524028	C₂²	semidirect
70. C₂×#14524027	C₂²	semidirect
71. C₂×#14524027	C₂²	semidirect
72. C₂×#14524026	C₂²	semidirect
73. C₂×#14524025	C₂²	semidirect
74. C₂×#14524025	C₂²	semidirect
76. #123×D₆₇	C₂²	semidirect
77. C₂×#14524023	C₂²	semidirect
78. C₂×#14524023	C₂²	semidirect
79. C₂×#14524021	C₂²	semidirect
80. C₂×#14524021	C₂²	semidirect
81. C₂×#14524021	C₂²	semidirect
82. C₂×#14524020	C₂²	semidirect
84. C₂×#14524018	C₂²	semidirect
85. C₂×#14524018	C₂²	semidirect
86. C₂×#14524018	C₂²	semidirect
87. C₂×#14524018	C₂²	semidirect
88. C₂×#14524018	C₂²	semidirect
89. C₂×#14524018	C₂²	semidirect
92. C₂×#14524016	C₂²	semidirect
96. C₂×#14524013	C₂²	semidirect
97. C₂×#14524013	C₂²	semidirect
98. #16863878	C₂²	semidirect
99. #16863870	C₂²	semidirect
100. C₂×Q₈×Dic₆₇	C₂²	semidirect
101. C₂×C₄×Dic₁₃₄	C₂²	semidirect
103. C₂×C₄×D₂₆₈	C₂²	semidirect
104. C₂×C₄×D₂₆₈	C₂²	semidirect
105. C₂×C₄×D₂₆₈	C₂²	semidirect
106. C₂×C₄×D₂₆₈	C₂²	semidirect
107. C₂×C₄×D₂₆₈	C₂²	semidirect
111. C₂×#14524005	C₂²	semidirect
112. C₂×#14524005	C₂²	semidirect
113. C₂×#14524005	C₂²	semidirect
114. C₂×#14524005	C₂²	semidirect
115. C₂×#14524005	C₂²	semidirect
116. C₂×#14524005	C₂²	semidirect
117. C₂×#14524005	C₂²	semidirect
118. C₂×#14524005	C₂²	semidirect
119. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
120. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
121. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
122. C₂×#14524002	C₂²	semidirect
123. C₂×#14524001	C₂²	semidirect
124. C₂×#14524000	C₂²	semidirect
125. C₂×#14524000	C₂²	semidirect
126. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
127. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
128. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
129. C₂²×(C₂×D₆₇)⋊C₄	C₂²	semidirect
130. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
131. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
132. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
133. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
134. C₂²×C₄×Dic₆₇	C₂²	semidirect
135. #552×C₆₇	C₂²	semidirect
136. C₂×#126×C₆₇	C₂²	semidirect
137. C₂×#125×C₆₇	C₂²	semidirect
138. C₂×#125×C₆₇	C₂²	semidirect
140. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
142. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
144. C₂×#117×C₆₇	C₂²	semidirect
145. C₂×#117×C₆₇	C₂²	semidirect
146. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
152. C₂×#11761628	C₂³	semidirect
189. C₂²×C₄×D₆₇	C₂³	semidirect
190. #14524042	C₂³	semidirect
192. #14524038	C₂³	semidirect
193. #14524038	C₂³	semidirect
194. #14524038	C₂³	semidirect
195. #14524037	C₂³	semidirect
196. #14524036	C₂³	semidirect
197. #14524034	C₂³	semidirect
198. #14524033	C₂³	semidirect
199. #14524032	C₂³	semidirect
200. #14524032	C₂³	semidirect
201. #14524031	C₂³	semidirect
202. #14524029	C₂³	semidirect
203. #14524029	C₂³	semidirect
204. #14524028	C₂³	semidirect
205. #14524028	C₂³	semidirect
206. #14524028	C₂³	semidirect
207. #14524028	C₂³	semidirect
208. #14524028	C₂³	semidirect
209. #14524028	C₂³	semidirect
210. #14524028	C₂³	semidirect
211. #14524027	C₂³	semidirect
212. #14524027	C₂³	semidirect
213. #14524026	C₂³	semidirect
214. #14524025	C₂³	semidirect
215. #14524025	C₂³	semidirect
217. #14524023	C₂³	semidirect
218. #14524023	C₂³	semidirect
219. #14524021	C₂³	semidirect
220. #14524021	C₂³	semidirect
221. #14524021	C₂³	semidirect
222. #14524020	C₂³	semidirect
224. #14524018	C₂³	semidirect
225. #14524018	C₂³	semidirect
226. #14524018	C₂³	semidirect
227. #14524018	C₂³	semidirect
228. #14524018	C₂³	semidirect
229. #14524018	C₂³	semidirect
232. #14524016	C₂³	semidirect
236. #14524013	C₂³	semidirect
237. #14524013	C₂³	semidirect
238. Q₈×Dic₆₇	C₂³	semidirect
239. C₄×Dic₁₃₄	C₂³	semidirect
241. C₄×D₂₆₈	C₂³	semidirect
242. C₄×D₂₆₈	C₂³	semidirect
243. C₄×D₂₆₈	C₂³	semidirect
244. C₄×D₂₆₈	C₂³	semidirect
245. C₄×D₂₆₈	C₂³	semidirect
249. #14524005	C₂³	semidirect
250. #14524005	C₂³	semidirect
251. #14524005	C₂³	semidirect
252. #14524005	C₂³	semidirect
253. #14524005	C₂³	semidirect
254. #14524005	C₂³	semidirect
255. #14524005	C₂³	semidirect
256. C₄×C₂²⋊D₆₇	C₂³	semidirect
257. C₄×C₂²⋊D₆₇	C₂³	semidirect
258. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
259. #14524002	C₂³	semidirect
260. #14524001	C₂³	semidirect
261. #14524000	C₂³	semidirect
262. #14524000	C₂³	semidirect
278. C₄⋊C₄×D₆₇	C₂³	semidirect
279. C₄⋊C₄×D₆₇	C₂³	semidirect
280. C₄⋊C₄×D₆₇	C₂³	semidirect
305. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
306. C₂²⋊C₄×D₆₇	C₂³	semidirect
307. C₂²⋊C₄×D₆₇	C₂³	semidirect
308. C₂²⋊C₄×D₆₇	C₂³	semidirect
309. C₂²⋊C₄×D₆₇	C₂³	semidirect
316. C₂×C₄×Dic₆₇	C₂³	semidirect
322. #126×C₆₇	C₂³	semidirect
323. #125×C₆₇	C₂³	semidirect
324. #125×C₆₇	C₂³	semidirect
326. C₂²⋊Q₈×C₆₇	C₂³	semidirect
327. C₂²⋊Q₈×C₆₇	C₂³	semidirect
328. C₄×Q₈×C₆₇	C₂³	semidirect
330. #117×C₆₇	C₂³	semidirect
331. #117×C₆₇	C₂³	semidirect
342. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
380. C₂×D₂₆₈	#41	semidirect
606. D₂₆₈	C₂×#41	semidirect
670. C₂×C₆₇	#3513	semidirect
683. C₂×#552	D₆₇	semidirect
702. C₆₇	C₂×#3513	semidirect
713. #552	C₂×D₆₇	semidirect
734. C₂×#126	C₂×D₆₇	semidirect
737. C₂×#125	C₂×D₆₇	semidirect
738. C₂×#125	C₂×D₆₇	semidirect
766. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
767. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
787. C₂×C₄×Q₈	C₂×D₆₇	semidirect
813. C₂×#117	C₂×D₆₇	semidirect
814. C₂×#117	C₂×D₆₇	semidirect
818. C₂²×C₄⋊C₄	C₂×D₆₇	semidirect
880. #126	C₂²×D₆₇	semidirect
883. #125	C₂²×D₆₇	semidirect
884. #125	C₂²×D₆₇	semidirect
910. C₂²⋊Q₈	C₂²×D₆₇	semidirect
911. C₂²⋊Q₈	C₂²×D₆₇	semidirect
929. C₄×Q₈	C₂²×D₆₇	semidirect
954. #117	C₂²×D₆₇	semidirect
955. #117	C₂²×D₆₇	semidirect
984. C₂×C₄⋊C₄	C₂²×D₆₇	semidirect
1351. C₂	#22574154	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574154	2
C₂×#16864131	2
C₂×#16864102	2
C₂×#16864099	2
C₂×#16864090	2
C₂×#16864071	2
C₂×#16864070	2
C₂×#16864047	2
C₂×#16864038	2
C₂×#16864037	2
C₂×D₄×D₂₆₈	2
C₂×#16864019	2
C₂×#16864002	2
C₂×#16863994	2
C₂×#16863985	2
C₂×#16863932	2
C₂×#16863926	2
C₂×#16863908	2
C₂×#123×D₆₇	2
C₂×#16863878	2
C₂×#16863870	2
C₂²×#14524005	2
C₂×#552×C₆₇	2
C₂×#3513	67

Subgroups — C2×#22574154 #31763807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574154 #31763807