Subgroups — #31020449

Order 17152.

2060 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16864087	C₂	1	1	yes	maximal, characteristic
2	#22563398	C₂	1	1	yes	maximal, characteristic, complemented
3	#22563394	C₂	1	1	yes	maximal, characteristic, complemented
4	#22563391	C₂	1	1	yes	maximal, characteristic, complemented
5	#22563370	C₂	1	1	yes	maximal, characteristic, complemented
6	#22563329	C₂	1	1	yes	maximal, characteristic, complemented
7	#22563300	C₂	1	1	yes	maximal, characteristic, complemented
8	#22563288	C₂	1	1	yes	maximal, characteristic, complemented
9	#22563196	C₂	1	1	yes	maximal, characteristic
10	#22563194	C₂	1	1	yes	maximal, characteristic
11	#22563166	C₂	1	1	yes	maximal, characteristic, complemented
12	#22563117	C₂	1	1	yes	maximal, characteristic
13	#22563075	C₂	1	1	yes	maximal, characteristic, complemented
14	#22563070	C₂	1	1	yes	maximal, characteristic, complemented
15	#22563068	C₂	1	1	yes	maximal, characteristic, complemented
16	#22563066	C₂	1	1	yes	maximal, characteristic, complemented
17	#22563011	C₂	1	1	yes	maximal, characteristic, complemented
18	#22563010	C₂	1	1	yes	maximal, characteristic, complemented
19	#22562984	C₂	1	1	yes	maximal, characteristic, complemented
20	#22562980	C₂	1	1	yes	maximal, characteristic, complemented
21	#22562947	C₂	1	1	yes	maximal, characteristic, complemented
22	#22562941	C₂	1	1	yes	maximal, characteristic, complemented
23	#22562941	C₂	1	1	yes	maximal, characteristic, complemented
24	#22562873	C₂	1	1	yes	maximal, characteristic
25	#22562840	C₂	1	1	yes	maximal, characteristic
26	#22562834	C₂	1	1	yes	maximal, characteristic, complemented
27	#22562815	C₂	1	1	yes	maximal, characteristic, complemented
28	#22562730	C₂	1	1	yes	maximal, characteristic
29	#22562689	C₂	1	1	yes	maximal, characteristic, complemented
30	#387×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
31	C₆₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
32	#16864087	C₄	1	16	yes	complemented
33	C₂×#14524037	C₂²	1	1	yes	characteristic
34	C₂×#14524037	C₂²	1	1	yes	characteristic
35	C₂×#14524035	C₂²	1	1	yes	characteristic
36	C₂×#14524033	C₂²	1	1	yes	characteristic
37	C₂×#14524033	C₂²	1	1	yes	characteristic
38	C₂×#14524028	C₂²	1	1	yes	characteristic
39	C₂×#14524028	C₂²	1	1	yes	characteristic
40	C₂×#14524019	C₂²	1	1	yes	characteristic
41	C₂×#14524019	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
43	C₂×#14524005	C₂²	1	1	yes	characteristic
44	C₂×#14524005	C₂²	1	1	yes	characteristic
45	C₂×#14524001	C₂²	1	1	yes	characteristic
46	C₂×#14524001	C₂²	1	1	yes	characteristic
47	C₂×#14524000	C₂²	1	1	yes	characteristic
48	C₂×#14524000	C₂²	1	1	yes	characteristic
49	C₂×#14524000	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
52	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
53	#16863303	C₂²	1	1	yes	characteristic
54	#16863303	C₂²	1	1	yes	characteristic
55	#16863293	C₂²	1	1	yes	characteristic
56	#16863293	C₂²	1	1	yes	characteristic
57	#16863293	C₂²	1	1	yes	characteristic
58	#16863293	C₂²	1	1	yes	characteristic
59	#16863293	C₂²	1	1	yes	characteristic
60	#16863293	C₂²	1	1	yes	characteristic
61	#16863293	C₂²	1	1	yes	characteristic
62	#16863293	C₂²	1	1	yes	characteristic
63	#16863292	C₂²	1	1	yes	characteristic
64	#16863292	C₂²	1	1	yes	characteristic
65	#16863291	C₂²	1	1	yes	characteristic
66	#16863291	C₂²	1	1	yes	characteristic
67	#16863291	C₂²	1	1	yes	characteristic
68	#16863291	C₂²	1	1	yes	characteristic
69	#16863291	C₂²	1	1	yes	characteristic
70	#16863291	C₂²	1	1	yes	characteristic
71	#16863288	C₂²	1	1	yes	characteristic
72	#16863288	C₂²	1	1	yes	characteristic
73	#16863288	C₂²	1	1	yes	characteristic
74	#16863288	C₂²	1	1	yes	characteristic
75	#16863287	C₂²	1	1	yes	characteristic
76	#16863287	C₂²	1	1	yes	characteristic
77	#16863286	C₂²	1	1	yes	characteristic
78	#16863286	C₂²	1	1	yes	characteristic
79	#16863285	C₂²	1	1	yes	characteristic
80	#16863285	C₂²	1	1	yes	characteristic
81	#16863283	C₂²	1	1	yes	characteristic
82	#16863283	C₂²	1	1	yes	characteristic
83	#16863283	C₂²	1	1	yes	characteristic
84	#16863283	C₂²	1	1	yes	characteristic
85	#16863283	C₂²	1	1	yes	characteristic
86	#16863283	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	#16863281	C₂²	1	1	yes	characteristic
92	#16863281	C₂²	1	1	yes	characteristic
93	#16863281	C₂²	1	1	yes	characteristic
94	#16863281	C₂²	1	1	yes	characteristic
95	#16863280	C₂²	1	1	yes	characteristic
96	#16863280	C₂²	1	1	yes	characteristic
97	#16863280	C₂²	1	1	yes	characteristic
98	#16863280	C₂²	1	1	yes	characteristic
99	#16863279	C₂²	1	1	yes	characteristic
100	#16863279	C₂²	1	1	yes	characteristic
101	#16863279	C₂²	1	1	yes	characteristic
102	#16863279	C₂²	1	1	yes	characteristic
103	#16863279	C₂²	1	1	yes	characteristic
104	#16863279	C₂²	1	1	yes	characteristic
105	#16863278	C₂²	1	1	yes	characteristic
106	#16863278	C₂²	1	1	yes	characteristic
107	#16863278	C₂²	1	1	yes	characteristic
108	#16863278	C₂²	1	1	yes	characteristic
109	#16863278	C₂²	1	1	yes	characteristic
110	#16863278	C₂²	1	1	yes	characteristic
111	#16863277	C₂²	1	1	yes	characteristic
112	#16863277	C₂²	1	1	yes	characteristic
113	#16863277	C₂²	1	1	yes	characteristic
114	#16863277	C₂²	1	1	yes	characteristic
115	#16863274	C₂²	1	1	yes	characteristic
116	#16863274	C₂²	1	1	yes	characteristic
117	#16863270	C₂²	1	1	yes	characteristic
118	#16863270	C₂²	1	1	yes	characteristic
119	#16863270	C₂²	1	1	yes	characteristic
120	#16863270	C₂²	1	1	yes	characteristic
121	#16863270	C₂²	1	1	yes	characteristic
122	#16863270	C₂²	1	1	yes	characteristic
123	#16863270	C₂²	1	1	yes	characteristic
124	#16863270	C₂²	1	1	yes	characteristic
125	#16863270	C₂²	1	1	yes	characteristic
126	#16863270	C₂²	1	1	yes	characteristic
127	#16863267	C₂²	1	1	yes	characteristic
128	#16863267	C₂²	1	1	yes	characteristic
129	#16863267	C₂²	1	1	yes	characteristic
130	#16863267	C₂²	1	1	yes	characteristic
131	#16863266	C₂²	1	1	yes	characteristic
132	#16863265	C₂²	1	1	yes	characteristic
133	#16863263	C₂²	1	1	yes	characteristic
134	#16863262	C₂²	1	1	yes	characteristic
135	#16863262	C₂²	1	1	yes	characteristic
136	#16863261	C₂²	1	1	yes	characteristic
137	#16863260	C₂²	1	1	yes	characteristic
138	#16863258	C₂²	1	1	yes	characteristic
139	#16863258	C₂²	1	1	yes	characteristic
140	#16863258	C₂²	1	1	yes	characteristic
141	#16863255	C₂²	1	1	yes	characteristic
142	#16863255	C₂²	1	1	yes	characteristic
143	#16863255	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×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
147	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
148	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
149	C₄×Dic₆₇⋊C₄	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	#16863247	C₂²	1	1	yes	characteristic
154	#16863247	C₂²	1	1	yes	characteristic
155	#16863247	C₂²	1	1	yes	characteristic
156	#16863247	C₂²	1	1	yes	characteristic
157	#16863247	C₂²	1	1	yes	characteristic
158	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
159	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
160	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
161	C₄×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
162	#16863243	C₂²	1	1	yes	characteristic
163	#16863243	C₂²	1	1	yes	characteristic
164	#16863243	C₂²	1	1	yes	characteristic
165	#16863243	C₂²	1	1	yes	characteristic
166	#16863243	C₂²	1	1	yes	characteristic
167	#16863241	C₂²	1	1	yes	characteristic
168	#95×D₆₇	C₂²	1	1	yes	characteristic
169	#95×D₆₇	C₂²	1	1	yes	characteristic
170	#95×D₆₇	C₂²	1	1	yes	characteristic
171	#95×D₆₇	C₂²	1	1	yes	characteristic
172	#95×D₆₇	C₂²	1	1	yes	characteristic
173	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
174	#391×C₆₇	C₂²	1	1	yes	characteristic
175	#391×C₆₇	C₂²	1	1	yes	characteristic
176	#389×C₆₇	C₂²	1	1	yes	characteristic
177	#389×C₆₇	C₂²	1	1	yes	characteristic
178	#387×C₆₇	C₂²	1	1	yes	characteristic
179	#387×C₆₇	C₂²	1	1	yes	characteristic
180	#387×C₆₇	C₂²	1	1	yes	characteristic
181	#387×C₆₇	C₂²	1	1	yes	characteristic
182	#383×C₆₇	C₂²	1	1	yes	characteristic
183	#383×C₆₇	C₂²	1	1	yes	characteristic
184	#382×C₆₇	C₂²	1	1	yes	characteristic
185	#382×C₆₇	C₂²	1	1	yes	characteristic
186	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
187	#376×C₆₇	C₂²	1	1	yes	characteristic
188	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
189	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
199	#14524037	C₂×C₄	1	8	yes	complemented
200	#14524037	C₂×C₄	1	8	yes	complemented
201	#14524035	C₂×C₄	1	8	yes	complemented
202	#14524033	C₂×C₄	1	8	yes	complemented
203	#14524033	C₂×C₄	1	8	yes	complemented
204	#14524028	C₂×C₄	1	8	yes	—
205	#14524028	C₂×C₄	1	8	yes	—
206	#14524019	C₂×C₄	1	8	yes	complemented
207	#14524019	C₂×C₄	1	8	yes	complemented
208	C₄×D₂₆₈	C₂×C₄	1	8	yes	—
209	#14524005	—	4	2	no	—
210	#14524005	—	4	2	no	—
211	#14524001	—	4	2	no	—
212	#14524001	C₂×C₄	1	8	yes	complemented
213	#14524000	—	4	2	no	—
214	#14524000	C₂×C₄	1	8	yes	complemented
215	#14524000	C₂×C₄	1	8	yes	complemented
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×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
238	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
251	C₄⋊C₄×D₆₇	—	4	2	no	—
252	C₄⋊C₄×D₆₇	C₂×C₄	1	8	yes	complemented
253	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
289	C₄²×D₆₇	—	4	2	no	—
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	C₆₇⋊#95	C₂³	1	1	yes	characteristic
321	C₆₇⋊#95	C₂³	1	1	yes	characteristic
322	C₆₇⋊#95	C₂³	1	1	yes	characteristic
323	C₆₇⋊#95	C₂³	1	1	yes	characteristic
324	C₆₇⋊#95	C₂³	1	1	yes	characteristic
325	C₆₇⋊#95	C₂³	1	1	yes	characteristic
326	C₆₇⋊#95	C₂³	1	1	yes	characteristic
327	C₆₇⋊#95	C₂³	1	1	yes	characteristic
328	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
329	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
330	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
346	#95×C₆₇	C₂³	1	1	yes	characteristic
347	#95×C₆₇	C₂³	1	1	yes	characteristic
348	#95×C₆₇	C₂³	1	1	yes	characteristic
349	#95×C₆₇	C₂³	1	1	yes	characteristic
350	#95×C₆₇	C₂³	1	1	yes	characteristic
351	#95×C₆₇	C₂³	1	1	yes	characteristic
352	#95×C₆₇	C₂³	1	1	yes	characteristic
353	#95×C₆₇	C₂³	1	1	yes	characteristic
354	#95×C₆₇	C₂³	1	1	yes	characteristic
355	#95×C₆₇	C₂³	1	1	yes	characteristic
356	#95×C₆₇	C₂³	1	1	yes	characteristic
357	#95×C₆₇	C₂³	1	1	yes	characteristic
358	#95×C₆₇	C₂³	1	1	yes	characteristic
359	#95×C₆₇	C₂³	1	1	yes	characteristic
360	#95×C₆₇	C₂³	1	1	yes	characteristic
361	#95×C₆₇	C₂³	1	1	yes	characteristic
362	#95×C₆₇	C₂³	1	1	yes	characteristic
363	#95×C₆₇	C₂³	1	1	yes	characteristic
364	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
365	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
366	C₂×D₂₆₈	—	2	2	no	—
367	C₂×D₂₆₈	—	2	2	no	—
368	C₂×D₂₆₈	C₂²×C₄	1	4	yes	—
369	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
370	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
371	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
373	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
374	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
375	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
376	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
378	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
381	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
382	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×D₆₇	—	2	2	no	—
384	C₂×C₄×D₆₇	—	2	2	no	—
385	C₂×C₄×D₆₇	—	2	2	no	—
386	C₂×C₄×D₆₇	—	2	2	no	—
387	C₂×C₄×D₆₇	—	2	2	no	—
388	C₂×C₄×D₆₇	—	2	2	no	—
389	C₂×C₄×D₆₇	—	2	2	no	—
390	C₂×C₄×D₆₇	—	2	2	no	—
391	C₂×C₄×D₆₇	—	2	2	no	—
392	C₂×C₄×D₆₇	—	2	2	no	—
393	C₂×C₄×D₆₇	—	4	1	no	—
394	C₂×C₄×D₆₇	—	4	1	no	—
395	C₂×C₄×D₆₇	—	4	1	no	—
396	C₂×C₄×D₆₇	—	4	1	no	—
397	C₂×C₄×D₆₇	—	4	1	no	—
398	C₂×C₄×D₆₇	—	4	1	no	—
399	C₂×C₄×D₆₇	—	4	1	no	—
400	C₂×C₄×D₆₇	—	4	1	no	—
401	C₂×C₄×D₆₇	—	4	1	no	—
402	C₂×C₄×D₆₇	—	4	1	no	—
403	C₂×C₄×D₆₇	—	4	1	no	—
404	C₂×C₄×D₆₇	—	4	1	no	—
405	C₂×C₄×D₆₇	—	4	1	no	—
406	C₂×C₄×D₆₇	—	4	1	no	—
407	C₂×C₄×D₆₇	—	4	1	no	—
408	C₂×C₄×D₆₇	—	4	1	no	—
409	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
410	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
411	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
412	C₂×C₄×D₆₇	C₂²×C₄	1	4	yes	—
413	C₄⋊Dic₆₇	—	2	2	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	C₄⋊Dic₆₇	—	4	1	no	—
421	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
422	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
423	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
424	Dic₆₇⋊C₄	—	2	2	no	—
425	Dic₆₇⋊C₄	—	4	1	no	—
426	Dic₆₇⋊C₄	—	4	1	no	—
427	Dic₆₇⋊C₄	—	4	1	no	—
428	Dic₆₇⋊C₄	—	4	1	no	—
429	Dic₆₇⋊C₄	—	4	1	no	—
430	Dic₆₇⋊C₄	—	4	1	no	—
431	Dic₆₇⋊C₄	—	4	1	no	—
432	Dic₆₇⋊C₄	—	4	1	no	—
433	Dic₆₇⋊C₄	—	4	1	no	—
434	Dic₆₇⋊C₄	—	4	1	no	—
435	Dic₆₇⋊C₄	—	4	1	no	—
436	Dic₆₇⋊C₄	—	4	1	no	—
437	Dic₆₇⋊C₄	—	4	1	no	—
438	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
439	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
440	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
441	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
442	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
443	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
444	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
445	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
446	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
447	Dic₆₇⋊C₄	C₂²×C₄	1	4	yes	—
448	(C₂×D₆₇)⋊C₄	—	2	2	no	—
449	(C₂×D₆₇)⋊C₄	—	2	2	no	—
450	(C₂×D₆₇)⋊C₄	—	2	2	no	—
451	(C₂×D₆₇)⋊C₄	—	2	2	no	—
452	(C₂×D₆₇)⋊C₄	—	4	1	no	—
453	(C₂×D₆₇)⋊C₄	—	4	1	no	—
454	(C₂×D₆₇)⋊C₄	—	4	1	no	—
455	(C₂×D₆₇)⋊C₄	—	4	1	no	—
456	(C₂×D₆₇)⋊C₄	—	4	1	no	—
457	(C₂×D₆₇)⋊C₄	—	4	1	no	—
458	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
459	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
460	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
461	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
462	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
463	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
464	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
465	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	4	yes	—
466	C₄×Dic₆₇	—	2	2	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	C₄×Dic₆₇	—	4	1	no	—
475	C₄×Dic₆₇	—	4	1	no	—
476	C₄×Dic₆₇	—	4	1	no	—
477	C₄×Dic₆₇	—	4	1	no	—
478	C₄×Dic₆₇	—	4	1	no	—
479	C₄×Dic₆₇	—	4	1	no	—
480	C₄×Dic₆₇	—	4	1	no	—
481	C₄×Dic₆₇	—	4	1	no	—
482	C₄×Dic₆₇	C₂²×C₄	1	4	yes	—
483	C₄×Dic₆₇	C₂²×C₄	1	4	yes	—
484	C₂×Q₈×C₆₇	—	4	1	no	—
485	C₂×Q₈×C₆₇	—	4	1	no	—
486	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
487	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
488	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
489	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
490	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₂²×C₄×C₆₇	C₂⁴	1	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	—	4	1	no	—
503	C₄⋊C₄×C₆₇	—	4	1	no	—
504	C₄⋊C₄×C₆₇	—	4	1	no	—
505	C₄⋊C₄×C₆₇	—	4	1	no	—
506	C₄⋊C₄×C₆₇	—	4	1	no	—
507	C₄⋊C₄×C₆₇	—	4	1	no	—
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	C₄²×C₆₇	—	4	1	no	—
512	C₄²×C₆₇	—	4	1	no	—
513	C₄²×C₆₇	—	4	1	no	—
514	C₄²×C₆₇	—	4	1	no	—
515	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
516	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
517	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
518	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
519	C₂²×D₆₇	—	2	1	no	—
520	C₂²×D₆₇	—	2	1	no	—
521	C₂²×D₆₇	—	2	1	no	—
522	C₂²×D₆₇	—	2	1	no	—
523	C₂²×D₆₇	—	2	1	no	—
524	C₂²×D₆₇	—	2	1	no	—
525	C₂²×D₆₇	—	2	1	no	—
526	C₂²×D₆₇	—	2	1	no	—
527	C₂²×D₆₇	—	2	1	no	—
528	C₂²×D₆₇	—	2	1	no	—
529	C₂²×D₆₇	C₂³×C₄	1	2	yes	—
530	C₂²×D₆₇	C₂³×C₄	1	2	yes	—
531	C₂²×D₆₇	H(5,𝔽₂)	1	2	yes	—
532	C₂²×D₆₇	2₋¹⁺⁴	1	2	yes	—
533	Q₈×C₆₇	—	4	4	no	—
534	C₂×C₄×C₆₇	—	2	1	no	—
535	C₂×C₄×C₆₇	—	2	1	no	—
536	C₂×C₄×C₆₇	—	2	1	no	—
537	C₂×C₄×C₆₇	—	2	1	no	—
538	C₂×C₄×C₆₇	—	2	1	no	—
539	C₂×C₄×C₆₇	—	2	1	no	—
540	C₂×C₄×C₆₇	—	2	1	no	—
541	C₂×C₄×C₆₇	—	2	1	no	—
542	C₂×C₄×C₆₇	—	2	1	no	—
543	C₂×C₄×C₆₇	—	2	1	no	—
544	C₂×C₄×C₆₇	—	2	1	no	—
545	C₂×C₄×C₆₇	—	2	1	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	1	no	—
548	C₂×C₄×C₆₇	—	2	1	no	—
549	C₂×C₄×C₆₇	—	2	1	no	—
550	C₂×C₄×C₆₇	—	2	1	no	—
551	C₂×C₄×C₆₇	—	2	1	no	—
552	C₂×C₄×C₆₇	—	2	1	no	—
553	C₂×C₄×C₆₇	—	2	1	no	—
554	C₂×C₄×C₆₇	—	2	1	no	—
555	C₂×C₄×C₆₇	—	2	1	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	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
577	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
578	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
579	C₂×Dic₆₇	—	2	1	no	—
580	C₂×Dic₆₇	—	2	1	no	—
581	C₂×Dic₆₇	—	2	1	no	—
582	C₂×Dic₆₇	—	2	1	no	—
583	C₂×Dic₆₇	—	2	1	no	—
584	C₂×Dic₆₇	—	2	1	no	—
585	C₂×Dic₆₇	—	2	1	no	—
586	C₂×Dic₆₇	—	2	1	no	—
587	C₂×Dic₆₇	—	2	1	no	—
588	C₂×Dic₆₇	—	2	1	no	—
589	C₂×Dic₆₇	—	2	1	no	—
590	C₂×Dic₆₇	—	2	1	no	—
591	C₂×Dic₆₇	—	2	1	no	—
592	C₂×Dic₆₇	—	2	1	no	—
593	C₂×Dic₆₇	—	2	1	no	—
594	C₂×Dic₆₇	—	2	1	no	—
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	C₂³×C₄	1	2	yes	—
615	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
616	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
617	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
618	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
619	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
620	C₂×Dic₆₇	2₋¹⁺⁴	1	2	yes	—
621	D₂₆₈	—	2	8	no	—
622	C₄×D₆₇	—	2	8	no	—
623	C₄×D₆₇	—	2	8	no	—
624	C₄×D₆₇	—	4	4	no	—
625	C₄×D₆₇	—	4	4	no	—
626	C₄×D₆₇	—	4	4	no	—
627	C₄×D₆₇	—	4	4	no	—
628	C₄×D₆₇	—	8	2	no	—
629	C₄×D₆₇	—	8	2	no	—
630	C₄×D₆₇	—	8	2	no	—
631	C₄×D₆₇	—	8	2	no	—
632	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
633	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
634	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
635	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
636	C₂²×C₆₇	#585	1	1	yes	characteristic
637	C₂²×C₆₇	#585	1	1	yes	characteristic
638	C₂²×C₆₇	#585	1	1	yes	characteristic
639	C₂×D₆₇	—	2	2	no	—
640	C₂×D₆₇	—	2	2	no	—
641	C₂×D₆₇	—	2	2	no	—
642	C₂×D₆₇	—	2	2	no	—
643	C₂×D₆₇	—	2	2	no	—
644	C₂×D₆₇	—	2	2	no	—
645	C₂×D₆₇	—	2	2	no	—
646	C₂×D₆₇	—	2	2	no	—
647	C₂×D₆₇	—	2	2	no	—
648	C₂×D₆₇	—	4	1	no	—
649	C₂×D₆₇	—	4	1	no	—
650	C₂×D₆₇	—	4	1	no	—
651	C₂×D₆₇	—	4	1	no	—
652	C₂×D₆₇	#520	1	4	yes	—
653	C₄×C₆₇	—	2	2	no	—
654	C₄×C₆₇	—	2	2	no	—
655	C₄×C₆₇	—	2	2	no	—
656	C₄×C₆₇	—	2	2	no	—
657	C₄×C₆₇	—	2	2	no	—
658	C₄×C₆₇	—	2	2	no	—
659	C₄×C₆₇	—	2	2	no	—
660	C₄×C₆₇	—	4	1	no	—
661	C₄×C₆₇	—	4	1	no	—
662	C₄×C₆₇	—	4	1	no	—
663	C₄×C₆₇	—	4	1	no	—
664	C₄×C₆₇	—	4	1	no	—
665	C₄×C₆₇	—	4	1	no	—
666	C₄×C₆₇	—	4	1	no	—
667	C₄×C₆₇	—	4	1	no	—
668	Dic₆₇	—	2	2	no	—
669	Dic₆₇	—	2	2	no	—
670	Dic₆₇	—	2	2	no	—
671	Dic₆₇	—	2	2	no	—
672	Dic₆₇	—	2	2	no	—
673	Dic₆₇	—	2	2	no	—
674	Dic₆₇	—	2	2	no	—
675	Dic₆₇	—	4	1	no	—
676	Dic₆₇	—	4	1	no	—
677	Dic₆₇	—	4	1	no	—
678	Dic₆₇	—	4	1	no	—
679	Dic₆₇	—	4	1	no	—
680	Dic₆₇	—	4	1	no	—
681	Dic₆₇	—	4	1	no	—
682	#34459	—	67	1	no	maximal, Sylow
683	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
684	C₂×C₆₇	#3428	1	1	yes	characteristic
685	C₂×C₆₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
686	C₂×C₆₇	#3533	1	1	yes	characteristic
687	C₂×C₆₇	#3535	1	1	yes	characteristic
688	C₂×C₆₇	#3563	1	1	yes	characteristic
689	C₂×C₆₇	#3564	1	1	yes	characteristic
690	D₆₇	—	2	4	no	—
691	D₆₇	—	4	2	no	—
692	C₂×#552	—	67	1	no	—
693	#2383	—	67	1	no	—
694	#2382	—	67	1	no	—
695	#2382	—	67	1	no	—
696	#2378	—	67	1	no	—
697	#2373	—	67	1	no	—
698	#2370	—	67	1	no	—
699	#2368	—	67	1	no	—
700	#2359	—	67	1	no	—
701	#2359	—	67	1	no	—
702	#2355	—	67	1	no	—
703	#2349	—	67	1	no	—
704	#2344	—	67	1	no	—
705	#2343	—	67	1	no	—
706	#2343	—	67	1	no	—
707	#2343	—	67	1	no	—
708	#2336	—	67	1	no	—
709	#2336	—	67	1	no	—
710	#2334	—	67	1	no	—
711	#2334	—	67	1	no	—
712	#2330	—	67	1	no	—
713	#2329	—	67	1	no	—
714	#2329	—	67	1	no	—
715	#2322	—	67	1	no	—
716	#2320	D₆₇	1	1	yes	characteristic, complemented
717	#2318	—	67	1	no	—
718	#2317	—	67	1	no	—
719	#2314	—	67	1	no	—
720	C₄×#123	—	67	1	no	—
721	#2296	—	67	1	no	—
722	C₂×#387	—	67	1	no	—
723	C₆₇	#34459	1	1	yes	characteristic, complemented, Sylow
724	#552	—	67	16	no	—
725	C₂×#126	—	67	1	no	—
726	C₂×#126	—	67	1	no	—
727	C₂×#125	—	67	1	no	—
728	C₂×#125	—	67	1	no	—
729	C₂×#125	—	67	1	no	—
730	C₂×#123	—	67	1	no	—
731	C₂×#123	—	67	1	no	—
732	C₂×C₂²⋊Q₈	—	67	1	no	—
733	C₂×C₂²⋊Q₈	—	67	1	no	—
734	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
735	C₂×C₄×D₄	—	67	1	no	—
736	C₂×C₄×D₄	—	67	1	no	—
737	C₂×C₄×D₄	—	67	1	no	—
738	C₂×#117	—	67	1	no	—
739	C₂×#117	—	67	1	no	—
740	C₂×#117	—	67	1	no	—
741	C₂×#117	—	67	1	no	—
742	C₂×#117	—	67	1	no	—
743	C₂²×C₄⋊C₄	—	67	1	no	—
744	C₂²×C₄⋊C₄	—	67	1	no	—
745	C₂²×C₄²	—	67	1	no	—
746	#391	—	67	1	no	—
747	#391	—	67	1	no	—
748	#391	C₂×D₆₇	1	1	yes	characteristic
749	#391	C₂×D₆₇	1	1	yes	characteristic
750	#389	—	67	1	no	—
751	#389	—	67	1	no	—
752	#389	—	67	1	no	—
753	#389	—	67	1	no	—
754	#389	—	67	1	no	—
755	#389	—	67	1	no	—
756	#389	—	67	1	no	—
757	#389	—	67	1	no	—
758	#389	—	67	1	no	—
759	#389	—	67	1	no	—
760	#389	—	67	1	no	—
761	#389	—	67	1	no	—
762	#389	—	67	1	no	—
763	#389	—	67	1	no	—
764	#389	—	67	1	no	—
765	#389	—	67	1	no	—
766	#389	C₂×D₆₇	1	1	yes	characteristic
767	#389	C₂×D₆₇	1	1	yes	characteristic
768	#388	—	67	1	no	—
769	#388	—	67	1	no	—
770	#388	—	67	1	no	—
771	#388	—	67	1	no	—
772	#388	—	67	1	no	—
773	#388	—	67	1	no	—
774	#388	—	67	1	no	—
775	#388	—	67	1	no	—
776	#388	—	67	1	no	—
777	#388	—	67	1	no	—
778	#387	—	67	1	no	—
779	#387	—	67	1	no	—
780	#387	—	67	1	no	—
781	#387	—	67	1	no	—
782	#387	—	67	1	no	—
783	#387	—	67	1	no	—
784	#387	—	67	1	no	—
785	#387	—	67	1	no	—
786	#387	—	67	1	no	—
787	#387	—	67	1	no	—
788	#387	—	67	1	no	—
789	#387	—	67	1	no	—
790	#387	—	67	1	no	—
791	#387	—	67	1	no	—
792	#387	—	67	1	no	—
793	#387	—	67	1	no	—
794	#387	—	67	1	no	—
795	#387	—	67	1	no	—
796	#387	—	67	1	no	—
797	#387	—	67	1	no	—
798	#387	—	67	1	no	—
799	#387	—	67	1	no	—
800	#387	—	67	1	no	—
801	#387	—	67	1	no	—
802	#387	—	67	1	no	—
803	#387	—	67	1	no	—
804	#387	—	67	1	no	—
805	#387	—	67	1	no	—
806	#387	—	67	1	no	—
807	#387	—	67	1	no	—
808	#387	—	67	1	no	—
809	#387	—	67	1	no	—
810	#387	—	67	1	no	—
811	#387	—	67	1	no	—
812	#387	C₂×D₆₇	1	1	yes	characteristic
813	#387	C₂×D₆₇	1	1	yes	characteristic
814	#387	C₂×D₆₇	1	1	yes	characteristic
815	#387	C₂×D₆₇	1	1	yes	characteristic
816	#386	—	67	1	no	—
817	#386	—	67	1	no	—
818	#385	—	67	1	no	—
819	#385	—	67	1	no	—
820	#385	—	67	1	no	—
821	#385	—	67	1	no	—
822	#385	—	67	1	no	—
823	#385	—	67	1	no	—
824	#385	—	67	1	no	—
825	#385	—	67	1	no	—
826	#385	—	67	1	no	—
827	#385	—	67	1	no	—
828	#385	—	67	1	no	—
829	#385	—	67	1	no	—
830	#385	—	67	1	no	—
831	#385	—	67	1	no	—
832	#384	—	67	1	no	—
833	#384	—	67	1	no	—
834	#383	—	67	1	no	—
835	#383	C₂×D₆₇	1	1	yes	characteristic
836	#383	C₂×D₆₇	1	1	yes	characteristic
837	#382	—	67	1	no	—
838	#382	—	67	1	no	—
839	#382	—	67	1	no	—
840	#382	—	67	1	no	—
841	#382	C₂×D₆₇	1	1	yes	characteristic
842	#382	C₂×D₆₇	1	1	yes	characteristic
843	#381	—	67	1	no	—
844	#381	—	67	1	no	—
845	#381	—	67	1	no	—
846	#380	—	67	1	no	—
847	#380	—	67	1	no	—
848	#380	—	67	1	no	—
849	C₄×C₄⋊C₄	—	67	1	no	—
850	C₄×C₄⋊C₄	—	67	1	no	—
851	C₄×C₄⋊C₄	—	67	1	no	—
852	C₄×C₄⋊C₄	—	67	1	no	—
853	C₄×C₄⋊C₄	—	67	1	no	—
854	C₄×C₄⋊C₄	—	67	1	no	—
855	C₄×C₄⋊C₄	—	67	1	no	—
856	C₄×C₄⋊C₄	—	67	1	no	—
857	C₄×C₄⋊C₄	—	67	1	no	—
858	C₄×C₄⋊C₄	—	67	1	no	—
859	C₄×C₄⋊C₄	—	67	1	no	—
860	C₄×C₄⋊C₄	—	67	1	no	—
861	C₄×C₄⋊C₄	—	67	1	no	—
862	C₄×C₄⋊C₄	—	67	1	no	—
863	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
864	C₄×C₂²⋊C₄	—	67	1	no	—
865	C₄×C₂²⋊C₄	—	67	1	no	—
866	C₄×C₂²⋊C₄	—	67	1	no	—
867	C₄×C₂²⋊C₄	—	67	1	no	—
868	C₄×C₂²⋊C₄	—	67	1	no	—
869	C₄×C₂²⋊C₄	—	67	1	no	—
870	C₄×C₂²⋊C₄	—	67	1	no	—
871	C₄×C₂²⋊C₄	—	67	1	no	—
872	C₄×C₂²⋊C₄	—	67	1	no	—
873	#376	—	67	1	no	—
874	#376	C₂×D₆₇	1	1	yes	characteristic
875	C₂×#95	—	67	1	no	—
876	C₂×#95	—	67	1	no	—
877	C₂×#95	—	67	1	no	—
878	C₂×#95	—	67	1	no	—
879	C₂×#95	—	67	1	no	—
880	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
881	C₂²×D₄	—	67	1	no	—
882	C₂³×C₄	—	67	1	no	—
883	C₂³×C₄	—	67	1	no	—
884	C₂³×C₄	—	67	1	no	—
885	C₂³×C₄	—	67	1	no	—
886	C₂³×C₄	—	67	1	no	—
887	C₂³×C₄	—	67	1	no	—
888	C₂³×C₄	—	67	1	no	—
889	C₂³×C₄	—	67	1	no	—
890	C₂³×C₄	—	67	1	no	—
891	C₂³×C₄	—	67	1	no	—
892	#126	—	67	8	no	—
893	#126	—	67	8	no	—
894	#125	—	67	8	no	—
895	#125	—	67	8	no	—
896	#125	—	67	8	no	—
897	#123	—	67	8	no	—
898	#123	—	67	8	no	—
899	C₂²⋊Q₈	—	67	8	no	—
900	C₂²⋊Q₈	—	67	8	no	—
901	C₄×Q₈	C₄×D₆₇	1	8	yes	complemented
902	C₄×D₄	—	268	2	no	—
903	C₄×D₄	—	268	2	no	—
904	C₄×D₄	—	67	8	no	—
905	#117	—	268	2	no	—
906	#117	—	268	2	no	—
907	#117	—	67	8	no	—
908	#117	—	67	8	no	—
909	#117	—	67	8	no	—
910	C₂×C₄⋊C₄	—	268	2	no	—
911	C₂×C₄⋊C₄	—	67	1	no	—
912	C₂×C₄⋊C₄	—	67	1	no	—
913	C₂×C₄⋊C₄	—	67	1	no	—
914	C₂×C₄⋊C₄	—	67	1	no	—
915	C₂×C₄⋊C₄	—	67	1	no	—
916	C₂×C₄⋊C₄	—	67	1	no	—
917	C₂×C₄⋊C₄	—	67	1	no	—
918	C₂×C₄⋊C₄	—	67	1	no	—
919	C₂×C₄⋊C₄	—	67	1	no	—
920	C₂×C₄⋊C₄	—	67	1	no	—
921	C₂×C₄⋊C₄	—	67	1	no	—
922	C₂×C₄⋊C₄	—	67	1	no	—
923	C₂×C₄⋊C₄	—	67	1	no	—
924	C₂×C₄⋊C₄	—	67	1	no	—
925	C₂×C₄⋊C₄	—	67	1	no	—
926	C₂×C₄⋊C₄	—	67	1	no	—
927	C₂×C₄⋊C₄	—	67	1	no	—
928	C₂×C₄⋊C₄	—	67	1	no	—
929	C₂×C₄⋊C₄	—	67	1	no	—
930	C₂×C₄⋊C₄	—	67	1	no	—
931	C₂×C₄⋊C₄	—	67	1	no	—
932	C₂×C₄⋊C₄	—	67	1	no	—
933	C₂×C₄⋊C₄	—	67	1	no	—
934	C₂×C₄⋊C₄	—	67	1	no	—
935	C₂×C₄⋊C₄	—	67	1	no	—
936	C₂×C₄⋊C₄	—	67	1	no	—
937	C₂×C₄⋊C₄	—	67	1	no	—
938	C₂×C₄⋊C₄	—	67	1	no	—
939	C₂×C₄⋊C₄	—	67	1	no	—
940	C₂×C₄⋊C₄	—	67	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	8	no	—
945	C₂×C₄⋊C₄	—	67	1	no	—
946	C₂×C₄⋊C₄	—	67	1	no	—
947	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
953	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
954	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
955	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
956	C₂×C₂²⋊C₄	—	67	1	no	—
957	C₂×C₂²⋊C₄	—	67	1	no	—
958	C₂×C₂²⋊C₄	—	67	1	no	—
959	C₂×C₂²⋊C₄	—	67	1	no	—
960	C₂×C₂²⋊C₄	—	67	1	no	—
961	C₂×C₂²⋊C₄	—	67	1	no	—
962	C₂×C₂²⋊C₄	—	67	1	no	—
963	C₂×C₂²⋊C₄	—	67	1	no	—
964	C₂×C₂²⋊C₄	—	67	1	no	—
965	C₂×C₂²⋊C₄	—	67	1	no	—
966	C₂×C₂²⋊C₄	—	67	1	no	—
967	C₂×C₂²⋊C₄	—	67	1	no	—
968	C₂×C₂²⋊C₄	—	67	1	no	—
969	C₂×C₂²⋊C₄	—	67	1	no	—
970	C₂×C₂²⋊C₄	—	67	1	no	—
971	C₂×C₂²⋊C₄	—	67	1	no	—
972	C₂×C₂²⋊C₄	—	67	1	no	—
973	C₂×C₂²⋊C₄	—	67	1	no	—
974	C₂×C₄²	—	268	2	no	—
975	C₂×C₄²	—	67	1	no	—
976	C₂×C₄²	—	67	1	no	—
977	C₂×C₄²	—	67	1	no	—
978	C₂×C₄²	—	67	1	no	—
979	C₂×C₄²	—	67	1	no	—
980	C₂×C₄²	—	67	1	no	—
981	C₂×C₄²	—	67	1	no	—
982	C₂×C₄²	—	67	1	no	—
983	C₂×C₄²	—	67	1	no	—
984	C₂×C₄²	—	67	1	no	—
985	C₂×C₄²	—	67	1	no	—
986	C₂×C₄²	—	67	1	no	—
987	C₂×C₄²	—	67	1	no	—
988	C₂×C₄²	—	67	1	no	—
989	C₂×C₄²	—	67	1	no	—
990	C₂×C₄²	—	67	1	no	—
991	C₂×C₄²	—	67	1	no	—
992	C₂×C₄²	—	67	1	no	—
993	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
994	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
995	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
996	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
997	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
998	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
999	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1000	#95	—	67	1	no	—
1001	#95	—	67	1	no	—
1002	#95	—	67	1	no	—
1003	#95	—	67	1	no	—
1004	#95	—	67	1	no	—
1005	#95	—	67	1	no	—
1006	#95	—	67	1	no	—
1007	#95	—	67	1	no	—
1008	#95	—	67	1	no	—
1009	#95	—	67	1	no	—
1010	#95	—	67	1	no	—
1011	#95	—	67	1	no	—
1012	#95	—	67	1	no	—
1013	#95	—	67	1	no	—
1014	#95	—	67	1	no	—
1015	#95	—	67	1	no	—
1016	#95	—	67	1	no	—
1017	#95	—	67	1	no	—
1018	#95	—	67	1	no	—
1019	#95	—	67	1	no	—
1020	#95	—	67	1	no	—
1021	#95	—	67	1	no	—
1022	#95	—	67	1	no	—
1023	#95	—	67	1	no	—
1024	#95	—	67	1	no	—
1025	#95	—	67	1	no	—
1026	#95	—	67	1	no	—
1027	#95	—	67	1	no	—
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	C₂²×D₆₇	1	1	yes	characteristic
1039	#95	C₂²×D₆₇	1	1	yes	characteristic
1040	#95	C₂²×D₆₇	1	1	yes	characteristic
1041	#95	C₂²×D₆₇	1	1	yes	characteristic
1042	#95	C₂²×D₆₇	1	1	yes	characteristic
1043	#95	C₂²×D₆₇	1	1	yes	characteristic
1044	#95	C₂²×D₆₇	1	1	yes	characteristic
1045	#95	C₂²×D₆₇	1	1	yes	characteristic
1046	#95	C₂²×D₆₇	1	1	yes	characteristic
1047	#95	C₂²×D₆₇	1	1	yes	characteristic
1048	#95	C₂²×D₆₇	1	1	yes	characteristic
1049	#95	C₂²×D₆₇	1	1	yes	characteristic
1050	#95	C₂²×D₆₇	1	1	yes	characteristic
1051	#95	C₂²×D₆₇	1	1	yes	characteristic
1052	#95	C₂²×D₆₇	1	1	yes	characteristic
1053	#95	C₂²×D₆₇	1	1	yes	characteristic
1054	#95	C₂²×D₆₇	1	1	yes	characteristic
1055	#95	C₂²×D₆₇	1	1	yes	characteristic
1056	C₂⁴	—	67	1	no	—
1057	C₂⁴	—	67	1	no	—
1058	C₂×Q₈	—	4	1	no	—
1059	C₂×Q₈	—	4	1	no	—
1060	C₂×Q₈	C₂×C₄×D₆₇	1	4	yes	—
1061	C₂×D₄	—	67	4	no	—
1062	C₂×D₄	—	134	2	no	—
1063	C₂×D₄	—	134	2	no	—
1064	C₂²×C₄	—	268	1	no	—
1065	C₂²×C₄	—	268	1	no	—
1066	C₂²×C₄	—	268	1	no	—
1067	C₂²×C₄	—	268	1	no	—
1068	C₂²×C₄	—	268	1	no	—
1069	C₂²×C₄	—	268	1	no	—
1070	C₂²×C₄	—	268	1	no	—
1071	C₂²×C₄	—	268	1	no	—
1072	C₂²×C₄	—	268	1	no	—
1073	C₂²×C₄	—	268	1	no	—
1074	C₂²×C₄	—	268	1	no	—
1075	C₂²×C₄	—	268	1	no	—
1076	C₂²×C₄	—	268	1	no	—
1077	C₂²×C₄	—	268	1	no	—
1078	C₂²×C₄	—	268	1	no	—
1079	C₂²×C₄	—	268	1	no	—
1080	C₂²×C₄	—	67	4	no	—
1081	C₂²×C₄	—	67	4	no	—
1082	C₂²×C₄	—	67	1	no	—
1083	C₂²×C₄	—	67	1	no	—
1084	C₂²×C₄	—	67	1	no	—
1085	C₂²×C₄	—	67	1	no	—
1086	C₂²×C₄	—	67	1	no	—
1087	C₂²×C₄	—	67	1	no	—
1088	C₂²×C₄	—	67	1	no	—
1089	C₂²×C₄	—	67	4	no	—
1090	C₂²×C₄	—	67	4	no	—
1091	C₂²×C₄	—	67	1	no	—
1092	C₂²×C₄	—	67	1	no	—
1093	C₂²×C₄	—	67	1	no	—
1094	C₂²×C₄	—	67	1	no	—
1095	C₂²×C₄	—	67	1	no	—
1096	C₂²×C₄	—	67	1	no	—
1097	C₂²×C₄	—	67	1	no	—
1098	C₂²×C₄	—	134	2	no	—
1099	C₂²×C₄	—	134	2	no	—
1100	C₂²×C₄	—	134	2	no	—
1101	C₂²×C₄	—	134	2	no	—
1102	C₂²×C₄	—	134	2	no	—
1103	C₂²×C₄	—	134	2	no	—
1104	C₂²×C₄	—	134	2	no	—
1105	C₂²×C₄	—	134	2	no	—
1106	C₂²×C₄	—	134	2	no	—
1107	C₂²×C₄	—	134	2	no	—
1108	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1109	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1110	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1111	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1112	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1113	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1114	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1115	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1116	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1117	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1118	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1119	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1120	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1121	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1122	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1123	C₄⋊C₄	—	4	1	no	—
1124	C₄⋊C₄	—	4	1	no	—
1125	C₄⋊C₄	—	4	1	no	—
1126	C₄⋊C₄	—	4	1	no	—
1127	C₄⋊C₄	—	4	1	no	—
1128	C₄⋊C₄	—	4	1	no	—
1129	C₄⋊C₄	—	268	1	no	—
1130	C₄⋊C₄	—	268	1	no	—
1131	C₄⋊C₄	—	268	1	no	—
1132	C₄⋊C₄	—	268	1	no	—
1133	C₄⋊C₄	—	268	1	no	—
1134	C₄⋊C₄	—	268	1	no	—
1135	C₄⋊C₄	—	268	1	no	—
1136	C₄⋊C₄	—	268	1	no	—
1137	C₄⋊C₄	—	268	1	no	—
1138	C₄⋊C₄	—	268	1	no	—
1139	C₄⋊C₄	—	268	1	no	—
1140	C₄⋊C₄	—	268	1	no	—
1141	C₄⋊C₄	—	268	1	no	—
1142	C₄⋊C₄	—	268	1	no	—
1143	C₄⋊C₄	—	268	1	no	—
1144	C₄⋊C₄	—	268	1	no	—
1145	C₄⋊C₄	—	268	1	no	—
1146	C₄⋊C₄	—	268	1	no	—
1147	C₄⋊C₄	—	268	1	no	—
1148	C₄⋊C₄	—	268	1	no	—
1149	C₄⋊C₄	—	67	4	no	—
1150	C₄⋊C₄	—	67	4	no	—
1151	C₄⋊C₄	—	67	4	no	—
1152	C₄⋊C₄	—	67	4	no	—
1153	C₄⋊C₄	—	67	4	no	—
1154	C₄⋊C₄	—	67	4	no	—
1155	C₄⋊C₄	—	67	4	no	—
1156	C₄⋊C₄	—	67	4	no	—
1157	C₄⋊C₄	—	67	4	no	—
1158	C₄⋊C₄	—	67	4	no	—
1159	C₄⋊C₄	—	67	4	no	—
1160	C₄⋊C₄	—	67	4	no	—
1161	C₄⋊C₄	—	67	4	no	—
1162	C₄⋊C₄	—	134	2	no	—
1163	C₄⋊C₄	—	134	2	no	—
1164	C₄⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
1165	C₄⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
1166	C₄⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
1167	C₂²⋊C₄	—	268	1	no	—
1168	C₂²⋊C₄	—	268	1	no	—
1169	C₂²⋊C₄	—	268	1	no	—
1170	C₂²⋊C₄	—	268	1	no	—
1171	C₂²⋊C₄	—	268	1	no	—
1172	C₂²⋊C₄	—	268	1	no	—
1173	C₂²⋊C₄	—	67	4	no	—
1174	C₂²⋊C₄	—	67	4	no	—
1175	C₂²⋊C₄	—	67	4	no	—
1176	C₂²⋊C₄	—	67	4	no	—
1177	C₂²⋊C₄	—	67	4	no	—
1178	C₂²⋊C₄	—	67	4	no	—
1179	C₂²⋊C₄	—	67	4	no	—
1180	C₂²⋊C₄	—	67	4	no	—
1181	C₂²⋊C₄	—	134	2	no	—
1182	C₂²⋊C₄	—	134	2	no	—
1183	C₂²⋊C₄	—	134	2	no	—
1184	C₂²⋊C₄	—	134	2	no	—
1185	C₄²	—	4	1	no	—
1186	C₄²	—	4	1	no	—
1187	C₄²	—	4	1	no	—
1188	C₄²	—	4	1	no	—
1189	C₄²	—	268	1	no	—
1190	C₄²	—	268	1	no	—
1191	C₄²	—	268	1	no	—
1192	C₄²	—	268	1	no	—
1193	C₄²	—	268	1	no	—
1194	C₄²	—	268	1	no	—
1195	C₄²	—	268	1	no	—
1196	C₄²	—	268	1	no	—
1197	C₄²	—	268	1	no	—
1198	C₄²	—	268	1	no	—
1199	C₄²	—	268	1	no	—
1200	C₄²	—	268	1	no	—
1201	C₄²	—	268	1	no	—
1202	C₄²	—	268	1	no	—
1203	C₄²	—	268	1	no	—
1204	C₄²	—	67	4	no	—
1205	C₄²	—	67	4	no	—
1206	C₄²	—	134	2	no	—
1207	C₄²	C₂×C₄×D₆₇	1	4	yes	—
1208	C₄²	C₂×C₄×D₆₇	1	4	yes	—
1209	C₄²	C₂×C₄×D₆₇	1	4	yes	—
1210	C₂³	—	67	2	no	—
1211	C₂³	—	67	2	no	—
1212	C₂³	—	67	2	no	—
1213	C₂³	—	67	2	no	—
1214	C₂³	—	134	1	no	—
1215	C₂³	—	134	1	no	—
1216	C₂³	—	134	1	no	—
1217	C₂³	—	134	1	no	—
1218	C₂³	—	134	1	no	—
1219	C₂³	—	134	1	no	—
1220	C₂³	—	134	1	no	—
1221	C₂³	—	134	1	no	—
1222	C₂³	—	134	1	no	—
1223	C₂³	—	134	1	no	—
1224	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1225	Q₈	—	4	4	no	—
1226	D₄	—	134	8	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	2	1	no	—
1264	C₂×C₄	—	2	1	no	—
1265	C₂×C₄	—	268	4	no	—
1266	C₂×C₄	—	268	4	no	—
1267	C₂×C₄	—	268	4	no	—
1268	C₂×C₄	—	268	4	no	—
1269	C₂×C₄	—	536	2	no	—
1270	C₂×C₄	—	536	2	no	—
1271	C₂×C₄	—	536	2	no	—
1272	C₂×C₄	—	536	2	no	—
1273	C₂×C₄	—	67	2	no	—
1274	C₂×C₄	—	67	2	no	—
1275	C₂×C₄	—	67	2	no	—
1276	C₂×C₄	—	67	2	no	—
1277	C₂×C₄	—	67	2	no	—
1278	C₂×C₄	—	67	2	no	—
1279	C₂×C₄	—	67	2	no	—
1280	C₂×C₄	—	134	8	no	—
1281	C₂×C₄	—	134	8	no	—
1282	C₂×C₄	—	134	1	no	—
1283	C₂×C₄	—	134	1	no	—
1284	C₂×C₄	—	134	1	no	—
1285	C₂×C₄	—	134	1	no	—
1286	C₂×C₄	—	134	1	no	—
1287	C₂×C₄	—	134	1	no	—
1288	C₂×C₄	—	134	1	no	—
1289	C₂×C₄	—	134	1	no	—
1290	C₂×C₄	—	134	1	no	—
1291	C₂×C₄	—	134	1	no	—
1292	C₂×C₄	—	134	1	no	—
1293	C₂×C₄	—	134	1	no	—
1294	C₂×C₄	—	134	1	no	—
1295	C₂×C₄	—	134	1	no	—
1296	C₂×C₄	—	134	1	no	—
1297	C₂×C₄	—	134	1	no	—
1298	C₂×C₄	—	134	1	no	—
1299	C₂×C₄	—	134	1	no	—
1300	C₂×C₄	—	134	1	no	—
1301	C₂×C₄	—	134	1	no	—
1302	C₂×C₄	—	134	1	no	—
1303	C₂×C₄	—	134	1	no	—
1304	C₂×C₄	—	134	1	no	—
1305	C₂×C₄	—	134	1	no	—
1306	C₂×C₄	—	134	1	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	C₂²×C₄×D₆₇	1	2	yes	—
1318	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1319	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1320	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1321	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1322	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1323	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1324	C₂²	—	268	1	no	—
1325	C₂²	—	268	1	no	—
1326	C₂²	—	268	1	no	—
1327	C₂²	—	268	1	no	—
1328	C₂²	—	67	4	no	—
1329	C₂²	—	134	2	no	—
1330	C₂²	—	134	2	no	—
1331	C₂²	—	134	2	no	—
1332	C₂²	—	134	2	no	—
1333	C₂²	—	134	2	no	—
1334	C₂²	—	134	2	no	—
1335	C₂²	—	134	2	no	—
1336	C₂²	—	134	2	no	—
1337	C₂²	—	134	2	no	—
1338	C₂²	C₂³×C₄×D₆₇	1	1	yes	characteristic
1339	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1340	C₂²	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1341	C₂²	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1342	C₂²	#16864232	1	1	yes	characteristic
1343	C₂²	#16864232	1	1	yes	characteristic
1344	C₂²	#16864233	1	1	yes	characteristic
1345	C₄	—	2	2	no	—
1346	C₄	—	2	2	no	—
1347	C₄	—	2	2	no	—
1348	C₄	—	2	2	no	—
1349	C₄	—	2	2	no	—
1350	C₄	—	2	2	no	—
1351	C₄	—	2	2	no	—
1352	C₄	—	4	1	no	—
1353	C₄	—	4	1	no	—
1354	C₄	—	4	1	no	—
1355	C₄	—	4	1	no	—
1356	C₄	—	4	1	no	—
1357	C₄	—	4	1	no	—
1358	C₄	—	4	1	no	—
1359	C₄	—	4	1	no	—
1360	C₄	—	268	1	no	—
1361	C₄	—	268	1	no	—
1362	C₄	—	268	1	no	—
1363	C₄	—	268	1	no	—
1364	C₄	—	268	1	no	—
1365	C₄	—	268	1	no	—
1366	C₄	—	268	1	no	—
1367	C₄	—	134	2	no	—
1368	C₄	—	134	2	no	—
1369	C₄	—	134	2	no	—
1370	C₄	—	134	2	no	—
1371	C₄	—	134	2	no	—
1372	C₄	—	134	2	no	—
1373	C₄	—	134	2	no	—
1374	C₂	—	268	2	no	—
1375	C₂	—	134	4	no	—
1376	C₂	#520×D₆₇	1	1	yes	characteristic
1377	C₂	#22573410	1	1	yes	characteristic
1378	C₂	#22573418	1	1	yes	characteristic
1379	C₂	#22574372	1	1	yes	characteristic
1380	C₂	#22574411	1	1	yes	characteristic
1381	C₂	#22574807	1	1	yes	characteristic
1382	C₂	#22574822	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator	C₂²×C₆₇	C₂⁴×C₄
Fitting	C₆₇×#2320	C₂
socle, cosocle	C₂³×C₆₇	C₂⁵
prime radical	C₂²×D₂₆₈	C₂³
hypercenter	#2320	D₆₇
hypocenter	C₆₇	#34459
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2320

Complements

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

N	H ≅ G/N	type
2. #22563398	C₂	semidirect
3. #22563394	C₂	semidirect
4. #22563391	C₂	semidirect
5. #22563370	C₂	semidirect
6. #22563329	C₂	semidirect
7. #22563300	C₂	semidirect
8. #22563288	C₂	semidirect
11. #22563166	C₂	semidirect
13. #22563075	C₂	semidirect
14. #22563070	C₂	semidirect
15. #22563068	C₂	semidirect
16. #22563066	C₂	semidirect
17. #22563011	C₂	semidirect
18. #22563010	C₂	semidirect
19. #22562984	C₂	semidirect
20. #22562980	C₂	semidirect
21. #22562947	C₂	semidirect
22. #22562941	C₂	semidirect
23. #22562941	C₂	semidirect
26. #22562834	C₂	semidirect
27. #22562815	C₂	semidirect
29. #22562689	C₂	semidirect
30. #387×D₆₇	C₂	semidirect
31. C₆₇×#2320	C₂	semidirect
32. #16864087	C₄	semidirect
199. #14524037	C₂×C₄	semidirect
200. #14524037	C₂×C₄	semidirect
201. #14524035	C₂×C₄	semidirect
202. #14524033	C₂×C₄	semidirect
203. #14524033	C₂×C₄	semidirect
206. #14524019	C₂×C₄	semidirect
207. #14524019	C₂×C₄	semidirect
212. #14524001	C₂×C₄	semidirect
214. #14524000	C₂×C₄	semidirect
215. #14524000	C₂×C₄	semidirect
252. C₄⋊C₄×D₆₇	C₂×C₄	semidirect
329. C₄×Q₈×C₆₇	C₂×C₄	semidirect
716. #2320	D₆₇	semidirect
723. C₆₇	#34459	semidirect
901. C₄×Q₈	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16864087	2
#22563398	2
#22563394	2
#22563391	2
#22563370	2
#22563329	2
#22563300	2
#22563288	2
#22563196	2
#22563194	2
#22563166	2
#22563117	2
#22563075	2
#22563070	2
#22563068	2
#22563066	2
#22563011	2
#22563010	2
#22562984	2
#22562980	2
#22562947	2
#22562941	2
#22562873	2
#22562840	2
#22562834	2
#22562815	2
#22562730	2
#22562689	2
#387×D₆₇	2
C₆₇×#2320	2
#34459	67