Subgroups — #11743862

Order 896.

1040 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#90401	C₂	1	1	yes	maximal, characteristic, complemented
3	#90397	C₂	1	1	yes	maximal, characteristic, complemented
4	#90393	C₂	1	1	yes	maximal, characteristic, complemented
5	#90393	C₂	1	1	yes	maximal, characteristic, complemented
6	#90372	C₂	1	1	yes	maximal, characteristic, complemented
7	#90360	C₂	1	1	yes	maximal, characteristic, complemented
8	#90355	C₂	1	1	yes	maximal, characteristic, complemented
9	#90355	C₂	1	1	yes	maximal, characteristic, complemented
10	#90353	C₂	1	1	yes	maximal, characteristic, complemented
11	#90349	C₂	1	1	yes	maximal, characteristic, complemented
12	#90340	C₂	1	1	yes	maximal, characteristic, complemented
13	#90339	C₂	1	1	yes	maximal, characteristic, complemented
14	#90332	C₂	1	1	yes	maximal, characteristic, complemented
15	#90331	C₂	1	1	yes	maximal, characteristic, complemented
16	#90328	C₂	1	1	yes	maximal, characteristic, complemented
17	#90313	C₂	1	1	yes	maximal, characteristic, complemented
18	#90283	C₂	1	1	yes	maximal, characteristic
19	#90278	C₂	1	1	yes	maximal, characteristic, complemented
20	#90250	C₂	1	1	yes	maximal, characteristic, complemented
21	#90247	C₂	1	1	yes	maximal, characteristic, complemented
22	#90229	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#1159	C₂	1	1	yes	maximal, characteristic, complemented
24	#90224	C₂	1	1	yes	maximal, characteristic, complemented
25	#90219	C₂	1	1	yes	maximal, characteristic, complemented
26	#90218	C₂	1	1	yes	maximal, characteristic, complemented
27	#90207	C₂	1	1	yes	maximal, characteristic, complemented
28	#90186	C₂	1	1	yes	maximal, characteristic, complemented
29	#90186	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#6448	C₂	1	1	yes	maximal, characteristic, complemented
31	#90177	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₇	C₂²	1	1	yes	characteristic
33	C₂×#1159	C₂²	1	1	yes	characteristic
34	C₂²×Dic₁₄	C₂²	1	1	yes	characteristic
35	C₇×#126	C₂²	1	1	yes	characteristic, complemented
36	C₇×#126	C₂²	1	1	yes	characteristic, complemented
37	C₇×#124	C₂²	1	1	yes	characteristic, complemented
38	C₇×#123	C₂²	1	1	yes	characteristic
39	C₇×#123	C₂²	1	1	yes	characteristic, complemented
40	C₇×#123	C₂²	1	1	yes	characteristic, complemented
41	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₇×#120	C₂²	1	1	yes	characteristic
44	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
46	C₇×#117	C₂²	1	1	yes	characteristic
47	C₇×#117	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	#6516	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
53	#6510	C₂²	1	1	yes	characteristic, complemented
54	#6509	C₂²	1	1	yes	characteristic, complemented
55	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
56	#6507	C₂²	1	1	yes	characteristic, complemented
57	#6503	C₂²	1	1	yes	characteristic
58	#6503	C₂²	1	1	yes	characteristic
59	#6502	C₂²	1	1	yes	characteristic
60	#6502	C₂²	1	1	yes	characteristic
61	#6500	C₂²	1	1	yes	characteristic
62	#6499	C₂²	1	1	yes	characteristic, complemented
63	#6498	C₂²	1	1	yes	characteristic
64	#6498	C₂²	1	1	yes	characteristic, complemented
65	#6498	C₂²	1	1	yes	characteristic, complemented
66	D₄×Dic₇	C₂²	1	1	yes	characteristic
67	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
68	#6492	C₂²	1	1	yes	characteristic
69	#6492	C₂²	1	1	yes	characteristic, complemented
70	#6492	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
79	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
80	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
81	#6489	C₂²	1	1	yes	characteristic
82	#6489	C₂²	1	1	yes	characteristic, complemented
83	#6487	C₂²	1	1	yes	characteristic
84	#6487	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic
86	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
87	#6461	C₂²	1	1	yes	characteristic, complemented
88	#6461	C₂²	1	1	yes	characteristic, complemented
89	#6461	C₂²	1	1	yes	characteristic, complemented
90	#6461	C₂²	1	1	yes	characteristic, complemented
91	#6461	C₂²	1	1	yes	characteristic, complemented
92	#6461	C₂²	1	1	yes	characteristic, complemented
93	#6460	C₂²	1	1	yes	characteristic, complemented
94	#6459	C₂²	1	1	yes	characteristic, complemented
95	#6459	C₂²	1	1	yes	characteristic, complemented
96	#6459	C₂²	1	1	yes	characteristic, complemented
97	#6459	C₂²	1	1	yes	characteristic, complemented
98	#6457	C₂²	1	1	yes	characteristic, complemented
99	#6457	C₂²	1	1	yes	characteristic, complemented
100	#6457	C₂²	1	1	yes	characteristic, complemented
101	#6457	C₂²	1	1	yes	characteristic, complemented
102	#6456	C₂²	1	1	yes	characteristic, complemented
103	#6455	C₂²	1	1	yes	characteristic, complemented
104	#6455	C₂²	1	1	yes	characteristic, complemented
105	#6455	C₂²	1	1	yes	characteristic, complemented
106	#6452	C₂²	1	1	yes	characteristic, complemented
107	#6452	C₂²	1	1	yes	characteristic, complemented
108	#6451	C₂²	1	1	yes	characteristic, complemented
109	#6451	C₂²	1	1	yes	characteristic, complemented
110	#6451	C₂²	1	1	yes	characteristic, complemented
111	#6450	C₂²	1	1	yes	characteristic, complemented
112	#6450	C₂²	1	1	yes	characteristic, complemented
113	#6450	C₂²	1	1	yes	characteristic, complemented
114	#6450	C₂²	1	1	yes	characteristic, complemented
115	#6450	C₂²	1	1	yes	characteristic, complemented
116	#6450	C₂²	1	1	yes	characteristic, complemented
117	#6450	C₂²	1	1	yes	characteristic, complemented
118	#6450	C₂²	1	1	yes	characteristic, complemented
119	#6449	C₂²	1	1	yes	characteristic
120	#6449	C₂²	1	1	yes	characteristic, complemented
121	#6449	C₂²	1	1	yes	characteristic, complemented
122	#6448	C₂²	1	1	yes	characteristic
123	#6448	C₂²	1	1	yes	characteristic
124	#6448	C₂²	1	1	yes	characteristic
125	#6448	C₂²	1	1	yes	characteristic
126	#6448	C₂²	1	1	yes	characteristic
127	#6448	C₂²	1	1	yes	characteristic
128	#6448	C₂²	1	1	yes	characteristic
129	#6448	C₂²	1	1	yes	characteristic
130	#6448	C₂²	1	1	yes	characteristic
131	#6448	C₂²	1	1	yes	characteristic
132	#6448	C₂²	1	1	yes	characteristic, complemented
133	#6448	C₂²	1	1	yes	characteristic, complemented
134	#6448	C₂²	1	1	yes	characteristic, complemented
135	#6448	C₂²	1	1	yes	characteristic, complemented
136	#6448	C₂²	1	1	yes	characteristic, complemented
137	#6448	C₂²	1	1	yes	characteristic, complemented
138	#6447	C₂²	1	1	yes	characteristic
139	#6447	C₂²	1	1	yes	characteristic
140	#6446	C₂²	1	1	yes	characteristic, complemented
141	#6446	C₂²	1	1	yes	characteristic, complemented
142	#6446	C₂²	1	1	yes	characteristic, complemented
143	#6446	C₂²	1	1	yes	characteristic, complemented
144	#6445	C₂²	1	1	yes	characteristic
145	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
146	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
147	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
148	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
149	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
150	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
154	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
155	#6442	C₂²	1	1	yes	characteristic, complemented
156	#6442	C₂²	1	1	yes	characteristic, complemented
157	#6442	C₂²	1	1	yes	characteristic, complemented
158	#6442	C₂²	1	1	yes	characteristic, complemented
159	#6442	C₂²	1	1	yes	characteristic, complemented
160	#6442	C₂²	1	1	yes	characteristic, complemented
161	#6441	C₂²	1	1	yes	characteristic
162	#6441	C₂²	1	1	yes	characteristic
163	#6441	C₂²	1	1	yes	characteristic, complemented
164	#6441	C₂²	1	1	yes	characteristic, complemented
165	#6441	C₂²	1	1	yes	characteristic, complemented
166	#6441	C₂²	1	1	yes	characteristic, complemented
167	#6440	C₂²	1	1	yes	characteristic
168	#6440	C₂²	1	1	yes	characteristic
169	#6440	C₂²	1	1	yes	characteristic
170	#6440	C₂²	1	1	yes	characteristic
171	#6440	C₂²	1	1	yes	characteristic
172	#6440	C₂²	1	1	yes	characteristic, complemented
173	#6440	C₂²	1	1	yes	characteristic, complemented
174	#6440	C₂²	1	1	yes	characteristic, complemented
175	#6439	C₂²	1	1	yes	characteristic, complemented
176	#6439	C₂²	1	1	yes	characteristic, complemented
177	#6438	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
179	#6435	C₂²	1	1	yes	characteristic, complemented
180	#6435	C₂²	1	1	yes	characteristic, complemented
181	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
182	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
183	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
187	#3510	—	7	1	no	maximal, Sylow
188	C₂⁴×C₇	C₂³	1	1	yes	characteristic
189	C₂³×D₇	C₂³	1	1	yes	characteristic
190	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
191	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₇	—	2	4	no	—
200	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
210	C₂²×Dic₇	C₂³	1	1	yes	characteristic
211	C₂²×Dic₇	C₂³	1	1	yes	characteristic
212	C₂²×Dic₇	C₂³	1	1	yes	characteristic
213	C₂²×Dic₇	C₂³	1	1	yes	characteristic
214	C₂²×Dic₇	C₂³	1	1	yes	characteristic
215	C₂²×Dic₇	C₂³	1	1	yes	characteristic
216	C₂²×Dic₇	C₂³	1	1	yes	characteristic
217	#1159	—	2	4	no	—
218	C₂×D₂₈	C₂³	1	1	yes	characteristic
219	C₂×D₂₈	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
227	C₂×Dic₁₄	—	2	4	no	—
228	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
229	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
230	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
231	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
232	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
233	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
234	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
235	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
236	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
253	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₄²×C₇	C₂³	1	1	yes	characteristic
259	C₄²×C₇	C₂³	1	1	yes	characteristic
260	C₄²×C₇	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
275	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
305	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
306	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
307	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
308	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
309	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
310	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
311	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
312	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
313	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
314	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
315	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
316	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
317	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
318	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
319	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
320	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
321	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
322	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
323	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
327	C₄×Dic₇	C₂³	1	1	yes	characteristic
328	C₄×Dic₇	C₂³	1	1	yes	characteristic
329	C₄×Dic₇	C₂³	1	1	yes	characteristic
330	C₄×Dic₇	C₂³	1	1	yes	characteristic
331	C₄×Dic₇	C₂³	1	1	yes	characteristic
332	C₄×Dic₇	C₂³	1	1	yes	characteristic
333	C₄×Dic₇	C₂³	1	1	yes	characteristic
334	C₄×Dic₇	C₂³	1	1	yes	characteristic
335	C₄×Dic₇	C₂³	1	1	yes	characteristic
336	C₄×Dic₇	C₂³	1	1	yes	characteristic
337	C₄×Dic₇	C₂³	1	1	yes	characteristic
338	C₄×Dic₇	C₂³	1	1	yes	characteristic
339	C₄×Dic₇	C₂³	1	1	yes	characteristic
340	C₄×Dic₇	C₂³	1	1	yes	characteristic
341	C₄×Dic₇	C₂³	1	1	yes	characteristic
342	C₄×Dic₇	C₂³	1	1	yes	characteristic
343	C₄×Dic₇	C₂³	1	1	yes	characteristic
344	C₄×Dic₇	C₂³	1	1	yes	characteristic
345	C₄×Dic₇	C₂³	1	1	yes	characteristic
346	#559	—	7	1	no	—
347	#559	—	7	1	no	—
348	#559	—	7	1	no	—
349	#559	—	7	1	no	—
350	#556	—	7	1	no	—
351	#556	—	7	1	no	—
352	#556	—	7	1	no	—
353	#556	—	7	1	no	—
354	#551	—	7	1	no	—
355	#551	—	7	1	no	—
356	#551	—	7	1	no	—
357	#551	—	7	1	no	—
358	#551	—	7	1	no	—
359	#551	—	7	1	no	—
360	#551	—	7	1	no	—
361	#551	D₇	1	1	yes	characteristic, complemented
362	#542	—	7	1	no	—
363	#542	—	7	1	no	—
364	#542	—	7	1	no	—
365	#542	—	7	1	no	—
366	#536	—	7	1	no	—
367	#535	—	7	1	no	—
368	#533	—	7	1	no	—
369	#529	—	7	1	no	—
370	#529	—	7	1	no	—
371	#529	—	7	1	no	—
372	#529	—	7	1	no	—
373	C₂×#124	—	7	1	no	—
374	#519	—	7	1	no	—
375	#518	—	7	1	no	—
376	C₄×#41	—	7	1	no	—
377	C₂³×C₇	—	2	2	no	—
378	C₂³×C₇	—	4	1	no	—
379	C₂³×C₇	—	4	1	no	—
380	C₂³×C₇	C₂⁴	1	1	yes	characteristic
381	C₂³×C₇	C₂⁴	1	1	yes	characteristic
382	C₂³×C₇	C₂⁴	1	1	yes	characteristic
383	C₂³×C₇	C₂⁴	1	1	yes	characteristic
384	C₂²×D₇	—	2	2	no	—
385	C₂²×D₇	—	4	1	no	—
386	C₂²×D₇	—	4	1	no	—
387	C₂²×D₇	C₂⁴	1	1	yes	characteristic
388	C₂²×D₇	C₂⁴	1	1	yes	characteristic
389	C₂²×D₇	C₂⁴	1	1	yes	characteristic
390	C₇×Q₈	—	4	1	no	—
391	C₇×D₄	—	2	2	no	—
392	C₇×D₄	—	4	1	no	—
393	C₇×D₄	—	4	1	no	—
394	C₂×C₄×C₇	—	2	2	no	—
395	C₂×C₄×C₇	—	4	1	no	—
396	C₂×C₄×C₇	—	4	1	no	—
397	C₂×C₄×C₇	—	4	1	no	—
398	C₂×C₄×C₇	—	4	1	no	—
399	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
405	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
406	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
407	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
410	C₂²⋊D₇	—	2	2	no	—
411	C₂²⋊D₇	—	2	2	no	—
412	C₂²⋊D₇	—	2	2	no	—
413	C₂²⋊D₇	—	2	2	no	—
414	C₂²⋊D₇	—	2	2	no	—
415	C₂²⋊D₇	—	2	2	no	—
416	C₂²⋊D₇	—	4	1	no	—
417	C₂²⋊D₇	—	4	1	no	—
418	C₂²⋊D₇	—	4	1	no	—
419	C₂²⋊D₇	—	4	1	no	—
420	C₂×Dic₇	—	2	2	no	—
421	C₂×Dic₇	—	2	2	no	—
422	C₂×Dic₇	—	4	1	no	—
423	C₂×Dic₇	—	4	1	no	—
424	C₂×Dic₇	—	4	1	no	—
425	C₂×Dic₇	—	4	1	no	—
426	C₂×Dic₇	#41	1	4	yes	—
427	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
432	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
433	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
434	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
435	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
436	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
437	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
440	D₂₈	—	4	1	no	—
441	D₂₈	—	4	1	no	—
442	C₄×D₇	—	2	2	no	—
443	C₄×D₇	—	4	1	no	—
444	C₄×D₇	—	4	1	no	—
445	C₄×D₇	—	4	1	no	—
446	C₄×D₇	—	4	1	no	—
447	C₄×D₇	—	4	1	no	—
448	C₄×D₇	—	4	1	no	—
449	Dic₁₄	—	2	2	no	—
450	Dic₁₄	—	2	2	no	—
451	Dic₁₄	—	2	2	no	—
452	Dic₁₄	—	2	2	no	—
453	Dic₁₄	—	2	2	no	—
454	Dic₁₄	—	4	1	no	—
455	Dic₁₄	—	4	1	no	—
456	Dic₁₄	—	4	1	no	—
457	C₂×#41	—	7	1	no	—
458	C₂²×Q₈	—	7	1	no	—
459	C₂²×D₄	—	7	1	no	—
460	C₄⋊Q₈	—	7	1	no	—
461	C₄⋊Q₈	—	7	1	no	—
462	C₄⋊Q₈	—	7	1	no	—
463	C₄⋊Q₈	—	7	1	no	—
464	#127	—	7	1	no	—
465	#127	—	7	1	no	—
466	#126	—	7	1	no	—
467	#126	—	7	1	no	—
468	#126	—	7	1	no	—
469	#126	—	7	1	no	—
470	#126	—	7	1	no	—
471	#126	—	7	1	no	—
472	#126	—	7	1	no	—
473	#126	—	7	1	no	—
474	#126	—	7	1	no	—
475	#126	—	7	1	no	—
476	#126	—	7	1	no	—
477	#126	—	7	1	no	—
478	#126	—	7	1	no	—
479	#126	—	7	1	no	—
480	#126	C₂×D₇	1	1	yes	characteristic, complemented
481	#126	C₂×D₇	1	1	yes	characteristic, complemented
482	#125	—	7	1	no	—
483	#125	—	7	1	no	—
484	#124	—	7	1	no	—
485	#124	—	7	1	no	—
486	#124	—	7	1	no	—
487	#124	—	7	1	no	—
488	#124	—	7	1	no	—
489	#124	—	7	1	no	—
490	#124	—	7	1	no	—
491	#124	—	7	1	no	—
492	#124	—	7	1	no	—
493	#124	—	7	1	no	—
494	#124	—	7	1	no	—
495	#124	—	7	1	no	—
496	#124	—	7	1	no	—
497	#124	—	7	1	no	—
498	#124	—	7	1	no	—
499	#124	—	7	1	no	—
500	#124	—	7	1	no	—
501	#124	—	7	1	no	—
502	#124	—	7	1	no	—
503	#124	C₂×D₇	1	1	yes	characteristic, complemented
504	#123	—	7	1	no	—
505	#123	—	7	1	no	—
506	#123	—	7	1	no	—
507	#123	—	7	1	no	—
508	#123	—	7	1	no	—
509	#123	—	7	1	no	—
510	#123	—	7	1	no	—
511	#123	—	7	1	no	—
512	#123	—	7	1	no	—
513	#123	—	7	1	no	—
514	#123	—	7	1	no	—
515	#123	—	7	1	no	—
516	#123	—	7	1	no	—
517	#123	—	7	1	no	—
518	#123	—	7	1	no	—
519	#123	—	7	1	no	—
520	#123	—	7	1	no	—
521	#123	C₂×D₇	1	1	yes	characteristic
522	#123	C₂×D₇	1	1	yes	characteristic, complemented
523	#123	C₂×D₇	1	1	yes	characteristic, complemented
524	C₂²⋊Q₈	—	7	1	no	—
525	C₂²⋊Q₈	—	7	1	no	—
526	C₂²⋊Q₈	—	7	1	no	—
527	C₂²⋊Q₈	—	7	1	no	—
528	C₂²⋊Q₈	—	7	1	no	—
529	C₂²⋊Q₈	—	7	1	no	—
530	C₂²⋊Q₈	—	7	1	no	—
531	C₂²⋊Q₈	—	7	1	no	—
532	C₂²⋊Q₈	—	7	1	no	—
533	C₂²⋊Q₈	—	7	1	no	—
534	C₂²⋊Q₈	—	7	1	no	—
535	C₂²⋊Q₈	—	7	1	no	—
536	C₂²⋊Q₈	—	7	1	no	—
537	C₂²⋊Q₈	—	7	1	no	—
538	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
539	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
540	#121	—	7	1	no	—
541	#121	—	7	1	no	—
542	#121	—	7	1	no	—
543	#121	—	7	1	no	—
544	#120	—	7	1	no	—
545	#120	—	7	1	no	—
546	#120	—	7	1	no	—
547	#120	C₂×D₇	1	1	yes	characteristic
548	C₄×Q₈	—	7	1	no	—
549	C₄×Q₈	—	7	1	no	—
550	C₄×Q₈	—	7	1	no	—
551	C₄×Q₈	—	7	1	no	—
552	C₄×Q₈	—	7	1	no	—
553	C₄×Q₈	—	7	1	no	—
554	C₄×Q₈	—	7	1	no	—
555	C₄×Q₈	—	7	1	no	—
556	C₄×Q₈	—	7	1	no	—
557	C₄×Q₈	—	7	1	no	—
558	C₄×Q₈	—	7	1	no	—
559	C₄×Q₈	—	7	1	no	—
560	C₄×Q₈	—	7	1	no	—
561	C₄×Q₈	—	7	1	no	—
562	C₄×D₄	—	7	1	no	—
563	C₄×D₄	—	7	1	no	—
564	C₄×D₄	—	7	1	no	—
565	C₄×D₄	—	7	1	no	—
566	C₄×D₄	—	7	1	no	—
567	C₄×D₄	—	7	1	no	—
568	C₄×D₄	—	7	1	no	—
569	C₄×D₄	—	7	1	no	—
570	C₄×D₄	—	7	1	no	—
571	C₄×D₄	—	7	1	no	—
572	C₄×D₄	—	7	1	no	—
573	C₄×D₄	—	7	1	no	—
574	C₄×D₄	—	7	1	no	—
575	C₄×D₄	—	7	1	no	—
576	C₄×D₄	—	7	1	no	—
577	C₄×D₄	—	7	1	no	—
578	C₄×D₄	—	7	1	no	—
579	C₄×D₄	—	7	1	no	—
580	C₄×D₄	—	7	1	no	—
581	C₄×D₄	—	7	1	no	—
582	C₄×D₄	C₂×D₇	1	1	yes	characteristic
583	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
584	#117	—	7	1	no	—
585	#117	—	7	1	no	—
586	#117	—	7	1	no	—
587	#117	—	7	1	no	—
588	#117	—	7	1	no	—
589	#117	—	7	1	no	—
590	#117	—	7	1	no	—
591	#117	—	7	1	no	—
592	#117	—	7	1	no	—
593	#117	—	7	1	no	—
594	#117	—	7	1	no	—
595	#117	—	7	1	no	—
596	#117	—	7	1	no	—
597	#117	—	7	1	no	—
598	#117	—	7	1	no	—
599	#117	C₂×D₇	1	1	yes	characteristic
600	#117	C₂×D₇	1	1	yes	characteristic, complemented
601	C₂×C₂²⋊C₄	—	7	1	no	—
602	C₂×C₂²⋊C₄	—	7	1	no	—
603	C₂×C₂²⋊C₄	—	7	1	no	—
604	C₂×C₂²⋊C₄	—	7	1	no	—
605	C₂×C₂²⋊C₄	—	7	1	no	—
606	C₂×C₂²⋊C₄	—	7	1	no	—
607	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
609	C₂×C₄²	—	7	1	no	—
610	C₂×C₄²	—	7	1	no	—
611	C₂×C₄²	—	7	1	no	—
612	C₂²×C₇	—	2	1	no	—
613	C₂²×C₇	—	2	1	no	—
614	C₂²×C₇	—	2	1	no	—
615	C₂²×C₇	—	2	1	no	—
616	C₂²×C₇	—	2	1	no	—
617	C₂²×C₇	—	2	1	no	—
618	C₂²×C₇	—	2	1	no	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	2	1	no	—
621	C₂²×C₇	—	2	1	no	—
622	C₂²×C₇	—	2	1	no	—
623	C₂²×C₇	—	8	2	no	—
624	C₂²×C₇	C₂×#41	1	2	yes	—
625	C₂²×C₇	C₂⁵	1	1	yes	characteristic
626	C₂×D₇	—	2	1	no	—
627	C₂×D₇	—	2	1	no	—
628	C₂×D₇	—	2	1	no	—
629	C₂×D₇	—	2	1	no	—
630	C₂×D₇	—	2	1	no	—
631	C₂×D₇	—	2	1	no	—
632	C₂×D₇	—	2	1	no	—
633	C₂×D₇	—	2	1	no	—
634	C₂×D₇	—	2	1	no	—
635	C₂×D₇	—	8	2	no	—
636	C₄×C₇	—	2	1	no	—
637	C₄×C₇	—	2	1	no	—
638	C₄×C₇	—	2	1	no	—
639	C₄×C₇	—	2	1	no	—
640	C₄×C₇	—	2	1	no	—
641	C₄×C₇	—	2	1	no	—
642	C₄×C₇	—	2	1	no	—
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	1	no	—
645	C₄×C₇	—	2	1	no	—
646	C₄×C₇	—	2	1	no	—
647	Dic₇	—	2	1	no	—
648	Dic₇	—	2	1	no	—
649	Dic₇	—	2	1	no	—
650	Dic₇	—	2	1	no	—
651	Dic₇	—	2	1	no	—
652	Dic₇	—	2	1	no	—
653	Dic₇	—	2	1	no	—
654	Dic₇	—	2	1	no	—
655	Dic₇	—	2	1	no	—
656	Dic₇	—	2	1	no	—
657	Dic₇	—	2	1	no	—
658	Dic₇	C₂×#41	1	2	yes	—
659	Dic₇	C₂×#41	1	2	yes	—
660	C₂⁴	—	7	1	no	—
661	C₂⁴	C₂²×D₇	1	1	yes	characteristic
662	#41	—	14	4	no	—
663	C₂×Q₈	—	7	1	no	—
664	C₂×Q₈	—	7	1	no	—
665	C₂×Q₈	—	7	1	no	—
666	C₂×Q₈	—	7	1	no	—
667	C₂×Q₈	—	7	1	no	—
668	C₂×Q₈	—	7	1	no	—
669	C₂×Q₈	—	7	1	no	—
670	C₂×Q₈	—	7	1	no	—
671	C₂×Q₈	—	14	4	no	—
672	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
673	C₂×D₄	—	7	1	no	—
674	C₂×D₄	—	7	1	no	—
675	C₂×D₄	—	7	1	no	—
676	C₂×D₄	—	7	1	no	—
677	C₂×D₄	—	7	1	no	—
678	C₂×D₄	—	7	1	no	—
679	C₂×D₄	—	7	1	no	—
680	C₂×D₄	—	7	1	no	—
681	C₂×D₄	—	7	1	no	—
682	C₂×D₄	—	7	1	no	—
683	C₂×D₄	—	7	1	no	—
684	C₂×D₄	—	7	1	no	—
685	C₂×D₄	—	14	4	no	—
686	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
687	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
688	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
689	C₂²×C₄	—	7	1	no	—
690	C₂²×C₄	—	7	1	no	—
691	C₂²×C₄	—	7	1	no	—
692	C₂²×C₄	—	7	1	no	—
693	C₂²×C₄	—	7	1	no	—
694	C₂²×C₄	—	7	1	no	—
695	C₂²×C₄	—	7	1	no	—
696	C₂²×C₄	—	7	1	no	—
697	C₂²×C₄	—	7	1	no	—
698	C₂²×C₄	—	7	1	no	—
699	C₂²×C₄	—	7	1	no	—
700	C₂²×C₄	—	7	1	no	—
701	C₂²×C₄	—	7	1	no	—
702	C₂²×C₄	—	7	1	no	—
703	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
705	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
706	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
707	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
708	C₄⋊C₄	—	7	1	no	—
709	C₄⋊C₄	—	7	1	no	—
710	C₄⋊C₄	—	7	1	no	—
711	C₄⋊C₄	—	7	1	no	—
712	C₄⋊C₄	—	7	1	no	—
713	C₄⋊C₄	—	7	1	no	—
714	C₄⋊C₄	—	7	1	no	—
715	C₄⋊C₄	—	7	1	no	—
716	C₄⋊C₄	—	7	1	no	—
717	C₄⋊C₄	—	7	1	no	—
718	C₄⋊C₄	—	7	1	no	—
719	C₄⋊C₄	—	7	1	no	—
720	C₄⋊C₄	—	7	1	no	—
721	C₄⋊C₄	—	7	1	no	—
722	C₄⋊C₄	—	7	1	no	—
723	C₄⋊C₄	—	7	1	no	—
724	C₄⋊C₄	—	7	1	no	—
725	C₄⋊C₄	—	7	1	no	—
726	C₄⋊C₄	—	7	1	no	—
727	C₄⋊C₄	—	7	1	no	—
728	C₄⋊C₄	—	7	1	no	—
729	C₄⋊C₄	—	7	1	no	—
730	C₄⋊C₄	—	7	1	no	—
731	C₄⋊C₄	—	7	1	no	—
732	C₄⋊C₄	—	7	1	no	—
733	C₄⋊C₄	—	7	1	no	—
734	C₄⋊C₄	—	7	1	no	—
735	C₄⋊C₄	—	7	1	no	—
736	C₄⋊C₄	—	7	1	no	—
737	C₄⋊C₄	—	7	1	no	—
738	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
746	C₂²⋊C₄	—	7	1	no	—
747	C₂²⋊C₄	—	7	1	no	—
748	C₂²⋊C₄	—	7	1	no	—
749	C₂²⋊C₄	—	7	1	no	—
750	C₂²⋊C₄	—	7	1	no	—
751	C₂²⋊C₄	—	7	1	no	—
752	C₂²⋊C₄	—	7	1	no	—
753	C₂²⋊C₄	—	7	1	no	—
754	C₂²⋊C₄	—	7	1	no	—
755	C₂²⋊C₄	—	7	1	no	—
756	C₂²⋊C₄	—	7	1	no	—
757	C₂²⋊C₄	—	7	1	no	—
758	C₂²⋊C₄	—	7	1	no	—
759	C₂²⋊C₄	—	7	1	no	—
760	C₂²⋊C₄	—	7	1	no	—
761	C₂²⋊C₄	—	7	1	no	—
762	C₂²⋊C₄	—	7	1	no	—
763	C₂²⋊C₄	—	7	1	no	—
764	C₂²⋊C₄	—	7	1	no	—
765	C₂²⋊C₄	—	7	1	no	—
766	C₂²⋊C₄	—	7	1	no	—
767	C₂²⋊C₄	—	7	1	no	—
768	C₂²⋊C₄	—	7	1	no	—
769	C₂²⋊C₄	—	7	1	no	—
770	C₂²⋊C₄	—	7	1	no	—
771	C₂²⋊C₄	—	7	1	no	—
772	C₂²⋊C₄	—	7	1	no	—
773	C₂²⋊C₄	—	7	1	no	—
774	C₂²⋊C₄	—	7	1	no	—
775	C₂²⋊C₄	—	7	1	no	—
776	C₂²⋊C₄	—	7	1	no	—
777	C₂²⋊C₄	—	7	1	no	—
778	C₂²⋊C₄	—	7	1	no	—
779	C₂²⋊C₄	—	7	1	no	—
780	C₂²⋊C₄	—	7	1	no	—
781	C₂²⋊C₄	—	7	1	no	—
782	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
784	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
785	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
786	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
787	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
788	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
789	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
790	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
791	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
792	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
796	C₄²	—	7	1	no	—
797	C₄²	—	7	1	no	—
798	C₄²	—	7	1	no	—
799	C₄²	—	7	1	no	—
800	C₄²	—	7	1	no	—
801	C₄²	—	7	1	no	—
802	C₄²	—	7	1	no	—
803	C₄²	—	7	1	no	—
804	C₄²	—	7	1	no	—
805	C₄²	—	7	1	no	—
806	C₄²	—	7	1	no	—
807	C₄²	—	7	1	no	—
808	C₄²	—	7	1	no	—
809	C₄²	—	7	1	no	—
810	C₄²	—	7	1	no	—
811	C₄²	—	7	1	no	—
812	C₄²	—	7	1	no	—
813	C₄²	—	7	1	no	—
814	C₄²	—	7	1	no	—
815	C₄²	C₂²×D₇	1	1	yes	characteristic
816	C₄²	C₂²×D₇	1	1	yes	characteristic
817	C₄²	C₂²×D₇	1	1	yes	characteristic
818	C₂×C₇	—	2	2	no	—
819	C₂×C₇	—	4	1	no	—
820	C₂×C₇	—	4	1	no	—
821	C₂×C₇	—	4	1	no	—
822	C₂×C₇	C₂²×#41	1	1	yes	characteristic
823	C₂×C₇	#585	1	1	yes	characteristic
824	C₂×C₇	#585	1	1	yes	characteristic
825	D₇	—	4	1	no	—
826	D₇	—	4	1	no	—
827	D₇	—	4	1	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	7	1	no	—
832	C₂³	—	7	1	no	—
833	C₂³	—	7	1	no	—
834	C₂³	—	14	2	no	—
835	C₂³	—	28	1	no	—
836	C₂³	—	28	1	no	—
837	C₂³	C₂³×D₇	1	1	yes	characteristic
838	C₂³	C₂³×D₇	1	1	yes	characteristic
839	C₂³	C₂³×D₇	1	1	yes	characteristic
840	C₂³	C₂³×D₇	1	1	yes	characteristic
841	Q₈	—	4	1	no	—
842	Q₈	—	14	2	no	—
843	Q₈	—	14	2	no	—
844	Q₈	—	14	2	no	—
845	Q₈	—	14	2	no	—
846	Q₈	—	14	2	no	—
847	Q₈	—	28	1	no	—
848	Q₈	—	28	1	no	—
849	Q₈	—	28	1	no	—
850	D₄	—	2	2	no	—
851	D₄	—	4	1	no	—
852	D₄	—	4	1	no	—
853	D₄	—	14	2	no	—
854	D₄	—	14	2	no	—
855	D₄	—	14	2	no	—
856	D₄	—	14	2	no	—
857	D₄	—	14	2	no	—
858	D₄	—	14	2	no	—
859	D₄	—	28	1	no	—
860	D₄	—	28	1	no	—
861	D₄	—	28	1	no	—
862	D₄	—	28	1	no	—
863	D₄	—	28	1	no	—
864	D₄	—	28	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	7	4	no	—
871	C₂×C₄	—	7	1	no	—
872	C₂×C₄	—	7	1	no	—
873	C₂×C₄	—	7	1	no	—
874	C₂×C₄	—	7	1	no	—
875	C₂×C₄	—	7	1	no	—
876	C₂×C₄	—	7	1	no	—
877	C₂×C₄	—	7	1	no	—
878	C₂×C₄	—	7	1	no	—
879	C₂×C₄	—	7	1	no	—
880	C₂×C₄	—	7	1	no	—
881	C₂×C₄	—	7	1	no	—
882	C₂×C₄	—	7	1	no	—
883	C₂×C₄	—	7	1	no	—
884	C₂×C₄	—	14	2	no	—
885	C₂×C₄	—	14	2	no	—
886	C₂×C₄	—	14	2	no	—
887	C₂×C₄	—	28	1	no	—
888	C₂×C₄	—	28	1	no	—
889	C₂×C₄	—	28	1	no	—
890	C₂×C₄	—	28	1	no	—
891	C₂×C₄	—	28	1	no	—
892	C₂×C₄	—	28	1	no	—
893	C₂×C₄	—	28	1	no	—
894	C₂×C₄	—	28	1	no	—
895	C₂×C₄	—	28	1	no	—
896	C₂×C₄	—	28	1	no	—
897	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
898	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
899	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
908	C₇	#3510	1	1	yes	characteristic, complemented, Sylow
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	8	2	no	—
921	C₂²	—	14	1	no	—
922	C₂²	—	14	1	no	—
923	C₂²	—	14	1	no	—
924	C₂²	—	14	1	no	—
925	C₂²	—	14	1	no	—
926	C₂²	—	14	1	no	—
927	C₂²	—	14	1	no	—
928	C₂²	—	14	1	no	—
929	C₂²	—	14	1	no	—
930	C₂²	—	56	2	no	—
931	C₂²	D₇×#41	1	2	yes	—
932	C₂²	C₂⁴×D₇	1	1	yes	characteristic
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	7	2	no	—
945	C₄	—	7	2	no	—
946	C₄	—	14	1	no	—
947	C₄	—	14	1	no	—
948	C₄	—	14	1	no	—
949	C₄	—	14	1	no	—
950	C₄	—	14	1	no	—
951	C₄	—	14	1	no	—
952	C₄	—	14	1	no	—
953	C₄	—	14	1	no	—
954	C₄	—	14	1	no	—
955	C₄	—	14	1	no	—
956	C₄	—	14	1	no	—
957	C₂	—	2	2	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	—	28	1	no	—
962	C₂	—	28	1	no	—
963	C₂	—	28	1	no	—
964	C₂	C₂×D₇×#41	1	1	yes	characteristic
965	C₂	#90616	1	1	yes	characteristic
966	C₂	#90618	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#551	C₂
prime radical	#90283	C₂
hypercenter	#551	D₇
hypocenter	C₇	#3510
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. C₇×#551	C₂	semidirect
2. #90401	C₂	semidirect
3. #90397	C₂	semidirect
4. #90393	C₂	semidirect
5. #90393	C₂	semidirect
6. #90372	C₂	semidirect
7. #90360	C₂	semidirect
8. #90355	C₂	semidirect
9. #90355	C₂	semidirect
10. #90353	C₂	semidirect
11. #90349	C₂	semidirect
12. #90340	C₂	semidirect
13. #90339	C₂	semidirect
14. #90332	C₂	semidirect
15. #90331	C₂	semidirect
16. #90328	C₂	semidirect
17. #90313	C₂	semidirect
19. #90278	C₂	semidirect
20. #90250	C₂	semidirect
21. #90247	C₂	semidirect
22. #90229	C₂	semidirect
23. C₄×#1159	C₂	semidirect
24. #90224	C₂	semidirect
25. #90219	C₂	semidirect
26. #90218	C₂	semidirect
27. #90207	C₂	semidirect
28. #90186	C₂	semidirect
29. #90186	C₂	semidirect
30. C₂×#6448	C₂	semidirect
31. #90177	C₂	semidirect
35. C₇×#126	C₂²	semidirect
36. C₇×#126	C₂²	semidirect
37. C₇×#124	C₂²	semidirect
39. C₇×#123	C₂²	semidirect
40. C₇×#123	C₂²	semidirect
42. C₇×C₂²⋊Q₈	C₂²	semidirect
45. C₄×C₇×D₄	C₂²	semidirect
47. C₇×#117	C₂²	semidirect
53. #6510	C₂²	semidirect
54. #6509	C₂²	semidirect
55. Q₈×Dic₇	C₂²	semidirect
56. #6507	C₂²	semidirect
62. #6499	C₂²	semidirect
64. #6498	C₂²	semidirect
65. #6498	C₂²	semidirect
67. D₄×Dic₇	C₂²	semidirect
69. #6492	C₂²	semidirect
70. #6492	C₂²	semidirect
76. C₄×C₂²⋊D₇	C₂²	semidirect
77. C₄×C₂²⋊D₇	C₂²	semidirect
78. C₄×C₂²⋊D₇	C₂²	semidirect
82. #6489	C₂²	semidirect
84. #6487	C₂²	semidirect
86. C₂×C₄×Dic₇	C₂²	semidirect
87. #6461	C₂²	semidirect
88. #6461	C₂²	semidirect
89. #6461	C₂²	semidirect
90. #6461	C₂²	semidirect
91. #6461	C₂²	semidirect
92. #6461	C₂²	semidirect
93. #6460	C₂²	semidirect
94. #6459	C₂²	semidirect
95. #6459	C₂²	semidirect
96. #6459	C₂²	semidirect
97. #6459	C₂²	semidirect
98. #6457	C₂²	semidirect
99. #6457	C₂²	semidirect
100. #6457	C₂²	semidirect
101. #6457	C₂²	semidirect
102. #6456	C₂²	semidirect
103. #6455	C₂²	semidirect
104. #6455	C₂²	semidirect
105. #6455	C₂²	semidirect
106. #6452	C₂²	semidirect
107. #6452	C₂²	semidirect
108. #6451	C₂²	semidirect
109. #6451	C₂²	semidirect
110. #6451	C₂²	semidirect
111. #6450	C₂²	semidirect
112. #6450	C₂²	semidirect
113. #6450	C₂²	semidirect
114. #6450	C₂²	semidirect
115. #6450	C₂²	semidirect
116. #6450	C₂²	semidirect
117. #6450	C₂²	semidirect
118. #6450	C₂²	semidirect
120. #6449	C₂²	semidirect
121. #6449	C₂²	semidirect
132. #6448	C₂²	semidirect
133. #6448	C₂²	semidirect
134. #6448	C₂²	semidirect
135. #6448	C₂²	semidirect
136. #6448	C₂²	semidirect
137. #6448	C₂²	semidirect
140. #6446	C₂²	semidirect
141. #6446	C₂²	semidirect
142. #6446	C₂²	semidirect
143. #6446	C₂²	semidirect
150. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
151. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
152. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
155. #6442	C₂²	semidirect
156. #6442	C₂²	semidirect
157. #6442	C₂²	semidirect
158. #6442	C₂²	semidirect
159. #6442	C₂²	semidirect
160. #6442	C₂²	semidirect
163. #6441	C₂²	semidirect
164. #6441	C₂²	semidirect
165. #6441	C₂²	semidirect
166. #6441	C₂²	semidirect
172. #6440	C₂²	semidirect
173. #6440	C₂²	semidirect
174. #6440	C₂²	semidirect
175. #6439	C₂²	semidirect
176. #6439	C₂²	semidirect
177. #6438	C₂²	semidirect
178. C₄×D₂₈	C₂²	semidirect
179. #6435	C₂²	semidirect
180. #6435	C₂²	semidirect
181. C₄²×D₇	C₂²	semidirect
182. C₄×Dic₁₄	C₂²	semidirect
183. C₄×Dic₁₄	C₂²	semidirect
184. C₄×Dic₁₄	C₂²	semidirect
185. C₄×Dic₁₄	C₂²	semidirect
186. C₄×Dic₁₄	C₂²	semidirect
361. #551	D₇	semidirect
480. #126	C₂×D₇	semidirect
481. #126	C₂×D₇	semidirect
503. #124	C₂×D₇	semidirect
522. #123	C₂×D₇	semidirect
523. #123	C₂×D₇	semidirect
539. C₂²⋊Q₈	C₂×D₇	semidirect
583. C₄×D₄	C₂×D₇	semidirect
600. #117	C₂×D₇	semidirect
908. C₇	#3510	semidirect

Maximal subgroups

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

subgroup	index
C₇×#551	2
#90401	2
#90397	2
#90393	2
#90372	2
#90360	2
#90355	2
#90353	2
#90349	2
#90340	2
#90339	2
#90332	2
#90331	2
#90328	2
#90313	2
#90283	2
#90278	2
#90250	2
#90247	2
#90229	2
C₄×#1159	2
#90224	2
#90219	2
#90218	2
#90207	2
#90186	2
C₂×#6448	2
#90177	2
#3510	7