Subgroups — #14219443

Order 1792.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3480	C₂	1	1	yes	maximal, characteristic
2	#11740725	C₂	1	1	yes	maximal, characteristic, complemented
3	#11740725	C₂	1	2	yes	maximal, complemented
4	#11740724	C₂	1	2	yes	maximal, complemented
5	#11740723	C₂	1	1	yes	maximal, characteristic, complemented
6	#11740578	C₂	1	2	yes	maximal, complemented
7	#11740577	C₂	1	1	yes	maximal, characteristic, complemented
8	#11740576	C₂	1	1	yes	maximal, characteristic, complemented
9	#11740575	C₂	1	2	yes	maximal, complemented
10	#11740574	C₂	1	1	yes	maximal, characteristic, complemented
11	#11740573	C₂	1	2	yes	maximal, complemented
12	#11740572	C₂	1	2	yes	maximal, complemented
13	#11740571	C₂	1	1	yes	maximal, characteristic, complemented
14	#11739967	C₂	1	1	yes	maximal, characteristic, complemented
15	#11739966	C₂	1	1	yes	maximal, characteristic, complemented
16	#11739963	C₂	1	1	yes	maximal, characteristic, complemented
17	#11739962	C₂	1	1	yes	maximal, characteristic, complemented
18	#11739960	C₂	1	1	yes	maximal, characteristic, complemented
19	#11739960	C₂	1	2	yes	maximal, complemented
20	#11739959	C₂	1	2	yes	maximal, complemented
21	#11739958	C₂	1	1	yes	maximal, characteristic, complemented
22	#11739882	C₂	1	1	yes	maximal, characteristic, complemented
23	#11739881	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#559	C₄	1	1	yes	characteristic
25	C₇×#559	C₄	1	2	yes	—
26	C₇×#557	C₄	1	1	yes	characteristic
27	C₇×#556	C₄	1	1	yes	characteristic
28	C₇×#556	C₄	1	2	yes	—
29	C₇×#553	C₄	1	1	yes	characteristic
30	C₇×#553	C₄	1	1	yes	characteristic
31	C₇×#553	C₄	1	2	yes	—
32	C₇×#553	C₄	1	2	yes	—
33	C₇×#550	C₄	1	1	yes	characteristic
34	C₇×#548	C₄	1	1	yes	characteristic
35	C₇×#548	C₄	1	1	yes	characteristic
36	C₇×#532	C₂²	1	1	yes	characteristic
37	C₇×#532	C₂²	1	2	yes	—
38	C₇×#529	C₂²	1	1	yes	characteristic
39	C₇×#529	C₂²	1	2	yes	—
40	C₇×#529	C₂²	1	2	yes	—
41	C₇×#529	C₂²	1	1	yes	characteristic
42	C₄×C₇×#41	C₂²	1	1	yes	characteristic
43	C₄×C₇×#41	C₂²	1	1	yes	characteristic
44	C₄×C₇×#41	C₂²	1	1	yes	characteristic
45	C₄×C₇×#41	C₂²	1	2	yes	—
46	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
47	#90006	C₂²	1	2	yes	—
48	#90006	C₂²	1	2	yes	—
49	#90006	C₂²	1	1	yes	characteristic
50	#90006	C₂²	1	2	yes	—
51	#90006	C₂²	1	2	yes	—
52	#90006	C₂²	1	1	yes	characteristic
53	#90006	C₂²	1	2	yes	—
54	#89796	C₂²	1	1	yes	characteristic
55	#89796	C₂²	1	1	yes	characteristic
56	#89796	C₂²	1	1	yes	characteristic
57	#89796	C₂²	1	1	yes	characteristic
58	#89796	C₂²	1	1	yes	characteristic
59	#89796	C₂²	1	2	yes	—
60	#89796	C₂²	1	2	yes	—
61	#89796	C₂²	1	2	yes	—
62	#89796	C₂²	1	2	yes	—
63	#89796	C₂²	1	1	yes	characteristic
64	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
65	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic
66	#89784	C₂²	1	1	yes	characteristic
67	#89784	C₂²	1	1	yes	characteristic
68	#89784	C₂²	1	2	yes	—
69	#89784	C₂²	1	1	yes	characteristic
70	#89784	C₂²	1	1	yes	characteristic
71	#89784	C₂²	1	2	yes	—
72	#89784	C₂²	1	2	yes	—
73	#89783	C₂²	1	2	yes	—
74	#89783	C₂²	1	2	yes	—
75	#89783	C₂²	1	2	yes	—
76	#89783	C₂²	1	2	yes	—
77	#89783	C₂²	1	2	yes	—
78	#89783	C₂²	1	2	yes	—
79	#89783	C₂²	1	2	yes	—
80	#89783	C₂²	1	2	yes	—
81	#89783	C₂²	1	2	yes	—
82	#89783	C₂²	1	2	yes	—
83	#89783	C₂²	1	2	yes	—
84	#89783	C₂²	1	2	yes	—
85	#89783	C₂²	1	2	yes	—
86	#89783	C₂²	1	2	yes	—
87	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
88	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
89	D₄×C₇⋊C₈	C₂²	1	2	yes	—
90	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
91	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
92	D₄×C₇⋊C₈	C₂²	1	2	yes	—
93	D₄×C₇⋊C₈	C₂²	1	2	yes	—
94	#89772	C₂²	1	1	yes	characteristic
95	#89772	C₂²	1	1	yes	characteristic
96	#89772	C₂²	1	1	yes	characteristic
97	#89772	C₂²	1	1	yes	characteristic
98	#89772	C₂²	1	2	yes	—
99	#89772	C₂²	1	2	yes	—
100	#89772	C₂²	1	2	yes	—
101	#89772	C₂²	1	2	yes	—
102	#89772	C₂²	1	2	yes	—
103	#89772	C₂²	1	2	yes	—
104	#89771	C₂²	1	1	yes	characteristic
105	#89771	C₂²	1	1	yes	characteristic
106	#89771	C₂²	1	2	yes	—
107	#89771	C₂²	1	2	yes	—
108	#89769	C₂²	1	2	yes	—
109	#89769	C₂²	1	2	yes	—
110	#89769	C₂²	1	2	yes	—
111	#89698	C₂²	1	2	yes	—
112	#89698	C₂²	1	2	yes	—
113	#89698	C₂²	1	2	yes	—
114	#89698	C₂²	1	1	yes	characteristic
115	#89698	C₂²	1	2	yes	—
116	#89698	C₂²	1	2	yes	—
117	#89698	C₂²	1	1	yes	characteristic
118	#89698	C₂²	1	2	yes	—
119	#89697	C₂²	1	1	yes	characteristic
120	#89697	C₂²	1	1	yes	characteristic
121	#89697	C₂²	1	1	yes	characteristic
122	#89697	C₂²	1	2	yes	—
123	#89697	C₂²	1	1	yes	characteristic
124	#89697	C₂²	1	1	yes	characteristic
125	#89697	C₂²	1	2	yes	—
126	#89697	C₂²	1	1	yes	characteristic
127	#89696	C₂²	1	2	yes	—
128	#89696	C₂²	1	1	yes	characteristic
129	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic
130	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	2	yes	—
131	C₄×#1136	C₂²	1	1	yes	characteristic
132	C₄×#1136	C₂²	1	2	yes	—
133	C₂×#6377	C₂²	1	2	yes	—
134	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic
135	#60302	—	7	1	no	maximal, Sylow
136	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	2	yes	—
139	C₂×C₇×#41	C₂³	1	1	yes	characteristic
140	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
141	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
142	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
143	C₇×#127	C₂×C₄	1	1	yes	characteristic
144	C₇×#127	C₂×C₄	1	2	yes	—
145	C₇×#126	C₂×C₄	1	2	yes	—
146	C₇×#126	C₂×C₄	1	2	yes	—
147	C₇×#126	C₂×C₄	1	2	yes	—
148	C₇×#126	C₂×C₄	1	2	yes	—
149	C₇×#126	C₂×C₄	1	2	yes	—
150	C₇×#126	C₂×C₄	1	2	yes	—
151	C₇×#125	C₂×C₄	1	1	yes	characteristic
152	C₇×#125	C₂×C₄	1	2	yes	—
153	C₇×#125	C₂×C₄	1	2	yes	—
154	C₇×#125	C₂×C₄	1	1	yes	characteristic
155	C₇×#124	C₂×C₄	1	1	yes	characteristic
156	C₇×#124	C₂×C₄	1	1	yes	characteristic
157	C₇×#124	C₂×C₄	1	2	yes	—
158	C₇×#124	C₂×C₄	1	2	yes	—
159	C₇×#124	C₂×C₄	1	2	yes	—
160	C₇×#124	C₂×C₄	1	2	yes	—
161	C₇×#124	C₂×C₄	1	2	yes	—
162	C₇×#123	C₂×C₄	1	2	yes	—
163	C₇×#123	C₂×C₄	1	2	yes	—
164	C₇×#123	C₂×C₄	1	2	yes	—
165	C₇×#123	C₂×C₄	1	2	yes	—
166	C₇×#123	C₂×C₄	1	2	yes	—
167	C₇×#123	C₂×C₄	1	2	yes	—
168	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
169	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
170	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
171	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
172	C₇×#121	C₂×C₄	1	1	yes	characteristic
173	C₇×#121	C₂×C₄	1	1	yes	characteristic
174	C₇×#121	C₂×C₄	1	2	yes	—
175	C₇×#121	C₂×C₄	1	2	yes	—
176	C₇×#121	C₂×C₄	1	1	yes	characteristic
177	C₇×#121	C₂×C₄	1	1	yes	characteristic
178	C₇×#121	C₂×C₄	1	2	yes	—
179	C₇×#121	C₂×C₄	1	2	yes	—
180	C₇×#121	C₂×C₄	1	2	yes	—
181	C₇×#121	C₂×C₄	1	2	yes	—
182	C₇×#121	C₂×C₄	1	2	yes	—
183	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
184	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
185	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
186	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
187	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
188	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
189	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
190	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
191	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
192	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
193	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
194	C₄×C₇×Q₈	C₂³	1	2	yes	—
195	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
196	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
197	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
198	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
199	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
200	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
201	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
202	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
203	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
204	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
205	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
206	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
207	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
208	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
209	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
210	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
211	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
212	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
213	C₄×C₇×D₄	C₂³	1	2	yes	—
214	C₄×C₇×D₄	C₂³	1	2	yes	—
215	C₄×C₇×D₄	C₂³	1	2	yes	—
216	C₄×C₇×D₄	C₂³	1	2	yes	—
217	C₄×C₇×D₄	C₂³	1	2	yes	—
218	C₇×#117	C₂×C₄	1	1	yes	characteristic
219	C₇×#117	C₂×C₄	1	1	yes	characteristic
220	C₇×#117	C₂×C₄	1	2	yes	—
221	C₇×#117	C₂×C₄	1	2	yes	—
222	C₇×#117	C₂³	1	2	yes	—
223	C₇×#117	C₂³	1	1	yes	characteristic
224	C₇×#117	C₂³	1	1	yes	characteristic
225	C₇×#117	C₂³	1	1	yes	characteristic
226	C₇×#117	C₂³	1	2	yes	—
227	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
228	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
229	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇	C₂³	1	2	yes	—
235	C₂×#1136	C₂³	1	1	yes	characteristic
236	C₂×#1136	C₂³	1	1	yes	characteristic
237	C₂×#1136	C₂³	1	2	yes	—
238	C₂×#1136	C₂³	1	2	yes	—
239	C₂×#1136	C₂³	1	2	yes	—
240	C₂×#1136	C₂³	1	2	yes	—
241	C₂×#1136	C₂³	1	2	yes	—
242	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
243	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
244	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
245	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
246	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
247	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
248	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
249	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
250	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
251	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
252	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
253	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
254	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
255	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
256	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
257	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
258	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
259	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
260	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
261	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
262	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
263	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
264	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
265	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
266	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
267	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
268	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
269	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
270	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
271	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
272	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
273	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
274	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
275	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
276	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
277	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
278	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
279	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
280	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
281	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
282	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
283	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
284	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
285	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
286	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
287	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
288	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
289	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
290	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
291	#6377	C₂³	1	1	yes	characteristic
292	#6377	C₂³	1	2	yes	—
293	#6377	C₂³	1	2	yes	—
294	#6377	C₂³	1	2	yes	—
295	#6377	C₂³	1	1	yes	characteristic
296	#6377	C₂³	1	2	yes	—
297	#6377	C₂³	1	2	yes	—
298	#6377	C₂³	1	2	yes	—
299	#6377	C₂³	1	2	yes	—
300	#6377	C₂³	1	2	yes	—
301	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
302	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
303	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
304	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
305	C₄×C₇⋊C₈	C₂³	1	2	yes	—
306	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
307	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
308	C₄×C₇⋊C₈	C₂³	1	2	yes	—
309	C₄×C₇⋊C₈	C₂³	1	2	yes	—
310	C₄×C₇⋊C₈	C₂³	1	2	yes	—
311	#3480	D₇	1	1	yes	characteristic
312	#2995	—	7	2	no	—
313	#2994	—	7	1	no	—
314	#2993	—	7	1	no	—
315	#2992	—	7	2	no	—
316	#2990	—	7	1	no	—
317	#2989	—	7	1	no	—
318	#2984	—	7	1	no	—
319	#2983	—	7	1	no	—
320	#2981	—	7	1	no	—
321	#2981	—	7	2	no	—
322	#2980	—	7	2	no	—
323	#2979	—	7	1	no	—
324	#2970	—	7	1	no	—
325	#2969	—	7	1	no	—
326	#2968	—	7	2	no	—
327	#2967	—	7	2	no	—
328	#2966	—	7	1	no	—
329	#2965	—	7	1	no	—
330	#2925	—	7	1	no	—
331	#2925	—	7	2	no	—
332	#2923	—	7	2	no	—
333	#2922	—	7	1	no	—
334	C₇×#41	—	4	2	no	—
335	C₇×#41	—	4	1	no	—
336	C₇×#41	—	4	2	no	—
337	C₇×#41	—	4	1	no	—
338	C₇×#41	—	4	2	no	—
339	C₇×#41	—	4	2	no	—
340	C₂×C₇×Q₈	—	4	2	no	—
341	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
343	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
345	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
346	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
351	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
352	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
353	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
354	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
355	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
356	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
357	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
358	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
359	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
360	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
361	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
362	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
363	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
364	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
365	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
366	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
367	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
368	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
369	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
370	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
371	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
376	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
377	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
378	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
379	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
380	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
381	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
382	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
383	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
384	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
385	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
386	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
387	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
390	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
391	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
392	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
393	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
394	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
395	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
396	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
397	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
398	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
399	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
400	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
401	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
402	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
403	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
404	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
405	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
406	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
408	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
409	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
410	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
411	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
412	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
414	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
415	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
416	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
417	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
418	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
419	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
420	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
421	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
422	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
423	C₄²×C₇	C₂²×C₄	1	2	yes	—
424	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
425	C₄²×C₇	C₂²×C₄	1	2	yes	—
426	C₄²×C₇	C₂²×C₄	1	2	yes	—
427	C₄²×C₇	C₂²×C₄	1	2	yes	—
428	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
429	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
430	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
431	C₄²×C₇	C₂²×C₄	1	2	yes	—
432	C₄²×C₇	C₂²×C₄	1	2	yes	—
433	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
434	C₄²×C₇	C₂⁴	1	1	yes	characteristic
435	C₄²×C₇	C₂⁴	1	1	yes	characteristic
436	C₄²×C₇	C₂⁴	1	1	yes	characteristic
437	C₄²×C₇	C₂⁴	1	2	yes	—
438	C₄²×C₇	C₂⁴	1	1	yes	characteristic
439	C₄²×C₇	C₂⁴	1	2	yes	—
440	#1136	—	4	1	no	—
441	#1136	—	4	2	no	—
442	#1136	—	4	2	no	—
443	#1136	—	4	1	no	—
444	#1136	—	4	2	no	—
445	#1136	—	4	2	no	—
446	#1136	—	4	2	no	—
447	C₂×C₇⋊C₈	—	4	2	no	—
448	C₂×C₇⋊C₈	—	4	1	no	—
449	C₂×C₇⋊C₈	—	4	2	no	—
450	C₂×C₇⋊C₈	—	4	2	no	—
451	C₂×C₇⋊C₈	—	4	2	no	—
452	C₂×C₇⋊C₈	—	4	2	no	—
453	C₂×C₇⋊C₈	—	4	1	no	—
454	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
455	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
456	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
457	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
458	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
459	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
460	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
461	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
462	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
463	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
464	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
465	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
466	#559	Dic₇	1	1	yes	characteristic
467	#559	Dic₇	1	2	yes	—
468	#557	Dic₇	1	1	yes	characteristic
469	#556	Dic₇	1	1	yes	characteristic
470	#556	Dic₇	1	2	yes	—
471	#553	Dic₇	1	1	yes	characteristic
472	#553	Dic₇	1	1	yes	characteristic
473	#553	Dic₇	1	2	yes	—
474	#553	Dic₇	1	2	yes	—
475	#550	Dic₇	1	1	yes	characteristic
476	#548	Dic₇	1	1	yes	characteristic
477	#548	Dic₇	1	1	yes	characteristic
478	#532	C₂×D₇	1	1	yes	characteristic
479	#532	C₂×D₇	1	2	yes	—
480	#529	C₂×D₇	1	1	yes	characteristic
481	#529	C₂×D₇	1	2	yes	—
482	#529	C₂×D₇	1	2	yes	—
483	#529	C₂×D₇	1	1	yes	characteristic
484	C₄×#41	C₂×D₇	1	1	yes	characteristic
485	C₄×#41	C₂×D₇	1	1	yes	characteristic
486	C₄×#41	C₂×D₇	1	1	yes	characteristic
487	C₄×#41	C₂×D₇	1	2	yes	—
488	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic
489	#446	—	7	1	no	—
490	#446	—	7	1	no	—
491	#446	—	7	1	no	—
492	#446	—	7	2	no	—
493	#446	—	7	2	no	—
494	#446	—	7	2	no	—
495	#446	—	7	2	no	—
496	#446	—	7	1	no	—
497	#446	—	7	1	no	—
498	#446	—	7	1	no	—
499	C₈×Q₈	—	7	1	no	—
500	C₈×Q₈	—	7	1	no	—
501	#436	—	7	1	no	—
502	#436	—	7	1	no	—
503	#436	—	7	1	no	—
504	#436	—	7	2	no	—
505	#436	—	7	2	no	—
506	#436	—	7	1	no	—
507	#436	—	7	2	no	—
508	#435	—	7	2	no	—
509	#435	—	7	2	no	—
510	#435	—	7	2	no	—
511	#435	—	7	2	no	—
512	#435	—	7	2	no	—
513	#435	—	7	2	no	—
514	#435	—	7	2	no	—
515	#435	—	7	2	no	—
516	#435	—	7	2	no	—
517	#435	—	7	2	no	—
518	#435	—	7	2	no	—
519	#435	—	7	2	no	—
520	#435	—	7	2	no	—
521	#435	—	7	2	no	—
522	C₈×D₄	—	7	1	no	—
523	C₈×D₄	—	7	2	no	—
524	C₈×D₄	—	7	2	no	—
525	C₈×D₄	—	7	2	no	—
526	C₈×D₄	—	7	1	no	—
527	C₈×D₄	—	7	1	no	—
528	C₈×D₄	—	7	1	no	—
529	#433	—	7	1	no	—
530	#433	—	7	1	no	—
531	#433	—	7	1	no	—
532	#433	—	7	1	no	—
533	#433	—	7	2	no	—
534	#433	—	7	2	no	—
535	#433	—	7	2	no	—
536	#433	—	7	2	no	—
537	#433	—	7	2	no	—
538	#433	—	7	2	no	—
539	#432	—	7	2	no	—
540	#432	—	7	2	no	—
541	#432	—	7	2	no	—
542	#432	—	7	2	no	—
543	#432	—	7	1	no	—
544	#432	—	7	2	no	—
545	#432	—	7	2	no	—
546	#432	—	7	1	no	—
547	#431	—	7	1	no	—
548	#431	—	7	1	no	—
549	#431	—	7	1	no	—
550	#431	—	7	1	no	—
551	#431	—	7	2	no	—
552	#431	—	7	1	no	—
553	#431	—	7	1	no	—
554	#431	—	7	2	no	—
555	#424	—	7	1	no	—
556	#424	—	7	1	no	—
557	#424	—	7	2	no	—
558	#424	—	7	2	no	—
559	#423	—	7	2	no	—
560	#423	—	7	1	no	—
561	C₂×C₄⋊C₈	—	7	1	no	—
562	C₂×C₄⋊C₈	—	7	2	no	—
563	#408	—	7	1	no	—
564	#408	—	7	1	no	—
565	#408	—	7	2	no	—
566	#408	—	7	2	no	—
567	#408	—	7	2	no	—
568	#408	—	7	2	no	—
569	#408	—	7	2	no	—
570	#405	—	7	2	no	—
571	#405	—	7	2	no	—
572	#405	—	7	2	no	—
573	C₄×M₁₆	—	7	1	no	—
574	C₄×M₁₆	—	7	2	no	—
575	C₂×#97	—	7	2	no	—
576	C₂×C₄×C₈	—	7	1	no	—
577	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
578	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
579	C₂³×C₇	C₂³×C₄	1	2	yes	—
580	C₂³×C₇	C₂³×C₄	1	2	yes	—
581	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
582	C₇×Q₈	—	2	2	no	—
583	C₇×Q₈	—	2	2	no	—
584	C₇×Q₈	—	4	2	no	—
585	C₇×Q₈	—	4	1	no	—
586	C₇×Q₈	—	4	2	no	—
587	C₇×D₄	—	2	2	no	—
588	C₇×D₄	—	2	2	no	—
589	C₇×D₄	—	4	2	no	—
590	C₇×D₄	—	4	2	no	—
591	C₇×D₄	—	4	2	no	—
592	C₇×D₄	—	4	1	no	—
593	C₇×D₄	—	4	2	no	—
594	C₇×D₄	—	4	1	no	—
595	C₇×D₄	—	4	2	no	—
596	C₇×D₄	—	4	1	no	—
597	C₇×D₄	—	4	2	no	—
598	C₇×D₄	—	4	2	no	—
599	C₇×D₄	—	4	2	no	—
600	C₂×C₄×C₇	—	2	2	no	—
601	C₂×C₄×C₇	—	2	2	no	—
602	C₂×C₄×C₇	—	2	2	no	—
603	C₂×C₄×C₇	—	2	2	no	—
604	C₂×C₄×C₇	—	2	1	no	—
605	C₂×C₄×C₇	—	2	1	no	—
606	C₂×C₄×C₇	—	2	2	no	—
607	C₂×C₄×C₇	—	2	2	no	—
608	C₂×C₄×C₇	—	2	1	no	—
609	C₂×C₄×C₇	—	2	1	no	—
610	C₂×C₄×C₇	—	2	2	no	—
611	C₂×C₄×C₇	—	2	1	no	—
612	C₂×C₄×C₇	—	2	1	no	—
613	C₂×C₄×C₇	—	4	1	no	—
614	C₂×C₄×C₇	—	4	2	no	—
615	C₂×C₄×C₇	—	4	1	no	—
616	C₂×C₄×C₇	—	4	2	no	—
617	C₂×C₄×C₇	—	4	1	no	—
618	C₂×C₄×C₇	—	4	2	no	—
619	C₂×C₄×C₇	—	4	2	no	—
620	C₂×C₄×C₇	—	4	2	no	—
621	C₂×C₄×C₇	—	4	2	no	—
622	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
623	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
624	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
625	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
626	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
627	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
628	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
629	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
630	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
631	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
632	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
633	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
634	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
635	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
636	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
637	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
638	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
639	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
640	C₇⋊C₈	—	2	1	no	—
641	C₇⋊C₈	—	2	2	no	—
642	C₇⋊C₈	—	2	1	no	—
643	C₇⋊C₈	—	2	1	no	—
644	C₇⋊C₈	—	2	1	no	—
645	C₇⋊C₈	—	2	2	no	—
646	C₇⋊C₈	—	2	1	no	—
647	C₇⋊C₈	—	2	2	no	—
648	C₇⋊C₈	—	2	2	no	—
649	C₇⋊C₈	—	2	1	no	—
650	C₇⋊C₈	—	2	1	no	—
651	C₇⋊C₈	—	2	1	no	—
652	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
653	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
654	C₂×#41	C₂²×D₇	1	1	yes	characteristic
655	C₂×#41	C₂²×D₇	1	2	yes	—
656	C₂²×Q₈	C₂×Dic₇	1	1	yes	characteristic
657	C₂×M₁₆	—	7	1	no	—
658	C₂×M₁₆	—	7	1	no	—
659	C₂×M₁₆	—	7	2	no	—
660	C₂×M₁₆	—	7	2	no	—
661	C₂×M₁₆	—	7	2	no	—
662	C₂×M₁₆	—	7	2	no	—
663	C₂×M₁₆	—	7	2	no	—
664	C₂²×C₈	—	7	1	no	—
665	C₂²×C₈	—	7	1	no	—
666	C₂²×C₈	—	7	2	no	—
667	C₂²×C₈	—	7	2	no	—
668	C₂²×C₈	—	7	2	no	—
669	C₂²×C₈	—	7	2	no	—
670	C₂²×C₈	—	7	2	no	—
671	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
672	C₄⋊Q₈	C₂×Dic₇	1	2	yes	—
673	#127	C₂×Dic₇	1	1	yes	characteristic
674	#127	C₂×Dic₇	1	2	yes	—
675	#126	C₂×Dic₇	1	2	yes	—
676	#126	C₂×Dic₇	1	2	yes	—
677	#126	C₂×Dic₇	1	2	yes	—
678	#126	C₂×Dic₇	1	2	yes	—
679	#126	C₂×Dic₇	1	2	yes	—
680	#126	C₂×Dic₇	1	2	yes	—
681	#125	C₂×Dic₇	1	1	yes	characteristic
682	#125	C₂×Dic₇	1	2	yes	—
683	#125	C₂×Dic₇	1	2	yes	—
684	#125	C₂×Dic₇	1	1	yes	characteristic
685	#124	C₂×Dic₇	1	1	yes	characteristic
686	#124	C₂×Dic₇	1	1	yes	characteristic
687	#124	C₂×Dic₇	1	2	yes	—
688	#124	C₂×Dic₇	1	2	yes	—
689	#124	C₂×Dic₇	1	2	yes	—
690	#124	C₂×Dic₇	1	2	yes	—
691	#124	C₂×Dic₇	1	2	yes	—
692	#123	C₂×Dic₇	1	2	yes	—
693	#123	C₂×Dic₇	1	2	yes	—
694	#123	C₂×Dic₇	1	2	yes	—
695	#123	C₂×Dic₇	1	2	yes	—
696	#123	C₂×Dic₇	1	2	yes	—
697	#123	C₂×Dic₇	1	2	yes	—
698	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
699	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
700	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
701	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
702	#121	C₂×Dic₇	1	1	yes	characteristic
703	#121	C₂×Dic₇	1	1	yes	characteristic
704	#121	C₂×Dic₇	1	2	yes	—
705	#121	C₂×Dic₇	1	2	yes	—
706	#121	C₂×Dic₇	1	1	yes	characteristic
707	#121	C₂×Dic₇	1	1	yes	characteristic
708	#121	C₂×Dic₇	1	2	yes	—
709	#121	C₂×Dic₇	1	2	yes	—
710	#121	C₂×Dic₇	1	2	yes	—
711	#121	C₂×Dic₇	1	2	yes	—
712	#121	C₂×Dic₇	1	2	yes	—
713	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
714	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
715	C₄×Q₈	C₂×Dic₇	1	2	yes	—
716	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
717	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
718	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
719	C₄×Q₈	C₂×Dic₇	1	2	yes	—
720	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
721	C₄×Q₈	C₂×Dic₇	1	2	yes	—
722	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
723	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
724	C₄×Q₈	C₂²×D₇	1	2	yes	—
725	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
726	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
727	C₄×D₄	C₂×Dic₇	1	2	yes	—
728	C₄×D₄	C₂×Dic₇	1	2	yes	—
729	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
730	C₄×D₄	C₂×Dic₇	1	2	yes	—
731	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
732	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
733	C₄×D₄	C₂×Dic₇	1	2	yes	—
734	C₄×D₄	C₂×Dic₇	1	2	yes	—
735	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
736	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
737	C₄×D₄	C₂×Dic₇	1	2	yes	—
738	C₄×D₄	C₂×Dic₇	1	2	yes	—
739	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
740	C₄×D₄	C₂×Dic₇	1	2	yes	—
741	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
742	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
743	C₄×D₄	C₂²×D₇	1	2	yes	—
744	C₄×D₄	C₂²×D₇	1	2	yes	—
745	C₄×D₄	C₂²×D₇	1	2	yes	—
746	C₄×D₄	C₂²×D₇	1	2	yes	—
747	C₄×D₄	C₂²×D₇	1	2	yes	—
748	#117	C₂×Dic₇	1	1	yes	characteristic
749	#117	C₂×Dic₇	1	1	yes	characteristic
750	#117	C₂×Dic₇	1	2	yes	—
751	#117	C₂×Dic₇	1	2	yes	—
752	#117	C₂²×D₇	1	1	yes	characteristic
753	#117	C₂²×D₇	1	1	yes	characteristic
754	#117	C₂²×D₇	1	2	yes	—
755	#117	C₂²×D₇	1	1	yes	characteristic
756	#117	C₂²×D₇	1	2	yes	—
757	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂×Dic₇	1	2	yes	—
759	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
760	C₂×C₄²	C₂²×D₇	1	2	yes	—
761	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
762	C₂×C₄²	C₂²×D₇	1	2	yes	—
763	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
764	C₂×C₄²	C₂²×D₇	1	2	yes	—
765	C₄⋊C₈	—	7	1	no	—
766	C₄⋊C₈	—	7	2	no	—
767	C₄⋊C₈	—	7	2	no	—
768	C₄⋊C₈	—	7	2	no	—
769	C₄⋊C₈	—	7	1	no	—
770	C₄⋊C₈	—	7	1	no	—
771	C₄⋊C₈	—	7	2	no	—
772	C₄⋊C₈	—	7	1	no	—
773	C₄⋊C₈	—	7	1	no	—
774	C₄⋊C₈	—	7	1	no	—
775	C₄⋊C₈	—	7	2	no	—
776	C₄⋊C₈	—	7	2	no	—
777	C₄⋊C₈	—	7	1	no	—
778	C₄⋊C₈	—	7	1	no	—
779	C₄⋊C₈	—	7	1	no	—
780	C₄⋊C₈	—	7	1	no	—
781	C₄⋊C₈	—	7	1	no	—
782	C₄⋊C₈	—	7	1	no	—
783	C₄⋊C₈	—	7	2	no	—
784	C₄⋊C₈	—	7	2	no	—
785	C₄⋊C₈	—	7	2	no	—
786	C₄⋊C₈	—	7	2	no	—
787	C₂²⋊C₈	—	7	1	no	—
788	C₂²⋊C₈	—	7	1	no	—
789	C₂²⋊C₈	—	7	1	no	—
790	C₂²⋊C₈	—	7	1	no	—
791	C₂²⋊C₈	—	7	2	no	—
792	C₂²⋊C₈	—	7	2	no	—
793	C₂²⋊C₈	—	7	1	no	—
794	C₂²⋊C₈	—	7	2	no	—
795	C₂²⋊C₈	—	7	1	no	—
796	C₂²⋊C₈	—	7	1	no	—
797	C₂²⋊C₈	—	7	2	no	—
798	C₂²⋊C₈	—	7	2	no	—
799	C₂²⋊C₈	—	7	1	no	—
800	C₂²⋊C₈	—	7	2	no	—
801	C₂²⋊C₈	—	7	2	no	—
802	C₂²⋊C₈	—	7	2	no	—
803	C₂²⋊C₈	—	7	2	no	—
804	C₂²⋊C₈	—	7	2	no	—
805	C₂²⋊C₈	—	7	2	no	—
806	C₂²⋊C₈	—	7	2	no	—
807	#97	—	7	1	no	—
808	#97	—	7	2	no	—
809	#97	—	7	2	no	—
810	#97	—	7	2	no	—
811	#97	—	7	1	no	—
812	#97	—	7	2	no	—
813	#97	—	7	2	no	—
814	#97	—	7	2	no	—
815	#97	—	7	2	no	—
816	#97	—	7	2	no	—
817	C₄×C₈	—	7	1	no	—
818	C₄×C₈	—	7	1	no	—
819	C₄×C₈	—	7	1	no	—
820	C₄×C₈	—	7	1	no	—
821	C₄×C₈	—	7	2	no	—
822	C₄×C₈	—	7	1	no	—
823	C₄×C₈	—	7	1	no	—
824	C₄×C₈	—	7	2	no	—
825	C₄×C₈	—	7	2	no	—
826	C₄×C₈	—	7	2	no	—
827	C₂²×C₇	—	2	1	no	—
828	C₂²×C₇	—	2	1	no	—
829	C₂²×C₇	—	2	2	no	—
830	C₂²×C₇	—	2	1	no	—
831	C₂²×C₇	—	2	2	no	—
832	C₂²×C₇	—	2	1	no	—
833	C₂²×C₇	—	2	1	no	—
834	C₂²×C₇	—	2	1	no	—
835	C₂²×C₇	—	2	2	no	—
836	C₂²×C₇	—	2	2	no	—
837	C₂²×C₇	—	2	1	no	—
838	C₂²×C₇	—	2	1	no	—
839	C₂²×C₇	—	2	1	no	—
840	C₂²×C₇	—	2	2	no	—
841	C₂²×C₇	—	2	2	no	—
842	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
843	C₄×C₇	—	2	1	no	—
844	C₄×C₇	—	2	2	no	—
845	C₄×C₇	—	2	1	no	—
846	C₄×C₇	—	2	1	no	—
847	C₄×C₇	—	2	2	no	—
848	C₄×C₇	—	2	1	no	—
849	C₄×C₇	—	2	1	no	—
850	C₄×C₇	—	2	1	no	—
851	C₄×C₇	—	2	2	no	—
852	C₄×C₇	—	2	2	no	—
853	C₄×C₇	—	2	1	no	—
854	C₄×C₇	—	2	1	no	—
855	C₄×C₇	—	2	1	no	—
856	C₄×C₇	—	2	2	no	—
857	C₄×C₇	—	2	1	no	—
858	C₄×C₇	—	2	2	no	—
859	C₄×C₇	#568	1	2	yes	—
860	C₄×C₇	#585	1	1	yes	characteristic
861	C₄×C₇	#585	1	1	yes	characteristic
862	#41	—	4	1	no	—
863	#41	—	4	2	no	—
864	#41	—	4	1	no	—
865	#41	—	4	2	no	—
866	#41	—	4	2	no	—
867	#41	—	4	2	no	—
868	C₂×Q₈	—	4	2	no	—
869	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
870	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
871	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
872	C₂×Q₈	C₂²×Dic₇	1	2	yes	—
873	C₂×Q₈	C₂²×Dic₇	1	2	yes	—
874	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
875	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
876	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
877	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
878	C₂×D₄	C₂²×Dic₇	1	2	yes	—
879	C₂×D₄	C₂²×Dic₇	1	2	yes	—
880	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
881	C₂×D₄	C₂²×Dic₇	1	2	yes	—
882	C₂×D₄	C₂²×Dic₇	1	2	yes	—
883	C₂×D₄	C₂²×Dic₇	1	2	yes	—
884	C₂×D₄	C₂²×Dic₇	1	2	yes	—
885	C₂×D₄	C₂²×Dic₇	1	2	yes	—
886	C₂×D₄	C₂²×Dic₇	1	2	yes	—
887	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
888	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
889	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
890	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
891	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
892	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
893	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
894	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
895	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
896	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
897	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
898	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
899	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
900	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
901	C₂²×C₄	C₂³×D₇	1	2	yes	—
902	C₂²×C₄	C₂³×D₇	1	2	yes	—
903	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
904	M₁₆	—	28	1	no	—
905	M₁₆	—	28	2	no	—
906	M₁₆	—	28	2	no	—
907	M₁₆	—	28	1	no	—
908	M₁₆	—	28	2	no	—
909	M₁₆	—	28	2	no	—
910	M₁₆	—	28	2	no	—
911	C₂×C₈	—	7	1	no	—
912	C₂×C₈	—	7	1	no	—
913	C₂×C₈	—	7	1	no	—
914	C₂×C₈	—	7	1	no	—
915	C₂×C₈	—	7	1	no	—
916	C₂×C₈	—	7	2	no	—
917	C₂×C₈	—	7	2	no	—
918	C₂×C₈	—	7	1	no	—
919	C₂×C₈	—	7	1	no	—
920	C₂×C₈	—	7	1	no	—
921	C₂×C₈	—	7	2	no	—
922	C₂×C₈	—	7	2	no	—
923	C₂×C₈	—	28	2	no	—
924	C₂×C₈	—	28	1	no	—
925	C₂×C₈	—	28	2	no	—
926	C₂×C₈	—	28	2	no	—
927	C₂×C₈	—	28	2	no	—
928	C₂×C₈	—	28	2	no	—
929	C₂×C₈	—	28	1	no	—
930	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
931	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
932	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
933	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
934	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
935	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
936	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
937	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
938	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
939	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
940	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
941	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
942	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
943	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
944	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
945	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
946	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
947	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
948	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
949	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
950	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
951	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
952	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
953	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
954	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
955	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
956	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
957	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
958	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
959	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
960	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
961	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
962	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
963	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
964	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
965	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
966	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
967	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
968	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
969	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
970	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
971	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
972	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
973	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
974	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
975	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
976	C₄²	C₂²×Dic₇	1	1	yes	characteristic
977	C₄²	C₂²×Dic₇	1	2	yes	—
978	C₄²	C₂²×Dic₇	1	1	yes	characteristic
979	C₄²	C₂²×Dic₇	1	2	yes	—
980	C₄²	C₂²×Dic₇	1	2	yes	—
981	C₄²	C₂²×Dic₇	1	2	yes	—
982	C₄²	C₂²×Dic₇	1	1	yes	characteristic
983	C₄²	C₂²×Dic₇	1	1	yes	characteristic
984	C₄²	C₂²×Dic₇	1	1	yes	characteristic
985	C₄²	C₂²×Dic₇	1	2	yes	—
986	C₄²	C₂²×Dic₇	1	2	yes	—
987	C₄²	C₂²×Dic₇	1	1	yes	characteristic
988	C₄²	C₂³×D₇	1	1	yes	characteristic
989	C₄²	C₂³×D₇	1	1	yes	characteristic
990	C₄²	C₂³×D₇	1	2	yes	—
991	C₄²	C₂³×D₇	1	1	yes	characteristic
992	C₄²	C₂³×D₇	1	2	yes	—
993	C₄²	C₂³×D₇	1	1	yes	characteristic
994	C₂×C₇	—	4	1	no	—
995	C₂×C₇	—	4	1	no	—
996	C₂×C₇	—	4	1	no	—
997	C₂×C₇	—	4	2	no	—
998	C₂×C₇	—	4	2	no	—
999	C₂×C₇	#3428	1	1	yes	characteristic
1000	C₂×C₇	C₂×#568	1	1	yes	characteristic
1001	C₂×C₇	#3573	1	1	yes	characteristic
1002	C₂³	C₂³×Dic₇	1	1	yes	characteristic
1003	C₂³	C₂³×Dic₇	1	1	yes	characteristic
1004	C₂³	C₂³×Dic₇	1	2	yes	—
1005	C₂³	C₂³×Dic₇	1	2	yes	—
1006	C₂³	C₂³×Dic₇	1	1	yes	characteristic
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	2	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	4	1	no	—
1011	Q₈	—	4	2	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	4	2	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	4	2	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	1	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	1	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	4	1	no	—
1024	D₄	—	4	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	4	1	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	1	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	—	4	1	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1048	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1049	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1050	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1051	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1052	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1053	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1054	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1055	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1056	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1057	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1058	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1059	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1060	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1061	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1062	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1063	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1064	C₂×C₄	C₂⁴×D₇	1	1	yes	characteristic
1065	C₈	—	14	1	no	—
1066	C₈	—	14	1	no	—
1067	C₈	—	14	1	no	—
1068	C₈	—	14	2	no	—
1069	C₈	—	14	1	no	—
1070	C₈	—	14	2	no	—
1071	C₈	—	14	1	no	—
1072	C₈	—	14	2	no	—
1073	C₈	—	14	1	no	—
1074	C₈	—	14	1	no	—
1075	C₈	—	14	2	no	—
1076	C₈	—	14	1	no	—
1077	C₇	#60302	1	1	yes	characteristic, complemented, Sylow
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	C₂⁴×Dic₇	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	#90510	1	2	yes	—
1111	C₄	#90616	1	1	yes	characteristic
1112	C₄	#90616	1	1	yes	characteristic
1113	C₂	—	4	1	no	—
1114	C₂	—	4	1	no	—
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	4	2	no	—
1118	C₂	C₂×#90510	1	1	yes	characteristic
1119	C₂	#11744328	1	1	yes	characteristic
1120	C₂	#11744364	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇
commutator, socle	C₂²×C₇	C₂⁴×C₄
Fitting, prime radical	C₇×#3480	C₂
cosocle	C₂×C₄×C₇	C₂⁵
hypercenter	#3480	D₇
hypocenter	C₇	#60302
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ #3480

Complements

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

N	H ≅ G/N	type
2. #11740725	C₂	semidirect
3. #11740725	C₂	semidirect
4. #11740724	C₂	semidirect
5. #11740723	C₂	semidirect
6. #11740578	C₂	semidirect
7. #11740577	C₂	semidirect
8. #11740576	C₂	semidirect
9. #11740575	C₂	semidirect
10. #11740574	C₂	semidirect
11. #11740573	C₂	semidirect
12. #11740572	C₂	semidirect
13. #11740571	C₂	semidirect
14. #11739967	C₂	semidirect
15. #11739966	C₂	semidirect
16. #11739963	C₂	semidirect
17. #11739962	C₂	semidirect
18. #11739960	C₂	semidirect
19. #11739960	C₂	semidirect
20. #11739959	C₂	semidirect
21. #11739958	C₂	semidirect
22. #11739882	C₂	semidirect
23. #11739881	C₂	semidirect
1077. C₇	#60302	semidirect

Maximal subgroups

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

subgroup	index
C₇×#3480	2
#11740725	2
#11740724	2
#11740723	2
#11740578	2
#11740577	2
#11740576	2
#11740575	2
#11740574	2
#11740573	2
#11740572	2
#11740571	2
#11739967	2
#11739966	2
#11739963	2
#11739962	2
#11739960	2
#11739959	2
#11739958	2
#11739882	2
#11739881	2
#60302	7