Subgroups — C₇×#62781 #13239997

Order 1792.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3521	C₂	1	8	yes	maximal, complemented
2	C₇×#3515	C₂	1	4	yes	maximal, complemented
3	C₇×#3514	C₂	1	4	yes	maximal, complemented
4	C₇×#3507	C₂	1	2	yes	maximal, complemented
5	C₇×#3505	C₂	1	4	yes	maximal, complemented
6	C₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3493	C₂	1	2	yes	maximal, complemented
9	C₇×#3491	C₂	1	4	yes	maximal, complemented
10	C₇×#3485	C₂	1	2	yes	maximal, complemented
11	C₇×#3482	C₂	1	4	yes	maximal, complemented
12	C₇×#3481	C₂	1	4	yes	maximal, complemented
13	C₇×#3475	C₂	1	8	yes	maximal, complemented
14	C₇×#3461	C₂	1	2	yes	maximal, complemented
15	C₇×#3459	C₂	1	4	yes	maximal, complemented
16	C₇×#3444	C₂	1	2	yes	maximal, complemented
17	C₂×C₇×#529	C₂	1	4	yes	maximal, complemented
18	C₄×C₇×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
21	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
22	C₇×#559	C₂²	1	4	yes	complemented
23	C₇×#557	C₂²	1	4	yes	complemented
24	C₇×#556	C₂²	1	8	yes	complemented
25	C₇×#556	C₂²	1	8	yes	complemented
26	C₇×#556	C₂²	1	4	yes	complemented
27	C₇×#555	C₂²	1	8	yes	complemented
28	C₇×#554	C₂²	1	8	yes	complemented
29	C₇×#554	C₂²	1	4	yes	complemented
30	C₇×#554	C₂²	1	4	yes	complemented
31	C₇×#553	C₂²	1	16	yes	complemented
32	C₇×#553	C₂²	1	8	yes	complemented
33	C₇×#553	C₂²	1	8	yes	complemented
34	C₇×#552	C₂²	1	16	yes	complemented
35	C₇×#552	C₂²	1	8	yes	complemented
36	C₇×#552	C₂²	1	8	yes	complemented
37	C₇×#552	C₂²	1	16	yes	complemented
38	C₇×#552	C₂²	1	8	yes	complemented
39	C₇×#551	C₂²	1	16	yes	complemented
40	C₇×#551	C₂²	1	16	yes	complemented
41	C₇×#551	C₂²	1	16	yes	complemented
42	C₇×D₄×Q₈	C₂²	1	4	yes	complemented
43	C₇×#548	C₂²	1	8	yes	complemented
44	C₇×#547	C₂²	1	8	yes	complemented
45	C₇×#547	C₂²	1	8	yes	complemented
46	C₇×#547	C₂²	1	4	yes	complemented
47	C₇×#546	C₂²	1	8	yes	complemented
48	C₇×#546	C₂²	1	8	yes	complemented
49	C₇×#546	C₂²	1	8	yes	complemented
50	C₇×#546	C₂²	1	8	yes	complemented
51	C₇×D₄²	C₂²	1	4	yes	complemented
52	C₇×#544	C₂²	1	2	yes	complemented
53	C₇×#543	C₂²	1	4	yes	complemented
54	C₇×#542	C₂²	1	8	yes	complemented
55	C₇×#541	C₂²	1	8	yes	complemented
56	C₇×#539	C₂²	1	8	yes	complemented
57	C₇×#539	C₂²	1	16	yes	complemented
58	C₇×#539	C₂²	1	8	yes	complemented
59	C₇×#538	C₂²	1	8	yes	complemented
60	C₇×#538	C₂²	1	16	yes	complemented
61	C₇×#537	C₂²	1	2	yes	—
62	C₇×#536	C₂²	1	4	yes	complemented
63	C₇×#534	C₂²	1	4	yes	—
64	C₇×#534	C₂²	1	8	yes	complemented
65	C₇×#533	C₂²	1	2	yes	complemented
66	C₇×#533	C₂²	1	2	yes	complemented
67	C₇×#533	C₂²	1	2	yes	complemented
68	C₇×#533	C₂²	1	8	yes	complemented
69	C₇×#532	C₂²	1	2	yes	—
70	C₇×#532	C₂²	1	2	yes	complemented
71	C₇×#532	C₂²	1	2	yes	complemented
72	C₇×#529	C₂²	1	4	yes	complemented
73	C₇×#529	C₂²	1	8	yes	complemented
74	C₇×#529	C₂²	1	8	yes	complemented
75	C₇×#529	C₂²	1	8	yes	complemented
76	C₇×#529	C₂²	1	8	yes	complemented
77	C₇×#529	C₂²	1	8	yes	complemented
78	C₇×#529	C₂²	1	8	yes	complemented
79	C₇×#529	C₂²	1	8	yes	complemented
80	C₇×#529	C₂²	1	4	yes	complemented
81	C₇×#529	C₂²	1	4	yes	complemented
82	C₇×#529	C₂²	1	4	yes	complemented
83	C₇×#529	C₂²	1	4	yes	complemented
84	C₇×#529	C₂²	1	4	yes	complemented
85	C₇×#529	C₂²	1	16	yes	complemented
86	C₇×#529	C₂²	1	8	yes	complemented
87	C₂×C₇×#126	C₂²	1	8	yes	complemented
88	C₂×C₇×#125	C₂²	1	4	yes	complemented
89	C₂×C₇×#124	C₂²	1	4	yes	complemented
90	C₇×#525	C₂²	1	4	yes	complemented
91	C₇×#525	C₂²	1	4	yes	complemented
92	C₇×#525	C₂²	1	4	yes	complemented
93	C₇×#525	C₂²	1	16	yes	complemented
94	C₂×C₇×#123	C₂²	1	8	yes	complemented
95	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
96	C₂×C₇×#121	C₂²	1	4	yes	—
97	C₇×#520	C₂²	1	4	yes	complemented
98	C₇×#520	C₂²	1	8	yes	complemented
99	C₇×#518	C₂²	1	2	yes	—
100	C₇×#518	C₂²	1	8	yes	complemented
101	C₇×#518	C₂²	1	8	yes	complemented
102	C₄×C₇×#41	C₂²	1	4	yes	complemented
103	C₄×C₇×#41	C₂²	1	4	yes	complemented
104	C₄×C₇×#41	C₂²	1	4	yes	complemented
105	C₄×C₇×#41	C₂²	1	4	yes	complemented
106	C₄×C₇×#41	C₂²	1	4	yes	complemented
107	C₄×C₇×#41	C₂²	1	8	yes	complemented
108	C₄×C₇×#41	C₂²	1	4	yes	complemented
109	C₄×C₇×#41	C₂²	1	4	yes	complemented
110	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	complemented
113	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
114	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
115	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
116	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
117	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
118	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
119	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
120	C₂×C₇×#117	C₂²	1	2	yes	complemented
121	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₇×#117	C₂²	1	8	yes	complemented
123	C₂²×C₄²×C₇	C₂²	1	2	yes	complemented
124	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
125	#62781	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₇×H(5,𝔽₂)	—	2	16	no	—
127	C₂×C₇×#41	—	2	8	no	—
128	C₂×C₇×#41	C₂³	1	4	yes	—
129	C₂×C₇×#41	C₂³	1	4	yes	—
130	C₂×C₇×#41	C₂³	1	4	yes	—
131	C₂×C₇×#41	C₂³	1	8	yes	—
132	C₂×C₇×#41	C₂³	1	4	yes	—
133	C₂×C₇×#41	C₂³	1	4	yes	—
134	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
135	C₂²×C₇×Q₈	C₂³	1	4	yes	—
136	C₂²×C₇×D₄	C₂³	1	2	yes	—
137	C₂²×C₇×D₄	C₂³	1	8	yes	—
138	C₂²×C₇×D₄	C₂³	1	8	yes	—
139	C₂²×C₇×D₄	C₂³	1	4	yes	—
140	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₇	C₂³	1	2	yes	—
145	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₇	C₂³	1	8	yes	—
148	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
149	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
150	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
151	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
152	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
153	C₇×#127	C₂³	1	2	yes	—
154	C₇×#126	C₂³	1	8	yes	—
155	C₇×#126	C₂³	1	16	yes	—
156	C₇×#126	C₂³	1	16	yes	—
157	C₇×#126	C₂³	1	16	yes	—
158	C₇×#126	C₂³	1	8	yes	—
159	C₇×#126	C₂³	1	16	yes	—
160	C₇×#126	C₂³	1	16	yes	—
161	C₇×#126	C₂³	1	16	yes	—
162	C₇×#125	C₂³	1	4	yes	—
163	C₇×#125	C₂³	1	8	yes	—
164	C₇×#125	C₂³	1	8	yes	—
165	C₇×#125	C₂³	1	8	yes	—
166	C₇×#125	C₂³	1	4	yes	—
167	C₇×#125	C₂³	1	4	yes	—
168	C₇×#125	C₂³	1	16	yes	—
169	C₇×#125	C₂³	1	8	yes	—
170	C₇×#125	C₂³	1	16	yes	—
171	C₇×#124	C₂³	1	4	yes	—
172	C₇×#124	C₂³	1	8	yes	—
173	C₇×#124	C₂³	1	8	yes	—
174	C₇×#124	C₂³	1	8	yes	—
175	C₇×#124	C₂³	1	4	yes	—
176	C₇×#124	C₂³	1	4	yes	—
177	C₇×#124	C₂³	1	8	yes	—
178	C₇×#124	C₂³	1	16	yes	—
179	C₇×#123	C₂³	1	8	yes	—
180	C₇×#123	C₂³	1	16	yes	—
181	C₇×#123	C₂³	1	16	yes	—
182	C₇×#123	C₂³	1	16	yes	—
183	C₇×#123	C₂³	1	8	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	4	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	4	yes	—
197	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
198	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
199	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
200	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
201	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
204	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
205	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
206	C₇×#121	C₂³	1	4	yes	—
207	C₇×#121	C₂³	1	8	yes	—
208	C₇×#121	C₂³	1	8	yes	—
209	C₇×#121	C₂³	1	8	yes	—
210	C₇×#121	C₂³	1	4	yes	—
211	C₇×#121	C₂³	1	4	yes	—
212	C₇×#121	C₂³	1	4	yes	—
213	C₇×#121	C₂³	1	4	yes	—
214	C₇×#121	C₂³	1	4	yes	—
215	C₇×#121	C₂³	1	16	yes	—
216	C₇×#121	C₂³	1	16	yes	—
217	C₇×#121	C₂³	1	16	yes	—
218	C₇×#121	C₂³	1	8	yes	—
219	C₇×#120	C₂³	1	8	yes	—
220	C₇×#120	C₂³	1	16	yes	—
221	C₇×#120	C₂³	1	16	yes	—
222	C₄×C₇×Q₈	C₂³	1	4	yes	—
223	C₄×C₇×Q₈	C₂³	1	4	yes	—
224	C₄×C₇×Q₈	C₂³	1	4	yes	—
225	C₄×C₇×Q₈	C₂³	1	4	yes	—
226	C₄×C₇×Q₈	C₂³	1	4	yes	—
227	C₄×C₇×Q₈	C₂³	1	8	yes	—
228	C₄×C₇×Q₈	C₂³	1	8	yes	—
229	C₄×C₇×Q₈	C₂³	1	8	yes	—
230	C₄×C₇×Q₈	C₂³	1	4	yes	—
231	C₄×C₇×Q₈	C₂³	1	4	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×D₄	C₂³	1	4	yes	—
237	C₄×C₇×D₄	C₂³	1	4	yes	—
238	C₄×C₇×D₄	C₂³	1	4	yes	—
239	C₄×C₇×D₄	C₂³	1	4	yes	—
240	C₄×C₇×D₄	C₂³	1	8	yes	—
241	C₄×C₇×D₄	C₂³	1	16	yes	—
242	C₄×C₇×D₄	C₂³	1	4	yes	—
243	C₄×C₇×D₄	C₂³	1	4	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	8	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	8	yes	—
254	C₄×C₇×D₄	C₂³	1	8	yes	—
255	C₄×C₇×D₄	C₂³	1	8	yes	—
256	C₄×C₇×D₄	C₂³	1	8	yes	—
257	C₄×C₇×D₄	C₂³	1	8	yes	—
258	C₄×C₇×D₄	C₂³	1	4	yes	—
259	C₄×C₇×D₄	C₂³	1	16	yes	—
260	C₄×C₇×D₄	C₂³	1	8	yes	—
261	C₄×C₇×D₄	C₂³	1	8	yes	—
262	C₄×C₇×D₄	C₂³	1	8	yes	—
263	C₄×C₇×D₄	C₂³	1	8	yes	—
264	C₄×C₇×D₄	C₂³	1	4	yes	—
265	C₄×C₇×D₄	C₂³	1	4	yes	—
266	C₄×C₇×D₄	C₂³	1	4	yes	—
267	C₇×#117	C₂³	1	8	yes	—
268	C₇×#117	C₂³	1	8	yes	—
269	C₇×#117	C₂³	1	8	yes	—
270	C₇×#117	C₂³	1	4	yes	—
271	C₇×#117	C₂³	1	4	yes	—
272	C₇×#117	C₂³	1	16	yes	—
273	C₇×#117	C₂³	1	16	yes	—
274	C₇×#117	C₂³	1	16	yes	—
275	C₇×#117	C₂³	1	4	yes	—
276	C₇×#117	C₂³	1	8	yes	—
277	C₇×#117	C₂³	1	16	yes	—
278	C₇×#117	C₂³	1	8	yes	—
279	C₇×#117	C₂³	1	4	yes	—
280	C₇×#117	C₂³	1	4	yes	—
281	C₇×#117	C₂³	1	8	yes	—
282	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
283	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
285	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
286	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
287	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
288	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
289	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
290	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
291	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
292	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
293	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
294	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
295	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
296	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
297	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
298	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
299	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
300	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
301	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
302	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₇	C₂³	1	4	yes	—
304	C₂×C₄²×C₇	C₂³	1	2	yes	—
305	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
308	C₂×C₄²×C₇	C₂³	1	4	yes	—
309	C₂×C₄²×C₇	C₂³	1	2	yes	—
310	C₂×C₄²×C₇	C₂³	1	2	yes	—
311	C₂×C₄²×C₇	C₂³	1	2	yes	—
312	C₂×C₄²×C₇	C₂³	1	2	yes	—
313	C₂×C₄²×C₇	C₂³	1	4	yes	—
314	C₂×C₄²×C₇	C₂³	1	4	yes	—
315	C₂×C₄²×C₇	C₂³	1	2	yes	—
316	C₂×C₄²×C₇	C₂³	1	2	yes	—
317	C₂×C₄²×C₇	C₂³	1	8	yes	—
318	C₂×C₄²×C₇	C₂³	1	8	yes	—
319	#3521	C₂×C₇	1	8	yes	complemented
320	#3515	C₂×C₇	1	4	yes	complemented
321	#3514	C₂×C₇	1	4	yes	complemented
322	#3507	C₂×C₇	1	2	yes	complemented
323	#3505	C₂×C₇	1	4	yes	complemented
324	#3501	C₂×C₇	1	1	yes	characteristic, complemented
325	#3496	C₂×C₇	1	1	yes	characteristic, complemented
326	#3493	C₂×C₇	1	2	yes	complemented
327	#3491	C₂×C₇	1	4	yes	complemented
328	#3485	C₂×C₇	1	2	yes	complemented
329	#3482	C₂×C₇	1	4	yes	complemented
330	#3481	C₂×C₇	1	4	yes	complemented
331	#3475	C₂×C₇	1	8	yes	complemented
332	#3461	C₂×C₇	1	2	yes	complemented
333	#3459	C₂×C₇	1	4	yes	complemented
334	#3444	C₂×C₇	1	2	yes	complemented
335	C₂×#529	C₂×C₇	1	4	yes	complemented
336	C₄×H(5,𝔽₂)	C₂×C₇	1	2	yes	complemented
337	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
338	C₂⁴×C₇	C₂⁴	1	8	yes	—
339	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
340	C₂⁴×C₇	C₂⁴	1	2	yes	—
341	C₇×#41	—	2	16	no	—
342	C₇×#41	—	2	16	no	—
343	C₇×#41	—	2	32	no	—
344	C₇×#41	—	2	16	no	—
345	C₇×#41	—	4	8	no	—
346	C₇×#41	—	4	8	no	—
347	C₂×C₇×Q₈	—	2	4	no	—
348	C₂×C₇×Q₈	—	4	8	no	—
349	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
350	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
351	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
352	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
353	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
354	C₂×C₇×D₄	—	2	8	no	—
355	C₂×C₇×D₄	—	2	32	no	—
356	C₂×C₇×D₄	—	2	32	no	—
357	C₂×C₇×D₄	—	4	8	no	—
358	C₂×C₇×D₄	#41	1	8	yes	complemented
359	C₂×C₇×D₄	C₂⁴	1	8	yes	—
360	C₂×C₇×D₄	C₂⁴	1	8	yes	—
361	C₂×C₇×D₄	C₂⁴	1	16	yes	—
362	C₂×C₇×D₄	C₂⁴	1	4	yes	—
363	C₂×C₇×D₄	C₂⁴	1	4	yes	—
364	C₂×C₇×D₄	C₂⁴	1	4	yes	—
365	C₂×C₇×D₄	C₂⁴	1	8	yes	—
366	C₂×C₇×D₄	C₂⁴	1	8	yes	—
367	C₂×C₇×D₄	C₂⁴	1	8	yes	—
368	C₂×C₇×D₄	C₂⁴	1	4	yes	—
369	C₂²×C₄×C₇	—	2	8	no	—
370	C₂²×C₄×C₇	—	2	4	no	—
371	C₂²×C₄×C₇	—	4	4	no	—
372	C₂²×C₄×C₇	—	4	16	no	—
373	C₂²×C₄×C₇	—	4	4	no	—
374	C₂²×C₄×C₇	—	4	2	no	—
375	C₂²×C₄×C₇	—	4	2	no	—
376	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
379	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
380	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
383	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
386	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
387	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
389	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
391	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
394	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
395	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
400	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
401	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
402	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
403	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
404	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
405	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
406	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
407	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
408	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
409	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
410	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
411	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
412	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
413	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
414	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
415	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
416	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
417	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
418	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
419	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
420	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
421	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
422	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
423	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
424	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
425	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
426	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
427	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
428	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
429	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
430	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
431	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
432	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
433	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
434	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
435	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
436	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
437	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
438	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
439	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
440	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
441	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
442	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
443	C₄²×C₇	C₂⁴	1	1	yes	characteristic
444	C₄²×C₇	C₂⁴	1	1	yes	characteristic
445	C₄²×C₇	C₂⁴	1	4	yes	—
446	C₄²×C₇	C₂⁴	1	2	yes	—
447	C₄²×C₇	C₂⁴	1	2	yes	—
448	C₄²×C₇	C₂⁴	1	4	yes	—
449	C₄²×C₇	C₂⁴	1	4	yes	—
450	C₄²×C₇	C₂⁴	1	2	yes	—
451	C₄²×C₇	C₂⁴	1	2	yes	—
452	C₄²×C₇	C₂⁴	1	4	yes	—
453	C₄²×C₇	C₂⁴	1	2	yes	—
454	C₄²×C₇	C₂⁴	1	4	yes	—
455	C₄²×C₇	C₂⁴	1	8	yes	—
456	C₄²×C₇	C₂⁴	1	16	yes	—
457	C₄²×C₇	C₂⁴	1	8	yes	—
458	C₄²×C₇	C₂⁴	1	1	yes	characteristic
459	C₄²×C₇	C₂⁴	1	2	yes	—
460	C₄²×C₇	C₂⁴	1	1	yes	characteristic
461	C₄²×C₇	C₂⁴	1	8	yes	—
462	C₄²×C₇	C₂⁴	1	4	yes	—
463	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
464	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
465	#559	C₂²×C₇	1	4	yes	complemented
466	#557	C₂²×C₇	1	4	yes	complemented
467	#556	C₂²×C₇	1	8	yes	complemented
468	#556	C₂²×C₇	1	8	yes	complemented
469	#556	C₂²×C₇	1	4	yes	complemented
470	#555	C₂²×C₇	1	8	yes	complemented
471	#554	C₂²×C₇	1	8	yes	complemented
472	#554	C₂²×C₇	1	4	yes	complemented
473	#554	C₂²×C₇	1	4	yes	complemented
474	#553	C₂²×C₇	1	16	yes	complemented
475	#553	C₂²×C₇	1	8	yes	complemented
476	#553	C₂²×C₇	1	8	yes	complemented
477	#552	C₂²×C₇	1	16	yes	complemented
478	#552	C₂²×C₇	1	8	yes	complemented
479	#552	C₂²×C₇	1	8	yes	complemented
480	#552	C₂²×C₇	1	16	yes	complemented
481	#552	C₂²×C₇	1	8	yes	complemented
482	#551	C₂²×C₇	1	16	yes	complemented
483	#551	C₂²×C₇	1	16	yes	complemented
484	#551	C₂²×C₇	1	16	yes	complemented
485	D₄×Q₈	C₂²×C₇	1	4	yes	complemented
486	#548	C₂²×C₇	1	8	yes	complemented
487	#547	C₂²×C₇	1	8	yes	complemented
488	#547	C₂²×C₇	1	8	yes	complemented
489	#547	C₂²×C₇	1	4	yes	complemented
490	#546	C₂²×C₇	1	8	yes	complemented
491	#546	C₂²×C₇	1	8	yes	complemented
492	#546	C₂²×C₇	1	8	yes	complemented
493	#546	C₂²×C₇	1	8	yes	complemented
494	D₄²	C₂²×C₇	1	4	yes	complemented
495	#544	C₂²×C₇	1	2	yes	complemented
496	#543	C₂²×C₇	1	4	yes	complemented
497	#542	C₂²×C₇	1	8	yes	complemented
498	#541	C₂²×C₇	1	8	yes	complemented
499	#539	C₂²×C₇	1	8	yes	complemented
500	#539	C₂²×C₇	1	16	yes	complemented
501	#539	C₂²×C₇	1	8	yes	complemented
502	#538	C₂²×C₇	1	8	yes	complemented
503	#538	C₂²×C₇	1	16	yes	complemented
504	#537	C₂²×C₇	1	2	yes	—
505	#536	C₂²×C₇	1	4	yes	complemented
506	#534	C₂²×C₇	1	4	yes	—
507	#534	C₂²×C₇	1	8	yes	complemented
508	#533	C₂²×C₇	1	2	yes	complemented
509	#533	C₂²×C₇	1	2	yes	complemented
510	#533	C₂²×C₇	1	2	yes	complemented
511	#533	C₂²×C₇	1	8	yes	complemented
512	#532	C₂²×C₇	1	2	yes	—
513	#532	C₂²×C₇	1	2	yes	complemented
514	#532	C₂²×C₇	1	2	yes	complemented
515	#529	C₂²×C₇	1	4	yes	complemented
516	#529	C₂²×C₇	1	8	yes	complemented
517	#529	C₂²×C₇	1	8	yes	complemented
518	#529	C₂²×C₇	1	8	yes	complemented
519	#529	C₂²×C₇	1	8	yes	complemented
520	#529	C₂²×C₇	1	8	yes	complemented
521	#529	C₂²×C₇	1	8	yes	complemented
522	#529	C₂²×C₇	1	8	yes	complemented
523	#529	C₂²×C₇	1	4	yes	complemented
524	#529	C₂²×C₇	1	4	yes	complemented
525	#529	C₂²×C₇	1	4	yes	complemented
526	#529	C₂²×C₇	1	4	yes	complemented
527	#529	C₂²×C₇	1	4	yes	complemented
528	#529	C₂²×C₇	1	16	yes	complemented
529	#529	C₂²×C₇	1	8	yes	complemented
530	C₂×#126	C₂²×C₇	1	8	yes	complemented
531	C₂×#125	C₂²×C₇	1	4	yes	complemented
532	C₂×#124	C₂²×C₇	1	4	yes	complemented
533	#525	C₂²×C₇	1	4	yes	complemented
534	#525	C₂²×C₇	1	4	yes	complemented
535	#525	C₂²×C₇	1	4	yes	complemented
536	#525	C₂²×C₇	1	16	yes	complemented
537	C₂×#123	C₂²×C₇	1	8	yes	complemented
538	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
539	C₂×#121	C₂²×C₇	1	4	yes	—
540	#520	C₂²×C₇	1	4	yes	complemented
541	#520	C₂²×C₇	1	8	yes	complemented
542	#518	C₂²×C₇	1	2	yes	—
543	#518	C₂²×C₇	1	8	yes	complemented
544	#518	C₂²×C₇	1	8	yes	complemented
545	C₄×#41	C₂²×C₇	1	4	yes	complemented
546	C₄×#41	C₂²×C₇	1	4	yes	complemented
547	C₄×#41	C₂²×C₇	1	4	yes	complemented
548	C₄×#41	C₂²×C₇	1	4	yes	complemented
549	C₄×#41	C₂²×C₇	1	4	yes	complemented
550	C₄×#41	C₂²×C₇	1	8	yes	complemented
551	C₄×#41	C₂²×C₇	1	4	yes	complemented
552	C₄×#41	C₂²×C₇	1	4	yes	complemented
553	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
554	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
555	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	complemented
556	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
557	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
558	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
559	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
560	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
561	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
562	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
563	C₂×#117	C₂²×C₇	1	2	yes	complemented
564	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
565	C₂×#117	C₂²×C₇	1	8	yes	complemented
566	C₂²×C₄²	C₂²×C₇	1	2	yes	complemented
567	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
568	C₂³×C₇	—	2	2	no	—
569	C₂³×C₇	—	2	16	no	—
570	C₂³×C₇	—	4	2	no	—
571	C₂³×C₇	—	4	2	no	—
572	C₂³×C₇	—	4	1	no	—
573	C₂³×C₇	—	4	1	no	—
574	C₂³×C₇	—	4	8	no	—
575	C₂³×C₇	—	4	8	no	—
576	C₂³×C₇	C₂×#41	1	8	yes	—
577	C₂³×C₇	C₂⁵	1	8	yes	—
578	C₂³×C₇	C₂⁵	1	2	yes	—
579	C₂³×C₇	C₂⁵	1	4	yes	—
580	C₂³×C₇	C₂⁵	1	1	yes	characteristic
581	C₇×Q₈	—	2	8	no	—
582	C₇×Q₈	—	2	8	no	—
583	C₇×Q₈	—	2	8	no	—
584	C₇×Q₈	—	4	8	no	—
585	C₇×Q₈	—	4	4	no	—
586	C₇×D₄	—	2	32	no	—
587	C₇×D₄	—	2	16	no	—
588	C₇×D₄	—	2	16	no	—
589	C₇×D₄	—	2	8	no	—
590	C₇×D₄	—	2	8	no	—
591	C₇×D₄	—	4	8	no	—
592	C₇×D₄	—	4	8	no	—
593	C₇×D₄	—	4	4	no	—
594	C₇×D₄	—	4	8	no	—
595	C₇×D₄	C₂×#41	1	16	yes	—
596	C₂×C₄×C₇	—	2	2	no	—
597	C₂×C₄×C₇	—	2	4	no	—
598	C₂×C₄×C₇	—	2	8	no	—
599	C₂×C₄×C₇	—	2	8	no	—
600	C₂×C₄×C₇	—	2	16	no	—
601	C₂×C₄×C₇	—	2	4	no	—
602	C₂×C₄×C₇	—	2	4	no	—
603	C₂×C₄×C₇	—	2	16	no	—
604	C₂×C₄×C₇	—	2	2	no	—
605	C₂×C₄×C₇	—	2	8	no	—
606	C₂×C₄×C₇	—	2	2	no	—
607	C₂×C₄×C₇	—	2	16	no	—
608	C₂×C₄×C₇	—	2	8	no	—
609	C₂×C₄×C₇	—	2	4	no	—
610	C₂×C₄×C₇	—	2	4	no	—
611	C₂×C₄×C₇	—	4	2	no	—
612	C₂×C₄×C₇	—	4	4	no	—
613	C₂×C₄×C₇	—	4	1	no	—
614	C₂×C₄×C₇	—	4	2	no	—
615	C₂×C₄×C₇	—	4	16	no	—
616	C₂×C₄×C₇	—	4	4	no	—
617	C₂×C₄×C₇	—	4	2	no	—
618	C₂×C₄×C₇	—	4	8	no	—
619	C₂×C₄×C₇	—	4	2	no	—
620	C₂×C₄×C₇	—	4	1	no	—
621	C₂×C₄×C₇	—	4	8	no	—
622	C₂×C₄×C₇	—	4	8	no	—
623	C₂×C₄×C₇	C₂×#41	1	4	yes	—
624	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
625	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
626	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
627	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
628	C₂×C₄×C₇	C₂⁵	1	2	yes	—
629	C₂×C₄×C₇	C₂⁵	1	4	yes	—
630	C₂×C₄×C₇	C₂⁵	1	8	yes	—
631	C₂×C₄×C₇	C₂⁵	1	4	yes	—
632	C₂×C₄×C₇	C₂⁵	1	2	yes	—
633	C₂×C₄×C₇	C₂⁵	1	4	yes	—
634	C₂×C₄×C₇	C₂⁵	1	8	yes	—
635	C₂×C₄×C₇	C₂⁵	1	8	yes	—
636	C₂×C₄×C₇	C₂⁵	1	2	yes	—
637	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
638	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
639	H(5,𝔽₂)	—	2	16	no	—
640	C₂×#41	—	2	8	no	—
641	C₂×#41	C₂³×C₇	1	4	yes	—
642	C₂×#41	C₂³×C₇	1	4	yes	—
643	C₂×#41	C₂³×C₇	1	4	yes	—
644	C₂×#41	C₂³×C₇	1	8	yes	—
645	C₂×#41	C₂³×C₇	1	4	yes	—
646	C₂×#41	C₂³×C₇	1	4	yes	—
647	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
648	C₂²×Q₈	C₂³×C₇	1	4	yes	—
649	C₂²×D₄	C₂³×C₇	1	2	yes	—
650	C₂²×D₄	C₂³×C₇	1	8	yes	—
651	C₂²×D₄	C₂³×C₇	1	8	yes	—
652	C₂²×D₄	C₂³×C₇	1	4	yes	—
653	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₇	1	2	yes	—
655	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
656	C₂³×C₄	C₂³×C₇	1	8	yes	—
657	C₂³×C₄	C₂³×C₇	1	2	yes	—
658	C₂³×C₄	C₂³×C₇	1	2	yes	—
659	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
660	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
661	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
662	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
663	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
664	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
665	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
666	#127	C₂³×C₇	1	2	yes	—
667	#126	C₂³×C₇	1	8	yes	—
668	#126	C₂³×C₇	1	16	yes	—
669	#126	C₂³×C₇	1	16	yes	—
670	#126	C₂³×C₇	1	16	yes	—
671	#126	C₂³×C₇	1	8	yes	—
672	#126	C₂³×C₇	1	16	yes	—
673	#126	C₂³×C₇	1	16	yes	—
674	#126	C₂³×C₇	1	16	yes	—
675	#125	C₂³×C₇	1	4	yes	—
676	#125	C₂³×C₇	1	8	yes	—
677	#125	C₂³×C₇	1	8	yes	—
678	#125	C₂³×C₇	1	8	yes	—
679	#125	C₂³×C₇	1	4	yes	—
680	#125	C₂³×C₇	1	4	yes	—
681	#125	C₂³×C₇	1	16	yes	—
682	#125	C₂³×C₇	1	8	yes	—
683	#125	C₂³×C₇	1	16	yes	—
684	#124	C₂³×C₇	1	4	yes	—
685	#124	C₂³×C₇	1	8	yes	—
686	#124	C₂³×C₇	1	8	yes	—
687	#124	C₂³×C₇	1	8	yes	—
688	#124	C₂³×C₇	1	4	yes	—
689	#124	C₂³×C₇	1	4	yes	—
690	#124	C₂³×C₇	1	8	yes	—
691	#124	C₂³×C₇	1	16	yes	—
692	#123	C₂³×C₇	1	8	yes	—
693	#123	C₂³×C₇	1	16	yes	—
694	#123	C₂³×C₇	1	16	yes	—
695	#123	C₂³×C₇	1	16	yes	—
696	#123	C₂³×C₇	1	8	yes	—
697	#123	C₂³×C₇	1	8	yes	—
698	#123	C₂³×C₇	1	16	yes	—
699	#123	C₂³×C₇	1	16	yes	—
700	#123	C₂³×C₇	1	16	yes	—
701	#123	C₂³×C₇	1	16	yes	—
702	#123	C₂³×C₇	1	16	yes	—
703	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
704	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
705	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
706	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
707	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
708	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
709	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
710	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
711	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
712	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
713	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
714	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
715	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
716	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
717	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
718	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
719	#121	C₂³×C₇	1	4	yes	—
720	#121	C₂³×C₇	1	8	yes	—
721	#121	C₂³×C₇	1	8	yes	—
722	#121	C₂³×C₇	1	8	yes	—
723	#121	C₂³×C₇	1	4	yes	—
724	#121	C₂³×C₇	1	4	yes	—
725	#121	C₂³×C₇	1	4	yes	—
726	#121	C₂³×C₇	1	4	yes	—
727	#121	C₂³×C₇	1	4	yes	—
728	#121	C₂³×C₇	1	16	yes	—
729	#121	C₂³×C₇	1	16	yes	—
730	#121	C₂³×C₇	1	16	yes	—
731	#121	C₂³×C₇	1	8	yes	—
732	#120	C₂³×C₇	1	8	yes	—
733	#120	C₂³×C₇	1	16	yes	—
734	#120	C₂³×C₇	1	16	yes	—
735	C₄×Q₈	C₂³×C₇	1	4	yes	—
736	C₄×Q₈	C₂³×C₇	1	4	yes	—
737	C₄×Q₈	C₂³×C₇	1	4	yes	—
738	C₄×Q₈	C₂³×C₇	1	4	yes	—
739	C₄×Q₈	C₂³×C₇	1	4	yes	—
740	C₄×Q₈	C₂³×C₇	1	8	yes	—
741	C₄×Q₈	C₂³×C₇	1	8	yes	—
742	C₄×Q₈	C₂³×C₇	1	8	yes	—
743	C₄×Q₈	C₂³×C₇	1	4	yes	—
744	C₄×Q₈	C₂³×C₇	1	4	yes	—
745	C₄×Q₈	C₂³×C₇	1	8	yes	—
746	C₄×Q₈	C₂³×C₇	1	4	yes	—
747	C₄×Q₈	C₂³×C₇	1	4	yes	—
748	C₄×Q₈	C₂³×C₇	1	4	yes	—
749	C₄×D₄	C₂³×C₇	1	4	yes	—
750	C₄×D₄	C₂³×C₇	1	4	yes	—
751	C₄×D₄	C₂³×C₇	1	4	yes	—
752	C₄×D₄	C₂³×C₇	1	4	yes	—
753	C₄×D₄	C₂³×C₇	1	8	yes	—
754	C₄×D₄	C₂³×C₇	1	16	yes	—
755	C₄×D₄	C₂³×C₇	1	4	yes	—
756	C₄×D₄	C₂³×C₇	1	4	yes	—
757	C₄×D₄	C₂³×C₇	1	8	yes	—
758	C₄×D₄	C₂³×C₇	1	8	yes	—
759	C₄×D₄	C₂³×C₇	1	8	yes	—
760	C₄×D₄	C₂³×C₇	1	8	yes	—
761	C₄×D₄	C₂³×C₇	1	8	yes	—
762	C₄×D₄	C₂³×C₇	1	16	yes	—
763	C₄×D₄	C₂³×C₇	1	16	yes	—
764	C₄×D₄	C₂³×C₇	1	16	yes	—
765	C₄×D₄	C₂³×C₇	1	8	yes	—
766	C₄×D₄	C₂³×C₇	1	8	yes	—
767	C₄×D₄	C₂³×C₇	1	8	yes	—
768	C₄×D₄	C₂³×C₇	1	8	yes	—
769	C₄×D₄	C₂³×C₇	1	8	yes	—
770	C₄×D₄	C₂³×C₇	1	8	yes	—
771	C₄×D₄	C₂³×C₇	1	4	yes	—
772	C₄×D₄	C₂³×C₇	1	16	yes	—
773	C₄×D₄	C₂³×C₇	1	8	yes	—
774	C₄×D₄	C₂³×C₇	1	8	yes	—
775	C₄×D₄	C₂³×C₇	1	8	yes	—
776	C₄×D₄	C₂³×C₇	1	8	yes	—
777	C₄×D₄	C₂³×C₇	1	4	yes	—
778	C₄×D₄	C₂³×C₇	1	4	yes	—
779	C₄×D₄	C₂³×C₇	1	4	yes	—
780	#117	C₂³×C₇	1	8	yes	—
781	#117	C₂³×C₇	1	8	yes	—
782	#117	C₂³×C₇	1	8	yes	—
783	#117	C₂³×C₇	1	4	yes	—
784	#117	C₂³×C₇	1	4	yes	—
785	#117	C₂³×C₇	1	16	yes	—
786	#117	C₂³×C₇	1	16	yes	—
787	#117	C₂³×C₇	1	16	yes	—
788	#117	C₂³×C₇	1	4	yes	—
789	#117	C₂³×C₇	1	8	yes	—
790	#117	C₂³×C₇	1	16	yes	—
791	#117	C₂³×C₇	1	8	yes	—
792	#117	C₂³×C₇	1	4	yes	—
793	#117	C₂³×C₇	1	4	yes	—
794	#117	C₂³×C₇	1	8	yes	—
795	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
797	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
798	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
799	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
800	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
801	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
802	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
803	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
804	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
805	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
815	C₂×C₄²	C₂³×C₇	1	4	yes	—
816	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
817	C₂×C₄²	C₂³×C₇	1	2	yes	—
818	C₂×C₄²	C₂³×C₇	1	8	yes	—
819	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
820	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
821	C₂×C₄²	C₂³×C₇	1	4	yes	—
822	C₂×C₄²	C₂³×C₇	1	2	yes	—
823	C₂×C₄²	C₂³×C₇	1	2	yes	—
824	C₂×C₄²	C₂³×C₇	1	8	yes	—
825	C₂×C₄²	C₂³×C₇	1	2	yes	—
826	C₂×C₄²	C₂³×C₇	1	2	yes	—
827	C₂×C₄²	C₂³×C₇	1	4	yes	—
828	C₂×C₄²	C₂³×C₇	1	4	yes	—
829	C₂×C₄²	C₂³×C₇	1	2	yes	—
830	C₂×C₄²	C₂³×C₇	1	2	yes	—
831	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
832	C₂²×C₇	—	2	1	no	—
833	C₂²×C₇	—	2	1	no	—
834	C₂²×C₇	—	2	4	no	—
835	C₂²×C₇	—	2	4	no	—
836	C₂²×C₇	—	2	2	no	—
837	C₂²×C₇	—	2	8	no	—
838	C₂²×C₇	—	2	8	no	—
839	C₂²×C₇	—	2	2	no	—
840	C₂²×C₇	—	2	2	no	—
841	C₂²×C₇	—	2	8	no	—
842	C₂²×C₇	—	4	8	no	—
843	C₂²×C₇	—	4	4	no	—
844	C₂²×C₇	—	8	16	no	—
845	C₂²×C₇	C₂²×#41	1	8	yes	—
846	C₂²×C₇	C₂²×#41	1	2	yes	—
847	C₂²×C₇	C₂⁶	1	1	yes	characteristic
848	C₄×C₇	—	2	1	no	—
849	C₄×C₇	—	2	1	no	—
850	C₄×C₇	—	2	8	no	—
851	C₄×C₇	—	2	4	no	—
852	C₄×C₇	—	2	1	no	—
853	C₄×C₇	—	2	4	no	—
854	C₄×C₇	—	2	1	no	—
855	C₄×C₇	—	2	2	no	—
856	C₄×C₇	—	2	8	no	—
857	C₄×C₇	—	2	4	no	—
858	C₄×C₇	—	2	2	no	—
859	C₄×C₇	—	2	8	no	—
860	C₄×C₇	C₂²×#41	1	4	yes	—
861	C₄×C₇	#585	1	2	yes	—
862	C₄×C₇	#585	1	2	yes	—
863	C₂⁴	C₂⁴×C₇	1	8	yes	—
864	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
865	C₂⁴	C₂⁴×C₇	1	2	yes	—
866	#41	—	2	16	no	—
867	#41	—	2	16	no	—
868	#41	—	2	32	no	—
869	#41	—	2	16	no	—
870	#41	—	4	8	no	—
871	#41	—	4	8	no	—
872	C₂×Q₈	—	2	4	no	—
873	C₂×Q₈	—	4	8	no	—
874	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
875	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
876	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
877	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
878	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
879	C₂×D₄	—	2	8	no	—
880	C₂×D₄	—	2	32	no	—
881	C₂×D₄	—	2	32	no	—
882	C₂×D₄	—	4	8	no	—
883	C₂×D₄	C₇×#41	1	8	yes	complemented
884	C₂×D₄	C₂⁴×C₇	1	8	yes	—
885	C₂×D₄	C₂⁴×C₇	1	8	yes	—
886	C₂×D₄	C₂⁴×C₇	1	16	yes	—
887	C₂×D₄	C₂⁴×C₇	1	4	yes	—
888	C₂×D₄	C₂⁴×C₇	1	4	yes	—
889	C₂×D₄	C₂⁴×C₇	1	4	yes	—
890	C₂×D₄	C₂⁴×C₇	1	8	yes	—
891	C₂×D₄	C₂⁴×C₇	1	8	yes	—
892	C₂×D₄	C₂⁴×C₇	1	8	yes	—
893	C₂×D₄	C₂⁴×C₇	1	4	yes	—
894	C₂²×C₄	—	2	8	no	—
895	C₂²×C₄	—	2	4	no	—
896	C₂²×C₄	—	4	4	no	—
897	C₂²×C₄	—	4	16	no	—
898	C₂²×C₄	—	4	4	no	—
899	C₂²×C₄	—	4	2	no	—
900	C₂²×C₄	—	4	2	no	—
901	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
902	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
906	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
907	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
908	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
911	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
912	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
913	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
914	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
915	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
916	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
918	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
919	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
920	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
921	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
923	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
925	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
926	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
927	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
928	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
929	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
930	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
931	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
932	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
933	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
934	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
935	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
936	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
937	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
938	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
939	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
940	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
941	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
942	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
943	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
944	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
945	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
946	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
947	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
948	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
949	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
950	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
951	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
952	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
953	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
954	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
955	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
956	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
957	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
958	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
959	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
960	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
961	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
962	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
963	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
964	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
965	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
966	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
967	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
968	C₄²	C₂⁴×C₇	1	1	yes	characteristic
969	C₄²	C₂⁴×C₇	1	2	yes	—
970	C₄²	C₂⁴×C₇	1	1	yes	characteristic
971	C₄²	C₂⁴×C₇	1	1	yes	characteristic
972	C₄²	C₂⁴×C₇	1	1	yes	characteristic
973	C₄²	C₂⁴×C₇	1	4	yes	—
974	C₄²	C₂⁴×C₇	1	2	yes	—
975	C₄²	C₂⁴×C₇	1	2	yes	—
976	C₄²	C₂⁴×C₇	1	8	yes	—
977	C₄²	C₂⁴×C₇	1	4	yes	—
978	C₄²	C₂⁴×C₇	1	4	yes	—
979	C₄²	C₂⁴×C₇	1	4	yes	—
980	C₄²	C₂⁴×C₇	1	2	yes	—
981	C₄²	C₂⁴×C₇	1	2	yes	—
982	C₄²	C₂⁴×C₇	1	4	yes	—
983	C₄²	C₂⁴×C₇	1	2	yes	—
984	C₄²	C₂⁴×C₇	1	4	yes	—
985	C₄²	C₂⁴×C₇	1	8	yes	—
986	C₄²	C₂⁴×C₇	1	16	yes	—
987	C₄²	C₂⁴×C₇	1	8	yes	—
988	C₂×C₇	—	2	2	no	—
989	C₂×C₇	—	2	8	no	—
990	C₂×C₇	—	4	2	no	—
991	C₂×C₇	—	4	8	no	—
992	C₂×C₇	C₂³×#41	1	1	yes	characteristic
993	C₂×C₇	C₂×#585	1	1	yes	characteristic
994	C₂×C₇	C₂×#585	1	1	yes	characteristic
995	C₂³	—	2	2	no	—
996	C₂³	—	2	16	no	—
997	C₂³	—	4	2	no	—
998	C₂³	—	4	2	no	—
999	C₂³	—	4	1	no	—
1000	C₂³	—	4	1	no	—
1001	C₂³	—	4	8	no	—
1002	C₂³	—	4	8	no	—
1003	C₂³	C₂×C₇×#41	1	8	yes	—
1004	C₂³	C₂⁵×C₇	1	8	yes	—
1005	C₂³	C₂⁵×C₇	1	2	yes	—
1006	C₂³	C₂⁵×C₇	1	4	yes	—
1007	C₂³	C₂⁵×C₇	1	1	yes	characteristic
1008	Q₈	—	2	8	no	—
1009	Q₈	—	2	8	no	—
1010	Q₈	—	2	8	no	—
1011	Q₈	—	4	8	no	—
1012	Q₈	—	4	4	no	—
1013	D₄	—	2	32	no	—
1014	D₄	—	2	16	no	—
1015	D₄	—	2	16	no	—
1016	D₄	—	2	8	no	—
1017	D₄	—	2	8	no	—
1018	D₄	—	4	8	no	—
1019	D₄	—	4	8	no	—
1020	D₄	—	4	4	no	—
1021	D₄	—	4	8	no	—
1022	D₄	C₂×C₇×#41	1	16	yes	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	4	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	8	no	—
1027	C₂×C₄	—	2	16	no	—
1028	C₂×C₄	—	2	4	no	—
1029	C₂×C₄	—	2	4	no	—
1030	C₂×C₄	—	2	16	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	8	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	16	no	—
1035	C₂×C₄	—	2	8	no	—
1036	C₂×C₄	—	2	4	no	—
1037	C₂×C₄	—	2	4	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	4	1	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	—	4	16	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	8	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	1	no	—
1048	C₂×C₄	—	4	8	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	C₂×C₇×#41	1	4	yes	—
1051	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1052	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1053	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1054	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1055	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1056	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1057	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1058	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1059	C₂×C₄	C₂⁵×C₇	1	4	yes	—
1060	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1061	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1062	C₂×C₄	C₂⁵×C₇	1	8	yes	—
1063	C₂×C₄	C₂⁵×C₇	1	2	yes	—
1064	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1065	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1066	C₇	#62781	1	1	yes	characteristic, direct product factor, Sylow
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	4	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	8	no	—
1073	C₂²	—	2	8	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	8	no	—
1077	C₂²	—	4	8	no	—
1078	C₂²	—	4	4	no	—
1079	C₂²	—	8	16	no	—
1080	C₂²	C₂²×C₇×#41	1	8	yes	—
1081	C₂²	C₂²×C₇×#41	1	2	yes	—
1082	C₂²	C₂⁶×C₇	1	1	yes	characteristic
1083	C₄	—	2	1	no	—
1084	C₄	—	2	1	no	—
1085	C₄	—	2	8	no	—
1086	C₄	—	2	4	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	4	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	8	no	—
1092	C₄	—	2	4	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	8	no	—
1095	C₄	C₂²×C₇×#41	1	4	yes	—
1096	C₄	C₇×#585	1	2	yes	—
1097	C₄	C₇×#585	1	2	yes	—
1098	C₂	—	2	2	no	—
1099	C₂	—	2	8	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	4	8	no	—
1102	C₂	C₂³×C₇×#41	1	1	yes	characteristic
1103	C₂	C₂×C₇×#585	1	1	yes	characteristic
1104	C₂	C₂×C₇×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
socle	C₂²×C₇	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3521	C₂	semidirect
2. C₇×#3515	C₂	semidirect
3. C₇×#3514	C₂	semidirect
4. C₇×#3507	C₂	semidirect
5. C₇×#3505	C₂	semidirect
6. C₇×#3501	C₂	semidirect
7. C₇×#3496	C₂	semidirect
8. C₇×#3493	C₂	semidirect
9. C₇×#3491	C₂	semidirect
10. C₇×#3485	C₂	semidirect
11. C₇×#3482	C₂	semidirect
12. C₇×#3481	C₂	semidirect
13. C₇×#3475	C₂	semidirect
14. C₇×#3461	C₂	semidirect
15. C₇×#3459	C₂	semidirect
16. C₇×#3444	C₂	semidirect
17. C₂×C₇×#529	C₂	semidirect
18. C₄×C₇×H(5,𝔽₂)	C₂	semidirect
19. C₂×C₄×C₇×#41	C₂	semidirect
22. C₇×#559	C₂²	semidirect
23. C₇×#557	C₂²	semidirect
24. C₇×#556	C₂²	semidirect
25. C₇×#556	C₂²	semidirect
26. C₇×#556	C₂²	semidirect
27. C₇×#555	C₂²	semidirect
28. C₇×#554	C₂²	semidirect
29. C₇×#554	C₂²	semidirect
30. C₇×#554	C₂²	semidirect
31. C₇×#553	C₂²	semidirect
32. C₇×#553	C₂²	semidirect
33. C₇×#553	C₂²	semidirect
34. C₇×#552	C₂²	semidirect
35. C₇×#552	C₂²	semidirect
36. C₇×#552	C₂²	semidirect
37. C₇×#552	C₂²	semidirect
38. C₇×#552	C₂²	semidirect
39. C₇×#551	C₂²	semidirect
40. C₇×#551	C₂²	semidirect
41. C₇×#551	C₂²	semidirect
42. C₇×D₄×Q₈	C₂²	semidirect
43. C₇×#548	C₂²	semidirect
44. C₇×#547	C₂²	semidirect
45. C₇×#547	C₂²	semidirect
46. C₇×#547	C₂²	semidirect
47. C₇×#546	C₂²	semidirect
48. C₇×#546	C₂²	semidirect
49. C₇×#546	C₂²	semidirect
50. C₇×#546	C₂²	semidirect
51. C₇×D₄²	C₂²	semidirect
52. C₇×#544	C₂²	semidirect
53. C₇×#543	C₂²	semidirect
54. C₇×#542	C₂²	semidirect
55. C₇×#541	C₂²	semidirect
56. C₇×#539	C₂²	semidirect
57. C₇×#539	C₂²	semidirect
58. C₇×#539	C₂²	semidirect
59. C₇×#538	C₂²	semidirect
60. C₇×#538	C₂²	semidirect
62. C₇×#536	C₂²	semidirect
64. C₇×#534	C₂²	semidirect
65. C₇×#533	C₂²	semidirect
66. C₇×#533	C₂²	semidirect
67. C₇×#533	C₂²	semidirect
68. C₇×#533	C₂²	semidirect
70. C₇×#532	C₂²	semidirect
71. C₇×#532	C₂²	semidirect
72. C₇×#529	C₂²	semidirect
73. C₇×#529	C₂²	semidirect
74. C₇×#529	C₂²	semidirect
75. C₇×#529	C₂²	semidirect
76. C₇×#529	C₂²	semidirect
77. C₇×#529	C₂²	semidirect
78. C₇×#529	C₂²	semidirect
79. C₇×#529	C₂²	semidirect
80. C₇×#529	C₂²	semidirect
81. C₇×#529	C₂²	semidirect
82. C₇×#529	C₂²	semidirect
83. C₇×#529	C₂²	semidirect
84. C₇×#529	C₂²	semidirect
85. C₇×#529	C₂²	semidirect
86. C₇×#529	C₂²	semidirect
87. C₂×C₇×#126	C₂²	semidirect
88. C₂×C₇×#125	C₂²	semidirect
89. C₂×C₇×#124	C₂²	semidirect
90. C₇×#525	C₂²	semidirect
91. C₇×#525	C₂²	semidirect
92. C₇×#525	C₂²	semidirect
93. C₇×#525	C₂²	semidirect
94. C₂×C₇×#123	C₂²	semidirect
95. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
97. C₇×#520	C₂²	semidirect
98. C₇×#520	C₂²	semidirect
100. C₇×#518	C₂²	semidirect
101. C₇×#518	C₂²	semidirect
102. C₄×C₇×#41	C₂²	semidirect
103. C₄×C₇×#41	C₂²	semidirect
104. C₄×C₇×#41	C₂²	semidirect
105. C₄×C₇×#41	C₂²	semidirect
106. C₄×C₇×#41	C₂²	semidirect
107. C₄×C₇×#41	C₂²	semidirect
108. C₄×C₇×#41	C₂²	semidirect
109. C₄×C₇×#41	C₂²	semidirect
110. C₂×C₄×C₇×Q₈	C₂²	semidirect
111. C₂×C₄×C₇×Q₈	C₂²	semidirect
112. C₂×C₄×C₇×Q₈	C₂²	semidirect
115. C₂×C₄×C₇×D₄	C₂²	semidirect
116. C₂×C₄×C₇×D₄	C₂²	semidirect
117. C₂×C₄×C₇×D₄	C₂²	semidirect
118. C₂×C₄×C₇×D₄	C₂²	semidirect
119. C₂×C₄×C₇×D₄	C₂²	semidirect
120. C₂×C₇×#117	C₂²	semidirect
121. C₂×C₇×#117	C₂²	semidirect
122. C₂×C₇×#117	C₂²	semidirect
123. C₂²×C₄²×C₇	C₂²	semidirect
124. C₂²×C₄²×C₇	C₂²	semidirect
125. #62781	C₇	direct (N × H)
319. #3521	C₂×C₇	semidirect
320. #3515	C₂×C₇	semidirect
321. #3514	C₂×C₇	semidirect
322. #3507	C₂×C₇	semidirect
323. #3505	C₂×C₇	semidirect
324. #3501	C₂×C₇	semidirect
325. #3496	C₂×C₇	semidirect
326. #3493	C₂×C₇	semidirect
327. #3491	C₂×C₇	semidirect
328. #3485	C₂×C₇	semidirect
329. #3482	C₂×C₇	semidirect
330. #3481	C₂×C₇	semidirect
331. #3475	C₂×C₇	semidirect
332. #3461	C₂×C₇	semidirect
333. #3459	C₂×C₇	semidirect
334. #3444	C₂×C₇	semidirect
335. C₂×#529	C₂×C₇	semidirect
336. C₄×H(5,𝔽₂)	C₂×C₇	semidirect
337. C₂×C₄×#41	C₂×C₇	semidirect
358. C₂×C₇×D₄	#41	semidirect
465. #559	C₂²×C₇	semidirect
466. #557	C₂²×C₇	semidirect
467. #556	C₂²×C₇	semidirect
468. #556	C₂²×C₇	semidirect
469. #556	C₂²×C₇	semidirect
470. #555	C₂²×C₇	semidirect
471. #554	C₂²×C₇	semidirect
472. #554	C₂²×C₇	semidirect
473. #554	C₂²×C₇	semidirect
474. #553	C₂²×C₇	semidirect
475. #553	C₂²×C₇	semidirect
476. #553	C₂²×C₇	semidirect
477. #552	C₂²×C₇	semidirect
478. #552	C₂²×C₇	semidirect
479. #552	C₂²×C₇	semidirect
480. #552	C₂²×C₇	semidirect
481. #552	C₂²×C₇	semidirect
482. #551	C₂²×C₇	semidirect
483. #551	C₂²×C₇	semidirect
484. #551	C₂²×C₇	semidirect
485. D₄×Q₈	C₂²×C₇	semidirect
486. #548	C₂²×C₇	semidirect
487. #547	C₂²×C₇	semidirect
488. #547	C₂²×C₇	semidirect
489. #547	C₂²×C₇	semidirect
490. #546	C₂²×C₇	semidirect
491. #546	C₂²×C₇	semidirect
492. #546	C₂²×C₇	semidirect
493. #546	C₂²×C₇	semidirect
494. D₄²	C₂²×C₇	semidirect
495. #544	C₂²×C₇	semidirect
496. #543	C₂²×C₇	semidirect
497. #542	C₂²×C₇	semidirect
498. #541	C₂²×C₇	semidirect
499. #539	C₂²×C₇	semidirect
500. #539	C₂²×C₇	semidirect
501. #539	C₂²×C₇	semidirect
502. #538	C₂²×C₇	semidirect
503. #538	C₂²×C₇	semidirect
505. #536	C₂²×C₇	semidirect
507. #534	C₂²×C₇	semidirect
508. #533	C₂²×C₇	semidirect
509. #533	C₂²×C₇	semidirect
510. #533	C₂²×C₇	semidirect
511. #533	C₂²×C₇	semidirect
513. #532	C₂²×C₇	semidirect
514. #532	C₂²×C₇	semidirect
515. #529	C₂²×C₇	semidirect
516. #529	C₂²×C₇	semidirect
517. #529	C₂²×C₇	semidirect
518. #529	C₂²×C₇	semidirect
519. #529	C₂²×C₇	semidirect
520. #529	C₂²×C₇	semidirect
521. #529	C₂²×C₇	semidirect
522. #529	C₂²×C₇	semidirect
523. #529	C₂²×C₇	semidirect
524. #529	C₂²×C₇	semidirect
525. #529	C₂²×C₇	semidirect
526. #529	C₂²×C₇	semidirect
527. #529	C₂²×C₇	semidirect
528. #529	C₂²×C₇	semidirect
529. #529	C₂²×C₇	semidirect
530. C₂×#126	C₂²×C₇	semidirect
531. C₂×#125	C₂²×C₇	semidirect
532. C₂×#124	C₂²×C₇	semidirect
533. #525	C₂²×C₇	semidirect
534. #525	C₂²×C₇	semidirect
535. #525	C₂²×C₇	semidirect
536. #525	C₂²×C₇	semidirect
537. C₂×#123	C₂²×C₇	semidirect
538. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
540. #520	C₂²×C₇	semidirect
541. #520	C₂²×C₇	semidirect
543. #518	C₂²×C₇	semidirect
544. #518	C₂²×C₇	semidirect
545. C₄×#41	C₂²×C₇	semidirect
546. C₄×#41	C₂²×C₇	semidirect
547. C₄×#41	C₂²×C₇	semidirect
548. C₄×#41	C₂²×C₇	semidirect
549. C₄×#41	C₂²×C₇	semidirect
550. C₄×#41	C₂²×C₇	semidirect
551. C₄×#41	C₂²×C₇	semidirect
552. C₄×#41	C₂²×C₇	semidirect
553. C₂×C₄×Q₈	C₂²×C₇	semidirect
554. C₂×C₄×Q₈	C₂²×C₇	semidirect
555. C₂×C₄×Q₈	C₂²×C₇	semidirect
558. C₂×C₄×D₄	C₂²×C₇	semidirect
559. C₂×C₄×D₄	C₂²×C₇	semidirect
560. C₂×C₄×D₄	C₂²×C₇	semidirect
561. C₂×C₄×D₄	C₂²×C₇	semidirect
562. C₂×C₄×D₄	C₂²×C₇	semidirect
563. C₂×#117	C₂²×C₇	semidirect
564. C₂×#117	C₂²×C₇	semidirect
565. C₂×#117	C₂²×C₇	semidirect
566. C₂²×C₄²	C₂²×C₇	semidirect
567. C₂²×C₄²	C₂²×C₇	semidirect
883. C₂×D₄	C₇×#41	semidirect
1066. C₇	#62781	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×#3521	2
C₇×#3515	2
C₇×#3514	2
C₇×#3507	2
C₇×#3505	2
C₇×#3501	2
C₇×#3496	2
C₇×#3493	2
C₇×#3491	2
C₇×#3485	2
C₇×#3482	2
C₇×#3481	2
C₇×#3475	2
C₇×#3461	2
C₇×#3459	2
C₇×#3444	2
C₂×C₇×#529	2
C₄×C₇×H(5,𝔽₂)	2
C₂×C₄×C₇×#41	2
#62781	7

Subgroups — C7×#62781 #13239997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62781 #13239997