Subgroups — C₇×#62819 #13240035

Order 1792.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3541	C₂	1	8	yes	maximal, complemented
2	C₇×#3538	C₂	1	4	yes	maximal, complemented
3	C₇×#3536	C₂	1	4	yes	maximal, complemented
4	C₇×#3535	C₂	1	8	yes	maximal, complemented
5	C₇×#3520	C₂	1	8	yes	maximal, complemented
6	C₇×#3505	C₂	1	4	yes	maximal, complemented
7	C₇×#3501	C₂	1	4	yes	maximal, complemented
8	C₇×#3495	C₂	1	4	yes	maximal, complemented
9	C₇×#3492	C₂	1	2	yes	maximal, complemented
10	C₇×#3492	C₂	1	4	yes	maximal, complemented
11	C₇×#3490	C₂	1	4	yes	maximal, complemented
12	C₇×#3489	C₂	1	4	yes	maximal, complemented
13	C₇×#3486	C₂	1	2	yes	maximal, complemented
14	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂²×C₇×#41	C₂²	1	2	yes	complemented
18	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
20	C₇×#563	C₂²	1	16	yes	complemented
21	C₇×#562	C₂²	1	16	yes	complemented
22	C₇×#556	C₂²	1	8	yes	complemented
23	C₇×#554	C₂²	1	8	yes	complemented
24	C₇×#554	C₂²	1	16	yes	complemented
25	C₇×#554	C₂²	1	8	yes	complemented
26	C₇×#554	C₂²	1	16	yes	complemented
27	C₇×#553	C₂²	1	8	yes	complemented
28	C₇×#553	C₂²	1	16	yes	complemented
29	C₇×#552	C₂²	1	16	yes	complemented
30	C₇×#552	C₂²	1	8	yes	complemented
31	C₇×#552	C₂²	1	8	yes	complemented
32	C₇×#552	C₂²	1	8	yes	complemented
33	C₇×#551	C₂²	1	16	yes	complemented
34	C₇×#551	C₂²	1	16	yes	complemented
35	C₇×#551	C₂²	1	16	yes	complemented
36	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
37	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
38	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
39	C₇×#548	C₂²	1	8	yes	complemented
40	C₇×#548	C₂²	1	8	yes	complemented
41	C₇×#548	C₂²	1	8	yes	complemented
42	C₇×#547	C₂²	1	16	yes	complemented
43	C₇×#547	C₂²	1	8	yes	complemented
44	C₇×#547	C₂²	1	8	yes	complemented
45	C₇×#546	C₂²	1	16	yes	complemented
46	C₇×#546	C₂²	1	16	yes	complemented
47	C₇×#546	C₂²	1	8	yes	complemented
48	C₇×#544	C₂²	1	2	yes	complemented
49	C₇×#544	C₂²	1	4	yes	complemented
50	C₇×#544	C₂²	1	8	yes	complemented
51	C₇×#543	C₂²	1	4	yes	—
52	C₇×#543	C₂²	1	8	yes	complemented
53	C₇×#542	C₂²	1	8	yes	complemented
54	C₇×#542	C₂²	1	16	yes	complemented
55	C₇×#541	C₂²	1	8	yes	complemented
56	C₇×#539	C₂²	1	8	yes	complemented
57	C₇×#539	C₂²	1	8	yes	complemented
58	C₇×#539	C₂²	1	8	yes	complemented
59	C₇×#539	C₂²	1	8	yes	complemented
60	C₇×#539	C₂²	1	16	yes	complemented
61	C₇×#538	C₂²	1	8	yes	complemented
62	C₇×#538	C₂²	1	8	yes	complemented
63	C₇×#538	C₂²	1	8	yes	complemented
64	C₇×#537	C₂²	1	2	yes	complemented
65	C₇×#537	C₂²	1	4	yes	complemented
66	C₇×#537	C₂²	1	8	yes	complemented
67	C₇×#536	C₂²	1	4	yes	complemented
68	C₇×#536	C₂²	1	8	yes	complemented
69	C₇×#536	C₂²	1	8	yes	complemented
70	C₇×#534	C₂²	1	4	yes	—
71	C₇×#533	C₂²	1	8	yes	complemented
72	C₇×#529	C₂²	1	8	yes	complemented
73	C₇×#525	C₂²	1	4	yes	—
74	C₇×#525	C₂²	1	4	yes	—
75	C₇×#525	C₂²	1	4	yes	—
76	C₇×#525	C₂²	1	4	yes	—
77	C₇×#525	C₂²	1	4	yes	complemented
78	C₇×#525	C₂²	1	4	yes	complemented
79	C₇×#525	C₂²	1	4	yes	complemented
80	C₇×#525	C₂²	1	4	yes	complemented
81	C₇×#525	C₂²	1	8	yes	complemented
82	C₇×#525	C₂²	1	8	yes	complemented
83	C₇×#525	C₂²	1	8	yes	complemented
84	C₂×C₇×#123	C₂²	1	4	yes	complemented
85	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
86	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
87	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
88	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
89	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
90	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
91	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
92	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
93	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
94	C₂×C₇×#121	C₂²	1	2	yes	—
95	C₂×C₇×#121	C₂²	1	2	yes	complemented
96	C₂×C₇×#120	C₂²	1	4	yes	—
97	C₇×#520	C₂²	1	4	yes	complemented
98	C₇×#520	C₂²	1	8	yes	complemented
99	C₇×#519	C₂²	1	2	yes	complemented
100	C₇×#518	C₂²	1	8	yes	—
101	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
102	C₂×C₄×C₇×D₄	C₂²	1	4	yes	complemented
103	C₂×C₇×#117	C₂²	1	2	yes	complemented
104	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
106	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
107	#62819	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₇	C₂³	1	1	yes	characteristic
109	C₇×2₋¹⁺⁴	—	4	8	no	—
110	C₂×C₇×#41	—	4	8	no	—
111	C₂×C₇×#41	C₂³	1	4	yes	—
112	C₂×C₇×#41	C₂³	1	4	yes	—
113	C₂×C₇×#41	C₂³	1	4	yes	—
114	C₂×C₇×#41	C₂³	1	4	yes	—
115	C₂×C₇×#41	C₂³	1	8	yes	—
116	C₂×C₇×#41	C₂³	1	8	yes	—
117	C₂×C₇×#41	C₂³	1	8	yes	complemented
118	C₂²×C₇×Q₈	—	4	4	no	—
119	C₂²×C₇×Q₈	C₂³	1	2	yes	—
120	C₂²×C₇×Q₈	C₂³	1	4	yes	—
121	C₂²×C₇×Q₈	C₂³	1	2	yes	—
122	C₂²×C₇×Q₈	C₂³	1	4	yes	—
123	C₂²×C₇×Q₈	C₂³	1	2	yes	—
124	C₂²×C₇×Q₈	C₂³	1	8	yes	complemented
125	C₂²×C₇×D₄	C₂³	1	4	yes	—
126	C₂²×C₇×D₄	C₂³	1	4	yes	—
127	C₂²×C₇×D₄	C₂³	1	2	yes	—
128	C₂²×C₇×D₄	C₂³	1	4	yes	—
129	C₂³×C₄×C₇	—	4	4	no	—
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	4	yes	—
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₇	C₂³	1	2	yes	—
141	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
142	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
143	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
144	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
145	C₇×#126	C₂³	1	16	yes	—
146	C₇×#126	C₂³	1	16	yes	—
147	C₇×#126	C₂³	1	16	yes	complemented
148	C₇×#126	C₂³	1	16	yes	complemented
149	C₇×#126	C₂³	1	16	yes	complemented
150	C₇×#125	C₂³	1	8	yes	complemented
151	C₇×#125	C₂³	1	16	yes	complemented
152	C₇×#125	C₂³	1	16	yes	complemented
153	C₇×#125	C₂³	1	16	yes	complemented
154	C₇×#125	C₂³	1	16	yes	complemented
155	C₇×#124	C₂³	1	16	yes	—
156	C₇×#124	C₂³	1	16	yes	—
157	C₇×#124	C₂³	1	8	yes	complemented
158	C₇×#124	C₂³	1	16	yes	complemented
159	C₇×#123	C₂³	1	8	yes	—
160	C₇×#123	C₂³	1	8	yes	—
161	C₇×#123	C₂³	1	8	yes	—
162	C₇×#123	C₂³	1	8	yes	—
163	C₇×#123	C₂³	1	16	yes	—
164	C₇×#123	C₂³	1	16	yes	—
165	C₇×#123	C₂³	1	16	yes	—
166	C₇×#123	C₂³	1	16	yes	—
167	C₇×#123	C₂³	1	16	yes	—
168	C₇×#123	C₂³	1	16	yes	complemented
169	C₇×#123	C₂³	1	16	yes	complemented
170	C₇×#123	C₂³	1	16	yes	complemented
171	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
172	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
173	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
174	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
175	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
176	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
179	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
180	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
181	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
182	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
183	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
184	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
185	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
186	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
187	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
188	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
189	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
190	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
193	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
194	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
195	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
196	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
197	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
198	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
199	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
200	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
201	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
202	C₇×#121	C₂³	1	4	yes	—
203	C₇×#121	C₂³	1	4	yes	—
204	C₇×#121	C₂³	1	4	yes	—
205	C₇×#121	C₂³	1	4	yes	—
206	C₇×#121	C₂³	1	4	yes	—
207	C₇×#121	C₂³	1	4	yes	—
208	C₇×#121	C₂³	1	4	yes	—
209	C₇×#121	C₂³	1	4	yes	—
210	C₇×#121	C₂³	1	8	yes	—
211	C₇×#121	C₂³	1	8	yes	—
212	C₇×#121	C₂³	1	8	yes	—
213	C₇×#121	C₂³	1	8	yes	—
214	C₇×#121	C₂³	1	16	yes	—
215	C₇×#121	C₂³	1	16	yes	—
216	C₇×#121	C₂³	1	8	yes	complemented
217	C₇×#121	C₂³	1	16	yes	complemented
218	C₇×#120	C₂³	1	8	yes	—
219	C₇×#120	C₂³	1	8	yes	—
220	C₇×#120	C₂³	1	8	yes	—
221	C₇×#120	C₂³	1	8	yes	—
222	C₇×#120	C₂³	1	16	yes	—
223	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
224	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
225	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
226	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
227	C₄×C₇×D₄	C₂³	1	8	yes	—
228	C₄×C₇×D₄	C₂³	1	8	yes	—
229	C₄×C₇×D₄	C₂³	1	8	yes	—
230	C₄×C₇×D₄	C₂³	1	8	yes	—
231	C₄×C₇×D₄	C₂³	1	8	yes	—
232	C₄×C₇×D₄	C₂³	1	8	yes	—
233	C₄×C₇×D₄	C₂³	1	8	yes	—
234	C₄×C₇×D₄	C₂³	1	8	yes	—
235	C₄×C₇×D₄	C₂³	1	16	yes	—
236	C₄×C₇×D₄	C₂³	1	16	yes	—
237	C₄×C₇×D₄	C₂³	1	16	yes	—
238	C₄×C₇×D₄	C₂³	1	16	yes	—
239	C₄×C₇×D₄	C₂³	1	16	yes	—
240	C₄×C₇×D₄	C₂³	1	16	yes	—
241	C₄×C₇×D₄	C₂³	1	16	yes	complemented
242	C₄×C₇×D₄	C₂³	1	8	yes	complemented
243	C₇×#117	C₂³	1	4	yes	—
244	C₇×#117	C₂³	1	4	yes	—
245	C₇×#117	C₂³	1	4	yes	—
246	C₇×#117	C₂³	1	4	yes	—
247	C₇×#117	C₂³	1	16	yes	—
248	C₇×#117	C₂³	1	8	yes	—
249	C₇×#117	C₂³	1	8	yes	—
250	C₇×#117	C₂³	1	8	yes	complemented
251	C₇×#117	C₂³	1	16	yes	complemented
252	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
253	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
254	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
255	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
256	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
257	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
259	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
260	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
263	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
264	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
265	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
266	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
267	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
268	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
269	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
270	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
271	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
272	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
273	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
274	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
275	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
276	C₂×C₄²×C₇	C₂³	1	4	yes	—
277	#3541	C₂×C₇	1	8	yes	complemented
278	#3538	C₂×C₇	1	4	yes	complemented
279	#3536	C₂×C₇	1	4	yes	complemented
280	#3535	C₂×C₇	1	8	yes	complemented
281	#3520	C₂×C₇	1	8	yes	complemented
282	#3505	C₂×C₇	1	4	yes	complemented
283	#3501	C₂×C₇	1	4	yes	complemented
284	#3495	C₂×C₇	1	4	yes	complemented
285	#3492	C₂×C₇	1	2	yes	complemented
286	#3492	C₂×C₇	1	4	yes	complemented
287	#3490	C₂×C₇	1	4	yes	complemented
288	#3489	C₂×C₇	1	4	yes	complemented
289	#3486	C₂×C₇	1	2	yes	complemented
290	C₂×#525	C₂×C₇	1	2	yes	complemented
291	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
292	C₂⁴×C₇	—	2	4	no	—
293	C₂⁴×C₇	—	4	2	no	—
294	C₂⁴×C₇	—	4	2	no	—
295	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
296	C₂⁴×C₇	C₂⁴	1	2	yes	—
297	C₂⁴×C₇	C₂⁴	1	2	yes	—
298	C₂⁴×C₇	C₂⁴	1	4	yes	—
299	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
300	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
301	C₇×#41	—	2	16	no	—
302	C₇×#41	—	4	8	no	—
303	C₇×#41	—	4	8	no	—
304	C₇×#41	—	4	16	no	—
305	C₇×#41	—	4	16	no	—
306	C₇×#41	—	4	8	no	—
307	C₇×#41	—	4	16	no	—
308	C₂×C₇×Q₈	—	2	8	no	—
309	C₂×C₇×Q₈	—	4	4	no	—
310	C₂×C₇×Q₈	—	4	8	no	—
311	C₂×C₇×Q₈	—	4	8	no	—
312	C₂×C₇×Q₈	—	4	4	no	—
313	C₂×C₇×Q₈	—	4	16	no	—
314	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
315	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
316	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
317	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
318	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
319	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
320	C₂×C₇×D₄	—	2	16	no	—
321	C₂×C₇×D₄	—	4	4	no	—
322	C₂×C₇×D₄	—	4	8	no	—
323	C₂×C₇×D₄	—	4	8	no	—
324	C₂×C₇×D₄	C₂⁴	1	8	yes	—
325	C₂×C₇×D₄	C₂⁴	1	8	yes	—
326	C₂×C₇×D₄	C₂⁴	1	8	yes	—
327	C₂×C₇×D₄	C₂⁴	1	8	yes	—
328	C₂×C₇×D₄	C₂⁴	1	4	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	4	yes	—
334	C₂²×C₄×C₇	—	2	4	no	—
335	C₂²×C₄×C₇	—	2	8	no	—
336	C₂²×C₄×C₇	—	4	4	no	—
337	C₂²×C₄×C₇	—	4	4	no	—
338	C₂²×C₄×C₇	—	4	4	no	—
339	C₂²×C₄×C₇	—	4	4	no	—
340	C₂²×C₄×C₇	—	4	8	no	—
341	C₂²×C₄×C₇	—	4	4	no	—
342	C₂²×C₄×C₇	—	4	2	no	—
343	C₂²×C₄×C₇	—	4	4	no	—
344	C₂²×C₄×C₇	—	4	4	no	—
345	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
347	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
348	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
349	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
354	C₂²×C₄×C₇	C₂⁴	1	8	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	4	yes	—
359	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
362	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
364	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
365	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
366	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
367	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
371	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
374	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
375	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
376	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
377	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
378	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
379	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
380	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
381	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
382	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
383	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
384	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
385	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
386	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
387	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
388	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
389	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
390	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
391	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
392	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
393	C₇×C₄⋊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	16	yes	—
397	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
398	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
399	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
400	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
401	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
402	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
403	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
404	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
405	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
406	C₇×C₂²⋊C₄	C₂⁴	1	8	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	C₄²×C₇	C₂⁴	1	8	yes	—
411	C₄²×C₇	C₂⁴	1	8	yes	—
412	C₄²×C₇	C₂⁴	1	16	yes	—
413	C₄²×C₇	C₂⁴	1	16	yes	—
414	C₂×2₋¹⁺⁴	C₂²×C₇	1	2	yes	complemented
415	C₂²×#41	C₂²×C₇	1	2	yes	complemented
416	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
417	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
418	#563	C₂²×C₇	1	16	yes	complemented
419	#562	C₂²×C₇	1	16	yes	complemented
420	#556	C₂²×C₇	1	8	yes	complemented
421	#554	C₂²×C₇	1	8	yes	complemented
422	#554	C₂²×C₇	1	16	yes	complemented
423	#554	C₂²×C₇	1	8	yes	complemented
424	#554	C₂²×C₇	1	16	yes	complemented
425	#553	C₂²×C₇	1	8	yes	complemented
426	#553	C₂²×C₇	1	16	yes	complemented
427	#552	C₂²×C₇	1	16	yes	complemented
428	#552	C₂²×C₇	1	8	yes	complemented
429	#552	C₂²×C₇	1	8	yes	complemented
430	#552	C₂²×C₇	1	8	yes	complemented
431	#551	C₂²×C₇	1	16	yes	complemented
432	#551	C₂²×C₇	1	16	yes	complemented
433	#551	C₂²×C₇	1	16	yes	complemented
434	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
435	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
436	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
437	#548	C₂²×C₇	1	8	yes	complemented
438	#548	C₂²×C₇	1	8	yes	complemented
439	#548	C₂²×C₇	1	8	yes	complemented
440	#547	C₂²×C₇	1	16	yes	complemented
441	#547	C₂²×C₇	1	8	yes	complemented
442	#547	C₂²×C₇	1	8	yes	complemented
443	#546	C₂²×C₇	1	16	yes	complemented
444	#546	C₂²×C₇	1	16	yes	complemented
445	#546	C₂²×C₇	1	8	yes	complemented
446	#544	C₂²×C₇	1	2	yes	complemented
447	#544	C₂²×C₇	1	4	yes	complemented
448	#544	C₂²×C₇	1	8	yes	complemented
449	#543	C₂²×C₇	1	4	yes	—
450	#543	C₂²×C₇	1	8	yes	complemented
451	#542	C₂²×C₇	1	8	yes	complemented
452	#542	C₂²×C₇	1	16	yes	complemented
453	#541	C₂²×C₇	1	8	yes	complemented
454	#539	C₂²×C₇	1	8	yes	complemented
455	#539	C₂²×C₇	1	8	yes	complemented
456	#539	C₂²×C₇	1	8	yes	complemented
457	#539	C₂²×C₇	1	8	yes	complemented
458	#539	C₂²×C₇	1	16	yes	complemented
459	#538	C₂²×C₇	1	8	yes	complemented
460	#538	C₂²×C₇	1	8	yes	complemented
461	#538	C₂²×C₇	1	8	yes	complemented
462	#537	C₂²×C₇	1	2	yes	complemented
463	#537	C₂²×C₇	1	4	yes	complemented
464	#537	C₂²×C₇	1	8	yes	complemented
465	#536	C₂²×C₇	1	4	yes	complemented
466	#536	C₂²×C₇	1	8	yes	complemented
467	#536	C₂²×C₇	1	8	yes	complemented
468	#534	C₂²×C₇	1	4	yes	—
469	#533	C₂²×C₇	1	8	yes	complemented
470	#529	C₂²×C₇	1	8	yes	complemented
471	#525	C₂²×C₇	1	4	yes	—
472	#525	C₂²×C₇	1	4	yes	—
473	#525	C₂²×C₇	1	4	yes	—
474	#525	C₂²×C₇	1	4	yes	—
475	#525	C₂²×C₇	1	4	yes	complemented
476	#525	C₂²×C₇	1	4	yes	complemented
477	#525	C₂²×C₇	1	4	yes	complemented
478	#525	C₂²×C₇	1	4	yes	complemented
479	#525	C₂²×C₇	1	8	yes	complemented
480	#525	C₂²×C₇	1	8	yes	complemented
481	#525	C₂²×C₇	1	8	yes	complemented
482	C₂×#123	C₂²×C₇	1	4	yes	complemented
483	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
484	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
485	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
486	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
487	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
488	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
489	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
490	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
491	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
492	C₂×#121	C₂²×C₇	1	2	yes	—
493	C₂×#121	C₂²×C₇	1	2	yes	complemented
494	C₂×#120	C₂²×C₇	1	4	yes	—
495	#520	C₂²×C₇	1	4	yes	complemented
496	#520	C₂²×C₇	1	8	yes	complemented
497	#519	C₂²×C₇	1	2	yes	complemented
498	#518	C₂²×C₇	1	8	yes	—
499	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
500	C₂×C₄×D₄	C₂²×C₇	1	4	yes	complemented
501	C₂×#117	C₂²×C₇	1	2	yes	complemented
502	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
503	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
504	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
505	C₂³×C₇	—	2	2	no	—
506	C₂³×C₇	—	2	2	no	—
507	C₂³×C₇	—	2	2	no	—
508	C₂³×C₇	—	2	4	no	—
509	C₂³×C₇	—	2	4	no	—
510	C₂³×C₇	—	2	4	no	—
511	C₂³×C₇	—	2	2	no	—
512	C₂³×C₇	—	2	4	no	—
513	C₂³×C₇	—	2	8	no	—
514	C₂³×C₇	—	4	1	no	—
515	C₂³×C₇	—	4	2	no	—
516	C₂³×C₇	—	4	1	no	—
517	C₂³×C₇	—	4	1	no	—
518	C₂³×C₇	—	4	2	no	—
519	C₂³×C₇	—	4	1	no	—
520	C₂³×C₇	—	4	4	no	—
521	C₂³×C₇	—	4	4	no	—
522	C₂³×C₇	—	4	16	no	—
523	C₂³×C₇	2₋¹⁺⁴	1	4	yes	complemented
524	C₂³×C₇	C₂⁵	1	2	yes	—
525	C₂³×C₇	C₂⁵	1	8	yes	—
526	C₂³×C₇	C₂⁵	1	1	yes	characteristic
527	C₂³×C₇	C₂⁵	1	2	yes	—
528	C₂³×C₇	C₂⁵	1	1	yes	characteristic
529	C₂³×C₇	C₂⁵	1	1	yes	characteristic
530	C₇×Q₈	—	2	16	no	—
531	C₇×Q₈	—	2	8	no	—
532	C₇×Q₈	—	4	8	no	—
533	C₇×Q₈	—	4	8	no	—
534	C₇×Q₈	—	4	4	no	—
535	C₇×Q₈	—	4	8	no	—
536	C₇×D₄	—	2	16	no	—
537	C₇×D₄	—	2	16	no	—
538	C₇×D₄	—	2	16	no	—
539	C₇×D₄	—	2	16	no	—
540	C₇×D₄	—	2	8	no	—
541	C₇×D₄	—	4	8	no	—
542	C₇×D₄	—	4	4	no	—
543	C₇×D₄	—	4	8	no	—
544	C₇×D₄	—	4	8	no	—
545	C₇×D₄	—	4	8	no	—
546	C₂×C₄×C₇	—	2	2	no	—
547	C₂×C₄×C₇	—	2	4	no	—
548	C₂×C₄×C₇	—	2	8	no	—
549	C₂×C₄×C₇	—	2	8	no	—
550	C₂×C₄×C₇	—	2	8	no	—
551	C₂×C₄×C₇	—	2	4	no	—
552	C₂×C₄×C₇	—	2	4	no	—
553	C₂×C₄×C₇	—	2	4	no	—
554	C₂×C₄×C₇	—	2	4	no	—
555	C₂×C₄×C₇	—	2	4	no	—
556	C₂×C₄×C₇	—	2	4	no	—
557	C₂×C₄×C₇	—	2	16	no	—
558	C₂×C₄×C₇	—	4	1	no	—
559	C₂×C₄×C₇	—	4	2	no	—
560	C₂×C₄×C₇	—	4	2	no	—
561	C₂×C₄×C₇	—	4	2	no	—
562	C₂×C₄×C₇	—	4	1	no	—
563	C₂×C₄×C₇	—	4	2	no	—
564	C₂×C₄×C₇	—	4	2	no	—
565	C₂×C₄×C₇	—	4	4	no	—
566	C₂×C₄×C₇	—	4	4	no	—
567	C₂×C₄×C₇	—	4	4	no	—
568	C₂×C₄×C₇	—	4	4	no	—
569	C₂×C₄×C₇	—	4	4	no	—
570	C₂×C₄×C₇	—	4	8	no	—
571	C₂×C₄×C₇	—	4	4	no	—
572	C₂×C₄×C₇	—	4	16	no	—
573	C₂×C₄×C₇	—	4	16	no	—
574	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
575	C₂×C₄×C₇	C₂⁵	1	8	yes	—
576	C₂×C₄×C₇	C₂⁵	1	8	yes	—
577	C₂×C₄×C₇	C₂⁵	1	2	yes	—
578	C₂×C₄×C₇	C₂⁵	1	8	yes	—
579	C₂×C₄×C₇	C₂⁵	1	8	yes	—
580	C₂×C₄×C₇	C₂⁵	1	8	yes	—
581	C₂×C₄×C₇	C₂⁵	1	2	yes	—
582	C₂×C₄×C₇	C₂⁵	1	2	yes	—
583	C₂×C₄×C₇	C₂⁵	1	2	yes	—
584	C₂⁵	C₂³×C₇	1	1	yes	characteristic
585	2₋¹⁺⁴	—	4	8	no	—
586	C₂×#41	—	4	8	no	—
587	C₂×#41	C₂³×C₇	1	4	yes	—
588	C₂×#41	C₂³×C₇	1	8	yes	—
589	C₂×#41	C₂³×C₇	1	4	yes	—
590	C₂×#41	C₂³×C₇	1	4	yes	—
591	C₂×#41	C₂³×C₇	1	4	yes	—
592	C₂×#41	C₂³×C₇	1	8	yes	—
593	C₂×#41	C₂³×C₇	1	8	yes	complemented
594	C₂²×Q₈	—	4	4	no	—
595	C₂²×Q₈	C₂³×C₇	1	2	yes	—
596	C₂²×Q₈	C₂³×C₇	1	4	yes	—
597	C₂²×Q₈	C₂³×C₇	1	2	yes	—
598	C₂²×Q₈	C₂³×C₇	1	2	yes	—
599	C₂²×Q₈	C₂³×C₇	1	4	yes	—
600	C₂²×Q₈	C₂³×C₇	1	8	yes	complemented
601	C₂²×D₄	C₂³×C₇	1	4	yes	—
602	C₂²×D₄	C₂³×C₇	1	4	yes	—
603	C₂²×D₄	C₂³×C₇	1	4	yes	—
604	C₂²×D₄	C₂³×C₇	1	2	yes	—
605	C₂³×C₄	—	4	4	no	—
606	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₇	1	2	yes	—
608	C₂³×C₄	C₂³×C₇	1	2	yes	—
609	C₂³×C₄	C₂³×C₇	1	2	yes	—
610	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₇	1	2	yes	—
612	C₂³×C₄	C₂³×C₇	1	4	yes	—
613	C₂³×C₄	C₂³×C₇	1	2	yes	—
614	C₂³×C₄	C₂³×C₇	1	2	yes	—
615	C₂³×C₄	C₂³×C₇	1	2	yes	—
616	C₂³×C₄	C₂³×C₇	1	2	yes	—
617	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
618	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
619	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
620	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
621	#126	C₂³×C₇	1	16	yes	—
622	#126	C₂³×C₇	1	16	yes	—
623	#126	C₂³×C₇	1	16	yes	complemented
624	#126	C₂³×C₇	1	16	yes	complemented
625	#126	C₂³×C₇	1	16	yes	complemented
626	#125	C₂³×C₇	1	8	yes	complemented
627	#125	C₂³×C₇	1	16	yes	complemented
628	#125	C₂³×C₇	1	16	yes	complemented
629	#125	C₂³×C₇	1	16	yes	complemented
630	#125	C₂³×C₇	1	16	yes	complemented
631	#124	C₂³×C₇	1	16	yes	—
632	#124	C₂³×C₇	1	16	yes	—
633	#124	C₂³×C₇	1	8	yes	complemented
634	#124	C₂³×C₇	1	16	yes	complemented
635	#123	C₂³×C₇	1	8	yes	—
636	#123	C₂³×C₇	1	8	yes	—
637	#123	C₂³×C₇	1	8	yes	—
638	#123	C₂³×C₇	1	8	yes	—
639	#123	C₂³×C₇	1	16	yes	—
640	#123	C₂³×C₇	1	16	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	complemented
645	#123	C₂³×C₇	1	16	yes	complemented
646	#123	C₂³×C₇	1	16	yes	complemented
647	C₂²⋊Q₈	C₂³×C₇	1	8	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	4	yes	—
653	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
654	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
655	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
656	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
657	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
658	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
659	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
660	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
661	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
662	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
663	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
664	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
665	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
666	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
667	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
668	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
669	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
670	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
671	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
672	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
673	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
674	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
675	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
676	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
677	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
678	#121	C₂³×C₇	1	4	yes	—
679	#121	C₂³×C₇	1	4	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	4	yes	—
684	#121	C₂³×C₇	1	4	yes	—
685	#121	C₂³×C₇	1	4	yes	—
686	#121	C₂³×C₇	1	8	yes	—
687	#121	C₂³×C₇	1	8	yes	—
688	#121	C₂³×C₇	1	8	yes	—
689	#121	C₂³×C₇	1	8	yes	—
690	#121	C₂³×C₇	1	16	yes	—
691	#121	C₂³×C₇	1	16	yes	—
692	#121	C₂³×C₇	1	8	yes	complemented
693	#121	C₂³×C₇	1	16	yes	complemented
694	#120	C₂³×C₇	1	8	yes	—
695	#120	C₂³×C₇	1	8	yes	—
696	#120	C₂³×C₇	1	8	yes	—
697	#120	C₂³×C₇	1	8	yes	—
698	#120	C₂³×C₇	1	16	yes	—
699	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
700	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
701	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
702	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
703	C₄×D₄	C₂³×C₇	1	8	yes	—
704	C₄×D₄	C₂³×C₇	1	8	yes	—
705	C₄×D₄	C₂³×C₇	1	8	yes	—
706	C₄×D₄	C₂³×C₇	1	8	yes	—
707	C₄×D₄	C₂³×C₇	1	8	yes	—
708	C₄×D₄	C₂³×C₇	1	8	yes	—
709	C₄×D₄	C₂³×C₇	1	8	yes	—
710	C₄×D₄	C₂³×C₇	1	8	yes	—
711	C₄×D₄	C₂³×C₇	1	16	yes	—
712	C₄×D₄	C₂³×C₇	1	16	yes	—
713	C₄×D₄	C₂³×C₇	1	16	yes	—
714	C₄×D₄	C₂³×C₇	1	16	yes	—
715	C₄×D₄	C₂³×C₇	1	16	yes	—
716	C₄×D₄	C₂³×C₇	1	16	yes	—
717	C₄×D₄	C₂³×C₇	1	16	yes	complemented
718	C₄×D₄	C₂³×C₇	1	8	yes	complemented
719	#117	C₂³×C₇	1	4	yes	—
720	#117	C₂³×C₇	1	4	yes	—
721	#117	C₂³×C₇	1	4	yes	—
722	#117	C₂³×C₇	1	4	yes	—
723	#117	C₂³×C₇	1	16	yes	—
724	#117	C₂³×C₇	1	8	yes	—
725	#117	C₂³×C₇	1	8	yes	—
726	#117	C₂³×C₇	1	8	yes	complemented
727	#117	C₂³×C₇	1	16	yes	complemented
728	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
730	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
731	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
732	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
733	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
734	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
735	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
736	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
738	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
739	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
740	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
741	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
742	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
752	C₂×C₄²	C₂³×C₇	1	4	yes	—
753	C₂²×C₇	—	2	8	no	—
754	C₂²×C₇	—	2	1	no	—
755	C₂²×C₇	—	2	1	no	—
756	C₂²×C₇	—	2	2	no	—
757	C₂²×C₇	—	2	1	no	—
758	C₂²×C₇	—	2	1	no	—
759	C₂²×C₇	—	2	1	no	—
760	C₂²×C₇	—	2	1	no	—
761	C₂²×C₇	—	2	2	no	—
762	C₂²×C₇	—	2	2	no	—
763	C₂²×C₇	—	2	8	no	—
764	C₂²×C₇	—	2	8	no	—
765	C₂²×C₇	—	2	2	no	—
766	C₂²×C₇	—	2	8	no	—
767	C₂²×C₇	—	2	2	no	—
768	C₂²×C₇	—	4	4	no	—
769	C₂²×C₇	—	4	8	no	—
770	C₂²×C₇	—	4	8	no	—
771	C₂²×C₇	—	4	4	no	—
772	C₂²×C₇	—	8	8	no	—
773	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
774	C₂²×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
775	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
776	C₂²×C₇	#585	1	2	yes	—
777	C₂²×C₇	C₂⁶	1	1	yes	characteristic
778	C₄×C₇	—	2	2	no	—
779	C₄×C₇	—	2	2	no	—
780	C₄×C₇	—	2	2	no	—
781	C₄×C₇	—	2	8	no	—
782	C₄×C₇	—	2	8	no	—
783	C₄×C₇	—	2	8	no	—
784	C₄×C₇	—	2	8	no	—
785	C₄×C₇	—	2	8	no	—
786	C₄×C₇	C₂×H(5,𝔽₂)	1	4	yes	—
787	C₂⁴	—	2	4	no	—
788	C₂⁴	—	4	2	no	—
789	C₂⁴	—	4	2	no	—
790	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
791	C₂⁴	C₂⁴×C₇	1	2	yes	—
792	C₂⁴	C₂⁴×C₇	1	2	yes	—
793	C₂⁴	C₂⁴×C₇	1	4	yes	—
794	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
795	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
796	#41	—	2	16	no	—
797	#41	—	4	8	no	—
798	#41	—	4	8	no	—
799	#41	—	4	16	no	—
800	#41	—	4	16	no	—
801	#41	—	4	8	no	—
802	#41	—	4	16	no	—
803	C₂×Q₈	—	2	8	no	—
804	C₂×Q₈	—	4	4	no	—
805	C₂×Q₈	—	4	8	no	—
806	C₂×Q₈	—	4	8	no	—
807	C₂×Q₈	—	4	4	no	—
808	C₂×Q₈	—	4	16	no	—
809	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
810	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
811	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
812	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
813	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
814	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
815	C₂×D₄	—	2	16	no	—
816	C₂×D₄	—	4	4	no	—
817	C₂×D₄	—	4	8	no	—
818	C₂×D₄	—	4	8	no	—
819	C₂×D₄	C₂⁴×C₇	1	8	yes	—
820	C₂×D₄	C₂⁴×C₇	1	8	yes	—
821	C₂×D₄	C₂⁴×C₇	1	8	yes	—
822	C₂×D₄	C₂⁴×C₇	1	8	yes	—
823	C₂×D₄	C₂⁴×C₇	1	4	yes	—
824	C₂×D₄	C₂⁴×C₇	1	8	yes	—
825	C₂×D₄	C₂⁴×C₇	1	8	yes	—
826	C₂×D₄	C₂⁴×C₇	1	8	yes	—
827	C₂×D₄	C₂⁴×C₇	1	8	yes	—
828	C₂×D₄	C₂⁴×C₇	1	4	yes	—
829	C₂²×C₄	—	2	4	no	—
830	C₂²×C₄	—	2	8	no	—
831	C₂²×C₄	—	4	4	no	—
832	C₂²×C₄	—	4	4	no	—
833	C₂²×C₄	—	4	4	no	—
834	C₂²×C₄	—	4	4	no	—
835	C₂²×C₄	—	4	8	no	—
836	C₂²×C₄	—	4	4	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	4	no	—
839	C₂²×C₄	—	4	4	no	—
840	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
842	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
843	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
844	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
850	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
853	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
854	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
855	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
856	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
857	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
859	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
861	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
862	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
866	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
867	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
869	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
870	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
871	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
872	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
873	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
874	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
875	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
876	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
877	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
878	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
879	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
880	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
881	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
882	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
883	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
884	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
885	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
886	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
887	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
888	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
889	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
890	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
891	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
892	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
893	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
894	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
895	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
896	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
897	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
898	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
899	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
900	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
901	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
902	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
903	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
904	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
905	C₄²	C₂⁴×C₇	1	8	yes	—
906	C₄²	C₂⁴×C₇	1	8	yes	—
907	C₄²	C₂⁴×C₇	1	16	yes	—
908	C₄²	C₂⁴×C₇	1	16	yes	—
909	C₂×C₇	—	2	2	no	—
910	C₂×C₇	—	2	2	no	—
911	C₂×C₇	—	2	2	no	—
912	C₂×C₇	—	2	4	no	—
913	C₂×C₇	—	4	2	no	—
914	C₂×C₇	—	4	8	no	—
915	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
916	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
917	C₂×C₇	C₂×#585	1	1	yes	characteristic
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	4	no	—
922	C₂³	—	2	4	no	—
923	C₂³	—	2	4	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	4	no	—
926	C₂³	—	2	8	no	—
927	C₂³	—	4	1	no	—
928	C₂³	—	4	2	no	—
929	C₂³	—	4	1	no	—
930	C₂³	—	4	1	no	—
931	C₂³	—	4	2	no	—
932	C₂³	—	4	1	no	—
933	C₂³	—	4	4	no	—
934	C₂³	—	4	4	no	—
935	C₂³	—	4	16	no	—
936	C₂³	C₇×2₋¹⁺⁴	1	4	yes	complemented
937	C₂³	C₂⁵×C₇	1	2	yes	—
938	C₂³	C₂⁵×C₇	1	8	yes	—
939	C₂³	C₂⁵×C₇	1	1	yes	characteristic
940	C₂³	C₂⁵×C₇	1	2	yes	—
941	C₂³	C₂⁵×C₇	1	1	yes	characteristic
942	C₂³	C₂⁵×C₇	1	1	yes	characteristic
943	Q₈	—	2	16	no	—
944	Q₈	—	2	8	no	—
945	Q₈	—	4	8	no	—
946	Q₈	—	4	8	no	—
947	Q₈	—	4	4	no	—
948	Q₈	—	4	8	no	—
949	D₄	—	2	16	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	16	no	—
953	D₄	—	2	8	no	—
954	D₄	—	4	8	no	—
955	D₄	—	4	4	no	—
956	D₄	—	4	8	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	8	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	4	no	—
961	C₂×C₄	—	2	8	no	—
962	C₂×C₄	—	2	8	no	—
963	C₂×C₄	—	2	8	no	—
964	C₂×C₄	—	2	4	no	—
965	C₂×C₄	—	2	4	no	—
966	C₂×C₄	—	2	4	no	—
967	C₂×C₄	—	2	4	no	—
968	C₂×C₄	—	2	4	no	—
969	C₂×C₄	—	2	4	no	—
970	C₂×C₄	—	2	16	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	2	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	1	no	—
976	C₂×C₄	—	4	2	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	8	no	—
984	C₂×C₄	—	4	4	no	—
985	C₂×C₄	—	4	16	no	—
986	C₂×C₄	—	4	16	no	—
987	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
988	C₂×C₄	C₂⁵×C₇	1	8	yes	—
989	C₂×C₄	C₂⁵×C₇	1	8	yes	—
990	C₂×C₄	C₂⁵×C₇	1	2	yes	—
991	C₂×C₄	C₂⁵×C₇	1	8	yes	—
992	C₂×C₄	C₂⁵×C₇	1	8	yes	—
993	C₂×C₄	C₂⁵×C₇	1	8	yes	—
994	C₂×C₄	C₂⁵×C₇	1	2	yes	—
995	C₂×C₄	C₂⁵×C₇	1	2	yes	—
996	C₂×C₄	C₂⁵×C₇	1	2	yes	—
997	C₇	#62819	1	1	yes	characteristic, direct product factor, Sylow
998	C₂²	—	2	8	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	8	no	—
1009	C₂²	—	2	8	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	8	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	4	4	no	—
1014	C₂²	—	4	8	no	—
1015	C₂²	—	4	8	no	—
1016	C₂²	—	4	4	no	—
1017	C₂²	—	8	8	no	—
1018	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
1019	C₂²	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
1020	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
1021	C₂²	C₇×#585	1	2	yes	—
1022	C₂²	C₂⁶×C₇	1	1	yes	characteristic
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	8	no	—
1027	C₄	—	2	8	no	—
1028	C₄	—	2	8	no	—
1029	C₄	—	2	8	no	—
1030	C₄	—	2	8	no	—
1031	C₄	C₂×C₇×H(5,𝔽₂)	1	4	yes	—
1032	C₂	—	2	2	no	—
1033	C₂	—	2	2	no	—
1034	C₂	—	2	2	no	—
1035	C₂	—	2	4	no	—
1036	C₂	—	4	2	no	—
1037	C₂	—	4	8	no	—
1038	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1039	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1040	C₂	C₂×C₇×#585	1	1	yes	characteristic

	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×#3541	C₂	semidirect
2. C₇×#3538	C₂	semidirect
3. C₇×#3536	C₂	semidirect
4. C₇×#3535	C₂	semidirect
5. C₇×#3520	C₂	semidirect
6. C₇×#3505	C₂	semidirect
7. C₇×#3501	C₂	semidirect
8. C₇×#3495	C₂	semidirect
9. C₇×#3492	C₂	semidirect
10. C₇×#3492	C₂	semidirect
11. C₇×#3490	C₂	semidirect
12. C₇×#3489	C₂	semidirect
13. C₇×#3486	C₂	semidirect
14. C₂×C₇×#525	C₂	semidirect
15. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
16. C₂×C₇×2₋¹⁺⁴	C₂²	semidirect
17. C₂²×C₇×#41	C₂²	semidirect
18. C₂³×C₇×Q₈	C₂²	semidirect
20. C₇×#563	C₂²	semidirect
21. C₇×#562	C₂²	semidirect
22. C₇×#556	C₂²	semidirect
23. C₇×#554	C₂²	semidirect
24. C₇×#554	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
27. C₇×#553	C₂²	semidirect
28. C₇×#553	C₂²	semidirect
29. C₇×#552	C₂²	semidirect
30. C₇×#552	C₂²	semidirect
31. C₇×#552	C₂²	semidirect
32. C₇×#552	C₂²	semidirect
33. C₇×#551	C₂²	semidirect
34. C₇×#551	C₂²	semidirect
35. C₇×#551	C₂²	semidirect
36. C₇×D₄×Q₈	C₂²	semidirect
37. C₇×D₄×Q₈	C₂²	semidirect
38. C₇×D₄×Q₈	C₂²	semidirect
39. C₇×#548	C₂²	semidirect
40. C₇×#548	C₂²	semidirect
41. C₇×#548	C₂²	semidirect
42. C₇×#547	C₂²	semidirect
43. C₇×#547	C₂²	semidirect
44. C₇×#547	C₂²	semidirect
45. C₇×#546	C₂²	semidirect
46. C₇×#546	C₂²	semidirect
47. C₇×#546	C₂²	semidirect
48. C₇×#544	C₂²	semidirect
49. C₇×#544	C₂²	semidirect
50. C₇×#544	C₂²	semidirect
52. C₇×#543	C₂²	semidirect
53. C₇×#542	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×#539	C₂²	semidirect
60. C₇×#539	C₂²	semidirect
61. C₇×#538	C₂²	semidirect
62. C₇×#538	C₂²	semidirect
63. C₇×#538	C₂²	semidirect
64. C₇×#537	C₂²	semidirect
65. C₇×#537	C₂²	semidirect
66. C₇×#537	C₂²	semidirect
67. C₇×#536	C₂²	semidirect
68. C₇×#536	C₂²	semidirect
69. C₇×#536	C₂²	semidirect
71. C₇×#533	C₂²	semidirect
72. C₇×#529	C₂²	semidirect
77. C₇×#525	C₂²	semidirect
78. C₇×#525	C₂²	semidirect
79. C₇×#525	C₂²	semidirect
80. C₇×#525	C₂²	semidirect
81. C₇×#525	C₂²	semidirect
82. C₇×#525	C₂²	semidirect
83. C₇×#525	C₂²	semidirect
84. C₂×C₇×#123	C₂²	semidirect
87. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
88. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
89. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
90. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
91. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
92. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₇×#121	C₂²	semidirect
97. C₇×#520	C₂²	semidirect
98. C₇×#520	C₂²	semidirect
99. C₇×#519	C₂²	semidirect
102. C₂×C₄×C₇×D₄	C₂²	semidirect
103. C₂×C₇×#117	C₂²	semidirect
104. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
105. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
107. #62819	C₇	direct (N × H)
117. C₂×C₇×#41	C₂³	semidirect
124. C₂²×C₇×Q₈	C₂³	semidirect
141. C₇×C₄⋊Q₈	C₂³	semidirect
142. C₇×C₄⋊Q₈	C₂³	semidirect
143. C₇×C₄⋊Q₈	C₂³	semidirect
144. C₇×C₄⋊Q₈	C₂³	semidirect
147. C₇×#126	C₂³	semidirect
148. C₇×#126	C₂³	semidirect
149. C₇×#126	C₂³	semidirect
150. C₇×#125	C₂³	semidirect
151. C₇×#125	C₂³	semidirect
152. C₇×#125	C₂³	semidirect
153. C₇×#125	C₂³	semidirect
154. C₇×#125	C₂³	semidirect
157. C₇×#124	C₂³	semidirect
158. C₇×#124	C₂³	semidirect
168. C₇×#123	C₂³	semidirect
169. C₇×#123	C₂³	semidirect
170. C₇×#123	C₂³	semidirect
193. C₇×C₂²⋊Q₈	C₂³	semidirect
194. C₇×C₂²⋊Q₈	C₂³	semidirect
195. C₇×C₂²⋊Q₈	C₂³	semidirect
196. C₇×C₂²⋊Q₈	C₂³	semidirect
197. C₇×C₂²⋊Q₈	C₂³	semidirect
198. C₇×C₂²⋊Q₈	C₂³	semidirect
199. C₇×C₂²⋊Q₈	C₂³	semidirect
200. C₇×C₂²⋊Q₈	C₂³	semidirect
201. C₇×C₂²⋊Q₈	C₂³	semidirect
216. C₇×#121	C₂³	semidirect
217. C₇×#121	C₂³	semidirect
223. C₄×C₇×Q₈	C₂³	semidirect
224. C₄×C₇×Q₈	C₂³	semidirect
225. C₄×C₇×Q₈	C₂³	semidirect
226. C₄×C₇×Q₈	C₂³	semidirect
241. C₄×C₇×D₄	C₂³	semidirect
242. C₄×C₇×D₄	C₂³	semidirect
250. C₇×#117	C₂³	semidirect
251. C₇×#117	C₂³	semidirect
264. C₂×C₇×C₄⋊C₄	C₂³	semidirect
265. C₂×C₇×C₄⋊C₄	C₂³	semidirect
277. #3541	C₂×C₇	semidirect
278. #3538	C₂×C₇	semidirect
279. #3536	C₂×C₇	semidirect
280. #3535	C₂×C₇	semidirect
281. #3520	C₂×C₇	semidirect
282. #3505	C₂×C₇	semidirect
283. #3501	C₂×C₇	semidirect
284. #3495	C₂×C₇	semidirect
285. #3492	C₂×C₇	semidirect
286. #3492	C₂×C₇	semidirect
287. #3490	C₂×C₇	semidirect
288. #3489	C₂×C₇	semidirect
289. #3486	C₂×C₇	semidirect
290. C₂×#525	C₂×C₇	semidirect
291. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
414. C₂×2₋¹⁺⁴	C₂²×C₇	semidirect
415. C₂²×#41	C₂²×C₇	semidirect
416. C₂³×Q₈	C₂²×C₇	semidirect
418. #563	C₂²×C₇	semidirect
419. #562	C₂²×C₇	semidirect
420. #556	C₂²×C₇	semidirect
421. #554	C₂²×C₇	semidirect
422. #554	C₂²×C₇	semidirect
423. #554	C₂²×C₇	semidirect
424. #554	C₂²×C₇	semidirect
425. #553	C₂²×C₇	semidirect
426. #553	C₂²×C₇	semidirect
427. #552	C₂²×C₇	semidirect
428. #552	C₂²×C₇	semidirect
429. #552	C₂²×C₇	semidirect
430. #552	C₂²×C₇	semidirect
431. #551	C₂²×C₇	semidirect
432. #551	C₂²×C₇	semidirect
433. #551	C₂²×C₇	semidirect
434. D₄×Q₈	C₂²×C₇	semidirect
435. D₄×Q₈	C₂²×C₇	semidirect
436. D₄×Q₈	C₂²×C₇	semidirect
437. #548	C₂²×C₇	semidirect
438. #548	C₂²×C₇	semidirect
439. #548	C₂²×C₇	semidirect
440. #547	C₂²×C₇	semidirect
441. #547	C₂²×C₇	semidirect
442. #547	C₂²×C₇	semidirect
443. #546	C₂²×C₇	semidirect
444. #546	C₂²×C₇	semidirect
445. #546	C₂²×C₇	semidirect
446. #544	C₂²×C₇	semidirect
447. #544	C₂²×C₇	semidirect
448. #544	C₂²×C₇	semidirect
450. #543	C₂²×C₇	semidirect
451. #542	C₂²×C₇	semidirect
452. #542	C₂²×C₇	semidirect
453. #541	C₂²×C₇	semidirect
454. #539	C₂²×C₇	semidirect
455. #539	C₂²×C₇	semidirect
456. #539	C₂²×C₇	semidirect
457. #539	C₂²×C₇	semidirect
458. #539	C₂²×C₇	semidirect
459. #538	C₂²×C₇	semidirect
460. #538	C₂²×C₇	semidirect
461. #538	C₂²×C₇	semidirect
462. #537	C₂²×C₇	semidirect
463. #537	C₂²×C₇	semidirect
464. #537	C₂²×C₇	semidirect
465. #536	C₂²×C₇	semidirect
466. #536	C₂²×C₇	semidirect
467. #536	C₂²×C₇	semidirect
469. #533	C₂²×C₇	semidirect
470. #529	C₂²×C₇	semidirect
475. #525	C₂²×C₇	semidirect
476. #525	C₂²×C₇	semidirect
477. #525	C₂²×C₇	semidirect
478. #525	C₂²×C₇	semidirect
479. #525	C₂²×C₇	semidirect
480. #525	C₂²×C₇	semidirect
481. #525	C₂²×C₇	semidirect
482. C₂×#123	C₂²×C₇	semidirect
485. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
486. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
487. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
488. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
489. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
490. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
491. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
493. C₂×#121	C₂²×C₇	semidirect
495. #520	C₂²×C₇	semidirect
496. #520	C₂²×C₇	semidirect
497. #519	C₂²×C₇	semidirect
500. C₂×C₄×D₄	C₂²×C₇	semidirect
501. C₂×#117	C₂²×C₇	semidirect
502. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
503. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
523. C₂³×C₇	2₋¹⁺⁴	semidirect
593. C₂×#41	C₂³×C₇	semidirect
600. C₂²×Q₈	C₂³×C₇	semidirect
617. C₄⋊Q₈	C₂³×C₇	semidirect
618. C₄⋊Q₈	C₂³×C₇	semidirect
619. C₄⋊Q₈	C₂³×C₇	semidirect
620. C₄⋊Q₈	C₂³×C₇	semidirect
623. #126	C₂³×C₇	semidirect
624. #126	C₂³×C₇	semidirect
625. #126	C₂³×C₇	semidirect
626. #125	C₂³×C₇	semidirect
627. #125	C₂³×C₇	semidirect
628. #125	C₂³×C₇	semidirect
629. #125	C₂³×C₇	semidirect
630. #125	C₂³×C₇	semidirect
633. #124	C₂³×C₇	semidirect
634. #124	C₂³×C₇	semidirect
644. #123	C₂³×C₇	semidirect
645. #123	C₂³×C₇	semidirect
646. #123	C₂³×C₇	semidirect
669. C₂²⋊Q₈	C₂³×C₇	semidirect
670. C₂²⋊Q₈	C₂³×C₇	semidirect
671. C₂²⋊Q₈	C₂³×C₇	semidirect
672. C₂²⋊Q₈	C₂³×C₇	semidirect
673. C₂²⋊Q₈	C₂³×C₇	semidirect
674. C₂²⋊Q₈	C₂³×C₇	semidirect
675. C₂²⋊Q₈	C₂³×C₇	semidirect
676. C₂²⋊Q₈	C₂³×C₇	semidirect
677. C₂²⋊Q₈	C₂³×C₇	semidirect
692. #121	C₂³×C₇	semidirect
693. #121	C₂³×C₇	semidirect
699. C₄×Q₈	C₂³×C₇	semidirect
700. C₄×Q₈	C₂³×C₇	semidirect
701. C₄×Q₈	C₂³×C₇	semidirect
702. C₄×Q₈	C₂³×C₇	semidirect
717. C₄×D₄	C₂³×C₇	semidirect
718. C₄×D₄	C₂³×C₇	semidirect
726. #117	C₂³×C₇	semidirect
727. #117	C₂³×C₇	semidirect
740. C₂×C₄⋊C₄	C₂³×C₇	semidirect
741. C₂×C₄⋊C₄	C₂³×C₇	semidirect
936. C₂³	C₇×2₋¹⁺⁴	semidirect
997. C₇	#62819	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×#3541	2
C₇×#3538	2
C₇×#3536	2
C₇×#3535	2
C₇×#3520	2
C₇×#3505	2
C₇×#3501	2
C₇×#3495	2
C₇×#3492	2
C₇×#3490	2
C₇×#3489	2
C₇×#3486	2
C₂×C₇×#525	2
C₂²×C₇×C₂²⋊Q₈	2
#62819	7

Subgroups — C7×#62819 #13240035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62819 #13240035