Subgroups — #31019408

Order 17152.

2202 conjugacy classes of subgroups.

The subgroup lattice has 1464 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	#22563395	C₂	1	1	yes	maximal, characteristic, complemented
3	#22563375	C₂	1	1	yes	maximal, characteristic, complemented
4	#22563357	C₂	1	1	yes	maximal, characteristic, complemented
5	#22563333	C₂	1	1	yes	maximal, characteristic, complemented
6	#22563309	C₂	1	1	yes	maximal, characteristic, complemented
7	#22563294	C₂	1	1	yes	maximal, characteristic, complemented
8	#22563261	C₂	1	1	yes	maximal, characteristic
9	#22563229	C₂	1	1	yes	maximal, characteristic
10	#22563218	C₂	1	1	yes	maximal, characteristic, complemented
11	#22563218	C₂	1	1	yes	maximal, characteristic, complemented
12	#22563205	C₂	1	1	yes	maximal, characteristic, complemented
13	#22563149	C₂	1	1	yes	maximal, characteristic, complemented
14	#22563138	C₂	1	1	yes	maximal, characteristic, complemented
15	#22563119	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₄⋊Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#22563015	C₂	1	1	yes	maximal, characteristic, complemented
18	#22563003	C₂	1	1	yes	maximal, characteristic, complemented
19	#22562988	C₂	1	1	yes	maximal, characteristic, complemented
20	#22562988	C₂	1	1	yes	maximal, characteristic, complemented
21	#22562951	C₂	1	1	yes	maximal, characteristic, complemented
22	#22562944	C₂	1	1	yes	maximal, characteristic, complemented
23	#22562893	C₂	1	1	yes	maximal, characteristic, complemented
24	#22562881	C₂	1	1	yes	maximal, characteristic, complemented
25	#22562881	C₂	1	1	yes	maximal, characteristic, complemented
26	#22562881	C₂	1	1	yes	maximal, characteristic, complemented
27	#22562812	C₂	1	1	yes	maximal, characteristic, complemented
28	#123×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
29	#123×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16863295	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#539×C₆₇	C₂	1	1	yes	maximal, characteristic
32	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic
33	C₂×D₄×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×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
37	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
38	C₂×#14524002	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄×Dic₆₇	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	#16863299	C₂²	1	1	yes	characteristic
48	#16863295	C₂²	1	1	yes	characteristic
49	#16863295	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	#16863295	C₂²	1	1	yes	characteristic
57	#16863295	C₂²	1	1	yes	characteristic
58	#16863295	C₂²	1	1	yes	characteristic
59	#16863295	C₂²	1	1	yes	characteristic
60	#16863295	C₂²	1	1	yes	characteristic
61	#16863295	C₂²	1	1	yes	characteristic
62	#16863295	C₂²	1	1	yes	characteristic
63	#16863295	C₂²	1	1	yes	characteristic
64	#16863295	C₂²	1	1	yes	characteristic
65	#16863295	C₂²	1	1	yes	characteristic
66	#16863295	C₂²	1	1	yes	characteristic
67	#16863295	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	#16863289	C₂²	1	1	yes	characteristic
81	#16863289	C₂²	1	1	yes	characteristic
82	#16863289	C₂²	1	1	yes	characteristic
83	#16863289	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	#16863282	C₂²	1	1	yes	characteristic
105	#16863282	C₂²	1	1	yes	characteristic
106	#16863282	C₂²	1	1	yes	characteristic
107	#16863282	C₂²	1	1	yes	characteristic
108	#16863282	C₂²	1	1	yes	characteristic
109	#16863282	C₂²	1	1	yes	characteristic
110	#16863282	C₂²	1	1	yes	characteristic
111	#16863282	C₂²	1	1	yes	characteristic
112	#16863276	C₂²	1	1	yes	characteristic
113	#16863276	C₂²	1	1	yes	characteristic
114	#16863276	C₂²	1	1	yes	characteristic
115	#16863276	C₂²	1	1	yes	characteristic
116	#16863276	C₂²	1	1	yes	characteristic
117	#16863276	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	#16863271	C₂²	1	1	yes	characteristic
127	#16863271	C₂²	1	1	yes	characteristic
128	#16863271	C₂²	1	1	yes	characteristic
129	#16863271	C₂²	1	1	yes	characteristic
130	#16863271	C₂²	1	1	yes	characteristic
131	#16863271	C₂²	1	1	yes	characteristic
132	#16863266	C₂²	1	1	yes	characteristic
133	#16863264	C₂²	1	1	yes	characteristic
134	#16863262	C₂²	1	1	yes	characteristic
135	#16863262	C₂²	1	1	yes	characteristic
136	#16863259	C₂²	1	1	yes	characteristic
137	#16863259	C₂²	1	1	yes	characteristic
138	#16863259	C₂²	1	1	yes	characteristic
139	#16863256	C₂²	1	1	yes	characteristic
140	#16863256	C₂²	1	1	yes	characteristic
141	#16863256	C₂²	1	1	yes	characteristic
142	#16863256	C₂²	1	1	yes	characteristic
143	#16863256	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	C₄×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	C₂²⋊C₄×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	C₂×C₆₇⋊#95	C₂²	1	1	yes	characteristic
170	C₂×C₆₇⋊#95	C₂²	1	1	yes	characteristic
171	C₂×C₆₇⋊#95	C₂²	1	1	yes	characteristic
172	#539×C₆₇	C₄	1	16	yes	complemented
173	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
174	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
175	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
176	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
177	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
178	C₂×#123×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×D₄×C₆₇	C₂²	1	1	yes	characteristic
186	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
187	C₂²×C₄⋊C₄×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	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
195	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
196	Q₈×Dic₆₇	—	4	2	no	—
197	D₄×Dic₆₇	—	4	2	no	—
198	D₄×Dic₆₇	—	4	2	no	—
199	D₄×Dic₆₇	—	4	2	no	—
200	D₄×Dic₆₇	—	4	2	no	—
201	D₄×Dic₆₇	—	4	2	no	—
202	#14524002	—	4	2	no	—
203	C₂×C₄⋊Dic₆₇	—	4	2	no	—
204	C₂×C₄⋊Dic₆₇	—	4	2	no	—
205	C₂×C₄⋊Dic₆₇	—	4	2	no	—
206	C₂×C₄⋊Dic₆₇	—	4	2	no	—
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×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊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×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
251	C₂×C₄×Dic₆₇	—	4	2	no	—
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	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
264	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
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×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₆₇	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	C₆₇⋊#95	C₂³	1	1	yes	characteristic
315	C₆₇⋊#95	C₂³	1	1	yes	characteristic
316	C₆₇⋊#95	C₂³	1	1	yes	characteristic
317	C₆₇⋊#95	C₂³	1	1	yes	characteristic
318	C₆₇⋊#95	C₂³	1	1	yes	characteristic
319	C₆₇⋊#95	C₂³	1	1	yes	characteristic
320	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
321	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
325	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
329	#126×C₆₇	C₂×C₄	1	8	yes	complemented
330	#126×C₆₇	C₂×C₄	1	8	yes	complemented
331	#125×C₆₇	C₂×C₄	1	8	yes	complemented
332	#125×C₆₇	C₂×C₄	1	8	yes	complemented
333	#123×C₆₇	C₂×C₄	1	8	yes	complemented
334	#123×C₆₇	C₂×C₄	1	8	yes	complemented
335	#123×C₆₇	C₂×C₄	1	8	yes	complemented
336	#123×C₆₇	C₂×C₄	1	8	yes	complemented
337	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
338	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
339	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
340	#121×C₆₇	C₂×C₄	1	8	yes	—
341	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
342	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
343	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	complemented
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×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
349	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
350	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
351	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
352	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
353	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
354	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
355	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
356	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
357	C₂×C₄⋊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×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
361	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
362	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
363	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
364	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
365	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
366	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
367	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
368	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
369	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
370	C₂²×Dic₆₇	—	2	2	no	—
371	C₂²×Dic₆₇	—	2	2	no	—
372	C₂²×Dic₆₇	—	2	2	no	—
373	C₂²×Dic₆₇	—	2	2	no	—
374	C₂²×Dic₆₇	—	2	2	no	—
375	C₂²×Dic₆₇	—	2	2	no	—
376	C₂²×Dic₆₇	—	2	2	no	—
377	C₂²×Dic₆₇	—	2	2	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	—	4	1	no	—
383	C₂²×Dic₆₇	—	4	1	no	—
384	C₂²×Dic₆₇	—	4	1	no	—
385	C₂²×Dic₆₇	—	4	1	no	—
386	C₂²×Dic₆₇	—	4	1	no	—
387	C₂²×Dic₆₇	—	4	1	no	—
388	C₂²×Dic₆₇	—	4	1	no	—
389	C₂²×Dic₆₇	—	4	1	no	—
390	C₂²×Dic₆₇	—	4	1	no	—
391	C₂²×Dic₆₇	—	4	1	no	—
392	C₂²×Dic₆₇	—	4	1	no	—
393	C₂²×Dic₆₇	—	4	1	no	—
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	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
409	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
410	C₄⋊Dic₆₇	—	2	2	no	—
411	C₄⋊Dic₆₇	—	2	2	no	—
412	C₄⋊Dic₆₇	—	2	2	no	—
413	C₄⋊Dic₆₇	—	2	2	no	—
414	C₄⋊Dic₆₇	—	2	2	no	—
415	C₄⋊Dic₆₇	—	2	2	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	C₄⋊Dic₆₇	—	4	1	no	—
421	C₄⋊Dic₆₇	—	4	1	no	—
422	C₄⋊Dic₆₇	—	4	1	no	—
423	C₄⋊Dic₆₇	—	4	1	no	—
424	C₄⋊Dic₆₇	—	4	1	no	—
425	C₄⋊Dic₆₇	—	4	1	no	—
426	C₄⋊Dic₆₇	—	4	1	no	—
427	C₄⋊Dic₆₇	—	4	1	no	—
428	C₄⋊Dic₆₇	—	4	1	no	—
429	C₄⋊Dic₆₇	—	4	1	no	—
430	C₄⋊Dic₆₇	—	4	1	no	—
431	C₄⋊Dic₆₇	—	4	1	no	—
432	C₄⋊Dic₆₇	—	4	1	no	—
433	C₄⋊Dic₆₇	—	4	1	no	—
434	C₄⋊Dic₆₇	—	4	1	no	—
435	C₄⋊Dic₆₇	—	4	1	no	—
436	C₄⋊Dic₆₇	—	4	1	no	—
437	C₄⋊Dic₆₇	—	4	1	no	—
438	C₂²⋊Dic₆₇	—	2	2	no	—
439	C₂²⋊Dic₆₇	—	2	2	no	—
440	C₂²⋊Dic₆₇	—	2	2	no	—
441	C₂²⋊Dic₆₇	—	2	2	no	—
442	C₂²⋊Dic₆₇	—	2	2	no	—
443	C₂²⋊Dic₆₇	—	2	2	no	—
444	C₂²⋊Dic₆₇	—	4	1	no	—
445	C₂²⋊Dic₆₇	—	4	1	no	—
446	C₂²⋊Dic₆₇	—	4	1	no	—
447	C₂²⋊Dic₆₇	—	4	1	no	—
448	C₂²⋊Dic₆₇	—	4	1	no	—
449	C₂²⋊Dic₆₇	—	4	1	no	—
450	C₂²⋊Dic₆₇	—	4	1	no	—
451	C₂²⋊Dic₆₇	—	4	1	no	—
452	C₂²⋊Dic₆₇	—	4	1	no	—
453	C₂²⋊Dic₆₇	—	4	1	no	—
454	C₄×Dic₆₇	—	2	2	no	—
455	C₄×Dic₆₇	—	2	2	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	C₄×Dic₆₇	—	4	1	no	—
461	C₄×Dic₆₇	—	4	1	no	—
462	C₄×Dic₆₇	—	4	1	no	—
463	C₄×Dic₆₇	—	4	1	no	—
464	C₄×Dic₆₇	—	4	1	no	—
465	C₄×Dic₆₇	—	4	1	no	—
466	C₄×Dic₆₇	—	4	1	no	—
467	C₄×Dic₆₇	—	4	1	no	—
468	C₄×Dic₆₇	—	4	1	no	—
469	C₄×Dic₆₇	—	4	1	no	—
470	C₄×Dic₆₇	—	4	1	no	—
471	C₄×Dic₆₇	—	4	1	no	—
472	C₄×Dic₆₇	—	4	1	no	—
473	C₄×Dic₆₇	—	4	1	no	—
474	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
475	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
476	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
477	C₂×Q₈×C₆₇	—	4	1	no	—
478	C₂×Q₈×C₆₇	—	4	1	no	—
479	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
480	C₂×D₄×C₆₇	—	2	2	no	—
481	C₂×D₄×C₆₇	—	2	2	no	—
482	C₂×D₄×C₆₇	—	2	2	no	—
483	C₂×D₄×C₆₇	—	2	2	no	—
484	C₂×D₄×C₆₇	—	4	1	no	—
485	C₂×D₄×C₆₇	—	4	1	no	—
486	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
487	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
488	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
489	C₂²×C₄×C₆₇	—	2	2	no	—
490	C₂²×C₄×C₆₇	—	2	2	no	—
491	C₂²×C₄×C₆₇	—	4	1	no	—
492	C₂²×C₄×C₆₇	—	4	1	no	—
493	C₂²×C₄×C₆₇	—	4	1	no	—
494	C₂²×C₄×C₆₇	—	4	1	no	—
495	C₂²×C₄×C₆₇	—	4	1	no	—
496	C₂²×C₄×C₆₇	—	4	1	no	—
497	C₂²×C₄×C₆₇	—	4	1	no	—
498	C₂²×C₄×C₆₇	—	4	1	no	—
499	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
500	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
501	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
502	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
503	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
504	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
507	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
510	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
511	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
512	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
513	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
514	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
515	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
516	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
517	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
518	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
519	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
520	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
521	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
522	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
523	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
524	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
525	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
526	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
527	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
528	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
529	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
530	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
531	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
532	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
533	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
534	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
535	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
536	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
537	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
538	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
539	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
540	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
541	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
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	—	2	1	no	—
547	C₂³×C₆₇	—	2	1	no	—
548	C₂³×C₆₇	—	2	1	no	—
549	C₂³×C₆₇	—	2	1	no	—
550	C₂³×C₆₇	—	2	1	no	—
551	C₂³×C₆₇	—	2	1	no	—
552	C₂³×C₆₇	—	2	1	no	—
553	C₂³×C₆₇	—	2	1	no	—
554	C₂³×C₆₇	—	2	1	no	—
555	C₂³×C₆₇	—	2	1	no	—
556	C₂³×C₆₇	—	2	1	no	—
557	C₂³×C₆₇	—	2	1	no	—
558	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
559	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
560	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
561	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
562	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
563	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
564	Q₈×C₆₇	—	4	4	no	—
565	D₄×C₆₇	—	2	8	no	—
566	D₄×C₆₇	—	2	8	no	—
567	D₄×C₆₇	—	4	4	no	—
568	C₂×C₄×C₆₇	—	2	8	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	—	2	1	no	—
581	C₂×C₄×C₆₇	—	2	1	no	—
582	C₂×C₄×C₆₇	—	2	1	no	—
583	C₂×C₄×C₆₇	—	2	1	no	—
584	C₂×C₄×C₆₇	—	2	1	no	—
585	C₂×C₄×C₆₇	—	2	1	no	—
586	C₂×C₄×C₆₇	—	2	1	no	—
587	C₂×C₄×C₆₇	—	2	1	no	—
588	C₂×C₄×C₆₇	—	2	1	no	—
589	C₂×C₄×C₆₇	—	2	1	no	—
590	C₂×C₄×C₆₇	—	2	1	no	—
591	C₂×C₄×C₆₇	—	2	1	no	—
592	C₂×C₄×C₆₇	—	2	1	no	—
593	C₂×C₄×C₆₇	—	4	4	no	—
594	C₂×C₄×C₆₇	—	4	4	no	—
595	C₂×C₄×C₆₇	—	4	4	no	—
596	C₂×C₄×C₆₇	—	4	4	no	—
597	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
598	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
599	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
600	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
601	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
602	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
603	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
604	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
605	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
606	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
607	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
608	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
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	—	2	1	no	—
642	C₂×Dic₆₇	—	2	1	no	—
643	C₂×Dic₆₇	—	2	1	no	—
644	C₂×Dic₆₇	—	2	1	no	—
645	C₂×Dic₆₇	—	2	1	no	—
646	C₂×Dic₆₇	—	2	1	no	—
647	C₂×Dic₆₇	—	2	1	no	—
648	C₂×Dic₆₇	—	2	1	no	—
649	C₂×Dic₆₇	—	2	1	no	—
650	C₂×Dic₆₇	—	2	1	no	—
651	C₂×Dic₆₇	—	2	1	no	—
652	C₂×Dic₆₇	—	2	1	no	—
653	C₂×Dic₆₇	—	2	1	no	—
654	C₂×Dic₆₇	—	2	1	no	—
655	C₂×Dic₆₇	—	4	4	no	—
656	C₂×Dic₆₇	—	4	4	no	—
657	C₂×Dic₆₇	—	8	2	no	—
658	C₂×Dic₆₇	—	8	2	no	—
659	C₂×Dic₆₇	—	8	2	no	—
660	C₂×Dic₆₇	—	8	2	no	—
661	C₂×Dic₆₇	—	8	2	no	—
662	C₂×Dic₆₇	—	8	2	no	—
663	C₂×Dic₆₇	H(5,𝔽₂)	1	2	yes	—
664	C₂×Dic₆₇	2₋¹⁺⁴	1	2	yes	—
665	C₂²×C₆₇	—	2	2	no	—
666	C₂²×C₆₇	—	2	2	no	—
667	C₂²×C₆₇	—	2	2	no	—
668	C₂²×C₆₇	—	2	2	no	—
669	C₂²×C₆₇	—	2	2	no	—
670	C₂²×C₆₇	—	2	2	no	—
671	C₂²×C₆₇	—	2	2	no	—
672	C₂²×C₆₇	—	2	2	no	—
673	C₂²×C₆₇	—	2	2	no	—
674	C₂²×C₆₇	—	2	2	no	—
675	C₂²×C₆₇	—	2	2	no	—
676	C₂²×C₆₇	—	2	2	no	—
677	C₂²×C₆₇	—	4	1	no	—
678	C₂²×C₆₇	—	4	1	no	—
679	C₂²×C₆₇	—	4	1	no	—
680	C₂²×C₆₇	—	4	1	no	—
681	C₂²×C₆₇	—	4	1	no	—
682	C₂²×C₆₇	—	4	1	no	—
683	C₂²×C₆₇	—	4	1	no	—
684	C₂²×C₆₇	—	4	1	no	—
685	C₂²×C₆₇	#520	1	4	yes	—
686	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
687	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
688	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
689	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
690	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
691	C₂²×C₆₇	#585	1	1	yes	characteristic
692	C₂²×C₆₇	#585	1	1	yes	characteristic
693	C₄×C₆₇	—	2	2	no	—
694	C₄×C₆₇	—	2	2	no	—
695	C₄×C₆₇	—	2	2	no	—
696	C₄×C₆₇	—	2	2	no	—
697	C₄×C₆₇	—	2	2	no	—
698	C₄×C₆₇	—	2	2	no	—
699	C₄×C₆₇	—	2	2	no	—
700	C₄×C₆₇	—	2	2	no	—
701	C₄×C₆₇	—	2	2	no	—
702	C₄×C₆₇	—	2	2	no	—
703	C₄×C₆₇	—	2	2	no	—
704	C₄×C₆₇	—	2	2	no	—
705	Dic₆₇	—	2	2	no	—
706	Dic₆₇	—	2	2	no	—
707	Dic₆₇	—	4	1	no	—
708	Dic₆₇	—	4	1	no	—
709	Dic₆₇	—	4	1	no	—
710	Dic₆₇	—	4	1	no	—
711	Dic₆₇	—	4	1	no	—
712	Dic₆₇	—	4	1	no	—
713	Dic₆₇	—	4	1	no	—
714	Dic₆₇	—	4	1	no	—
715	Dic₆₇	—	4	1	no	—
716	Dic₆₇	—	4	1	no	—
717	Dic₆₇	—	4	1	no	—
718	Dic₆₇	—	4	1	no	—
719	Dic₆₇	—	4	1	no	—
720	Dic₆₇	—	4	1	no	—
721	#34417	—	67	1	no	maximal, Sylow
722	C₂×C₆₇	—	2	4	no	—
723	C₂×C₆₇	—	4	2	no	—
724	C₂×C₆₇	—	4	2	no	—
725	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
726	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
728	C₂×C₆₇	#3534	1	1	yes	characteristic
729	C₂×C₆₇	#3535	1	1	yes	characteristic
730	C₂×C₆₇	#3552	1	1	yes	characteristic
731	C₂×C₆₇	#3553	1	1	yes	characteristic
732	C₂×#539	D₆₇	1	1	yes	characteristic
733	#2383	—	67	1	no	—
734	#2382	—	67	1	no	—
735	#2378	—	67	1	no	—
736	#2376	—	67	1	no	—
737	#2373	—	67	1	no	—
738	#2370	—	67	1	no	—
739	#2368	—	67	1	no	—
740	#2364	—	67	1	no	—
741	#2361	—	67	1	no	—
742	#2360	—	67	1	no	—
743	#2360	—	67	1	no	—
744	#2359	—	67	1	no	—
745	#2353	—	67	1	no	—
746	#2352	—	67	1	no	—
747	#2349	—	67	1	no	—
748	D₄×C₄⋊C₄	—	67	1	no	—
749	#2336	—	67	1	no	—
750	#2335	—	67	1	no	—
751	#2334	—	67	1	no	—
752	#2334	—	67	1	no	—
753	#2330	—	67	1	no	—
754	#2329	—	67	1	no	—
755	#2323	—	67	1	no	—
756	#2322	—	67	1	no	—
757	#2322	—	67	1	no	—
758	#2322	—	67	1	no	—
759	#2313	—	67	1	no	—
760	C₄×#123	—	67	1	no	—
761	C₄×#123	—	67	1	no	—
762	C₂×#389	—	67	1	no	—
763	C₆₇	#34417	1	1	yes	characteristic, complemented, Sylow
764	#539	Dic₆₇	1	16	yes	complemented
765	C₂×#126	C₂×D₆₇	1	1	yes	characteristic
766	C₂×#126	C₂×D₆₇	1	1	yes	characteristic
767	C₂×#125	C₂×D₆₇	1	1	yes	characteristic
768	C₂×#125	C₂×D₆₇	1	1	yes	characteristic
769	C₂×#123	C₂×D₆₇	1	1	yes	characteristic
770	C₂×#123	C₂×D₆₇	1	1	yes	characteristic
771	C₂×#123	C₂×D₆₇	1	1	yes	characteristic
772	C₂×#123	C₂×D₆₇	1	1	yes	characteristic
773	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
774	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
775	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
776	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
777	C₂×C₄×Q₈	—	67	1	no	—
778	C₂×C₄×D₄	—	67	1	no	—
779	C₂×C₄×D₄	—	67	1	no	—
780	C₂×C₄×D₄	—	67	1	no	—
781	C₂×C₄×D₄	—	67	1	no	—
782	C₂×C₄×D₄	—	67	1	no	—
783	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
784	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
785	C₂×#117	—	67	1	no	—
786	C₂²×C₄⋊C₄	—	67	1	no	—
787	C₂²×C₄⋊C₄	—	67	1	no	—
788	C₂²×C₄⋊C₄	—	67	1	no	—
789	C₂²×C₄⋊C₄	—	67	1	no	—
790	C₂²×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
791	C₂²×C₄²	—	67	1	no	—
792	#391	—	67	1	no	—
793	#391	—	67	1	no	—
794	#391	—	67	1	no	—
795	#390	—	67	1	no	—
796	#389	—	67	1	no	—
797	#389	—	67	1	no	—
798	#389	—	67	1	no	—
799	#389	—	67	1	no	—
800	#389	—	67	1	no	—
801	#389	—	67	1	no	—
802	#389	—	67	1	no	—
803	#389	—	67	1	no	—
804	#389	—	67	1	no	—
805	#389	—	67	1	no	—
806	#389	—	67	1	no	—
807	#389	—	67	1	no	—
808	#389	—	67	1	no	—
809	#389	—	67	1	no	—
810	#389	—	67	1	no	—
811	#389	—	67	1	no	—
812	#389	—	67	1	no	—
813	#389	—	67	1	no	—
814	#389	—	67	1	no	—
815	#389	—	67	1	no	—
816	#388	—	67	1	no	—
817	#388	—	67	1	no	—
818	#388	—	67	1	no	—
819	#388	—	67	1	no	—
820	#388	—	67	1	no	—
821	#388	—	67	1	no	—
822	#388	—	67	1	no	—
823	#388	—	67	1	no	—
824	#388	—	67	1	no	—
825	#388	—	67	1	no	—
826	#388	—	67	1	no	—
827	#388	—	67	1	no	—
828	#388	—	67	1	no	—
829	#388	—	67	1	no	—
830	#388	—	67	1	no	—
831	#388	—	67	1	no	—
832	#387	—	67	1	no	—
833	#387	—	67	1	no	—
834	#387	—	67	1	no	—
835	#387	—	67	1	no	—
836	#387	—	67	1	no	—
837	#387	—	67	1	no	—
838	#387	—	67	1	no	—
839	#387	—	67	1	no	—
840	#387	—	67	1	no	—
841	#387	—	67	1	no	—
842	#387	—	67	1	no	—
843	#387	—	67	1	no	—
844	#387	—	67	1	no	—
845	#387	—	67	1	no	—
846	#387	—	67	1	no	—
847	#387	—	67	1	no	—
848	#387	—	67	1	no	—
849	#387	—	67	1	no	—
850	#387	—	67	1	no	—
851	#387	—	67	1	no	—
852	#387	—	67	1	no	—
853	#387	—	67	1	no	—
854	#387	—	67	1	no	—
855	#387	—	67	1	no	—
856	#387	—	67	1	no	—
857	#387	—	67	1	no	—
858	#387	—	67	1	no	—
859	#387	—	67	1	no	—
860	#386	—	67	1	no	—
861	#386	—	67	1	no	—
862	#386	—	67	1	no	—
863	#386	—	67	1	no	—
864	#386	—	67	1	no	—
865	#386	—	67	1	no	—
866	#385	—	67	1	no	—
867	#385	—	67	1	no	—
868	#385	—	67	1	no	—
869	#385	—	67	1	no	—
870	#385	—	67	1	no	—
871	#385	—	67	1	no	—
872	#385	—	67	1	no	—
873	#385	—	67	1	no	—
874	#385	—	67	1	no	—
875	#385	—	67	1	no	—
876	#385	—	67	1	no	—
877	#385	—	67	1	no	—
878	#385	—	67	1	no	—
879	#385	—	67	1	no	—
880	#384	—	67	1	no	—
881	#383	—	67	1	no	—
882	#382	—	67	1	no	—
883	#382	—	67	1	no	—
884	#381	—	67	1	no	—
885	#381	—	67	1	no	—
886	#381	—	67	1	no	—
887	#380	—	67	1	no	—
888	#380	—	67	1	no	—
889	#380	—	67	1	no	—
890	#380	—	67	1	no	—
891	#380	—	67	1	no	—
892	C₄×C₄⋊C₄	—	67	1	no	—
893	C₄×C₄⋊C₄	—	67	1	no	—
894	C₄×C₄⋊C₄	—	67	1	no	—
895	C₄×C₄⋊C₄	—	67	1	no	—
896	C₄×C₄⋊C₄	—	67	1	no	—
897	C₄×C₄⋊C₄	—	67	1	no	—
898	C₄×C₄⋊C₄	—	67	1	no	—
899	C₄×C₄⋊C₄	—	67	1	no	—
900	C₄×C₄⋊C₄	—	67	1	no	—
901	C₄×C₄⋊C₄	—	67	1	no	—
902	C₄×C₄⋊C₄	—	67	1	no	—
903	C₄×C₂²⋊C₄	—	67	1	no	—
904	C₄×C₂²⋊C₄	—	67	1	no	—
905	C₄×C₂²⋊C₄	—	67	1	no	—
906	C₄×C₂²⋊C₄	—	67	1	no	—
907	C₄×C₂²⋊C₄	—	67	1	no	—
908	C₄×C₂²⋊C₄	—	67	1	no	—
909	C₄×C₂²⋊C₄	—	67	1	no	—
910	C₄×C₂²⋊C₄	—	67	1	no	—
911	C₄×C₂²⋊C₄	—	67	1	no	—
912	C₄×C₂²⋊C₄	—	67	1	no	—
913	C₄×C₂²⋊C₄	—	67	1	no	—
914	C₄×C₂²⋊C₄	—	67	1	no	—
915	C₄×C₂²⋊C₄	—	67	1	no	—
916	#376	—	67	1	no	—
917	C₂×#95	—	67	1	no	—
918	C₂×#95	—	67	1	no	—
919	C₂×#95	—	67	1	no	—
920	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
921	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
922	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
923	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
924	C₂³×C₄	—	67	1	no	—
925	C₂³×C₄	—	67	1	no	—
926	C₂³×C₄	—	67	1	no	—
927	C₂³×C₄	—	67	1	no	—
928	C₂³×C₄	—	67	1	no	—
929	C₂³×C₄	—	67	1	no	—
930	C₂³×C₄	—	67	1	no	—
931	C₂³×C₄	—	67	1	no	—
932	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
933	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
934	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
935	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
936	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
937	#126	C₂×Dic₆₇	1	8	yes	complemented
938	#126	C₂×Dic₆₇	1	8	yes	complemented
939	#125	C₂×Dic₆₇	1	8	yes	complemented
940	#125	C₂×Dic₆₇	1	8	yes	complemented
941	#123	C₂×Dic₆₇	1	8	yes	complemented
942	#123	C₂×Dic₆₇	1	8	yes	complemented
943	#123	C₂×Dic₆₇	1	8	yes	complemented
944	#123	C₂×Dic₆₇	1	8	yes	complemented
945	C₂²⋊Q₈	C₂×Dic₆₇	1	8	yes	complemented
946	C₂²⋊Q₈	C₂×Dic₆₇	1	8	yes	complemented
947	C₂²⋊Q₈	C₂×Dic₆₇	1	8	yes	complemented
948	#121	C₂×Dic₆₇	1	8	yes	—
949	C₄×Q₈	—	268	2	no	—
950	C₄×D₄	—	268	2	no	—
951	C₄×D₄	—	268	2	no	—
952	C₄×D₄	—	268	2	no	—
953	C₄×D₄	—	268	2	no	—
954	C₄×D₄	—	268	2	no	—
955	C₄×D₄	C₂×Dic₆₇	1	8	yes	complemented
956	C₄×D₄	C₂×Dic₆₇	1	8	yes	complemented
957	#117	—	268	2	no	—
958	C₂×C₄⋊C₄	—	268	2	no	—
959	C₂×C₄⋊C₄	—	268	2	no	—
960	C₂×C₄⋊C₄	—	268	2	no	—
961	C₂×C₄⋊C₄	—	268	2	no	—
962	C₂×C₄⋊C₄	—	67	1	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	1	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	1	no	—
972	C₂×C₄⋊C₄	—	67	1	no	—
973	C₂×C₄⋊C₄	—	67	1	no	—
974	C₂×C₄⋊C₄	—	67	1	no	—
975	C₂×C₄⋊C₄	—	67	1	no	—
976	C₂×C₄⋊C₄	—	67	1	no	—
977	C₂×C₄⋊C₄	—	67	1	no	—
978	C₂×C₄⋊C₄	—	67	1	no	—
979	C₂×C₄⋊C₄	—	67	1	no	—
980	C₂×C₄⋊C₄	—	67	1	no	—
981	C₂×C₄⋊C₄	—	67	1	no	—
982	C₂×C₄⋊C₄	—	67	1	no	—
983	C₂×C₄⋊C₄	—	67	1	no	—
984	C₂×C₄⋊C₄	—	67	1	no	—
985	C₂×C₄⋊C₄	—	67	1	no	—
986	C₂×C₄⋊C₄	—	67	1	no	—
987	C₂×C₄⋊C₄	—	67	1	no	—
988	C₂×C₄⋊C₄	—	67	1	no	—
989	C₂×C₄⋊C₄	—	67	1	no	—
990	C₂×C₄⋊C₄	C₂×Dic₆₇	1	8	yes	complemented
991	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
994	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
995	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
996	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
998	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
999	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1000	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1001	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1002	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1003	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1004	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1005	C₂×C₂²⋊C₄	—	67	1	no	—
1006	C₂×C₂²⋊C₄	—	67	1	no	—
1007	C₂×C₂²⋊C₄	—	67	1	no	—
1008	C₂×C₂²⋊C₄	—	67	1	no	—
1009	C₂×C₂²⋊C₄	—	67	1	no	—
1010	C₂×C₂²⋊C₄	—	67	1	no	—
1011	C₂×C₂²⋊C₄	—	67	1	no	—
1012	C₂×C₂²⋊C₄	—	67	1	no	—
1013	C₂×C₂²⋊C₄	—	67	1	no	—
1014	C₂×C₂²⋊C₄	—	67	1	no	—
1015	C₂×C₂²⋊C₄	—	67	1	no	—
1016	C₂×C₂²⋊C₄	—	67	1	no	—
1017	C₂×C₂²⋊C₄	—	67	1	no	—
1018	C₂×C₂²⋊C₄	—	67	1	no	—
1019	C₂×C₂²⋊C₄	—	67	1	no	—
1020	C₂×C₂²⋊C₄	—	67	1	no	—
1021	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1031	C₂×C₄²	—	268	2	no	—
1032	C₂×C₄²	—	67	1	no	—
1033	C₂×C₄²	—	67	1	no	—
1034	C₂×C₄²	—	67	1	no	—
1035	C₂×C₄²	—	67	1	no	—
1036	C₂×C₄²	—	67	1	no	—
1037	C₂×C₄²	—	67	1	no	—
1038	C₂×C₄²	—	67	1	no	—
1039	C₂×C₄²	—	67	1	no	—
1040	C₂×C₄²	—	67	1	no	—
1041	C₂×C₄²	—	67	1	no	—
1042	C₂×C₄²	—	67	1	no	—
1043	C₂×C₄²	—	67	1	no	—
1044	C₂×C₄²	—	67	1	no	—
1045	C₂×C₄²	—	67	1	no	—
1046	C₂×C₄²	—	67	1	no	—
1047	C₂×C₄²	—	67	1	no	—
1048	C₂×C₄²	—	67	1	no	—
1049	C₂×C₄²	—	67	1	no	—
1050	C₂×C₄²	—	67	1	no	—
1051	C₂×C₄²	—	67	1	no	—
1052	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1053	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
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	#95	—	67	1	no	—
1081	#95	—	67	1	no	—
1082	#95	—	67	1	no	—
1083	#95	—	67	1	no	—
1084	#95	—	67	1	no	—
1085	#95	—	67	1	no	—
1086	#95	—	67	1	no	—
1087	#95	—	67	1	no	—
1088	#95	—	67	1	no	—
1089	#95	—	67	1	no	—
1090	#95	—	67	1	no	—
1091	#95	—	67	1	no	—
1092	#95	—	67	1	no	—
1093	#95	—	67	1	no	—
1094	#95	—	67	1	no	—
1095	#95	—	67	1	no	—
1096	#95	—	67	1	no	—
1097	#95	—	67	1	no	—
1098	#95	—	67	1	no	—
1099	#95	—	67	1	no	—
1100	#95	—	67	1	no	—
1101	#95	—	67	1	no	—
1102	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1103	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1104	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1105	C₂×Q₈	—	4	1	no	—
1106	C₂×Q₈	—	4	1	no	—
1107	C₂×Q₈	C₂²×Dic₆₇	1	4	yes	—
1108	C₂×D₄	—	2	2	no	—
1109	C₂×D₄	—	2	2	no	—
1110	C₂×D₄	—	2	2	no	—
1111	C₂×D₄	—	2	2	no	—
1112	C₂×D₄	—	4	1	no	—
1113	C₂×D₄	—	4	1	no	—
1114	C₂×D₄	C₂²×Dic₆₇	1	4	yes	—
1115	C₂×D₄	C₂²×Dic₆₇	1	4	yes	—
1116	C₂×D₄	C₂²×Dic₆₇	1	4	yes	—
1117	C₂²×C₄	—	2	2	no	—
1118	C₂²×C₄	—	2	2	no	—
1119	C₂²×C₄	—	4	1	no	—
1120	C₂²×C₄	—	4	1	no	—
1121	C₂²×C₄	—	4	1	no	—
1122	C₂²×C₄	—	4	1	no	—
1123	C₂²×C₄	—	4	1	no	—
1124	C₂²×C₄	—	4	1	no	—
1125	C₂²×C₄	—	4	1	no	—
1126	C₂²×C₄	—	4	1	no	—
1127	C₂²×C₄	—	268	1	no	—
1128	C₂²×C₄	—	268	1	no	—
1129	C₂²×C₄	—	268	1	no	—
1130	C₂²×C₄	—	268	1	no	—
1131	C₂²×C₄	—	268	1	no	—
1132	C₂²×C₄	—	268	1	no	—
1133	C₂²×C₄	—	268	1	no	—
1134	C₂²×C₄	—	268	1	no	—
1135	C₂²×C₄	—	268	1	no	—
1136	C₂²×C₄	—	268	1	no	—
1137	C₂²×C₄	—	268	1	no	—
1138	C₂²×C₄	—	268	1	no	—
1139	C₂²×C₄	—	268	1	no	—
1140	C₂²×C₄	—	268	1	no	—
1141	C₂²×C₄	—	268	1	no	—
1142	C₂²×C₄	—	268	1	no	—
1143	C₂²×C₄	—	67	1	no	—
1144	C₂²×C₄	—	67	1	no	—
1145	C₂²×C₄	—	67	1	no	—
1146	C₂²×C₄	—	67	1	no	—
1147	C₂²×C₄	—	67	1	no	—
1148	C₂²×C₄	—	67	1	no	—
1149	C₂²×C₄	—	67	1	no	—
1150	C₂²×C₄	—	67	1	no	—
1151	C₂²×C₄	—	67	1	no	—
1152	C₂²×C₄	—	67	1	no	—
1153	C₂²×C₄	—	67	1	no	—
1154	C₂²×C₄	—	67	1	no	—
1155	C₂²×C₄	—	67	1	no	—
1156	C₂²×C₄	—	67	1	no	—
1157	C₂²×C₄	—	67	1	no	—
1158	C₂²×C₄	—	67	1	no	—
1159	C₂²×C₄	—	134	2	no	—
1160	C₂²×C₄	—	134	2	no	—
1161	C₂²×C₄	—	134	2	no	—
1162	C₂²×C₄	—	134	2	no	—
1163	C₂²×C₄	—	134	2	no	—
1164	C₂²×C₄	—	134	2	no	—
1165	C₂²×C₄	—	134	2	no	—
1166	C₂²×C₄	—	134	2	no	—
1167	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
1168	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
1169	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
1170	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
1171	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
1172	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1173	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1174	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1175	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1176	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1177	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1178	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1179	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1180	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1181	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1182	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1183	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1184	C₄⋊C₄	—	268	1	no	—
1185	C₄⋊C₄	—	268	1	no	—
1186	C₄⋊C₄	—	268	1	no	—
1187	C₄⋊C₄	—	268	1	no	—
1188	C₄⋊C₄	—	268	1	no	—
1189	C₄⋊C₄	—	268	1	no	—
1190	C₄⋊C₄	—	268	1	no	—
1191	C₄⋊C₄	—	268	1	no	—
1192	C₄⋊C₄	—	268	1	no	—
1193	C₄⋊C₄	—	268	1	no	—
1194	C₄⋊C₄	—	268	1	no	—
1195	C₄⋊C₄	—	268	1	no	—
1196	C₄⋊C₄	—	268	1	no	—
1197	C₄⋊C₄	—	268	1	no	—
1198	C₄⋊C₄	—	268	1	no	—
1199	C₄⋊C₄	—	268	1	no	—
1200	C₄⋊C₄	—	268	1	no	—
1201	C₄⋊C₄	—	268	1	no	—
1202	C₄⋊C₄	—	268	1	no	—
1203	C₄⋊C₄	—	268	1	no	—
1204	C₄⋊C₄	—	268	1	no	—
1205	C₄⋊C₄	—	268	1	no	—
1206	C₄⋊C₄	—	134	2	no	—
1207	C₄⋊C₄	—	134	2	no	—
1208	C₄⋊C₄	—	134	2	no	—
1209	C₄⋊C₄	—	134	2	no	—
1210	C₄⋊C₄	—	134	2	no	—
1211	C₄⋊C₄	—	134	2	no	—
1212	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1213	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1214	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1215	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1216	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1217	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1218	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1219	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1220	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1221	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1222	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1223	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1224	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1225	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1226	C₂²⋊C₄	—	268	1	no	—
1227	C₂²⋊C₄	—	268	1	no	—
1228	C₂²⋊C₄	—	268	1	no	—
1229	C₂²⋊C₄	—	268	1	no	—
1230	C₂²⋊C₄	—	268	1	no	—
1231	C₂²⋊C₄	—	268	1	no	—
1232	C₂²⋊C₄	—	268	1	no	—
1233	C₂²⋊C₄	—	268	1	no	—
1234	C₂²⋊C₄	—	268	1	no	—
1235	C₂²⋊C₄	—	268	1	no	—
1236	C₂²⋊C₄	—	134	2	no	—
1237	C₂²⋊C₄	—	134	2	no	—
1238	C₂²⋊C₄	—	134	2	no	—
1239	C₂²⋊C₄	—	134	2	no	—
1240	C₂²⋊C₄	—	134	2	no	—
1241	C₂²⋊C₄	—	134	2	no	—
1242	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1243	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1244	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1245	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1246	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1247	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1248	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1249	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1250	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1251	C₂²⋊C₄	C₂²×Dic₆₇	1	4	yes	—
1252	C₄²	—	268	1	no	—
1253	C₄²	—	268	1	no	—
1254	C₄²	—	268	1	no	—
1255	C₄²	—	268	1	no	—
1256	C₄²	—	268	1	no	—
1257	C₄²	—	268	1	no	—
1258	C₄²	—	268	1	no	—
1259	C₄²	—	268	1	no	—
1260	C₄²	—	268	1	no	—
1261	C₄²	—	268	1	no	—
1262	C₄²	—	268	1	no	—
1263	C₄²	—	268	1	no	—
1264	C₄²	—	268	1	no	—
1265	C₄²	—	268	1	no	—
1266	C₄²	—	268	1	no	—
1267	C₄²	—	268	1	no	—
1268	C₄²	—	268	1	no	—
1269	C₄²	—	268	1	no	—
1270	C₄²	—	134	2	no	—
1271	C₄²	—	134	2	no	—
1272	C₄²	C₂²×Dic₆₇	1	4	yes	—
1273	C₄²	C₂²×Dic₆₇	1	4	yes	—
1274	C₂³	—	2	1	no	—
1275	C₂³	—	2	1	no	—
1276	C₂³	—	2	1	no	—
1277	C₂³	—	2	1	no	—
1278	C₂³	—	2	1	no	—
1279	C₂³	—	2	1	no	—
1280	C₂³	—	2	1	no	—
1281	C₂³	—	2	1	no	—
1282	C₂³	—	2	1	no	—
1283	C₂³	—	2	1	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	1	no	—
1290	C₂³	C₂³×Dic₆₇	1	2	yes	—
1291	C₂³	C₂³×Dic₆₇	1	2	yes	—
1292	C₂³	C₂³×Dic₆₇	1	2	yes	—
1293	C₂³	#14524089	1	2	yes	—
1294	C₂³	#14524090	1	2	yes	—
1295	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1296	Q₈	—	4	4	no	—
1297	D₄	—	2	8	no	—
1298	D₄	—	2	8	no	—
1299	D₄	—	4	4	no	—
1300	C₂×C₄	—	2	8	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	4	4	no	—
1326	C₂×C₄	—	4	4	no	—
1327	C₂×C₄	—	4	4	no	—
1328	C₂×C₄	—	4	4	no	—
1329	C₂×C₄	—	268	4	no	—
1330	C₂×C₄	—	268	4	no	—
1331	C₂×C₄	—	536	2	no	—
1332	C₂×C₄	—	536	2	no	—
1333	C₂×C₄	—	536	2	no	—
1334	C₂×C₄	—	536	2	no	—
1335	C₂×C₄	—	536	2	no	—
1336	C₂×C₄	—	536	2	no	—
1337	C₂×C₄	—	67	2	no	—
1338	C₂×C₄	—	67	2	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	—	134	1	no	—
1354	C₂×C₄	—	134	1	no	—
1355	C₂×C₄	—	134	1	no	—
1356	C₂×C₄	—	134	1	no	—
1357	C₂×C₄	—	134	1	no	—
1358	C₂×C₄	—	134	1	no	—
1359	C₂×C₄	—	134	1	no	—
1360	C₂×C₄	—	134	1	no	—
1361	C₂×C₄	—	134	1	no	—
1362	C₂×C₄	—	134	1	no	—
1363	C₂×C₄	—	134	1	no	—
1364	C₂×C₄	—	134	1	no	—
1365	C₂×C₄	—	134	1	no	—
1366	C₂×C₄	—	134	1	no	—
1367	C₂×C₄	—	134	1	no	—
1368	C₂×C₄	—	134	1	no	—
1369	C₂×C₄	—	134	1	no	—
1370	C₂×C₄	—	134	1	no	—
1371	C₂×C₄	—	134	1	no	—
1372	C₂×C₄	—	134	1	no	—
1373	C₂×C₄	—	134	1	no	—
1374	C₂×C₄	—	134	1	no	—
1375	C₂×C₄	—	134	1	no	—
1376	C₂×C₄	—	134	1	no	—
1377	C₂×C₄	—	134	1	no	—
1378	C₂×C₄	—	134	1	no	—
1379	C₂×C₄	—	134	1	no	—
1380	C₂×C₄	—	134	1	no	—
1381	C₂×C₄	—	134	1	no	—
1382	C₂×C₄	—	134	1	no	—
1383	C₂×C₄	—	134	1	no	—
1384	C₂×C₄	—	134	1	no	—
1385	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1386	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1387	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1388	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1389	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1390	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1391	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1392	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1393	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1394	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1395	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1396	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1397	C₂²	—	2	2	no	—
1398	C₂²	—	2	2	no	—
1399	C₂²	—	2	2	no	—
1400	C₂²	—	2	2	no	—
1401	C₂²	—	2	2	no	—
1402	C₂²	—	2	2	no	—
1403	C₂²	—	2	2	no	—
1404	C₂²	—	2	2	no	—
1405	C₂²	—	2	2	no	—
1406	C₂²	—	2	2	no	—
1407	C₂²	—	2	2	no	—
1408	C₂²	—	2	2	no	—
1409	C₂²	—	4	1	no	—
1410	C₂²	—	4	1	no	—
1411	C₂²	—	4	1	no	—
1412	C₂²	—	4	1	no	—
1413	C₂²	—	4	1	no	—
1414	C₂²	—	4	1	no	—
1415	C₂²	—	4	1	no	—
1416	C₂²	—	4	1	no	—
1417	C₂²	#16863879	1	4	yes	—
1418	C₂²	C₂⁴×Dic₆₇	1	1	yes	characteristic
1419	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1420	C₂²	C₂×#14524089	1	1	yes	characteristic
1421	C₂²	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1422	C₂²	C₂×#14524090	1	1	yes	characteristic
1423	C₂²	#16864231	1	1	yes	characteristic
1424	C₂²	#16864233	1	1	yes	characteristic
1425	C₄	—	2	2	no	—
1426	C₄	—	2	2	no	—
1427	C₄	—	2	2	no	—
1428	C₄	—	2	2	no	—
1429	C₄	—	2	2	no	—
1430	C₄	—	2	2	no	—
1431	C₄	—	2	2	no	—
1432	C₄	—	2	2	no	—
1433	C₄	—	2	2	no	—
1434	C₄	—	2	2	no	—
1435	C₄	—	2	2	no	—
1436	C₄	—	2	2	no	—
1437	C₄	—	268	1	no	—
1438	C₄	—	268	1	no	—
1439	C₄	—	268	1	no	—
1440	C₄	—	268	1	no	—
1441	C₄	—	268	1	no	—
1442	C₄	—	268	1	no	—
1443	C₄	—	268	1	no	—
1444	C₄	—	268	1	no	—
1445	C₄	—	268	1	no	—
1446	C₄	—	268	1	no	—
1447	C₄	—	268	1	no	—
1448	C₄	—	268	1	no	—
1449	C₄	—	268	1	no	—
1450	C₄	—	268	1	no	—
1451	C₄	—	134	2	no	—
1452	C₄	—	134	2	no	—
1453	C₂	—	2	4	no	—
1454	C₂	—	4	2	no	—
1455	C₂	—	4	2	no	—
1456	C₂	C₂×#16863879	1	1	yes	characteristic
1457	C₂	H(5,𝔽₂)×Dic₆₇	1	1	yes	characteristic
1458	C₂	2₋¹⁺⁴×Dic₆₇	1	1	yes	characteristic
1459	C₂	#22574397	1	1	yes	characteristic
1460	C₂	#22574416	1	1	yes	characteristic
1461	C₂	#22574642	1	1	yes	characteristic
1462	C₂	#22574659	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator	C₂²×C₆₇	C₂⁴×C₄
Fitting	C₂×#539×C₆₇	C₂
socle, cosocle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#121×C₆₇	C₂²
hypercenter	C₂×#539	D₆₇
hypocenter	C₆₇	#34417
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#539

Complements

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

N	H ≅ G/N	type
1. #22563401	C₂	semidirect
2. #22563395	C₂	semidirect
3. #22563375	C₂	semidirect
4. #22563357	C₂	semidirect
5. #22563333	C₂	semidirect
6. #22563309	C₂	semidirect
7. #22563294	C₂	semidirect
10. #22563218	C₂	semidirect
11. #22563218	C₂	semidirect
12. #22563205	C₂	semidirect
13. #22563149	C₂	semidirect
14. #22563138	C₂	semidirect
15. #22563119	C₂	semidirect
16. D₄×C₄⋊Dic₆₇	C₂	semidirect
17. #22563015	C₂	semidirect
18. #22563003	C₂	semidirect
19. #22562988	C₂	semidirect
20. #22562988	C₂	semidirect
21. #22562951	C₂	semidirect
22. #22562944	C₂	semidirect
23. #22562893	C₂	semidirect
24. #22562881	C₂	semidirect
25. #22562881	C₂	semidirect
26. #22562881	C₂	semidirect
27. #22562812	C₂	semidirect
28. #123×Dic₆₇	C₂	semidirect
29. #123×Dic₆₇	C₂	semidirect
30. C₂×#16863295	C₂	semidirect
172. #539×C₆₇	C₄	semidirect
329. #126×C₆₇	C₂×C₄	semidirect
330. #126×C₆₇	C₂×C₄	semidirect
331. #125×C₆₇	C₂×C₄	semidirect
332. #125×C₆₇	C₂×C₄	semidirect
333. #123×C₆₇	C₂×C₄	semidirect
334. #123×C₆₇	C₂×C₄	semidirect
335. #123×C₆₇	C₂×C₄	semidirect
336. #123×C₆₇	C₂×C₄	semidirect
337. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
338. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
339. C₂²⋊Q₈×C₆₇	C₂×C₄	semidirect
341. C₄×D₄×C₆₇	C₂×C₄	semidirect
342. C₄×D₄×C₆₇	C₂×C₄	semidirect
343. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
763. C₆₇	#34417	semidirect
764. #539	Dic₆₇	semidirect
937. #126	C₂×Dic₆₇	semidirect
938. #126	C₂×Dic₆₇	semidirect
939. #125	C₂×Dic₆₇	semidirect
940. #125	C₂×Dic₆₇	semidirect
941. #123	C₂×Dic₆₇	semidirect
942. #123	C₂×Dic₆₇	semidirect
943. #123	C₂×Dic₆₇	semidirect
944. #123	C₂×Dic₆₇	semidirect
945. C₂²⋊Q₈	C₂×Dic₆₇	semidirect
946. C₂²⋊Q₈	C₂×Dic₆₇	semidirect
947. C₂²⋊Q₈	C₂×Dic₆₇	semidirect
955. C₄×D₄	C₂×Dic₆₇	semidirect
956. C₄×D₄	C₂×Dic₆₇	semidirect
990. C₂×C₄⋊C₄	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
#22563395	2
#22563375	2
#22563357	2
#22563333	2
#22563309	2
#22563294	2
#22563261	2
#22563229	2
#22563218	2
#22563205	2
#22563149	2
#22563138	2
#22563119	2
D₄×C₄⋊Dic₆₇	2
#22563015	2
#22563003	2
#22562988	2
#22562951	2
#22562944	2
#22562893	2
#22562881	2
#22562812	2
#123×Dic₆₇	2
C₂×#16863295	2
C₂×#539×C₆₇	2
#34417	67