Subgroups — C₇×#3562 #11744514

Order 896.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#562	C₂	1	2	yes	maximal, complemented
2	C₇×#560	C₂	1	2	yes	maximal, complemented
3	C₇×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#553	C₂	1	2	yes	maximal, complemented
6	C₇×#551	C₂	1	2	yes	maximal, complemented
7	C₇×#550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#540	C₂	1	2	yes	maximal, complemented
16	C₇×#539	C₂	1	2	yes	maximal, complemented
17	C₇×#538	C₂	1	2	yes	maximal, complemented
18	C₇×#538	C₂	1	2	yes	maximal, complemented
19	C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#41	C₂²	1	1	yes	characteristic
25	C₂×C₇×#41	C₂²	1	1	yes	characteristic
26	C₂×C₇×#41	C₂²	1	1	yes	characteristic
27	C₂×C₇×#41	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₇×D₄	C₂²	1	1	yes	characteristic
30	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₇×#127	C₂²	1	1	yes	characteristic
33	C₇×#127	C₂²	1	1	yes	characteristic
34	C₇×#127	C₂²	1	2	yes	complemented
35	C₇×#126	C₂²	1	1	yes	characteristic
36	C₇×#126	C₂²	1	2	yes	—
37	C₇×#126	C₂²	1	2	yes	—
38	C₇×#126	C₂²	1	2	yes	complemented
39	C₇×#126	C₂²	1	1	yes	characteristic, complemented
40	C₇×#126	C₂²	1	2	yes	complemented
41	C₇×#126	C₂²	1	2	yes	complemented
42	C₇×#125	C₂²	1	1	yes	characteristic, complemented
43	C₇×#125	C₂²	1	1	yes	characteristic, complemented
44	C₇×#125	C₂²	1	2	yes	complemented
45	C₇×#125	C₂²	1	2	yes	complemented
46	C₇×#124	C₂²	1	1	yes	characteristic
47	C₇×#124	C₂²	1	1	yes	characteristic
48	C₇×#124	C₂²	1	1	yes	characteristic
49	C₇×#124	C₂²	1	1	yes	characteristic
50	C₇×#124	C₂²	1	1	yes	characteristic
51	C₇×#124	C₂²	1	2	yes	—
52	C₇×#124	C₂²	1	1	yes	characteristic, complemented
53	C₇×#124	C₂²	1	2	yes	complemented
54	C₇×#124	C₂²	1	2	yes	complemented
55	C₇×#123	C₂²	1	1	yes	characteristic
56	C₇×#123	C₂²	1	2	yes	—
57	C₇×#123	C₂²	1	2	yes	—
58	C₇×#123	C₂²	1	2	yes	—
59	C₇×#123	C₂²	1	1	yes	characteristic, complemented
60	C₇×#123	C₂²	1	2	yes	complemented
61	C₇×#123	C₂²	1	2	yes	complemented
62	C₇×#123	C₂²	1	2	yes	complemented
63	C₇×#123	C₂²	1	2	yes	complemented
64	C₇×#123	C₂²	1	2	yes	complemented
65	C₇×#123	C₂²	1	2	yes	complemented
66	C₇×#123	C₂²	1	2	yes	complemented
67	C₇×#123	C₂²	1	2	yes	complemented
68	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
69	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
70	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
71	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
72	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
73	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
74	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₇×#121	C₂²	1	1	yes	characteristic
78	C₇×#121	C₂²	1	1	yes	characteristic
79	C₇×#121	C₂²	1	2	yes	—
80	C₇×#121	C₂²	1	2	yes	—
81	C₇×#121	C₂²	1	2	yes	—
82	C₇×#121	C₂²	1	2	yes	—
83	C₇×#121	C₂²	1	1	yes	characteristic
84	C₇×#121	C₂²	1	2	yes	—
85	C₇×#121	C₂²	1	2	yes	—
86	C₇×#121	C₂²	1	2	yes	complemented
87	C₇×#121	C₂²	1	2	yes	complemented
88	C₇×#121	C₂²	1	2	yes	complemented
89	C₇×#121	C₂²	1	2	yes	complemented
90	C₇×#121	C₂²	1	2	yes	complemented
91	C₇×#121	C₂²	1	1	yes	characteristic, complemented
92	C₇×#121	C₂²	1	2	yes	complemented
93	C₇×#121	C₂²	1	2	yes	complemented
94	C₇×#120	C₂²	1	2	yes	—
95	C₇×#120	C₂²	1	2	yes	—
96	C₇×#120	C₂²	1	2	yes	—
97	C₇×#120	C₂²	1	2	yes	—
98	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
103	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
104	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
106	C₄×C₇×D₄	C₂²	1	2	yes	complemented
107	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₇×D₄	C₂²	1	2	yes	complemented
109	C₄×C₇×D₄	C₂²	1	2	yes	complemented
110	C₄×C₇×D₄	C₂²	1	2	yes	complemented
111	C₄×C₇×D₄	C₂²	1	2	yes	complemented
112	C₄×C₇×D₄	C₂²	1	2	yes	complemented
113	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₇×D₄	C₂²	1	2	yes	complemented
115	C₇×#117	C₂²	1	1	yes	characteristic
116	C₇×#117	C₂²	1	1	yes	characteristic, complemented
117	C₇×#117	C₂²	1	2	yes	complemented
118	C₇×#117	C₂²	1	2	yes	complemented
119	C₂×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
120	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₂×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
123	#3562	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂⁴×C₇	C₂³	1	2	yes	—
125	C₇×#41	—	4	2	no	—
126	C₇×#41	—	4	2	no	—
127	C₇×#41	—	4	2	no	—
128	C₇×#41	—	4	2	no	—
129	C₂×C₇×Q₈	—	4	2	no	—
130	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
131	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
132	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
133	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
134	C₂×C₇×Q₈	C₂³	1	2	yes	—
135	C₂×C₇×D₄	—	4	2	no	—
136	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
137	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
138	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
139	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
140	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
141	C₂×C₇×D₄	C₂³	1	2	yes	—
142	C₂×C₇×D₄	C₂³	1	2	yes	—
143	C₂×C₇×D₄	C₂³	1	2	yes	—
144	C₂×C₇×D₄	C₂³	1	2	yes	—
145	C₂×C₇×D₄	C₂³	1	2	yes	—
146	C₂×C₇×D₄	C₂³	1	2	yes	—
147	C₂×C₇×D₄	C₂³	1	2	yes	—
148	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
149	C₂×C₇×D₄	C₂³	1	2	yes	—
150	C₂×C₇×D₄	C₂³	1	2	yes	—
151	C₂×C₇×D₄	C₂³	1	2	yes	—
152	C₂×C₇×D₄	C₂³	1	2	yes	—
153	C₂×C₇×D₄	C₂³	1	2	yes	—
154	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
156	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
159	C₂²×C₄×C₇	C₂³	1	2	yes	—
160	C₂²×C₄×C₇	C₂³	1	2	yes	—
161	C₂²×C₄×C₇	C₂³	1	2	yes	—
162	C₂²×C₄×C₇	C₂³	1	2	yes	—
163	C₂²×C₄×C₇	C₂³	1	2	yes	—
164	C₂²×C₄×C₇	C₂³	1	2	yes	—
165	C₂²×C₄×C₇	C₂³	1	2	yes	—
166	C₂²×C₄×C₇	C₂³	1	2	yes	—
167	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₇×C₄⋊C₄	C₂³	1	2	yes	—
169	C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₇×C₄⋊C₄	C₂³	1	2	yes	—
184	C₇×C₄⋊C₄	C₂³	1	2	yes	—
185	C₇×C₄⋊C₄	C₂³	1	2	yes	—
186	C₇×C₄⋊C₄	C₂³	1	2	yes	—
187	C₇×C₄⋊C₄	C₂³	1	2	yes	—
188	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₇×C₄⋊C₄	C₂³	1	2	yes	—
190	C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₄²×C₇	C₂³	1	1	yes	characteristic
221	C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₄²×C₇	C₂³	1	1	yes	characteristic
224	C₄²×C₇	C₂³	1	1	yes	characteristic
225	C₄²×C₇	C₂³	1	2	yes	—
226	C₄²×C₇	C₂³	1	1	yes	characteristic
227	C₄²×C₇	C₂³	1	2	yes	—
228	C₄²×C₇	C₂³	1	2	yes	—
229	#562	C₂×C₇	1	2	yes	complemented
230	#560	C₂×C₇	1	2	yes	complemented
231	#559	C₂×C₇	1	1	yes	characteristic, complemented
232	#556	C₂×C₇	1	1	yes	characteristic, complemented
233	#553	C₂×C₇	1	2	yes	complemented
234	#551	C₂×C₇	1	2	yes	complemented
235	#550	C₂×C₇	1	1	yes	characteristic, complemented
236	#548	C₂×C₇	1	1	yes	characteristic, complemented
237	#548	C₂×C₇	1	1	yes	characteristic, complemented
238	#547	C₂×C₇	1	1	yes	characteristic, complemented
239	#546	C₂×C₇	1	1	yes	characteristic, complemented
240	#546	C₂×C₇	1	1	yes	characteristic, complemented
241	#541	C₂×C₇	1	1	yes	characteristic, complemented
242	#540	C₂×C₇	1	1	yes	characteristic, complemented
243	#540	C₂×C₇	1	2	yes	complemented
244	#539	C₂×C₇	1	2	yes	complemented
245	#538	C₂×C₇	1	2	yes	complemented
246	#538	C₂×C₇	1	2	yes	complemented
247	#536	C₂×C₇	1	1	yes	characteristic, complemented
248	#535	C₂×C₇	1	1	yes	characteristic, complemented
249	#532	C₂×C₇	1	1	yes	characteristic, complemented
250	#529	C₂×C₇	1	1	yes	characteristic, complemented
251	#529	C₂×C₇	1	1	yes	characteristic, complemented
252	C₂³×C₇	—	4	2	no	—
253	C₂³×C₇	—	4	2	no	—
254	C₂³×C₇	—	4	2	no	—
255	C₂³×C₇	C₂⁴	1	1	yes	characteristic
256	C₂³×C₇	C₂⁴	1	2	yes	—
257	C₂³×C₇	C₂⁴	1	2	yes	—
258	C₂³×C₇	C₂⁴	1	1	yes	characteristic
259	C₂³×C₇	C₂⁴	1	1	yes	characteristic
260	C₂³×C₇	C₂⁴	1	2	yes	—
261	C₇×Q₈	—	2	2	no	—
262	C₇×Q₈	—	2	2	no	—
263	C₇×Q₈	—	2	2	no	—
264	C₇×Q₈	—	4	2	no	—
265	C₇×Q₈	—	4	1	no	—
266	C₇×D₄	—	2	2	no	—
267	C₇×D₄	—	2	2	no	—
268	C₇×D₄	—	2	2	no	—
269	C₇×D₄	—	4	2	no	—
270	C₇×D₄	—	4	1	no	—
271	C₇×D₄	—	4	2	no	—
272	C₇×D₄	—	4	2	no	—
273	C₇×D₄	—	4	2	no	—
274	C₇×D₄	—	4	2	no	—
275	C₇×D₄	—	4	2	no	—
276	C₇×D₄	—	4	1	no	—
277	C₇×D₄	—	4	2	no	—
278	C₇×D₄	—	4	1	no	—
279	C₇×D₄	—	4	2	no	—
280	C₇×D₄	—	4	2	no	—
281	C₇×D₄	—	4	2	no	—
282	C₇×D₄	—	4	2	no	—
283	C₇×D₄	—	4	2	no	—
284	C₂×C₄×C₇	—	2	2	no	—
285	C₂×C₄×C₇	—	2	2	no	—
286	C₂×C₄×C₇	—	2	2	no	—
287	C₂×C₄×C₇	—	4	2	no	—
288	C₂×C₄×C₇	—	4	1	no	—
289	C₂×C₄×C₇	—	4	2	no	—
290	C₂×C₄×C₇	—	4	2	no	—
291	C₂×C₄×C₇	—	4	1	no	—
292	C₂×C₄×C₇	—	4	2	no	—
293	C₂×C₄×C₇	—	4	2	no	—
294	C₂×C₄×C₇	—	4	2	no	—
295	C₂×C₄×C₇	—	4	2	no	—
296	C₂×C₄×C₇	—	4	2	no	—
297	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
298	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
300	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
302	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
303	C₂×C₄×C₇	C₂⁴	1	2	yes	—
304	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
305	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
306	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₂×C₄×C₇	C₂⁴	1	2	yes	—
308	C₂×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂×C₄×C₇	C₂⁴	1	2	yes	—
310	C₂×C₄×C₇	C₂⁴	1	2	yes	—
311	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
312	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
314	C₂×#41	C₂²×C₇	1	1	yes	characteristic
315	C₂×#41	C₂²×C₇	1	1	yes	characteristic
316	C₂×#41	C₂²×C₇	1	1	yes	characteristic
317	C₂×#41	C₂²×C₇	1	1	yes	characteristic, complemented
318	C₂²×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
319	C₂²×D₄	C₂²×C₇	1	1	yes	characteristic
320	C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
321	C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
322	#127	C₂²×C₇	1	1	yes	characteristic
323	#127	C₂²×C₇	1	1	yes	characteristic
324	#127	C₂²×C₇	1	2	yes	complemented
325	#126	C₂²×C₇	1	1	yes	characteristic
326	#126	C₂²×C₇	1	2	yes	—
327	#126	C₂²×C₇	1	2	yes	—
328	#126	C₂²×C₇	1	2	yes	complemented
329	#126	C₂²×C₇	1	1	yes	characteristic, complemented
330	#126	C₂²×C₇	1	2	yes	complemented
331	#126	C₂²×C₇	1	2	yes	complemented
332	#125	C₂²×C₇	1	1	yes	characteristic, complemented
333	#125	C₂²×C₇	1	1	yes	characteristic, complemented
334	#125	C₂²×C₇	1	2	yes	complemented
335	#125	C₂²×C₇	1	2	yes	complemented
336	#124	C₂²×C₇	1	1	yes	characteristic
337	#124	C₂²×C₇	1	1	yes	characteristic
338	#124	C₂²×C₇	1	1	yes	characteristic
339	#124	C₂²×C₇	1	1	yes	characteristic
340	#124	C₂²×C₇	1	1	yes	characteristic
341	#124	C₂²×C₇	1	2	yes	—
342	#124	C₂²×C₇	1	1	yes	characteristic, complemented
343	#124	C₂²×C₇	1	2	yes	complemented
344	#124	C₂²×C₇	1	2	yes	complemented
345	#123	C₂²×C₇	1	1	yes	characteristic
346	#123	C₂²×C₇	1	2	yes	—
347	#123	C₂²×C₇	1	2	yes	—
348	#123	C₂²×C₇	1	2	yes	—
349	#123	C₂²×C₇	1	1	yes	characteristic, complemented
350	#123	C₂²×C₇	1	2	yes	complemented
351	#123	C₂²×C₇	1	2	yes	complemented
352	#123	C₂²×C₇	1	2	yes	complemented
353	#123	C₂²×C₇	1	2	yes	complemented
354	#123	C₂²×C₇	1	2	yes	complemented
355	#123	C₂²×C₇	1	2	yes	complemented
356	#123	C₂²×C₇	1	2	yes	complemented
357	#123	C₂²×C₇	1	2	yes	complemented
358	C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
359	C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
360	C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
361	C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
362	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
363	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
364	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
365	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
366	C₂²⋊Q₈	C₂²×C₇	1	2	yes	complemented
367	#121	C₂²×C₇	1	1	yes	characteristic
368	#121	C₂²×C₇	1	1	yes	characteristic
369	#121	C₂²×C₇	1	2	yes	—
370	#121	C₂²×C₇	1	2	yes	—
371	#121	C₂²×C₇	1	2	yes	—
372	#121	C₂²×C₇	1	2	yes	—
373	#121	C₂²×C₇	1	1	yes	characteristic
374	#121	C₂²×C₇	1	2	yes	—
375	#121	C₂²×C₇	1	2	yes	—
376	#121	C₂²×C₇	1	2	yes	complemented
377	#121	C₂²×C₇	1	2	yes	complemented
378	#121	C₂²×C₇	1	2	yes	complemented
379	#121	C₂²×C₇	1	2	yes	complemented
380	#121	C₂²×C₇	1	2	yes	complemented
381	#121	C₂²×C₇	1	1	yes	characteristic, complemented
382	#121	C₂²×C₇	1	2	yes	complemented
383	#121	C₂²×C₇	1	2	yes	complemented
384	#120	C₂²×C₇	1	2	yes	—
385	#120	C₂²×C₇	1	2	yes	—
386	#120	C₂²×C₇	1	2	yes	—
387	#120	C₂²×C₇	1	2	yes	—
388	C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
389	C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
390	C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
391	C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
392	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
393	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
394	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
395	C₄×D₄	C₂²×C₇	1	1	yes	characteristic
396	C₄×D₄	C₂²×C₇	1	2	yes	complemented
397	C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
398	C₄×D₄	C₂²×C₇	1	2	yes	complemented
399	C₄×D₄	C₂²×C₇	1	2	yes	complemented
400	C₄×D₄	C₂²×C₇	1	2	yes	complemented
401	C₄×D₄	C₂²×C₇	1	2	yes	complemented
402	C₄×D₄	C₂²×C₇	1	2	yes	complemented
403	C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
404	C₄×D₄	C₂²×C₇	1	2	yes	complemented
405	#117	C₂²×C₇	1	1	yes	characteristic
406	#117	C₂²×C₇	1	1	yes	characteristic, complemented
407	#117	C₂²×C₇	1	2	yes	complemented
408	#117	C₂²×C₇	1	2	yes	complemented
409	C₂×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
410	C₂×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
412	C₂×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	—	2	1	no	—
415	C₂²×C₇	—	2	1	no	—
416	C₂²×C₇	—	2	2	no	—
417	C₂²×C₇	—	2	2	no	—
418	C₂²×C₇	—	2	2	no	—
419	C₂²×C₇	—	2	1	no	—
420	C₂²×C₇	—	2	1	no	—
421	C₂²×C₇	—	2	2	no	—
422	C₂²×C₇	—	2	2	no	—
423	C₂²×C₇	—	2	2	no	—
424	C₂²×C₇	—	2	1	no	—
425	C₂²×C₇	—	2	1	no	—
426	C₂²×C₇	—	2	2	no	—
427	C₂²×C₇	—	2	2	no	—
428	C₂²×C₇	—	2	2	no	—
429	C₂²×C₇	—	2	1	no	—
430	C₂²×C₇	—	2	1	no	—
431	C₂²×C₇	—	8	4	no	—
432	C₂²×C₇	C₂⁵	1	1	yes	characteristic
433	C₄×C₇	—	2	1	no	—
434	C₄×C₇	—	2	1	no	—
435	C₄×C₇	—	2	1	no	—
436	C₄×C₇	—	2	2	no	—
437	C₄×C₇	—	2	2	no	—
438	C₄×C₇	—	2	2	no	—
439	C₄×C₇	—	2	1	no	—
440	C₄×C₇	—	2	2	no	—
441	C₄×C₇	—	2	1	no	—
442	C₄×C₇	—	2	1	no	—
443	C₄×C₇	—	2	1	no	—
444	C₄×C₇	—	2	2	no	—
445	C₄×C₇	—	2	1	no	—
446	C₄×C₇	—	2	1	no	—
447	C₄×C₇	—	2	1	no	—
448	C₄×C₇	—	2	1	no	—
449	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
450	C₂⁴	C₂³×C₇	1	2	yes	—
451	#41	—	4	2	no	—
452	#41	—	4	2	no	—
453	#41	—	4	2	no	—
454	#41	—	4	2	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	C₂³×C₇	1	1	yes	characteristic
457	C₂×Q₈	C₂³×C₇	1	1	yes	characteristic
458	C₂×Q₈	C₂³×C₇	1	1	yes	characteristic
459	C₂×Q₈	C₂³×C₇	1	1	yes	characteristic
460	C₂×Q₈	C₂³×C₇	1	2	yes	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
463	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
464	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
465	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
466	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
467	C₂×D₄	C₂³×C₇	1	2	yes	—
468	C₂×D₄	C₂³×C₇	1	2	yes	—
469	C₂×D₄	C₂³×C₇	1	2	yes	—
470	C₂×D₄	C₂³×C₇	1	2	yes	—
471	C₂×D₄	C₂³×C₇	1	2	yes	—
472	C₂×D₄	C₂³×C₇	1	2	yes	—
473	C₂×D₄	C₂³×C₇	1	2	yes	—
474	C₂×D₄	C₂³×C₇	1	1	yes	characteristic
475	C₂×D₄	C₂³×C₇	1	2	yes	—
476	C₂×D₄	C₂³×C₇	1	2	yes	—
477	C₂×D₄	C₂³×C₇	1	2	yes	—
478	C₂×D₄	C₂³×C₇	1	2	yes	—
479	C₂×D₄	C₂³×C₇	1	2	yes	—
480	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
481	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
482	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
483	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
484	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
485	C₂²×C₄	C₂³×C₇	1	2	yes	—
486	C₂²×C₄	C₂³×C₇	1	2	yes	—
487	C₂²×C₄	C₂³×C₇	1	2	yes	—
488	C₂²×C₄	C₂³×C₇	1	2	yes	—
489	C₂²×C₄	C₂³×C₇	1	2	yes	—
490	C₂²×C₄	C₂³×C₇	1	2	yes	—
491	C₂²×C₄	C₂³×C₇	1	2	yes	—
492	C₂²×C₄	C₂³×C₇	1	2	yes	—
493	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
494	C₄⋊C₄	C₂³×C₇	1	2	yes	—
495	C₄⋊C₄	C₂³×C₇	1	2	yes	—
496	C₄⋊C₄	C₂³×C₇	1	2	yes	—
497	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
499	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
500	C₄⋊C₄	C₂³×C₇	1	2	yes	—
501	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
502	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
503	C₄⋊C₄	C₂³×C₇	1	2	yes	—
504	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
506	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
508	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
509	C₄⋊C₄	C₂³×C₇	1	2	yes	—
510	C₄⋊C₄	C₂³×C₇	1	2	yes	—
511	C₄⋊C₄	C₂³×C₇	1	2	yes	—
512	C₄⋊C₄	C₂³×C₇	1	2	yes	—
513	C₄⋊C₄	C₂³×C₇	1	2	yes	—
514	C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
515	C₄⋊C₄	C₂³×C₇	1	2	yes	—
516	C₄⋊C₄	C₂³×C₇	1	2	yes	—
517	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
518	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
519	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
520	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
521	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
522	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
523	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
524	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
525	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
526	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
527	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
528	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
529	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
530	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
531	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
532	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
533	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
534	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
535	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
536	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
537	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
538	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
539	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
540	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
541	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
542	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
543	C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
544	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
545	C₂²⋊C₄	C₂³×C₇	1	2	yes	—
546	C₄²	C₂³×C₇	1	1	yes	characteristic
547	C₄²	C₂³×C₇	1	1	yes	characteristic
548	C₄²	C₂³×C₇	1	1	yes	characteristic
549	C₄²	C₂³×C₇	1	1	yes	characteristic
550	C₄²	C₂³×C₇	1	1	yes	characteristic
551	C₄²	C₂³×C₇	1	2	yes	—
552	C₄²	C₂³×C₇	1	1	yes	characteristic
553	C₄²	C₂³×C₇	1	2	yes	—
554	C₄²	C₂³×C₇	1	2	yes	—
555	C₂×C₇	—	4	1	no	—
556	C₂×C₇	—	4	1	no	—
557	C₂×C₇	—	4	2	no	—
558	C₂×C₇	—	4	2	no	—
559	C₂×C₇	—	4	2	no	—
560	C₂×C₇	—	4	1	no	—
561	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂×C₇	#585	1	1	yes	characteristic
563	C₂×C₇	#585	1	1	yes	characteristic
564	C₂³	—	4	2	no	—
565	C₂³	—	4	2	no	—
566	C₂³	—	4	2	no	—
567	C₂³	C₂⁴×C₇	1	1	yes	characteristic
568	C₂³	C₂⁴×C₇	1	2	yes	—
569	C₂³	C₂⁴×C₇	1	2	yes	—
570	C₂³	C₂⁴×C₇	1	1	yes	characteristic
571	C₂³	C₂⁴×C₇	1	1	yes	characteristic
572	C₂³	C₂⁴×C₇	1	2	yes	—
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	4	2	no	—
577	Q₈	—	4	1	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
610	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
611	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
612	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
613	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
614	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
615	C₂×C₄	C₂⁴×C₇	1	2	yes	—
616	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
617	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
618	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
619	C₂×C₄	C₂⁴×C₇	1	2	yes	—
620	C₂×C₄	C₂⁴×C₇	1	2	yes	—
621	C₂×C₄	C₂⁴×C₇	1	2	yes	—
622	C₂×C₄	C₂⁴×C₇	1	2	yes	—
623	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
624	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
625	C₂×C₄	C₂⁴×C₇	1	1	yes	characteristic
626	C₇	#3562	1	1	yes	characteristic, direct product factor, Sylow
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	8	4	no	—
646	C₂²	C₂⁵×C₇	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	C₇×H(5,𝔽₂)	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	1	no	—
668	C₂	—	4	1	no	—
669	C₂	—	4	2	no	—
670	C₂	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂	C₇×#585	1	1	yes	characteristic
672	C₂	C₇×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×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×#562	C₂	semidirect
2. C₇×#560	C₂	semidirect
3. C₇×#559	C₂	semidirect
4. C₇×#556	C₂	semidirect
5. C₇×#553	C₂	semidirect
6. C₇×#551	C₂	semidirect
7. C₇×#550	C₂	semidirect
8. C₇×#548	C₂	semidirect
9. C₇×#548	C₂	semidirect
10. C₇×#547	C₂	semidirect
11. C₇×#546	C₂	semidirect
12. C₇×#546	C₂	semidirect
13. C₇×#541	C₂	semidirect
14. C₇×#540	C₂	semidirect
15. C₇×#540	C₂	semidirect
16. C₇×#539	C₂	semidirect
17. C₇×#538	C₂	semidirect
18. C₇×#538	C₂	semidirect
19. C₇×#536	C₂	semidirect
20. C₇×#535	C₂	semidirect
21. C₇×#532	C₂	semidirect
22. C₇×#529	C₂	semidirect
23. C₇×#529	C₂	semidirect
27. C₂×C₇×#41	C₂²	semidirect
28. C₂²×C₇×Q₈	C₂²	semidirect
30. C₇×C₄⋊Q₈	C₂²	semidirect
31. C₇×C₄⋊Q₈	C₂²	semidirect
34. C₇×#127	C₂²	semidirect
38. C₇×#126	C₂²	semidirect
39. C₇×#126	C₂²	semidirect
40. C₇×#126	C₂²	semidirect
41. C₇×#126	C₂²	semidirect
42. C₇×#125	C₂²	semidirect
43. C₇×#125	C₂²	semidirect
44. C₇×#125	C₂²	semidirect
45. C₇×#125	C₂²	semidirect
52. C₇×#124	C₂²	semidirect
53. C₇×#124	C₂²	semidirect
54. C₇×#124	C₂²	semidirect
59. C₇×#123	C₂²	semidirect
60. C₇×#123	C₂²	semidirect
61. C₇×#123	C₂²	semidirect
62. C₇×#123	C₂²	semidirect
63. C₇×#123	C₂²	semidirect
64. C₇×#123	C₂²	semidirect
65. C₇×#123	C₂²	semidirect
66. C₇×#123	C₂²	semidirect
67. C₇×#123	C₂²	semidirect
70. C₇×C₂²⋊Q₈	C₂²	semidirect
71. C₇×C₂²⋊Q₈	C₂²	semidirect
72. C₇×C₂²⋊Q₈	C₂²	semidirect
73. C₇×C₂²⋊Q₈	C₂²	semidirect
74. C₇×C₂²⋊Q₈	C₂²	semidirect
75. C₇×C₂²⋊Q₈	C₂²	semidirect
76. C₇×C₂²⋊Q₈	C₂²	semidirect
86. C₇×#121	C₂²	semidirect
87. C₇×#121	C₂²	semidirect
88. C₇×#121	C₂²	semidirect
89. C₇×#121	C₂²	semidirect
90. C₇×#121	C₂²	semidirect
91. C₇×#121	C₂²	semidirect
92. C₇×#121	C₂²	semidirect
93. C₇×#121	C₂²	semidirect
98. C₄×C₇×Q₈	C₂²	semidirect
99. C₄×C₇×Q₈	C₂²	semidirect
100. C₄×C₇×Q₈	C₂²	semidirect
101. C₄×C₇×Q₈	C₂²	semidirect
106. C₄×C₇×D₄	C₂²	semidirect
107. C₄×C₇×D₄	C₂²	semidirect
108. C₄×C₇×D₄	C₂²	semidirect
109. C₄×C₇×D₄	C₂²	semidirect
110. C₄×C₇×D₄	C₂²	semidirect
111. C₄×C₇×D₄	C₂²	semidirect
112. C₄×C₇×D₄	C₂²	semidirect
113. C₄×C₇×D₄	C₂²	semidirect
114. C₄×C₇×D₄	C₂²	semidirect
116. C₇×#117	C₂²	semidirect
117. C₇×#117	C₂²	semidirect
118. C₇×#117	C₂²	semidirect
119. C₂×C₇×C₄⋊C₄	C₂²	semidirect
122. C₂×C₄²×C₇	C₂²	semidirect
123. #3562	C₇	direct (N × H)
229. #562	C₂×C₇	semidirect
230. #560	C₂×C₇	semidirect
231. #559	C₂×C₇	semidirect
232. #556	C₂×C₇	semidirect
233. #553	C₂×C₇	semidirect
234. #551	C₂×C₇	semidirect
235. #550	C₂×C₇	semidirect
236. #548	C₂×C₇	semidirect
237. #548	C₂×C₇	semidirect
238. #547	C₂×C₇	semidirect
239. #546	C₂×C₇	semidirect
240. #546	C₂×C₇	semidirect
241. #541	C₂×C₇	semidirect
242. #540	C₂×C₇	semidirect
243. #540	C₂×C₇	semidirect
244. #539	C₂×C₇	semidirect
245. #538	C₂×C₇	semidirect
246. #538	C₂×C₇	semidirect
247. #536	C₂×C₇	semidirect
248. #535	C₂×C₇	semidirect
249. #532	C₂×C₇	semidirect
250. #529	C₂×C₇	semidirect
251. #529	C₂×C₇	semidirect
317. C₂×#41	C₂²×C₇	semidirect
318. C₂²×Q₈	C₂²×C₇	semidirect
320. C₄⋊Q₈	C₂²×C₇	semidirect
321. C₄⋊Q₈	C₂²×C₇	semidirect
324. #127	C₂²×C₇	semidirect
328. #126	C₂²×C₇	semidirect
329. #126	C₂²×C₇	semidirect
330. #126	C₂²×C₇	semidirect
331. #126	C₂²×C₇	semidirect
332. #125	C₂²×C₇	semidirect
333. #125	C₂²×C₇	semidirect
334. #125	C₂²×C₇	semidirect
335. #125	C₂²×C₇	semidirect
342. #124	C₂²×C₇	semidirect
343. #124	C₂²×C₇	semidirect
344. #124	C₂²×C₇	semidirect
349. #123	C₂²×C₇	semidirect
350. #123	C₂²×C₇	semidirect
351. #123	C₂²×C₇	semidirect
352. #123	C₂²×C₇	semidirect
353. #123	C₂²×C₇	semidirect
354. #123	C₂²×C₇	semidirect
355. #123	C₂²×C₇	semidirect
356. #123	C₂²×C₇	semidirect
357. #123	C₂²×C₇	semidirect
360. C₂²⋊Q₈	C₂²×C₇	semidirect
361. C₂²⋊Q₈	C₂²×C₇	semidirect
362. C₂²⋊Q₈	C₂²×C₇	semidirect
363. C₂²⋊Q₈	C₂²×C₇	semidirect
364. C₂²⋊Q₈	C₂²×C₇	semidirect
365. C₂²⋊Q₈	C₂²×C₇	semidirect
366. C₂²⋊Q₈	C₂²×C₇	semidirect
376. #121	C₂²×C₇	semidirect
377. #121	C₂²×C₇	semidirect
378. #121	C₂²×C₇	semidirect
379. #121	C₂²×C₇	semidirect
380. #121	C₂²×C₇	semidirect
381. #121	C₂²×C₇	semidirect
382. #121	C₂²×C₇	semidirect
383. #121	C₂²×C₇	semidirect
388. C₄×Q₈	C₂²×C₇	semidirect
389. C₄×Q₈	C₂²×C₇	semidirect
390. C₄×Q₈	C₂²×C₇	semidirect
391. C₄×Q₈	C₂²×C₇	semidirect
396. C₄×D₄	C₂²×C₇	semidirect
397. C₄×D₄	C₂²×C₇	semidirect
398. C₄×D₄	C₂²×C₇	semidirect
399. C₄×D₄	C₂²×C₇	semidirect
400. C₄×D₄	C₂²×C₇	semidirect
401. C₄×D₄	C₂²×C₇	semidirect
402. C₄×D₄	C₂²×C₇	semidirect
403. C₄×D₄	C₂²×C₇	semidirect
404. C₄×D₄	C₂²×C₇	semidirect
406. #117	C₂²×C₇	semidirect
407. #117	C₂²×C₇	semidirect
408. #117	C₂²×C₇	semidirect
409. C₂×C₄⋊C₄	C₂²×C₇	semidirect
412. C₂×C₄²	C₂²×C₇	semidirect
626. C₇	#3562	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×#562	2
C₇×#560	2
C₇×#559	2
C₇×#556	2
C₇×#553	2
C₇×#551	2
C₇×#550	2
C₇×#548	2
C₇×#547	2
C₇×#546	2
C₇×#541	2
C₇×#540	2
C₇×#539	2
C₇×#538	2
C₇×#536	2
C₇×#535	2
C₇×#532	2
C₇×#529	2
#3562	7

Subgroups — C7×#3562 #11744514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#3562 #11744514