Subgroups — #31020121

Order 17152.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22563401	C₂	1	1	yes	maximal, characteristic, complemented
2	#22563390	C₂	1	1	yes	maximal, characteristic, complemented
3	#22563383	C₂	1	1	yes	maximal, characteristic, complemented
4	#22563375	C₂	1	1	yes	maximal, characteristic, complemented
5	#22563345	C₂	1	1	yes	maximal, characteristic, complemented
6	#22563333	C₂	1	1	yes	maximal, characteristic, complemented
7	#22563294	C₂	1	1	yes	maximal, characteristic, complemented
8	#22563294	C₂	1	1	yes	maximal, characteristic, complemented
9	#22563284	C₂	1	1	yes	maximal, characteristic, complemented
10	#22563269	C₂	1	1	yes	maximal, characteristic, complemented
11	#22563240	C₂	1	1	yes	maximal, characteristic, complemented
12	#22563205	C₂	1	1	yes	maximal, characteristic, complemented
13	#22563174	C₂	1	1	yes	maximal, characteristic, complemented
14	#22563166	C₂	1	1	yes	maximal, characteristic, complemented
15	#22563102	C₂	1	1	yes	maximal, characteristic, complemented
16	#22563069	C₂	1	1	yes	maximal, characteristic, complemented
17	#22563024	C₂	1	1	yes	maximal, characteristic, complemented
18	#22563024	C₂	1	1	yes	maximal, characteristic, complemented
19	#22563024	C₂	1	1	yes	maximal, characteristic, complemented
20	#22563003	C₂	1	1	yes	maximal, characteristic, complemented
21	#22562988	C₂	1	1	yes	maximal, characteristic, complemented
22	#22562988	C₂	1	1	yes	maximal, characteristic, complemented
23	#22562976	C₂	1	1	yes	maximal, characteristic
24	#22562967	C₂	1	1	yes	maximal, characteristic, complemented
25	#22562922	C₂	1	1	yes	maximal, characteristic, complemented
26	#22562914	C₂	1	1	yes	maximal, characteristic
27	#22562842	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂²⋊Q₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
29	#123×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
30	#22562654	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic
32	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
33	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
34	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
35	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
36	C₂×#14524002	C₂²	1	1	yes	characteristic
37	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
38	#16863303	C₂²	1	1	yes	characteristic
39	#16863303	C₂²	1	1	yes	characteristic
40	#16863303	C₂²	1	1	yes	characteristic
41	#16863303	C₂²	1	1	yes	characteristic
42	#16863303	C₂²	1	1	yes	characteristic
43	#16863303	C₂²	1	1	yes	characteristic
44	#16863303	C₂²	1	1	yes	characteristic
45	#16863303	C₂²	1	1	yes	characteristic
46	#16863303	C₂²	1	1	yes	characteristic
47	#16863303	C₂²	1	1	yes	characteristic
48	#16863299	C₂²	1	1	yes	characteristic
49	#16863299	C₂²	1	1	yes	characteristic
50	#16863295	C₂²	1	1	yes	characteristic
51	#16863295	C₂²	1	1	yes	characteristic
52	#16863295	C₂²	1	1	yes	characteristic
53	#16863295	C₂²	1	1	yes	characteristic
54	#16863295	C₂²	1	1	yes	characteristic
55	#16863295	C₂²	1	1	yes	characteristic
56	#16863289	C₂²	1	1	yes	characteristic
57	#16863289	C₂²	1	1	yes	characteristic
58	#16863289	C₂²	1	1	yes	characteristic
59	#16863289	C₂²	1	1	yes	characteristic
60	#16863289	C₂²	1	1	yes	characteristic
61	#16863289	C₂²	1	1	yes	characteristic
62	#16863289	C₂²	1	1	yes	characteristic
63	#16863289	C₂²	1	1	yes	characteristic
64	#16863289	C₂²	1	1	yes	characteristic
65	#16863289	C₂²	1	1	yes	characteristic
66	#16863289	C₂²	1	1	yes	characteristic
67	#16863289	C₂²	1	1	yes	characteristic
68	#16863289	C₂²	1	1	yes	characteristic
69	#16863289	C₂²	1	1	yes	characteristic
70	#16863289	C₂²	1	1	yes	characteristic
71	#16863289	C₂²	1	1	yes	characteristic
72	#16863289	C₂²	1	1	yes	characteristic
73	#16863289	C₂²	1	1	yes	characteristic
74	#16863289	C₂²	1	1	yes	characteristic
75	#16863289	C₂²	1	1	yes	characteristic
76	#16863289	C₂²	1	1	yes	characteristic
77	#16863289	C₂²	1	1	yes	characteristic
78	#16863289	C₂²	1	1	yes	characteristic
79	#16863289	C₂²	1	1	yes	characteristic
80	#16863282	C₂²	1	1	yes	characteristic
81	#16863282	C₂²	1	1	yes	characteristic
82	#16863282	C₂²	1	1	yes	characteristic
83	#16863282	C₂²	1	1	yes	characteristic
84	#16863282	C₂²	1	1	yes	characteristic
85	#16863282	C₂²	1	1	yes	characteristic
86	#16863282	C₂²	1	1	yes	characteristic
87	#16863282	C₂²	1	1	yes	characteristic
88	#16863282	C₂²	1	1	yes	characteristic
89	#16863282	C₂²	1	1	yes	characteristic
90	#16863282	C₂²	1	1	yes	characteristic
91	#16863282	C₂²	1	1	yes	characteristic
92	#16863282	C₂²	1	1	yes	characteristic
93	#16863282	C₂²	1	1	yes	characteristic
94	#16863282	C₂²	1	1	yes	characteristic
95	#16863282	C₂²	1	1	yes	characteristic
96	#16863282	C₂²	1	1	yes	characteristic
97	#16863282	C₂²	1	1	yes	characteristic
98	#16863282	C₂²	1	1	yes	characteristic
99	#16863282	C₂²	1	1	yes	characteristic
100	#16863282	C₂²	1	1	yes	characteristic
101	#16863282	C₂²	1	1	yes	characteristic
102	#16863282	C₂²	1	1	yes	characteristic
103	#16863282	C₂²	1	1	yes	characteristic
104	#16863276	C₂²	1	1	yes	characteristic
105	#16863276	C₂²	1	1	yes	characteristic
106	#16863276	C₂²	1	1	yes	characteristic
107	#16863276	C₂²	1	1	yes	characteristic
108	#16863276	C₂²	1	1	yes	characteristic
109	#16863276	C₂²	1	1	yes	characteristic
110	#16863276	C₂²	1	1	yes	characteristic
111	#16863276	C₂²	1	1	yes	characteristic
112	#16863271	C₂²	1	1	yes	characteristic
113	#16863271	C₂²	1	1	yes	characteristic
114	#16863271	C₂²	1	1	yes	characteristic
115	#16863271	C₂²	1	1	yes	characteristic
116	#16863271	C₂²	1	1	yes	characteristic
117	#16863271	C₂²	1	1	yes	characteristic
118	#16863271	C₂²	1	1	yes	characteristic
119	#16863271	C₂²	1	1	yes	characteristic
120	#16863271	C₂²	1	1	yes	characteristic
121	#16863271	C₂²	1	1	yes	characteristic
122	#16863271	C₂²	1	1	yes	characteristic
123	#16863271	C₂²	1	1	yes	characteristic
124	#16863271	C₂²	1	1	yes	characteristic
125	#16863271	C₂²	1	1	yes	characteristic
126	#16863266	C₂²	1	1	yes	characteristic
127	#16863264	C₂²	1	1	yes	characteristic
128	#16863264	C₂²	1	1	yes	characteristic
129	#16863264	C₂²	1	1	yes	characteristic
130	#16863264	C₂²	1	1	yes	characteristic
131	#16863262	C₂²	1	1	yes	characteristic
132	#16863262	C₂²	1	1	yes	characteristic
133	#16863262	C₂²	1	1	yes	characteristic
134	#16863259	C₂²	1	1	yes	characteristic
135	#16863259	C₂²	1	1	yes	characteristic
136	#16863256	C₂²	1	1	yes	characteristic
137	#16863256	C₂²	1	1	yes	characteristic
138	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
139	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
140	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
141	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
142	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
143	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
144	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
145	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
146	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
147	C₄⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
148	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
149	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
150	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
153	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
154	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
155	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
156	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
157	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
158	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
159	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
160	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
161	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×Dic₆₇	C₂²	1	1	yes	characteristic
164	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
165	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
166	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
167	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
168	#16863242	C₂²	1	1	yes	characteristic
169	#16863242	C₂²	1	1	yes	characteristic
170	C₂×C₆₇⋊#95	C₂²	1	1	yes	characteristic
171	C₂×C₆₇⋊#95	C₂²	1	1	yes	characteristic
172	#542×C₆₇	C₄	1	16	yes	complemented
173	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
174	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
175	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
176	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
177	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
178	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
179	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
180	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
181	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
182	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
183	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
184	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
185	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
186	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
187	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
188	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
189	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
190	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
191	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
192	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
193	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
194	Q₈×Dic₆₇	—	4	2	no	—
195	Q₈×Dic₆₇	—	4	2	no	—
196	D₄×Dic₆₇	—	4	2	no	—
197	D₄×Dic₆₇	—	4	2	no	—
198	#14524002	—	4	2	no	—
199	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×Dic₆₇	—	4	2	no	—
240	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
244	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
248	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
249	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
250	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
251	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
252	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
253	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
254	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
257	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
258	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
259	C₂×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	C₆₇⋊#95	C₂³	1	1	yes	characteristic
263	C₆₇⋊#95	C₂³	1	1	yes	characteristic
264	C₆₇⋊#95	C₂³	1	1	yes	characteristic
265	C₆₇⋊#95	C₂³	1	1	yes	characteristic
266	C₆₇⋊#95	C₂³	1	1	yes	characteristic
267	C₆₇⋊#95	C₂³	1	1	yes	characteristic
268	C₆₇⋊#95	C₂³	1	1	yes	characteristic
269	C₆₇⋊#95	C₂³	1	1	yes	characteristic
270	C₆₇⋊#95	C₂³	1	1	yes	characteristic
271	C₆₇⋊#95	C₂³	1	1	yes	characteristic
272	C₆₇⋊#95	C₂³	1	1	yes	characteristic
273	C₆₇⋊#95	C₂³	1	1	yes	characteristic
274	C₆₇⋊#95	C₂³	1	1	yes	characteristic
275	C₆₇⋊#95	C₂³	1	1	yes	characteristic
276	C₆₇⋊#95	C₂³	1	1	yes	characteristic
277	C₆₇⋊#95	C₂³	1	1	yes	characteristic
278	C₆₇⋊#95	C₂³	1	1	yes	characteristic
279	C₆₇⋊#95	C₂³	1	1	yes	characteristic
280	C₆₇⋊#95	C₂³	1	1	yes	characteristic
281	C₆₇⋊#95	C₂³	1	1	yes	characteristic
282	C₆₇⋊#95	C₂³	1	1	yes	characteristic
283	C₆₇⋊#95	C₂³	1	1	yes	characteristic
284	C₆₇⋊#95	C₂³	1	1	yes	characteristic
285	C₆₇⋊#95	C₂³	1	1	yes	characteristic
286	C₆₇⋊#95	C₂³	1	1	yes	characteristic
287	C₆₇⋊#95	C₂³	1	1	yes	characteristic
288	C₆₇⋊#95	C₂³	1	1	yes	characteristic
289	C₆₇⋊#95	C₂³	1	1	yes	characteristic
290	C₆₇⋊#95	C₂³	1	1	yes	characteristic
291	C₆₇⋊#95	C₂³	1	1	yes	characteristic
292	C₆₇⋊#95	C₂³	1	1	yes	characteristic
293	C₆₇⋊#95	C₂³	1	1	yes	characteristic
294	C₆₇⋊#95	C₂³	1	1	yes	characteristic
295	C₆₇⋊#95	C₂³	1	1	yes	characteristic
296	C₆₇⋊#95	C₂³	1	1	yes	characteristic
297	C₆₇⋊#95	C₂³	1	1	yes	characteristic
298	C₆₇⋊#95	C₂³	1	1	yes	characteristic
299	C₆₇⋊#95	C₂³	1	1	yes	characteristic
300	C₆₇⋊#95	C₂³	1	1	yes	characteristic
301	C₆₇⋊#95	C₂³	1	1	yes	characteristic
302	C₆₇⋊#95	C₂³	1	1	yes	characteristic
303	C₆₇⋊#95	C₂³	1	1	yes	characteristic
304	C₆₇⋊#95	C₂³	1	1	yes	characteristic
305	C₆₇⋊#95	C₂³	1	1	yes	characteristic
306	C₆₇⋊#95	C₂³	1	1	yes	characteristic
307	C₆₇⋊#95	C₂³	1	1	yes	characteristic
308	C₆₇⋊#95	C₂³	1	1	yes	characteristic
309	C₆₇⋊#95	C₂³	1	1	yes	characteristic
310	C₆₇⋊#95	C₂³	1	1	yes	characteristic
311	C₆₇⋊#95	C₂³	1	1	yes	characteristic
312	C₆₇⋊#95	C₂³	1	1	yes	characteristic
313	C₆₇⋊#95	C₂³	1	1	yes	characteristic
314	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₄⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
324	#126×C₆₇	C₂×C₄	1	8	yes	complemented
325	#126×C₆₇	C₂×C₄	1	8	yes	complemented
326	#124×C₆₇	C₂×C₄	1	8	yes	complemented
327	#124×C₆₇	C₂×C₄	1	8	yes	complemented
328	#124×C₆₇	C₂×C₄	1	8	yes	complemented
329	#123×C₆₇	C₂×C₄	1	8	yes	complemented
330	#123×C₆₇	C₂×C₄	1	8	yes	complemented
331	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
332	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
333	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
334	#121×C₆₇	C₂×C₄	1	8	yes	—
335	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
336	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
337	#117×C₆₇	C₂×C₄	1	8	yes	complemented
338	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
347	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
352	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
353	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
354	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
356	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
357	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
358	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
359	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
360	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
361	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
362	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
363	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
364	C₂²×Dic₆₇	—	2	2	no	—
365	C₂²×Dic₆₇	—	2	2	no	—
366	C₂²×Dic₆₇	—	2	2	no	—
367	C₂²×Dic₆₇	—	4	1	no	—
368	C₂²×Dic₆₇	—	4	1	no	—
369	C₂²×Dic₆₇	—	4	1	no	—
370	C₂²×Dic₆₇	—	4	1	no	—
371	C₂²×Dic₆₇	—	4	1	no	—
372	C₂²×Dic₆₇	—	4	1	no	—
373	C₂²×Dic₆₇	—	4	1	no	—
374	C₂²×Dic₆₇	—	4	1	no	—
375	C₂²×Dic₆₇	—	4	1	no	—
376	C₂²×Dic₆₇	—	4	1	no	—
377	C₂²×Dic₆₇	—	4	1	no	—
378	C₂²×Dic₆₇	—	4	1	no	—
379	C₂²×Dic₆₇	—	4	1	no	—
380	C₂²×Dic₆₇	—	4	1	no	—
381	C₂²×Dic₆₇	—	4	1	no	—
382	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
383	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
384	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
385	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
394	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
398	C₄⋊Dic₆₇	—	2	2	no	—
399	C₄⋊Dic₆₇	—	2	2	no	—
400	C₄⋊Dic₆₇	—	2	2	no	—
401	C₄⋊Dic₆₇	—	2	2	no	—
402	C₄⋊Dic₆₇	—	2	2	no	—
403	C₄⋊Dic₆₇	—	4	1	no	—
404	C₄⋊Dic₆₇	—	4	1	no	—
405	C₄⋊Dic₆₇	—	4	1	no	—
406	C₄⋊Dic₆₇	—	4	1	no	—
407	C₄⋊Dic₆₇	—	4	1	no	—
408	C₄⋊Dic₆₇	—	4	1	no	—
409	C₄⋊Dic₆₇	—	4	1	no	—
410	C₄⋊Dic₆₇	—	4	1	no	—
411	C₄⋊Dic₆₇	—	4	1	no	—
412	C₄⋊Dic₆₇	—	4	1	no	—
413	C₄⋊Dic₆₇	—	4	1	no	—
414	C₄⋊Dic₆₇	—	4	1	no	—
415	C₄⋊Dic₆₇	—	4	1	no	—
416	C₄⋊Dic₆₇	—	4	1	no	—
417	C₄⋊Dic₆₇	—	4	1	no	—
418	C₄⋊Dic₆₇	—	4	1	no	—
419	C₄⋊Dic₆₇	—	4	1	no	—
420	C₂²⋊Dic₆₇	—	2	2	no	—
421	C₂²⋊Dic₆₇	—	2	2	no	—
422	C₂²⋊Dic₆₇	—	2	2	no	—
423	C₂²⋊Dic₆₇	—	4	1	no	—
424	C₂²⋊Dic₆₇	—	4	1	no	—
425	C₂²⋊Dic₆₇	—	4	1	no	—
426	C₂²⋊Dic₆₇	—	4	1	no	—
427	C₂²⋊Dic₆₇	—	4	1	no	—
428	C₂²⋊Dic₆₇	—	4	1	no	—
429	C₂²⋊Dic₆₇	—	4	1	no	—
430	C₂²⋊Dic₆₇	—	4	1	no	—
431	C₂²⋊Dic₆₇	—	4	1	no	—
432	C₂²⋊Dic₆₇	—	4	1	no	—
433	C₂²⋊Dic₆₇	—	4	1	no	—
434	C₂²⋊Dic₆₇	—	4	1	no	—
435	C₂²⋊Dic₆₇	—	4	1	no	—
436	C₂²⋊Dic₆₇	—	4	1	no	—
437	C₂²⋊Dic₆₇	—	4	1	no	—
438	C₄×Dic₆₇	—	2	2	no	—
439	C₄×Dic₆₇	—	2	2	no	—
440	C₄×Dic₆₇	—	2	2	no	—
441	C₄×Dic₆₇	—	4	1	no	—
442	C₄×Dic₆₇	—	4	1	no	—
443	C₄×Dic₆₇	—	4	1	no	—
444	C₄×Dic₆₇	—	4	1	no	—
445	C₄×Dic₆₇	—	4	1	no	—
446	C₄×Dic₆₇	—	4	1	no	—
447	C₄×Dic₆₇	—	4	1	no	—
448	C₄×Dic₆₇	—	4	1	no	—
449	C₄×Dic₆₇	—	4	1	no	—
450	C₄×Dic₆₇	—	4	1	no	—
451	C₄×Dic₆₇	—	4	1	no	—
452	C₄×Dic₆₇	—	4	1	no	—
453	C₄×Dic₆₇	—	4	1	no	—
454	C₄×Dic₆₇	—	4	1	no	—
455	C₄×Dic₆₇	—	4	1	no	—
456	C₄×Dic₆₇	—	4	1	no	—
457	C₄×Dic₆₇	—	4	1	no	—
458	C₄×Dic₆₇	—	4	1	no	—
459	C₄×Dic₆₇	—	4	1	no	—
460	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
461	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
462	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
463	C₂×Q₈×C₆₇	—	4	1	no	—
464	C₂×Q₈×C₆₇	—	4	1	no	—
465	C₂×Q₈×C₆₇	—	4	1	no	—
466	C₂×Q₈×C₆₇	—	4	1	no	—
467	C₂×Q₈×C₆₇	—	4	1	no	—
468	C₂×Q₈×C₆₇	—	4	1	no	—
469	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
470	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
471	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
472	C₂×D₄×C₆₇	—	4	1	no	—
473	C₂×D₄×C₆₇	—	4	1	no	—
474	C₂×D₄×C₆₇	—	4	1	no	—
475	C₂×D₄×C₆₇	—	4	1	no	—
476	C₂×D₄×C₆₇	—	4	1	no	—
477	C₂×D₄×C₆₇	—	4	1	no	—
478	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
479	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
480	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
481	C₂²×C₄×C₆₇	—	4	1	no	—
482	C₂²×C₄×C₆₇	—	4	1	no	—
483	C₂²×C₄×C₆₇	—	4	1	no	—
484	C₂²×C₄×C₆₇	—	4	1	no	—
485	C₂²×C₄×C₆₇	—	4	1	no	—
486	C₂²×C₄×C₆₇	—	4	1	no	—
487	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
488	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
489	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
490	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
492	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
493	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
494	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
503	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
504	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
505	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
506	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
507	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
508	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
509	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
510	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
511	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
512	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
513	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
514	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
515	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
516	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
517	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
518	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
519	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
520	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
521	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
522	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
523	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
524	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
525	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
526	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
527	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
528	C₂³×C₆₇	—	2	1	no	—
529	C₂³×C₆₇	—	2	1	no	—
530	C₂³×C₆₇	—	2	1	no	—
531	C₂³×C₆₇	—	2	1	no	—
532	C₂³×C₆₇	—	2	1	no	—
533	C₂³×C₆₇	—	2	1	no	—
534	C₂³×C₆₇	—	2	1	no	—
535	C₂³×C₆₇	—	2	1	no	—
536	C₂³×C₆₇	—	2	1	no	—
537	C₂³×C₆₇	—	2	1	no	—
538	C₂³×C₆₇	—	2	1	no	—
539	C₂³×C₆₇	—	2	1	no	—
540	C₂³×C₆₇	—	2	1	no	—
541	C₂³×C₆₇	—	2	1	no	—
542	C₂³×C₆₇	—	2	1	no	—
543	C₂³×C₆₇	—	2	1	no	—
544	C₂³×C₆₇	—	2	1	no	—
545	C₂³×C₆₇	—	2	1	no	—
546	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
547	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
548	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
549	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
550	Q₈×C₆₇	—	4	4	no	—
551	Q₈×C₆₇	—	4	4	no	—
552	Q₈×C₆₇	—	4	4	no	—
553	D₄×C₆₇	—	4	4	no	—
554	D₄×C₆₇	—	4	4	no	—
555	D₄×C₆₇	—	4	4	no	—
556	C₂×C₄×C₆₇	—	2	1	no	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	1	no	—
559	C₂×C₄×C₆₇	—	2	1	no	—
560	C₂×C₄×C₆₇	—	2	1	no	—
561	C₂×C₄×C₆₇	—	2	1	no	—
562	C₂×C₄×C₆₇	—	2	1	no	—
563	C₂×C₄×C₆₇	—	2	1	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	1	no	—
566	C₂×C₄×C₆₇	—	2	1	no	—
567	C₂×C₄×C₆₇	—	2	1	no	—
568	C₂×C₄×C₆₇	—	2	1	no	—
569	C₂×C₄×C₆₇	—	2	1	no	—
570	C₂×C₄×C₆₇	—	2	1	no	—
571	C₂×C₄×C₆₇	—	2	1	no	—
572	C₂×C₄×C₆₇	—	2	1	no	—
573	C₂×C₄×C₆₇	—	2	1	no	—
574	C₂×C₄×C₆₇	—	2	1	no	—
575	C₂×C₄×C₆₇	—	2	1	no	—
576	C₂×C₄×C₆₇	—	2	1	no	—
577	C₂×C₄×C₆₇	—	2	1	no	—
578	C₂×C₄×C₆₇	—	2	1	no	—
579	C₂×C₄×C₆₇	—	2	1	no	—
580	C₂×C₄×C₆₇	—	4	4	no	—
581	C₂×C₄×C₆₇	—	4	4	no	—
582	C₂×C₄×C₆₇	—	4	4	no	—
583	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
584	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
585	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
586	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
587	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
588	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
589	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
590	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
591	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
592	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
593	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
594	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
595	C₂×Dic₆₇	—	2	1	no	—
596	C₂×Dic₆₇	—	2	1	no	—
597	C₂×Dic₆₇	—	2	1	no	—
598	C₂×Dic₆₇	—	2	1	no	—
599	C₂×Dic₆₇	—	2	1	no	—
600	C₂×Dic₆₇	—	2	1	no	—
601	C₂×Dic₆₇	—	2	1	no	—
602	C₂×Dic₆₇	—	2	1	no	—
603	C₂×Dic₆₇	—	2	1	no	—
604	C₂×Dic₆₇	—	2	1	no	—
605	C₂×Dic₆₇	—	2	1	no	—
606	C₂×Dic₆₇	—	2	1	no	—
607	C₂×Dic₆₇	—	2	1	no	—
608	C₂×Dic₆₇	—	2	1	no	—
609	C₂×Dic₆₇	—	2	1	no	—
610	C₂×Dic₆₇	—	2	1	no	—
611	C₂×Dic₆₇	—	2	1	no	—
612	C₂×Dic₆₇	—	2	1	no	—
613	C₂×Dic₆₇	—	2	1	no	—
614	C₂×Dic₆₇	—	2	1	no	—
615	C₂×Dic₆₇	—	2	1	no	—
616	C₂×Dic₆₇	—	2	1	no	—
617	C₂×Dic₆₇	—	2	1	no	—
618	C₂×Dic₆₇	—	2	1	no	—
619	C₂×Dic₆₇	—	2	1	no	—
620	C₂×Dic₆₇	—	2	1	no	—
621	C₂×Dic₆₇	—	2	1	no	—
622	C₂×Dic₆₇	—	2	1	no	—
623	C₂×Dic₆₇	—	2	1	no	—
624	C₂×Dic₆₇	—	2	1	no	—
625	C₂×Dic₆₇	—	2	1	no	—
626	C₂×Dic₆₇	—	2	1	no	—
627	C₂×Dic₆₇	—	2	1	no	—
628	C₂×Dic₆₇	—	2	1	no	—
629	C₂×Dic₆₇	—	2	1	no	—
630	C₂×Dic₆₇	—	2	1	no	—
631	C₂×Dic₆₇	—	2	1	no	—
632	C₂×Dic₆₇	—	2	1	no	—
633	C₂×Dic₆₇	—	2	1	no	—
634	C₂×Dic₆₇	—	2	1	no	—
635	C₂×Dic₆₇	—	2	1	no	—
636	C₂×Dic₆₇	—	2	1	no	—
637	C₂×Dic₆₇	—	2	1	no	—
638	C₂×Dic₆₇	—	2	1	no	—
639	C₂×Dic₆₇	—	2	1	no	—
640	C₂×Dic₆₇	—	2	1	no	—
641	C₂×Dic₆₇	—	4	4	no	—
642	C₂×Dic₆₇	—	4	4	no	—
643	C₂×Dic₆₇	—	8	2	no	—
644	C₂×Dic₆₇	—	8	2	no	—
645	C₂×Dic₆₇	—	8	2	no	—
646	C₂×Dic₆₇	—	8	2	no	—
647	C₂×Dic₆₇	H(5,𝔽₂)	1	2	yes	—
648	C₂×Dic₆₇	2₋¹⁺⁴	1	2	yes	—
649	C₂²×C₆₇	—	2	2	no	—
650	C₂²×C₆₇	—	2	2	no	—
651	C₂²×C₆₇	—	2	2	no	—
652	C₂²×C₆₇	—	2	2	no	—
653	C₂²×C₆₇	—	2	2	no	—
654	C₂²×C₆₇	—	2	2	no	—
655	C₂²×C₆₇	—	2	2	no	—
656	C₂²×C₆₇	—	2	2	no	—
657	C₂²×C₆₇	—	2	2	no	—
658	C₂²×C₆₇	—	4	1	no	—
659	C₂²×C₆₇	—	4	1	no	—
660	C₂²×C₆₇	—	4	1	no	—
661	C₂²×C₆₇	—	4	1	no	—
662	C₂²×C₆₇	—	4	1	no	—
663	C₂²×C₆₇	—	4	1	no	—
664	C₂²×C₆₇	—	4	1	no	—
665	C₂²×C₆₇	—	4	1	no	—
666	C₂²×C₆₇	—	4	1	no	—
667	C₂²×C₆₇	—	4	1	no	—
668	C₂²×C₆₇	—	4	1	no	—
669	C₂²×C₆₇	—	4	1	no	—
670	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
671	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
673	C₂²×C₆₇	#585	1	1	yes	characteristic
674	C₂²×C₆₇	#585	1	1	yes	characteristic
675	C₂²×C₆₇	#585	1	1	yes	characteristic
676	C₂²×C₆₇	#585	1	1	yes	characteristic
677	C₄×C₆₇	—	2	2	no	—
678	C₄×C₆₇	—	2	2	no	—
679	C₄×C₆₇	—	2	2	no	—
680	C₄×C₆₇	—	2	2	no	—
681	C₄×C₆₇	—	2	2	no	—
682	C₄×C₆₇	—	2	2	no	—
683	C₄×C₆₇	—	2	2	no	—
684	C₄×C₆₇	—	2	2	no	—
685	C₄×C₆₇	—	2	2	no	—
686	C₄×C₆₇	—	2	2	no	—
687	C₄×C₆₇	—	2	2	no	—
688	C₄×C₆₇	—	2	2	no	—
689	Dic₆₇	—	2	2	no	—
690	Dic₆₇	—	2	2	no	—
691	Dic₆₇	—	4	1	no	—
692	Dic₆₇	—	4	1	no	—
693	Dic₆₇	—	4	1	no	—
694	Dic₆₇	—	4	1	no	—
695	Dic₆₇	—	4	1	no	—
696	Dic₆₇	—	4	1	no	—
697	Dic₆₇	—	4	1	no	—
698	Dic₆₇	—	4	1	no	—
699	Dic₆₇	—	4	1	no	—
700	Dic₆₇	—	4	1	no	—
701	Dic₆₇	—	4	1	no	—
702	Dic₆₇	—	4	1	no	—
703	Dic₆₇	—	4	1	no	—
704	Dic₆₇	—	4	1	no	—
705	#34448	—	67	1	no	maximal, Sylow
706	C₂×C₆₇	—	4	2	no	—
707	C₂×C₆₇	—	4	2	no	—
708	C₂×C₆₇	—	4	2	no	—
709	C₂×C₆₇	#3428	1	1	yes	characteristic
710	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
711	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
712	C₂×C₆₇	#3533	1	1	yes	characteristic
713	C₂×C₆₇	#3541	1	1	yes	characteristic
714	C₂×C₆₇	#3557	1	1	yes	characteristic
715	C₂×C₆₇	#3568	1	1	yes	characteristic
716	C₂×#542	D₆₇	1	1	yes	characteristic
717	#2383	—	67	1	no	—
718	#2381	—	67	1	no	—
719	#2379	—	67	1	no	—
720	#2378	—	67	1	no	—
721	#2374	—	67	1	no	—
722	#2373	—	67	1	no	—
723	#2368	—	67	1	no	—
724	#2368	—	67	1	no	—
725	#2367	—	67	1	no	—
726	#2365	—	67	1	no	—
727	#2362	—	67	1	no	—
728	#2359	—	67	1	no	—
729	#2356	—	67	1	no	—
730	#2355	—	67	1	no	—
731	#2347	—	67	1	no	—
732	#2343	—	67	1	no	—
733	#2337	—	67	1	no	—
734	#2337	—	67	1	no	—
735	#2337	—	67	1	no	—
736	#2335	—	67	1	no	—
737	#2334	—	67	1	no	—
738	#2334	—	67	1	no	—
739	#2333	—	67	1	no	—
740	#2332	—	67	1	no	—
741	#2326	—	67	1	no	—
742	#2325	—	67	1	no	—
743	#2318	—	67	1	no	—
744	C₄×C₂²⋊Q₈	—	67	1	no	—
745	C₄×#123	—	67	1	no	—
746	#2290	—	67	1	no	—
747	C₆₇	#34448	1	1	yes	characteristic, complemented, Sylow
748	#542	Dic₆₇	1	16	yes	complemented
749	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
750	C₂×#126	C₂×D₆₇	1	1	yes	characteristic
751	C₂×#126	C₂×D₆₇	1	1	yes	characteristic
752	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
753	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
754	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
755	C₂×#123	C₂×D₆₇	1	1	yes	characteristic
756	C₂×#123	C₂×D₆₇	1	1	yes	characteristic
757	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
758	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
759	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
760	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
761	C₂×C₄×Q₈	—	67	1	no	—
762	C₂×C₄×Q₈	—	67	1	no	—
763	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
764	C₂×C₄×D₄	—	67	1	no	—
765	C₂×C₄×D₄	—	67	1	no	—
766	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
767	C₂×#117	—	67	1	no	—
768	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
769	C₂²×C₄²	—	67	1	no	—
770	#391	—	67	1	no	—
771	#391	—	67	1	no	—
772	#391	—	67	1	no	—
773	#391	—	67	1	no	—
774	#391	—	67	1	no	—
775	#391	—	67	1	no	—
776	#391	—	67	1	no	—
777	#391	—	67	1	no	—
778	#391	—	67	1	no	—
779	#391	—	67	1	no	—
780	#390	—	67	1	no	—
781	#390	—	67	1	no	—
782	#389	—	67	1	no	—
783	#389	—	67	1	no	—
784	#389	—	67	1	no	—
785	#389	—	67	1	no	—
786	#389	—	67	1	no	—
787	#389	—	67	1	no	—
788	#388	—	67	1	no	—
789	#388	—	67	1	no	—
790	#388	—	67	1	no	—
791	#388	—	67	1	no	—
792	#388	—	67	1	no	—
793	#388	—	67	1	no	—
794	#388	—	67	1	no	—
795	#388	—	67	1	no	—
796	#388	—	67	1	no	—
797	#388	—	67	1	no	—
798	#388	—	67	1	no	—
799	#388	—	67	1	no	—
800	#388	—	67	1	no	—
801	#388	—	67	1	no	—
802	#388	—	67	1	no	—
803	#388	—	67	1	no	—
804	#388	—	67	1	no	—
805	#388	—	67	1	no	—
806	#388	—	67	1	no	—
807	#388	—	67	1	no	—
808	#388	—	67	1	no	—
809	#388	—	67	1	no	—
810	#388	—	67	1	no	—
811	#388	—	67	1	no	—
812	#387	—	67	1	no	—
813	#387	—	67	1	no	—
814	#387	—	67	1	no	—
815	#387	—	67	1	no	—
816	#387	—	67	1	no	—
817	#387	—	67	1	no	—
818	#387	—	67	1	no	—
819	#387	—	67	1	no	—
820	#387	—	67	1	no	—
821	#387	—	67	1	no	—
822	#387	—	67	1	no	—
823	#387	—	67	1	no	—
824	#387	—	67	1	no	—
825	#387	—	67	1	no	—
826	#387	—	67	1	no	—
827	#387	—	67	1	no	—
828	#387	—	67	1	no	—
829	#387	—	67	1	no	—
830	#387	—	67	1	no	—
831	#387	—	67	1	no	—
832	#387	—	67	1	no	—
833	#387	—	67	1	no	—
834	#387	—	67	1	no	—
835	#387	—	67	1	no	—
836	#386	—	67	1	no	—
837	#386	—	67	1	no	—
838	#386	—	67	1	no	—
839	#386	—	67	1	no	—
840	#386	—	67	1	no	—
841	#386	—	67	1	no	—
842	#386	—	67	1	no	—
843	#386	—	67	1	no	—
844	#385	—	67	1	no	—
845	#385	—	67	1	no	—
846	#385	—	67	1	no	—
847	#385	—	67	1	no	—
848	#385	—	67	1	no	—
849	#385	—	67	1	no	—
850	#385	—	67	1	no	—
851	#385	—	67	1	no	—
852	#385	—	67	1	no	—
853	#385	—	67	1	no	—
854	#385	—	67	1	no	—
855	#385	—	67	1	no	—
856	#385	—	67	1	no	—
857	#385	—	67	1	no	—
858	#384	—	67	1	no	—
859	#383	—	67	1	no	—
860	#383	—	67	1	no	—
861	#383	—	67	1	no	—
862	#383	—	67	1	no	—
863	#382	—	67	1	no	—
864	#382	—	67	1	no	—
865	#382	—	67	1	no	—
866	#381	—	67	1	no	—
867	#381	—	67	1	no	—
868	#380	—	67	1	no	—
869	#380	—	67	1	no	—
870	C₄×C₄⋊C₄	—	67	1	no	—
871	C₄×C₄⋊C₄	—	67	1	no	—
872	C₄×C₄⋊C₄	—	67	1	no	—
873	C₄×C₄⋊C₄	—	67	1	no	—
874	C₄×C₄⋊C₄	—	67	1	no	—
875	C₄×C₄⋊C₄	—	67	1	no	—
876	C₄×C₄⋊C₄	—	67	1	no	—
877	C₄×C₄⋊C₄	—	67	1	no	—
878	C₄×C₄⋊C₄	—	67	1	no	—
879	C₄×C₄⋊C₄	—	67	1	no	—
880	C₄×C₄⋊C₄	—	67	1	no	—
881	C₄×C₄⋊C₄	—	67	1	no	—
882	C₄×C₄⋊C₄	—	67	1	no	—
883	C₄×C₄⋊C₄	—	67	1	no	—
884	C₄×C₄⋊C₄	—	67	1	no	—
885	C₄×C₄⋊C₄	—	67	1	no	—
886	C₄×C₂²⋊C₄	—	67	1	no	—
887	C₄×C₂²⋊C₄	—	67	1	no	—
888	C₄×C₂²⋊C₄	—	67	1	no	—
889	C₄×C₂²⋊C₄	—	67	1	no	—
890	C₄×C₂²⋊C₄	—	67	1	no	—
891	C₄×C₂²⋊C₄	—	67	1	no	—
892	C₄×C₂²⋊C₄	—	67	1	no	—
893	C₄×C₂²⋊C₄	—	67	1	no	—
894	C₄×C₂²⋊C₄	—	67	1	no	—
895	C₄×C₂²⋊C₄	—	67	1	no	—
896	C₄×C₂²⋊C₄	—	67	1	no	—
897	C₄×C₂²⋊C₄	—	67	1	no	—
898	C₄×C₂²⋊C₄	—	67	1	no	—
899	C₄×C₂²⋊C₄	—	67	1	no	—
900	#376	—	67	1	no	—
901	#376	—	67	1	no	—
902	C₂×#95	—	67	1	no	—
903	C₂×#95	—	67	1	no	—
904	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
905	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
906	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
907	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
908	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
909	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
910	C₂³×C₄	—	67	1	no	—
911	C₂³×C₄	—	67	1	no	—
912	C₂³×C₄	—	67	1	no	—
913	C₂³×C₄	—	67	1	no	—
914	C₂³×C₄	—	67	1	no	—
915	C₂³×C₄	—	67	1	no	—
916	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
917	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
918	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
919	C₄⋊Q₈	C₂×Dic₆₇	1	8	yes	complemented
920	#126	C₂×Dic₆₇	1	8	yes	complemented
921	#126	C₂×Dic₆₇	1	8	yes	complemented
922	#124	C₂×Dic₆₇	1	8	yes	complemented
923	#124	C₂×Dic₆₇	1	8	yes	complemented
924	#124	C₂×Dic₆₇	1	8	yes	complemented
925	#123	C₂×Dic₆₇	1	8	yes	complemented
926	#123	C₂×Dic₆₇	1	8	yes	complemented
927	C₂²⋊Q₈	C₂×Dic₆₇	1	8	yes	complemented
928	C₂²⋊Q₈	C₂×Dic₆₇	1	8	yes	complemented
929	C₂²⋊Q₈	C₂×Dic₆₇	1	8	yes	complemented
930	#121	C₂×Dic₆₇	1	8	yes	—
931	C₄×Q₈	—	268	2	no	—
932	C₄×Q₈	—	268	2	no	—
933	C₄×Q₈	C₂×Dic₆₇	1	8	yes	complemented
934	C₄×D₄	—	268	2	no	—
935	C₄×D₄	—	268	2	no	—
936	C₄×D₄	C₂×Dic₆₇	1	8	yes	complemented
937	#117	—	268	2	no	—
938	#117	C₂×Dic₆₇	1	8	yes	complemented
939	C₂×C₄⋊C₄	—	67	1	no	—
940	C₂×C₄⋊C₄	—	67	1	no	—
941	C₂×C₄⋊C₄	—	67	1	no	—
942	C₂×C₄⋊C₄	—	67	1	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	1	no	—
947	C₂×C₄⋊C₄	—	67	1	no	—
948	C₂×C₄⋊C₄	—	67	1	no	—
949	C₂×C₄⋊C₄	—	67	1	no	—
950	C₂×C₄⋊C₄	—	67	1	no	—
951	C₂×C₄⋊C₄	—	67	1	no	—
952	C₂×C₄⋊C₄	—	67	1	no	—
953	C₂×C₄⋊C₄	—	67	1	no	—
954	C₂×C₄⋊C₄	—	67	1	no	—
955	C₂×C₄⋊C₄	—	67	1	no	—
956	C₂×C₄⋊C₄	—	67	1	no	—
957	C₂×C₄⋊C₄	—	67	1	no	—
958	C₂×C₄⋊C₄	—	67	1	no	—
959	C₂×C₄⋊C₄	—	67	1	no	—
960	C₂×C₄⋊C₄	—	67	1	no	—
961	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
970	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
971	C₂×C₂²⋊C₄	—	67	1	no	—
972	C₂×C₂²⋊C₄	—	67	1	no	—
973	C₂×C₂²⋊C₄	—	67	1	no	—
974	C₂×C₂²⋊C₄	—	67	1	no	—
975	C₂×C₂²⋊C₄	—	67	1	no	—
976	C₂×C₂²⋊C₄	—	67	1	no	—
977	C₂×C₂²⋊C₄	—	67	1	no	—
978	C₂×C₂²⋊C₄	—	67	1	no	—
979	C₂×C₂²⋊C₄	—	67	1	no	—
980	C₂×C₂²⋊C₄	—	67	1	no	—
981	C₂×C₂²⋊C₄	—	67	1	no	—
982	C₂×C₂²⋊C₄	—	67	1	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	1	no	—
987	C₂×C₂²⋊C₄	—	67	1	no	—
988	C₂×C₂²⋊C₄	—	67	1	no	—
989	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
990	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
991	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
992	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
993	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
994	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
995	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
998	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1001	C₂×C₄²	—	268	2	no	—
1002	C₂×C₄²	—	67	1	no	—
1003	C₂×C₄²	—	67	1	no	—
1004	C₂×C₄²	—	67	1	no	—
1005	C₂×C₄²	—	67	1	no	—
1006	C₂×C₄²	—	67	1	no	—
1007	C₂×C₄²	—	67	1	no	—
1008	C₂×C₄²	—	67	1	no	—
1009	C₂×C₄²	—	67	1	no	—
1010	C₂×C₄²	—	67	1	no	—
1011	C₂×C₄²	—	67	1	no	—
1012	C₂×C₄²	—	67	1	no	—
1013	C₂×C₄²	—	67	1	no	—
1014	C₂×C₄²	—	67	1	no	—
1015	C₂×C₄²	—	67	1	no	—
1016	C₂×C₄²	—	67	1	no	—
1017	C₂×C₄²	—	67	1	no	—
1018	C₂×C₄²	—	67	1	no	—
1019	C₂×C₄²	—	67	1	no	—
1020	C₂×C₄²	—	67	1	no	—
1021	C₂×C₄²	—	67	1	no	—
1022	C₂×C₄²	—	67	1	no	—
1023	C₂×C₄²	—	67	1	no	—
1024	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1025	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1026	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1027	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1028	#95	—	67	1	no	—
1029	#95	—	67	1	no	—
1030	#95	—	67	1	no	—
1031	#95	—	67	1	no	—
1032	#95	—	67	1	no	—
1033	#95	—	67	1	no	—
1034	#95	—	67	1	no	—
1035	#95	—	67	1	no	—
1036	#95	—	67	1	no	—
1037	#95	—	67	1	no	—
1038	#95	—	67	1	no	—
1039	#95	—	67	1	no	—
1040	#95	—	67	1	no	—
1041	#95	—	67	1	no	—
1042	#95	—	67	1	no	—
1043	#95	—	67	1	no	—
1044	#95	—	67	1	no	—
1045	#95	—	67	1	no	—
1046	#95	—	67	1	no	—
1047	#95	—	67	1	no	—
1048	#95	—	67	1	no	—
1049	#95	—	67	1	no	—
1050	#95	—	67	1	no	—
1051	#95	—	67	1	no	—
1052	#95	—	67	1	no	—
1053	#95	—	67	1	no	—
1054	#95	—	67	1	no	—
1055	#95	—	67	1	no	—
1056	#95	—	67	1	no	—
1057	#95	—	67	1	no	—
1058	#95	—	67	1	no	—
1059	#95	—	67	1	no	—
1060	#95	—	67	1	no	—
1061	#95	—	67	1	no	—
1062	#95	—	67	1	no	—
1063	#95	—	67	1	no	—
1064	#95	—	67	1	no	—
1065	#95	—	67	1	no	—
1066	#95	—	67	1	no	—
1067	#95	—	67	1	no	—
1068	#95	—	67	1	no	—
1069	#95	—	67	1	no	—
1070	#95	—	67	1	no	—
1071	#95	—	67	1	no	—
1072	#95	—	67	1	no	—
1073	#95	—	67	1	no	—
1074	#95	—	67	1	no	—
1075	#95	—	67	1	no	—
1076	#95	—	67	1	no	—
1077	#95	—	67	1	no	—
1078	#95	—	67	1	no	—
1079	#95	—	67	1	no	—
1080	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1081	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1082	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1083	C₂×Q₈	—	4	1	no	—
1084	C₂×Q₈	—	4	1	no	—
1085	C₂×Q₈	—	4	1	no	—
1086	C₂×Q₈	—	4	1	no	—
1087	C₂×Q₈	—	4	1	no	—
1088	C₂×Q₈	—	4	1	no	—
1089	C₂×Q₈	C₂²×Dic₆₇	1	4	yes	—
1090	C₂×Q₈	C₂²×Dic₆₇	1	4	yes	—
1091	C₂×Q₈	C₂²×Dic₆₇	1	4	yes	—
1092	C₂×D₄	—	4	1	no	—
1093	C₂×D₄	—	4	1	no	—
1094	C₂×D₄	—	4	1	no	—
1095	C₂×D₄	—	4	1	no	—
1096	C₂×D₄	—	4	1	no	—
1097	C₂×D₄	—	4	1	no	—
1098	C₂×D₄	C₂²×Dic₆₇	1	4	yes	—
1099	C₂×D₄	C₂²×Dic₆₇	1	4	yes	—
1100	C₂×D₄	C₂²×Dic₆₇	1	4	yes	—
1101	C₂²×C₄	—	4	1	no	—
1102	C₂²×C₄	—	4	1	no	—
1103	C₂²×C₄	—	4	1	no	—
1104	C₂²×C₄	—	4	1	no	—
1105	C₂²×C₄	—	4	1	no	—
1106	C₂²×C₄	—	4	1	no	—
1107	C₂²×C₄	—	268	1	no	—
1108	C₂²×C₄	—	268	1	no	—
1109	C₂²×C₄	—	268	1	no	—
1110	C₂²×C₄	—	268	1	no	—
1111	C₂²×C₄	—	268	1	no	—
1112	C₂²×C₄	—	268	1	no	—
1113	C₂²×C₄	—	268	1	no	—
1114	C₂²×C₄	—	268	1	no	—
1115	C₂²×C₄	—	268	1	no	—
1116	C₂²×C₄	—	268	1	no	—
1117	C₂²×C₄	—	268	1	no	—
1118	C₂²×C₄	—	268	1	no	—
1119	C₂²×C₄	—	268	1	no	—
1120	C₂²×C₄	—	268	1	no	—
1121	C₂²×C₄	—	268	1	no	—
1122	C₂²×C₄	—	67	1	no	—
1123	C₂²×C₄	—	67	1	no	—
1124	C₂²×C₄	—	67	1	no	—
1125	C₂²×C₄	—	67	1	no	—
1126	C₂²×C₄	—	67	1	no	—
1127	C₂²×C₄	—	67	1	no	—
1128	C₂²×C₄	—	67	1	no	—
1129	C₂²×C₄	—	67	1	no	—
1130	C₂²×C₄	—	67	1	no	—
1131	C₂²×C₄	—	67	1	no	—
1132	C₂²×C₄	—	67	1	no	—
1133	C₂²×C₄	—	67	1	no	—
1134	C₂²×C₄	—	67	1	no	—
1135	C₂²×C₄	—	67	1	no	—
1136	C₂²×C₄	—	67	1	no	—
1137	C₂²×C₄	—	67	1	no	—
1138	C₂²×C₄	—	134	2	no	—
1139	C₂²×C₄	—	134	2	no	—
1140	C₂²×C₄	—	134	2	no	—
1141	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
1142	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
1143	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
1144	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1145	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1146	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1147	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1148	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1149	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1150	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1151	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1152	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1153	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1154	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1155	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1156	C₄⋊C₄	—	268	1	no	—
1157	C₄⋊C₄	—	268	1	no	—
1158	C₄⋊C₄	—	268	1	no	—
1159	C₄⋊C₄	—	268	1	no	—
1160	C₄⋊C₄	—	268	1	no	—
1161	C₄⋊C₄	—	268	1	no	—
1162	C₄⋊C₄	—	268	1	no	—
1163	C₄⋊C₄	—	268	1	no	—
1164	C₄⋊C₄	—	268	1	no	—
1165	C₄⋊C₄	—	268	1	no	—
1166	C₄⋊C₄	—	268	1	no	—
1167	C₄⋊C₄	—	268	1	no	—
1168	C₄⋊C₄	—	268	1	no	—
1169	C₄⋊C₄	—	268	1	no	—
1170	C₄⋊C₄	—	268	1	no	—
1171	C₄⋊C₄	—	268	1	no	—
1172	C₄⋊C₄	—	268	1	no	—
1173	C₄⋊C₄	—	134	2	no	—
1174	C₄⋊C₄	—	134	2	no	—
1175	C₄⋊C₄	—	134	2	no	—
1176	C₄⋊C₄	—	134	2	no	—
1177	C₄⋊C₄	—	134	2	no	—
1178	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1179	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1180	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1181	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1182	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1183	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1184	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1185	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1186	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1187	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1188	C₂²⋊C₄	—	268	1	no	—
1189	C₂²⋊C₄	—	268	1	no	—
1190	C₂²⋊C₄	—	268	1	no	—
1191	C₂²⋊C₄	—	268	1	no	—
1192	C₂²⋊C₄	—	268	1	no	—
1193	C₂²⋊C₄	—	268	1	no	—
1194	C₂²⋊C₄	—	268	1	no	—
1195	C₂²⋊C₄	—	268	1	no	—
1196	C₂²⋊C₄	—	268	1	no	—
1197	C₂²⋊C₄	—	268	1	no	—
1198	C₂²⋊C₄	—	268	1	no	—
1199	C₂²⋊C₄	—	268	1	no	—
1200	C₂²⋊C₄	—	268	1	no	—
1201	C₂²⋊C₄	—	268	1	no	—
1202	C₂²⋊C₄	—	268	1	no	—
1203	C₂²⋊C₄	—	134	2	no	—
1204	C₂²⋊C₄	—	134	2	no	—
1205	C₂²⋊C₄	—	134	2	no	—
1206	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1207	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1208	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1209	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1210	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1211	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1212	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1213	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1214	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1215	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1216	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1217	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1218	C₄²	—	268	1	no	—
1219	C₄²	—	268	1	no	—
1220	C₄²	—	268	1	no	—
1221	C₄²	—	268	1	no	—
1222	C₄²	—	268	1	no	—
1223	C₄²	—	268	1	no	—
1224	C₄²	—	268	1	no	—
1225	C₄²	—	268	1	no	—
1226	C₄²	—	268	1	no	—
1227	C₄²	—	268	1	no	—
1228	C₄²	—	268	1	no	—
1229	C₄²	—	268	1	no	—
1230	C₄²	—	268	1	no	—
1231	C₄²	—	268	1	no	—
1232	C₄²	—	268	1	no	—
1233	C₄²	—	268	1	no	—
1234	C₄²	—	268	1	no	—
1235	C₄²	—	268	1	no	—
1236	C₄²	—	268	1	no	—
1237	C₄²	—	134	2	no	—
1238	C₄²	—	134	2	no	—
1239	C₄²	—	134	2	no	—
1240	C₄²	C₂²×Dic₆₇	1	4	yes	—
1241	C₄²	C₂²×Dic₆₇	1	4	yes	—
1242	C₄²	C₂²×Dic₆₇	1	4	yes	—
1243	C₄²	C₂²×Dic₆₇	1	4	yes	—
1244	C₂³	—	2	1	no	—
1245	C₂³	—	2	1	no	—
1246	C₂³	—	2	1	no	—
1247	C₂³	—	2	1	no	—
1248	C₂³	—	2	1	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	2	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	2	1	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	1	no	—
1256	C₂³	—	2	1	no	—
1257	C₂³	—	2	1	no	—
1258	C₂³	—	2	1	no	—
1259	C₂³	—	2	1	no	—
1260	C₂³	—	2	1	no	—
1261	C₂³	—	2	1	no	—
1262	C₂³	C₂³×Dic₆₇	1	2	yes	—
1263	C₂³	C₂³×Dic₆₇	1	2	yes	—
1264	C₂³	C₂³×Dic₆₇	1	2	yes	—
1265	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1266	Q₈	—	4	4	no	—
1267	Q₈	—	4	4	no	—
1268	Q₈	—	4	4	no	—
1269	D₄	—	4	4	no	—
1270	D₄	—	4	4	no	—
1271	D₄	—	4	4	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	4	4	no	—
1297	C₂×C₄	—	4	4	no	—
1298	C₂×C₄	—	4	4	no	—
1299	C₂×C₄	—	268	4	no	—
1300	C₂×C₄	—	268	4	no	—
1301	C₂×C₄	—	536	2	no	—
1302	C₂×C₄	—	536	2	no	—
1303	C₂×C₄	—	536	2	no	—
1304	C₂×C₄	—	536	2	no	—
1305	C₂×C₄	—	67	2	no	—
1306	C₂×C₄	—	67	2	no	—
1307	C₂×C₄	—	134	1	no	—
1308	C₂×C₄	—	134	1	no	—
1309	C₂×C₄	—	134	1	no	—
1310	C₂×C₄	—	134	1	no	—
1311	C₂×C₄	—	134	1	no	—
1312	C₂×C₄	—	134	1	no	—
1313	C₂×C₄	—	134	1	no	—
1314	C₂×C₄	—	134	1	no	—
1315	C₂×C₄	—	134	1	no	—
1316	C₂×C₄	—	134	1	no	—
1317	C₂×C₄	—	134	1	no	—
1318	C₂×C₄	—	134	1	no	—
1319	C₂×C₄	—	134	1	no	—
1320	C₂×C₄	—	134	1	no	—
1321	C₂×C₄	—	134	1	no	—
1322	C₂×C₄	—	134	1	no	—
1323	C₂×C₄	—	134	1	no	—
1324	C₂×C₄	—	134	1	no	—
1325	C₂×C₄	—	134	1	no	—
1326	C₂×C₄	—	134	1	no	—
1327	C₂×C₄	—	134	1	no	—
1328	C₂×C₄	—	134	1	no	—
1329	C₂×C₄	—	134	1	no	—
1330	C₂×C₄	—	134	1	no	—
1331	C₂×C₄	—	134	1	no	—
1332	C₂×C₄	—	134	1	no	—
1333	C₂×C₄	—	134	1	no	—
1334	C₂×C₄	—	134	1	no	—
1335	C₂×C₄	—	134	1	no	—
1336	C₂×C₄	—	134	1	no	—
1337	C₂×C₄	—	134	1	no	—
1338	C₂×C₄	—	134	1	no	—
1339	C₂×C₄	—	134	1	no	—
1340	C₂×C₄	—	134	1	no	—
1341	C₂×C₄	—	134	1	no	—
1342	C₂×C₄	—	134	1	no	—
1343	C₂×C₄	—	134	1	no	—
1344	C₂×C₄	—	134	1	no	—
1345	C₂×C₄	—	134	1	no	—
1346	C₂×C₄	—	134	1	no	—
1347	C₂×C₄	—	134	1	no	—
1348	C₂×C₄	—	134	1	no	—
1349	C₂×C₄	—	134	1	no	—
1350	C₂×C₄	—	134	1	no	—
1351	C₂×C₄	—	134	1	no	—
1352	C₂×C₄	—	134	1	no	—
1353	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1354	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1355	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1356	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1357	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1358	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1359	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1360	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1361	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1362	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1363	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1364	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1365	C₂²	—	2	2	no	—
1366	C₂²	—	2	2	no	—
1367	C₂²	—	2	2	no	—
1368	C₂²	—	2	2	no	—
1369	C₂²	—	2	2	no	—
1370	C₂²	—	2	2	no	—
1371	C₂²	—	2	2	no	—
1372	C₂²	—	2	2	no	—
1373	C₂²	—	2	2	no	—
1374	C₂²	—	4	1	no	—
1375	C₂²	—	4	1	no	—
1376	C₂²	—	4	1	no	—
1377	C₂²	—	4	1	no	—
1378	C₂²	—	4	1	no	—
1379	C₂²	—	4	1	no	—
1380	C₂²	—	4	1	no	—
1381	C₂²	—	4	1	no	—
1382	C₂²	—	4	1	no	—
1383	C₂²	—	4	1	no	—
1384	C₂²	—	4	1	no	—
1385	C₂²	—	4	1	no	—
1386	C₂²	C₂⁴×Dic₆₇	1	1	yes	characteristic
1387	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1388	C₂²	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1389	C₂²	#16864231	1	1	yes	characteristic
1390	C₂²	#16864232	1	1	yes	characteristic
1391	C₂²	#16864232	1	1	yes	characteristic
1392	C₂²	#16864233	1	1	yes	characteristic
1393	C₄	—	2	2	no	—
1394	C₄	—	2	2	no	—
1395	C₄	—	2	2	no	—
1396	C₄	—	2	2	no	—
1397	C₄	—	2	2	no	—
1398	C₄	—	2	2	no	—
1399	C₄	—	2	2	no	—
1400	C₄	—	2	2	no	—
1401	C₄	—	2	2	no	—
1402	C₄	—	2	2	no	—
1403	C₄	—	2	2	no	—
1404	C₄	—	2	2	no	—
1405	C₄	—	268	1	no	—
1406	C₄	—	268	1	no	—
1407	C₄	—	268	1	no	—
1408	C₄	—	268	1	no	—
1409	C₄	—	268	1	no	—
1410	C₄	—	268	1	no	—
1411	C₄	—	268	1	no	—
1412	C₄	—	268	1	no	—
1413	C₄	—	268	1	no	—
1414	C₄	—	268	1	no	—
1415	C₄	—	268	1	no	—
1416	C₄	—	268	1	no	—
1417	C₄	—	268	1	no	—
1418	C₄	—	268	1	no	—
1419	C₄	—	134	2	no	—
1420	C₄	—	134	2	no	—
1421	C₂	—	4	2	no	—
1422	C₂	—	4	2	no	—
1423	C₂	—	4	2	no	—
1424	C₂	#22573412	1	1	yes	characteristic
1425	C₂	H(5,𝔽₂)×Dic₆₇	1	1	yes	characteristic
1426	C₂	2₋¹⁺⁴×Dic₆₇	1	1	yes	characteristic
1427	C₂	#22574372	1	1	yes	characteristic
1428	C₂	#22574493	1	1	yes	characteristic
1429	C₂	#22574707	1	1	yes	characteristic
1430	C₂	#22574901	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator	C₂²×C₆₇	C₂⁴×C₄
Fitting	C₂×#542×C₆₇	C₂
socle, cosocle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#121×C₆₇	C₂²
hypercenter	C₂×#542	D₆₇
hypocenter	C₆₇	#34448
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

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

N	H ≅ G/N	type
1. #22563401	C₂	semidirect
2. #22563390	C₂	semidirect
3. #22563383	C₂	semidirect
4. #22563375	C₂	semidirect
5. #22563345	C₂	semidirect
6. #22563333	C₂	semidirect
7. #22563294	C₂	semidirect
8. #22563294	C₂	semidirect
9. #22563284	C₂	semidirect
10. #22563269	C₂	semidirect
11. #22563240	C₂	semidirect
12. #22563205	C₂	semidirect
13. #22563174	C₂	semidirect
14. #22563166	C₂	semidirect
15. #22563102	C₂	semidirect
16. #22563069	C₂	semidirect
17. #22563024	C₂	semidirect
18. #22563024	C₂	semidirect
19. #22563024	C₂	semidirect
20. #22563003	C₂	semidirect
21. #22562988	C₂	semidirect
22. #22562988	C₂	semidirect
24. #22562967	C₂	semidirect
25. #22562922	C₂	semidirect
27. #22562842	C₂	semidirect
28. C₂²⋊Q₈×Dic₆₇	C₂	semidirect
29. #123×Dic₆₇	C₂	semidirect
30. #22562654	C₂	semidirect
172. #542×C₆₇	C₄	semidirect
323. C₄⋊Q₈×C₆₇	C₂×C₄	semidirect
324. #126×C₆₇	C₂×C₄	semidirect
325. #126×C₆₇	C₂×C₄	semidirect
326. #124×C₆₇	C₂×C₄	semidirect
327. #124×C₆₇	C₂×C₄	semidirect
328. #124×C₆₇	C₂×C₄	semidirect
329. #123×C₆₇	C₂×C₄	semidirect
330. #123×C₆₇	C₂×C₄	semidirect
331. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
332. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
333. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
335. C₄×Q₈×C₆₇	C₂×C₄	semidirect
336. C₄×D₄×C₆₇	C₂×C₄	semidirect
337. #117×C₆₇	C₂×C₄	semidirect
747. C₆₇	#34448	semidirect
748. #542	Dic₆₇	semidirect
919. C₄⋊Q₈	C₂×Dic₆₇	semidirect
920. #126	C₂×Dic₆₇	semidirect
921. #126	C₂×Dic₆₇	semidirect
922. #124	C₂×Dic₆₇	semidirect
923. #124	C₂×Dic₆₇	semidirect
924. #124	C₂×Dic₆₇	semidirect
925. #123	C₂×Dic₆₇	semidirect
926. #123	C₂×Dic₆₇	semidirect
927. C₂²⋊Q₈	C₂×Dic₆₇	semidirect
928. C₂²⋊Q₈	C₂×Dic₆₇	semidirect
929. C₂²⋊Q₈	C₂×Dic₆₇	semidirect
933. C₄×Q₈	C₂×Dic₆₇	semidirect
936. C₄×D₄	C₂×Dic₆₇	semidirect
938. #117	C₂×Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22563401	2
#22563390	2
#22563383	2
#22563375	2
#22563345	2
#22563333	2
#22563294	2
#22563284	2
#22563269	2
#22563240	2
#22563205	2
#22563174	2
#22563166	2
#22563102	2
#22563069	2
#22563024	2
#22563003	2
#22562988	2
#22562976	2
#22562967	2
#22562922	2
#22562914	2
#22562842	2
C₂²⋊Q₈×Dic₆₇	2
#123×Dic₆₇	2
#22562654	2
C₂×#542×C₆₇	2
#34448	67