Subgroups — C₇×#62886 #13240102

Order 1792.

6918 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3551	C₂	1	4	yes	maximal, complemented
2	C₇×#3550	C₂	1	4	yes	maximal, complemented
3	C₇×#3547	C₂	1	8	yes	maximal, complemented
4	C₇×#3545	C₂	1	4	yes	maximal, complemented
5	C₇×#3544	C₂	1	4	yes	maximal, complemented
6	C₇×#3541	C₂	1	8	yes	maximal, complemented
7	C₇×#3540	C₂	1	4	yes	maximal, complemented
8	C₇×#3538	C₂	1	4	yes	maximal, complemented
9	C₇×#3533	C₂	1	8	yes	maximal, complemented
10	C₇×#3495	C₂	1	4	yes	maximal, complemented
11	C₇×#3493	C₂	1	2	yes	maximal, complemented
12	C₇×#3489	C₂	1	4	yes	maximal, complemented
13	C₇×#3486	C₂	1	2	yes	maximal, complemented
14	C₇×#3449	C₂	1	2	yes	maximal, complemented
15	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₇×#41	C₂²	1	2	yes	complemented
19	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₇×#563	C₂²	1	8	yes	complemented
21	C₇×#563	C₂²	1	4	yes	complemented
22	C₇×#563	C₂²	1	8	yes	complemented
23	C₇×#563	C₂²	1	8	yes	complemented
24	C₇×#562	C₂²	1	16	yes	complemented
25	C₇×#562	C₂²	1	8	yes	complemented
26	C₇×H(3,𝔽₄)	C₂²	1	4	yes	complemented
27	C₇×#560	C₂²	1	8	yes	complemented
28	C₇×#559	C₂²	1	8	yes	complemented
29	C₇×Q₈²	C₂²	1	4	yes	complemented
30	C₇×#556	C₂²	1	8	yes	complemented
31	C₇×#556	C₂²	1	8	yes	complemented
32	C₇×#555	C₂²	1	8	yes	complemented
33	C₇×#555	C₂²	1	4	yes	complemented
34	C₇×#555	C₂²	1	8	yes	complemented
35	C₇×#554	C₂²	1	8	yes	complemented
36	C₇×#554	C₂²	1	8	yes	complemented
37	C₇×#553	C₂²	1	8	yes	complemented
38	C₇×#553	C₂²	1	16	yes	complemented
39	C₇×#552	C₂²	1	8	yes	complemented
40	C₇×#552	C₂²	1	16	yes	complemented
41	C₇×#552	C₂²	1	8	yes	complemented
42	C₇×#552	C₂²	1	8	yes	complemented
43	C₇×#551	C₂²	1	16	yes	complemented
44	C₇×#551	C₂²	1	8	yes	complemented
45	C₇×#551	C₂²	1	8	yes	complemented
46	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
47	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
48	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
49	C₇×#548	C₂²	1	8	yes	complemented
50	C₇×#548	C₂²	1	8	yes	complemented
51	C₇×#548	C₂²	1	8	yes	complemented
52	C₇×#547	C₂²	1	16	yes	complemented
53	C₇×#547	C₂²	1	8	yes	complemented
54	C₇×#546	C₂²	1	16	yes	complemented
55	C₇×#546	C₂²	1	8	yes	complemented
56	C₇×#544	C₂²	1	2	yes	complemented
57	C₇×#544	C₂²	1	16	yes	complemented
58	C₇×#542	C₂²	1	8	yes	complemented
59	C₇×#542	C₂²	1	16	yes	complemented
60	C₇×#542	C₂²	1	16	yes	complemented
61	C₇×#542	C₂²	1	16	yes	complemented
62	C₇×#541	C₂²	1	8	yes	complemented
63	C₇×#540	C₂²	1	16	yes	complemented
64	C₇×#539	C₂²	1	16	yes	complemented
65	C₇×#538	C₂²	1	8	yes	complemented
66	C₇×#538	C₂²	1	16	yes	complemented
67	C₇×#538	C₂²	1	16	yes	complemented
68	C₇×#537	C₂²	1	4	yes	—
69	C₇×#537	C₂²	1	2	yes	—
70	C₇×#537	C₂²	1	4	yes	complemented
71	C₇×#537	C₂²	1	8	yes	complemented
72	C₇×#536	C₂²	1	4	yes	—
73	C₇×#536	C₂²	1	2	yes	—
74	C₇×#536	C₂²	1	4	yes	complemented
75	C₇×#536	C₂²	1	4	yes	complemented
76	C₇×#536	C₂²	1	4	yes	complemented
77	C₇×#536	C₂²	1	4	yes	complemented
78	C₇×#536	C₂²	1	2	yes	complemented
79	C₇×#536	C₂²	1	4	yes	complemented
80	C₇×#536	C₂²	1	8	yes	complemented
81	C₇×#536	C₂²	1	8	yes	complemented
82	C₇×#535	C₂²	1	4	yes	—
83	C₇×#535	C₂²	1	2	yes	—
84	C₇×#535	C₂²	1	2	yes	complemented
85	C₇×#534	C₂²	1	4	yes	—
86	C₇×#534	C₂²	1	4	yes	complemented
87	C₇×#533	C₂²	1	8	yes	complemented
88	C₇×#532	C₂²	1	4	yes	—
89	C₇×#532	C₂²	1	4	yes	complemented
90	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
91	C₇×#529	C₂²	1	8	yes	complemented
92	C₇×#529	C₂²	1	8	yes	complemented
93	C₂×C₇×#124	C₂²	1	2	yes	—
94	C₇×#525	C₂²	1	4	yes	—
95	C₇×#525	C₂²	1	4	yes	—
96	C₇×#525	C₂²	1	4	yes	complemented
97	C₇×#525	C₂²	1	4	yes	complemented
98	C₇×#525	C₂²	1	8	yes	complemented
99	C₇×#525	C₂²	1	8	yes	complemented
100	C₂×C₇×#123	C₂²	1	4	yes	complemented
101	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
102	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
103	C₇×#520	C₂²	1	4	yes	complemented
104	C₇×#519	C₂²	1	2	yes	complemented
105	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₇×#117	C₂²	1	2	yes	complemented
107	#62886	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₇×2₋¹⁺⁴	—	4	8	no	—
109	C₂×C₇×#41	—	4	4	no	—
110	C₂×C₇×#41	—	4	8	no	—
111	C₂×C₇×#41	C₂³	1	4	yes	—
112	C₂×C₇×#41	C₂³	1	2	yes	—
113	C₂×C₇×#41	C₂³	1	2	yes	—
114	C₂×C₇×#41	C₂³	1	2	yes	—
115	C₂×C₇×#41	C₂³	1	2	yes	—
116	C₂×C₇×#41	C₂³	1	4	yes	—
117	C₂×C₇×#41	C₂³	1	4	yes	—
118	C₂×C₇×#41	C₂³	1	4	yes	—
119	C₂×C₇×#41	C₂³	1	8	yes	—
120	C₂×C₇×#41	C₂³	1	8	yes	—
121	C₂²×C₇×Q₈	—	4	4	no	—
122	C₂²×C₇×Q₈	C₂³	1	2	yes	—
123	C₂²×C₇×Q₈	C₂³	1	2	yes	—
124	C₂²×C₇×Q₈	C₂³	1	4	yes	—
125	C₂²×C₇×Q₈	C₂³	1	4	yes	—
126	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₇×Q₈	C₂³	1	2	yes	—
128	C₂²×C₇×Q₈	C₂³	1	8	yes	—
129	C₂²×C₇×D₄	C₂³	1	2	yes	—
130	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
131	C₂²×C₇×D₄	C₂³	1	4	yes	—
132	C₂²×C₇×D₄	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₇	C₂³	1	4	yes	—
137	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
138	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
139	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
140	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
141	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
142	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
143	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
144	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
145	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
146	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
147	C₇×#127	C₂³	1	4	yes	—
148	C₇×#127	C₂³	1	4	yes	—
149	C₇×#126	C₂³	1	16	yes	—
150	C₇×#126	C₂³	1	16	yes	—
151	C₇×#126	C₂³	1	16	yes	—
152	C₇×#126	C₂³	1	16	yes	—
153	C₇×#126	C₂³	1	16	yes	—
154	C₇×#126	C₂³	1	16	yes	—
155	C₇×#125	C₂³	1	8	yes	—
156	C₇×#125	C₂³	1	8	yes	—
157	C₇×#125	C₂³	1	16	yes	—
158	C₇×#125	C₂³	1	16	yes	—
159	C₇×#125	C₂³	1	16	yes	—
160	C₇×#124	C₂³	1	4	yes	—
161	C₇×#124	C₂³	1	8	yes	—
162	C₇×#124	C₂³	1	4	yes	—
163	C₇×#124	C₂³	1	8	yes	—
164	C₇×#124	C₂³	1	8	yes	—
165	C₇×#124	C₂³	1	4	yes	—
166	C₇×#124	C₂³	1	4	yes	—
167	C₇×#124	C₂³	1	4	yes	—
168	C₇×#124	C₂³	1	4	yes	—
169	C₇×#124	C₂³	1	8	yes	—
170	C₇×#124	C₂³	1	16	yes	—
171	C₇×#124	C₂³	1	8	yes	—
172	C₇×#124	C₂³	1	16	yes	—
173	C₇×#124	C₂³	1	16	yes	—
174	C₇×#123	C₂³	1	8	yes	—
175	C₇×#123	C₂³	1	8	yes	—
176	C₇×#123	C₂³	1	8	yes	—
177	C₇×#123	C₂³	1	8	yes	—
178	C₇×#123	C₂³	1	4	yes	—
179	C₇×#123	C₂³	1	8	yes	—
180	C₇×#123	C₂³	1	4	yes	—
181	C₇×#123	C₂³	1	8	yes	—
182	C₇×#123	C₂³	1	4	yes	—
183	C₇×#123	C₂³	1	4	yes	—
184	C₇×#123	C₂³	1	16	yes	—
185	C₇×#123	C₂³	1	16	yes	—
186	C₇×#123	C₂³	1	16	yes	—
187	C₇×#123	C₂³	1	16	yes	—
188	C₇×#123	C₂³	1	16	yes	—
189	C₇×#123	C₂³	1	16	yes	—
190	C₇×#123	C₂³	1	16	yes	—
191	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
192	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
193	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
194	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
195	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
196	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
197	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
198	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
199	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
200	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
201	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
204	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
205	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
206	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
207	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
208	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
209	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
210	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
211	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
212	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
213	C₇×#121	C₂³	1	4	yes	—
214	C₇×#121	C₂³	1	4	yes	—
215	C₇×#121	C₂³	1	8	yes	—
216	C₇×#121	C₂³	1	4	yes	—
217	C₇×#121	C₂³	1	8	yes	—
218	C₇×#121	C₂³	1	4	yes	—
219	C₇×#121	C₂³	1	8	yes	—
220	C₇×#121	C₂³	1	16	yes	—
221	C₇×#121	C₂³	1	8	yes	—
222	C₇×#121	C₂³	1	8	yes	—
223	C₇×#121	C₂³	1	8	yes	—
224	C₇×#121	C₂³	1	8	yes	—
225	C₇×#121	C₂³	1	8	yes	—
226	C₇×#121	C₂³	1	16	yes	—
227	C₇×#121	C₂³	1	16	yes	—
228	C₇×#121	C₂³	1	16	yes	—
229	C₇×#121	C₂³	1	16	yes	—
230	C₇×#120	C₂³	1	8	yes	—
231	C₇×#120	C₂³	1	4	yes	—
232	C₇×#120	C₂³	1	4	yes	—
233	C₇×#120	C₂³	1	8	yes	—
234	C₇×#120	C₂³	1	4	yes	—
235	C₇×#120	C₂³	1	4	yes	—
236	C₇×#120	C₂³	1	16	yes	—
237	C₄×C₇×Q₈	C₂³	1	8	yes	—
238	C₄×C₇×Q₈	C₂³	1	8	yes	—
239	C₄×C₇×Q₈	C₂³	1	8	yes	—
240	C₄×C₇×Q₈	C₂³	1	8	yes	—
241	C₄×C₇×Q₈	C₂³	1	16	yes	—
242	C₄×C₇×D₄	C₂³	1	16	yes	—
243	C₄×C₇×D₄	C₂³	1	8	yes	—
244	C₄×C₇×D₄	C₂³	1	8	yes	—
245	C₄×C₇×D₄	C₂³	1	8	yes	—
246	C₄×C₇×D₄	C₂³	1	8	yes	—
247	C₄×C₇×D₄	C₂³	1	8	yes	—
248	C₄×C₇×D₄	C₂³	1	16	yes	—
249	C₄×C₇×D₄	C₂³	1	16	yes	—
250	C₄×C₇×D₄	C₂³	1	16	yes	—
251	C₄×C₇×D₄	C₂³	1	16	yes	—
252	C₄×C₇×D₄	C₂³	1	8	yes	—
253	C₄×C₇×D₄	C₂³	1	16	yes	—
254	C₇×#117	C₂³	1	4	yes	—
255	C₇×#117	C₂³	1	4	yes	—
256	C₇×#117	C₂³	1	4	yes	—
257	C₇×#117	C₂³	1	2	yes	—
258	C₇×#117	C₂³	1	2	yes	—
259	C₇×#117	C₂³	1	4	yes	—
260	C₇×#117	C₂³	1	4	yes	—
261	C₇×#117	C₂³	1	8	yes	—
262	C₇×#117	C₂³	1	8	yes	—
263	C₇×#117	C₂³	1	16	yes	—
264	C₇×#117	C₂³	1	16	yes	—
265	C₇×#117	C₂³	1	16	yes	—
266	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
267	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
268	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
269	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
270	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
271	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
272	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
273	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
274	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
275	C₂×C₄²×C₇	C₂³	1	2	yes	—
276	C₂×C₄²×C₇	C₂³	1	4	yes	—
277	#3551	C₂×C₇	1	4	yes	complemented
278	#3550	C₂×C₇	1	4	yes	complemented
279	#3547	C₂×C₇	1	8	yes	complemented
280	#3545	C₂×C₇	1	4	yes	complemented
281	#3544	C₂×C₇	1	4	yes	complemented
282	#3541	C₂×C₇	1	8	yes	complemented
283	#3540	C₂×C₇	1	4	yes	complemented
284	#3538	C₂×C₇	1	4	yes	complemented
285	#3533	C₂×C₇	1	8	yes	complemented
286	#3495	C₂×C₇	1	4	yes	complemented
287	#3493	C₂×C₇	1	2	yes	complemented
288	#3489	C₂×C₇	1	4	yes	complemented
289	#3486	C₂×C₇	1	2	yes	complemented
290	#3449	C₂×C₇	1	2	yes	complemented
291	C₂×#536	C₂×C₇	1	1	yes	characteristic, complemented
292	C₂⁴×C₇	C₂⁴	1	2	yes	—
293	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
294	C₂⁴×C₇	C₂⁴	1	4	yes	—
295	C₇×#41	—	2	16	no	—
296	C₇×#41	—	4	4	no	—
297	C₇×#41	—	4	4	no	—
298	C₇×#41	—	4	4	no	—
299	C₇×#41	—	4	4	no	—
300	C₇×#41	—	4	8	no	—
301	C₇×#41	—	4	8	no	—
302	C₇×#41	—	4	16	no	—
303	C₇×#41	—	4	8	no	—
304	C₇×#41	—	4	16	no	—
305	C₂×C₇×Q₈	—	2	8	no	—
306	C₂×C₇×Q₈	—	4	4	no	—
307	C₂×C₇×Q₈	—	4	2	no	—
308	C₂×C₇×Q₈	—	4	8	no	—
309	C₂×C₇×Q₈	—	4	8	no	—
310	C₂×C₇×Q₈	—	4	4	no	—
311	C₂×C₇×Q₈	—	4	16	no	—
312	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
313	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
314	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
315	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
316	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
317	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
318	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
319	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
320	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
321	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
322	C₂×C₇×D₄	—	4	4	no	—
323	C₂×C₇×D₄	—	4	2	no	—
324	C₂×C₇×D₄	—	4	4	no	—
325	C₂×C₇×D₄	—	4	8	no	—
326	C₂×C₇×D₄	C₂⁴	1	8	yes	—
327	C₂×C₇×D₄	C₂⁴	1	4	yes	—
328	C₂×C₇×D₄	C₂⁴	1	8	yes	—
329	C₂×C₇×D₄	C₂⁴	1	8	yes	—
330	C₂×C₇×D₄	C₂⁴	1	8	yes	—
331	C₂×C₇×D₄	C₂⁴	1	8	yes	—
332	C₂×C₇×D₄	C₂⁴	1	8	yes	—
333	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
334	C₂×C₇×D₄	C₂⁴	1	8	yes	—
335	C₂×C₇×D₄	C₂⁴	1	2	yes	—
336	C₂×C₇×D₄	C₂⁴	1	2	yes	—
337	C₂×C₇×D₄	C₂⁴	1	2	yes	—
338	C₂×C₇×D₄	C₂⁴	1	2	yes	—
339	C₂×C₇×D₄	C₂⁴	1	8	yes	—
340	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
341	C₂×C₇×D₄	C₂⁴	1	2	yes	—
342	C₂×C₇×D₄	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₇	—	2	4	no	—
344	C₂²×C₄×C₇	—	2	8	no	—
345	C₂²×C₄×C₇	—	4	8	no	—
346	C₂²×C₄×C₇	—	4	4	no	—
347	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
350	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
353	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
358	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
359	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
360	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
361	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
362	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
363	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
364	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
365	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
366	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
367	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
368	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
369	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
370	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
371	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
372	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
373	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
374	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
375	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
376	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
377	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
378	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
379	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
380	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
381	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
382	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
383	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
384	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
385	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
386	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
387	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
388	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
389	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
390	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
391	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
392	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
393	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
394	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
395	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
396	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
397	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
398	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
399	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
400	C₄²×C₇	C₂⁴	1	4	yes	—
401	C₄²×C₇	C₂⁴	1	4	yes	—
402	C₄²×C₇	C₂⁴	1	8	yes	—
403	C₄²×C₇	C₂⁴	1	4	yes	—
404	C₄²×C₇	C₂⁴	1	4	yes	—
405	C₄²×C₇	C₂⁴	1	8	yes	—
406	C₄²×C₇	C₂⁴	1	16	yes	—
407	C₄²×C₇	C₂⁴	1	8	yes	—
408	C₂×2₋¹⁺⁴	C₂²×C₇	1	2	yes	—
409	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
410	C₂²×#41	C₂²×C₇	1	2	yes	complemented
411	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
412	#563	C₂²×C₇	1	8	yes	complemented
413	#563	C₂²×C₇	1	4	yes	complemented
414	#563	C₂²×C₇	1	8	yes	complemented
415	#563	C₂²×C₇	1	8	yes	complemented
416	#562	C₂²×C₇	1	16	yes	complemented
417	#562	C₂²×C₇	1	8	yes	complemented
418	H(3,𝔽₄)	C₂²×C₇	1	4	yes	complemented
419	#560	C₂²×C₇	1	8	yes	complemented
420	#559	C₂²×C₇	1	8	yes	complemented
421	Q₈²	C₂²×C₇	1	4	yes	complemented
422	#556	C₂²×C₇	1	8	yes	complemented
423	#556	C₂²×C₇	1	8	yes	complemented
424	#555	C₂²×C₇	1	8	yes	complemented
425	#555	C₂²×C₇	1	4	yes	complemented
426	#555	C₂²×C₇	1	8	yes	complemented
427	#554	C₂²×C₇	1	8	yes	complemented
428	#554	C₂²×C₇	1	8	yes	complemented
429	#553	C₂²×C₇	1	8	yes	complemented
430	#553	C₂²×C₇	1	16	yes	complemented
431	#552	C₂²×C₇	1	8	yes	complemented
432	#552	C₂²×C₇	1	16	yes	complemented
433	#552	C₂²×C₇	1	8	yes	complemented
434	#552	C₂²×C₇	1	8	yes	complemented
435	#551	C₂²×C₇	1	16	yes	complemented
436	#551	C₂²×C₇	1	8	yes	complemented
437	#551	C₂²×C₇	1	8	yes	complemented
438	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
439	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
440	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
441	#548	C₂²×C₇	1	8	yes	complemented
442	#548	C₂²×C₇	1	8	yes	complemented
443	#548	C₂²×C₇	1	8	yes	complemented
444	#547	C₂²×C₇	1	16	yes	complemented
445	#547	C₂²×C₇	1	8	yes	complemented
446	#546	C₂²×C₇	1	16	yes	complemented
447	#546	C₂²×C₇	1	8	yes	complemented
448	#544	C₂²×C₇	1	2	yes	complemented
449	#544	C₂²×C₇	1	16	yes	complemented
450	#542	C₂²×C₇	1	8	yes	complemented
451	#542	C₂²×C₇	1	16	yes	complemented
452	#542	C₂²×C₇	1	16	yes	complemented
453	#542	C₂²×C₇	1	16	yes	complemented
454	#541	C₂²×C₇	1	8	yes	complemented
455	#540	C₂²×C₇	1	16	yes	complemented
456	#539	C₂²×C₇	1	16	yes	complemented
457	#538	C₂²×C₇	1	8	yes	complemented
458	#538	C₂²×C₇	1	16	yes	complemented
459	#538	C₂²×C₇	1	16	yes	complemented
460	#537	C₂²×C₇	1	4	yes	—
461	#537	C₂²×C₇	1	2	yes	—
462	#537	C₂²×C₇	1	4	yes	complemented
463	#537	C₂²×C₇	1	8	yes	complemented
464	#536	C₂²×C₇	1	4	yes	—
465	#536	C₂²×C₇	1	2	yes	—
466	#536	C₂²×C₇	1	4	yes	complemented
467	#536	C₂²×C₇	1	4	yes	complemented
468	#536	C₂²×C₇	1	4	yes	complemented
469	#536	C₂²×C₇	1	4	yes	complemented
470	#536	C₂²×C₇	1	2	yes	complemented
471	#536	C₂²×C₇	1	4	yes	complemented
472	#536	C₂²×C₇	1	8	yes	complemented
473	#536	C₂²×C₇	1	8	yes	complemented
474	#535	C₂²×C₇	1	4	yes	—
475	#535	C₂²×C₇	1	2	yes	—
476	#535	C₂²×C₇	1	2	yes	complemented
477	#534	C₂²×C₇	1	4	yes	—
478	#534	C₂²×C₇	1	4	yes	complemented
479	#533	C₂²×C₇	1	8	yes	complemented
480	#532	C₂²×C₇	1	4	yes	—
481	#532	C₂²×C₇	1	4	yes	complemented
482	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
483	#529	C₂²×C₇	1	8	yes	complemented
484	#529	C₂²×C₇	1	8	yes	complemented
485	C₂×#124	C₂²×C₇	1	2	yes	—
486	#525	C₂²×C₇	1	4	yes	—
487	#525	C₂²×C₇	1	4	yes	—
488	#525	C₂²×C₇	1	4	yes	complemented
489	#525	C₂²×C₇	1	4	yes	complemented
490	#525	C₂²×C₇	1	8	yes	complemented
491	#525	C₂²×C₇	1	8	yes	complemented
492	C₂×#123	C₂²×C₇	1	4	yes	complemented
493	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
494	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
495	#520	C₂²×C₇	1	4	yes	complemented
496	#519	C₂²×C₇	1	2	yes	complemented
497	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
498	C₂×#117	C₂²×C₇	1	2	yes	complemented
499	C₂³×C₇	—	2	2	no	—
500	C₂³×C₇	—	2	4	no	—
501	C₂³×C₇	—	4	2	no	—
502	C₂³×C₇	—	4	4	no	—
503	C₂³×C₇	—	4	4	no	—
504	C₂³×C₇	—	4	8	no	—
505	C₂³×C₇	C₂⁵	1	2	yes	—
506	C₂³×C₇	C₂⁵	1	2	yes	—
507	C₂³×C₇	C₂⁵	1	2	yes	—
508	C₂³×C₇	C₂⁵	1	8	yes	—
509	C₂³×C₇	C₂⁵	1	1	yes	characteristic
510	C₇×Q₈	—	2	16	no	—
511	C₇×Q₈	—	2	8	no	—
512	C₇×Q₈	—	4	4	no	—
513	C₇×Q₈	—	4	4	no	—
514	C₇×Q₈	—	4	8	no	—
515	C₇×Q₈	—	4	1	no	—
516	C₇×Q₈	—	4	2	no	—
517	C₇×Q₈	—	4	1	no	—
518	C₇×Q₈	—	4	4	no	—
519	C₇×Q₈	—	4	8	no	—
520	C₇×D₄	—	2	16	no	—
521	C₇×D₄	—	2	8	no	—
522	C₇×D₄	—	4	2	no	—
523	C₇×D₄	—	4	2	no	—
524	C₇×D₄	—	4	2	no	—
525	C₇×D₄	—	4	2	no	—
526	C₇×D₄	—	4	4	no	—
527	C₇×D₄	—	4	1	no	—
528	C₇×D₄	—	4	2	no	—
529	C₇×D₄	—	4	1	no	—
530	C₇×D₄	—	4	8	no	—
531	C₇×D₄	—	4	8	no	—
532	C₇×D₄	—	4	8	no	—
533	C₇×D₄	—	4	8	no	—
534	C₇×D₄	—	4	8	no	—
535	C₇×D₄	—	4	8	no	—
536	C₇×D₄	—	4	8	no	—
537	C₂×C₄×C₇	—	2	2	no	—
538	C₂×C₄×C₇	—	2	4	no	—
539	C₂×C₄×C₇	—	2	8	no	—
540	C₂×C₄×C₇	—	2	4	no	—
541	C₂×C₄×C₇	—	2	4	no	—
542	C₂×C₄×C₇	—	2	4	no	—
543	C₂×C₄×C₇	—	2	4	no	—
544	C₂×C₄×C₇	—	2	4	no	—
545	C₂×C₄×C₇	—	2	4	no	—
546	C₂×C₄×C₇	—	2	16	no	—
547	C₂×C₄×C₇	—	4	4	no	—
548	C₂×C₄×C₇	—	4	8	no	—
549	C₂×C₄×C₇	—	4	8	no	—
550	C₂×C₄×C₇	—	4	16	no	—
551	C₂×C₄×C₇	—	4	8	no	—
552	C₂×C₄×C₇	—	4	4	no	—
553	C₂×C₄×C₇	—	4	16	no	—
554	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
555	C₂×C₄×C₇	C₂⁵	1	8	yes	—
556	C₂×C₄×C₇	C₂⁵	1	8	yes	—
557	C₂×C₄×C₇	C₂⁵	1	8	yes	—
558	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
559	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
560	C₂×C₄×C₇	C₂⁵	1	2	yes	—
561	C₂×C₄×C₇	C₂⁵	1	8	yes	—
562	C₂×C₄×C₇	C₂⁵	1	8	yes	—
563	C₂×C₄×C₇	C₂⁵	1	2	yes	—
564	C₂×C₄×C₇	C₂⁵	1	2	yes	—
565	2₋¹⁺⁴	—	4	8	no	—
566	C₂×#41	—	4	4	no	—
567	C₂×#41	—	4	8	no	—
568	C₂×#41	C₂³×C₇	1	4	yes	—
569	C₂×#41	C₂³×C₇	1	2	yes	—
570	C₂×#41	C₂³×C₇	1	2	yes	—
571	C₂×#41	C₂³×C₇	1	8	yes	—
572	C₂×#41	C₂³×C₇	1	8	yes	—
573	C₂×#41	C₂³×C₇	1	2	yes	—
574	C₂×#41	C₂³×C₇	1	4	yes	—
575	C₂×#41	C₂³×C₇	1	2	yes	—
576	C₂×#41	C₂³×C₇	1	4	yes	—
577	C₂×#41	C₂³×C₇	1	4	yes	—
578	C₂²×Q₈	—	4	4	no	—
579	C₂²×Q₈	C₂³×C₇	1	2	yes	—
580	C₂²×Q₈	C₂³×C₇	1	8	yes	—
581	C₂²×Q₈	C₂³×C₇	1	2	yes	—
582	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
583	C₂²×Q₈	C₂³×C₇	1	4	yes	—
584	C₂²×Q₈	C₂³×C₇	1	2	yes	—
585	C₂²×Q₈	C₂³×C₇	1	4	yes	—
586	C₂²×D₄	C₂³×C₇	1	2	yes	—
587	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₇	1	4	yes	—
589	C₂²×D₄	C₂³×C₇	1	2	yes	—
590	C₂³×C₄	C₂³×C₇	1	2	yes	—
591	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
592	C₂³×C₄	C₂³×C₇	1	4	yes	—
593	C₂³×C₄	C₂³×C₇	1	2	yes	—
594	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
595	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
596	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
597	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
598	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
599	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
600	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
601	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
602	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
603	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
604	#127	C₂³×C₇	1	4	yes	—
605	#127	C₂³×C₇	1	4	yes	—
606	#126	C₂³×C₇	1	16	yes	—
607	#126	C₂³×C₇	1	16	yes	—
608	#126	C₂³×C₇	1	16	yes	—
609	#126	C₂³×C₇	1	16	yes	—
610	#126	C₂³×C₇	1	16	yes	—
611	#126	C₂³×C₇	1	16	yes	—
612	#125	C₂³×C₇	1	8	yes	—
613	#125	C₂³×C₇	1	8	yes	—
614	#125	C₂³×C₇	1	16	yes	—
615	#125	C₂³×C₇	1	16	yes	—
616	#125	C₂³×C₇	1	16	yes	—
617	#124	C₂³×C₇	1	4	yes	—
618	#124	C₂³×C₇	1	8	yes	—
619	#124	C₂³×C₇	1	4	yes	—
620	#124	C₂³×C₇	1	8	yes	—
621	#124	C₂³×C₇	1	8	yes	—
622	#124	C₂³×C₇	1	4	yes	—
623	#124	C₂³×C₇	1	4	yes	—
624	#124	C₂³×C₇	1	4	yes	—
625	#124	C₂³×C₇	1	4	yes	—
626	#124	C₂³×C₇	1	8	yes	—
627	#124	C₂³×C₇	1	16	yes	—
628	#124	C₂³×C₇	1	8	yes	—
629	#124	C₂³×C₇	1	16	yes	—
630	#124	C₂³×C₇	1	16	yes	—
631	#123	C₂³×C₇	1	8	yes	—
632	#123	C₂³×C₇	1	8	yes	—
633	#123	C₂³×C₇	1	8	yes	—
634	#123	C₂³×C₇	1	8	yes	—
635	#123	C₂³×C₇	1	4	yes	—
636	#123	C₂³×C₇	1	8	yes	—
637	#123	C₂³×C₇	1	4	yes	—
638	#123	C₂³×C₇	1	8	yes	—
639	#123	C₂³×C₇	1	4	yes	—
640	#123	C₂³×C₇	1	4	yes	—
641	#123	C₂³×C₇	1	16	yes	—
642	#123	C₂³×C₇	1	16	yes	—
643	#123	C₂³×C₇	1	16	yes	—
644	#123	C₂³×C₇	1	16	yes	—
645	#123	C₂³×C₇	1	16	yes	—
646	#123	C₂³×C₇	1	16	yes	—
647	#123	C₂³×C₇	1	16	yes	—
648	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
649	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
650	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
651	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
652	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
653	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
654	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
655	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
656	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
657	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
658	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
659	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
660	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
661	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
662	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
663	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
664	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
665	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
666	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
667	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
668	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
669	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
670	#121	C₂³×C₇	1	4	yes	—
671	#121	C₂³×C₇	1	4	yes	—
672	#121	C₂³×C₇	1	8	yes	—
673	#121	C₂³×C₇	1	4	yes	—
674	#121	C₂³×C₇	1	8	yes	—
675	#121	C₂³×C₇	1	4	yes	—
676	#121	C₂³×C₇	1	8	yes	—
677	#121	C₂³×C₇	1	16	yes	—
678	#121	C₂³×C₇	1	8	yes	—
679	#121	C₂³×C₇	1	8	yes	—
680	#121	C₂³×C₇	1	8	yes	—
681	#121	C₂³×C₇	1	8	yes	—
682	#121	C₂³×C₇	1	8	yes	—
683	#121	C₂³×C₇	1	16	yes	—
684	#121	C₂³×C₇	1	16	yes	—
685	#121	C₂³×C₇	1	16	yes	—
686	#121	C₂³×C₇	1	16	yes	—
687	#120	C₂³×C₇	1	8	yes	—
688	#120	C₂³×C₇	1	4	yes	—
689	#120	C₂³×C₇	1	4	yes	—
690	#120	C₂³×C₇	1	8	yes	—
691	#120	C₂³×C₇	1	4	yes	—
692	#120	C₂³×C₇	1	4	yes	—
693	#120	C₂³×C₇	1	16	yes	—
694	C₄×Q₈	C₂³×C₇	1	8	yes	—
695	C₄×Q₈	C₂³×C₇	1	8	yes	—
696	C₄×Q₈	C₂³×C₇	1	8	yes	—
697	C₄×Q₈	C₂³×C₇	1	8	yes	—
698	C₄×Q₈	C₂³×C₇	1	16	yes	—
699	C₄×D₄	C₂³×C₇	1	16	yes	—
700	C₄×D₄	C₂³×C₇	1	8	yes	—
701	C₄×D₄	C₂³×C₇	1	8	yes	—
702	C₄×D₄	C₂³×C₇	1	8	yes	—
703	C₄×D₄	C₂³×C₇	1	8	yes	—
704	C₄×D₄	C₂³×C₇	1	8	yes	—
705	C₄×D₄	C₂³×C₇	1	16	yes	—
706	C₄×D₄	C₂³×C₇	1	16	yes	—
707	C₄×D₄	C₂³×C₇	1	16	yes	—
708	C₄×D₄	C₂³×C₇	1	16	yes	—
709	C₄×D₄	C₂³×C₇	1	8	yes	—
710	C₄×D₄	C₂³×C₇	1	16	yes	—
711	#117	C₂³×C₇	1	4	yes	—
712	#117	C₂³×C₇	1	4	yes	—
713	#117	C₂³×C₇	1	4	yes	—
714	#117	C₂³×C₇	1	2	yes	—
715	#117	C₂³×C₇	1	2	yes	—
716	#117	C₂³×C₇	1	4	yes	—
717	#117	C₂³×C₇	1	4	yes	—
718	#117	C₂³×C₇	1	8	yes	—
719	#117	C₂³×C₇	1	8	yes	—
720	#117	C₂³×C₇	1	16	yes	—
721	#117	C₂³×C₇	1	16	yes	—
722	#117	C₂³×C₇	1	16	yes	—
723	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
725	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
726	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
727	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
732	C₂×C₄²	C₂³×C₇	1	2	yes	—
733	C₂×C₄²	C₂³×C₇	1	4	yes	—
734	C₂²×C₇	—	2	2	no	—
735	C₂²×C₇	—	2	2	no	—
736	C₂²×C₇	—	2	2	no	—
737	C₂²×C₇	—	2	2	no	—
738	C₂²×C₇	—	2	8	no	—
739	C₂²×C₇	—	2	4	no	—
740	C₂²×C₇	—	2	8	no	—
741	C₂²×C₇	—	2	4	no	—
742	C₂²×C₇	—	2	8	no	—
743	C₂²×C₇	—	2	4	no	—
744	C₂²×C₇	—	4	4	no	—
745	C₂²×C₇	—	8	4	no	—
746	C₂²×C₇	—	8	8	no	—
747	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
748	C₂²×C₇	C₂⁶	1	1	yes	characteristic
749	C₄×C₇	—	2	2	no	—
750	C₄×C₇	—	2	2	no	—
751	C₄×C₇	—	2	1	no	—
752	C₄×C₇	—	2	1	no	—
753	C₄×C₇	—	2	8	no	—
754	C₄×C₇	—	2	8	no	—
755	C₄×C₇	—	2	8	no	—
756	C₄×C₇	—	2	8	no	—
757	C₄×C₇	—	2	8	no	—
758	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
759	C₂⁴	C₂⁴×C₇	1	2	yes	—
760	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
761	C₂⁴	C₂⁴×C₇	1	4	yes	—
762	#41	—	2	16	no	—
763	#41	—	4	4	no	—
764	#41	—	4	4	no	—
765	#41	—	4	4	no	—
766	#41	—	4	4	no	—
767	#41	—	4	8	no	—
768	#41	—	4	8	no	—
769	#41	—	4	16	no	—
770	#41	—	4	8	no	—
771	#41	—	4	16	no	—
772	C₂×Q₈	—	2	8	no	—
773	C₂×Q₈	—	4	4	no	—
774	C₂×Q₈	—	4	2	no	—
775	C₂×Q₈	—	4	8	no	—
776	C₂×Q₈	—	4	8	no	—
777	C₂×Q₈	—	4	4	no	—
778	C₂×Q₈	—	4	16	no	—
779	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
780	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
781	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
782	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
783	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
784	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
785	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
786	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
787	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
788	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
789	C₂×D₄	—	4	4	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	4	no	—
792	C₂×D₄	—	4	8	no	—
793	C₂×D₄	C₂⁴×C₇	1	8	yes	—
794	C₂×D₄	C₂⁴×C₇	1	4	yes	—
795	C₂×D₄	C₂⁴×C₇	1	8	yes	—
796	C₂×D₄	C₂⁴×C₇	1	8	yes	—
797	C₂×D₄	C₂⁴×C₇	1	8	yes	—
798	C₂×D₄	C₂⁴×C₇	1	8	yes	—
799	C₂×D₄	C₂⁴×C₇	1	8	yes	—
800	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
801	C₂×D₄	C₂⁴×C₇	1	8	yes	—
802	C₂×D₄	C₂⁴×C₇	1	2	yes	—
803	C₂×D₄	C₂⁴×C₇	1	2	yes	—
804	C₂×D₄	C₂⁴×C₇	1	2	yes	—
805	C₂×D₄	C₂⁴×C₇	1	2	yes	—
806	C₂×D₄	C₂⁴×C₇	1	8	yes	—
807	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
808	C₂×D₄	C₂⁴×C₇	1	2	yes	—
809	C₂×D₄	C₂⁴×C₇	1	4	yes	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	8	no	—
812	C₂²×C₄	—	4	8	no	—
813	C₂²×C₄	—	4	4	no	—
814	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
817	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
819	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
820	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
825	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
826	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
827	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
828	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
829	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
830	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
831	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
832	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
833	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
834	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
835	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
836	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
837	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
838	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
839	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
840	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
841	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
842	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
843	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
844	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
845	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
846	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
847	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
848	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
849	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
850	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
851	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
852	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
853	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
854	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
855	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
856	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
857	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
858	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
859	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
860	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
861	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
862	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
863	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
864	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
865	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
866	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
867	C₄²	C₂⁴×C₇	1	4	yes	—
868	C₄²	C₂⁴×C₇	1	4	yes	—
869	C₄²	C₂⁴×C₇	1	8	yes	—
870	C₄²	C₂⁴×C₇	1	4	yes	—
871	C₄²	C₂⁴×C₇	1	4	yes	—
872	C₄²	C₂⁴×C₇	1	8	yes	—
873	C₄²	C₂⁴×C₇	1	16	yes	—
874	C₄²	C₂⁴×C₇	1	8	yes	—
875	C₂×C₇	—	2	2	no	—
876	C₂×C₇	—	4	2	no	—
877	C₂×C₇	—	4	2	no	—
878	C₂×C₇	—	4	8	no	—
879	C₂×C₇	—	4	2	no	—
880	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
881	C₂×C₇	2₋¹⁺⁶	1	2	yes	—
882	C₂³	—	2	2	no	—
883	C₂³	—	2	4	no	—
884	C₂³	—	4	2	no	—
885	C₂³	—	4	4	no	—
886	C₂³	—	4	4	no	—
887	C₂³	—	4	8	no	—
888	C₂³	C₂⁵×C₇	1	2	yes	—
889	C₂³	C₂⁵×C₇	1	2	yes	—
890	C₂³	C₂⁵×C₇	1	2	yes	—
891	C₂³	C₂⁵×C₇	1	8	yes	—
892	C₂³	C₂⁵×C₇	1	1	yes	characteristic
893	Q₈	—	2	16	no	—
894	Q₈	—	2	8	no	—
895	Q₈	—	4	4	no	—
896	Q₈	—	4	4	no	—
897	Q₈	—	4	8	no	—
898	Q₈	—	4	1	no	—
899	Q₈	—	4	2	no	—
900	Q₈	—	4	1	no	—
901	Q₈	—	4	4	no	—
902	Q₈	—	4	8	no	—
903	D₄	—	2	16	no	—
904	D₄	—	2	8	no	—
905	D₄	—	4	2	no	—
906	D₄	—	4	2	no	—
907	D₄	—	4	2	no	—
908	D₄	—	4	2	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	1	no	—
911	D₄	—	4	2	no	—
912	D₄	—	4	1	no	—
913	D₄	—	4	8	no	—
914	D₄	—	4	8	no	—
915	D₄	—	4	8	no	—
916	D₄	—	4	8	no	—
917	D₄	—	4	8	no	—
918	D₄	—	4	8	no	—
919	D₄	—	4	8	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	4	no	—
922	C₂×C₄	—	2	8	no	—
923	C₂×C₄	—	2	4	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	4	no	—
926	C₂×C₄	—	2	4	no	—
927	C₂×C₄	—	2	4	no	—
928	C₂×C₄	—	2	4	no	—
929	C₂×C₄	—	2	16	no	—
930	C₂×C₄	—	4	4	no	—
931	C₂×C₄	—	4	8	no	—
932	C₂×C₄	—	4	8	no	—
933	C₂×C₄	—	4	16	no	—
934	C₂×C₄	—	4	8	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	16	no	—
937	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
938	C₂×C₄	C₂⁵×C₇	1	8	yes	—
939	C₂×C₄	C₂⁵×C₇	1	8	yes	—
940	C₂×C₄	C₂⁵×C₇	1	8	yes	—
941	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
942	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
943	C₂×C₄	C₂⁵×C₇	1	2	yes	—
944	C₂×C₄	C₂⁵×C₇	1	8	yes	—
945	C₂×C₄	C₂⁵×C₇	1	8	yes	—
946	C₂×C₄	C₂⁵×C₇	1	2	yes	—
947	C₂×C₄	C₂⁵×C₇	1	2	yes	—
948	C₇	#62886	1	1	yes	characteristic, direct product factor, Sylow
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	8	no	—
954	C₂²	—	2	4	no	—
955	C₂²	—	2	8	no	—
956	C₂²	—	2	4	no	—
957	C₂²	—	2	8	no	—
958	C₂²	—	2	4	no	—
959	C₂²	—	4	4	no	—
960	C₂²	—	8	4	no	—
961	C₂²	—	8	8	no	—
962	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
963	C₂²	C₂⁶×C₇	1	1	yes	characteristic
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	8	no	—
969	C₄	—	2	8	no	—
970	C₄	—	2	8	no	—
971	C₄	—	2	8	no	—
972	C₄	—	2	8	no	—
973	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
974	C₂	—	2	2	no	—
975	C₂	—	4	2	no	—
976	C₂	—	4	2	no	—
977	C₂	—	4	2	no	—
978	C₂	—	4	8	no	—
979	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
980	C₂	C₇×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3551	C₂	semidirect
2. C₇×#3550	C₂	semidirect
3. C₇×#3547	C₂	semidirect
4. C₇×#3545	C₂	semidirect
5. C₇×#3544	C₂	semidirect
6. C₇×#3541	C₂	semidirect
7. C₇×#3540	C₂	semidirect
8. C₇×#3538	C₂	semidirect
9. C₇×#3533	C₂	semidirect
10. C₇×#3495	C₂	semidirect
11. C₇×#3493	C₂	semidirect
12. C₇×#3489	C₂	semidirect
13. C₇×#3486	C₂	semidirect
14. C₇×#3449	C₂	semidirect
15. C₂×C₇×#536	C₂	semidirect
18. C₂²×C₇×#41	C₂²	semidirect
19. C₂³×C₇×Q₈	C₂²	semidirect
20. C₇×#563	C₂²	semidirect
21. C₇×#563	C₂²	semidirect
22. C₇×#563	C₂²	semidirect
23. C₇×#563	C₂²	semidirect
24. C₇×#562	C₂²	semidirect
25. C₇×#562	C₂²	semidirect
26. C₇×H(3,𝔽₄)	C₂²	semidirect
27. C₇×#560	C₂²	semidirect
28. C₇×#559	C₂²	semidirect
29. C₇×Q₈²	C₂²	semidirect
30. C₇×#556	C₂²	semidirect
31. C₇×#556	C₂²	semidirect
32. C₇×#555	C₂²	semidirect
33. C₇×#555	C₂²	semidirect
34. C₇×#555	C₂²	semidirect
35. C₇×#554	C₂²	semidirect
36. C₇×#554	C₂²	semidirect
37. C₇×#553	C₂²	semidirect
38. C₇×#553	C₂²	semidirect
39. C₇×#552	C₂²	semidirect
40. C₇×#552	C₂²	semidirect
41. C₇×#552	C₂²	semidirect
42. C₇×#552	C₂²	semidirect
43. C₇×#551	C₂²	semidirect
44. C₇×#551	C₂²	semidirect
45. C₇×#551	C₂²	semidirect
46. C₇×D₄×Q₈	C₂²	semidirect
47. C₇×D₄×Q₈	C₂²	semidirect
48. C₇×D₄×Q₈	C₂²	semidirect
49. C₇×#548	C₂²	semidirect
50. C₇×#548	C₂²	semidirect
51. C₇×#548	C₂²	semidirect
52. C₇×#547	C₂²	semidirect
53. C₇×#547	C₂²	semidirect
54. C₇×#546	C₂²	semidirect
55. C₇×#546	C₂²	semidirect
56. C₇×#544	C₂²	semidirect
57. C₇×#544	C₂²	semidirect
58. C₇×#542	C₂²	semidirect
59. C₇×#542	C₂²	semidirect
60. C₇×#542	C₂²	semidirect
61. C₇×#542	C₂²	semidirect
62. C₇×#541	C₂²	semidirect
63. C₇×#540	C₂²	semidirect
64. C₇×#539	C₂²	semidirect
65. C₇×#538	C₂²	semidirect
66. C₇×#538	C₂²	semidirect
67. C₇×#538	C₂²	semidirect
70. C₇×#537	C₂²	semidirect
71. C₇×#537	C₂²	semidirect
74. C₇×#536	C₂²	semidirect
75. C₇×#536	C₂²	semidirect
76. C₇×#536	C₂²	semidirect
77. C₇×#536	C₂²	semidirect
78. C₇×#536	C₂²	semidirect
79. C₇×#536	C₂²	semidirect
80. C₇×#536	C₂²	semidirect
81. C₇×#536	C₂²	semidirect
84. C₇×#535	C₂²	semidirect
86. C₇×#534	C₂²	semidirect
87. C₇×#533	C₂²	semidirect
89. C₇×#532	C₂²	semidirect
90. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
91. C₇×#529	C₂²	semidirect
92. C₇×#529	C₂²	semidirect
96. C₇×#525	C₂²	semidirect
97. C₇×#525	C₂²	semidirect
98. C₇×#525	C₂²	semidirect
99. C₇×#525	C₂²	semidirect
100. C₂×C₇×#123	C₂²	semidirect
101. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
102. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
103. C₇×#520	C₂²	semidirect
104. C₇×#519	C₂²	semidirect
105. C₂×C₇×#117	C₂²	semidirect
106. C₂×C₇×#117	C₂²	semidirect
107. #62886	C₇	direct (N × H)
277. #3551	C₂×C₇	semidirect
278. #3550	C₂×C₇	semidirect
279. #3547	C₂×C₇	semidirect
280. #3545	C₂×C₇	semidirect
281. #3544	C₂×C₇	semidirect
282. #3541	C₂×C₇	semidirect
283. #3540	C₂×C₇	semidirect
284. #3538	C₂×C₇	semidirect
285. #3533	C₂×C₇	semidirect
286. #3495	C₂×C₇	semidirect
287. #3493	C₂×C₇	semidirect
288. #3489	C₂×C₇	semidirect
289. #3486	C₂×C₇	semidirect
290. #3449	C₂×C₇	semidirect
291. C₂×#536	C₂×C₇	semidirect
410. C₂²×#41	C₂²×C₇	semidirect
411. C₂³×Q₈	C₂²×C₇	semidirect
412. #563	C₂²×C₇	semidirect
413. #563	C₂²×C₇	semidirect
414. #563	C₂²×C₇	semidirect
415. #563	C₂²×C₇	semidirect
416. #562	C₂²×C₇	semidirect
417. #562	C₂²×C₇	semidirect
418. H(3,𝔽₄)	C₂²×C₇	semidirect
419. #560	C₂²×C₇	semidirect
420. #559	C₂²×C₇	semidirect
421. Q₈²	C₂²×C₇	semidirect
422. #556	C₂²×C₇	semidirect
423. #556	C₂²×C₇	semidirect
424. #555	C₂²×C₇	semidirect
425. #555	C₂²×C₇	semidirect
426. #555	C₂²×C₇	semidirect
427. #554	C₂²×C₇	semidirect
428. #554	C₂²×C₇	semidirect
429. #553	C₂²×C₇	semidirect
430. #553	C₂²×C₇	semidirect
431. #552	C₂²×C₇	semidirect
432. #552	C₂²×C₇	semidirect
433. #552	C₂²×C₇	semidirect
434. #552	C₂²×C₇	semidirect
435. #551	C₂²×C₇	semidirect
436. #551	C₂²×C₇	semidirect
437. #551	C₂²×C₇	semidirect
438. D₄×Q₈	C₂²×C₇	semidirect
439. D₄×Q₈	C₂²×C₇	semidirect
440. D₄×Q₈	C₂²×C₇	semidirect
441. #548	C₂²×C₇	semidirect
442. #548	C₂²×C₇	semidirect
443. #548	C₂²×C₇	semidirect
444. #547	C₂²×C₇	semidirect
445. #547	C₂²×C₇	semidirect
446. #546	C₂²×C₇	semidirect
447. #546	C₂²×C₇	semidirect
448. #544	C₂²×C₇	semidirect
449. #544	C₂²×C₇	semidirect
450. #542	C₂²×C₇	semidirect
451. #542	C₂²×C₇	semidirect
452. #542	C₂²×C₇	semidirect
453. #542	C₂²×C₇	semidirect
454. #541	C₂²×C₇	semidirect
455. #540	C₂²×C₇	semidirect
456. #539	C₂²×C₇	semidirect
457. #538	C₂²×C₇	semidirect
458. #538	C₂²×C₇	semidirect
459. #538	C₂²×C₇	semidirect
462. #537	C₂²×C₇	semidirect
463. #537	C₂²×C₇	semidirect
466. #536	C₂²×C₇	semidirect
467. #536	C₂²×C₇	semidirect
468. #536	C₂²×C₇	semidirect
469. #536	C₂²×C₇	semidirect
470. #536	C₂²×C₇	semidirect
471. #536	C₂²×C₇	semidirect
472. #536	C₂²×C₇	semidirect
473. #536	C₂²×C₇	semidirect
476. #535	C₂²×C₇	semidirect
478. #534	C₂²×C₇	semidirect
479. #533	C₂²×C₇	semidirect
481. #532	C₂²×C₇	semidirect
482. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
483. #529	C₂²×C₇	semidirect
484. #529	C₂²×C₇	semidirect
488. #525	C₂²×C₇	semidirect
489. #525	C₂²×C₇	semidirect
490. #525	C₂²×C₇	semidirect
491. #525	C₂²×C₇	semidirect
492. C₂×#123	C₂²×C₇	semidirect
493. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
494. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
495. #520	C₂²×C₇	semidirect
496. #519	C₂²×C₇	semidirect
497. C₂×#117	C₂²×C₇	semidirect
498. C₂×#117	C₂²×C₇	semidirect
948. C₇	#62886	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3551	2
C₇×#3550	2
C₇×#3547	2
C₇×#3545	2
C₇×#3544	2
C₇×#3541	2
C₇×#3540	2
C₇×#3538	2
C₇×#3533	2
C₇×#3495	2
C₇×#3493	2
C₇×#3489	2
C₇×#3486	2
C₇×#3449	2
C₂×C₇×#536	2
#62886	7

Subgroups — C7×#62886 #13240102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62886 #13240102