Subgroups — #31720495

Order 17152.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569223	C₂	1	2	yes	maximal, complemented
2	#22569214	C₂	1	2	yes	maximal, complemented
3	#22569205	C₂	1	2	yes	maximal, complemented
4	#22569205	C₂	1	2	yes	maximal, complemented
5	#22569196	C₂	1	2	yes	maximal, complemented
6	#22569196	C₂	1	2	yes	maximal, complemented
7	#22569185	C₂	1	2	yes	maximal, complemented
8	#22569176	C₂	1	2	yes	maximal, complemented
9	#22569158	C₂	1	1	yes	maximal, characteristic, complemented
10	#22569150	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
12	#22568936	C₂	1	1	yes	maximal, characteristic, complemented
13	#22568936	C₂	1	1	yes	maximal, characteristic, complemented
14	#22568913	C₂	1	1	yes	maximal, characteristic, complemented
15	#22568904	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16863468	C₂	1	1	yes	maximal, characteristic, complemented
17	#22568875	C₂	1	1	yes	maximal, characteristic, complemented
18	#22568867	C₂	1	1	yes	maximal, characteristic, complemented
19	#22568867	C₂	1	1	yes	maximal, characteristic, complemented
20	#22568637	C₂	1	1	yes	maximal, characteristic, complemented
21	#22568628	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863352	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic
24	C₂×#14524050	C₂²	1	1	yes	characteristic
25	C₂×#14524050	C₂²	1	1	yes	characteristic
26	C₂²×#11761612	C₂²	1	1	yes	characteristic
27	C₂²×#11761612	C₂²	1	1	yes	characteristic
28	C₂²×#11761612	C₂²	1	1	yes	characteristic
29	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
30	#16863527	C₂²	1	2	yes	complemented
31	#16863527	C₂²	1	2	yes	complemented
32	#16863527	C₂²	1	2	yes	complemented
33	#16863527	C₂²	1	2	yes	complemented
34	#16863527	C₂²	1	2	yes	complemented
35	#16863527	C₂²	1	2	yes	complemented
36	#16863527	C₂²	1	2	yes	complemented
37	Q₈×C₆₇⋊C₈	C₂²	1	2	yes	complemented
38	#16863474	C₂²	1	2	yes	—
39	#16863474	C₂²	1	2	yes	complemented
40	#16863474	C₂²	1	2	yes	complemented
41	#16863474	C₂²	1	2	yes	complemented
42	#16863474	C₂²	1	2	yes	complemented
43	#16863468	C₂²	1	1	yes	characteristic
44	#16863468	C₂²	1	2	yes	—
45	#16863468	C₂²	1	1	yes	characteristic
46	#16863468	C₂²	1	1	yes	characteristic
47	#16863468	C₂²	1	1	yes	characteristic
48	#16863468	C₂²	1	1	yes	characteristic
49	#16863468	C₂²	1	1	yes	characteristic
50	#16863468	C₂²	1	1	yes	characteristic
51	#16863468	C₂²	1	1	yes	characteristic
52	#16863468	C₂²	1	2	yes	—
53	#16863468	C₂²	1	2	yes	complemented
54	#16863468	C₂²	1	2	yes	complemented
55	#16863468	C₂²	1	2	yes	complemented
56	#16863468	C₂²	1	2	yes	complemented
57	#16863468	C₂²	1	2	yes	complemented
58	#16863468	C₂²	1	2	yes	complemented
59	#16863468	C₂²	1	2	yes	complemented
60	#16863468	C₂²	1	2	yes	complemented
61	D₄×C₆₇⋊C₈	C₂²	1	2	yes	—
62	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
63	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
64	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
65	D₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
66	#16863457	C₂²	1	2	yes	complemented
67	#16863457	C₂²	1	2	yes	complemented
68	#16863457	C₂²	1	2	yes	complemented
69	#16863457	C₂²	1	2	yes	complemented
70	#16863457	C₂²	1	2	yes	complemented
71	#16863457	C₂²	1	2	yes	complemented
72	#16863453	C₂²	1	2	yes	complemented
73	#16863453	C₂²	1	2	yes	complemented
74	#16863453	C₂²	1	2	yes	complemented
75	#16863449	C₂²	1	2	yes	complemented
76	#16863449	C₂²	1	2	yes	complemented
77	#16863449	C₂²	1	2	yes	complemented
78	#16863423	C₂²	1	1	yes	characteristic
79	#16863423	C₂²	1	1	yes	characteristic
80	#16863423	C₂²	1	1	yes	characteristic
81	#16863423	C₂²	1	1	yes	characteristic
82	#16863420	C₂²	1	1	yes	characteristic
83	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
84	#16863363	C₂²	1	1	yes	characteristic
85	#16863363	C₂²	1	1	yes	characteristic
86	#16863360	C₂²	1	1	yes	characteristic
87	#16863360	C₂²	1	1	yes	characteristic
88	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
89	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
90	#16863352	C₂²	1	1	yes	characteristic
91	#16863352	C₂²	1	1	yes	characteristic
92	#16863352	C₂²	1	1	yes	characteristic
93	#16863352	C₂²	1	1	yes	characteristic
94	#16863352	C₂²	1	1	yes	characteristic
95	#16863352	C₂²	1	1	yes	characteristic
96	#16863352	C₂²	1	1	yes	characteristic
97	#16863352	C₂²	1	1	yes	characteristic
98	#16863352	C₂²	1	2	yes	complemented
99	#16863352	C₂²	1	2	yes	complemented
100	#16863352	C₂²	1	2	yes	complemented
101	#16863352	C₂²	1	2	yes	complemented
102	#16863352	C₂²	1	2	yes	complemented
103	#16863352	C₂²	1	2	yes	complemented
104	C₄×#11761612	C₂²	1	1	yes	characteristic
105	C₄×#11761612	C₂²	1	2	yes	complemented
106	C₄×#11761612	C₂²	1	2	yes	complemented
107	C₄×#11761612	C₂²	1	2	yes	complemented
108	C₂×#14523954	C₂²	1	1	yes	characteristic
109	C₂×#14523954	C₂²	1	2	yes	complemented
110	C₂×#14523954	C₂²	1	2	yes	complemented
111	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	complemented
112	#556×C₆₇	C₄	1	1	yes	characteristic
113	#555×C₆₇	C₄	1	1	yes	characteristic
114	#554×C₆₇	C₄	1	1	yes	characteristic
115	#553×C₆₇	C₄	1	1	yes	characteristic
116	#553×C₆₇	C₄	1	1	yes	characteristic
117	#552×C₆₇	C₄	1	1	yes	characteristic
118	#552×C₆₇	C₄	1	1	yes	characteristic
119	#552×C₆₇	C₄	1	2	yes	—
120	#551×C₆₇	C₄	1	2	yes	—
121	#551×C₆₇	C₄	1	2	yes	—
122	#547×C₆₇	C₄	1	1	yes	characteristic
123	#546×C₆₇	C₄	1	2	yes	—
124	#533×C₆₇	C₂²	1	1	yes	characteristic
125	#529×C₆₇	C₂²	1	2	yes	—
126	#529×C₆₇	C₂²	1	2	yes	—
127	#529×C₆₇	C₂²	1	2	yes	—
128	#525×C₆₇	C₂²	1	1	yes	characteristic
129	#525×C₆₇	C₂²	1	1	yes	characteristic
130	C₄×#41×C₆₇	C₂²	1	2	yes	—
131	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
132	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
134	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
135	#14524050	—	2	4	no	—
136	#14524050	—	2	4	no	—
137	C₂×#11761612	—	2	4	no	—
138	C₂×#11761612	—	2	4	no	—
139	C₂×#11761612	—	2	4	no	—
140	C₂×#11761612	C₂³	1	1	yes	characteristic
141	C₂×#11761612	C₂³	1	1	yes	characteristic
142	C₂×#11761612	C₂³	1	1	yes	characteristic
143	C₂×#11761612	C₂³	1	2	yes	—
144	C₂×#11761612	C₂³	1	2	yes	—
145	C₂×#11761612	C₂³	1	2	yes	—
146	C₂×#11761612	C₂³	1	1	yes	characteristic
147	C₂×#11761612	C₂³	1	1	yes	characteristic
148	C₂×#11761612	C₂³	1	1	yes	characteristic
149	C₂×#11761612	C₂³	1	1	yes	characteristic
150	C₂×#11761612	C₂³	1	2	yes	—
151	C₂×#11761612	C₂³	1	1	yes	characteristic
152	C₂²×C₆₇⋊C₈	—	2	4	no	—
153	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
155	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
156	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
157	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
158	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
159	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
161	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
162	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
163	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
164	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
165	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
166	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
167	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
168	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
169	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
170	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
171	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
172	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
173	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
174	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
175	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
176	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
177	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
178	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
179	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
180	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
181	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
182	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
183	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
184	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
185	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
186	C₂²⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
187	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
188	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
189	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
190	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
191	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
192	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
193	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
194	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
195	#14523954	C₂³	1	1	yes	characteristic
196	#14523954	C₂³	1	1	yes	characteristic
197	#14523954	C₂³	1	1	yes	characteristic
198	#14523954	C₂³	1	1	yes	characteristic
199	#14523954	C₂³	1	2	yes	—
200	#14523954	C₂³	1	2	yes	—
201	#14523954	C₂³	1	2	yes	—
202	#14523954	C₂³	1	2	yes	—
203	#14523954	C₂³	1	2	yes	—
204	#14523954	C₂³	1	2	yes	—
205	#14523954	C₂³	1	2	yes	—
206	#14523954	C₂³	1	2	yes	—
207	#14523954	C₂³	1	2	yes	—
208	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
209	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
210	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
211	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
212	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
213	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
214	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
215	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
216	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
217	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
218	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
220	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
223	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
224	#126×C₆₇	C₂×C₄	1	2	yes	—
225	#126×C₆₇	C₂×C₄	1	2	yes	—
226	#126×C₆₇	C₂×C₄	1	2	yes	—
227	#126×C₆₇	C₂×C₄	1	2	yes	—
228	#126×C₆₇	C₂×C₄	1	2	yes	—
229	#126×C₆₇	C₂×C₄	1	2	yes	—
230	#125×C₆₇	C₂×C₄	1	2	yes	—
231	#125×C₆₇	C₂×C₄	1	2	yes	—
232	#125×C₆₇	C₂×C₄	1	2	yes	—
233	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
234	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
235	#124×C₆₇	C₂×C₄	1	2	yes	—
236	#124×C₆₇	C₂×C₄	1	2	yes	—
237	#124×C₆₇	C₂×C₄	1	2	yes	—
238	#123×C₆₇	C₂×C₄	1	2	yes	—
239	#123×C₆₇	C₂×C₄	1	2	yes	—
240	#123×C₆₇	C₂×C₄	1	2	yes	—
241	#123×C₆₇	C₂×C₄	1	2	yes	—
242	#123×C₆₇	C₂×C₄	1	2	yes	—
243	#123×C₆₇	C₂×C₄	1	2	yes	—
244	#123×C₆₇	C₂×C₄	1	2	yes	—
245	#123×C₆₇	C₂×C₄	1	2	yes	—
246	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
247	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
248	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
249	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
250	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
251	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
252	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
253	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
254	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
255	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
256	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
257	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
258	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
259	#121×C₆₇	C₂×C₄	1	2	yes	—
260	#121×C₆₇	C₂×C₄	1	2	yes	—
261	#121×C₆₇	C₂×C₄	1	2	yes	—
262	#120×C₆₇	C₂×C₄	1	2	yes	—
263	#120×C₆₇	C₂×C₄	1	2	yes	—
264	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
265	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
266	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
267	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
268	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
269	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
270	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
271	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
272	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
273	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
274	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
275	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
276	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
277	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
278	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
279	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
280	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₆₇	C₂³	1	2	yes	—
285	C₄×D₄×C₆₇	C₂³	1	2	yes	—
286	C₄×D₄×C₆₇	C₂³	1	2	yes	—
287	C₄×D₄×C₆₇	C₂³	1	2	yes	—
288	#117×C₆₇	C₂×C₄	1	2	yes	—
289	#117×C₆₇	C₂×C₄	1	2	yes	—
290	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
291	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
292	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
293	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
294	#117×C₆₇	C₂×C₄	1	2	yes	—
295	#117×C₆₇	C₂×C₄	1	2	yes	—
296	#117×C₆₇	C₂×C₄	1	2	yes	—
297	#117×C₆₇	C₂³	1	1	yes	characteristic
298	#117×C₆₇	C₂³	1	1	yes	characteristic
299	#117×C₆₇	C₂³	1	1	yes	characteristic
300	#117×C₆₇	C₂³	1	2	yes	—
301	#117×C₆₇	C₂³	1	2	yes	—
302	#117×C₆₇	C₂³	1	2	yes	—
303	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
305	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
306	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
309	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
310	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
312	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
313	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
314	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
315	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
316	#11761612	—	2	2	no	—
317	#11761612	—	2	2	no	—
318	#11761612	—	2	2	no	—
319	#11761612	—	2	2	no	—
320	#11761612	—	2	2	no	—
321	#11761612	—	2	4	no	—
322	#11761612	—	2	4	no	—
323	#11761612	—	2	2	no	—
324	#11761612	—	2	2	no	—
325	#11761612	—	2	4	no	—
326	#11761612	—	2	4	no	—
327	#11761612	#41	1	4	yes	complemented
328	C₂×C₆₇⋊C₈	—	2	2	no	—
329	C₂×C₆₇⋊C₈	—	2	2	no	—
330	C₂×C₆₇⋊C₈	—	2	2	no	—
331	C₂×C₆₇⋊C₈	—	2	2	no	—
332	C₂×C₆₇⋊C₈	—	2	2	no	—
333	C₂×C₆₇⋊C₈	—	2	2	no	—
334	C₂×C₆₇⋊C₈	—	2	2	no	—
335	C₂×C₆₇⋊C₈	—	2	4	no	—
336	C₂×C₆₇⋊C₈	—	2	4	no	—
337	C₂×C₆₇⋊C₈	—	2	4	no	—
338	C₂×C₆₇⋊C₈	—	2	4	no	—
339	C₂×C₆₇⋊C₈	#41	1	4	yes	complemented
340	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
341	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
342	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
343	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
344	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
345	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
346	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
347	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
348	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
350	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
351	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
352	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
353	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
354	#41×C₆₇	—	2	2	no	—
355	#41×C₆₇	—	2	2	no	—
356	#41×C₆₇	—	4	4	no	—
357	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
358	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
359	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
360	C₂×D₄×C₆₇	—	4	2	no	—
361	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
362	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
363	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
364	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
365	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
366	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
367	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
368	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
369	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
370	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
371	C₂²×C₄×C₆₇	—	2	2	no	—
372	C₂²×C₄×C₆₇	—	2	2	no	—
373	C₂²×C₄×C₆₇	—	2	2	no	—
374	C₂²×C₄×C₆₇	—	2	2	no	—
375	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
376	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
378	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
379	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
382	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
383	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
384	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
385	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
386	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
388	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
389	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
392	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
396	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
403	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
405	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
411	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
418	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
419	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
420	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
421	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
423	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
428	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
431	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
432	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
433	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
435	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
443	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
444	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
446	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
447	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
448	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
449	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
450	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
451	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
452	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
453	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
454	C₄²×C₆₇	C₂⁴	1	2	yes	—
455	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₄²×C₆₇	C₂⁴	1	2	yes	—
458	C₄²×C₆₇	C₂⁴	1	2	yes	—
459	C₂³×C₆₇	—	2	2	no	—
460	C₂³×C₆₇	—	2	2	no	—
461	C₂³×C₆₇	—	2	2	no	—
462	C₂³×C₆₇	—	4	1	no	—
463	C₂³×C₆₇	—	4	1	no	—
464	C₂³×C₆₇	—	4	1	no	—
465	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
466	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
467	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
468	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
469	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
470	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
471	Q₈×C₆₇	—	2	2	no	—
472	Q₈×C₆₇	—	4	2	no	—
473	Q₈×C₆₇	—	4	2	no	—
474	D₄×C₆₇	—	2	4	no	—
475	D₄×C₆₇	—	2	2	no	—
476	D₄×C₆₇	—	2	2	no	—
477	D₄×C₆₇	—	2	4	no	—
478	D₄×C₆₇	—	2	2	no	—
479	D₄×C₆₇	—	4	1	no	—
480	D₄×C₆₇	—	4	1	no	—
481	D₄×C₆₇	—	4	2	no	—
482	D₄×C₆₇	—	4	2	no	—
483	D₄×C₆₇	—	4	2	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	4	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	2	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	2	no	—
501	C₂×C₄×C₆₇	—	4	2	no	—
502	C₂×C₄×C₆₇	—	4	2	no	—
503	C₂×C₄×C₆₇	—	4	2	no	—
504	C₂×C₄×C₆₇	—	4	1	no	—
505	C₂×C₄×C₆₇	—	4	1	no	—
506	C₂×C₄×C₆₇	—	4	2	no	—
507	C₂×C₄×C₆₇	—	4	2	no	—
508	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
509	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
510	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
511	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
512	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
513	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
514	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
515	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
517	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
518	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
519	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
520	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
522	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
523	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
525	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
526	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
527	C₆₇⋊C₈	—	2	1	no	—
528	C₆₇⋊C₈	—	2	1	no	—
529	C₆₇⋊C₈	—	2	1	no	—
530	C₆₇⋊C₈	—	2	1	no	—
531	C₆₇⋊C₈	—	2	1	no	—
532	C₆₇⋊C₈	—	2	1	no	—
533	C₆₇⋊C₈	—	2	2	no	—
534	C₆₇⋊C₈	—	2	2	no	—
535	C₆₇⋊C₈	—	2	2	no	—
536	C₆₇⋊C₈	C₂×#41	1	2	yes	—
537	C₆₇⋊C₈	C₂×#41	1	4	yes	—
538	C₆₇⋊C₈	C₂×#41	1	2	yes	—
539	C₂²×C₆₇	—	2	1	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	2	1	no	—
542	C₂²×C₆₇	—	2	1	no	—
543	C₂²×C₆₇	—	2	1	no	—
544	C₂²×C₆₇	—	2	1	no	—
545	C₂²×C₆₇	—	2	1	no	—
546	C₂²×C₆₇	—	2	2	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	2	1	no	—
552	C₂²×C₆₇	—	2	2	no	—
553	C₂²×C₆₇	—	2	1	no	—
554	C₂²×C₆₇	—	2	1	no	—
555	C₂²×C₆₇	—	4	4	no	—
556	C₂²×C₆₇	—	8	2	no	—
557	C₂²×C₆₇	C₄×#41	1	2	yes	—
558	C₂²×C₆₇	#568	1	2	yes	—
559	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
560	C₄×C₆₇	—	2	1	no	—
561	C₄×C₆₇	—	2	1	no	—
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	1	no	—
564	C₄×C₆₇	—	2	2	no	—
565	C₄×C₆₇	—	2	2	no	—
566	C₄×C₆₇	—	2	2	no	—
567	C₄×C₆₇	—	2	1	no	—
568	C₄×C₆₇	—	2	1	no	—
569	C₄×C₆₇	—	2	2	no	—
570	C₄×C₆₇	—	2	1	no	—
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	2	2	no	—
574	C₄×C₆₇	—	2	1	no	—
575	C₄×C₆₇	C₄×#41	1	2	yes	—
576	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
577	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
578	#60216	—	67	1	no	maximal, Sylow
579	C₂×C₆₇	—	2	2	no	—
580	C₂×C₆₇	—	2	2	no	—
581	C₂×C₆₇	—	4	2	no	—
582	C₂×C₆₇	—	4	1	no	—
583	C₂×C₆₇	—	4	1	no	—
584	C₂×C₆₇	—	4	1	no	—
585	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
586	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
587	C₂×C₆₇	#3573	1	1	yes	characteristic
588	#3475	D₆₇	1	1	yes	characteristic
589	#2970	—	67	2	no	—
590	#2969	—	67	2	no	—
591	#2968	—	67	2	no	—
592	#2968	—	67	2	no	—
593	#2967	—	67	2	no	—
594	#2967	—	67	2	no	—
595	#2966	—	67	2	no	—
596	#2965	—	67	2	no	—
597	#2962	—	67	1	no	—
598	#2961	—	67	1	no	—
599	D₄×M₁₆	—	67	1	no	—
600	#2933	—	67	1	no	—
601	#2933	—	67	1	no	—
602	#2930	—	67	1	no	—
603	#2929	—	67	1	no	—
604	C₂×#435	—	67	1	no	—
605	#2925	—	67	1	no	—
606	#2924	—	67	1	no	—
607	#2924	—	67	1	no	—
608	#2875	—	67	1	no	—
609	#2873	—	67	1	no	—
610	C₂×#405	—	67	1	no	—
611	C₆₇	#60216	1	1	yes	characteristic, complemented, Sylow
612	C₂×#131	—	67	1	no	—
613	C₂×#131	—	67	1	no	—
614	C₂²×M₁₆	—	67	1	no	—
615	C₂²×M₁₆	—	67	1	no	—
616	C₂²×M₁₆	—	67	1	no	—
617	C₂³×C₈	—	67	1	no	—
618	#556	Dic₆₇	1	1	yes	characteristic
619	#555	Dic₆₇	1	1	yes	characteristic
620	#554	Dic₆₇	1	1	yes	characteristic
621	#553	Dic₆₇	1	1	yes	characteristic
622	#553	Dic₆₇	1	1	yes	characteristic
623	#552	Dic₆₇	1	1	yes	characteristic
624	#552	Dic₆₇	1	1	yes	characteristic
625	#552	Dic₆₇	1	2	yes	—
626	#551	Dic₆₇	1	2	yes	—
627	#551	Dic₆₇	1	2	yes	—
628	#547	Dic₆₇	1	1	yes	characteristic
629	#546	Dic₆₇	1	2	yes	—
630	#533	C₂×D₆₇	1	1	yes	characteristic
631	#529	C₂×D₆₇	1	2	yes	—
632	#529	C₂×D₆₇	1	2	yes	—
633	#529	C₂×D₆₇	1	2	yes	—
634	#525	C₂×D₆₇	1	1	yes	characteristic
635	#525	C₂×D₆₇	1	1	yes	characteristic
636	C₄×#41	C₂×D₆₇	1	2	yes	—
637	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
638	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
639	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
640	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
641	#446	—	67	2	no	—
642	#446	—	67	2	no	—
643	#446	—	67	2	no	—
644	#446	—	67	2	no	—
645	#446	—	67	2	no	—
646	#446	—	67	2	no	—
647	#446	—	67	2	no	—
648	C₈×Q₈	—	67	2	no	—
649	#436	—	67	2	no	—
650	#436	—	67	2	no	—
651	#436	—	67	2	no	—
652	#436	—	67	2	no	—
653	#436	—	67	2	no	—
654	#435	—	67	1	no	—
655	#435	—	67	1	no	—
656	#435	—	67	1	no	—
657	#435	—	67	1	no	—
658	#435	—	67	1	no	—
659	#435	—	67	1	no	—
660	#435	—	67	1	no	—
661	#435	—	67	1	no	—
662	#435	—	67	2	no	—
663	#435	—	67	2	no	—
664	#435	—	67	2	no	—
665	#435	—	67	2	no	—
666	#435	—	67	2	no	—
667	#435	—	67	2	no	—
668	#435	—	67	2	no	—
669	#435	—	67	2	no	—
670	#435	—	67	2	no	—
671	#435	—	67	2	no	—
672	C₈×D₄	—	67	2	no	—
673	C₈×D₄	—	67	2	no	—
674	C₈×D₄	—	67	2	no	—
675	C₈×D₄	—	67	2	no	—
676	C₈×D₄	—	67	2	no	—
677	#433	—	67	2	no	—
678	#433	—	67	2	no	—
679	#433	—	67	2	no	—
680	#433	—	67	2	no	—
681	#433	—	67	2	no	—
682	#433	—	67	2	no	—
683	#432	—	67	2	no	—
684	#432	—	67	2	no	—
685	#432	—	67	2	no	—
686	#431	—	67	2	no	—
687	#431	—	67	2	no	—
688	#431	—	67	2	no	—
689	#424	—	67	1	no	—
690	#424	—	67	1	no	—
691	#424	—	67	1	no	—
692	#424	—	67	1	no	—
693	#423	—	67	1	no	—
694	C₂×C₄⋊C₈	—	67	1	no	—
695	#408	—	67	1	no	—
696	#408	—	67	1	no	—
697	#407	—	67	1	no	—
698	#407	—	67	1	no	—
699	C₂×C₂²⋊C₈	—	67	1	no	—
700	C₂×C₂²⋊C₈	—	67	1	no	—
701	#405	—	67	1	no	—
702	#405	—	67	1	no	—
703	#405	—	67	1	no	—
704	#405	—	67	1	no	—
705	#405	—	67	2	no	—
706	#405	—	67	2	no	—
707	#405	—	67	1	no	—
708	#405	—	67	1	no	—
709	#405	—	67	1	no	—
710	#405	—	67	2	no	—
711	#405	—	67	2	no	—
712	#405	—	67	1	no	—
713	#405	—	67	2	no	—
714	#405	—	67	2	no	—
715	C₄×M₁₆	—	67	2	no	—
716	C₄×M₁₆	—	67	2	no	—
717	C₄×M₁₆	—	67	1	no	—
718	C₄×M₁₆	—	67	2	no	—
719	C₂×#97	—	67	2	no	—
720	C₂×#97	—	67	1	no	—
721	C₂×#97	—	67	2	no	—
722	C₂×C₄×C₈	—	67	2	no	—
723	C₂×#41	C₂×Dic₆₇	1	2	yes	—
724	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
725	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
726	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
727	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
728	#131	—	134	4	no	—
729	#131	—	134	4	no	—
730	C₂×M₁₆	—	67	1	no	—
731	C₂×M₁₆	—	67	1	no	—
732	C₂×M₁₆	—	67	1	no	—
733	C₂×M₁₆	—	67	2	no	—
734	C₂×M₁₆	—	67	1	no	—
735	C₂×M₁₆	—	67	1	no	—
736	C₂×M₁₆	—	67	1	no	—
737	C₂×M₁₆	—	67	2	no	—
738	C₂×M₁₆	—	67	1	no	—
739	C₂×M₁₆	—	67	1	no	—
740	C₂×M₁₆	—	67	2	no	—
741	C₂×M₁₆	—	67	2	no	—
742	C₂×M₁₆	—	134	4	no	—
743	C₂×M₁₆	—	134	4	no	—
744	C₂×M₁₆	—	134	4	no	—
745	C₂²×C₈	—	67	1	no	—
746	C₂²×C₈	—	67	1	no	—
747	C₂²×C₈	—	67	1	no	—
748	C₂²×C₈	—	67	1	no	—
749	C₂²×C₈	—	67	1	no	—
750	C₂²×C₈	—	67	1	no	—
751	C₂²×C₈	—	67	2	no	—
752	C₂²×C₈	—	67	1	no	—
753	C₂²×C₈	—	67	2	no	—
754	C₂²×C₈	—	67	1	no	—
755	C₂²×C₈	—	67	2	no	—
756	C₂²×C₈	—	67	2	no	—
757	C₂²×C₈	—	134	4	no	—
758	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
759	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
760	#126	C₂×Dic₆₇	1	2	yes	—
761	#126	C₂×Dic₆₇	1	2	yes	—
762	#126	C₂×Dic₆₇	1	2	yes	—
763	#126	C₂×Dic₆₇	1	2	yes	—
764	#126	C₂×Dic₆₇	1	2	yes	—
765	#126	C₂×Dic₆₇	1	2	yes	—
766	#125	C₂×Dic₆₇	1	2	yes	—
767	#125	C₂×Dic₆₇	1	2	yes	—
768	#125	C₂×Dic₆₇	1	2	yes	—
769	#125	C₂×Dic₆₇	1	1	yes	characteristic
770	#125	C₂×Dic₆₇	1	1	yes	characteristic
771	#124	C₂×Dic₆₇	1	2	yes	—
772	#124	C₂×Dic₆₇	1	2	yes	—
773	#124	C₂×Dic₆₇	1	2	yes	—
774	#123	C₂×Dic₆₇	1	2	yes	—
775	#123	C₂×Dic₆₇	1	2	yes	—
776	#123	C₂×Dic₆₇	1	2	yes	—
777	#123	C₂×Dic₆₇	1	2	yes	—
778	#123	C₂×Dic₆₇	1	2	yes	—
779	#123	C₂×Dic₆₇	1	2	yes	—
780	#123	C₂×Dic₆₇	1	2	yes	—
781	#123	C₂×Dic₆₇	1	2	yes	—
782	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
787	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
788	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
789	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
790	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
791	#121	C₂×Dic₆₇	1	1	yes	characteristic
792	#121	C₂×Dic₆₇	1	1	yes	characteristic
793	#121	C₂×Dic₆₇	1	1	yes	characteristic
794	#121	C₂×Dic₆₇	1	1	yes	characteristic
795	#121	C₂×Dic₆₇	1	2	yes	—
796	#121	C₂×Dic₆₇	1	2	yes	—
797	#121	C₂×Dic₆₇	1	2	yes	—
798	#120	C₂×Dic₆₇	1	2	yes	—
799	#120	C₂×Dic₆₇	1	2	yes	—
800	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
801	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
802	C₄×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
803	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
804	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
805	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
806	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
807	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
808	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
809	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
810	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
811	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
812	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
813	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
814	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
815	C₄×D₄	C₂×Dic₆₇	1	1	yes	characteristic
816	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
817	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
818	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
819	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
820	C₄×D₄	C₂²×D₆₇	1	2	yes	—
821	C₄×D₄	C₂²×D₆₇	1	2	yes	—
822	C₄×D₄	C₂²×D₆₇	1	2	yes	—
823	C₄×D₄	C₂²×D₆₇	1	2	yes	—
824	#117	C₂×Dic₆₇	1	2	yes	—
825	#117	C₂×Dic₆₇	1	2	yes	—
826	#117	C₂×Dic₆₇	1	1	yes	characteristic
827	#117	C₂×Dic₆₇	1	1	yes	characteristic
828	#117	C₂×Dic₆₇	1	1	yes	characteristic
829	#117	C₂×Dic₆₇	1	1	yes	characteristic
830	#117	C₂×Dic₆₇	1	2	yes	—
831	#117	C₂×Dic₆₇	1	2	yes	—
832	#117	C₂×Dic₆₇	1	2	yes	—
833	#117	C₂²×D₆₇	1	1	yes	characteristic
834	#117	C₂²×D₆₇	1	1	yes	characteristic
835	#117	C₂²×D₆₇	1	1	yes	characteristic
836	#117	C₂²×D₆₇	1	2	yes	—
837	#117	C₂²×D₆₇	1	2	yes	—
838	#117	C₂²×D₆₇	1	2	yes	—
839	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	2	yes	—
845	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	2	yes	—
846	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
848	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
849	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
850	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
851	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
852	C₄⋊C₈	—	67	1	no	—
853	C₄⋊C₈	—	67	1	no	—
854	C₄⋊C₈	—	67	1	no	—
855	C₄⋊C₈	—	67	1	no	—
856	C₄⋊C₈	—	67	2	no	—
857	C₄⋊C₈	—	67	2	no	—
858	C₄⋊C₈	—	67	2	no	—
859	C₄⋊C₈	—	67	2	no	—
860	C₄⋊C₈	—	67	2	no	—
861	C₄⋊C₈	—	67	2	no	—
862	C₄⋊C₈	—	67	2	no	—
863	C₄⋊C₈	—	67	2	no	—
864	C₄⋊C₈	—	67	2	no	—
865	C₄⋊C₈	—	67	2	no	—
866	C₂²⋊C₈	—	67	1	no	—
867	C₂²⋊C₈	—	67	1	no	—
868	C₂²⋊C₈	—	67	1	no	—
869	C₂²⋊C₈	—	67	1	no	—
870	C₂²⋊C₈	—	67	1	no	—
871	C₂²⋊C₈	—	67	1	no	—
872	C₂²⋊C₈	—	67	1	no	—
873	C₂²⋊C₈	—	67	1	no	—
874	C₂²⋊C₈	—	67	2	no	—
875	C₂²⋊C₈	—	67	2	no	—
876	C₂²⋊C₈	—	67	2	no	—
877	C₂²⋊C₈	—	67	2	no	—
878	C₂²⋊C₈	—	67	2	no	—
879	C₂²⋊C₈	—	67	2	no	—
880	C₂²⋊C₈	—	67	2	no	—
881	C₂²⋊C₈	—	67	2	no	—
882	#97	—	67	1	no	—
883	#97	—	67	2	no	—
884	#97	—	67	1	no	—
885	#97	—	67	2	no	—
886	#97	—	67	2	no	—
887	#97	—	67	2	no	—
888	#97	—	67	1	no	—
889	#97	—	67	2	no	—
890	#97	—	67	1	no	—
891	#97	—	67	2	no	—
892	#97	—	67	2	no	—
893	#97	—	67	2	no	—
894	#97	—	67	2	no	—
895	C₄×C₈	—	67	2	no	—
896	C₄×C₈	—	67	2	no	—
897	C₄×C₈	—	67	2	no	—
898	C₄×C₈	—	67	2	no	—
899	C₄×C₈	—	67	2	no	—
900	C₄×C₈	—	67	2	no	—
901	C₄×C₈	—	67	2	no	—
902	C₄×C₈	—	67	2	no	—
903	C₄×C₈	—	67	2	no	—
904	C₂⁴	C₂²×Dic₆₇	1	1	yes	characteristic
905	C₂⁴	C₂²×Dic₆₇	1	1	yes	characteristic
906	#41	—	2	2	no	—
907	#41	—	2	2	no	—
908	#41	—	4	4	no	—
909	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
910	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
911	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
914	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
915	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
916	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
917	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
918	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
919	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
920	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
921	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
922	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
928	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
929	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
930	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
931	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
932	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
933	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
934	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
935	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
936	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
937	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
938	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
939	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
940	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
941	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
943	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
944	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
945	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
946	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
947	M₁₆	—	67	4	no	—
948	M₁₆	—	134	2	no	—
949	M₁₆	—	134	2	no	—
950	M₁₆	—	134	2	no	—
951	M₁₆	—	134	2	no	—
952	M₁₆	—	134	4	no	—
953	M₁₆	—	134	4	no	—
954	M₁₆	—	134	4	no	—
955	M₁₆	—	134	4	no	—
956	M₁₆	—	134	2	no	—
957	M₁₆	—	134	2	no	—
958	M₁₆	—	134	2	no	—
959	C₂×C₈	—	67	4	no	—
960	C₂×C₈	—	67	1	no	—
961	C₂×C₈	—	67	2	no	—
962	C₂×C₈	—	67	1	no	—
963	C₂×C₈	—	67	1	no	—
964	C₂×C₈	—	67	2	no	—
965	C₂×C₈	—	67	1	no	—
966	C₂×C₈	—	67	1	no	—
967	C₂×C₈	—	67	2	no	—
968	C₂×C₈	—	67	2	no	—
969	C₂×C₈	—	67	1	no	—
970	C₂×C₈	—	67	1	no	—
971	C₂×C₈	—	67	1	no	—
972	C₂×C₈	—	134	2	no	—
973	C₂×C₈	—	134	2	no	—
974	C₂×C₈	—	134	2	no	—
975	C₂×C₈	—	134	2	no	—
976	C₂×C₈	—	134	4	no	—
977	C₂×C₈	—	134	4	no	—
978	C₂×C₈	—	134	4	no	—
979	C₂×C₈	—	134	4	no	—
980	C₂×C₈	—	134	2	no	—
981	C₂×C₈	—	134	2	no	—
982	C₂×C₈	—	134	2	no	—
983	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
984	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
986	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
991	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
992	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
993	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
994	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
995	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
998	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
999	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1000	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1001	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1002	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1003	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1004	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1005	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1006	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1007	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1008	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1009	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1010	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1011	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1012	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1013	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1014	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1015	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1016	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1017	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1018	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1019	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1020	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1021	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1022	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1023	C₂²⋊C₄	C₂²×Dic₆₇	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1025	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1026	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1027	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1028	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1029	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1030	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1031	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1032	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1033	C₂²⋊C₄	C₂²×Dic₆₇	1	2	yes	—
1034	C₄²	C₂²×Dic₆₇	1	2	yes	—
1035	C₄²	C₂²×Dic₆₇	1	2	yes	—
1036	C₄²	C₂²×Dic₆₇	1	2	yes	—
1037	C₄²	C₂²×Dic₆₇	1	2	yes	—
1038	C₄²	C₂²×Dic₆₇	1	2	yes	—
1039	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
1040	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
1041	C₄²	C₂²×Dic₆₇	1	2	yes	—
1042	C₄²	C₂³×D₆₇	1	2	yes	—
1043	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1044	C₄²	C₂³×D₆₇	1	2	yes	—
1045	C₄²	C₂³×D₆₇	1	2	yes	—
1046	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1054	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1055	C₂³	C₂³×Dic₆₇	1	2	yes	—
1056	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1057	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1058	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	4	2	no	—
1061	Q₈	—	4	2	no	—
1062	D₄	—	2	4	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	4	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	4	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1097	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1098	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1099	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1100	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1101	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1102	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1103	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1104	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1105	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1106	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1107	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
1108	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1109	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1110	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1111	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
1112	C₂×C₄	#41×D₆₇	1	2	yes	—
1113	C₂×C₄	#41×D₆₇	1	2	yes	—
1114	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1115	C₈	—	67	2	no	—
1116	C₈	—	67	2	no	—
1117	C₈	—	67	4	no	—
1118	C₈	—	134	1	no	—
1119	C₈	—	134	1	no	—
1120	C₈	—	134	1	no	—
1121	C₈	—	134	2	no	—
1122	C₈	—	134	2	no	—
1123	C₈	—	134	2	no	—
1124	C₈	—	134	1	no	—
1125	C₈	—	134	1	no	—
1126	C₈	—	134	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	4	no	—
1144	C₂²	—	8	2	no	—
1145	C₂²	#41×Dic₆₇	1	2	yes	—
1146	C₂²	#16864163	1	2	yes	—
1147	C₂²	C₂⁴×Dic₆₇	1	1	yes	characteristic
1148	C₄	—	2	2	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	#41×Dic₆₇	1	2	yes	—
1164	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
1165	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
1166	C₂	—	2	2	no	—
1167	C₂	—	2	2	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	1	no	—
1171	C₂	—	4	2	no	—
1172	C₂	C₂×#41×Dic₆₇	1	1	yes	characteristic
1173	C₂	C₂×#16864163	1	1	yes	characteristic
1174	C₂	#22574921	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁴×C₄
Fitting, prime radical	C₆₇×#3475	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	#3475	D₆₇
hypocenter	C₆₇	#60216
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ #3475

Complements

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

N	H ≅ G/N	type
1. #22569223	C₂	semidirect
2. #22569214	C₂	semidirect
3. #22569205	C₂	semidirect
4. #22569205	C₂	semidirect
5. #22569196	C₂	semidirect
6. #22569196	C₂	semidirect
7. #22569185	C₂	semidirect
8. #22569176	C₂	semidirect
9. #22569158	C₂	semidirect
10. #22569150	C₂	semidirect
11. D₄×#11761612	C₂	semidirect
12. #22568936	C₂	semidirect
13. #22568936	C₂	semidirect
14. #22568913	C₂	semidirect
15. #22568904	C₂	semidirect
16. C₂×#16863468	C₂	semidirect
17. #22568875	C₂	semidirect
18. #22568867	C₂	semidirect
19. #22568867	C₂	semidirect
20. #22568637	C₂	semidirect
21. #22568628	C₂	semidirect
22. C₂×#16863352	C₂	semidirect
30. #16863527	C₂²	semidirect
31. #16863527	C₂²	semidirect
32. #16863527	C₂²	semidirect
33. #16863527	C₂²	semidirect
34. #16863527	C₂²	semidirect
35. #16863527	C₂²	semidirect
36. #16863527	C₂²	semidirect
37. Q₈×C₆₇⋊C₈	C₂²	semidirect
39. #16863474	C₂²	semidirect
40. #16863474	C₂²	semidirect
41. #16863474	C₂²	semidirect
42. #16863474	C₂²	semidirect
53. #16863468	C₂²	semidirect
54. #16863468	C₂²	semidirect
55. #16863468	C₂²	semidirect
56. #16863468	C₂²	semidirect
57. #16863468	C₂²	semidirect
58. #16863468	C₂²	semidirect
59. #16863468	C₂²	semidirect
60. #16863468	C₂²	semidirect
62. D₄×C₆₇⋊C₈	C₂²	semidirect
63. D₄×C₆₇⋊C₈	C₂²	semidirect
64. D₄×C₆₇⋊C₈	C₂²	semidirect
65. D₄×C₆₇⋊C₈	C₂²	semidirect
66. #16863457	C₂²	semidirect
67. #16863457	C₂²	semidirect
68. #16863457	C₂²	semidirect
69. #16863457	C₂²	semidirect
70. #16863457	C₂²	semidirect
71. #16863457	C₂²	semidirect
72. #16863453	C₂²	semidirect
73. #16863453	C₂²	semidirect
74. #16863453	C₂²	semidirect
75. #16863449	C₂²	semidirect
76. #16863449	C₂²	semidirect
77. #16863449	C₂²	semidirect
98. #16863352	C₂²	semidirect
99. #16863352	C₂²	semidirect
100. #16863352	C₂²	semidirect
101. #16863352	C₂²	semidirect
102. #16863352	C₂²	semidirect
103. #16863352	C₂²	semidirect
105. C₄×#11761612	C₂²	semidirect
106. C₄×#11761612	C₂²	semidirect
107. C₄×#11761612	C₂²	semidirect
109. C₂×#14523954	C₂²	semidirect
110. C₂×#14523954	C₂²	semidirect
111. C₂×C₄×C₆₇⋊C₈	C₂²	semidirect
327. #11761612	#41	semidirect
339. C₂×C₆₇⋊C₈	#41	semidirect
611. C₆₇	#60216	semidirect

Maximal subgroups

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

subgroup	index
#22569223	2
#22569214	2
#22569205	2
#22569196	2
#22569185	2
#22569176	2
#22569158	2
#22569150	2
D₄×#11761612	2
#22568936	2
#22568913	2
#22568904	2
C₂×#16863468	2
#22568875	2
#22568867	2
#22568637	2
#22568628	2
C₂×#16863352	2
C₆₇×#3475	2
#60216	67