Subgroups — C₇×#60210 #13237426

Order 1792.

1996 conjugacy classes of subgroups.

The subgroup lattice has 702 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×#2969	C₂	1	4	yes	maximal, complemented
3	C₇×#2968	C₂	1	4	yes	maximal, complemented
4	C₇×#2965	C₂	1	2	yes	maximal, complemented
5	C₇×#2965	C₂	1	4	yes	maximal, complemented
6	C₇×C₈×#41	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×#2933	C₂	1	4	yes	maximal, complemented
10	C₇×#2922	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₇×#131	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#131	C₂²	1	4	yes	—
15	C₂²×C₇×M₁₆	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	8	yes	complemented
36	C₇×#446	C₂²	1	4	yes	complemented
37	C₇×C₈×Q₈	C₂²	1	4	yes	complemented
38	C₇×#436	C₂²	1	8	yes	—
39	C₇×#436	C₂²	1	4	yes	complemented
40	C₇×#435	C₂²	1	8	yes	—
41	C₇×#435	C₂²	1	8	yes	—
42	C₇×#435	C₂²	1	8	yes	complemented
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×#431	C₂²	1	1	yes	characteristic
47	C₇×#431	C₂²	1	2	yes	—
48	C₇×#431	C₂²	1	1	yes	characteristic
49	C₇×#431	C₂²	1	2	yes	—
50	C₇×#431	C₂²	1	2	yes	—
51	C₇×#431	C₂²	1	4	yes	complemented
52	C₇×#431	C₂²	1	4	yes	complemented
53	C₇×#424	C₂²	1	4	yes	—
54	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
55	C₇×#408	C₂²	1	4	yes	—
56	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
57	C₇×#405	C₂²	1	4	yes	—
58	C₇×#405	C₂²	1	8	yes	complemented
59	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
60	C₄×C₇×M₁₆	C₂²	1	2	yes	—
61	C₄×C₇×M₁₆	C₂²	1	2	yes	—
62	C₄×C₇×M₁₆	C₂²	1	2	yes	—
63	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
64	C₄×C₇×M₁₆	C₂²	1	4	yes	complemented
65	C₂×C₇×#97	C₂²	1	2	yes	—
66	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
67	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
68	C₂×C₄×C₇×C₈	C₂²	1	4	yes	complemented
69	#60210	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	—	2	16	no	—
77	C₂×C₇×M₁₆	—	2	8	no	—
78	C₂×C₇×M₁₆	C₂³	1	2	yes	—
79	C₂×C₇×M₁₆	C₂³	1	4	yes	—
80	C₂×C₇×M₁₆	C₂³	1	8	yes	—
81	C₂×C₇×M₁₆	C₂³	1	2	yes	—
82	C₂²×C₇×C₈	C₂³	1	4	yes	—
83	C₂²×C₇×C₈	C₂³	1	4	yes	—
84	C₂²×C₇×C₈	C₂³	1	8	yes	—
85	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
86	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
88	C₇×#127	C₂×C₄	1	1	yes	characteristic
89	C₇×#126	C₂×C₄	1	4	yes	—
90	C₇×#126	C₂×C₄	1	4	yes	—
91	C₇×#125	C₂×C₄	1	2	yes	—
92	C₇×#125	C₂×C₄	1	2	yes	—
93	C₇×#125	C₂×C₄	1	2	yes	—
94	C₇×#124	C₂×C₄	1	2	yes	—
95	C₇×#124	C₂×C₄	1	2	yes	—
96	C₇×#124	C₂×C₄	1	2	yes	—
97	C₇×#123	C₂×C₄	1	4	yes	—
98	C₇×#123	C₂×C₄	1	4	yes	—
99	C₇×#123	C₂×C₄	1	4	yes	—
100	C₇×C₂²⋊Q₈	C₂×C₄	1	2	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×#121	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×#120	C₂×C₄	1	4	yes	—
113	C₄×C₇×Q₈	C₂×C₄	1	2	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	C₂³	1	2	yes	—
118	C₄×C₇×Q₈	C₂³	1	2	yes	—
119	C₄×C₇×D₄	C₂×C₄	1	4	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	2	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	C₂³	1	4	yes	—
128	C₄×C₇×D₄	C₂³	1	4	yes	—
129	C₄×C₇×D₄	C₂³	1	2	yes	—
130	C₄×C₇×D₄	C₂³	1	2	yes	—
131	C₇×#117	C₂×C₄	1	2	yes	—
132	C₇×#117	C₂×C₄	1	2	yes	—
133	C₇×#117	C₂×C₄	1	4	yes	—
134	C₇×#117	C₂×C₄	1	4	yes	—
135	C₇×#117	C₂³	1	2	yes	—
136	C₇×#117	C₂³	1	4	yes	—
137	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
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	C₂³	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	4	yes	—
150	C₇×C₄⋊C₈	C₂³	1	2	yes	—
151	C₇×C₄⋊C₈	C₂³	1	4	yes	—
152	C₇×C₄⋊C₈	C₂³	1	2	yes	—
153	C₇×C₄⋊C₈	C₂³	1	8	yes	—
154	C₇×C₄⋊C₈	C₂³	1	8	yes	—
155	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
156	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
157	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
158	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
159	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
160	C₇×#97	C₂³	1	2	yes	—
161	C₇×#97	C₂³	1	2	yes	—
162	C₇×#97	C₂³	1	4	yes	—
163	C₇×#97	C₂³	1	8	yes	—
164	C₄×C₇×C₈	C₂³	1	4	yes	—
165	C₄×C₇×C₈	C₂³	1	4	yes	—
166	C₄×C₇×C₈	C₂³	1	8	yes	—
167	C₄×C₇×C₈	C₂³	1	2	yes	—
168	C₄×C₇×C₈	C₂³	1	2	yes	—
169	C₄×C₇×C₈	C₂³	1	2	yes	—
170	C₄×C₇×C₈	C₂³	1	2	yes	—
171	#3444	C₂×C₇	1	1	yes	characteristic
172	#2969	C₂×C₇	1	4	yes	complemented
173	#2968	C₂×C₇	1	4	yes	complemented
174	#2965	C₂×C₇	1	2	yes	complemented
175	#2965	C₂×C₇	1	4	yes	complemented
176	C₈×#41	C₂×C₇	1	2	yes	complemented
177	#2962	C₂×C₇	1	2	yes	complemented
178	#2935	C₂×C₇	1	2	yes	complemented
179	#2933	C₂×C₇	1	4	yes	complemented
180	#2922	C₂×C₇	1	2	yes	complemented
181	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
182	C₄×#131	C₂×C₇	1	2	yes	complemented
183	C₂×C₄×M₁₆	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	8	no	—
187	C₇×#41	—	4	4	no	—
188	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
189	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
190	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
191	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
192	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
193	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
194	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
195	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
196	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
197	C₂²×C₄×C₇	—	2	4	no	—
198	C₂²×C₄×C₇	—	2	4	no	—
199	C₂²×C₄×C₇	—	4	2	no	—
200	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
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	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
221	C₇×M₁₆	—	2	4	no	—
222	C₇×M₁₆	—	2	8	no	—
223	C₇×M₁₆	—	2	16	no	—
224	C₇×M₁₆	#41	1	8	yes	complemented
225	C₂×C₇×C₈	—	2	8	no	—
226	C₂×C₇×C₈	—	2	8	no	—
227	C₂×C₇×C₈	—	2	16	no	—
228	C₂×C₇×C₈	C₂⁴	1	4	yes	—
229	C₂×C₇×C₈	C₂⁴	1	4	yes	—
230	C₂×C₇×C₈	C₂⁴	1	4	yes	—
231	C₂×C₇×C₈	C₂⁴	1	4	yes	—
232	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
233	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
234	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
235	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
236	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
237	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
238	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
239	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
240	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
241	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
242	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
243	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
244	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
245	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
246	C₇×C₂²⋊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	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
254	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
255	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
266	C₄²×C₇	C₂²×C₄	1	4	yes	—
267	C₄²×C₇	C₂⁴	1	1	yes	characteristic
268	C₄²×C₇	C₂⁴	1	1	yes	characteristic
269	C₄²×C₇	C₂⁴	1	4	yes	—
270	C₄²×C₇	C₂⁴	1	1	yes	characteristic
271	C₄²×C₇	C₂⁴	1	1	yes	characteristic
272	C₂×#131	C₂²×C₇	1	4	yes	—
273	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
274	#533	C₄×C₇	1	1	yes	characteristic
275	#533	C₄×C₇	1	1	yes	characteristic
276	#533	C₂²×C₇	1	1	yes	characteristic
277	#532	C₄×C₇	1	1	yes	characteristic
278	#532	C₄×C₇	1	1	yes	characteristic
279	#532	C₂²×C₇	1	1	yes	characteristic
280	#529	C₄×C₇	1	2	yes	—
281	#529	C₄×C₇	1	2	yes	—
282	#529	C₄×C₇	1	2	yes	—
283	#529	C₄×C₇	1	2	yes	—
284	#529	C₂²×C₇	1	2	yes	—
285	#529	C₂²×C₇	1	2	yes	—
286	#525	C₄×C₇	1	2	yes	—
287	#525	C₄×C₇	1	2	yes	—
288	#525	C₂²×C₇	1	2	yes	—
289	C₄×#41	C₂²×C₇	1	2	yes	—
290	C₄×#41	C₂²×C₇	1	2	yes	—
291	C₄×#41	C₂²×C₇	1	2	yes	—
292	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
293	#446	C₂²×C₇	1	8	yes	complemented
294	#446	C₂²×C₇	1	4	yes	complemented
295	C₈×Q₈	C₂²×C₇	1	4	yes	complemented
296	#436	C₂²×C₇	1	8	yes	—
297	#436	C₂²×C₇	1	4	yes	complemented
298	#435	C₂²×C₇	1	8	yes	—
299	#435	C₂²×C₇	1	8	yes	—
300	#435	C₂²×C₇	1	8	yes	complemented
301	C₈×D₄	C₂²×C₇	1	8	yes	—
302	C₈×D₄	C₂²×C₇	1	4	yes	complemented
303	#433	C₂²×C₇	1	8	yes	complemented
304	#431	C₂²×C₇	1	1	yes	characteristic
305	#431	C₂²×C₇	1	2	yes	—
306	#431	C₂²×C₇	1	1	yes	characteristic
307	#431	C₂²×C₇	1	2	yes	—
308	#431	C₂²×C₇	1	2	yes	—
309	#431	C₂²×C₇	1	4	yes	complemented
310	#431	C₂²×C₇	1	4	yes	complemented
311	#424	C₂²×C₇	1	4	yes	—
312	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
313	#408	C₂²×C₇	1	4	yes	—
314	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
315	#405	C₂²×C₇	1	4	yes	—
316	#405	C₂²×C₇	1	8	yes	complemented
317	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
318	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
319	C₄×M₁₆	C₂²×C₇	1	2	yes	—
320	C₄×M₁₆	C₂²×C₇	1	2	yes	—
321	C₄×M₁₆	C₂²×C₇	1	2	yes	—
322	C₄×M₁₆	C₂²×C₇	1	4	yes	complemented
323	C₂×#97	C₂²×C₇	1	2	yes	—
324	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
325	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
326	C₂×C₄×C₈	C₂²×C₇	1	4	yes	complemented
327	C₂³×C₇	—	2	2	no	—
328	C₂³×C₇	—	2	2	no	—
329	C₂³×C₇	—	4	1	no	—
330	C₂³×C₇	C₂³×C₄	1	4	yes	—
331	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
332	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
333	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
334	C₇×Q₈	—	2	4	no	—
335	C₇×Q₈	—	2	4	no	—
336	C₇×Q₈	—	4	2	no	—
337	C₇×D₄	—	2	8	no	—
338	C₇×D₄	—	2	8	no	—
339	C₇×D₄	—	2	4	no	—
340	C₇×D₄	—	2	4	no	—
341	C₇×D₄	—	4	2	no	—
342	C₇×D₄	—	4	4	no	—
343	C₂×C₄×C₇	—	2	2	no	—
344	C₂×C₄×C₇	—	2	2	no	—
345	C₂×C₄×C₇	—	2	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	8	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	8	no	—
356	C₂×C₄×C₇	—	2	2	no	—
357	C₂×C₄×C₇	—	2	8	no	—
358	C₂×C₄×C₇	—	2	2	no	—
359	C₂×C₄×C₇	—	4	1	no	—
360	C₂×C₄×C₇	—	4	1	no	—
361	C₂×C₄×C₇	—	4	1	no	—
362	C₂×C₄×C₇	#131	1	4	yes	complemented
363	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
364	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
365	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
366	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
367	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
369	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
370	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
371	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
372	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
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	C₂×#41	1	4	yes	—
378	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
379	C₇×C₈	—	2	4	no	—
380	C₇×C₈	—	2	4	no	—
381	C₇×C₈	—	2	4	no	—
382	C₇×C₈	C₂×#41	1	8	yes	—
383	C₂×#41	C₂×C₄×C₇	1	2	yes	—
384	C₂×#41	C₂×C₄×C₇	1	2	yes	—
385	C₂×#41	C₂³×C₇	1	2	yes	—
386	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
387	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
389	#131	—	2	16	no	—
390	C₂×M₁₆	—	2	8	no	—
391	C₂×M₁₆	C₂³×C₇	1	2	yes	—
392	C₂×M₁₆	C₂³×C₇	1	4	yes	—
393	C₂×M₁₆	C₂³×C₇	1	8	yes	—
394	C₂×M₁₆	C₂³×C₇	1	2	yes	—
395	C₂²×C₈	C₂³×C₇	1	4	yes	—
396	C₂²×C₈	C₂³×C₇	1	4	yes	—
397	C₂²×C₈	C₂³×C₇	1	8	yes	—
398	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
399	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
400	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
401	#127	C₂×C₄×C₇	1	1	yes	characteristic
402	#126	C₂×C₄×C₇	1	4	yes	—
403	#126	C₂×C₄×C₇	1	4	yes	—
404	#125	C₂×C₄×C₇	1	2	yes	—
405	#125	C₂×C₄×C₇	1	2	yes	—
406	#125	C₂×C₄×C₇	1	2	yes	—
407	#124	C₂×C₄×C₇	1	2	yes	—
408	#124	C₂×C₄×C₇	1	2	yes	—
409	#124	C₂×C₄×C₇	1	2	yes	—
410	#123	C₂×C₄×C₇	1	4	yes	—
411	#123	C₂×C₄×C₇	1	4	yes	—
412	#123	C₂×C₄×C₇	1	4	yes	—
413	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
414	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
415	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
416	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
417	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
418	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
419	#121	C₂×C₄×C₇	1	2	yes	—
420	#121	C₂×C₄×C₇	1	2	yes	—
421	#121	C₂×C₄×C₇	1	2	yes	—
422	#121	C₂×C₄×C₇	1	2	yes	—
423	#121	C₂×C₄×C₇	1	2	yes	—
424	#121	C₂×C₄×C₇	1	2	yes	—
425	#120	C₂×C₄×C₇	1	4	yes	—
426	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
427	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
428	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
429	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
430	C₄×Q₈	C₂³×C₇	1	2	yes	—
431	C₄×Q₈	C₂³×C₇	1	2	yes	—
432	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
433	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
434	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
435	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
436	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
437	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
438	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
439	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
440	C₄×D₄	C₂³×C₇	1	4	yes	—
441	C₄×D₄	C₂³×C₇	1	4	yes	—
442	C₄×D₄	C₂³×C₇	1	2	yes	—
443	C₄×D₄	C₂³×C₇	1	2	yes	—
444	#117	C₂×C₄×C₇	1	2	yes	—
445	#117	C₂×C₄×C₇	1	2	yes	—
446	#117	C₂×C₄×C₇	1	4	yes	—
447	#117	C₂×C₄×C₇	1	4	yes	—
448	#117	C₂³×C₇	1	2	yes	—
449	#117	C₂³×C₇	1	4	yes	—
450	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
451	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
452	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
453	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
454	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
455	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₇	1	4	yes	—
457	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
458	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
463	C₄⋊C₈	C₂³×C₇	1	2	yes	—
464	C₄⋊C₈	C₂³×C₇	1	4	yes	—
465	C₄⋊C₈	C₂³×C₇	1	2	yes	—
466	C₄⋊C₈	C₂³×C₇	1	8	yes	—
467	C₄⋊C₈	C₂³×C₇	1	8	yes	—
468	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
469	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
470	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
471	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
472	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
473	#97	C₂³×C₇	1	2	yes	—
474	#97	C₂³×C₇	1	2	yes	—
475	#97	C₂³×C₇	1	4	yes	—
476	#97	C₂³×C₇	1	8	yes	—
477	C₄×C₈	C₂³×C₇	1	2	yes	—
478	C₄×C₈	C₂³×C₇	1	2	yes	—
479	C₄×C₈	C₂³×C₇	1	2	yes	—
480	C₄×C₈	C₂³×C₇	1	4	yes	—
481	C₄×C₈	C₂³×C₇	1	2	yes	—
482	C₄×C₈	C₂³×C₇	1	4	yes	—
483	C₄×C₈	C₂³×C₇	1	8	yes	—
484	C₂²×C₇	—	2	1	no	—
485	C₂²×C₇	—	2	1	no	—
486	C₂²×C₇	—	2	1	no	—
487	C₂²×C₇	—	2	1	no	—
488	C₂²×C₇	—	2	1	no	—
489	C₂²×C₇	—	2	4	no	—
490	C₂²×C₇	—	2	1	no	—
491	C₂²×C₇	—	2	4	no	—
492	C₂²×C₇	—	2	1	no	—
493	C₂²×C₇	—	2	4	no	—
494	C₂²×C₇	—	4	4	no	—
495	C₂²×C₇	C₄×#41	1	2	yes	—
496	C₂²×C₇	C₂×#131	1	2	yes	—
497	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
498	C₄×C₇	—	2	1	no	—
499	C₄×C₇	—	2	1	no	—
500	C₄×C₇	—	2	4	no	—
501	C₄×C₇	—	2	1	no	—
502	C₄×C₇	—	2	1	no	—
503	C₄×C₇	—	2	4	no	—
504	C₄×C₇	—	2	1	no	—
505	C₄×C₇	—	2	1	no	—
506	C₄×C₇	—	2	1	no	—
507	C₄×C₇	—	2	4	no	—
508	C₄×C₇	C₄×#41	1	2	yes	—
509	C₄×C₇	C₂×#131	1	2	yes	—
510	C₄×C₇	C₂×#131	1	2	yes	—
511	C₄×C₇	#568	1	2	yes	—
512	C₄×C₇	C₂²×#41	1	2	yes	—
513	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
514	#41	—	2	8	no	—
515	#41	—	2	8	no	—
516	#41	—	4	4	no	—
517	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
518	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
519	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
520	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
521	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
522	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
523	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
524	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
525	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
530	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
531	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
532	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
533	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
535	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
536	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
537	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
538	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
539	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
540	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
541	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
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	C₂⁴×C₇	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
550	M₁₆	—	2	4	no	—
551	M₁₆	—	2	8	no	—
552	M₁₆	—	2	16	no	—
553	M₁₆	C₇×#41	1	8	yes	complemented
554	C₂×C₈	—	2	8	no	—
555	C₂×C₈	—	2	8	no	—
556	C₂×C₈	—	2	16	no	—
557	C₂×C₈	C₂⁴×C₇	1	4	yes	—
558	C₂×C₈	C₂⁴×C₇	1	4	yes	—
559	C₂×C₈	C₂⁴×C₇	1	4	yes	—
560	C₂×C₈	C₂⁴×C₇	1	4	yes	—
561	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
562	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
563	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
564	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
565	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
566	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
567	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
568	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
569	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
570	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
571	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
578	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
579	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
582	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
583	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
584	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
585	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
586	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
587	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
588	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
589	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
590	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
591	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
592	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
593	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
594	C₄²	C₂²×C₄×C₇	1	4	yes	—
595	C₄²	C₂²×C₄×C₇	1	4	yes	—
596	C₄²	C₂⁴×C₇	1	1	yes	characteristic
597	C₄²	C₂⁴×C₇	1	1	yes	characteristic
598	C₄²	C₂⁴×C₇	1	1	yes	characteristic
599	C₄²	C₂⁴×C₇	1	4	yes	—
600	C₄²	C₂⁴×C₇	1	1	yes	characteristic
601	C₂×C₇	—	2	2	no	—
602	C₂×C₇	—	2	2	no	—
603	C₂×C₇	—	4	4	no	—
604	C₂×C₇	—	4	1	no	—
605	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
606	C₂×C₇	C₂²×#131	1	1	yes	characteristic
607	C₂×C₇	C₂×#568	1	1	yes	characteristic
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	4	1	no	—
611	C₂³	C₂³×C₄×C₇	1	4	yes	—
612	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
613	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
614	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
615	Q₈	—	2	4	no	—
616	Q₈	—	2	4	no	—
617	Q₈	—	4	2	no	—
618	D₄	—	2	8	no	—
619	D₄	—	2	8	no	—
620	D₄	—	2	4	no	—
621	D₄	—	2	4	no	—
622	D₄	—	4	2	no	—
623	D₄	—	4	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	8	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	8	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	C₇×#131	1	4	yes	complemented
644	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
646	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
647	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
648	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
649	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
650	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
651	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
652	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
655	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
656	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
657	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
658	C₂×C₄	C₂×C₇×#41	1	4	yes	—
659	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
660	C₈	—	2	4	no	—
661	C₈	—	2	4	no	—
662	C₈	—	2	4	no	—
663	C₈	C₂×C₇×#41	1	8	yes	—
664	C₇	#60210	1	1	yes	characteristic, direct product factor, Sylow
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	4	4	no	—
676	C₂²	C₄×C₇×#41	1	2	yes	—
677	C₂²	C₂×C₇×#131	1	2	yes	—
678	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	4	no	—
689	C₄	C₄×C₇×#41	1	2	yes	—
690	C₄	C₂×C₇×#131	1	2	yes	—
691	C₄	C₂×C₇×#131	1	2	yes	—
692	C₄	C₇×#568	1	2	yes	—
693	C₄	C₂²×C₇×#41	1	2	yes	—
694	C₂	—	2	2	no	—
695	C₂	—	2	2	no	—
696	C₂	—	4	1	no	—
697	C₂	—	4	4	no	—
698	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
699	C₂	C₂²×C₇×#131	1	1	yes	characteristic
700	C₂	C₂×C₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₇	C₂⁴
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 ◁ C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2969	C₂	semidirect
3. C₇×#2968	C₂	semidirect
4. C₇×#2965	C₂	semidirect
5. C₇×#2965	C₂	semidirect
6. C₇×C₈×#41	C₂	semidirect
7. C₇×#2962	C₂	semidirect
8. C₇×#2935	C₂	semidirect
9. C₇×#2933	C₂	semidirect
10. C₇×#2922	C₂	semidirect
11. C₂×C₇×#431	C₂	semidirect
12. C₄×C₇×#131	C₂	semidirect
13. C₂×C₄×C₇×M₁₆	C₂	semidirect
35. C₇×#446	C₂²	semidirect
36. C₇×#446	C₂²	semidirect
37. C₇×C₈×Q₈	C₂²	semidirect
39. C₇×#436	C₂²	semidirect
42. C₇×#435	C₂²	semidirect
44. C₇×C₈×D₄	C₂²	semidirect
45. C₇×#433	C₂²	semidirect
51. C₇×#431	C₂²	semidirect
52. C₇×#431	C₂²	semidirect
58. C₇×#405	C₂²	semidirect
64. C₄×C₇×M₁₆	C₂²	semidirect
68. C₂×C₄×C₇×C₈	C₂²	semidirect
69. #60210	C₇	direct (N × H)
172. #2969	C₂×C₇	semidirect
173. #2968	C₂×C₇	semidirect
174. #2965	C₂×C₇	semidirect
175. #2965	C₂×C₇	semidirect
176. C₈×#41	C₂×C₇	semidirect
177. #2962	C₂×C₇	semidirect
178. #2935	C₂×C₇	semidirect
179. #2933	C₂×C₇	semidirect
180. #2922	C₂×C₇	semidirect
181. C₂×#431	C₂×C₇	semidirect
182. C₄×#131	C₂×C₇	semidirect
183. C₂×C₄×M₁₆	C₂×C₇	semidirect
224. C₇×M₁₆	#41	semidirect
293. #446	C₂²×C₇	semidirect
294. #446	C₂²×C₇	semidirect
295. C₈×Q₈	C₂²×C₇	semidirect
297. #436	C₂²×C₇	semidirect
300. #435	C₂²×C₇	semidirect
302. C₈×D₄	C₂²×C₇	semidirect
303. #433	C₂²×C₇	semidirect
309. #431	C₂²×C₇	semidirect
310. #431	C₂²×C₇	semidirect
316. #405	C₂²×C₇	semidirect
322. C₄×M₁₆	C₂²×C₇	semidirect
326. C₂×C₄×C₈	C₂²×C₇	semidirect
362. C₂×C₄×C₇	#131	semidirect
553. M₁₆	C₇×#41	semidirect
643. C₂×C₄	C₇×#131	semidirect
664. C₇	#60210	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×#2969	2
C₇×#2968	2
C₇×#2965	2
C₇×C₈×#41	2
C₇×#2962	2
C₇×#2935	2
C₇×#2933	2
C₇×#2922	2
C₂×C₇×#431	2
C₄×C₇×#131	2
C₂×C₄×C₇×M₁₆	2
#60210	7

Subgroups — C7×#60210 #13237426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60210 #13237426