Subgroups — #11743491

Order 896.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	#90403	C₂	1	1	yes	maximal, characteristic, complemented
3	#90401	C₂	1	1	yes	maximal, characteristic, complemented
4	#90397	C₂	1	1	yes	maximal, characteristic, complemented
5	#90396	C₂	1	1	yes	maximal, characteristic, complemented
6	#90369	C₂	1	1	yes	maximal, characteristic, complemented
7	#90366	C₂	1	1	yes	maximal, characteristic, complemented
8	D₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
9	#90360	C₂	1	1	yes	maximal, characteristic, complemented
10	#90358	C₂	1	1	yes	maximal, characteristic, complemented
11	#90350	C₂	1	1	yes	maximal, characteristic, complemented
12	#90349	C₂	1	1	yes	maximal, characteristic, complemented
13	#90349	C₂	1	1	yes	maximal, characteristic, complemented
14	#90331	C₂	1	1	yes	maximal, characteristic, complemented
15	#90319	C₂	1	1	yes	maximal, characteristic, complemented
16	#90312	C₂	1	1	yes	maximal, characteristic, complemented
17	#90307	C₂	1	1	yes	maximal, characteristic, complemented
18	#90303	C₂	1	1	yes	maximal, characteristic, complemented
19	#90301	C₂	1	1	yes	maximal, characteristic, complemented
20	#90296	C₂	1	1	yes	maximal, characteristic, complemented
21	#90294	C₂	1	1	yes	maximal, characteristic, complemented
22	#90285	C₂	1	1	yes	maximal, characteristic, complemented
23	#90284	C₂	1	1	yes	maximal, characteristic, complemented
24	#90282	C₂	1	1	yes	maximal, characteristic, complemented
25	#90280	C₂	1	1	yes	maximal, characteristic, complemented
26	#90254	C₂	1	1	yes	maximal, characteristic, complemented
27	#90251	C₂	1	1	yes	maximal, characteristic, complemented
28	#90248	C₂	1	1	yes	maximal, characteristic, complemented
29	#90247	C₂	1	1	yes	maximal, characteristic, complemented
30	#90186	C₂	1	1	yes	maximal, characteristic, complemented
31	#90181	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×#1159	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×#1157	C₂²	1	1	yes	characteristic
38	C₇×#126	C₂²	1	1	yes	characteristic, complemented
39	C₇×#126	C₂²	1	1	yes	characteristic, complemented
40	C₇×#124	C₂²	1	1	yes	characteristic, complemented
41	C₇×#124	C₂²	1	1	yes	characteristic, complemented
42	C₇×#123	C₂²	1	1	yes	characteristic, complemented
43	C₇×#123	C₂²	1	1	yes	characteristic, complemented
44	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₇×#121	C₂²	1	1	yes	characteristic
46	C₇×#121	C₂²	1	1	yes	characteristic, complemented
47	C₇×#121	C₂²	1	1	yes	characteristic, complemented
48	C₇×#120	C₂²	1	1	yes	characteristic, complemented
49	C₇×#120	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	#6516	C₂²	1	1	yes	characteristic
54	#6516	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
56	#6510	C₂²	1	1	yes	characteristic, complemented
57	#6509	C₂²	1	1	yes	characteristic, complemented
58	#6507	C₂²	1	1	yes	characteristic, complemented
59	#6502	C₂²	1	1	yes	characteristic
60	#6502	C₂²	1	1	yes	characteristic, complemented
61	#6502	C₂²	1	1	yes	characteristic, complemented
62	#6502	C₂²	1	1	yes	characteristic, complemented
63	#6502	C₂²	1	1	yes	characteristic, complemented
64	#6501	C₂²	1	1	yes	characteristic
65	#6501	C₂²	1	1	yes	characteristic, complemented
66	#6501	C₂²	1	1	yes	characteristic, complemented
67	#6501	C₂²	1	1	yes	characteristic, complemented
68	#6500	C₂²	1	1	yes	characteristic
69	#6500	C₂²	1	1	yes	characteristic
70	#6500	C₂²	1	1	yes	characteristic
71	#6500	C₂²	1	1	yes	characteristic
72	#6500	C₂²	1	1	yes	characteristic, complemented
73	#6500	C₂²	1	1	yes	characteristic, complemented
74	#6499	C₂²	1	1	yes	characteristic, complemented
75	#6499	C₂²	1	1	yes	characteristic, complemented
76	#6499	C₂²	1	1	yes	characteristic, complemented
77	#6499	C₂²	1	1	yes	characteristic, complemented
78	#6499	C₂²	1	1	yes	characteristic, complemented
79	#6498	C₂²	1	1	yes	characteristic, complemented
80	#6498	C₂²	1	1	yes	characteristic, complemented
81	#6498	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
84	#6493	C₂²	1	1	yes	characteristic, complemented
85	#6493	C₂²	1	1	yes	characteristic, complemented
86	#6492	C₂²	1	1	yes	characteristic, complemented
87	#6492	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
92	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
93	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	#6489	C₂²	1	1	yes	characteristic, complemented
95	#6489	C₂²	1	1	yes	characteristic, complemented
96	#6489	C₂²	1	1	yes	characteristic, complemented
97	#6487	C₂²	1	1	yes	characteristic, complemented
98	#6487	C₂²	1	1	yes	characteristic, complemented
99	#6461	C₂²	1	1	yes	characteristic, complemented
100	#6461	C₂²	1	1	yes	characteristic, complemented
101	#6461	C₂²	1	1	yes	characteristic, complemented
102	#6460	C₂²	1	1	yes	characteristic, complemented
103	#6460	C₂²	1	1	yes	characteristic, complemented
104	#6460	C₂²	1	1	yes	characteristic, complemented
105	#6459	C₂²	1	1	yes	characteristic, complemented
106	#6459	C₂²	1	1	yes	characteristic, complemented
107	#6459	C₂²	1	1	yes	characteristic, complemented
108	#6459	C₂²	1	1	yes	characteristic, complemented
109	#6457	C₂²	1	1	yes	characteristic, complemented
110	#6457	C₂²	1	1	yes	characteristic, complemented
111	#6457	C₂²	1	1	yes	characteristic, complemented
112	#6457	C₂²	1	1	yes	characteristic, complemented
113	#6456	C₂²	1	1	yes	characteristic, complemented
114	#6455	C₂²	1	1	yes	characteristic, complemented
115	#6455	C₂²	1	1	yes	characteristic, complemented
116	#6455	C₂²	1	1	yes	characteristic, complemented
117	#6455	C₂²	1	1	yes	characteristic, complemented
118	#6453	C₂²	1	1	yes	characteristic, complemented
119	#6452	C₂²	1	1	yes	characteristic, complemented
120	#6451	C₂²	1	1	yes	characteristic, complemented
121	#6451	C₂²	1	1	yes	characteristic, complemented
122	#6450	C₂²	1	1	yes	characteristic, complemented
123	#6449	C₂²	1	1	yes	characteristic
124	#6449	C₂²	1	1	yes	characteristic, complemented
125	#6449	C₂²	1	1	yes	characteristic, complemented
126	#6448	C₂²	1	1	yes	characteristic
127	#6448	C₂²	1	1	yes	characteristic
128	#6448	C₂²	1	1	yes	characteristic, complemented
129	#6448	C₂²	1	1	yes	characteristic, complemented
130	#6448	C₂²	1	1	yes	characteristic, complemented
131	#6448	C₂²	1	1	yes	characteristic, complemented
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	#6448	C₂²	1	1	yes	characteristic, complemented
139	#6447	C₂²	1	1	yes	characteristic
140	#6447	C₂²	1	1	yes	characteristic
141	#6447	C₂²	1	1	yes	characteristic
142	#6447	C₂²	1	1	yes	characteristic, complemented
143	#6446	C₂²	1	1	yes	characteristic
144	#6446	C₂²	1	1	yes	characteristic, complemented
145	#6446	C₂²	1	1	yes	characteristic, complemented
146	#6446	C₂²	1	1	yes	characteristic, complemented
147	#6446	C₂²	1	1	yes	characteristic, complemented
148	#6446	C₂²	1	1	yes	characteristic, complemented
149	#6446	C₂²	1	1	yes	characteristic, complemented
150	#6446	C₂²	1	1	yes	characteristic, complemented
151	#6446	C₂²	1	1	yes	characteristic, complemented
152	#6446	C₂²	1	1	yes	characteristic, complemented
153	#6445	C₂²	1	1	yes	characteristic
154	#6445	C₂²	1	1	yes	characteristic, complemented
155	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
156	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
161	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
162	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	#6442	C₂²	1	1	yes	characteristic, complemented
166	#6442	C₂²	1	1	yes	characteristic, complemented
167	#6442	C₂²	1	1	yes	characteristic, complemented
168	#6442	C₂²	1	1	yes	characteristic, complemented
169	#6442	C₂²	1	1	yes	characteristic, complemented
170	#6441	C₂²	1	1	yes	characteristic, complemented
171	#6441	C₂²	1	1	yes	characteristic, complemented
172	#6441	C₂²	1	1	yes	characteristic, complemented
173	#6441	C₂²	1	1	yes	characteristic, complemented
174	#6441	C₂²	1	1	yes	characteristic, complemented
175	#6441	C₂²	1	1	yes	characteristic, complemented
176	#6441	C₂²	1	1	yes	characteristic, complemented
177	#6440	C₂²	1	1	yes	characteristic, complemented
178	#6440	C₂²	1	1	yes	characteristic, complemented
179	#6439	C₂²	1	1	yes	characteristic, complemented
180	#6439	C₂²	1	1	yes	characteristic, complemented
181	#6438	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
183	#6435	C₂²	1	1	yes	characteristic, complemented
184	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
185	#6432	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
187	#3545	—	7	1	no	maximal, Sylow
188	C₂⁴×C₇	C₂³	1	1	yes	characteristic
189	C₂³×D₇	C₂³	1	1	yes	characteristic
190	C₂³×D₇	C₂³	1	1	yes	characteristic
191	C₂³×D₇	C₂³	1	1	yes	characteristic
192	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
193	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
196	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
197	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
198	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
199	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₇	—	4	2	no	—
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	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
219	C₂²×Dic₇	C₂³	1	1	yes	characteristic
220	C₂²×Dic₇	C₂³	1	1	yes	characteristic
221	C₂²×Dic₇	C₂³	1	1	yes	characteristic
222	C₂²×Dic₇	C₂³	1	1	yes	characteristic
223	C₂²×Dic₇	C₂³	1	1	yes	characteristic
224	Q₈×D₇	—	4	2	no	—
225	#1159	—	4	2	no	—
226	D₄×D₇	—	4	2	no	—
227	D₄×D₇	—	4	2	no	—
228	#1157	—	4	2	no	—
229	C₂×D₂₈	C₂³	1	1	yes	characteristic
230	C₂×D₂₈	C₂³	1	1	yes	characteristic
231	C₂×D₂₈	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
242	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
243	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
244	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
245	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
246	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
247	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
248	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
249	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₇×C₄⋊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	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₄²×C₇	C₂³	1	1	yes	characteristic
270	C₄²×C₇	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	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₇	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	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
311	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
312	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
315	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
316	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₇	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	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₇⋊C₄	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	C₄×Dic₇	C₂³	1	1	yes	characteristic
347	C₄×Dic₇	C₂³	1	1	yes	characteristic
348	C₄×Dic₇	C₂³	1	1	yes	characteristic
349	#563	—	7	1	no	—
350	#562	—	7	1	no	—
351	#562	—	7	1	no	—
352	H(3,𝔽₄)	—	7	1	no	—
353	#555	—	7	1	no	—
354	#555	—	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	#546	—	7	1	no	—
362	#546	—	7	1	no	—
363	#546	—	7	1	no	—
364	#546	—	7	1	no	—
365	#542	—	7	1	no	—
366	#542	—	7	1	no	—
367	#542	—	7	1	no	—
368	#542	—	7	1	no	—
369	#538	—	7	1	no	—
370	#538	—	7	1	no	—
371	#538	—	7	1	no	—
372	#538	D₇	1	1	yes	characteristic, complemented
373	#536	—	7	1	no	—
374	#536	—	7	1	no	—
375	#534	—	7	1	no	—
376	#534	—	7	1	no	—
377	#529	—	7	1	no	—
378	#529	—	7	1	no	—
379	C₂×#124	—	7	1	no	—
380	C₂³×C₇	—	4	1	no	—
381	C₂³×C₇	—	4	1	no	—
382	C₂³×C₇	—	4	1	no	—
383	C₂³×C₇	C₂⁴	1	1	yes	characteristic
384	C₂³×C₇	C₂⁴	1	1	yes	characteristic
385	C₂³×C₇	C₂⁴	1	1	yes	characteristic
386	C₂³×C₇	C₂⁴	1	1	yes	characteristic
387	C₂³×C₇	C₂⁴	1	1	yes	characteristic
388	C₂²×D₇	—	2	2	no	—
389	C₂²×D₇	—	2	2	no	—
390	C₂²×D₇	—	4	1	no	—
391	C₂²×D₇	—	4	1	no	—
392	C₂²×D₇	—	4	1	no	—
393	C₂²×D₇	—	4	1	no	—
394	C₂²×D₇	—	4	1	no	—
395	C₂²×D₇	—	4	1	no	—
396	C₂²×D₇	—	4	1	no	—
397	C₂²×D₇	C₂⁴	1	1	yes	characteristic
398	C₂²×D₇	C₂⁴	1	1	yes	characteristic
399	C₂²×D₇	C₂⁴	1	1	yes	characteristic
400	C₂²×D₇	C₂⁴	1	1	yes	characteristic
401	C₇×Q₈	—	4	1	no	—
402	C₇×D₄	—	4	1	no	—
403	C₇×D₄	—	4	1	no	—
404	C₇×D₄	—	4	1	no	—
405	C₇×D₄	—	4	1	no	—
406	C₇×D₄	—	4	1	no	—
407	C₇×D₄	—	4	1	no	—
408	C₇×D₄	—	4	1	no	—
409	C₂×C₄×C₇	—	4	1	no	—
410	C₂×C₄×C₇	—	4	1	no	—
411	C₂×C₄×C₇	—	4	1	no	—
412	C₂×C₄×C₇	—	4	1	no	—
413	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
418	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
419	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
420	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
421	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
423	C₂²⋊D₇	—	2	2	no	—
424	C₂²⋊D₇	—	2	2	no	—
425	C₂²⋊D₇	—	2	2	no	—
426	C₂²⋊D₇	—	4	1	no	—
427	C₂²⋊D₇	—	4	1	no	—
428	C₂²⋊D₇	—	4	1	no	—
429	C₂²⋊D₇	—	4	1	no	—
430	C₂²⋊D₇	—	4	1	no	—
431	C₂²⋊D₇	—	4	1	no	—
432	C₂²⋊D₇	—	4	1	no	—
433	C₂²⋊D₇	—	4	1	no	—
434	C₂²⋊D₇	—	4	1	no	—
435	C₂²⋊D₇	—	4	1	no	—
436	C₂²⋊D₇	—	4	1	no	—
437	C₂×Dic₇	—	4	1	no	—
438	C₂×Dic₇	—	4	1	no	—
439	C₂×Dic₇	—	4	1	no	—
440	C₂×Dic₇	—	4	1	no	—
441	C₂×Dic₇	—	4	1	no	—
442	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
443	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
444	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
445	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
446	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
447	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
448	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
449	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
450	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
451	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
452	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
453	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
454	D₂₈	—	2	2	no	—
455	D₂₈	—	4	1	no	—
456	D₂₈	—	4	1	no	—
457	C₄×D₇	—	2	2	no	—
458	C₄×D₇	—	2	2	no	—
459	C₄×D₇	—	2	2	no	—
460	C₄×D₇	—	4	1	no	—
461	C₄×D₇	—	4	1	no	—
462	C₄×D₇	—	4	1	no	—
463	C₄×D₇	—	4	1	no	—
464	C₄×D₇	—	4	1	no	—
465	C₄×D₇	—	4	1	no	—
466	C₄×D₇	—	4	1	no	—
467	Dic₁₄	—	4	1	no	—
468	Dic₁₄	—	4	1	no	—
469	Dic₁₄	—	4	1	no	—
470	Dic₁₄	—	4	1	no	—
471	Dic₁₄	—	4	1	no	—
472	Dic₁₄	—	4	1	no	—
473	Dic₁₄	—	4	1	no	—
474	C₂×#41	—	7	1	no	—
475	C₂×#41	—	7	1	no	—
476	C₂²×Q₈	—	7	1	no	—
477	C₂²×D₄	—	7	1	no	—
478	C₂²×D₄	—	7	1	no	—
479	C₂²×D₄	—	7	1	no	—
480	C₄⋊Q₈	—	7	1	no	—
481	C₄⋊Q₈	—	7	1	no	—
482	C₄⋊Q₈	—	7	1	no	—
483	C₄⋊Q₈	—	7	1	no	—
484	#126	—	7	1	no	—
485	#126	—	7	1	no	—
486	#126	—	7	1	no	—
487	#126	—	7	1	no	—
488	#126	—	7	1	no	—
489	#126	—	7	1	no	—
490	#126	—	7	1	no	—
491	#126	—	7	1	no	—
492	#126	—	7	1	no	—
493	#126	—	7	1	no	—
494	#126	C₂×D₇	1	1	yes	characteristic, complemented
495	#126	C₂×D₇	1	1	yes	characteristic, complemented
496	#125	—	7	1	no	—
497	#125	—	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	—	7	1	no	—
504	#124	—	7	1	no	—
505	#124	—	7	1	no	—
506	#124	—	7	1	no	—
507	#124	—	7	1	no	—
508	#124	—	7	1	no	—
509	#124	—	7	1	no	—
510	#124	—	7	1	no	—
511	#124	—	7	1	no	—
512	#124	—	7	1	no	—
513	#124	—	7	1	no	—
514	#124	—	7	1	no	—
515	#124	—	7	1	no	—
516	#124	—	7	1	no	—
517	#124	—	7	1	no	—
518	#124	C₂×D₇	1	1	yes	characteristic, complemented
519	#124	C₂×D₇	1	1	yes	characteristic, complemented
520	#123	—	7	1	no	—
521	#123	—	7	1	no	—
522	#123	—	7	1	no	—
523	#123	—	7	1	no	—
524	#123	—	7	1	no	—
525	#123	—	7	1	no	—
526	#123	—	7	1	no	—
527	#123	—	7	1	no	—
528	#123	—	7	1	no	—
529	#123	—	7	1	no	—
530	#123	—	7	1	no	—
531	#123	—	7	1	no	—
532	#123	—	7	1	no	—
533	#123	—	7	1	no	—
534	#123	—	7	1	no	—
535	#123	—	7	1	no	—
536	#123	—	7	1	no	—
537	#123	—	7	1	no	—
538	#123	—	7	1	no	—
539	#123	—	7	1	no	—
540	#123	—	7	1	no	—
541	#123	—	7	1	no	—
542	#123	C₂×D₇	1	1	yes	characteristic, complemented
543	#123	C₂×D₇	1	1	yes	characteristic, complemented
544	C₂²⋊Q₈	—	7	1	no	—
545	C₂²⋊Q₈	—	7	1	no	—
546	C₂²⋊Q₈	—	7	1	no	—
547	C₂²⋊Q₈	—	7	1	no	—
548	C₂²⋊Q₈	—	7	1	no	—
549	C₂²⋊Q₈	—	7	1	no	—
550	C₂²⋊Q₈	—	7	1	no	—
551	C₂²⋊Q₈	—	7	1	no	—
552	C₂²⋊Q₈	—	7	1	no	—
553	C₂²⋊Q₈	—	7	1	no	—
554	C₂²⋊Q₈	—	7	1	no	—
555	C₂²⋊Q₈	—	7	1	no	—
556	C₂²⋊Q₈	—	7	1	no	—
557	C₂²⋊Q₈	—	7	1	no	—
558	C₂²⋊Q₈	—	7	1	no	—
559	C₂²⋊Q₈	—	7	1	no	—
560	C₂²⋊Q₈	—	7	1	no	—
561	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
562	#121	—	7	1	no	—
563	#121	—	7	1	no	—
564	#121	—	7	1	no	—
565	#121	—	7	1	no	—
566	#121	—	7	1	no	—
567	#121	—	7	1	no	—
568	#121	—	7	1	no	—
569	#121	—	7	1	no	—
570	#121	—	7	1	no	—
571	#121	—	7	1	no	—
572	#121	—	7	1	no	—
573	#121	—	7	1	no	—
574	#121	—	7	1	no	—
575	#121	—	7	1	no	—
576	#121	—	7	1	no	—
577	#121	C₂×D₇	1	1	yes	characteristic
578	#121	C₂×D₇	1	1	yes	characteristic, complemented
579	#121	C₂×D₇	1	1	yes	characteristic, complemented
580	#120	—	7	1	no	—
581	#120	—	7	1	no	—
582	#120	—	7	1	no	—
583	#120	—	7	1	no	—
584	#120	—	7	1	no	—
585	#120	—	7	1	no	—
586	#120	—	7	1	no	—
587	#120	—	7	1	no	—
588	#120	—	7	1	no	—
589	#120	—	7	1	no	—
590	#120	C₂×D₇	1	1	yes	characteristic, complemented
591	#120	C₂×D₇	1	1	yes	characteristic, complemented
592	C₄×Q₈	—	7	1	no	—
593	C₄×Q₈	—	7	1	no	—
594	C₄×D₄	—	7	1	no	—
595	C₄×D₄	—	7	1	no	—
596	C₄×D₄	—	7	1	no	—
597	C₄×D₄	—	7	1	no	—
598	C₄×D₄	—	7	1	no	—
599	C₄×D₄	—	7	1	no	—
600	C₄×D₄	—	7	1	no	—
601	C₄×D₄	—	7	1	no	—
602	C₄×D₄	—	7	1	no	—
603	C₄×D₄	—	7	1	no	—
604	C₄×D₄	—	7	1	no	—
605	C₄×D₄	—	7	1	no	—
606	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
607	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
608	#117	—	7	1	no	—
609	#117	—	7	1	no	—
610	#117	—	7	1	no	—
611	#117	—	7	1	no	—
612	#117	—	7	1	no	—
613	#117	—	7	1	no	—
614	#117	—	7	1	no	—
615	#117	—	7	1	no	—
616	#117	—	7	1	no	—
617	#117	—	7	1	no	—
618	C₂×C₂²⋊C₄	—	7	1	no	—
619	C₂×C₂²⋊C₄	—	7	1	no	—
620	C₂×C₂²⋊C₄	—	7	1	no	—
621	C₂×C₂²⋊C₄	—	7	1	no	—
622	C₂×C₂²⋊C₄	—	7	1	no	—
623	C₂×C₂²⋊C₄	—	7	1	no	—
624	C₂×C₂²⋊C₄	—	7	1	no	—
625	C₂×C₂²⋊C₄	—	7	1	no	—
626	C₂×C₂²⋊C₄	—	7	1	no	—
627	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
628	C₂×C₄²	—	7	1	no	—
629	C₂²×C₇	—	2	1	no	—
630	C₂²×C₇	—	2	1	no	—
631	C₂²×C₇	—	2	1	no	—
632	C₂²×C₇	—	2	1	no	—
633	C₂²×C₇	—	2	1	no	—
634	C₂²×C₇	—	2	1	no	—
635	C₂²×C₇	—	2	1	no	—
636	C₂²×C₇	—	2	1	no	—
637	C₂²×C₇	—	2	1	no	—
638	C₂²×C₇	—	2	1	no	—
639	C₂²×C₇	—	2	1	no	—
640	C₂²×C₇	—	2	1	no	—
641	C₂²×C₇	—	2	1	no	—
642	C₂²×C₇	—	2	1	no	—
643	C₂²×C₇	—	2	1	no	—
644	C₂²×C₇	—	8	2	no	—
645	C₂²×C₇	C₂⁵	1	1	yes	characteristic
646	C₂×D₇	—	2	1	no	—
647	C₂×D₇	—	2	1	no	—
648	C₂×D₇	—	2	1	no	—
649	C₂×D₇	—	2	1	no	—
650	C₂×D₇	—	2	1	no	—
651	C₂×D₇	—	2	1	no	—
652	C₂×D₇	—	2	1	no	—
653	C₂×D₇	—	2	1	no	—
654	C₂×D₇	—	2	1	no	—
655	C₂×D₇	—	2	1	no	—
656	C₂×D₇	—	2	1	no	—
657	C₂×D₇	—	8	2	no	—
658	C₂×D₇	—	8	2	no	—
659	C₂×D₇	—	8	2	no	—
660	C₂×D₇	H(5,𝔽₂)	1	2	yes	—
661	C₄×C₇	—	2	1	no	—
662	C₄×C₇	—	2	1	no	—
663	C₄×C₇	—	2	1	no	—
664	C₄×C₇	—	2	1	no	—
665	C₄×C₇	—	2	1	no	—
666	C₄×C₇	—	2	1	no	—
667	C₄×C₇	—	2	1	no	—
668	C₄×C₇	—	2	1	no	—
669	C₄×C₇	—	2	1	no	—
670	C₄×C₇	—	2	1	no	—
671	Dic₇	—	2	1	no	—
672	Dic₇	—	2	1	no	—
673	Dic₇	—	2	1	no	—
674	Dic₇	—	2	1	no	—
675	Dic₇	—	2	1	no	—
676	Dic₇	—	2	1	no	—
677	Dic₇	—	2	1	no	—
678	Dic₇	—	2	1	no	—
679	Dic₇	—	2	1	no	—
680	Dic₇	—	2	1	no	—
681	Dic₇	—	2	1	no	—
682	Dic₇	—	2	1	no	—
683	C₂⁴	—	7	1	no	—
684	C₂⁴	—	7	1	no	—
685	C₂⁴	—	7	1	no	—
686	C₂⁴	C₂²×D₇	1	1	yes	characteristic
687	#41	—	28	2	no	—
688	#41	—	28	2	no	—
689	C₂×Q₈	—	7	1	no	—
690	C₂×Q₈	—	7	1	no	—
691	C₂×Q₈	—	7	1	no	—
692	C₂×Q₈	—	7	1	no	—
693	C₂×Q₈	—	7	1	no	—
694	C₂×Q₈	—	7	1	no	—
695	C₂×Q₈	—	7	1	no	—
696	C₂×Q₈	—	28	2	no	—
697	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
698	C₂×D₄	—	7	1	no	—
699	C₂×D₄	—	7	1	no	—
700	C₂×D₄	—	7	1	no	—
701	C₂×D₄	—	7	1	no	—
702	C₂×D₄	—	7	1	no	—
703	C₂×D₄	—	7	1	no	—
704	C₂×D₄	—	7	1	no	—
705	C₂×D₄	—	7	1	no	—
706	C₂×D₄	—	7	1	no	—
707	C₂×D₄	—	7	1	no	—
708	C₂×D₄	—	7	1	no	—
709	C₂×D₄	—	7	1	no	—
710	C₂×D₄	—	7	1	no	—
711	C₂×D₄	—	7	1	no	—
712	C₂×D₄	—	7	1	no	—
713	C₂×D₄	—	7	1	no	—
714	C₂×D₄	—	7	1	no	—
715	C₂×D₄	—	28	2	no	—
716	C₂×D₄	—	28	2	no	—
717	C₂×D₄	—	28	2	no	—
718	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
719	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
720	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
721	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
722	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
723	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
724	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
725	C₂²×C₄	—	7	1	no	—
726	C₂²×C₄	—	7	1	no	—
727	C₂²×C₄	—	7	1	no	—
728	C₂²×C₄	—	7	1	no	—
729	C₂²×C₄	—	7	1	no	—
730	C₂²×C₄	—	7	1	no	—
731	C₂²×C₄	—	7	1	no	—
732	C₂²×C₄	—	7	1	no	—
733	C₂²×C₄	—	7	1	no	—
734	C₂²×C₄	—	7	1	no	—
735	C₂²×C₄	—	7	1	no	—
736	C₂²×C₄	—	7	1	no	—
737	C₂²×C₄	—	7	1	no	—
738	C₂²×C₄	—	7	1	no	—
739	C₂²×C₄	—	7	1	no	—
740	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
741	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
742	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
743	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
744	C₄⋊C₄	—	7	1	no	—
745	C₄⋊C₄	—	7	1	no	—
746	C₄⋊C₄	—	7	1	no	—
747	C₄⋊C₄	—	7	1	no	—
748	C₄⋊C₄	—	7	1	no	—
749	C₄⋊C₄	—	7	1	no	—
750	C₄⋊C₄	—	7	1	no	—
751	C₄⋊C₄	—	7	1	no	—
752	C₄⋊C₄	—	7	1	no	—
753	C₄⋊C₄	—	7	1	no	—
754	C₄⋊C₄	—	7	1	no	—
755	C₄⋊C₄	—	7	1	no	—
756	C₄⋊C₄	—	7	1	no	—
757	C₄⋊C₄	—	7	1	no	—
758	C₄⋊C₄	—	7	1	no	—
759	C₄⋊C₄	—	7	1	no	—
760	C₄⋊C₄	—	7	1	no	—
761	C₄⋊C₄	—	7	1	no	—
762	C₄⋊C₄	—	7	1	no	—
763	C₄⋊C₄	—	7	1	no	—
764	C₄⋊C₄	—	7	1	no	—
765	C₄⋊C₄	—	7	1	no	—
766	C₄⋊C₄	—	7	1	no	—
767	C₄⋊C₄	—	7	1	no	—
768	C₄⋊C₄	—	7	1	no	—
769	C₄⋊C₄	—	7	1	no	—
770	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
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	—	7	1	no	—
783	C₂²⋊C₄	—	7	1	no	—
784	C₂²⋊C₄	—	7	1	no	—
785	C₂²⋊C₄	—	7	1	no	—
786	C₂²⋊C₄	—	7	1	no	—
787	C₂²⋊C₄	—	7	1	no	—
788	C₂²⋊C₄	—	7	1	no	—
789	C₂²⋊C₄	—	7	1	no	—
790	C₂²⋊C₄	—	7	1	no	—
791	C₂²⋊C₄	—	7	1	no	—
792	C₂²⋊C₄	—	7	1	no	—
793	C₂²⋊C₄	—	7	1	no	—
794	C₂²⋊C₄	—	7	1	no	—
795	C₂²⋊C₄	—	7	1	no	—
796	C₂²⋊C₄	—	7	1	no	—
797	C₂²⋊C₄	—	7	1	no	—
798	C₂²⋊C₄	—	7	1	no	—
799	C₂²⋊C₄	—	7	1	no	—
800	C₂²⋊C₄	—	7	1	no	—
801	C₂²⋊C₄	—	7	1	no	—
802	C₂²⋊C₄	—	7	1	no	—
803	C₂²⋊C₄	—	7	1	no	—
804	C₂²⋊C₄	—	7	1	no	—
805	C₂²⋊C₄	—	7	1	no	—
806	C₂²⋊C₄	—	7	1	no	—
807	C₂²⋊C₄	—	7	1	no	—
808	C₂²⋊C₄	—	7	1	no	—
809	C₂²⋊C₄	—	7	1	no	—
810	C₂²⋊C₄	—	7	1	no	—
811	C₂²⋊C₄	—	7	1	no	—
812	C₂²⋊C₄	—	7	1	no	—
813	C₂²⋊C₄	—	7	1	no	—
814	C₂²⋊C₄	—	7	1	no	—
815	C₂²⋊C₄	—	7	1	no	—
816	C₂²⋊C₄	—	7	1	no	—
817	C₂²⋊C₄	—	7	1	no	—
818	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
829	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
830	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
832	C₄²	—	7	1	no	—
833	C₄²	—	7	1	no	—
834	C₄²	—	7	1	no	—
835	C₄²	—	7	1	no	—
836	C₄²	—	7	1	no	—
837	C₄²	—	7	1	no	—
838	C₄²	—	7	1	no	—
839	C₄²	—	7	1	no	—
840	C₄²	—	7	1	no	—
841	C₄²	—	7	1	no	—
842	C₄²	C₂²×D₇	1	1	yes	characteristic
843	C₄²	C₂²×D₇	1	1	yes	characteristic
844	C₂×C₇	—	4	1	no	—
845	C₂×C₇	—	4	1	no	—
846	C₂×C₇	—	4	1	no	—
847	C₂×C₇	—	4	1	no	—
848	C₂×C₇	—	4	1	no	—
849	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
850	C₂×C₇	#585	1	1	yes	characteristic
851	C₂×C₇	#585	1	1	yes	characteristic
852	D₇	—	2	2	no	—
853	D₇	—	4	1	no	—
854	D₇	—	4	1	no	—
855	D₇	—	4	1	no	—
856	C₂³	—	4	1	no	—
857	C₂³	—	4	1	no	—
858	C₂³	—	4	1	no	—
859	C₂³	—	7	1	no	—
860	C₂³	—	7	1	no	—
861	C₂³	—	7	1	no	—
862	C₂³	—	7	1	no	—
863	C₂³	—	14	2	no	—
864	C₂³	—	14	2	no	—
865	C₂³	—	28	1	no	—
866	C₂³	—	28	1	no	—
867	C₂³	—	28	1	no	—
868	C₂³	—	28	1	no	—
869	C₂³	—	28	1	no	—
870	C₂³	—	28	1	no	—
871	C₂³	—	28	1	no	—
872	C₂³	C₂³×D₇	1	1	yes	characteristic
873	C₂³	C₂³×D₇	1	1	yes	characteristic
874	C₂³	C₂³×D₇	1	1	yes	characteristic
875	C₂³	C₂³×D₇	1	1	yes	characteristic
876	C₂³	C₂³×D₇	1	1	yes	characteristic
877	Q₈	—	4	1	no	—
878	Q₈	—	28	1	no	—
879	Q₈	—	28	1	no	—
880	Q₈	—	28	1	no	—
881	Q₈	—	28	1	no	—
882	Q₈	—	28	1	no	—
883	Q₈	—	28	1	no	—
884	Q₈	—	28	1	no	—
885	D₄	—	4	1	no	—
886	D₄	—	4	1	no	—
887	D₄	—	4	1	no	—
888	D₄	—	4	1	no	—
889	D₄	—	4	1	no	—
890	D₄	—	4	1	no	—
891	D₄	—	4	1	no	—
892	D₄	—	14	2	no	—
893	D₄	—	14	2	no	—
894	D₄	—	14	2	no	—
895	D₄	—	14	2	no	—
896	D₄	—	28	1	no	—
897	D₄	—	28	1	no	—
898	D₄	—	28	1	no	—
899	D₄	—	28	1	no	—
900	D₄	—	28	1	no	—
901	D₄	—	28	1	no	—
902	D₄	—	28	1	no	—
903	D₄	—	28	1	no	—
904	D₄	—	28	1	no	—
905	D₄	—	28	1	no	—
906	D₄	—	28	1	no	—
907	D₄	—	28	1	no	—
908	D₄	—	28	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	7	1	no	—
914	C₂×C₄	—	7	1	no	—
915	C₂×C₄	—	7	1	no	—
916	C₂×C₄	—	7	1	no	—
917	C₂×C₄	—	7	1	no	—
918	C₂×C₄	—	7	1	no	—
919	C₂×C₄	—	7	1	no	—
920	C₂×C₄	—	7	1	no	—
921	C₂×C₄	—	7	1	no	—
922	C₂×C₄	—	7	1	no	—
923	C₂×C₄	—	7	1	no	—
924	C₂×C₄	—	7	1	no	—
925	C₂×C₄	—	14	2	no	—
926	C₂×C₄	—	14	2	no	—
927	C₂×C₄	—	14	2	no	—
928	C₂×C₄	—	28	1	no	—
929	C₂×C₄	—	28	1	no	—
930	C₂×C₄	—	28	1	no	—
931	C₂×C₄	—	28	1	no	—
932	C₂×C₄	—	28	1	no	—
933	C₂×C₄	—	28	1	no	—
934	C₂×C₄	—	28	1	no	—
935	C₂×C₄	—	28	1	no	—
936	C₂×C₄	—	28	1	no	—
937	C₂×C₄	—	28	1	no	—
938	C₂×C₄	—	28	1	no	—
939	C₂×C₄	—	28	1	no	—
940	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
950	C₇	#3545	1	1	yes	characteristic, complemented, Sylow
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	7	2	no	—
967	C₂²	—	8	2	no	—
968	C₂²	—	14	1	no	—
969	C₂²	—	14	1	no	—
970	C₂²	—	14	1	no	—
971	C₂²	—	14	1	no	—
972	C₂²	—	14	1	no	—
973	C₂²	—	14	1	no	—
974	C₂²	—	14	1	no	—
975	C₂²	—	14	1	no	—
976	C₂²	—	14	1	no	—
977	C₂²	—	14	1	no	—
978	C₂²	—	14	1	no	—
979	C₂²	—	56	2	no	—
980	C₂²	—	56	2	no	—
981	C₂²	—	56	2	no	—
982	C₂²	C₂⁴×D₇	1	1	yes	characteristic
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	1	no	—
993	C₄	—	14	1	no	—
994	C₄	—	14	1	no	—
995	C₄	—	14	1	no	—
996	C₄	—	14	1	no	—
997	C₄	—	14	1	no	—
998	C₄	—	14	1	no	—
999	C₄	—	14	1	no	—
1000	C₄	—	14	1	no	—
1001	C₄	—	14	1	no	—
1002	C₄	—	14	1	no	—
1003	C₄	—	14	1	no	—
1004	C₄	—	14	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	4	1	no	—
1008	C₂	—	4	1	no	—
1009	C₂	—	4	1	no	—
1010	C₂	—	14	2	no	—
1011	C₂	—	28	1	no	—
1012	C₂	—	28	1	no	—
1013	C₂	—	28	1	no	—
1014	C₂	#90616	1	1	yes	characteristic
1015	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic
1016	C₂	#90618	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#538	C₂
hypercenter	#538	D₇
hypocenter	C₇	#3545
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. C₇×#538	C₂	semidirect
2. #90403	C₂	semidirect
3. #90401	C₂	semidirect
4. #90397	C₂	semidirect
5. #90396	C₂	semidirect
6. #90369	C₂	semidirect
7. #90366	C₂	semidirect
8. D₇×#124	C₂	semidirect
9. #90360	C₂	semidirect
10. #90358	C₂	semidirect
11. #90350	C₂	semidirect
12. #90349	C₂	semidirect
13. #90349	C₂	semidirect
14. #90331	C₂	semidirect
15. #90319	C₂	semidirect
16. #90312	C₂	semidirect
17. #90307	C₂	semidirect
18. #90303	C₂	semidirect
19. #90301	C₂	semidirect
20. #90296	C₂	semidirect
21. #90294	C₂	semidirect
22. #90285	C₂	semidirect
23. #90284	C₂	semidirect
24. #90282	C₂	semidirect
25. #90280	C₂	semidirect
26. #90254	C₂	semidirect
27. #90251	C₂	semidirect
28. #90248	C₂	semidirect
29. #90247	C₂	semidirect
30. #90186	C₂	semidirect
31. #90181	C₂	semidirect
32. C₂²×C₂²⋊D₇	C₂²	semidirect
33. C₂×Q₈×D₇	C₂²	semidirect
36. C₂×D₄×D₇	C₂²	semidirect
38. C₇×#126	C₂²	semidirect
39. C₇×#126	C₂²	semidirect
40. C₇×#124	C₂²	semidirect
41. C₇×#124	C₂²	semidirect
42. C₇×#123	C₂²	semidirect
43. C₇×#123	C₂²	semidirect
44. C₇×C₂²⋊Q₈	C₂²	semidirect
46. C₇×#121	C₂²	semidirect
47. C₇×#121	C₂²	semidirect
48. C₇×#120	C₂²	semidirect
49. C₇×#120	C₂²	semidirect
50. C₄×C₇×D₄	C₂²	semidirect
51. C₄×C₇×D₄	C₂²	semidirect
52. C₂×C₇×C₂²⋊C₄	C₂²	semidirect
54. #6516	C₂²	semidirect
55. C₂×C₂²⋊Dic₇	C₂²	semidirect
56. #6510	C₂²	semidirect
57. #6509	C₂²	semidirect
58. #6507	C₂²	semidirect
60. #6502	C₂²	semidirect
61. #6502	C₂²	semidirect
62. #6502	C₂²	semidirect
63. #6502	C₂²	semidirect
65. #6501	C₂²	semidirect
66. #6501	C₂²	semidirect
67. #6501	C₂²	semidirect
72. #6500	C₂²	semidirect
73. #6500	C₂²	semidirect
74. #6499	C₂²	semidirect
75. #6499	C₂²	semidirect
76. #6499	C₂²	semidirect
77. #6499	C₂²	semidirect
78. #6499	C₂²	semidirect
79. #6498	C₂²	semidirect
80. #6498	C₂²	semidirect
81. #6498	C₂²	semidirect
82. D₄×Dic₇	C₂²	semidirect
83. D₄×Dic₇	C₂²	semidirect
84. #6493	C₂²	semidirect
85. #6493	C₂²	semidirect
86. #6492	C₂²	semidirect
87. #6492	C₂²	semidirect
88. C₄×C₂²⋊D₇	C₂²	semidirect
89. C₄×C₂²⋊D₇	C₂²	semidirect
90. C₄×C₂²⋊D₇	C₂²	semidirect
91. C₄×C₂²⋊D₇	C₂²	semidirect
92. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
93. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
94. #6489	C₂²	semidirect
95. #6489	C₂²	semidirect
96. #6489	C₂²	semidirect
97. #6487	C₂²	semidirect
98. #6487	C₂²	semidirect
99. #6461	C₂²	semidirect
100. #6461	C₂²	semidirect
101. #6461	C₂²	semidirect
102. #6460	C₂²	semidirect
103. #6460	C₂²	semidirect
104. #6460	C₂²	semidirect
105. #6459	C₂²	semidirect
106. #6459	C₂²	semidirect
107. #6459	C₂²	semidirect
108. #6459	C₂²	semidirect
109. #6457	C₂²	semidirect
110. #6457	C₂²	semidirect
111. #6457	C₂²	semidirect
112. #6457	C₂²	semidirect
113. #6456	C₂²	semidirect
114. #6455	C₂²	semidirect
115. #6455	C₂²	semidirect
116. #6455	C₂²	semidirect
117. #6455	C₂²	semidirect
118. #6453	C₂²	semidirect
119. #6452	C₂²	semidirect
120. #6451	C₂²	semidirect
121. #6451	C₂²	semidirect
122. #6450	C₂²	semidirect
124. #6449	C₂²	semidirect
125. #6449	C₂²	semidirect
128. #6448	C₂²	semidirect
129. #6448	C₂²	semidirect
130. #6448	C₂²	semidirect
131. #6448	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
138. #6448	C₂²	semidirect
142. #6447	C₂²	semidirect
144. #6446	C₂²	semidirect
145. #6446	C₂²	semidirect
146. #6446	C₂²	semidirect
147. #6446	C₂²	semidirect
148. #6446	C₂²	semidirect
149. #6446	C₂²	semidirect
150. #6446	C₂²	semidirect
151. #6446	C₂²	semidirect
152. #6446	C₂²	semidirect
154. #6445	C₂²	semidirect
155. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
156. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
157. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
158. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
159. D₇×C₂²⋊C₄	C₂²	semidirect
160. D₇×C₂²⋊C₄	C₂²	semidirect
161. D₇×C₂²⋊C₄	C₂²	semidirect
162. D₇×C₂²⋊C₄	C₂²	semidirect
163. D₇×C₂²⋊C₄	C₂²	semidirect
164. D₇×C₂²⋊C₄	C₂²	semidirect
165. #6442	C₂²	semidirect
166. #6442	C₂²	semidirect
167. #6442	C₂²	semidirect
168. #6442	C₂²	semidirect
169. #6442	C₂²	semidirect
170. #6441	C₂²	semidirect
171. #6441	C₂²	semidirect
172. #6441	C₂²	semidirect
173. #6441	C₂²	semidirect
174. #6441	C₂²	semidirect
175. #6441	C₂²	semidirect
176. #6441	C₂²	semidirect
177. #6440	C₂²	semidirect
178. #6440	C₂²	semidirect
179. #6439	C₂²	semidirect
180. #6439	C₂²	semidirect
181. #6438	C₂²	semidirect
182. C₄×D₂₈	C₂²	semidirect
183. #6435	C₂²	semidirect
184. C₄²×D₇	C₂²	semidirect
185. #6432	C₂²	semidirect
186. C₄×Dic₁₄	C₂²	semidirect
372. #538	D₇	semidirect
494. #126	C₂×D₇	semidirect
495. #126	C₂×D₇	semidirect
518. #124	C₂×D₇	semidirect
519. #124	C₂×D₇	semidirect
542. #123	C₂×D₇	semidirect
543. #123	C₂×D₇	semidirect
561. C₂²⋊Q₈	C₂×D₇	semidirect
578. #121	C₂×D₇	semidirect
579. #121	C₂×D₇	semidirect
590. #120	C₂×D₇	semidirect
591. #120	C₂×D₇	semidirect
606. C₄×D₄	C₂×D₇	semidirect
607. C₄×D₄	C₂×D₇	semidirect
627. C₂×C₂²⋊C₄	C₂×D₇	semidirect
950. C₇	#3545	semidirect

Maximal subgroups

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

subgroup	index
C₇×#538	2
#90403	2
#90401	2
#90397	2
#90396	2
#90369	2
#90366	2
D₇×#124	2
#90360	2
#90358	2
#90350	2
#90349	2
#90331	2
#90319	2
#90312	2
#90307	2
#90303	2
#90301	2
#90296	2
#90294	2
#90285	2
#90284	2
#90282	2
#90280	2
#90254	2
#90251	2
#90248	2
#90247	2
#90186	2
#90181	2
#3545	7