Subgroups — C₇×#62838 #13240054

Order 1792.

6518 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3565	C₂	1	8	yes	maximal, complemented
2	C₇×#3555	C₂	1	4	yes	maximal, complemented
3	C₇×#3547	C₂	1	4	yes	maximal, complemented
4	C₇×#3541	C₂	1	8	yes	maximal, complemented
5	C₇×#3518	C₂	1	4	yes	maximal, complemented
6	C₇×#3516	C₂	1	8	yes	maximal, complemented
7	C₇×#3515	C₂	1	4	yes	maximal, complemented
8	C₇×#3512	C₂	1	2	yes	maximal, complemented
9	C₇×#3511	C₂	1	2	yes	maximal, complemented
10	C₇×#3511	C₂	1	4	yes	maximal, complemented
11	C₇×#3509	C₂	1	4	yes	maximal, complemented
12	C₇×#3504	C₂	1	2	yes	maximal, complemented
13	C₇×#3503	C₂	1	2	yes	maximal, complemented
14	C₇×#3493	C₂	1	4	yes	maximal, complemented
15	C₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#563	C₂²	1	16	yes	—
19	C₇×#562	C₂²	1	16	yes	—
20	C₇×Q₈²	C₂²	1	4	yes	complemented
21	C₇×#557	C₂²	1	8	yes	complemented
22	C₇×#557	C₂²	1	4	yes	complemented
23	C₇×#557	C₂²	1	8	yes	complemented
24	C₇×#556	C₂²	1	8	yes	—
25	C₇×#556	C₂²	1	8	yes	—
26	C₇×#556	C₂²	1	8	yes	—
27	C₇×#556	C₂²	1	16	yes	complemented
28	C₇×#556	C₂²	1	8	yes	complemented
29	C₇×#556	C₂²	1	4	yes	complemented
30	C₇×#555	C₂²	1	8	yes	—
31	C₇×#555	C₂²	1	8	yes	—
32	C₇×#555	C₂²	1	4	yes	complemented
33	C₇×#554	C₂²	1	8	yes	—
34	C₇×#554	C₂²	1	16	yes	—
35	C₇×#554	C₂²	1	8	yes	complemented
36	C₇×#554	C₂²	1	4	yes	complemented
37	C₇×#554	C₂²	1	4	yes	complemented
38	C₇×#553	C₂²	1	8	yes	—
39	C₇×#553	C₂²	1	8	yes	—
40	C₇×#553	C₂²	1	8	yes	—
41	C₇×#553	C₂²	1	16	yes	—
42	C₇×#553	C₂²	1	8	yes	complemented
43	C₇×#552	C₂²	1	8	yes	—
44	C₇×#552	C₂²	1	8	yes	—
45	C₇×#552	C₂²	1	8	yes	—
46	C₇×#552	C₂²	1	8	yes	complemented
47	C₇×#552	C₂²	1	16	yes	complemented
48	C₇×#552	C₂²	1	8	yes	complemented
49	C₇×D₄×Q₈	C₂²	1	8	yes	—
50	C₇×D₄×Q₈	C₂²	1	4	yes	complemented
51	C₇×#548	C₂²	1	8	yes	—
52	C₇×#548	C₂²	1	8	yes	—
53	C₇×#548	C₂²	1	8	yes	complemented
54	C₇×#547	C₂²	1	8	yes	—
55	C₇×#547	C₂²	1	4	yes	complemented
56	C₇×#544	C₂²	1	4	yes	—
57	C₇×#544	C₂²	1	8	yes	complemented
58	C₇×#544	C₂²	1	8	yes	complemented
59	C₇×#542	C₂²	1	16	yes	—
60	C₇×#542	C₂²	1	8	yes	—
61	C₇×#542	C₂²	1	8	yes	complemented
62	C₇×#542	C₂²	1	16	yes	complemented
63	C₇×#542	C₂²	1	8	yes	complemented
64	C₇×#541	C₂²	1	8	yes	—
65	C₇×#541	C₂²	1	16	yes	complemented
66	C₇×#541	C₂²	1	8	yes	complemented
67	C₇×#541	C₂²	1	4	yes	complemented
68	C₇×#540	C₂²	1	4	yes	complemented
69	C₇×#539	C₂²	1	16	yes	—
70	C₇×#538	C₂²	1	16	yes	—
71	C₇×#537	C₂²	1	4	yes	—
72	C₇×#537	C₂²	1	8	yes	—
73	C₇×#536	C₂²	1	8	yes	—
74	C₇×#533	C₂²	1	4	yes	—
75	C₇×#533	C₂²	1	4	yes	—
76	C₇×#533	C₂²	1	4	yes	—
77	C₇×#533	C₂²	1	4	yes	—
78	C₇×#533	C₂²	1	1	yes	characteristic
79	C₇×#533	C₂²	1	1	yes	characteristic
80	C₇×#533	C₂²	1	2	yes	—
81	C₇×#533	C₂²	1	2	yes	—
82	C₇×#533	C₂²	1	4	yes	complemented
83	C₇×#533	C₂²	1	4	yes	complemented
84	C₇×#533	C₂²	1	4	yes	complemented
85	C₇×#532	C₂²	1	1	yes	characteristic
86	C₇×#532	C₂²	1	2	yes	—
87	C₇×#532	C₂²	1	1	yes	characteristic
88	C₇×#532	C₂²	1	2	yes	—
89	C₇×#532	C₂²	1	4	yes	complemented
90	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
91	C₂×C₇×C₄⋊Q₈	C₂²	1	4	yes	complemented
92	C₇×#529	C₂²	1	4	yes	—
93	C₇×#529	C₂²	1	4	yes	—
94	C₇×#529	C₂²	1	2	yes	—
95	C₇×#529	C₂²	1	4	yes	—
96	C₇×#529	C₂²	1	4	yes	—
97	C₇×#529	C₂²	1	2	yes	—
98	C₇×#529	C₂²	1	4	yes	—
99	C₇×#529	C₂²	1	16	yes	—
100	C₇×#529	C₂²	1	8	yes	complemented
101	C₂×C₇×#125	C₂²	1	2	yes	—
102	C₂×C₇×#125	C₂²	1	4	yes	complemented
103	C₇×#525	C₂²	1	2	yes	—
104	C₇×#525	C₂²	1	2	yes	—
105	C₇×#525	C₂²	1	4	yes	—
106	C₇×#525	C₂²	1	4	yes	—
107	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
108	C₇×#520	C₂²	1	4	yes	—
109	C₇×#520	C₂²	1	4	yes	—
110	C₇×#520	C₂²	1	8	yes	complemented
111	C₇×#519	C₂²	1	8	yes	complemented
112	C₄×C₇×#41	C₂²	1	2	yes	—
113	C₄×C₇×#41	C₂²	1	2	yes	—
114	C₄×C₇×#41	C₂²	1	4	yes	—
115	C₄×C₇×#41	C₂²	1	4	yes	—
116	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	—
117	C₂×C₇×#117	C₂²	1	2	yes	—
118	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
119	#62838	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂×C₇×#41	C₂³	1	2	yes	—
121	C₂×C₇×#41	C₂³	1	2	yes	—
122	C₂×C₇×#41	C₂³	1	4	yes	—
123	C₂×C₇×#41	C₂³	1	4	yes	—
124	C₂×C₇×#41	C₂³	1	8	yes	—
125	C₂²×C₇×Q₈	C₂³	1	4	yes	—
126	C₂²×C₇×Q₈	C₂³	1	8	yes	—
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	2	yes	—
129	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
130	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
131	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
132	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
133	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
135	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
136	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
137	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
141	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
142	C₇×C₄⋊Q₈	C₂³	1	16	yes	—
143	C₇×#127	C₂³	1	1	yes	characteristic
144	C₇×#127	C₂³	1	1	yes	characteristic
145	C₇×#126	C₂³	1	8	yes	—
146	C₇×#126	C₂³	1	4	yes	—
147	C₇×#126	C₂³	1	4	yes	—
148	C₇×#126	C₂³	1	16	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	4	yes	—
156	C₇×#125	C₂³	1	4	yes	—
157	C₇×#125	C₂³	1	8	yes	—
158	C₇×#125	C₂³	1	1	yes	characteristic
159	C₇×#125	C₂³	1	16	yes	—
160	C₇×#125	C₂³	1	8	yes	—
161	C₇×#125	C₂³	1	1	yes	characteristic
162	C₇×#125	C₂³	1	4	yes	—
163	C₇×#125	C₂³	1	2	yes	—
164	C₇×#125	C₂³	1	4	yes	—
165	C₇×#125	C₂³	1	16	yes	—
166	C₇×#125	C₂³	1	8	yes	—
167	C₇×#125	C₂³	1	8	yes	—
168	C₇×#125	C₂³	1	16	yes	—
169	C₇×#125	C₂³	1	16	yes	—
170	C₇×#125	C₂³	1	16	yes	—
171	C₇×#124	C₂³	1	2	yes	—
172	C₇×#124	C₂³	1	2	yes	—
173	C₇×#124	C₂³	1	4	yes	—
174	C₇×#124	C₂³	1	4	yes	—
175	C₇×#124	C₂³	1	16	yes	—
176	C₇×#124	C₂³	1	8	yes	—
177	C₇×#124	C₂³	1	16	yes	—
178	C₇×#124	C₂³	1	16	yes	—
179	C₇×#124	C₂³	1	16	yes	—
180	C₇×#123	C₂³	1	4	yes	—
181	C₇×#123	C₂³	1	4	yes	—
182	C₇×#123	C₂³	1	4	yes	—
183	C₇×#123	C₂³	1	4	yes	—
184	C₇×#123	C₂³	1	8	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×C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
193	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
194	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
195	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
196	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
198	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
199	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
201	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
204	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
205	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
206	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
207	C₇×C₂²⋊Q₈	C₂³	1	16	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	4	yes	—
216	C₇×#121	C₂³	1	2	yes	—
217	C₇×#121	C₂³	1	4	yes	—
218	C₇×#121	C₂³	1	2	yes	—
219	C₇×#121	C₂³	1	4	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	16	yes	—
225	C₇×#121	C₂³	1	16	yes	—
226	C₇×#121	C₂³	1	16	yes	—
227	C₇×#120	C₂³	1	4	yes	—
228	C₇×#120	C₂³	1	4	yes	—
229	C₄×C₇×Q₈	C₂³	1	8	yes	—
230	C₄×C₇×Q₈	C₂³	1	8	yes	—
231	C₄×C₇×Q₈	C₂³	1	8	yes	—
232	C₄×C₇×Q₈	C₂³	1	8	yes	—
233	C₄×C₇×Q₈	C₂³	1	4	yes	—
234	C₄×C₇×Q₈	C₂³	1	4	yes	—
235	C₄×C₇×Q₈	C₂³	1	4	yes	—
236	C₄×C₇×Q₈	C₂³	1	4	yes	—
237	C₄×C₇×Q₈	C₂³	1	2	yes	—
238	C₄×C₇×Q₈	C₂³	1	4	yes	—
239	C₄×C₇×Q₈	C₂³	1	2	yes	—
240	C₄×C₇×Q₈	C₂³	1	16	yes	—
241	C₄×C₇×Q₈	C₂³	1	8	yes	—
242	C₄×C₇×Q₈	C₂³	1	8	yes	—
243	C₄×C₇×Q₈	C₂³	1	16	yes	—
244	C₄×C₇×Q₈	C₂³	1	8	yes	—
245	C₄×C₇×Q₈	C₂³	1	8	yes	—
246	C₄×C₇×Q₈	C₂³	1	8	yes	—
247	C₄×C₇×D₄	C₂³	1	4	yes	—
248	C₄×C₇×D₄	C₂³	1	8	yes	—
249	C₄×C₇×D₄	C₂³	1	4	yes	—
250	C₄×C₇×D₄	C₂³	1	4	yes	—
251	C₄×C₇×D₄	C₂³	1	4	yes	—
252	C₄×C₇×D₄	C₂³	1	4	yes	—
253	C₄×C₇×D₄	C₂³	1	4	yes	—
254	C₄×C₇×D₄	C₂³	1	8	yes	—
255	C₄×C₇×D₄	C₂³	1	8	yes	—
256	C₄×C₇×D₄	C₂³	1	4	yes	—
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	4	yes	—
259	C₄×C₇×D₄	C₂³	1	4	yes	—
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₄×C₇×D₄	C₂³	1	4	yes	—
262	C₄×C₇×D₄	C₂³	1	4	yes	—
263	C₄×C₇×D₄	C₂³	1	16	yes	—
264	C₄×C₇×D₄	C₂³	1	16	yes	—
265	C₄×C₇×D₄	C₂³	1	8	yes	—
266	C₄×C₇×D₄	C₂³	1	8	yes	—
267	C₄×C₇×D₄	C₂³	1	16	yes	—
268	C₄×C₇×D₄	C₂³	1	16	yes	—
269	C₄×C₇×D₄	C₂³	1	8	yes	—
270	C₇×#117	C₂³	1	8	yes	—
271	C₇×#117	C₂³	1	8	yes	—
272	C₇×#117	C₂³	1	4	yes	—
273	C₇×#117	C₂³	1	2	yes	—
274	C₇×#117	C₂³	1	2	yes	—
275	C₇×#117	C₂³	1	4	yes	—
276	C₇×#117	C₂³	1	4	yes	—
277	C₇×#117	C₂³	1	4	yes	—
278	C₇×#117	C₂³	1	4	yes	—
279	C₇×#117	C₂³	1	4	yes	—
280	C₇×#117	C₂³	1	8	yes	—
281	C₇×#117	C₂³	1	16	yes	—
282	C₇×#117	C₂³	1	16	yes	—
283	C₇×#117	C₂³	1	8	yes	—
284	C₇×#117	C₂³	1	8	yes	—
285	C₇×#117	C₂³	1	8	yes	—
286	C₇×#117	C₂³	1	16	yes	—
287	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
288	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
289	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
290	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
291	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
292	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
293	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
294	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
295	C₂×C₄²×C₇	C₂³	1	2	yes	—
296	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₇	C₂³	1	2	yes	—
298	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₇	C₂³	1	2	yes	—
300	C₂×C₄²×C₇	C₂³	1	2	yes	—
301	C₂×C₄²×C₇	C₂³	1	2	yes	—
302	C₂×C₄²×C₇	C₂³	1	4	yes	—
303	C₂×C₄²×C₇	C₂³	1	4	yes	—
304	C₂×C₄²×C₇	C₂³	1	4	yes	—
305	#3565	C₂×C₇	1	8	yes	complemented
306	#3555	C₂×C₇	1	4	yes	complemented
307	#3547	C₂×C₇	1	4	yes	complemented
308	#3541	C₂×C₇	1	8	yes	complemented
309	#3518	C₂×C₇	1	4	yes	complemented
310	#3516	C₂×C₇	1	8	yes	complemented
311	#3515	C₂×C₇	1	4	yes	complemented
312	#3512	C₂×C₇	1	2	yes	complemented
313	#3511	C₂×C₇	1	2	yes	complemented
314	#3511	C₂×C₇	1	4	yes	complemented
315	#3509	C₂×C₇	1	4	yes	complemented
316	#3504	C₂×C₇	1	2	yes	complemented
317	#3503	C₂×C₇	1	2	yes	complemented
318	#3493	C₂×C₇	1	4	yes	complemented
319	#3444	C₂×C₇	1	1	yes	characteristic, complemented
320	#3444	C₂×C₇	1	1	yes	characteristic, complemented
321	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
322	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
323	C₇×#41	—	2	8	no	—
324	C₇×#41	—	2	8	no	—
325	C₇×#41	—	4	8	no	—
326	C₇×#41	—	4	8	no	—
327	C₇×#41	—	4	16	no	—
328	C₂×C₇×Q₈	—	4	8	no	—
329	C₂×C₇×Q₈	—	4	16	no	—
330	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
331	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
332	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
333	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
334	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
335	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
336	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
337	C₂×C₇×D₄	C₂⁴	1	4	yes	—
338	C₂×C₇×D₄	C₂⁴	1	4	yes	—
339	C₂×C₇×D₄	C₂⁴	1	2	yes	—
340	C₂×C₇×D₄	C₂⁴	1	2	yes	—
341	C₂×C₇×D₄	C₂⁴	1	4	yes	—
342	C₂×C₇×D₄	C₂⁴	1	4	yes	—
343	C₂×C₇×D₄	C₂⁴	1	8	yes	—
344	C₂×C₇×D₄	C₂⁴	1	4	yes	—
345	C₂×C₇×D₄	C₂⁴	1	16	yes	—
346	C₂×C₇×D₄	C₂⁴	1	4	yes	—
347	C₂²×C₄×C₇	—	2	4	no	—
348	C₂²×C₄×C₇	—	4	4	no	—
349	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
356	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
357	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
358	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
363	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
364	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
365	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
366	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
367	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
369	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
370	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
371	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
372	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
373	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
374	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
375	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
376	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
377	C₇×C₄⋊C₄	C₂⁴	1	16	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	2	yes	—
382	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
383	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
384	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
385	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
386	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
387	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
388	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
389	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
390	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
391	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
392	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
393	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
394	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
395	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
396	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
397	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
398	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
399	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
400	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
401	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
402	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
403	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
404	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
405	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
406	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
407	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
408	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
409	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
410	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
411	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
412	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
413	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
414	C₄²×C₇	C₂⁴	1	1	yes	characteristic
415	C₄²×C₇	C₂⁴	1	1	yes	characteristic
416	C₄²×C₇	C₂⁴	1	2	yes	—
417	C₄²×C₇	C₂⁴	1	2	yes	—
418	C₄²×C₇	C₂⁴	1	1	yes	characteristic
419	C₄²×C₇	C₂⁴	1	1	yes	characteristic
420	C₄²×C₇	C₂⁴	1	2	yes	—
421	C₄²×C₇	C₂⁴	1	2	yes	—
422	C₄²×C₇	C₂⁴	1	2	yes	—
423	C₄²×C₇	C₂⁴	1	2	yes	—
424	C₄²×C₇	C₂⁴	1	8	yes	—
425	C₄²×C₇	C₂⁴	1	16	yes	—
426	C₄²×C₇	C₂⁴	1	4	yes	—
427	C₄²×C₇	C₂⁴	1	4	yes	—
428	C₄²×C₇	C₂⁴	1	4	yes	—
429	C₄²×C₇	C₂⁴	1	4	yes	—
430	C₄²×C₇	C₂⁴	1	16	yes	—
431	C₄²×C₇	C₂⁴	1	16	yes	—
432	#563	C₂²×C₇	1	16	yes	—
433	#562	C₂²×C₇	1	16	yes	—
434	Q₈²	C₂²×C₇	1	4	yes	complemented
435	#557	C₂²×C₇	1	4	yes	complemented
436	#557	C₂²×C₇	1	8	yes	complemented
437	#557	C₂²×C₇	1	8	yes	complemented
438	#556	C₂²×C₇	1	8	yes	—
439	#556	C₂²×C₇	1	8	yes	—
440	#556	C₂²×C₇	1	8	yes	—
441	#556	C₂²×C₇	1	8	yes	complemented
442	#556	C₂²×C₇	1	4	yes	complemented
443	#556	C₂²×C₇	1	16	yes	complemented
444	#555	C₂²×C₇	1	8	yes	—
445	#555	C₂²×C₇	1	8	yes	—
446	#555	C₂²×C₇	1	4	yes	complemented
447	#554	C₂²×C₇	1	8	yes	—
448	#554	C₂²×C₇	1	16	yes	—
449	#554	C₂²×C₇	1	4	yes	complemented
450	#554	C₂²×C₇	1	8	yes	complemented
451	#554	C₂²×C₇	1	4	yes	complemented
452	#553	C₂²×C₇	1	8	yes	—
453	#553	C₂²×C₇	1	8	yes	—
454	#553	C₂²×C₇	1	8	yes	—
455	#553	C₂²×C₇	1	16	yes	—
456	#553	C₂²×C₇	1	8	yes	complemented
457	#552	C₂²×C₇	1	8	yes	—
458	#552	C₂²×C₇	1	8	yes	—
459	#552	C₂²×C₇	1	8	yes	—
460	#552	C₂²×C₇	1	8	yes	complemented
461	#552	C₂²×C₇	1	8	yes	complemented
462	#552	C₂²×C₇	1	16	yes	complemented
463	D₄×Q₈	C₂²×C₇	1	8	yes	—
464	D₄×Q₈	C₂²×C₇	1	4	yes	complemented
465	#548	C₂²×C₇	1	8	yes	—
466	#548	C₂²×C₇	1	8	yes	—
467	#548	C₂²×C₇	1	8	yes	complemented
468	#547	C₂²×C₇	1	8	yes	—
469	#547	C₂²×C₇	1	4	yes	complemented
470	#544	C₂²×C₇	1	4	yes	—
471	#544	C₂²×C₇	1	8	yes	complemented
472	#544	C₂²×C₇	1	8	yes	complemented
473	#542	C₂²×C₇	1	8	yes	—
474	#542	C₂²×C₇	1	16	yes	—
475	#542	C₂²×C₇	1	8	yes	complemented
476	#542	C₂²×C₇	1	8	yes	complemented
477	#542	C₂²×C₇	1	16	yes	complemented
478	#541	C₂²×C₇	1	8	yes	—
479	#541	C₂²×C₇	1	8	yes	complemented
480	#541	C₂²×C₇	1	4	yes	complemented
481	#541	C₂²×C₇	1	16	yes	complemented
482	#540	C₂²×C₇	1	4	yes	complemented
483	#539	C₂²×C₇	1	16	yes	—
484	#538	C₂²×C₇	1	16	yes	—
485	#537	C₂²×C₇	1	4	yes	—
486	#537	C₂²×C₇	1	8	yes	—
487	#536	C₂²×C₇	1	8	yes	—
488	#533	C₂²×C₇	1	4	yes	—
489	#533	C₂²×C₇	1	4	yes	—
490	#533	C₂²×C₇	1	4	yes	—
491	#533	C₂²×C₇	1	4	yes	—
492	#533	C₂²×C₇	1	1	yes	characteristic
493	#533	C₂²×C₇	1	1	yes	characteristic
494	#533	C₂²×C₇	1	2	yes	—
495	#533	C₂²×C₇	1	2	yes	—
496	#533	C₂²×C₇	1	4	yes	complemented
497	#533	C₂²×C₇	1	4	yes	complemented
498	#533	C₂²×C₇	1	4	yes	complemented
499	#532	C₂²×C₇	1	1	yes	characteristic
500	#532	C₂²×C₇	1	2	yes	—
501	#532	C₂²×C₇	1	1	yes	characteristic
502	#532	C₂²×C₇	1	2	yes	—
503	#532	C₂²×C₇	1	4	yes	complemented
504	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
505	C₂×C₄⋊Q₈	C₂²×C₇	1	4	yes	complemented
506	#529	C₂²×C₇	1	2	yes	—
507	#529	C₂²×C₇	1	4	yes	—
508	#529	C₂²×C₇	1	4	yes	—
509	#529	C₂²×C₇	1	2	yes	—
510	#529	C₂²×C₇	1	4	yes	—
511	#529	C₂²×C₇	1	4	yes	—
512	#529	C₂²×C₇	1	4	yes	—
513	#529	C₂²×C₇	1	16	yes	—
514	#529	C₂²×C₇	1	8	yes	complemented
515	C₂×#125	C₂²×C₇	1	2	yes	—
516	C₂×#125	C₂²×C₇	1	4	yes	complemented
517	#525	C₂²×C₇	1	2	yes	—
518	#525	C₂²×C₇	1	2	yes	—
519	#525	C₂²×C₇	1	4	yes	—
520	#525	C₂²×C₇	1	4	yes	—
521	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
522	#520	C₂²×C₇	1	4	yes	—
523	#520	C₂²×C₇	1	4	yes	—
524	#520	C₂²×C₇	1	8	yes	complemented
525	#519	C₂²×C₇	1	8	yes	complemented
526	C₄×#41	C₂²×C₇	1	2	yes	—
527	C₄×#41	C₂²×C₇	1	2	yes	—
528	C₄×#41	C₂²×C₇	1	4	yes	—
529	C₄×#41	C₂²×C₇	1	4	yes	—
530	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	—
531	C₂×#117	C₂²×C₇	1	2	yes	—
532	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
533	C₂³×C₇	—	2	2	no	—
534	C₂³×C₇	—	4	2	no	—
535	C₂³×C₇	C₂⁵	1	2	yes	—
536	C₂³×C₇	C₂⁵	1	4	yes	—
537	C₂³×C₇	C₂⁵	1	4	yes	—
538	C₂³×C₇	C₂⁵	1	1	yes	characteristic
539	C₇×Q₈	—	2	4	no	—
540	C₇×Q₈	—	2	4	no	—
541	C₇×Q₈	—	2	16	no	—
542	C₇×Q₈	—	2	8	no	—
543	C₇×Q₈	—	4	8	no	—
544	C₇×Q₈	—	4	16	no	—
545	C₇×Q₈	—	4	4	no	—
546	C₇×D₄	—	2	8	no	—
547	C₇×D₄	—	2	8	no	—
548	C₇×D₄	—	2	4	no	—
549	C₇×D₄	—	2	4	no	—
550	C₇×D₄	—	2	8	no	—
551	C₇×D₄	—	4	4	no	—
552	C₇×D₄	—	4	4	no	—
553	C₇×D₄	—	4	4	no	—
554	C₇×D₄	—	4	8	no	—
555	C₇×D₄	—	4	16	no	—
556	C₂×C₄×C₇	—	2	2	no	—
557	C₂×C₄×C₇	—	2	4	no	—
558	C₂×C₄×C₇	—	2	4	no	—
559	C₂×C₄×C₇	—	2	8	no	—
560	C₂×C₄×C₇	—	2	8	no	—
561	C₂×C₄×C₇	—	2	4	no	—
562	C₂×C₄×C₇	—	2	4	no	—
563	C₂×C₄×C₇	—	2	4	no	—
564	C₂×C₄×C₇	—	2	8	no	—
565	C₂×C₄×C₇	—	2	8	no	—
566	C₂×C₄×C₇	—	4	2	no	—
567	C₂×C₄×C₇	—	4	2	no	—
568	C₂×C₄×C₇	—	4	2	no	—
569	C₂×C₄×C₇	—	4	8	no	—
570	C₂×C₄×C₇	—	4	16	no	—
571	C₂×C₄×C₇	—	4	8	no	—
572	C₂×C₄×C₇	—	4	16	no	—
573	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
574	C₂×C₄×C₇	C₂⁵	1	2	yes	—
575	C₂×C₄×C₇	C₂⁵	1	2	yes	—
576	C₂×C₄×C₇	C₂⁵	1	4	yes	—
577	C₂×C₄×C₇	C₂⁵	1	4	yes	—
578	C₂×C₄×C₇	C₂⁵	1	4	yes	—
579	C₂×C₄×C₇	C₂⁵	1	2	yes	—
580	C₂×C₄×C₇	C₂⁵	1	8	yes	—
581	C₂×C₄×C₇	C₂⁵	1	16	yes	—
582	C₂×C₄×C₇	C₂⁵	1	2	yes	—
583	C₂×C₄×C₇	C₂⁵	1	4	yes	—
584	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
585	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
586	C₂×C₄×C₇	C₂⁵	1	2	yes	—
587	C₂×#41	C₂³×C₇	1	2	yes	—
588	C₂×#41	C₂³×C₇	1	2	yes	—
589	C₂×#41	C₂³×C₇	1	4	yes	—
590	C₂×#41	C₂³×C₇	1	4	yes	—
591	C₂×#41	C₂³×C₇	1	8	yes	—
592	C₂²×Q₈	C₂³×C₇	1	4	yes	—
593	C₂²×Q₈	C₂³×C₇	1	8	yes	—
594	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₇	1	2	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	4	yes	—
600	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
601	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
602	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
603	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
604	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
605	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
606	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
607	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
608	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
609	C₄⋊Q₈	C₂³×C₇	1	16	yes	—
610	#127	C₂³×C₇	1	1	yes	characteristic
611	#127	C₂³×C₇	1	1	yes	characteristic
612	#126	C₂³×C₇	1	8	yes	—
613	#126	C₂³×C₇	1	4	yes	—
614	#126	C₂³×C₇	1	4	yes	—
615	#126	C₂³×C₇	1	16	yes	—
616	#126	C₂³×C₇	1	16	yes	—
617	#126	C₂³×C₇	1	16	yes	—
618	#126	C₂³×C₇	1	16	yes	—
619	#126	C₂³×C₇	1	16	yes	—
620	#126	C₂³×C₇	1	16	yes	—
621	#126	C₂³×C₇	1	16	yes	—
622	#125	C₂³×C₇	1	4	yes	—
623	#125	C₂³×C₇	1	4	yes	—
624	#125	C₂³×C₇	1	8	yes	—
625	#125	C₂³×C₇	1	1	yes	characteristic
626	#125	C₂³×C₇	1	16	yes	—
627	#125	C₂³×C₇	1	8	yes	—
628	#125	C₂³×C₇	1	1	yes	characteristic
629	#125	C₂³×C₇	1	4	yes	—
630	#125	C₂³×C₇	1	2	yes	—
631	#125	C₂³×C₇	1	4	yes	—
632	#125	C₂³×C₇	1	16	yes	—
633	#125	C₂³×C₇	1	8	yes	—
634	#125	C₂³×C₇	1	8	yes	—
635	#125	C₂³×C₇	1	16	yes	—
636	#125	C₂³×C₇	1	16	yes	—
637	#125	C₂³×C₇	1	16	yes	—
638	#124	C₂³×C₇	1	2	yes	—
639	#124	C₂³×C₇	1	2	yes	—
640	#124	C₂³×C₇	1	4	yes	—
641	#124	C₂³×C₇	1	4	yes	—
642	#124	C₂³×C₇	1	16	yes	—
643	#124	C₂³×C₇	1	8	yes	—
644	#124	C₂³×C₇	1	16	yes	—
645	#124	C₂³×C₇	1	16	yes	—
646	#124	C₂³×C₇	1	16	yes	—
647	#123	C₂³×C₇	1	4	yes	—
648	#123	C₂³×C₇	1	4	yes	—
649	#123	C₂³×C₇	1	4	yes	—
650	#123	C₂³×C₇	1	4	yes	—
651	#123	C₂³×C₇	1	8	yes	—
652	#123	C₂³×C₇	1	16	yes	—
653	#123	C₂³×C₇	1	16	yes	—
654	#123	C₂³×C₇	1	16	yes	—
655	#123	C₂³×C₇	1	16	yes	—
656	#123	C₂³×C₇	1	16	yes	—
657	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
658	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
659	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
660	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
661	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
662	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
663	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
664	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
665	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
666	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
667	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
668	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
669	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
670	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
671	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
672	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
673	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
674	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
675	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
676	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
677	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
678	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
679	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
680	#121	C₂³×C₇	1	4	yes	—
681	#121	C₂³×C₇	1	4	yes	—
682	#121	C₂³×C₇	1	4	yes	—
683	#121	C₂³×C₇	1	2	yes	—
684	#121	C₂³×C₇	1	4	yes	—
685	#121	C₂³×C₇	1	2	yes	—
686	#121	C₂³×C₇	1	4	yes	—
687	#121	C₂³×C₇	1	16	yes	—
688	#121	C₂³×C₇	1	8	yes	—
689	#121	C₂³×C₇	1	8	yes	—
690	#121	C₂³×C₇	1	8	yes	—
691	#121	C₂³×C₇	1	16	yes	—
692	#121	C₂³×C₇	1	16	yes	—
693	#121	C₂³×C₇	1	16	yes	—
694	#120	C₂³×C₇	1	4	yes	—
695	#120	C₂³×C₇	1	4	yes	—
696	C₄×Q₈	C₂³×C₇	1	8	yes	—
697	C₄×Q₈	C₂³×C₇	1	8	yes	—
698	C₄×Q₈	C₂³×C₇	1	8	yes	—
699	C₄×Q₈	C₂³×C₇	1	8	yes	—
700	C₄×Q₈	C₂³×C₇	1	4	yes	—
701	C₄×Q₈	C₂³×C₇	1	4	yes	—
702	C₄×Q₈	C₂³×C₇	1	4	yes	—
703	C₄×Q₈	C₂³×C₇	1	4	yes	—
704	C₄×Q₈	C₂³×C₇	1	2	yes	—
705	C₄×Q₈	C₂³×C₇	1	4	yes	—
706	C₄×Q₈	C₂³×C₇	1	2	yes	—
707	C₄×Q₈	C₂³×C₇	1	16	yes	—
708	C₄×Q₈	C₂³×C₇	1	8	yes	—
709	C₄×Q₈	C₂³×C₇	1	8	yes	—
710	C₄×Q₈	C₂³×C₇	1	16	yes	—
711	C₄×Q₈	C₂³×C₇	1	8	yes	—
712	C₄×Q₈	C₂³×C₇	1	8	yes	—
713	C₄×Q₈	C₂³×C₇	1	8	yes	—
714	C₄×D₄	C₂³×C₇	1	4	yes	—
715	C₄×D₄	C₂³×C₇	1	8	yes	—
716	C₄×D₄	C₂³×C₇	1	4	yes	—
717	C₄×D₄	C₂³×C₇	1	4	yes	—
718	C₄×D₄	C₂³×C₇	1	4	yes	—
719	C₄×D₄	C₂³×C₇	1	4	yes	—
720	C₄×D₄	C₂³×C₇	1	4	yes	—
721	C₄×D₄	C₂³×C₇	1	8	yes	—
722	C₄×D₄	C₂³×C₇	1	8	yes	—
723	C₄×D₄	C₂³×C₇	1	4	yes	—
724	C₄×D₄	C₂³×C₇	1	2	yes	—
725	C₄×D₄	C₂³×C₇	1	4	yes	—
726	C₄×D₄	C₂³×C₇	1	4	yes	—
727	C₄×D₄	C₂³×C₇	1	2	yes	—
728	C₄×D₄	C₂³×C₇	1	4	yes	—
729	C₄×D₄	C₂³×C₇	1	4	yes	—
730	C₄×D₄	C₂³×C₇	1	16	yes	—
731	C₄×D₄	C₂³×C₇	1	16	yes	—
732	C₄×D₄	C₂³×C₇	1	8	yes	—
733	C₄×D₄	C₂³×C₇	1	8	yes	—
734	C₄×D₄	C₂³×C₇	1	16	yes	—
735	C₄×D₄	C₂³×C₇	1	16	yes	—
736	C₄×D₄	C₂³×C₇	1	8	yes	—
737	#117	C₂³×C₇	1	8	yes	—
738	#117	C₂³×C₇	1	8	yes	—
739	#117	C₂³×C₇	1	4	yes	—
740	#117	C₂³×C₇	1	2	yes	—
741	#117	C₂³×C₇	1	2	yes	—
742	#117	C₂³×C₇	1	4	yes	—
743	#117	C₂³×C₇	1	4	yes	—
744	#117	C₂³×C₇	1	4	yes	—
745	#117	C₂³×C₇	1	4	yes	—
746	#117	C₂³×C₇	1	4	yes	—
747	#117	C₂³×C₇	1	8	yes	—
748	#117	C₂³×C₇	1	16	yes	—
749	#117	C₂³×C₇	1	16	yes	—
750	#117	C₂³×C₇	1	8	yes	—
751	#117	C₂³×C₇	1	8	yes	—
752	#117	C₂³×C₇	1	8	yes	—
753	#117	C₂³×C₇	1	16	yes	—
754	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
755	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
756	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
757	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
758	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
759	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
760	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
762	C₂×C₄²	C₂³×C₇	1	4	yes	—
763	C₂×C₄²	C₂³×C₇	1	2	yes	—
764	C₂×C₄²	C₂³×C₇	1	4	yes	—
765	C₂×C₄²	C₂³×C₇	1	4	yes	—
766	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₇	1	2	yes	—
768	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₇	1	2	yes	—
770	C₂×C₄²	C₂³×C₇	1	2	yes	—
771	C₂×C₄²	C₂³×C₇	1	2	yes	—
772	C₂²×C₇	—	2	2	no	—
773	C₂²×C₇	—	2	2	no	—
774	C₂²×C₇	—	2	4	no	—
775	C₂²×C₇	—	2	4	no	—
776	C₂²×C₇	—	2	4	no	—
777	C₂²×C₇	—	2	2	no	—
778	C₂²×C₇	—	2	2	no	—
779	C₂²×C₇	—	2	4	no	—
780	C₂²×C₇	—	2	8	no	—
781	C₂²×C₇	—	4	4	no	—
782	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
783	C₂²×C₇	C₂⁶	1	1	yes	characteristic
784	C₄×C₇	—	2	2	no	—
785	C₄×C₇	—	2	4	no	—
786	C₄×C₇	—	2	4	no	—
787	C₄×C₇	—	2	2	no	—
788	C₄×C₇	—	2	4	no	—
789	C₄×C₇	—	2	2	no	—
790	C₄×C₇	—	2	2	no	—
791	C₄×C₇	—	2	4	no	—
792	C₄×C₇	—	2	16	no	—
793	C₄×C₇	—	2	8	no	—
794	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
795	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
796	C₄×C₇	#585	1	4	yes	—
797	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
798	#41	—	2	8	no	—
799	#41	—	2	8	no	—
800	#41	—	4	8	no	—
801	#41	—	4	8	no	—
802	#41	—	4	16	no	—
803	C₂×Q₈	—	4	8	no	—
804	C₂×Q₈	—	4	16	no	—
805	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
807	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
808	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
809	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
810	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
811	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
812	C₂×D₄	C₂⁴×C₇	1	4	yes	—
813	C₂×D₄	C₂⁴×C₇	1	4	yes	—
814	C₂×D₄	C₂⁴×C₇	1	2	yes	—
815	C₂×D₄	C₂⁴×C₇	1	2	yes	—
816	C₂×D₄	C₂⁴×C₇	1	4	yes	—
817	C₂×D₄	C₂⁴×C₇	1	4	yes	—
818	C₂×D₄	C₂⁴×C₇	1	8	yes	—
819	C₂×D₄	C₂⁴×C₇	1	4	yes	—
820	C₂×D₄	C₂⁴×C₇	1	16	yes	—
821	C₂×D₄	C₂⁴×C₇	1	4	yes	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	4	4	no	—
824	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
828	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
829	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
831	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
832	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
833	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
834	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
838	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
839	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
840	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
841	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
842	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
844	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
845	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
846	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
847	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
848	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
849	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
850	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
851	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
852	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
853	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
854	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
855	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
856	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
857	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
858	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
859	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
860	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
861	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
862	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
863	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
864	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
865	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
866	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
867	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
868	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
869	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
870	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
871	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
872	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
873	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
874	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
875	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
876	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
877	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
878	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
879	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
880	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
881	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
882	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
883	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
884	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
885	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
886	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
887	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
888	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
889	C₄²	C₂⁴×C₇	1	1	yes	characteristic
890	C₄²	C₂⁴×C₇	1	1	yes	characteristic
891	C₄²	C₂⁴×C₇	1	2	yes	—
892	C₄²	C₂⁴×C₇	1	2	yes	—
893	C₄²	C₂⁴×C₇	1	1	yes	characteristic
894	C₄²	C₂⁴×C₇	1	1	yes	characteristic
895	C₄²	C₂⁴×C₇	1	2	yes	—
896	C₄²	C₂⁴×C₇	1	2	yes	—
897	C₄²	C₂⁴×C₇	1	2	yes	—
898	C₄²	C₂⁴×C₇	1	2	yes	—
899	C₄²	C₂⁴×C₇	1	8	yes	—
900	C₄²	C₂⁴×C₇	1	16	yes	—
901	C₄²	C₂⁴×C₇	1	4	yes	—
902	C₄²	C₂⁴×C₇	1	4	yes	—
903	C₄²	C₂⁴×C₇	1	4	yes	—
904	C₄²	C₂⁴×C₇	1	4	yes	—
905	C₄²	C₂⁴×C₇	1	16	yes	—
906	C₄²	C₂⁴×C₇	1	16	yes	—
907	C₂×C₇	—	2	2	no	—
908	C₂×C₇	—	4	4	no	—
909	C₂×C₇	—	4	4	no	—
910	C₂×C₇	—	4	2	no	—
911	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
912	C₂×C₇	C₂×#585	1	2	yes	—
913	C₂³	—	2	2	no	—
914	C₂³	—	4	2	no	—
915	C₂³	C₂⁵×C₇	1	2	yes	—
916	C₂³	C₂⁵×C₇	1	4	yes	—
917	C₂³	C₂⁵×C₇	1	4	yes	—
918	C₂³	C₂⁵×C₇	1	1	yes	characteristic
919	Q₈	—	2	4	no	—
920	Q₈	—	2	4	no	—
921	Q₈	—	2	16	no	—
922	Q₈	—	2	8	no	—
923	Q₈	—	4	8	no	—
924	Q₈	—	4	16	no	—
925	Q₈	—	4	4	no	—
926	D₄	—	2	8	no	—
927	D₄	—	2	8	no	—
928	D₄	—	2	4	no	—
929	D₄	—	2	4	no	—
930	D₄	—	2	8	no	—
931	D₄	—	4	4	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	4	no	—
934	D₄	—	4	8	no	—
935	D₄	—	4	16	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	4	no	—
938	C₂×C₄	—	2	4	no	—
939	C₂×C₄	—	2	8	no	—
940	C₂×C₄	—	2	8	no	—
941	C₂×C₄	—	2	4	no	—
942	C₂×C₄	—	2	4	no	—
943	C₂×C₄	—	2	4	no	—
944	C₂×C₄	—	2	8	no	—
945	C₂×C₄	—	2	8	no	—
946	C₂×C₄	—	4	2	no	—
947	C₂×C₄	—	4	2	no	—
948	C₂×C₄	—	4	2	no	—
949	C₂×C₄	—	4	8	no	—
950	C₂×C₄	—	4	16	no	—
951	C₂×C₄	—	4	8	no	—
952	C₂×C₄	—	4	16	no	—
953	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
954	C₂×C₄	C₂⁵×C₇	1	2	yes	—
955	C₂×C₄	C₂⁵×C₇	1	2	yes	—
956	C₂×C₄	C₂⁵×C₇	1	4	yes	—
957	C₂×C₄	C₂⁵×C₇	1	4	yes	—
958	C₂×C₄	C₂⁵×C₇	1	4	yes	—
959	C₂×C₄	C₂⁵×C₇	1	2	yes	—
960	C₂×C₄	C₂⁵×C₇	1	8	yes	—
961	C₂×C₄	C₂⁵×C₇	1	16	yes	—
962	C₂×C₄	C₂⁵×C₇	1	2	yes	—
963	C₂×C₄	C₂⁵×C₇	1	4	yes	—
964	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
965	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
966	C₂×C₄	C₂⁵×C₇	1	2	yes	—
967	C₇	#62838	1	1	yes	characteristic, direct product factor, Sylow
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	4	no	—
971	C₂²	—	2	4	no	—
972	C₂²	—	2	4	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	4	no	—
976	C₂²	—	2	8	no	—
977	C₂²	—	4	4	no	—
978	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
979	C₂²	C₂⁶×C₇	1	1	yes	characteristic
980	C₄	—	2	2	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	4	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	4	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	4	no	—
988	C₄	—	2	16	no	—
989	C₄	—	2	8	no	—
990	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
991	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
992	C₄	C₇×#585	1	4	yes	—
993	C₂	—	2	2	no	—
994	C₂	—	4	2	no	—
995	C₂	—	4	4	no	—
996	C₂	—	4	4	no	—
997	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
998	C₂	C₂×C₇×#585	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×#3565	C₂	semidirect
2. C₇×#3555	C₂	semidirect
3. C₇×#3547	C₂	semidirect
4. C₇×#3541	C₂	semidirect
5. C₇×#3518	C₂	semidirect
6. C₇×#3516	C₂	semidirect
7. C₇×#3515	C₂	semidirect
8. C₇×#3512	C₂	semidirect
9. C₇×#3511	C₂	semidirect
10. C₇×#3511	C₂	semidirect
11. C₇×#3509	C₂	semidirect
12. C₇×#3504	C₂	semidirect
13. C₇×#3503	C₂	semidirect
14. C₇×#3493	C₂	semidirect
15. C₇×#3444	C₂	semidirect
16. C₇×#3444	C₂	semidirect
17. C₂×C₇×#533	C₂	semidirect
20. C₇×Q₈²	C₂²	semidirect
21. C₇×#557	C₂²	semidirect
22. C₇×#557	C₂²	semidirect
23. C₇×#557	C₂²	semidirect
27. C₇×#556	C₂²	semidirect
28. C₇×#556	C₂²	semidirect
29. C₇×#556	C₂²	semidirect
32. C₇×#555	C₂²	semidirect
35. C₇×#554	C₂²	semidirect
36. C₇×#554	C₂²	semidirect
37. C₇×#554	C₂²	semidirect
42. C₇×#553	C₂²	semidirect
46. C₇×#552	C₂²	semidirect
47. C₇×#552	C₂²	semidirect
48. C₇×#552	C₂²	semidirect
50. C₇×D₄×Q₈	C₂²	semidirect
53. C₇×#548	C₂²	semidirect
55. C₇×#547	C₂²	semidirect
57. C₇×#544	C₂²	semidirect
58. C₇×#544	C₂²	semidirect
61. C₇×#542	C₂²	semidirect
62. C₇×#542	C₂²	semidirect
63. C₇×#542	C₂²	semidirect
65. C₇×#541	C₂²	semidirect
66. C₇×#541	C₂²	semidirect
67. C₇×#541	C₂²	semidirect
68. C₇×#540	C₂²	semidirect
82. C₇×#533	C₂²	semidirect
83. C₇×#533	C₂²	semidirect
84. C₇×#533	C₂²	semidirect
89. C₇×#532	C₂²	semidirect
91. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
100. C₇×#529	C₂²	semidirect
102. C₂×C₇×#125	C₂²	semidirect
110. C₇×#520	C₂²	semidirect
111. C₇×#519	C₂²	semidirect
119. #62838	C₇	direct (N × H)
305. #3565	C₂×C₇	semidirect
306. #3555	C₂×C₇	semidirect
307. #3547	C₂×C₇	semidirect
308. #3541	C₂×C₇	semidirect
309. #3518	C₂×C₇	semidirect
310. #3516	C₂×C₇	semidirect
311. #3515	C₂×C₇	semidirect
312. #3512	C₂×C₇	semidirect
313. #3511	C₂×C₇	semidirect
314. #3511	C₂×C₇	semidirect
315. #3509	C₂×C₇	semidirect
316. #3504	C₂×C₇	semidirect
317. #3503	C₂×C₇	semidirect
318. #3493	C₂×C₇	semidirect
319. #3444	C₂×C₇	semidirect
320. #3444	C₂×C₇	semidirect
321. C₂×#533	C₂×C₇	semidirect
434. Q₈²	C₂²×C₇	semidirect
435. #557	C₂²×C₇	semidirect
436. #557	C₂²×C₇	semidirect
437. #557	C₂²×C₇	semidirect
441. #556	C₂²×C₇	semidirect
442. #556	C₂²×C₇	semidirect
443. #556	C₂²×C₇	semidirect
446. #555	C₂²×C₇	semidirect
449. #554	C₂²×C₇	semidirect
450. #554	C₂²×C₇	semidirect
451. #554	C₂²×C₇	semidirect
456. #553	C₂²×C₇	semidirect
460. #552	C₂²×C₇	semidirect
461. #552	C₂²×C₇	semidirect
462. #552	C₂²×C₇	semidirect
464. D₄×Q₈	C₂²×C₇	semidirect
467. #548	C₂²×C₇	semidirect
469. #547	C₂²×C₇	semidirect
471. #544	C₂²×C₇	semidirect
472. #544	C₂²×C₇	semidirect
475. #542	C₂²×C₇	semidirect
476. #542	C₂²×C₇	semidirect
477. #542	C₂²×C₇	semidirect
479. #541	C₂²×C₇	semidirect
480. #541	C₂²×C₇	semidirect
481. #541	C₂²×C₇	semidirect
482. #540	C₂²×C₇	semidirect
496. #533	C₂²×C₇	semidirect
497. #533	C₂²×C₇	semidirect
498. #533	C₂²×C₇	semidirect
503. #532	C₂²×C₇	semidirect
505. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
514. #529	C₂²×C₇	semidirect
516. C₂×#125	C₂²×C₇	semidirect
524. #520	C₂²×C₇	semidirect
525. #519	C₂²×C₇	semidirect
967. C₇	#62838	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×#3565	2
C₇×#3555	2
C₇×#3547	2
C₇×#3541	2
C₇×#3518	2
C₇×#3516	2
C₇×#3515	2
C₇×#3512	2
C₇×#3511	2
C₇×#3509	2
C₇×#3504	2
C₇×#3503	2
C₇×#3493	2
C₇×#3444	2
C₂×C₇×#533	2
#62838	7

Subgroups — C7×#62838 #13240054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62838 #13240054