Subgroups — C₇×#60265 #13237481

Order 1792.

1918 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₇×#2994	C₂	1	4	yes	maximal, complemented
3	C₇×#2992	C₂	1	4	yes	maximal, complemented
4	C₇×#2990	C₂	1	4	yes	maximal, complemented
5	C₇×#2989	C₂	1	2	yes	maximal, complemented
6	C₇×#2988	C₂	1	2	yes	maximal, complemented
7	C₇×#2962	C₂	1	2	yes	maximal, complemented
8	C₇×#2935	C₂	1	2	yes	maximal, complemented
9	C₇×#2929	C₂	1	4	yes	maximal, complemented
10	C₇×#2925	C₂	1	2	yes	maximal, complemented
11	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2906	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#131	C₂²	1	4	yes	—
15	C₂³×C₇×C₈	C₂²	1	2	yes	—
16	C₇×#533	C₄	1	1	yes	characteristic
17	C₇×#533	C₄	1	1	yes	characteristic
18	C₇×#533	C₂²	1	1	yes	characteristic
19	C₇×#532	C₄	1	1	yes	characteristic
20	C₇×#532	C₄	1	1	yes	characteristic
21	C₇×#532	C₂²	1	1	yes	characteristic
22	C₇×#529	C₄	1	2	yes	—
23	C₇×#529	C₄	1	2	yes	—
24	C₇×#529	C₄	1	2	yes	—
25	C₇×#529	C₄	1	2	yes	—
26	C₇×#529	C₂²	1	2	yes	—
27	C₇×#529	C₂²	1	2	yes	—
28	C₇×#525	C₄	1	2	yes	—
29	C₇×#525	C₄	1	2	yes	—
30	C₇×#525	C₂²	1	2	yes	—
31	C₄×C₇×#41	C₂²	1	2	yes	—
32	C₄×C₇×#41	C₂²	1	2	yes	—
33	C₄×C₇×#41	C₂²	1	2	yes	—
34	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
35	C₇×#446	C₂²	1	4	yes	complemented
36	C₇×#446	C₂²	1	8	yes	complemented
37	C₇×C₈×Q₈	C₂²	1	4	yes	complemented
38	C₇×#436	C₂²	1	4	yes	complemented
39	C₇×#435	C₂²	1	8	yes	—
40	C₇×#435	C₂²	1	8	yes	—
41	C₇×#435	C₂²	1	8	yes	complemented
42	C₇×C₈×D₄	C₂²	1	8	yes	—
43	C₇×C₈×D₄	C₂²	1	8	yes	—
44	C₇×C₈×D₄	C₂²	1	4	yes	complemented
45	C₇×#433	C₂²	1	8	yes	complemented
46	C₇×#432	C₂²	1	2	yes	—
47	C₇×#432	C₂²	1	2	yes	—
48	C₇×#432	C₂²	1	4	yes	complemented
49	C₇×#431	C₂²	1	2	yes	—
50	C₇×#431	C₂²	1	2	yes	—
51	C₇×#431	C₂²	1	4	yes	complemented
52	C₇×#424	C₂²	1	4	yes	—
53	C₇×#424	C₂²	1	8	yes	complemented
54	C₇×#423	C₂²	1	1	yes	characteristic
55	C₇×#423	C₂²	1	1	yes	characteristic
56	C₇×#423	C₂²	1	4	yes	complemented
57	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
58	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
59	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
62	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
63	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
64	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	complemented
65	C₇×#408	C₂²	1	4	yes	—
66	C₇×#407	C₂²	1	2	yes	—
67	C₇×#405	C₂²	1	4	yes	—
68	C₄×C₇×M₁₆	C₂²	1	2	yes	—
69	#60265	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×C₇×#41	C₂×C₄	1	2	yes	—
71	C₂×C₇×#41	C₂×C₄	1	2	yes	—
72	C₂×C₇×#41	C₂³	1	2	yes	—
73	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₇×#131	—	4	8	no	—
77	C₂×C₇×M₁₆	C₂³	1	2	yes	—
78	C₂×C₇×M₁₆	C₂³	1	2	yes	—
79	C₂×C₇×M₁₆	C₂³	1	8	yes	—
80	C₂²×C₇×C₈	—	4	4	no	—
81	C₂²×C₇×C₈	C₂³	1	4	yes	—
82	C₂²×C₇×C₈	C₂³	1	2	yes	—
83	C₂²×C₇×C₈	C₂³	1	4	yes	—
84	C₂²×C₇×C₈	C₂³	1	2	yes	—
85	C₂²×C₇×C₈	C₂³	1	8	yes	—
86	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
89	C₇×#127	C₂×C₄	1	1	yes	characteristic
90	C₇×#126	C₂×C₄	1	4	yes	—
91	C₇×#126	C₂×C₄	1	4	yes	—
92	C₇×#125	C₂×C₄	1	2	yes	—
93	C₇×#125	C₂×C₄	1	2	yes	—
94	C₇×#125	C₂×C₄	1	2	yes	—
95	C₇×#124	C₂×C₄	1	2	yes	—
96	C₇×#124	C₂×C₄	1	2	yes	—
97	C₇×#124	C₂×C₄	1	2	yes	—
98	C₇×#123	C₂×C₄	1	4	yes	—
99	C₇×#123	C₂×C₄	1	4	yes	—
100	C₇×#123	C₂×C₄	1	4	yes	—
101	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
102	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
103	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
104	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
105	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
106	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
107	C₇×#121	C₂×C₄	1	2	yes	—
108	C₇×#121	C₂×C₄	1	2	yes	—
109	C₇×#121	C₂×C₄	1	2	yes	—
110	C₇×#121	C₂×C₄	1	2	yes	—
111	C₇×#121	C₂×C₄	1	2	yes	—
112	C₇×#121	C₂×C₄	1	2	yes	—
113	C₇×#120	C₂×C₄	1	4	yes	—
114	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
115	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
116	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
117	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
118	C₄×C₇×Q₈	C₂³	1	2	yes	—
119	C₄×C₇×Q₈	C₂³	1	2	yes	—
120	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
121	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
122	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
123	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
124	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
125	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
126	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
127	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
128	C₄×C₇×D₄	C₂³	1	4	yes	—
129	C₄×C₇×D₄	C₂³	1	4	yes	—
130	C₄×C₇×D₄	C₂³	1	2	yes	—
131	C₄×C₇×D₄	C₂³	1	2	yes	—
132	C₇×#117	C₂×C₄	1	2	yes	—
133	C₇×#117	C₂×C₄	1	2	yes	—
134	C₇×#117	C₂×C₄	1	4	yes	—
135	C₇×#117	C₂×C₄	1	4	yes	—
136	C₇×#117	C₂³	1	2	yes	—
137	C₇×#117	C₂³	1	4	yes	—
138	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
139	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
140	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
141	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
142	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
143	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
144	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₇	C₂³	1	4	yes	—
151	C₇×C₄⋊C₈	C₂³	1	2	yes	—
152	C₇×C₄⋊C₈	C₂³	1	2	yes	—
153	C₇×C₄⋊C₈	C₂³	1	4	yes	—
154	C₇×C₄⋊C₈	C₂³	1	2	yes	—
155	C₇×C₄⋊C₈	C₂³	1	4	yes	—
156	C₇×C₄⋊C₈	C₂³	1	2	yes	—
157	C₇×C₄⋊C₈	C₂³	1	2	yes	—
158	C₇×C₄⋊C₈	C₂³	1	8	yes	—
159	C₇×C₄⋊C₈	C₂³	1	2	yes	—
160	C₇×C₄⋊C₈	C₂³	1	2	yes	—
161	C₇×C₄⋊C₈	C₂³	1	2	yes	—
162	C₇×C₄⋊C₈	C₂³	1	8	yes	—
163	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
165	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
166	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
167	C₇×#97	C₂³	1	4	yes	—
168	C₇×#97	C₂³	1	8	yes	—
169	C₄×C₇×C₈	C₂³	1	4	yes	—
170	C₄×C₇×C₈	C₂³	1	8	yes	—
171	#3444	C₂×C₇	1	1	yes	characteristic
172	#2994	C₂×C₇	1	4	yes	complemented
173	#2992	C₂×C₇	1	4	yes	complemented
174	#2990	C₂×C₇	1	4	yes	complemented
175	#2989	C₂×C₇	1	2	yes	complemented
176	#2988	C₂×C₇	1	2	yes	complemented
177	#2962	C₂×C₇	1	2	yes	complemented
178	#2935	C₂×C₇	1	2	yes	complemented
179	#2929	C₂×C₇	1	4	yes	complemented
180	#2925	C₂×C₇	1	2	yes	complemented
181	#2920	C₂×C₇	1	1	yes	characteristic, complemented
182	#2906	C₂×C₇	1	2	yes	complemented
183	C₂²×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
184	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
185	C₇×#41	—	2	8	no	—
186	C₇×#41	—	2	4	no	—
187	C₇×#41	—	2	4	no	—
188	C₇×#41	—	4	4	no	—
189	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
190	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
191	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
192	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
193	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
194	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
195	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
196	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
197	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₇	—	2	4	no	—
199	C₂²×C₄×C₇	—	2	2	no	—
200	C₂²×C₄×C₇	—	2	2	no	—
201	C₂²×C₄×C₇	—	4	2	no	—
202	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
213	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
217	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
218	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
223	C₇×M₁₆	—	2	4	no	—
224	C₇×M₁₆	—	2	4	no	—
225	C₇×M₁₆	—	4	8	no	—
226	C₂×C₇×C₈	—	2	8	no	—
227	C₂×C₇×C₈	—	4	2	no	—
228	C₂×C₇×C₈	—	4	4	no	—
229	C₂×C₇×C₈	—	4	2	no	—
230	C₂×C₇×C₈	—	4	8	no	—
231	C₂×C₇×C₈	C₂⁴	1	4	yes	—
232	C₂×C₇×C₈	C₂⁴	1	4	yes	—
233	C₂×C₇×C₈	C₂⁴	1	4	yes	—
234	C₂×C₇×C₈	C₂⁴	1	4	yes	—
235	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
236	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
237	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
238	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
239	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
240	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
241	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
242	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
243	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
244	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
245	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
246	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
247	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
248	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
249	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
250	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
251	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
252	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
253	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
254	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
255	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
256	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
257	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
258	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
259	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
260	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
261	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
262	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
263	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
264	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
265	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
266	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
267	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
268	C₄²×C₇	C₂²×C₄	1	4	yes	—
269	C₄²×C₇	C₂²×C₄	1	4	yes	—
270	C₄²×C₇	C₂⁴	1	1	yes	characteristic
271	C₄²×C₇	C₂⁴	1	4	yes	—
272	C₄²×C₇	C₂⁴	1	1	yes	characteristic
273	C₄²×C₇	C₂⁴	1	1	yes	characteristic
274	C₄²×C₇	C₂⁴	1	1	yes	characteristic
275	C₂×#131	C₂²×C₇	1	4	yes	—
276	C₂³×C₈	C₂²×C₇	1	2	yes	—
277	#533	C₄×C₇	1	1	yes	characteristic
278	#533	C₄×C₇	1	1	yes	characteristic
279	#533	C₂²×C₇	1	1	yes	characteristic
280	#532	C₄×C₇	1	1	yes	characteristic
281	#532	C₄×C₇	1	1	yes	characteristic
282	#532	C₂²×C₇	1	1	yes	characteristic
283	#529	C₄×C₇	1	2	yes	—
284	#529	C₄×C₇	1	2	yes	—
285	#529	C₄×C₇	1	2	yes	—
286	#529	C₄×C₇	1	2	yes	—
287	#529	C₂²×C₇	1	2	yes	—
288	#529	C₂²×C₇	1	2	yes	—
289	#525	C₄×C₇	1	2	yes	—
290	#525	C₄×C₇	1	2	yes	—
291	#525	C₂²×C₇	1	2	yes	—
292	C₄×#41	C₂²×C₇	1	2	yes	—
293	C₄×#41	C₂²×C₇	1	2	yes	—
294	C₄×#41	C₂²×C₇	1	2	yes	—
295	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
296	#446	C₂²×C₇	1	4	yes	complemented
297	#446	C₂²×C₇	1	8	yes	complemented
298	C₈×Q₈	C₂²×C₇	1	4	yes	complemented
299	#436	C₂²×C₇	1	4	yes	complemented
300	#435	C₂²×C₇	1	8	yes	—
301	#435	C₂²×C₇	1	8	yes	—
302	#435	C₂²×C₇	1	8	yes	complemented
303	C₈×D₄	C₂²×C₇	1	8	yes	—
304	C₈×D₄	C₂²×C₇	1	8	yes	—
305	C₈×D₄	C₂²×C₇	1	4	yes	complemented
306	#433	C₂²×C₇	1	8	yes	complemented
307	#432	C₂²×C₇	1	2	yes	—
308	#432	C₂²×C₇	1	2	yes	—
309	#432	C₂²×C₇	1	4	yes	complemented
310	#431	C₂²×C₇	1	2	yes	—
311	#431	C₂²×C₇	1	2	yes	—
312	#431	C₂²×C₇	1	4	yes	complemented
313	#424	C₂²×C₇	1	4	yes	—
314	#424	C₂²×C₇	1	8	yes	complemented
315	#423	C₂²×C₇	1	1	yes	characteristic
316	#423	C₂²×C₇	1	1	yes	characteristic
317	#423	C₂²×C₇	1	4	yes	complemented
318	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
319	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
320	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
321	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
323	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
324	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
325	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	complemented
326	#408	C₂²×C₇	1	4	yes	—
327	#407	C₂²×C₇	1	2	yes	—
328	#405	C₂²×C₇	1	4	yes	—
329	C₄×M₁₆	C₂²×C₇	1	2	yes	—
330	C₂³×C₇	—	2	2	no	—
331	C₂³×C₇	—	2	2	no	—
332	C₂³×C₇	—	2	2	no	—
333	C₂³×C₇	C₂³×C₄	1	4	yes	—
334	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
335	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
336	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
337	C₇×Q₈	—	2	4	no	—
338	C₇×Q₈	—	2	4	no	—
339	C₇×Q₈	—	4	2	no	—
340	C₇×D₄	—	2	8	no	—
341	C₇×D₄	—	2	8	no	—
342	C₇×D₄	—	2	8	no	—
343	C₇×D₄	—	2	4	no	—
344	C₇×D₄	—	2	4	no	—
345	C₇×D₄	—	4	2	no	—
346	C₂×C₄×C₇	—	2	2	no	—
347	C₂×C₄×C₇	—	2	2	no	—
348	C₂×C₄×C₇	—	2	2	no	—
349	C₂×C₄×C₇	—	2	2	no	—
350	C₂×C₄×C₇	—	2	2	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	8	no	—
357	C₂×C₄×C₇	—	2	1	no	—
358	C₂×C₄×C₇	—	2	1	no	—
359	C₂×C₄×C₇	—	2	4	no	—
360	C₂×C₄×C₇	—	2	1	no	—
361	C₂×C₄×C₇	—	2	1	no	—
362	C₂×C₄×C₇	—	2	4	no	—
363	C₂×C₄×C₇	—	4	1	no	—
364	C₂×C₄×C₇	—	4	1	no	—
365	C₂×C₄×C₇	—	4	1	no	—
366	C₂×C₄×C₇	—	4	1	no	—
367	C₂×C₄×C₇	—	4	4	no	—
368	C₂×C₄×C₇	#131	1	4	yes	complemented
369	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
370	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
372	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
373	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
374	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
375	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
376	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
377	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
378	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
379	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
380	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
381	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
382	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
383	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
384	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
385	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
386	C₇×C₈	—	2	4	no	—
387	C₇×C₈	—	2	4	no	—
388	C₇×C₈	—	2	4	no	—
389	C₇×C₈	—	2	4	no	—
390	C₂×#41	C₂×C₄×C₇	1	2	yes	—
391	C₂×#41	C₂×C₄×C₇	1	2	yes	—
392	C₂×#41	C₂³×C₇	1	2	yes	—
393	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
394	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
396	#131	—	4	8	no	—
397	C₂×M₁₆	C₂³×C₇	1	2	yes	—
398	C₂×M₁₆	C₂³×C₇	1	2	yes	—
399	C₂×M₁₆	C₂³×C₇	1	8	yes	—
400	C₂²×C₈	—	4	4	no	—
401	C₂²×C₈	C₂³×C₇	1	4	yes	—
402	C₂²×C₈	C₂³×C₇	1	2	yes	—
403	C₂²×C₈	C₂³×C₇	1	4	yes	—
404	C₂²×C₈	C₂³×C₇	1	2	yes	—
405	C₂²×C₈	C₂³×C₇	1	8	yes	—
406	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
407	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
408	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
409	#127	C₂×C₄×C₇	1	1	yes	characteristic
410	#126	C₂×C₄×C₇	1	4	yes	—
411	#126	C₂×C₄×C₇	1	4	yes	—
412	#125	C₂×C₄×C₇	1	2	yes	—
413	#125	C₂×C₄×C₇	1	2	yes	—
414	#125	C₂×C₄×C₇	1	2	yes	—
415	#124	C₂×C₄×C₇	1	2	yes	—
416	#124	C₂×C₄×C₇	1	2	yes	—
417	#124	C₂×C₄×C₇	1	2	yes	—
418	#123	C₂×C₄×C₇	1	4	yes	—
419	#123	C₂×C₄×C₇	1	4	yes	—
420	#123	C₂×C₄×C₇	1	4	yes	—
421	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
422	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
423	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
424	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
425	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
426	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
427	#121	C₂×C₄×C₇	1	2	yes	—
428	#121	C₂×C₄×C₇	1	2	yes	—
429	#121	C₂×C₄×C₇	1	2	yes	—
430	#121	C₂×C₄×C₇	1	2	yes	—
431	#121	C₂×C₄×C₇	1	2	yes	—
432	#121	C₂×C₄×C₇	1	2	yes	—
433	#120	C₂×C₄×C₇	1	4	yes	—
434	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
435	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
436	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
437	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
438	C₄×Q₈	C₂³×C₇	1	2	yes	—
439	C₄×Q₈	C₂³×C₇	1	2	yes	—
440	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
441	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
442	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
443	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
444	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
445	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
446	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
447	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
448	C₄×D₄	C₂³×C₇	1	4	yes	—
449	C₄×D₄	C₂³×C₇	1	4	yes	—
450	C₄×D₄	C₂³×C₇	1	2	yes	—
451	C₄×D₄	C₂³×C₇	1	2	yes	—
452	#117	C₂×C₄×C₇	1	2	yes	—
453	#117	C₂×C₄×C₇	1	2	yes	—
454	#117	C₂×C₄×C₇	1	4	yes	—
455	#117	C₂×C₄×C₇	1	4	yes	—
456	#117	C₂³×C₇	1	2	yes	—
457	#117	C₂³×C₇	1	4	yes	—
458	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
459	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
460	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
461	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
462	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
463	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₇	1	4	yes	—
465	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
471	C₄⋊C₈	C₂³×C₇	1	2	yes	—
472	C₄⋊C₈	C₂³×C₇	1	2	yes	—
473	C₄⋊C₈	C₂³×C₇	1	4	yes	—
474	C₄⋊C₈	C₂³×C₇	1	2	yes	—
475	C₄⋊C₈	C₂³×C₇	1	4	yes	—
476	C₄⋊C₈	C₂³×C₇	1	2	yes	—
477	C₄⋊C₈	C₂³×C₇	1	2	yes	—
478	C₄⋊C₈	C₂³×C₇	1	8	yes	—
479	C₄⋊C₈	C₂³×C₇	1	2	yes	—
480	C₄⋊C₈	C₂³×C₇	1	2	yes	—
481	C₄⋊C₈	C₂³×C₇	1	2	yes	—
482	C₄⋊C₈	C₂³×C₇	1	8	yes	—
483	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
484	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
485	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
486	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
487	#97	C₂³×C₇	1	4	yes	—
488	#97	C₂³×C₇	1	8	yes	—
489	C₄×C₈	C₂³×C₇	1	4	yes	—
490	C₄×C₈	C₂³×C₇	1	8	yes	—
491	C₂²×C₇	—	2	8	no	—
492	C₂²×C₇	—	2	1	no	—
493	C₂²×C₇	—	2	1	no	—
494	C₂²×C₇	—	2	1	no	—
495	C₂²×C₇	—	2	1	no	—
496	C₂²×C₇	—	2	1	no	—
497	C₂²×C₇	—	2	1	no	—
498	C₂²×C₇	—	2	4	no	—
499	C₂²×C₇	—	2	4	no	—
500	C₂²×C₇	—	2	4	no	—
501	C₂²×C₇	#520	1	2	yes	—
502	C₂²×C₇	C₂×#131	1	2	yes	—
503	C₂²×C₇	#568	1	2	yes	—
504	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
505	C₄×C₇	—	2	1	no	—
506	C₄×C₇	—	2	1	no	—
507	C₄×C₇	—	2	4	no	—
508	C₄×C₇	—	2	1	no	—
509	C₄×C₇	—	2	1	no	—
510	C₄×C₇	—	2	4	no	—
511	C₄×C₇	—	2	1	no	—
512	C₄×C₇	—	2	1	no	—
513	C₄×C₇	—	2	1	no	—
514	C₄×C₇	—	2	1	no	—
515	C₄×C₇	—	2	4	no	—
516	C₄×C₇	#520	1	2	yes	—
517	C₄×C₇	C₂×#131	1	2	yes	—
518	C₄×C₇	C₂×#131	1	2	yes	—
519	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
520	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
521	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
522	#41	—	2	8	no	—
523	#41	—	2	4	no	—
524	#41	—	2	4	no	—
525	#41	—	4	4	no	—
526	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
527	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
528	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
529	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
530	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
531	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
532	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
533	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
534	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
542	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
544	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
546	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
547	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
548	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
549	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
550	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
551	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
552	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
553	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
554	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
555	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
559	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
560	M₁₆	—	2	4	no	—
561	M₁₆	—	2	4	no	—
562	M₁₆	—	4	8	no	—
563	C₂×C₈	—	2	8	no	—
564	C₂×C₈	—	4	2	no	—
565	C₂×C₈	—	4	4	no	—
566	C₂×C₈	—	4	2	no	—
567	C₂×C₈	—	4	8	no	—
568	C₂×C₈	C₂⁴×C₇	1	4	yes	—
569	C₂×C₈	C₂⁴×C₇	1	4	yes	—
570	C₂×C₈	C₂⁴×C₇	1	4	yes	—
571	C₂×C₈	C₂⁴×C₇	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
573	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
574	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
575	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
576	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
577	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
578	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
579	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
580	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
581	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
582	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
583	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
589	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
590	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
591	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
592	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
593	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
594	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
595	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
596	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
597	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
598	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
599	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
600	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
601	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
602	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
603	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
604	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
605	C₄²	C₂²×C₄×C₇	1	4	yes	—
606	C₄²	C₂²×C₄×C₇	1	4	yes	—
607	C₄²	C₂⁴×C₇	1	1	yes	characteristic
608	C₄²	C₂⁴×C₇	1	4	yes	—
609	C₄²	C₂⁴×C₇	1	1	yes	characteristic
610	C₄²	C₂⁴×C₇	1	1	yes	characteristic
611	C₄²	C₂⁴×C₇	1	1	yes	characteristic
612	C₂×C₇	—	2	2	no	—
613	C₂×C₇	—	2	2	no	—
614	C₂×C₇	—	2	2	no	—
615	C₂×C₇	—	4	4	no	—
616	C₂×C₇	C₂×#520	1	1	yes	characteristic
617	C₂×C₇	C₂²×#131	1	1	yes	characteristic
618	C₂×C₇	C₂×#568	1	1	yes	characteristic
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	C₂³×C₄×C₇	1	4	yes	—
623	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
624	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
625	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
626	Q₈	—	2	4	no	—
627	Q₈	—	2	4	no	—
628	Q₈	—	4	2	no	—
629	D₄	—	2	8	no	—
630	D₄	—	2	8	no	—
631	D₄	—	2	8	no	—
632	D₄	—	2	4	no	—
633	D₄	—	2	4	no	—
634	D₄	—	4	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	C₇×#131	1	4	yes	complemented
658	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
659	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
660	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
661	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
662	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
663	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
664	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
665	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
666	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
667	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
668	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
670	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
671	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
672	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
673	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
674	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
675	C₈	—	2	4	no	—
676	C₈	—	2	4	no	—
677	C₈	—	2	4	no	—
678	C₈	—	2	4	no	—
679	C₇	#60265	1	1	yes	characteristic, direct product factor, Sylow
680	C₂²	—	2	8	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	C₇×#520	1	2	yes	—
691	C₂²	C₂×C₇×#131	1	2	yes	—
692	C₂²	C₇×#568	1	2	yes	—
693	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
694	C₄	—	2	1	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	4	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	4	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	4	no	—
705	C₄	C₇×#520	1	2	yes	—
706	C₄	C₂×C₇×#131	1	2	yes	—
707	C₄	C₂×C₇×#131	1	2	yes	—
708	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
709	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
710	C₂	—	2	2	no	—
711	C₂	—	2	2	no	—
712	C₂	—	2	2	no	—
713	C₂	—	4	4	no	—
714	C₂	C₂×C₇×#520	1	1	yes	characteristic
715	C₂	C₂²×C₇×#131	1	1	yes	characteristic
716	C₂	C₂×C₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂⁴×C₄
prime radical	C₇×#3444	C₂
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
2. C₇×#2994	C₂	semidirect
3. C₇×#2992	C₂	semidirect
4. C₇×#2990	C₂	semidirect
5. C₇×#2989	C₂	semidirect
6. C₇×#2988	C₂	semidirect
7. C₇×#2962	C₂	semidirect
8. C₇×#2935	C₂	semidirect
9. C₇×#2929	C₂	semidirect
10. C₇×#2925	C₂	semidirect
11. C₇×#2920	C₂	semidirect
12. C₇×#2906	C₂	semidirect
13. C₂²×C₇×C₄⋊C₈	C₂	semidirect
35. C₇×#446	C₂²	semidirect
36. C₇×#446	C₂²	semidirect
37. C₇×C₈×Q₈	C₂²	semidirect
38. C₇×#436	C₂²	semidirect
41. C₇×#435	C₂²	semidirect
44. C₇×C₈×D₄	C₂²	semidirect
45. C₇×#433	C₂²	semidirect
48. C₇×#432	C₂²	semidirect
51. C₇×#431	C₂²	semidirect
53. C₇×#424	C₂²	semidirect
56. C₇×#423	C₂²	semidirect
64. C₂×C₇×C₄⋊C₈	C₂²	semidirect
69. #60265	C₇	direct (N × H)
172. #2994	C₂×C₇	semidirect
173. #2992	C₂×C₇	semidirect
174. #2990	C₂×C₇	semidirect
175. #2989	C₂×C₇	semidirect
176. #2988	C₂×C₇	semidirect
177. #2962	C₂×C₇	semidirect
178. #2935	C₂×C₇	semidirect
179. #2929	C₂×C₇	semidirect
180. #2925	C₂×C₇	semidirect
181. #2920	C₂×C₇	semidirect
182. #2906	C₂×C₇	semidirect
183. C₂²×C₄⋊C₈	C₂×C₇	semidirect
296. #446	C₂²×C₇	semidirect
297. #446	C₂²×C₇	semidirect
298. C₈×Q₈	C₂²×C₇	semidirect
299. #436	C₂²×C₇	semidirect
302. #435	C₂²×C₇	semidirect
305. C₈×D₄	C₂²×C₇	semidirect
306. #433	C₂²×C₇	semidirect
309. #432	C₂²×C₇	semidirect
312. #431	C₂²×C₇	semidirect
314. #424	C₂²×C₇	semidirect
317. #423	C₂²×C₇	semidirect
325. C₂×C₄⋊C₈	C₂²×C₇	semidirect
368. C₂×C₄×C₇	#131	semidirect
657. C₂×C₄	C₇×#131	semidirect
679. C₇	#60265	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×#3444	2
C₇×#2994	2
C₇×#2992	2
C₇×#2990	2
C₇×#2989	2
C₇×#2988	2
C₇×#2962	2
C₇×#2935	2
C₇×#2929	2
C₇×#2925	2
C₇×#2920	2
C₇×#2906	2
C₂²×C₇×C₄⋊C₈	2
#60265	7

Subgroups — C7×#60265 #13237481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60265 #13237481