Subgroups — C₂×#22574770 #31763183

Order 17152.

7258 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574770	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864147	C₂	1	2	yes	maximal, complemented
3	C₂×#16864143	C₂	1	2	yes	maximal, complemented
4	C₂×#16864120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864115	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864074	C₂	1	2	yes	maximal, complemented
7	C₂×#16864073	C₂	1	2	yes	maximal, complemented
8	C₂×#16864061	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×Q₈×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16864057	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16864053	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16864039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16864034	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16864021	C₂	1	2	yes	maximal, complemented
15	C₂×#16864017	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16864016	C₂	1	2	yes	maximal, complemented
17	C₂×#16864015	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16864014	C₂	1	2	yes	maximal, complemented
19	C₂×#16863982	C₂	1	2	yes	maximal, complemented
20	C₂×#16863971	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16863951	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863924	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#124×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#536×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761629	C₂²	1	1	yes	characteristic
26	C₂²×Q₈×D₆₇	C₂²	1	1	yes	characteristic
27	C₂²×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic
29	#16864147	C₂²	1	32	yes	complemented
30	#16864143	C₂²	1	32	yes	complemented
31	#16864120	C₂²	1	16	yes	complemented
32	#16864115	C₂²	1	16	yes	complemented
33	#16864074	C₂²	1	32	yes	complemented
34	#16864073	C₂²	1	32	yes	complemented
35	#16864061	C₂²	1	16	yes	complemented
36	Q₈×C₂²⋊D₆₇	C₂²	1	16	yes	complemented
37	#16864057	C₂²	1	16	yes	complemented
38	#16864053	C₂²	1	16	yes	complemented
39	#16864039	C₂²	1	16	yes	complemented
40	#16864034	C₂²	1	16	yes	complemented
41	#16864021	C₂²	1	32	yes	complemented
42	#16864017	C₂²	1	16	yes	complemented
43	#16864016	C₂²	1	32	yes	complemented
44	#16864015	C₂²	1	16	yes	complemented
45	#16864014	C₂²	1	32	yes	complemented
46	#16863982	C₂²	1	32	yes	complemented
47	#16863971	C₂²	1	16	yes	complemented
48	#16863951	C₂²	1	16	yes	complemented
49	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
50	C₂×#14524042	C₂²	1	2	yes	complemented
51	C₂×#14524041	C₂²	1	2	yes	complemented
52	C₂×#14524041	C₂²	1	1	yes	characteristic, complemented
53	#16863924	C₂²	1	16	yes	complemented
54	C₂×#14524038	C₂²	1	2	yes	complemented
55	C₂×#14524038	C₂²	1	2	yes	complemented
56	C₂×#14524038	C₂²	1	2	yes	complemented
57	C₂×#14524038	C₂²	1	1	yes	characteristic, complemented
58	C₂×#14524036	C₂²	1	2	yes	complemented
59	C₂×#14524036	C₂²	1	2	yes	complemented
60	C₂×#14524036	C₂²	1	1	yes	characteristic, complemented
61	C₂×#14524036	C₂²	1	2	yes	complemented
62	C₂×#14524034	C₂²	1	2	yes	complemented
63	C₂×#14524033	C₂²	1	1	yes	characteristic, complemented
64	C₂×#14524032	C₂²	1	1	yes	characteristic
65	C₂×#14524032	C₂²	1	1	yes	characteristic
66	C₂×#14524032	C₂²	1	2	yes	complemented
67	C₂×#14524031	C₂²	1	1	yes	characteristic
68	C₂×#14524030	C₂²	1	1	yes	characteristic
69	C₂×#14524030	C₂²	1	2	yes	complemented
70	C₂×#14524029	C₂²	1	2	yes	—
71	C₂×#14524029	C₂²	1	2	yes	—
72	C₂×#14524029	C₂²	1	2	yes	complemented
73	C₂×#14524029	C₂²	1	2	yes	complemented
74	C₂×#14524029	C₂²	1	1	yes	characteristic, complemented
75	#124×D₆₇	C₂²	1	16	yes	complemented
76	C₂×#14524028	C₂²	1	1	yes	characteristic
77	C₂×#14524028	C₂²	1	2	yes	complemented
78	C₂×#14524028	C₂²	1	2	yes	complemented
79	C₂×#14524027	C₂²	1	2	yes	complemented
80	C₂×#14524026	C₂²	1	2	yes	—
81	C₂×#14524025	C₂²	1	2	yes	—
82	C₂×#14524025	C₂²	1	1	yes	characteristic
83	C₂×#14524025	C₂²	1	2	yes	complemented
84	C₂×#14524023	C₂²	1	2	yes	—
85	C₂×#14524023	C₂²	1	2	yes	complemented
86	C₂×#14524022	C₂²	1	2	yes	complemented
87	C₂×#14524022	C₂²	1	2	yes	complemented
88	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
89	C₂×#14524021	C₂²	1	1	yes	characteristic
90	C₂×#14524021	C₂²	1	2	yes	—
91	C₂×#14524021	C₂²	1	2	yes	complemented
92	C₂×#14524021	C₂²	1	2	yes	complemented
93	C₂×#14524021	C₂²	1	2	yes	complemented
94	C₂×#14524021	C₂²	1	2	yes	complemented
95	C₂×#14524020	C₂²	1	2	yes	complemented
96	C₂×#14524020	C₂²	1	2	yes	complemented
97	C₂×#14524019	C₂²	1	2	yes	—
98	C₂×#14524019	C₂²	1	1	yes	characteristic
99	C₂×#14524019	C₂²	1	1	yes	characteristic
100	C₂×#14524019	C₂²	1	2	yes	complemented
101	C₂×#14524019	C₂²	1	1	yes	characteristic, complemented
102	C₂×#14524017	C₂²	1	1	yes	characteristic
103	C₂×#14524017	C₂²	1	2	yes	complemented
104	C₂×#14524016	C₂²	1	2	yes	—
105	C₂×#14524016	C₂²	1	1	yes	characteristic
106	C₂×#14524015	C₂²	1	2	yes	—
107	C₂×#14524014	C₂²	1	1	yes	characteristic
108	C₂×#14524014	C₂²	1	2	yes	complemented
109	C₂×#14524013	C₂²	1	2	yes	—
110	C₂×#14524011	C₂²	1	2	yes	—
111	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
116	C₂×#14524008	C₂²	1	2	yes	complemented
117	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
118	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
119	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
120	C₂×#14524005	C₂²	1	2	yes	—
121	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
123	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
124	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
125	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
126	C₂×#14524001	C₂²	1	2	yes	—
127	C₂×#14524001	C₂²	1	2	yes	complemented
128	C₂×#14524000	C₂²	1	1	yes	characteristic, complemented
129	C₂×#14523999	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	1	yes	characteristic
135	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
136	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	#536×C₆₇	C₂²	1	16	yes	complemented
138	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
140	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
141	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
142	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
143	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
144	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
145	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
146	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₆₇	C₂³	1	2	yes	—
148	C₂×#11761629	—	4	4	no	—
149	C₂×#11761629	C₂³	1	8	yes	—
150	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
151	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
152	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
153	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
154	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
155	C₂×Q₈×D₆₇	—	4	4	no	—
156	C₂×Q₈×D₆₇	—	4	4	no	—
157	C₂×Q₈×D₆₇	C₂³	1	8	yes	—
158	C₂×Q₈×D₆₇	C₂³	1	8	yes	complemented
159	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
160	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
161	C₂²×D₂₆₈	C₂³	1	2	yes	—
162	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
163	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
164	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
165	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
166	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
167	C₂×D₄×D₆₇	—	4	4	no	—
168	C₂×D₄×D₆₇	C₂³	1	8	yes	—
169	C₂³×Dic₆₇	C₂³	1	2	yes	—
170	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
171	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
172	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
173	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
174	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
175	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
176	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
177	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
178	#14524043	C₂³	1	8	yes	complemented
179	#14524042	C₂³	1	16	yes	complemented
180	#14524041	C₂³	1	16	yes	complemented
181	#14524041	C₂³	1	8	yes	complemented
182	#14524038	C₂³	1	16	yes	complemented
183	#14524038	C₂³	1	8	yes	complemented
184	#14524038	C₂³	1	16	yes	complemented
185	#14524038	C₂³	1	16	yes	complemented
186	#14524036	C₂³	1	8	yes	complemented
187	#14524036	C₂³	1	16	yes	complemented
188	#14524036	C₂³	1	16	yes	complemented
189	#14524036	C₂³	1	16	yes	complemented
190	#14524034	C₂³	1	16	yes	complemented
191	#14524033	C₂³	1	8	yes	complemented
192	#14524032	C₂³	1	8	yes	—
193	#14524032	C₂³	1	8	yes	—
194	#14524032	C₂³	1	16	yes	complemented
195	#14524031	C₂³	1	8	yes	—
196	#14524030	C₂³	1	8	yes	—
197	#14524030	C₂³	1	16	yes	complemented
198	#14524029	C₂³	1	16	yes	—
199	#14524029	C₂³	1	16	yes	—
200	#14524029	C₂³	1	16	yes	complemented
201	#14524029	C₂³	1	16	yes	complemented
202	#14524029	C₂³	1	8	yes	complemented
203	#14524028	C₂³	1	8	yes	—
204	#14524028	C₂³	1	16	yes	complemented
205	#14524028	C₂³	1	16	yes	complemented
206	#14524027	C₂³	1	16	yes	complemented
207	#14524026	C₂³	1	16	yes	—
208	#14524025	C₂³	1	16	yes	—
209	#14524025	C₂³	1	8	yes	—
210	#14524025	C₂³	1	16	yes	complemented
211	#14524023	C₂³	1	16	yes	—
212	#14524023	C₂³	1	16	yes	complemented
213	#14524022	C₂³	1	16	yes	complemented
214	#14524022	C₂³	1	8	yes	complemented
215	#14524022	C₂³	1	16	yes	complemented
216	#14524021	C₂³	1	8	yes	—
217	#14524021	C₂³	1	16	yes	—
218	#14524021	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	16	yes	complemented
223	#14524020	C₂³	1	16	yes	complemented
224	#14524019	C₂³	1	16	yes	—
225	#14524019	C₂³	1	8	yes	—
226	#14524019	C₂³	1	8	yes	—
227	#14524019	C₂³	1	8	yes	complemented
228	#14524019	C₂³	1	16	yes	complemented
229	#14524017	C₂³	1	8	yes	—
230	#14524017	C₂³	1	16	yes	complemented
231	#14524016	C₂³	1	16	yes	—
232	#14524016	C₂³	1	8	yes	—
233	#14524015	C₂³	1	16	yes	—
234	#14524014	C₂³	1	8	yes	—
235	#14524014	C₂³	1	16	yes	complemented
236	#14524013	C₂³	1	16	yes	—
237	#14524011	C₂³	1	16	yes	—
238	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
239	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
240	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
241	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
242	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
243	#14524008	C₂³	1	16	yes	complemented
244	C₄×D₂₆₈	C₂³	1	8	yes	—
245	C₄×D₂₆₈	C₂³	1	8	yes	—
246	D₄×Dic₆₇	C₂³	1	8	yes	—
247	#14524005	C₂³	1	16	yes	—
248	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
249	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
250	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
251	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
252	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
253	#14524001	C₂³	1	16	yes	—
254	#14524001	C₂³	1	16	yes	complemented
255	#14524000	C₂³	1	8	yes	complemented
256	#14523999	C₂³	1	16	yes	complemented
257	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
258	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
263	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
264	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
265	C₂×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	2	yes	—
270	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
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	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
276	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
278	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
283	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
285	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	—
286	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
298	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
299	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
307	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
308	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
310	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
311	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
313	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
314	C₄²×D₆₇	C₂³	1	8	yes	—
315	C₂×#41×C₆₇	—	4	4	no	—
316	C₂×#41×C₆₇	C₂³	1	8	yes	—
317	C₂²×Q₈×C₆₇	—	4	4	no	—
318	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
319	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
320	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
321	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
322	C₂²×Q₈×C₆₇	C₂³	1	8	yes	complemented
323	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
325	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
327	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
328	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
329	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
330	#124×C₆₇	C₂³	1	8	yes	—
331	#124×C₆₇	C₂³	1	8	yes	—
332	#123×C₆₇	C₂³	1	16	yes	complemented
333	#123×C₆₇	C₂³	1	16	yes	complemented
334	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
335	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
336	#117×C₆₇	C₂³	1	8	yes	complemented
337	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
343	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
346	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
347	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
348	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
349	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
351	C₂³×D₆₇	—	2	8	no	—
352	C₂³×D₆₇	—	4	4	no	—
353	C₂³×D₆₇	—	4	4	no	—
354	C₂³×D₆₇	C₂⁴	1	2	yes	—
355	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
356	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
357	C₂³×D₆₇	C₂⁴	1	8	yes	—
358	#11761629	—	4	16	no	—
359	C₂×Dic₁₃₄	—	2	4	no	—
360	C₂×Dic₁₃₄	—	4	4	no	—
361	C₂×Dic₁₃₄	—	4	4	no	—
362	C₂×Dic₁₃₄	—	4	2	no	—
363	C₂×Dic₁₃₄	—	4	4	no	—
364	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
365	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
366	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
367	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
368	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
369	Q₈×D₆₇	—	4	16	no	—
370	Q₈×D₆₇	—	4	16	no	—
371	C₂×D₂₆₈	—	2	4	no	—
372	C₂×D₂₆₈	—	2	4	no	—
373	C₂×D₂₆₈	—	4	4	no	—
374	C₂×D₂₆₈	C₂⁴	1	4	yes	—
375	C₂×D₂₆₈	C₂⁴	1	4	yes	—
376	C₂×D₂₆₈	C₂⁴	1	8	yes	—
377	C₂×C₂²⋊D₆₇	—	2	4	no	—
378	C₂×C₂²⋊D₆₇	—	4	4	no	—
379	C₂×C₂²⋊D₆₇	—	4	4	no	—
380	C₂×C₂²⋊D₆₇	—	4	2	no	—
381	C₂×C₂²⋊D₆₇	—	4	4	no	—
382	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
383	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
384	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
385	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
386	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
387	D₄×D₆₇	—	4	16	no	—
388	C₂²×Dic₆₇	—	4	4	no	—
389	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
392	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
394	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
397	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
399	C₂×C₄×D₆₇	—	2	4	no	—
400	C₂×C₄×D₆₇	—	2	4	no	—
401	C₂×C₄×D₆₇	—	2	4	no	—
402	C₂×C₄×D₆₇	—	4	4	no	—
403	C₂×C₄×D₆₇	—	4	2	no	—
404	C₂×C₄×D₆₇	—	4	4	no	—
405	C₂×C₄×D₆₇	—	4	4	no	—
406	C₂×C₄×D₆₇	—	4	4	no	—
407	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
408	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
409	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
410	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
411	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
412	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
413	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
414	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
415	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
416	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
417	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
418	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
419	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
420	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
421	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
422	C₄⋊Dic₆₇	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	8	yes	—
428	Dic₆₇⋊C₄	C₂⁴	1	4	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	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
434	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
435	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
436	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
437	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
438	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
439	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
440	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
441	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
442	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
443	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
444	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
445	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
446	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
447	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
448	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
449	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
450	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
451	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
452	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
453	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
454	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
455	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
456	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
457	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
458	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
459	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
460	C₄×Dic₆₇	C₂⁴	1	4	yes	—
461	C₄×Dic₆₇	C₂⁴	1	4	yes	—
462	C₄×Dic₆₇	C₂⁴	1	4	yes	—
463	C₄×Dic₆₇	C₂⁴	1	8	yes	—
464	C₄×Dic₆₇	C₂⁴	1	8	yes	—
465	C₄×Dic₆₇	C₂⁴	1	4	yes	—
466	C₄×Dic₆₇	C₂⁴	1	8	yes	—
467	C₄×Dic₆₇	C₂⁴	1	8	yes	—
468	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
469	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
470	#41×C₆₇	—	4	16	no	—
471	C₂×Q₈×C₆₇	—	2	4	no	—
472	C₂×Q₈×C₆₇	—	2	4	no	—
473	C₂×Q₈×C₆₇	—	2	4	no	—
474	C₂×Q₈×C₆₇	—	4	4	no	—
475	C₂×Q₈×C₆₇	—	4	16	no	—
476	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
477	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
478	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
479	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
480	C₂×D₄×C₆₇	—	2	4	no	—
481	C₂×D₄×C₆₇	—	4	4	no	—
482	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
483	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
484	C₂²×C₄×C₆₇	—	2	4	no	—
485	C₂²×C₄×C₆₇	—	4	4	no	—
486	C₂²×C₄×C₆₇	—	4	4	no	—
487	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
488	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	4	yes	—
496	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
497	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
498	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
500	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
501	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
502	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
503	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
504	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
505	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
506	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
507	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
508	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
509	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
510	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
511	C₄²×C₆₇	C₂⁴	1	4	yes	—
512	C₄²×C₆₇	C₂⁴	1	4	yes	—
513	C₂³×C₆₇	—	2	2	no	—
514	C₂³×C₆₇	—	2	4	no	—
515	C₂³×C₆₇	—	2	2	no	—
516	C₂³×C₆₇	—	2	4	no	—
517	C₂³×C₆₇	—	2	4	no	—
518	C₂³×C₆₇	—	2	2	no	—
519	C₂³×C₆₇	C₂⁵	1	4	yes	—
520	C₂³×C₆₇	C₂⁵	1	2	yes	—
521	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
522	C₂²×D₆₇	—	2	2	no	—
523	C₂²×D₆₇	—	2	2	no	—
524	C₂²×D₆₇	—	2	2	no	—
525	C₂²×D₆₇	—	2	4	no	—
526	C₂²×D₆₇	—	2	2	no	—
527	C₂²×D₆₇	—	2	4	no	—
528	C₂²×D₆₇	—	2	4	no	—
529	C₂²×D₆₇	—	2	2	no	—
530	C₂²×D₆₇	—	2	16	no	—
531	C₂²×D₆₇	—	4	8	no	—
532	C₂²×D₆₇	—	4	8	no	—
533	C₂²×D₆₇	—	8	16	no	—
534	C₂²×D₆₇	2₋¹⁺⁴	1	4	yes	—
535	C₂²×D₆₇	C₂⁵	1	4	yes	—
536	C₂²×D₆₇	C₂⁵	1	2	yes	—
537	C₂²×D₆₇	C₂⁵	1	2	yes	—
538	Q₈×C₆₇	—	2	8	no	—
539	Q₈×C₆₇	—	2	8	no	—
540	Q₈×C₆₇	—	2	8	no	—
541	Q₈×C₆₇	—	4	8	no	—
542	D₄×C₆₇	—	2	8	no	—
543	D₄×C₆₇	—	4	8	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	4	no	—
546	C₂×C₄×C₆₇	—	2	4	no	—
547	C₂×C₄×C₆₇	—	2	4	no	—
548	C₂×C₄×C₆₇	—	2	2	no	—
549	C₂×C₄×C₆₇	—	2	2	no	—
550	C₂×C₄×C₆₇	—	2	2	no	—
551	C₂×C₄×C₆₇	—	2	2	no	—
552	C₂×C₄×C₆₇	—	2	8	no	—
553	C₂×C₄×C₆₇	—	4	8	no	—
554	C₂×C₄×C₆₇	—	4	8	no	—
555	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
556	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
557	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
558	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
559	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
560	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
561	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
562	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
563	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
564	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
565	C₂²⋊D₆₇	—	2	8	no	—
566	C₂²⋊D₆₇	—	4	8	no	—
567	C₂²⋊D₆₇	—	4	8	no	—
568	C₂²⋊D₆₇	—	4	4	no	—
569	C₂²⋊D₆₇	—	4	8	no	—
570	C₂×Dic₆₇	—	2	2	no	—
571	C₂×Dic₆₇	—	2	2	no	—
572	C₂×Dic₆₇	—	2	4	no	—
573	C₂×Dic₆₇	—	2	2	no	—
574	C₂×Dic₆₇	—	2	2	no	—
575	C₂×Dic₆₇	—	2	4	no	—
576	C₂×Dic₆₇	—	2	2	no	—
577	C₂×Dic₆₇	—	2	2	no	—
578	C₂×Dic₆₇	—	2	4	no	—
579	C₂×Dic₆₇	—	4	8	no	—
580	C₂×Dic₆₇	C₂⁵	1	2	yes	—
581	C₂×Dic₆₇	C₂⁵	1	2	yes	—
582	C₂×Dic₆₇	C₂⁵	1	4	yes	—
583	C₂×Dic₆₇	C₂⁵	1	2	yes	—
584	C₂×Dic₆₇	C₂⁵	1	4	yes	—
585	C₂×Dic₆₇	C₂⁵	1	2	yes	—
586	C₂×Dic₆₇	C₂⁵	1	2	yes	—
587	C₂×Dic₆₇	C₂⁵	1	4	yes	—
588	C₂×Dic₆₇	C₂⁵	1	2	yes	—
589	D₂₆₈	—	2	8	no	—
590	D₂₆₈	—	2	8	no	—
591	D₂₆₈	—	4	8	no	—
592	C₄×D₆₇	—	2	8	no	—
593	C₄×D₆₇	—	2	8	no	—
594	C₄×D₆₇	—	2	8	no	—
595	C₄×D₆₇	—	4	4	no	—
596	C₄×D₆₇	—	4	8	no	—
597	C₄×D₆₇	—	4	8	no	—
598	C₄×D₆₇	—	4	8	no	—
599	C₄×D₆₇	—	4	8	no	—
600	Dic₁₃₄	—	2	8	no	—
601	Dic₁₃₄	—	4	8	no	—
602	Dic₁₃₄	—	4	8	no	—
603	Dic₁₃₄	—	4	4	no	—
604	Dic₁₃₄	—	4	8	no	—
605	C₂²×C₆₇	—	2	4	no	—
606	C₂²×C₆₇	—	2	2	no	—
607	C₂²×C₆₇	—	2	2	no	—
608	C₂²×C₆₇	—	2	4	no	—
609	C₂²×C₆₇	—	2	4	no	—
610	C₂²×C₆₇	—	2	2	no	—
611	C₂²×C₆₇	—	4	8	no	—
612	C₂²×C₆₇	—	4	4	no	—
613	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
614	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
615	C₂²×C₆₇	#585	1	2	yes	—
616	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
617	C₂×D₆₇	—	2	2	no	—
618	C₂×D₆₇	—	2	2	no	—
619	C₂×D₆₇	—	2	8	no	—
620	C₂×D₆₇	—	2	2	no	—
621	C₂×D₆₇	—	2	4	no	—
622	C₂×D₆₇	—	2	2	no	—
623	C₂×D₆₇	—	2	4	no	—
624	C₂×D₆₇	—	2	4	no	—
625	C₂×D₆₇	—	2	2	no	—
626	C₂×D₆₇	—	4	4	no	—
627	C₂×D₆₇	—	4	8	no	—
628	C₂×D₆₇	—	8	16	no	—
629	C₂×D₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
630	C₄×C₆₇	—	2	4	no	—
631	C₄×C₆₇	—	2	4	no	—
632	C₄×C₆₇	—	2	4	no	—
633	C₄×C₆₇	—	2	2	no	—
634	C₄×C₆₇	—	2	2	no	—
635	C₄×C₆₇	—	2	2	no	—
636	C₄×C₆₇	—	2	2	no	—
637	C₄×C₆₇	—	2	2	no	—
638	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
639	Dic₆₇	—	2	4	no	—
640	Dic₆₇	—	2	2	no	—
641	Dic₆₇	—	2	2	no	—
642	Dic₆₇	—	2	2	no	—
643	Dic₆₇	—	2	2	no	—
644	Dic₆₇	—	2	2	no	—
645	Dic₆₇	—	2	4	no	—
646	Dic₆₇	—	2	2	no	—
647	Dic₆₇	—	2	4	no	—
648	C₂×#3561	—	67	1	no	maximal, Sylow
649	C₂×C₆₇	—	4	4	no	—
650	C₂×C₆₇	—	4	2	no	—
651	C₂×C₆₇	#3561	1	4	yes	complemented
652	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂×C₆₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
654	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
655	D₆₇	—	2	4	no	—
656	D₆₇	—	4	2	no	—
657	D₆₇	—	4	4	no	—
658	#3561	—	67	32	no	—
659	C₂×#563	—	67	2	no	—
660	C₂×#562	—	67	2	no	—
661	C₂×#556	—	67	1	no	—
662	C₂×#556	—	67	1	no	—
663	C₂×#551	—	67	2	no	—
664	C₂×#551	—	67	2	no	—
665	C₂×D₄×Q₈	—	67	1	no	—
666	C₂×D₄×Q₈	—	67	1	no	—
667	C₂×#548	—	67	1	no	—
668	C₂×#548	—	67	1	no	—
669	C₂×#546	—	67	1	no	—
670	C₂×#546	—	67	1	no	—
671	C₂×#543	—	67	2	no	—
672	C₂×#542	—	67	1	no	—
673	C₂×#542	—	67	2	no	—
674	C₂×#542	—	67	2	no	—
675	C₂×#542	—	67	1	no	—
676	C₂×#538	—	67	2	no	—
677	C₂×#536	—	67	1	no	—
678	C₂×#536	D₆₇	1	1	yes	characteristic, complemented
679	C₂×#533	—	67	1	no	—
680	C₂×#529	—	67	1	no	—
681	C₂²×#124	—	67	1	no	—
682	C₆₇	C₂×#3561	1	1	yes	characteristic, complemented, Sylow
683	C₂²×#41	—	67	1	no	—
684	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
685	C₂³×Q₈	—	67	1	no	—
686	C₂³×Q₈	—	67	1	no	—
687	C₂³×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
688	C₂³×D₄	—	67	1	no	—
689	#563	—	67	32	no	—
690	#562	—	67	32	no	—
691	#556	—	67	16	no	—
692	#556	—	67	16	no	—
693	#551	—	67	32	no	—
694	#551	—	67	32	no	—
695	D₄×Q₈	—	67	16	no	—
696	D₄×Q₈	—	67	16	no	—
697	#548	—	67	16	no	—
698	#548	—	67	16	no	—
699	#546	—	67	16	no	—
700	#546	—	67	16	no	—
701	#543	—	67	32	no	—
702	#542	—	67	16	no	—
703	#542	—	67	32	no	—
704	#542	—	67	32	no	—
705	#542	—	67	16	no	—
706	#538	—	67	32	no	—
707	#536	—	67	16	no	—
708	#536	C₂×D₆₇	1	16	yes	complemented
709	#533	—	67	16	no	—
710	C₂×C₄⋊Q₈	—	67	1	no	—
711	C₂×C₄⋊Q₈	—	67	2	no	—
712	C₂×C₄⋊Q₈	—	67	2	no	—
713	C₂×C₄⋊Q₈	—	67	1	no	—
714	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
715	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
716	#529	—	67	16	no	—
717	C₂×#126	—	67	1	no	—
718	C₂×#126	—	67	2	no	—
719	C₂×#126	—	67	2	no	—
720	C₂×#126	—	67	2	no	—
721	C₂×#126	—	67	1	no	—
722	C₂×#126	—	67	2	no	—
723	C₂×#126	—	67	2	no	—
724	C₂×#126	—	67	2	no	—
725	C₂×#125	—	67	1	no	—
726	C₂×#125	—	67	2	no	—
727	C₂×#124	—	67	1	no	—
728	C₂×#124	—	67	1	no	—
729	C₂×#124	—	67	2	no	—
730	C₂×#124	—	67	1	no	—
731	C₂×#124	—	67	2	no	—
732	C₂×#124	—	67	16	no	—
733	C₂×#124	—	67	2	no	—
734	C₂×#124	—	67	2	no	—
735	C₂×#124	—	67	1	no	—
736	C₂×#124	—	67	2	no	—
737	C₂×#124	—	67	2	no	—
738	C₂×#124	—	67	1	no	—
739	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
740	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
741	C₂×#123	—	67	2	no	—
742	C₂×#123	—	67	1	no	—
743	C₂×#123	—	67	2	no	—
744	C₂×#123	—	67	2	no	—
745	C₂×#123	—	67	1	no	—
746	C₂×#123	—	67	2	no	—
747	C₂×#123	—	67	2	no	—
748	C₂×#123	—	67	2	no	—
749	C₂×#123	C₂×D₆₇	1	2	yes	complemented
750	C₂×#123	C₂×D₆₇	1	2	yes	complemented
751	C₂×C₂²⋊Q₈	—	67	1	no	—
752	C₂×C₂²⋊Q₈	—	67	1	no	—
753	C₂×C₂²⋊Q₈	—	67	1	no	—
754	C₂×C₂²⋊Q₈	—	67	2	no	—
755	C₂×C₂²⋊Q₈	—	67	2	no	—
756	C₂×C₂²⋊Q₈	—	67	1	no	—
757	C₂×C₂²⋊Q₈	—	67	2	no	—
758	C₂×C₂²⋊Q₈	—	67	2	no	—
759	C₂×C₂²⋊Q₈	—	67	1	no	—
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	2	no	—
766	C₂×C₂²⋊Q₈	—	67	2	no	—
767	C₂×C₂²⋊Q₈	—	67	2	no	—
768	C₂×C₂²⋊Q₈	—	67	2	no	—
769	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
770	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
771	C₂×#121	—	67	2	no	—
772	C₂×#121	—	67	1	no	—
773	C₂×#121	—	67	2	no	—
774	C₂×#121	—	67	2	no	—
775	C₂×#121	—	67	1	no	—
776	C₂×#121	—	67	1	no	—
777	C₂×#121	—	67	2	no	—
778	C₂×#120	—	67	2	no	—
779	C₂×#120	—	67	2	no	—
780	C₂×C₄×Q₈	—	67	1	no	—
781	C₂×C₄×Q₈	—	67	1	no	—
782	C₂×C₄×Q₈	—	67	1	no	—
783	C₂×C₄×Q₈	—	67	2	no	—
784	C₂×C₄×Q₈	—	67	1	no	—
785	C₂×C₄×Q₈	—	67	1	no	—
786	C₂×C₄×D₄	—	67	1	no	—
787	C₂×C₄×D₄	—	67	1	no	—
788	C₂×C₄×D₄	—	67	1	no	—
789	C₂×C₄×D₄	—	67	2	no	—
790	C₂×C₄×D₄	—	67	2	no	—
791	C₂×C₄×D₄	—	67	2	no	—
792	C₂×C₄×D₄	—	67	2	no	—
793	C₂×C₄×D₄	—	67	1	no	—
794	C₂×C₄×D₄	—	67	1	no	—
795	C₂×#117	—	67	2	no	—
796	C₂×#117	—	67	2	no	—
797	C₂×#117	—	67	2	no	—
798	C₂×#117	—	67	1	no	—
799	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
800	C₂²×C₂²⋊C₄	—	67	2	no	—
801	C₂²×C₂²⋊C₄	—	67	2	no	—
802	C₂²×C₂²⋊C₄	—	67	2	no	—
803	C₂²×C₂²⋊C₄	—	67	2	no	—
804	C₂²×C₄²	—	67	1	no	—
805	C₂⁵	—	67	2	no	—
806	C₂×#41	—	4	4	no	—
807	C₂×#41	—	268	4	no	—
808	C₂×#41	—	67	8	no	—
809	C₂×#41	C₂²×D₆₇	1	8	yes	—
810	C₂²×Q₈	—	4	4	no	—
811	C₂²×Q₈	—	268	4	no	—
812	C₂²×Q₈	—	268	4	no	—
813	C₂²×Q₈	—	67	8	no	—
814	C₂²×Q₈	—	67	8	no	—
815	C₂²×Q₈	—	67	1	no	—
816	C₂²×Q₈	—	67	2	no	—
817	C₂²×Q₈	—	67	2	no	—
818	C₂²×Q₈	—	67	2	no	—
819	C₂²×Q₈	—	67	1	no	—
820	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
821	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
822	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
823	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
824	C₂²×Q₈	C₂²×D₆₇	1	8	yes	complemented
825	C₂²×D₄	—	268	4	no	—
826	C₂²×D₄	—	67	2	no	—
827	C₂²×D₄	—	67	2	no	—
828	C₂²×D₄	—	67	1	no	—
829	C₂²×D₄	—	67	2	no	—
830	C₂²×D₄	—	67	8	no	—
831	C₂²×D₄	—	67	1	no	—
832	C₂²×D₄	—	67	2	no	—
833	C₂²×D₄	—	67	1	no	—
834	C₂²×D₄	—	67	1	no	—
835	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
836	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
837	C₂³×C₄	—	67	2	no	—
838	C₂³×C₄	—	67	2	no	—
839	C₂³×C₄	—	67	1	no	—
840	C₂³×C₄	—	67	2	no	—
841	C₂³×C₄	—	67	2	no	—
842	C₂³×C₄	—	67	2	no	—
843	C₂³×C₄	—	67	1	no	—
844	C₂³×C₄	—	67	1	no	—
845	C₂³×C₄	—	67	1	no	—
846	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
847	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
848	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
849	C₄⋊Q₈	—	67	8	no	—
850	C₄⋊Q₈	—	67	16	no	—
851	C₄⋊Q₈	—	67	16	no	—
852	C₄⋊Q₈	—	67	8	no	—
853	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
854	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
855	#126	—	67	8	no	—
856	#126	—	67	16	no	—
857	#126	—	67	16	no	—
858	#126	—	67	16	no	—
859	#126	—	67	8	no	—
860	#126	—	67	16	no	—
861	#126	—	67	16	no	—
862	#126	—	67	16	no	—
863	#125	—	67	8	no	—
864	#125	—	67	16	no	—
865	#124	—	67	8	no	—
866	#124	—	67	8	no	—
867	#124	—	67	16	no	—
868	#124	—	67	8	no	—
869	#124	—	67	16	no	—
870	#124	—	67	16	no	—
871	#124	—	67	16	no	—
872	#124	—	67	8	no	—
873	#124	—	67	16	no	—
874	#124	—	67	16	no	—
875	#124	—	67	8	no	—
876	#124	C₂²×D₆₇	1	8	yes	—
877	#124	C₂²×D₆₇	1	8	yes	—
878	#123	—	67	16	no	—
879	#123	—	67	8	no	—
880	#123	—	67	16	no	—
881	#123	—	67	16	no	—
882	#123	—	67	8	no	—
883	#123	—	67	16	no	—
884	#123	—	67	16	no	—
885	#123	—	67	16	no	—
886	#123	C₂²×D₆₇	1	16	yes	complemented
887	#123	C₂²×D₆₇	1	16	yes	complemented
888	C₂²⋊Q₈	—	67	8	no	—
889	C₂²⋊Q₈	—	67	8	no	—
890	C₂²⋊Q₈	—	67	8	no	—
891	C₂²⋊Q₈	—	67	16	no	—
892	C₂²⋊Q₈	—	67	16	no	—
893	C₂²⋊Q₈	—	67	8	no	—
894	C₂²⋊Q₈	—	67	16	no	—
895	C₂²⋊Q₈	—	67	16	no	—
896	C₂²⋊Q₈	—	67	8	no	—
897	C₂²⋊Q₈	—	67	16	no	—
898	C₂²⋊Q₈	—	67	16	no	—
899	C₂²⋊Q₈	—	67	16	no	—
900	C₂²⋊Q₈	—	67	16	no	—
901	C₂²⋊Q₈	—	67	16	no	—
902	C₂²⋊Q₈	—	67	16	no	—
903	C₂²⋊Q₈	—	67	16	no	—
904	C₂²⋊Q₈	—	67	16	no	—
905	C₂²⋊Q₈	—	67	16	no	—
906	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
907	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
908	#121	—	67	16	no	—
909	#121	—	67	8	no	—
910	#121	—	67	16	no	—
911	#121	—	67	16	no	—
912	#121	—	67	8	no	—
913	#121	—	67	8	no	—
914	#121	—	67	16	no	—
915	#120	—	67	16	no	—
916	#120	—	67	16	no	—
917	C₄×Q₈	—	67	8	no	—
918	C₄×Q₈	—	67	8	no	—
919	C₄×Q₈	—	67	8	no	—
920	C₄×Q₈	—	67	16	no	—
921	C₄×Q₈	—	67	8	no	—
922	C₄×Q₈	—	67	8	no	—
923	C₄×D₄	—	67	8	no	—
924	C₄×D₄	—	67	8	no	—
925	C₄×D₄	—	67	8	no	—
926	C₄×D₄	—	67	16	no	—
927	C₄×D₄	—	67	16	no	—
928	C₄×D₄	—	67	16	no	—
929	C₄×D₄	—	67	16	no	—
930	C₄×D₄	—	67	8	no	—
931	C₄×D₄	—	67	8	no	—
932	#117	—	67	16	no	—
933	#117	—	67	16	no	—
934	#117	—	67	16	no	—
935	#117	—	67	8	no	—
936	#117	C₂²×D₆₇	1	8	yes	complemented
937	C₂×C₄⋊C₄	—	67	1	no	—
938	C₂×C₄⋊C₄	—	67	1	no	—
939	C₂×C₄⋊C₄	—	67	1	no	—
940	C₂×C₄⋊C₄	—	67	2	no	—
941	C₂×C₄⋊C₄	—	67	1	no	—
942	C₂×C₄⋊C₄	—	67	2	no	—
943	C₂×C₄⋊C₄	—	67	1	no	—
944	C₂×C₄⋊C₄	—	67	1	no	—
945	C₂×C₄⋊C₄	—	67	1	no	—
946	C₂×C₄⋊C₄	—	67	2	no	—
947	C₂×C₄⋊C₄	—	67	2	no	—
948	C₂×C₄⋊C₄	—	67	2	no	—
949	C₂×C₄⋊C₄	—	67	1	no	—
950	C₂×C₄⋊C₄	—	67	1	no	—
951	C₂×C₄⋊C₄	—	67	2	no	—
952	C₂×C₄⋊C₄	—	67	2	no	—
953	C₂×C₄⋊C₄	—	67	2	no	—
954	C₂×C₄⋊C₄	—	67	2	no	—
955	C₂×C₄⋊C₄	—	67	1	no	—
956	C₂×C₄⋊C₄	—	67	2	no	—
957	C₂×C₄⋊C₄	—	67	2	no	—
958	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
959	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
960	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
963	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
964	C₂×C₂²⋊C₄	—	67	2	no	—
965	C₂×C₂²⋊C₄	—	67	2	no	—
966	C₂×C₂²⋊C₄	—	67	2	no	—
967	C₂×C₂²⋊C₄	—	67	1	no	—
968	C₂×C₂²⋊C₄	—	67	2	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	1	no	—
973	C₂×C₂²⋊C₄	—	67	2	no	—
974	C₂×C₂²⋊C₄	—	67	2	no	—
975	C₂×C₂²⋊C₄	—	67	2	no	—
976	C₂×C₂²⋊C₄	—	67	2	no	—
977	C₂×C₂²⋊C₄	—	67	2	no	—
978	C₂×C₂²⋊C₄	—	67	2	no	—
979	C₂×C₂²⋊C₄	—	67	2	no	—
980	C₂×C₂²⋊C₄	—	67	2	no	—
981	C₂×C₂²⋊C₄	—	67	16	no	—
982	C₂×C₂²⋊C₄	—	67	2	no	—
983	C₂×C₂²⋊C₄	—	67	1	no	—
984	C₂×C₂²⋊C₄	—	67	1	no	—
985	C₂×C₂²⋊C₄	—	67	1	no	—
986	C₂×C₂²⋊C₄	—	67	2	no	—
987	C₂×C₂²⋊C₄	—	67	1	no	—
988	C₂×C₂²⋊C₄	—	67	2	no	—
989	C₂×C₂²⋊C₄	—	67	16	no	—
990	C₂×C₂²⋊C₄	—	67	16	no	—
991	C₂×C₂²⋊C₄	—	67	16	no	—
992	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
993	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
994	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
995	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
996	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
998	C₂×C₄²	—	67	2	no	—
999	C₂×C₄²	—	67	2	no	—
1000	C₂×C₄²	—	67	1	no	—
1001	C₂×C₄²	—	67	2	no	—
1002	C₂×C₄²	—	67	2	no	—
1003	C₂×C₄²	—	67	1	no	—
1004	C₂×C₄²	—	67	1	no	—
1005	C₂×C₄²	—	67	1	no	—
1006	C₂×C₄²	—	67	8	no	—
1007	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1008	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1009	C₂⁴	—	268	4	no	—
1010	C₂⁴	—	268	4	no	—
1011	C₂⁴	—	67	8	no	—
1012	C₂⁴	—	67	1	no	—
1013	C₂⁴	—	67	2	no	—
1014	C₂⁴	—	67	1	no	—
1015	C₂⁴	—	134	8	no	—
1016	C₂⁴	C₂³×D₆₇	1	2	yes	—
1017	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1018	#41	—	4	16	no	—
1019	#41	—	268	16	no	—
1020	C₂×Q₈	—	2	4	no	—
1021	C₂×Q₈	—	2	4	no	—
1022	C₂×Q₈	—	2	4	no	—
1023	C₂×Q₈	—	4	4	no	—
1024	C₂×Q₈	—	4	16	no	—
1025	C₂×Q₈	—	268	4	no	—
1026	C₂×Q₈	—	268	4	no	—
1027	C₂×Q₈	—	268	2	no	—
1028	C₂×Q₈	—	268	4	no	—
1029	C₂×Q₈	—	268	16	no	—
1030	C₂×Q₈	—	268	16	no	—
1031	C₂×Q₈	—	67	4	no	—
1032	C₂×Q₈	—	67	8	no	—
1033	C₂×Q₈	—	67	8	no	—
1034	C₂×Q₈	—	67	8	no	—
1035	C₂×Q₈	—	67	4	no	—
1036	C₂×Q₈	—	134	4	no	—
1037	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1038	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1039	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1040	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
1041	C₂×D₄	—	2	4	no	—
1042	C₂×D₄	—	4	4	no	—
1043	C₂×D₄	—	268	4	no	—
1044	C₂×D₄	—	268	16	no	—
1045	C₂×D₄	—	268	4	no	—
1046	C₂×D₄	—	268	4	no	—
1047	C₂×D₄	—	268	4	no	—
1048	C₂×D₄	—	268	2	no	—
1049	C₂×D₄	—	67	8	no	—
1050	C₂×D₄	—	67	8	no	—
1051	C₂×D₄	—	67	4	no	—
1052	C₂×D₄	—	67	8	no	—
1053	C₂×D₄	—	67	4	no	—
1054	C₂×D₄	—	67	8	no	—
1055	C₂×D₄	—	67	4	no	—
1056	C₂×D₄	—	67	4	no	—
1057	C₂×D₄	—	134	4	no	—
1058	C₂×D₄	—	134	4	no	—
1059	C₂×D₄	—	134	4	no	—
1060	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1061	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1062	C₂²×C₄	—	2	4	no	—
1063	C₂²×C₄	—	4	4	no	—
1064	C₂²×C₄	—	4	4	no	—
1065	C₂²×C₄	—	268	4	no	—
1066	C₂²×C₄	—	268	4	no	—
1067	C₂²×C₄	—	268	4	no	—
1068	C₂²×C₄	—	268	4	no	—
1069	C₂²×C₄	—	268	2	no	—
1070	C₂²×C₄	—	268	4	no	—
1071	C₂²×C₄	—	67	8	no	—
1072	C₂²×C₄	—	67	4	no	—
1073	C₂²×C₄	—	67	8	no	—
1074	C₂²×C₄	—	67	8	no	—
1075	C₂²×C₄	—	67	8	no	—
1076	C₂²×C₄	—	67	8	no	—
1077	C₂²×C₄	—	67	1	no	—
1078	C₂²×C₄	—	67	1	no	—
1079	C₂²×C₄	—	67	2	no	—
1080	C₂²×C₄	—	67	2	no	—
1081	C₂²×C₄	—	67	1	no	—
1082	C₂²×C₄	—	67	1	no	—
1083	C₂²×C₄	—	67	1	no	—
1084	C₂²×C₄	—	67	2	no	—
1085	C₂²×C₄	—	67	1	no	—
1086	C₂²×C₄	—	67	4	no	—
1087	C₂²×C₄	—	67	4	no	—
1088	C₂²×C₄	—	67	4	no	—
1089	C₂²×C₄	—	134	4	no	—
1090	C₂²×C₄	—	134	4	no	—
1091	C₂²×C₄	—	134	4	no	—
1092	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1093	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1094	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1095	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1096	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1097	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1098	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1099	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1100	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1101	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1102	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1103	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1104	C₄⋊C₄	—	67	4	no	—
1105	C₄⋊C₄	—	67	4	no	—
1106	C₄⋊C₄	—	67	4	no	—
1107	C₄⋊C₄	—	67	8	no	—
1108	C₄⋊C₄	—	67	4	no	—
1109	C₄⋊C₄	—	67	8	no	—
1110	C₄⋊C₄	—	67	4	no	—
1111	C₄⋊C₄	—	67	4	no	—
1112	C₄⋊C₄	—	67	4	no	—
1113	C₄⋊C₄	—	67	8	no	—
1114	C₄⋊C₄	—	67	8	no	—
1115	C₄⋊C₄	—	67	8	no	—
1116	C₄⋊C₄	—	67	4	no	—
1117	C₄⋊C₄	—	67	4	no	—
1118	C₄⋊C₄	—	67	8	no	—
1119	C₄⋊C₄	—	67	8	no	—
1120	C₄⋊C₄	—	67	8	no	—
1121	C₄⋊C₄	—	67	8	no	—
1122	C₄⋊C₄	—	67	4	no	—
1123	C₄⋊C₄	—	67	8	no	—
1124	C₄⋊C₄	—	67	8	no	—
1125	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1126	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1127	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1128	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1129	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1130	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1131	C₂²⋊C₄	—	67	8	no	—
1132	C₂²⋊C₄	—	67	8	no	—
1133	C₂²⋊C₄	—	67	8	no	—
1134	C₂²⋊C₄	—	67	4	no	—
1135	C₂²⋊C₄	—	67	8	no	—
1136	C₂²⋊C₄	—	67	4	no	—
1137	C₂²⋊C₄	—	67	8	no	—
1138	C₂²⋊C₄	—	67	4	no	—
1139	C₂²⋊C₄	—	67	4	no	—
1140	C₂²⋊C₄	—	67	8	no	—
1141	C₂²⋊C₄	—	67	8	no	—
1142	C₂²⋊C₄	—	67	8	no	—
1143	C₂²⋊C₄	—	67	8	no	—
1144	C₂²⋊C₄	—	67	8	no	—
1145	C₂²⋊C₄	—	67	8	no	—
1146	C₂²⋊C₄	—	67	8	no	—
1147	C₂²⋊C₄	—	67	8	no	—
1148	C₂²⋊C₄	—	67	8	no	—
1149	C₂²⋊C₄	—	67	4	no	—
1150	C₂²⋊C₄	—	67	4	no	—
1151	C₂²⋊C₄	—	67	4	no	—
1152	C₂²⋊C₄	—	67	8	no	—
1153	C₂²⋊C₄	—	67	4	no	—
1154	C₂²⋊C₄	—	67	8	no	—
1155	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1156	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1157	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1158	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1159	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1160	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1161	C₄²	—	67	4	no	—
1162	C₄²	—	67	4	no	—
1163	C₄²	—	67	4	no	—
1164	C₄²	—	67	8	no	—
1165	C₄²	—	67	8	no	—
1166	C₄²	—	67	4	no	—
1167	C₄²	—	67	8	no	—
1168	C₄²	—	67	8	no	—
1169	C₄²	C₂³×D₆₇	1	4	yes	—
1170	C₄²	C₂³×D₆₇	1	4	yes	—
1171	C₂³	—	2	2	no	—
1172	C₂³	—	2	4	no	—
1173	C₂³	—	2	2	no	—
1174	C₂³	—	2	4	no	—
1175	C₂³	—	2	4	no	—
1176	C₂³	—	2	2	no	—
1177	C₂³	—	268	8	no	—
1178	C₂³	—	268	8	no	—
1179	C₂³	—	536	16	no	—
1180	C₂³	—	67	4	no	—
1181	C₂³	—	67	2	no	—
1182	C₂³	—	67	4	no	—
1183	C₂³	—	67	2	no	—
1184	C₂³	—	134	16	no	—
1185	C₂³	—	134	2	no	—
1186	C₂³	—	134	4	no	—
1187	C₂³	—	134	2	no	—
1188	C₂³	—	134	4	no	—
1189	C₂³	—	134	4	no	—
1190	C₂³	—	134	2	no	—
1191	C₂³	—	134	2	no	—
1192	C₂³	—	134	2	no	—
1193	C₂³	C₂⁴×D₆₇	1	4	yes	—
1194	C₂³	C₂⁴×D₆₇	1	2	yes	—
1195	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1196	Q₈	—	2	8	no	—
1197	Q₈	—	2	8	no	—
1198	Q₈	—	2	8	no	—
1199	Q₈	—	4	8	no	—
1200	Q₈	—	268	8	no	—
1201	Q₈	—	268	8	no	—
1202	Q₈	—	268	4	no	—
1203	Q₈	—	268	8	no	—
1204	Q₈	—	134	8	no	—
1205	D₄	—	2	8	no	—
1206	D₄	—	4	8	no	—
1207	D₄	—	268	8	no	—
1208	D₄	—	268	8	no	—
1209	D₄	—	268	8	no	—
1210	D₄	—	268	8	no	—
1211	D₄	—	268	4	no	—
1212	D₄	—	134	8	no	—
1213	D₄	—	134	8	no	—
1214	D₄	—	134	8	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	2	4	no	—
1217	C₂×C₄	—	2	4	no	—
1218	C₂×C₄	—	2	4	no	—
1219	C₂×C₄	—	2	2	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	2	2	no	—
1223	C₂×C₄	—	2	8	no	—
1224	C₂×C₄	—	4	8	no	—
1225	C₂×C₄	—	4	8	no	—
1226	C₂×C₄	—	268	8	no	—
1227	C₂×C₄	—	268	8	no	—
1228	C₂×C₄	—	268	8	no	—
1229	C₂×C₄	—	268	8	no	—
1230	C₂×C₄	—	268	4	no	—
1231	C₂×C₄	—	268	8	no	—
1232	C₂×C₄	—	67	2	no	—
1233	C₂×C₄	—	67	2	no	—
1234	C₂×C₄	—	67	2	no	—
1235	C₂×C₄	—	67	4	no	—
1236	C₂×C₄	—	67	4	no	—
1237	C₂×C₄	—	67	2	no	—
1238	C₂×C₄	—	67	2	no	—
1239	C₂×C₄	—	67	4	no	—
1240	C₂×C₄	—	67	2	no	—
1241	C₂×C₄	—	134	8	no	—
1242	C₂×C₄	—	134	2	no	—
1243	C₂×C₄	—	134	4	no	—
1244	C₂×C₄	—	134	2	no	—
1245	C₂×C₄	—	134	2	no	—
1246	C₂×C₄	—	134	2	no	—
1247	C₂×C₄	—	134	2	no	—
1248	C₂×C₄	—	134	4	no	—
1249	C₂×C₄	—	134	2	no	—
1250	C₂×C₄	—	134	4	no	—
1251	C₂×C₄	—	134	8	no	—
1252	C₂×C₄	—	134	8	no	—
1253	C₂×C₄	#14524088	1	4	yes	—
1254	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1255	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1256	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1257	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1258	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1259	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1260	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1261	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1262	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1263	C₂²	—	2	2	no	—
1264	C₂²	—	2	4	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	4	no	—
1267	C₂²	—	2	4	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	4	8	no	—
1270	C₂²	—	4	4	no	—
1271	C₂²	—	268	8	no	—
1272	C₂²	—	268	4	no	—
1273	C₂²	—	536	16	no	—
1274	C₂²	—	67	4	no	—
1275	C₂²	—	134	2	no	—
1276	C₂²	—	134	4	no	—
1277	C₂²	—	134	2	no	—
1278	C₂²	—	134	4	no	—
1279	C₂²	—	134	4	no	—
1280	C₂²	—	134	2	no	—
1281	C₂²	—	134	2	no	—
1282	C₂²	—	134	2	no	—
1283	C₂²	—	134	8	no	—
1284	C₂²	C₂×#14524088	1	2	yes	—
1285	C₂²	2₋¹⁺⁴×D₆₇	1	2	yes	—
1286	C₂²	#16864233	1	2	yes	—
1287	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1288	C₄	—	2	2	no	—
1289	C₄	—	2	4	no	—
1290	C₄	—	2	4	no	—
1291	C₄	—	2	4	no	—
1292	C₄	—	2	2	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	134	2	no	—
1297	C₄	—	134	4	no	—
1298	C₄	—	134	2	no	—
1299	C₄	—	134	2	no	—
1300	C₄	—	134	2	no	—
1301	C₄	—	134	2	no	—
1302	C₄	—	134	4	no	—
1303	C₄	—	134	2	no	—
1304	C₄	—	134	4	no	—
1305	C₄	C₂×#14524088	1	4	yes	—
1306	C₂	—	4	4	no	—
1307	C₂	—	4	2	no	—
1308	C₂	—	268	4	no	—
1309	C₂	—	268	2	no	—
1310	C₂	—	134	4	no	—
1311	C₂	#22574770	1	4	yes	direct product factor
1312	C₂	C₂²×#14524088	1	1	yes	characteristic
1313	C₂	C₂×2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1314	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×#536×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#536	D₆₇
hypocenter	C₆₇	C₂×#3561
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#536

Complements

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

N	H ≅ G/N	type
1. #22574770	C₂	direct (N × H)
2. C₂×#16864147	C₂	semidirect
3. C₂×#16864143	C₂	semidirect
4. C₂×#16864120	C₂	semidirect
5. C₂×#16864115	C₂	semidirect
6. C₂×#16864074	C₂	semidirect
7. C₂×#16864073	C₂	semidirect
8. C₂×#16864061	C₂	semidirect
9. C₂×Q₈×C₂²⋊D₆₇	C₂	semidirect
10. C₂×#16864057	C₂	semidirect
11. C₂×#16864053	C₂	semidirect
12. C₂×#16864039	C₂	semidirect
13. C₂×#16864034	C₂	semidirect
14. C₂×#16864021	C₂	semidirect
15. C₂×#16864017	C₂	semidirect
16. C₂×#16864016	C₂	semidirect
17. C₂×#16864015	C₂	semidirect
18. C₂×#16864014	C₂	semidirect
19. C₂×#16863982	C₂	semidirect
20. C₂×#16863971	C₂	semidirect
21. C₂×#16863951	C₂	semidirect
22. C₂×#16863924	C₂	semidirect
23. C₂×#124×D₆₇	C₂	semidirect
24. C₂×#536×C₆₇	C₂	semidirect
27. C₂²×Q₈×D₆₇	C₂²	semidirect
29. #16864147	C₂²	semidirect
30. #16864143	C₂²	semidirect
31. #16864120	C₂²	semidirect
32. #16864115	C₂²	semidirect
33. #16864074	C₂²	semidirect
34. #16864073	C₂²	semidirect
35. #16864061	C₂²	semidirect
36. Q₈×C₂²⋊D₆₇	C₂²	semidirect
37. #16864057	C₂²	semidirect
38. #16864053	C₂²	semidirect
39. #16864039	C₂²	semidirect
40. #16864034	C₂²	semidirect
41. #16864021	C₂²	semidirect
42. #16864017	C₂²	semidirect
43. #16864016	C₂²	semidirect
44. #16864015	C₂²	semidirect
45. #16864014	C₂²	semidirect
46. #16863982	C₂²	semidirect
47. #16863971	C₂²	semidirect
48. #16863951	C₂²	semidirect
49. C₂×#14524043	C₂²	semidirect
50. C₂×#14524042	C₂²	semidirect
51. C₂×#14524041	C₂²	semidirect
52. C₂×#14524041	C₂²	semidirect
53. #16863924	C₂²	semidirect
54. C₂×#14524038	C₂²	semidirect
55. C₂×#14524038	C₂²	semidirect
56. C₂×#14524038	C₂²	semidirect
57. C₂×#14524038	C₂²	semidirect
58. C₂×#14524036	C₂²	semidirect
59. C₂×#14524036	C₂²	semidirect
60. C₂×#14524036	C₂²	semidirect
61. C₂×#14524036	C₂²	semidirect
62. C₂×#14524034	C₂²	semidirect
63. C₂×#14524033	C₂²	semidirect
66. C₂×#14524032	C₂²	semidirect
69. C₂×#14524030	C₂²	semidirect
72. C₂×#14524029	C₂²	semidirect
73. C₂×#14524029	C₂²	semidirect
74. C₂×#14524029	C₂²	semidirect
75. #124×D₆₇	C₂²	semidirect
77. C₂×#14524028	C₂²	semidirect
78. C₂×#14524028	C₂²	semidirect
79. C₂×#14524027	C₂²	semidirect
83. C₂×#14524025	C₂²	semidirect
85. C₂×#14524023	C₂²	semidirect
86. C₂×#14524022	C₂²	semidirect
87. C₂×#14524022	C₂²	semidirect
88. C₂×#14524022	C₂²	semidirect
91. C₂×#14524021	C₂²	semidirect
92. C₂×#14524021	C₂²	semidirect
93. C₂×#14524021	C₂²	semidirect
94. C₂×#14524021	C₂²	semidirect
95. C₂×#14524020	C₂²	semidirect
96. C₂×#14524020	C₂²	semidirect
100. C₂×#14524019	C₂²	semidirect
101. C₂×#14524019	C₂²	semidirect
103. C₂×#14524017	C₂²	semidirect
108. C₂×#14524014	C₂²	semidirect
111. C₂×Q₈×Dic₆₇	C₂²	semidirect
112. C₂×Q₈×Dic₆₇	C₂²	semidirect
113. C₂×Q₈×Dic₆₇	C₂²	semidirect
114. C₂×C₄×Dic₁₃₄	C₂²	semidirect
115. C₂×C₄×Dic₁₃₄	C₂²	semidirect
116. C₂×#14524008	C₂²	semidirect
123. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
124. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
125. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
127. C₂×#14524001	C₂²	semidirect
128. C₂×#14524000	C₂²	semidirect
129. C₂×#14523999	C₂²	semidirect
136. C₂³×Q₈×C₆₇	C₂²	semidirect
137. #536×C₆₇	C₂²	semidirect
138. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
139. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
142. C₂×#123×C₆₇	C₂²	semidirect
143. C₂×#123×C₆₇	C₂²	semidirect
144. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
145. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
146. C₂×#117×C₆₇	C₂²	semidirect
158. C₂×Q₈×D₆₇	C₂³	semidirect
178. #14524043	C₂³	semidirect
179. #14524042	C₂³	semidirect
180. #14524041	C₂³	semidirect
181. #14524041	C₂³	semidirect
182. #14524038	C₂³	semidirect
183. #14524038	C₂³	semidirect
184. #14524038	C₂³	semidirect
185. #14524038	C₂³	semidirect
186. #14524036	C₂³	semidirect
187. #14524036	C₂³	semidirect
188. #14524036	C₂³	semidirect
189. #14524036	C₂³	semidirect
190. #14524034	C₂³	semidirect
191. #14524033	C₂³	semidirect
194. #14524032	C₂³	semidirect
197. #14524030	C₂³	semidirect
200. #14524029	C₂³	semidirect
201. #14524029	C₂³	semidirect
202. #14524029	C₂³	semidirect
204. #14524028	C₂³	semidirect
205. #14524028	C₂³	semidirect
206. #14524027	C₂³	semidirect
210. #14524025	C₂³	semidirect
212. #14524023	C₂³	semidirect
213. #14524022	C₂³	semidirect
214. #14524022	C₂³	semidirect
215. #14524022	C₂³	semidirect
218. #14524021	C₂³	semidirect
219. #14524021	C₂³	semidirect
220. #14524021	C₂³	semidirect
221. #14524021	C₂³	semidirect
222. #14524020	C₂³	semidirect
223. #14524020	C₂³	semidirect
227. #14524019	C₂³	semidirect
228. #14524019	C₂³	semidirect
230. #14524017	C₂³	semidirect
235. #14524014	C₂³	semidirect
238. Q₈×Dic₆₇	C₂³	semidirect
239. Q₈×Dic₆₇	C₂³	semidirect
240. Q₈×Dic₆₇	C₂³	semidirect
241. C₄×Dic₁₃₄	C₂³	semidirect
242. C₄×Dic₁₃₄	C₂³	semidirect
243. #14524008	C₂³	semidirect
250. C₄×C₂²⋊D₆₇	C₂³	semidirect
251. C₄×C₂²⋊D₆₇	C₂³	semidirect
252. C₄×C₂²⋊D₆₇	C₂³	semidirect
254. #14524001	C₂³	semidirect
255. #14524000	C₂³	semidirect
256. #14523999	C₂³	semidirect
322. C₂²×Q₈×C₆₇	C₂³	semidirect
328. C₄⋊Q₈×C₆₇	C₂³	semidirect
329. C₄⋊Q₈×C₆₇	C₂³	semidirect
332. #123×C₆₇	C₂³	semidirect
333. #123×C₆₇	C₂³	semidirect
334. C₂²⋊Q₈×C₆₇	C₂³	semidirect
335. C₂²⋊Q₈×C₆₇	C₂³	semidirect
336. #117×C₆₇	C₂³	semidirect
651. C₂×C₆₇	#3561	semidirect
678. C₂×#536	D₆₇	semidirect
682. C₆₇	C₂×#3561	semidirect
687. C₂³×Q₈	C₂×D₆₇	semidirect
708. #536	C₂×D₆₇	semidirect
714. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
715. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
749. C₂×#123	C₂×D₆₇	semidirect
750. C₂×#123	C₂×D₆₇	semidirect
769. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
770. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
799. C₂×#117	C₂×D₆₇	semidirect
824. C₂²×Q₈	C₂²×D₆₇	semidirect
853. C₄⋊Q₈	C₂²×D₆₇	semidirect
854. C₄⋊Q₈	C₂²×D₆₇	semidirect
886. #123	C₂²×D₆₇	semidirect
887. #123	C₂²×D₆₇	semidirect
906. C₂²⋊Q₈	C₂²×D₆₇	semidirect
907. C₂²⋊Q₈	C₂²×D₆₇	semidirect
936. #117	C₂²×D₆₇	semidirect
1311. C₂	#22574770	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574770	2
C₂×#16864147	2
C₂×#16864143	2
C₂×#16864120	2
C₂×#16864115	2
C₂×#16864074	2
C₂×#16864073	2
C₂×#16864061	2
C₂×Q₈×C₂²⋊D₆₇	2
C₂×#16864057	2
C₂×#16864053	2
C₂×#16864039	2
C₂×#16864034	2
C₂×#16864021	2
C₂×#16864017	2
C₂×#16864016	2
C₂×#16864015	2
C₂×#16864014	2
C₂×#16863982	2
C₂×#16863971	2
C₂×#16863951	2
C₂×#16863924	2
C₂×#124×D₆₇	2
C₂×#536×C₆₇	2
C₂×#3561	67

Subgroups — C2×#22574770 #31763183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574770 #31763183