Subgroups — C₇×#35050 #13212266

Order 1792.

4146 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2849	C₂	1	2	yes	maximal, complemented
4	C₇×#2846	C₂	1	2	yes	maximal, complemented
5	C₇×#2626	C₂	1	2	yes	maximal, complemented
6	C₇×#2617	C₂	1	2	yes	maximal, complemented
7	C₇×#2561	C₂	1	2	yes	maximal, complemented
8	C₇×#2539	C₂	1	2	yes	maximal, complemented
9	C₇×#2534	C₂	1	4	yes	maximal, complemented
10	C₇×#2482	C₂	1	2	yes	maximal, complemented
11	C₇×#2411	C₂	1	4	yes	maximal, complemented
12	C₇×#2404	C₂	1	2	yes	maximal, complemented
13	C₇×#2321	C₂	1	4	yes	maximal, complemented
14	C₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁶×C₇	C₂²	1	1	yes	characteristic
16	C₂²×C₇×#41	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₇×#525	—	2	8	no	—
20	C₂×C₇×#123	C₂²	1	2	yes	complemented
21	C₂×C₇×#123	C₂²	1	4	yes	complemented
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₇×#120	C₂²	1	2	yes	—
27	C₂×C₇×#120	C₂²	1	4	yes	—
28	C₂×C₇×#120	C₂²	1	4	yes	—
29	C₂×C₇×#120	C₂²	1	4	yes	—
30	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
32	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₇×#117	C₂²	1	2	yes	complemented
34	C₂²×C₇×C₂²⋊C₄	—	2	8	no	—
35	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₇×#399	C₂²	1	4	yes	complemented
42	C₇×#397	C₂²	1	4	yes	complemented
43	C₇×#396	C₂²	1	8	yes	complemented
44	C₇×#394	C₂²	1	8	yes	complemented
45	C₇×#393	C₂²	1	4	yes	complemented
46	C₇×#392	C₂²	1	4	yes	complemented
47	C₇×#390	C₂²	1	8	yes	complemented
48	C₇×#388	C₂²	1	8	yes	complemented
49	C₇×#388	C₂²	1	8	yes	complemented
50	C₇×#386	C₂²	1	8	yes	complemented
51	C₇×#386	C₂²	1	4	yes	complemented
52	C₇×#386	C₂²	1	4	yes	complemented
53	C₇×#385	C₂²	1	4	yes	complemented
54	C₇×#385	C₂²	1	4	yes	complemented
55	C₇×#381	C₂²	1	2	yes	complemented
56	C₇×#381	C₂²	1	4	yes	complemented
57	C₇×#380	C₂²	1	2	yes	complemented
58	C₇×#380	C₂²	1	2	yes	complemented
59	C₇×#379	C₂²	1	4	yes	—
60	C₇×#379	C₂²	1	4	yes	—
61	C₇×#379	C₂²	1	2	yes	—
62	C₇×#379	C₂²	1	4	yes	—
63	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
64	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
65	#35050	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁵×C₇	—	2	4	no	—
67	C₂⁵×C₇	—	2	8	no	—
68	C₂⁵×C₇	—	4	4	no	—
69	C₂⁵×C₇	—	4	4	no	—
70	C₂⁵×C₇	C₂³	1	1	yes	characteristic
71	C₂⁵×C₇	C₂³	1	2	yes	—
72	C₂⁵×C₇	C₂³	1	2	yes	—
73	C₂⁵×C₇	C₂³	1	2	yes	—
74	C₂×C₇×#41	—	2	4	no	—
75	C₂×C₇×#41	—	4	4	no	—
76	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic, complemented
77	C₂²×C₇×D₄	C₂³	1	2	yes	—
78	C₂²×C₇×D₄	C₂³	1	2	yes	—
79	C₂²×C₇×D₄	C₂³	1	2	yes	—
80	C₂²×C₇×D₄	C₂³	1	8	yes	—
81	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic, complemented
82	C₂³×C₄×C₇	—	2	4	no	—
83	C₂³×C₄×C₇	—	4	4	no	—
84	C₂³×C₄×C₇	—	4	4	no	—
85	C₂³×C₄×C₇	D₄	1	8	yes	complemented
86	C₂³×C₄×C₇	C₂³	1	2	yes	—
87	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₇	C₂³	1	2	yes	—
91	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₇	C₂³	1	2	yes	complemented
96	C₇×#123	—	2	8	no	—
97	C₇×#123	—	4	8	no	—
98	C₇×C₂²⋊Q₈	—	2	4	no	—
99	C₇×C₂²⋊Q₈	—	2	4	no	—
100	C₇×#121	—	2	4	no	—
101	C₇×#121	—	2	4	no	—
102	C₇×#120	—	2	8	no	—
103	C₇×#120	—	2	16	no	—
104	C₇×#120	—	4	8	no	—
105	C₇×#120	—	4	8	no	—
106	C₄×C₇×D₄	—	2	8	no	—
107	C₄×C₇×D₄	—	2	8	no	—
108	C₇×#117	—	2	4	no	—
109	C₇×#117	—	4	4	no	—
110	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
111	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
112	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	complemented
113	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	complemented
114	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
115	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
116	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
118	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
119	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
120	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
121	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
122	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
133	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
134	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
135	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	complemented
136	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	complemented
137	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	complemented
138	C₂×C₄²×C₇	C₂³	1	2	yes	complemented
139	C₂×C₄²×C₇	C₂³	1	4	yes	complemented
140	C₇×#95	C₂³	1	4	yes	complemented
141	C₇×#95	C₂³	1	4	yes	complemented
142	C₇×#95	C₂³	1	8	yes	complemented
143	C₇×#95	C₂³	1	8	yes	complemented
144	C₂×#525	C₂×C₇	1	1	yes	characteristic, complemented
145	C₂³×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
146	#2849	C₂×C₇	1	2	yes	complemented
147	#2846	C₂×C₇	1	2	yes	complemented
148	#2626	C₂×C₇	1	2	yes	complemented
149	#2617	C₂×C₇	1	2	yes	complemented
150	#2561	C₂×C₇	1	2	yes	complemented
151	#2539	C₂×C₇	1	2	yes	complemented
152	#2534	C₂×C₇	1	4	yes	complemented
153	#2482	C₂×C₇	1	2	yes	complemented
154	#2411	C₂×C₇	1	4	yes	complemented
155	#2404	C₂×C₇	1	2	yes	complemented
156	#2321	C₂×C₇	1	4	yes	complemented
157	#2280	C₂×C₇	1	1	yes	characteristic, complemented
158	C₂⁴×C₇	—	2	4	no	—
159	C₂⁴×C₇	—	2	4	no	—
160	C₂⁴×C₇	—	2	4	no	—
161	C₂⁴×C₇	—	2	32	no	—
162	C₂⁴×C₇	—	2	4	no	—
163	C₂⁴×C₇	—	2	4	no	—
164	C₂⁴×C₇	—	2	4	no	—
165	C₂⁴×C₇	—	2	8	no	—
166	C₂⁴×C₇	—	2	8	no	—
167	C₂⁴×C₇	—	2	4	no	—
168	C₂⁴×C₇	—	2	8	no	—
169	C₂⁴×C₇	—	2	8	no	—
170	C₂⁴×C₇	—	4	4	no	—
171	C₂⁴×C₇	—	4	4	no	—
172	C₂⁴×C₇	—	4	4	no	—
173	C₂⁴×C₇	—	4	4	no	—
174	C₂⁴×C₇	—	4	64	no	—
175	C₂⁴×C₇	—	4	16	no	—
176	C₂⁴×C₇	—	4	16	no	—
177	C₂⁴×C₇	C₂×D₄	1	4	yes	—
178	C₂⁴×C₇	#41	1	8	yes	complemented
179	C₂⁴×C₇	C₂⁴	1	2	yes	—
180	C₂⁴×C₇	C₂⁴	1	4	yes	—
181	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
183	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
184	C₇×#41	—	4	16	no	—
185	C₂×C₇×Q₈	—	2	2	no	—
186	C₂×C₇×Q₈	—	4	2	no	—
187	C₂×C₇×D₄	—	2	4	no	—
188	C₂×C₇×D₄	—	2	4	no	—
189	C₂×C₇×D₄	—	2	4	no	—
190	C₂×C₇×D₄	—	2	8	no	—
191	C₂×C₇×D₄	—	2	8	no	—
192	C₂×C₇×D₄	—	2	8	no	—
193	C₂×C₇×D₄	—	2	16	no	—
194	C₂×C₇×D₄	—	2	2	no	—
195	C₂×C₇×D₄	—	4	2	no	—
196	C₂×C₇×D₄	—	4	8	no	—
197	C₂×C₇×D₄	—	4	8	no	—
198	C₂²×C₄×C₇	—	2	4	no	—
199	C₂²×C₄×C₇	—	2	4	no	—
200	C₂²×C₄×C₇	—	2	4	no	—
201	C₂²×C₄×C₇	—	2	4	no	—
202	C₂²×C₄×C₇	—	2	4	no	—
203	C₂²×C₄×C₇	—	2	8	no	—
204	C₂²×C₄×C₇	—	2	4	no	—
205	C₂²×C₄×C₇	—	4	16	no	—
206	C₂²×C₄×C₇	—	4	2	no	—
207	C₂²×C₄×C₇	—	4	2	no	—
208	C₂²×C₄×C₇	—	4	2	no	—
209	C₂²×C₄×C₇	—	4	2	no	—
210	C₂²×C₄×C₇	—	4	4	no	—
211	C₂²×C₄×C₇	—	4	4	no	—
212	C₂²×C₄×C₇	—	4	4	no	—
213	C₂²×C₄×C₇	—	4	16	no	—
214	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
215	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
216	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
220	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
222	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
229	C₇×C₄⋊C₄	—	2	2	no	—
230	C₇×C₄⋊C₄	—	2	2	no	—
231	C₇×C₄⋊C₄	—	2	4	no	—
232	C₇×C₄⋊C₄	—	2	4	no	—
233	C₇×C₄⋊C₄	—	4	4	no	—
234	C₇×C₄⋊C₄	—	4	8	no	—
235	C₇×C₂²⋊C₄	—	2	4	no	—
236	C₇×C₂²⋊C₄	—	2	4	no	—
237	C₇×C₂²⋊C₄	—	2	4	no	—
238	C₇×C₂²⋊C₄	—	2	16	no	—
239	C₇×C₂²⋊C₄	—	2	8	no	—
240	C₇×C₂²⋊C₄	—	2	8	no	—
241	C₇×C₂²⋊C₄	—	2	8	no	—
242	C₇×C₂²⋊C₄	—	2	8	no	—
243	C₇×C₂²⋊C₄	—	2	8	no	—
244	C₇×C₂²⋊C₄	—	2	8	no	—
245	C₇×C₂²⋊C₄	—	2	8	no	—
246	C₇×C₂²⋊C₄	—	2	4	no	—
247	C₇×C₂²⋊C₄	—	2	4	no	—
248	C₇×C₂²⋊C₄	—	4	8	no	—
249	C₇×C₂²⋊C₄	—	4	8	no	—
250	C₇×C₂²⋊C₄	—	4	8	no	—
251	C₄²×C₇	—	2	4	no	—
252	C₄²×C₇	—	4	4	no	—
253	C₂⁶	C₂²×C₇	1	1	yes	characteristic
254	C₂²×#41	C₂²×C₇	1	1	yes	characteristic, complemented
255	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
256	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
257	#525	—	2	8	no	—
258	C₂×#123	C₂²×C₇	1	2	yes	complemented
259	C₂×#123	C₂²×C₇	1	4	yes	complemented
260	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
261	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
262	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
263	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
264	C₂×#120	C₂²×C₇	1	4	yes	—
265	C₂×#120	C₂²×C₇	1	2	yes	—
266	C₂×#120	C₂²×C₇	1	4	yes	—
267	C₂×#120	C₂²×C₇	1	4	yes	—
268	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
269	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
270	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
271	C₂×#117	C₂²×C₇	1	2	yes	complemented
272	C₂²×C₂²⋊C₄	—	2	8	no	—
273	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
274	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
275	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
276	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
277	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
278	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
279	#399	C₂²×C₇	1	4	yes	complemented
280	#397	C₂²×C₇	1	4	yes	complemented
281	#396	C₂²×C₇	1	8	yes	complemented
282	#394	C₂²×C₇	1	8	yes	complemented
283	#393	C₂²×C₇	1	4	yes	complemented
284	#392	C₂²×C₇	1	4	yes	complemented
285	#390	C₂²×C₇	1	8	yes	complemented
286	#388	C₂²×C₇	1	8	yes	complemented
287	#388	C₂²×C₇	1	8	yes	complemented
288	#386	C₂²×C₇	1	8	yes	complemented
289	#386	C₂²×C₇	1	4	yes	complemented
290	#386	C₂²×C₇	1	4	yes	complemented
291	#385	C₂²×C₇	1	4	yes	complemented
292	#385	C₂²×C₇	1	4	yes	complemented
293	#381	C₂²×C₇	1	4	yes	complemented
294	#381	C₂²×C₇	1	2	yes	complemented
295	#380	C₂²×C₇	1	2	yes	complemented
296	#380	C₂²×C₇	1	2	yes	complemented
297	#379	C₂²×C₇	1	4	yes	—
298	#379	C₂²×C₇	1	4	yes	—
299	#379	C₂²×C₇	1	2	yes	—
300	#379	C₂²×C₇	1	4	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
302	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
303	C₂³×C₇	—	2	32	no	—
304	C₂³×C₇	—	2	8	no	—
305	C₂³×C₇	—	2	8	no	—
306	C₂³×C₇	—	2	8	no	—
307	C₂³×C₇	—	2	2	no	—
308	C₂³×C₇	—	2	2	no	—
309	C₂³×C₇	—	2	2	no	—
310	C₂³×C₇	—	2	2	no	—
311	C₂³×C₇	—	2	2	no	—
312	C₂³×C₇	—	2	2	no	—
313	C₂³×C₇	—	2	16	no	—
314	C₂³×C₇	—	2	16	no	—
315	C₂³×C₇	—	2	16	no	—
316	C₂³×C₇	—	2	4	no	—
317	C₂³×C₇	—	2	4	no	—
318	C₂³×C₇	—	2	8	no	—
319	C₂³×C₇	—	2	8	no	—
320	C₂³×C₇	—	2	2	no	—
321	C₂³×C₇	—	2	4	no	—
322	C₂³×C₇	—	2	4	no	—
323	C₂³×C₇	—	2	4	no	—
324	C₂³×C₇	—	4	16	no	—
325	C₂³×C₇	—	4	32	no	—
326	C₂³×C₇	—	4	32	no	—
327	C₂³×C₇	—	4	128	no	—
328	C₂³×C₇	—	4	8	no	—
329	C₂³×C₇	—	4	8	no	—
330	C₂³×C₇	—	4	8	no	—
331	C₂³×C₇	—	4	8	no	—
332	C₂³×C₇	—	4	16	no	—
333	C₂³×C₇	—	4	8	no	—
334	C₂³×C₇	—	4	8	no	—
335	C₂³×C₇	C₂²×D₄	1	2	yes	—
336	C₂³×C₇	C₂²×D₄	1	2	yes	—
337	C₂³×C₇	C₂²×D₄	1	2	yes	—
338	C₂³×C₇	C₂×#41	1	8	yes	—
339	C₂³×C₇	C₂×#41	1	4	yes	—
340	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
341	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
342	C₂³×C₇	C₂⁵	1	1	yes	characteristic
343	C₇×Q₈	—	4	4	no	—
344	C₇×D₄	—	4	4	no	—
345	C₇×D₄	—	4	8	no	—
346	C₇×D₄	—	4	8	no	—
347	C₇×D₄	—	4	8	no	—
348	C₇×D₄	—	8	16	no	—
349	C₂×C₄×C₇	—	2	8	no	—
350	C₂×C₄×C₇	—	2	8	no	—
351	C₂×C₄×C₇	—	2	2	no	—
352	C₂×C₄×C₇	—	2	2	no	—
353	C₂×C₄×C₇	—	2	2	no	—
354	C₂×C₄×C₇	—	2	2	no	—
355	C₂×C₄×C₇	—	2	2	no	—
356	C₂×C₄×C₇	—	2	2	no	—
357	C₂×C₄×C₇	—	2	4	no	—
358	C₂×C₄×C₇	—	2	2	no	—
359	C₂×C₄×C₇	—	2	4	no	—
360	C₂×C₄×C₇	—	2	8	no	—
361	C₂×C₄×C₇	—	2	8	no	—
362	C₂×C₄×C₇	—	2	8	no	—
363	C₂×C₄×C₇	—	2	4	no	—
364	C₂×C₄×C₇	—	2	4	no	—
365	C₂×C₄×C₇	—	2	8	no	—
366	C₂×C₄×C₇	—	4	4	no	—
367	C₂×C₄×C₇	—	4	4	no	—
368	C₂×C₄×C₇	—	4	4	no	—
369	C₂×C₄×C₇	—	4	4	no	—
370	C₂×C₄×C₇	—	4	8	no	—
371	C₂×C₄×C₇	—	4	8	no	—
372	C₂×C₄×C₇	—	4	8	no	—
373	C₂×C₄×C₇	—	4	8	no	—
374	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
378	C₂⁵	—	2	4	no	—
379	C₂⁵	—	2	8	no	—
380	C₂⁵	—	4	4	no	—
381	C₂⁵	—	4	4	no	—
382	C₂⁵	C₂³×C₇	1	1	yes	characteristic
383	C₂⁵	C₂³×C₇	1	2	yes	—
384	C₂⁵	C₂³×C₇	1	2	yes	—
385	C₂⁵	C₂³×C₇	1	2	yes	—
386	C₂×#41	—	2	4	no	—
387	C₂×#41	—	4	4	no	—
388	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic, complemented
389	C₂²×D₄	C₂³×C₇	1	2	yes	—
390	C₂²×D₄	C₂³×C₇	1	2	yes	—
391	C₂²×D₄	C₂³×C₇	1	2	yes	—
392	C₂²×D₄	C₂³×C₇	1	8	yes	—
393	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic, complemented
394	C₂³×C₄	—	2	4	no	—
395	C₂³×C₄	—	4	4	no	—
396	C₂³×C₄	—	4	4	no	—
397	C₂³×C₄	C₇×D₄	1	8	yes	complemented
398	C₂³×C₄	C₂³×C₇	1	2	yes	—
399	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₇	1	2	yes	—
402	C₂³×C₄	C₂³×C₇	1	2	yes	—
403	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₇	1	2	yes	complemented
408	#123	—	2	8	no	—
409	#123	—	4	8	no	—
410	C₂²⋊Q₈	—	2	4	no	—
411	C₂²⋊Q₈	—	2	4	no	—
412	#121	—	2	4	no	—
413	#121	—	2	4	no	—
414	#120	—	2	8	no	—
415	#120	—	2	16	no	—
416	#120	—	4	8	no	—
417	#120	—	4	8	no	—
418	C₄×D₄	—	2	8	no	—
419	C₄×D₄	—	2	8	no	—
420	#117	—	2	4	no	—
421	#117	—	4	4	no	—
422	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic, complemented
423	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic, complemented
424	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	complemented
425	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	complemented
426	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
427	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
428	C₂×C₂²⋊C₄	—	2	8	no	—
429	C₂×C₂²⋊C₄	—	2	8	no	—
430	C₂×C₂²⋊C₄	—	2	8	no	—
431	C₂×C₂²⋊C₄	—	2	8	no	—
432	C₂×C₂²⋊C₄	—	2	8	no	—
433	C₂×C₂²⋊C₄	—	2	8	no	—
434	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	complemented
448	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	complemented
449	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	complemented
450	C₂×C₄²	C₂³×C₇	1	2	yes	complemented
451	C₂×C₄²	C₂³×C₇	1	4	yes	complemented
452	#95	C₂³×C₇	1	4	yes	complemented
453	#95	C₂³×C₇	1	4	yes	complemented
454	#95	C₂³×C₇	1	8	yes	complemented
455	#95	C₂³×C₇	1	8	yes	complemented
456	C₂²×C₇	—	2	32	no	—
457	C₂²×C₇	—	2	2	no	—
458	C₂²×C₇	—	2	2	no	—
459	C₂²×C₇	—	2	2	no	—
460	C₂²×C₇	—	2	2	no	—
461	C₂²×C₇	—	2	2	no	—
462	C₂²×C₇	—	2	2	no	—
463	C₂²×C₇	—	2	8	no	—
464	C₂²×C₇	—	2	8	no	—
465	C₂²×C₇	—	2	8	no	—
466	C₂²×C₇	—	2	8	no	—
467	C₂²×C₇	—	2	16	no	—
468	C₂²×C₇	—	4	32	no	—
469	C₂²×C₇	—	4	32	no	—
470	C₂²×C₇	—	4	32	no	—
471	C₂²×C₇	—	4	4	no	—
472	C₂²×C₇	—	4	4	no	—
473	C₂²×C₇	—	4	8	no	—
474	C₂²×C₇	—	4	2	no	—
475	C₂²×C₇	—	4	2	no	—
476	C₂²×C₇	—	4	2	no	—
477	C₂²×C₇	—	4	8	no	—
478	C₂²×C₇	#525	1	4	yes	—
479	C₂²×C₇	#534	1	4	yes	—
480	C₂²×C₇	#535	1	4	yes	—
481	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
482	C₂²×C₇	C₂²×#41	1	2	yes	—
483	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
484	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
485	C₄×C₇	—	2	2	no	—
486	C₄×C₇	—	2	2	no	—
487	C₄×C₇	—	2	2	no	—
488	C₄×C₇	—	2	2	no	—
489	C₄×C₇	—	4	2	no	—
490	C₄×C₇	—	4	2	no	—
491	C₄×C₇	—	4	4	no	—
492	C₄×C₇	—	4	2	no	—
493	C₄×C₇	—	4	8	no	—
494	C₂⁴	—	2	4	no	—
495	C₂⁴	—	2	4	no	—
496	C₂⁴	—	2	4	no	—
497	C₂⁴	—	2	32	no	—
498	C₂⁴	—	2	4	no	—
499	C₂⁴	—	2	4	no	—
500	C₂⁴	—	2	4	no	—
501	C₂⁴	—	2	8	no	—
502	C₂⁴	—	2	8	no	—
503	C₂⁴	—	2	4	no	—
504	C₂⁴	—	2	8	no	—
505	C₂⁴	—	2	8	no	—
506	C₂⁴	—	4	4	no	—
507	C₂⁴	—	4	4	no	—
508	C₂⁴	—	4	4	no	—
509	C₂⁴	—	4	4	no	—
510	C₂⁴	—	4	64	no	—
511	C₂⁴	—	4	16	no	—
512	C₂⁴	—	4	16	no	—
513	C₂⁴	C₂×C₇×D₄	1	4	yes	—
514	C₂⁴	C₇×#41	1	8	yes	complemented
515	C₂⁴	C₂⁴×C₇	1	2	yes	—
516	C₂⁴	C₂⁴×C₇	1	4	yes	—
517	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
518	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
519	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
520	#41	—	4	16	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	4	2	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	8	no	—
528	C₂×D₄	—	2	8	no	—
529	C₂×D₄	—	2	16	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	—	4	8	no	—
533	C₂×D₄	—	4	8	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	8	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	16	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	16	no	—
550	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
551	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
552	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
553	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
554	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
555	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
556	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
558	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	4	4	no	—
570	C₄⋊C₄	—	4	8	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	16	no	—
575	C₂²⋊C₄	—	2	8	no	—
576	C₂²⋊C₄	—	2	8	no	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	8	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	4	8	no	—
585	C₂²⋊C₄	—	4	8	no	—
586	C₂²⋊C₄	—	4	8	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	4	4	no	—
589	C₂×C₇	—	2	4	no	—
590	C₂×C₇	—	2	4	no	—
591	C₂×C₇	—	2	4	no	—
592	C₂×C₇	—	4	8	no	—
593	C₂×C₇	—	8	2	no	—
594	C₂×C₇	C₂×#525	1	1	yes	characteristic
595	C₂×C₇	C₂×#534	1	1	yes	characteristic
596	C₂×C₇	C₂×#535	1	1	yes	characteristic
597	C₂×C₇	#3490	1	4	yes	—
598	C₂³	—	2	32	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	8	no	—
606	C₂³	—	2	8	no	—
607	C₂³	—	2	8	no	—
608	C₂³	—	2	16	no	—
609	C₂³	—	2	16	no	—
610	C₂³	—	2	4	no	—
611	C₂³	—	2	4	no	—
612	C₂³	—	2	8	no	—
613	C₂³	—	2	8	no	—
614	C₂³	—	2	16	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	4	16	no	—
620	C₂³	—	4	32	no	—
621	C₂³	—	4	32	no	—
622	C₂³	—	4	128	no	—
623	C₂³	—	4	8	no	—
624	C₂³	—	4	8	no	—
625	C₂³	—	4	8	no	—
626	C₂³	—	4	8	no	—
627	C₂³	—	4	16	no	—
628	C₂³	—	4	8	no	—
629	C₂³	—	4	8	no	—
630	C₂³	C₂²×C₇×D₄	1	2	yes	—
631	C₂³	C₂²×C₇×D₄	1	2	yes	—
632	C₂³	C₂²×C₇×D₄	1	2	yes	—
633	C₂³	C₂×C₇×#41	1	8	yes	—
634	C₂³	C₂×C₇×#41	1	4	yes	—
635	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
636	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
637	C₂³	C₂⁵×C₇	1	1	yes	characteristic
638	Q₈	—	4	4	no	—
639	D₄	—	4	4	no	—
640	D₄	—	4	8	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	8	16	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	8	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	8	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	8	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	8	no	—
666	C₂×C₄	—	4	8	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
670	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
671	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
672	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
673	C₇	#35050	1	1	yes	characteristic, direct product factor, Sylow
674	C₂²	—	2	32	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	8	no	—
682	C₂²	—	2	8	no	—
683	C₂²	—	2	8	no	—
684	C₂²	—	2	8	no	—
685	C₂²	—	2	16	no	—
686	C₂²	—	4	32	no	—
687	C₂²	—	4	32	no	—
688	C₂²	—	4	32	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	4	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	8	no	—
696	C₂²	C₇×#525	1	4	yes	—
697	C₂²	C₇×#534	1	4	yes	—
698	C₂²	C₇×#535	1	4	yes	—
699	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
700	C₂²	C₂²×C₇×#41	1	2	yes	—
701	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
702	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	8	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	2	4	no	—
715	C₂	—	4	8	no	—
716	C₂	—	8	2	no	—
717	C₂	C₂×C₇×#525	1	1	yes	characteristic
718	C₂	C₂×C₇×#534	1	1	yes	characteristic
719	C₂	C₂×C₇×#535	1	1	yes	characteristic
720	C₂	C₇×#3490	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#525	C₂	semidirect
2. C₂³×C₇×C₂²⋊C₄	C₂	semidirect
3. C₇×#2849	C₂	semidirect
4. C₇×#2846	C₂	semidirect
5. C₇×#2626	C₂	semidirect
6. C₇×#2617	C₂	semidirect
7. C₇×#2561	C₂	semidirect
8. C₇×#2539	C₂	semidirect
9. C₇×#2534	C₂	semidirect
10. C₇×#2482	C₂	semidirect
11. C₇×#2411	C₂	semidirect
12. C₇×#2404	C₂	semidirect
13. C₇×#2321	C₂	semidirect
14. C₇×#2280	C₂	semidirect
16. C₂²×C₇×#41	C₂²	semidirect
20. C₂×C₇×#123	C₂²	semidirect
21. C₂×C₇×#123	C₂²	semidirect
22. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
23. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₇×#121	C₂²	semidirect
25. C₂×C₇×#121	C₂²	semidirect
30. C₂×C₄×C₇×D₄	C₂²	semidirect
31. C₂×C₄×C₇×D₄	C₂²	semidirect
32. C₂×C₇×#117	C₂²	semidirect
33. C₂×C₇×#117	C₂²	semidirect
41. C₇×#399	C₂²	semidirect
42. C₇×#397	C₂²	semidirect
43. C₇×#396	C₂²	semidirect
44. C₇×#394	C₂²	semidirect
45. C₇×#393	C₂²	semidirect
46. C₇×#392	C₂²	semidirect
47. C₇×#390	C₂²	semidirect
48. C₇×#388	C₂²	semidirect
49. C₇×#388	C₂²	semidirect
50. C₇×#386	C₂²	semidirect
51. C₇×#386	C₂²	semidirect
52. C₇×#386	C₂²	semidirect
53. C₇×#385	C₂²	semidirect
54. C₇×#385	C₂²	semidirect
55. C₇×#381	C₂²	semidirect
56. C₇×#381	C₂²	semidirect
57. C₇×#380	C₂²	semidirect
58. C₇×#380	C₂²	semidirect
63. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
64. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
65. #35050	C₇	direct (N × H)
76. C₂²×C₇×Q₈	C₂³	semidirect
81. C₂²×C₇×D₄	C₂³	semidirect
85. C₂³×C₄×C₇	D₄	semidirect
95. C₂³×C₄×C₇	C₂³	semidirect
110. C₂×C₇×C₄⋊C₄	C₂³	semidirect
111. C₂×C₇×C₄⋊C₄	C₂³	semidirect
112. C₂×C₇×C₄⋊C₄	C₂³	semidirect
113. C₂×C₇×C₄⋊C₄	C₂³	semidirect
114. C₂×C₇×C₄⋊C₄	C₂³	semidirect
115. C₂×C₇×C₄⋊C₄	C₂³	semidirect
135. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
136. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
137. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
138. C₂×C₄²×C₇	C₂³	semidirect
139. C₂×C₄²×C₇	C₂³	semidirect
140. C₇×#95	C₂³	semidirect
141. C₇×#95	C₂³	semidirect
142. C₇×#95	C₂³	semidirect
143. C₇×#95	C₂³	semidirect
144. C₂×#525	C₂×C₇	semidirect
145. C₂³×C₂²⋊C₄	C₂×C₇	semidirect
146. #2849	C₂×C₇	semidirect
147. #2846	C₂×C₇	semidirect
148. #2626	C₂×C₇	semidirect
149. #2617	C₂×C₇	semidirect
150. #2561	C₂×C₇	semidirect
151. #2539	C₂×C₇	semidirect
152. #2534	C₂×C₇	semidirect
153. #2482	C₂×C₇	semidirect
154. #2411	C₂×C₇	semidirect
155. #2404	C₂×C₇	semidirect
156. #2321	C₂×C₇	semidirect
157. #2280	C₂×C₇	semidirect
178. C₂⁴×C₇	#41	semidirect
254. C₂²×#41	C₂²×C₇	semidirect
258. C₂×#123	C₂²×C₇	semidirect
259. C₂×#123	C₂²×C₇	semidirect
260. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
261. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
262. C₂×#121	C₂²×C₇	semidirect
263. C₂×#121	C₂²×C₇	semidirect
268. C₂×C₄×D₄	C₂²×C₇	semidirect
269. C₂×C₄×D₄	C₂²×C₇	semidirect
270. C₂×#117	C₂²×C₇	semidirect
271. C₂×#117	C₂²×C₇	semidirect
279. #399	C₂²×C₇	semidirect
280. #397	C₂²×C₇	semidirect
281. #396	C₂²×C₇	semidirect
282. #394	C₂²×C₇	semidirect
283. #393	C₂²×C₇	semidirect
284. #392	C₂²×C₇	semidirect
285. #390	C₂²×C₇	semidirect
286. #388	C₂²×C₇	semidirect
287. #388	C₂²×C₇	semidirect
288. #386	C₂²×C₇	semidirect
289. #386	C₂²×C₇	semidirect
290. #386	C₂²×C₇	semidirect
291. #385	C₂²×C₇	semidirect
292. #385	C₂²×C₇	semidirect
293. #381	C₂²×C₇	semidirect
294. #381	C₂²×C₇	semidirect
295. #380	C₂²×C₇	semidirect
296. #380	C₂²×C₇	semidirect
301. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
302. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
388. C₂²×Q₈	C₂³×C₇	semidirect
393. C₂²×D₄	C₂³×C₇	semidirect
397. C₂³×C₄	C₇×D₄	semidirect
407. C₂³×C₄	C₂³×C₇	semidirect
422. C₂×C₄⋊C₄	C₂³×C₇	semidirect
423. C₂×C₄⋊C₄	C₂³×C₇	semidirect
424. C₂×C₄⋊C₄	C₂³×C₇	semidirect
425. C₂×C₄⋊C₄	C₂³×C₇	semidirect
426. C₂×C₄⋊C₄	C₂³×C₇	semidirect
427. C₂×C₄⋊C₄	C₂³×C₇	semidirect
447. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
448. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
449. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
450. C₂×C₄²	C₂³×C₇	semidirect
451. C₂×C₄²	C₂³×C₇	semidirect
452. #95	C₂³×C₇	semidirect
453. #95	C₂³×C₇	semidirect
454. #95	C₂³×C₇	semidirect
455. #95	C₂³×C₇	semidirect
514. C₂⁴	C₇×#41	semidirect
673. C₇	#35050	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#525	2
C₂³×C₇×C₂²⋊C₄	2
C₇×#2849	2
C₇×#2846	2
C₇×#2626	2
C₇×#2617	2
C₇×#2561	2
C₇×#2539	2
C₇×#2534	2
C₇×#2482	2
C₇×#2411	2
C₇×#2404	2
C₇×#2321	2
C₇×#2280	2
#35050	7

Subgroups — C7×#35050 #13212266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#35050 #13212266