Subgroups — C₇×#23179 #13200395

Order 1792.

926 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#443	C₂	1	2	yes	maximal, complemented
3	C₇×#2935	C₂	1	2	yes	maximal, complemented
4	C₇×#1980	C₂	1	2	yes	maximal, complemented
5	C₇×#1974	C₂	1	2	yes	maximal, complemented
6	C₇×#1876	C₂	1	4	yes	maximal, complemented
7	C₄×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#135	C₂²	1	2	yes	—
10	C₂×C₇×#135	C₂²	1	2	yes	—
11	C₂×C₇×#131	C₂²	1	4	yes	—
12	C₇×#532	C₂²	1	2	yes	—
13	C₇×#495	C₄	1	2	yes	complemented
14	C₇×#495	C₄	1	2	yes	complemented
15	C₇×#494	C₄	1	1	yes	characteristic, complemented
16	C₇×#493	C₄	1	1	yes	characteristic, complemented
17	C₇×#492	C₄	1	2	yes	complemented
18	C₇×#443	—	2	8	no	—
19	C₇×#436	—	2	2	no	—
20	C₇×#435	—	2	4	no	—
21	C₇×C₈×D₄	—	2	2	no	—
22	C₂×C₇×#108	C₂²	1	1	yes	characteristic
23	C₂×C₇×#108	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#104	C₂²	1	4	yes	—
26	C₂×C₇×#104	C₂²	1	4	yes	—
27	C₇×#408	C₂²	1	4	yes	—
28	C₄×C₇×M₁₆	C₂²	1	2	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₇×#341	C₂²	1	2	yes	—
33	C₇×#336	C₂²	1	2	yes	—
34	#23179	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂×C₇×#41	C₂³	1	4	yes	—
36	C₇×#135	—	2	4	no	—
37	C₇×#135	—	2	4	no	—
38	C₇×#135	—	4	2	no	—
39	C₇×#135	—	4	2	no	—
40	C₂×C₇×Q₁₆	C₂×C₄	1	2	yes	—
41	C₂×C₇×Q₁₆	C₂×C₄	1	2	yes	—
42	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
43	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
44	C₂×C₇×D₈	C₂×C₄	1	2	yes	—
45	C₂×C₇×D₈	C₂×C₄	1	2	yes	—
46	C₇×#131	—	2	8	no	—
47	C₇×#131	—	4	4	no	—
48	C₂×C₇×M₁₆	—	2	4	no	—
49	C₂×C₇×M₁₆	C₂³	1	2	yes	—
50	C₂×C₇×M₁₆	C₂³	1	2	yes	—
51	C₂²×C₇×C₈	—	2	4	no	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	—
56	C₇×#127	C₂×C₄	1	2	yes	—
57	C₇×#124	C₂×C₄	1	4	yes	—
58	C₇×#121	—	2	2	no	—
59	C₇×#121	—	2	2	no	—
60	C₄×C₇×D₄	—	2	2	no	—
61	C₄×C₇×D₄	—	2	2	no	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₄²×C₇	C₂³	1	2	yes	—
64	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
65	C₇×#108	—	2	2	no	—
66	C₇×#108	D₄	1	4	yes	complemented
67	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
68	C₇×C₄⋊C₈	D₄	1	2	yes	—
69	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
70	C₇×#104	—	2	8	no	—
71	C₇×#104	—	4	4	no	—
72	C₇×C₂²⋊C₈	—	2	4	no	—
73	C₇×C₂²⋊C₈	—	2	4	no	—
74	C₇×#97	—	2	2	no	—
75	C₄×C₇×C₈	—	2	4	no	—
76	C₄×C₇×C₈	—	2	2	no	—
77	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
78	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
79	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
80	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
81	C₇×#95	—	2	1	no	—
82	#3147	C₂×C₇	1	1	yes	characteristic
83	C₂×#443	C₂×C₇	1	2	yes	complemented
84	#2935	C₂×C₇	1	2	yes	complemented
85	#1980	C₂×C₇	1	2	yes	complemented
86	#1974	C₂×C₇	1	2	yes	complemented
87	#1876	C₂×C₇	1	4	yes	complemented
88	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
89	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
90	C₇×#41	—	2	4	no	—
91	C₇×#41	—	2	4	no	—
92	C₇×#41	—	2	4	no	—
93	C₇×#41	—	2	4	no	—
94	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
95	C₂×C₇×D₄	—	2	4	no	—
96	C₂×C₇×D₄	—	2	2	no	—
97	C₂×C₇×D₄	—	2	2	no	—
98	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	—	2	4	no	—
101	C₂²×C₄×C₇	#41	1	1	yes	characteristic
102	C₂²×C₄×C₇	#41	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
104	C₇×Q₁₆	—	2	4	no	—
105	C₇×Q₁₆	—	4	2	no	—
106	C₇×SD₁₆	—	2	8	no	—
107	C₇×SD₁₆	—	4	4	no	—
108	C₇×D₈	—	2	4	no	—
109	C₇×D₈	—	4	2	no	—
110	C₇×M₁₆	—	2	2	no	—
111	C₇×M₁₆	—	2	2	no	—
112	C₇×M₁₆	—	2	2	no	—
113	C₇×M₁₆	—	4	8	no	—
114	C₇×M₁₆	C₂×D₄	1	4	yes	—
115	C₂×C₇×C₈	—	2	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	—	2	1	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	4	8	no	—
122	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
127	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
128	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
129	C₂×C₇×C₈	#41	1	2	yes	—
130	C₇×C₄⋊C₄	—	2	4	no	—
131	C₇×C₄⋊C₄	—	2	2	no	—
132	C₇×C₄⋊C₄	—	2	2	no	—
133	C₇×C₂²⋊C₄	—	2	4	no	—
134	C₇×C₂²⋊C₄	—	2	4	no	—
135	C₄²×C₇	—	2	2	no	—
136	C₄²×C₇	—	2	2	no	—
137	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
141	C₂×#135	C₂²×C₇	1	2	yes	—
142	C₂×#135	C₂²×C₇	1	2	yes	—
143	C₂×#131	C₂²×C₇	1	4	yes	—
144	#532	C₂²×C₇	1	2	yes	—
145	#495	C₄×C₇	1	2	yes	complemented
146	#495	C₄×C₇	1	2	yes	complemented
147	#494	C₄×C₇	1	1	yes	characteristic, complemented
148	#493	C₄×C₇	1	1	yes	characteristic, complemented
149	#492	C₄×C₇	1	2	yes	complemented
150	#443	—	2	8	no	—
151	#436	—	2	2	no	—
152	#435	—	2	4	no	—
153	C₈×D₄	—	2	2	no	—
154	C₂×#108	C₂²×C₇	1	1	yes	characteristic
155	C₂×#108	C₂²×C₇	1	1	yes	characteristic
156	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
157	C₂×#104	C₂²×C₇	1	4	yes	—
158	C₂×#104	C₂²×C₇	1	4	yes	—
159	#408	C₂²×C₇	1	4	yes	—
160	C₄×M₁₆	C₂²×C₇	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
162	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
163	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
164	#341	C₂²×C₇	1	2	yes	—
165	#336	C₂²×C₇	1	2	yes	—
166	C₂³×C₇	—	2	4	no	—
167	C₂³×C₇	C₂×#41	1	1	yes	characteristic
168	C₇×Q₈	—	2	4	no	—
169	C₇×Q₈	—	2	4	no	—
170	C₇×D₄	—	2	4	no	—
171	C₇×D₄	—	2	4	no	—
172	C₇×D₄	—	4	4	no	—
173	C₇×D₄	—	4	4	no	—
174	C₇×D₄	—	4	4	no	—
175	C₇×D₄	—	8	2	no	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	2	4	no	—
178	C₂×C₄×C₇	—	2	4	no	—
179	C₂×C₄×C₇	—	4	1	no	—
180	C₂×C₄×C₇	—	4	2	no	—
181	C₂×C₄×C₇	—	4	2	no	—
182	C₂×C₄×C₇	—	4	4	no	—
183	C₂×C₄×C₇	—	4	4	no	—
184	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
194	C₇×C₈	—	2	1	no	—
195	C₇×C₈	—	2	1	no	—
196	C₇×C₈	—	2	2	no	—
197	C₇×C₈	—	2	2	no	—
198	C₇×C₈	—	2	4	no	—
199	C₇×C₈	—	4	2	no	—
200	C₇×C₈	C₄×D₄	1	2	yes	—
201	C₇×C₈	C₄×D₄	1	2	yes	—
202	C₂×#41	C₂³×C₇	1	4	yes	—
203	#135	—	2	4	no	—
204	#135	—	2	4	no	—
205	#135	—	4	2	no	—
206	#135	—	4	2	no	—
207	C₂×Q₁₆	C₂×C₄×C₇	1	2	yes	—
208	C₂×Q₁₆	C₂×C₄×C₇	1	2	yes	—
209	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
210	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
211	C₂×D₈	C₂×C₄×C₇	1	2	yes	—
212	C₂×D₈	C₂×C₄×C₇	1	2	yes	—
213	#131	—	2	8	no	—
214	#131	—	4	4	no	—
215	C₂×M₁₆	—	2	4	no	—
216	C₂×M₁₆	C₂³×C₇	1	2	yes	—
217	C₂×M₁₆	C₂³×C₇	1	2	yes	—
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
220	C₂²×C₈	C₂³×C₇	1	2	yes	—
221	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
222	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
223	#127	C₂×C₄×C₇	1	2	yes	—
224	#124	C₂×C₄×C₇	1	4	yes	—
225	#121	—	2	2	no	—
226	#121	—	2	2	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄²	C₂³×C₇	1	2	yes	—
231	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
232	#108	—	2	2	no	—
233	#108	C₇×D₄	1	4	yes	complemented
234	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
235	C₄⋊C₈	C₇×D₄	1	2	yes	—
236	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
237	#104	—	2	8	no	—
238	#104	—	4	4	no	—
239	C₂²⋊C₈	—	2	4	no	—
240	C₂²⋊C₈	—	2	4	no	—
241	#97	—	2	2	no	—
242	C₄×C₈	—	2	4	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
245	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
246	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
247	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
248	#95	—	2	1	no	—
249	C₂²×C₇	—	2	1	no	—
250	C₂²×C₇	—	2	1	no	—
251	C₂²×C₇	—	4	4	no	—
252	C₂²×C₇	—	4	4	no	—
253	C₂²×C₇	—	4	4	no	—
254	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂²×C₇	#550	1	1	yes	characteristic
256	C₂²×C₇	#559	1	1	yes	characteristic
257	C₄×C₇	—	2	1	no	—
258	C₄×C₇	—	2	1	no	—
259	C₄×C₇	—	2	1	no	—
260	C₄×C₇	—	4	4	no	—
261	C₄×C₇	—	4	4	no	—
262	C₄×C₇	#443	1	2	yes	complemented
263	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
264	C₄×C₇	#518	1	1	yes	characteristic
265	C₄×C₇	D₄²	1	1	yes	characteristic
266	C₄×C₇	#550	1	1	yes	characteristic
267	#41	—	2	4	no	—
268	#41	—	2	4	no	—
269	#41	—	2	4	no	—
270	#41	—	2	4	no	—
271	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	C₇×#41	1	1	yes	characteristic
279	C₂²×C₄	C₇×#41	1	1	yes	characteristic
280	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
281	Q₁₆	—	2	4	no	—
282	Q₁₆	—	4	2	no	—
283	SD₁₆	—	2	8	no	—
284	SD₁₆	—	4	4	no	—
285	D₈	—	2	4	no	—
286	D₈	—	4	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	2	no	—
289	M₁₆	—	2	2	no	—
290	M₁₆	—	4	8	no	—
291	M₁₆	C₂×C₇×D₄	1	4	yes	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	8	no	—
299	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
300	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
302	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
303	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
304	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
305	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
306	C₂×C₈	C₇×#41	1	2	yes	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
315	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
316	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
317	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
318	C₂×C₇	—	2	1	no	—
319	C₂×C₇	—	2	1	no	—
320	C₂×C₇	—	8	4	no	—
321	C₂×C₇	#2366	1	1	yes	characteristic
322	C₂×C₇	C₂×#443	1	1	yes	characteristic
323	C₂×C₇	#2957	1	1	yes	characteristic
324	C₂³	—	2	4	no	—
325	C₂³	C₂×C₇×#41	1	1	yes	characteristic
326	Q₈	—	2	4	no	—
327	Q₈	—	2	4	no	—
328	D₄	—	2	4	no	—
329	D₄	—	2	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	4	no	—
333	D₄	—	8	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
343	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
344	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
345	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
346	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
348	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
350	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	2	4	no	—
357	C₈	—	4	2	no	—
358	C₈	C₄×C₇×D₄	1	2	yes	—
359	C₈	C₄×C₇×D₄	1	2	yes	—
360	C₇	#23179	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
367	C₂²	C₇×#550	1	1	yes	characteristic
368	C₂²	C₇×#559	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	4	no	—
374	C₄	C₇×#443	1	2	yes	complemented
375	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
376	C₄	C₇×#518	1	1	yes	characteristic
377	C₄	C₇×D₄²	1	1	yes	characteristic
378	C₄	C₇×#550	1	1	yes	characteristic
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	8	4	no	—
382	C₂	C₇×#2366	1	1	yes	characteristic
383	C₂	C₂×C₇×#443	1	1	yes	characteristic
384	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#3147	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#443	C₂	semidirect
3. C₇×#2935	C₂	semidirect
4. C₇×#1980	C₂	semidirect
5. C₇×#1974	C₂	semidirect
6. C₇×#1876	C₂	semidirect
7. C₄×C₇×#108	C₂	semidirect
8. C₇×C₈×C₄⋊C₄	C₂	semidirect
13. C₇×#495	C₄	semidirect
14. C₇×#495	C₄	semidirect
15. C₇×#494	C₄	semidirect
16. C₇×#493	C₄	semidirect
17. C₇×#492	C₄	semidirect
34. #23179	C₇	direct (N × H)
66. C₇×#108	D₄	semidirect
83. C₂×#443	C₂×C₇	semidirect
84. #2935	C₂×C₇	semidirect
85. #1980	C₂×C₇	semidirect
86. #1974	C₂×C₇	semidirect
87. #1876	C₂×C₇	semidirect
88. C₄×#108	C₂×C₇	semidirect
89. C₈×C₄⋊C₄	C₂×C₇	semidirect
145. #495	C₄×C₇	semidirect
146. #495	C₄×C₇	semidirect
147. #494	C₄×C₇	semidirect
148. #493	C₄×C₇	semidirect
149. #492	C₄×C₇	semidirect
233. #108	C₇×D₄	semidirect
262. C₄×C₇	#443	semidirect
360. C₇	#23179	direct (N × H)
374. C₄	C₇×#443	semidirect

Maximal subgroups

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

subgroup	index
C₇×#3147	2
C₂×C₇×#443	2
C₇×#2935	2
C₇×#1980	2
C₇×#1974	2
C₇×#1876	2
C₄×C₇×#108	2
C₇×C₈×C₄⋊C₄	2
#23179	7

Subgroups — C7×#23179 #13200395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23179 #13200395