Subgroups — C₇×#23180 #13200396

Order 1792.

914 conjugacy classes of subgroups.

The subgroup lattice has 380 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×#444	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×#1975	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×#1770	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×#444	—	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×C₇×#97	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	#23180	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	2	yes	—
68	C₇×C₄⋊C₈	D₄	1	2	yes	—
69	C₇×#104	—	2	8	no	—
70	C₇×#104	—	4	4	no	—
71	C₇×C₂²⋊C₈	—	2	4	no	—
72	C₇×C₂²⋊C₈	—	2	4	no	—
73	C₇×#97	—	2	4	no	—
74	C₇×#97	—	2	2	no	—
75	C₄×C₇×C₈	—	2	2	no	—
76	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
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	C₇×#95	—	2	1	no	—
81	#3147	C₂×C₇	1	1	yes	characteristic
82	C₂×#444	C₂×C₇	1	2	yes	complemented
83	#2935	C₂×C₇	1	2	yes	complemented
84	#1980	C₂×C₇	1	2	yes	complemented
85	#1975	C₂×C₇	1	2	yes	complemented
86	#1876	C₂×C₇	1	4	yes	complemented
87	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
88	#1770	C₂×C₇	1	1	yes	characteristic, complemented
89	C₇×#41	—	2	4	no	—
90	C₇×#41	—	2	4	no	—
91	C₇×#41	—	2	4	no	—
92	C₇×#41	—	2	4	no	—
93	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
94	C₂×C₇×D₄	—	2	4	no	—
95	C₂×C₇×D₄	—	2	2	no	—
96	C₂×C₇×D₄	—	2	2	no	—
97	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₇	—	2	4	no	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	#41	1	1	yes	characteristic
101	C₂²×C₄×C₇	#41	1	1	yes	characteristic
102	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
103	C₇×Q₁₆	—	2	4	no	—
104	C₇×Q₁₆	—	4	2	no	—
105	C₇×SD₁₆	—	2	8	no	—
106	C₇×SD₁₆	—	4	4	no	—
107	C₇×D₈	—	2	4	no	—
108	C₇×D₈	—	4	2	no	—
109	C₇×M₁₆	—	2	2	no	—
110	C₇×M₁₆	—	2	2	no	—
111	C₇×M₁₆	—	2	2	no	—
112	C₇×M₁₆	—	4	8	no	—
113	C₇×M₁₆	C₂×D₄	1	4	yes	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	—	2	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	1	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	4	8	no	—
121	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	4	yes	—
126	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
127	C₂×C₇×C₈	#41	1	2	yes	—
128	C₇×C₄⋊C₄	—	2	2	no	—
129	C₇×C₄⋊C₄	—	2	2	no	—
130	C₇×C₄⋊C₄	—	4	2	no	—
131	C₇×C₂²⋊C₄	—	2	4	no	—
132	C₇×C₂²⋊C₄	—	2	4	no	—
133	C₄²×C₇	—	2	2	no	—
134	C₄²×C₇	—	2	2	no	—
135	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂×#135	C₂²×C₇	1	2	yes	—
140	C₂×#135	C₂²×C₇	1	2	yes	—
141	C₂×#131	C₂²×C₇	1	4	yes	—
142	#532	C₂²×C₇	1	2	yes	—
143	#495	C₄×C₇	1	2	yes	complemented
144	#495	C₄×C₇	1	2	yes	complemented
145	#494	C₄×C₇	1	1	yes	characteristic, complemented
146	#493	C₄×C₇	1	1	yes	characteristic, complemented
147	#492	C₄×C₇	1	2	yes	complemented
148	#444	—	2	8	no	—
149	#436	—	2	2	no	—
150	#435	—	2	4	no	—
151	C₈×D₄	—	2	2	no	—
152	C₂×#108	C₂²×C₇	1	1	yes	characteristic
153	C₂×#108	C₂²×C₇	1	1	yes	characteristic
154	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
155	C₂×#104	C₂²×C₇	1	4	yes	—
156	C₂×#104	C₂²×C₇	1	4	yes	—
157	#408	C₂²×C₇	1	4	yes	—
158	C₄×M₁₆	C₂²×C₇	1	2	yes	—
159	C₂×#97	C₂²×C₇	1	2	yes	—
160	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
161	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
162	#341	C₂²×C₇	1	2	yes	—
163	#336	C₂²×C₇	1	2	yes	—
164	C₂³×C₇	—	2	4	no	—
165	C₂³×C₇	C₂×#41	1	1	yes	characteristic
166	C₇×Q₈	—	2	4	no	—
167	C₇×Q₈	—	2	4	no	—
168	C₇×D₄	—	2	4	no	—
169	C₇×D₄	—	2	4	no	—
170	C₇×D₄	—	4	4	no	—
171	C₇×D₄	—	4	4	no	—
172	C₇×D₄	—	4	4	no	—
173	C₇×D₄	—	8	2	no	—
174	C₂×C₄×C₇	—	2	2	no	—
175	C₂×C₄×C₇	—	2	4	no	—
176	C₂×C₄×C₇	—	4	1	no	—
177	C₂×C₄×C₇	—	4	4	no	—
178	C₂×C₄×C₇	—	4	4	no	—
179	C₂×C₄×C₇	—	4	2	no	—
180	C₂×C₄×C₇	—	4	2	no	—
181	C₂×C₄×C₇	—	4	2	no	—
182	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
192	C₇×C₈	—	2	1	no	—
193	C₇×C₈	—	2	1	no	—
194	C₇×C₈	—	2	4	no	—
195	C₇×C₈	—	2	4	no	—
196	C₇×C₈	—	4	2	no	—
197	C₇×C₈	C₄×D₄	1	2	yes	—
198	C₇×C₈	C₄×D₄	1	2	yes	—
199	C₂×#41	C₂³×C₇	1	4	yes	—
200	#135	—	2	4	no	—
201	#135	—	2	4	no	—
202	#135	—	4	2	no	—
203	#135	—	4	2	no	—
204	C₂×Q₁₆	C₂×C₄×C₇	1	2	yes	—
205	C₂×Q₁₆	C₂×C₄×C₇	1	2	yes	—
206	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
207	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
208	C₂×D₈	C₂×C₄×C₇	1	2	yes	—
209	C₂×D₈	C₂×C₄×C₇	1	2	yes	—
210	#131	—	2	8	no	—
211	#131	—	4	4	no	—
212	C₂×M₁₆	—	2	4	no	—
213	C₂×M₁₆	C₂³×C₇	1	2	yes	—
214	C₂×M₁₆	C₂³×C₇	1	2	yes	—
215	C₂²×C₈	—	2	4	no	—
216	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₇	1	2	yes	—
218	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
219	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	—
220	#127	C₂×C₄×C₇	1	2	yes	—
221	#124	C₂×C₄×C₇	1	4	yes	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄²	C₂³×C₇	1	2	yes	—
228	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
229	#108	—	2	2	no	—
230	#108	C₇×D₄	1	4	yes	complemented
231	C₄⋊C₈	C₇×D₄	1	2	yes	—
232	C₄⋊C₈	C₇×D₄	1	2	yes	—
233	#104	—	2	8	no	—
234	#104	—	4	4	no	—
235	C₂²⋊C₈	—	2	4	no	—
236	C₂²⋊C₈	—	2	4	no	—
237	#97	—	2	4	no	—
238	#97	—	2	2	no	—
239	C₄×C₈	—	2	2	no	—
240	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
241	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
242	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
243	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
244	#95	—	2	1	no	—
245	C₂²×C₇	—	2	1	no	—
246	C₂²×C₇	—	2	1	no	—
247	C₂²×C₇	—	4	4	no	—
248	C₂²×C₇	—	4	4	no	—
249	C₂²×C₇	—	4	4	no	—
250	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₇	#550	1	1	yes	characteristic
252	C₂²×C₇	#559	1	1	yes	characteristic
253	C₄×C₇	—	2	1	no	—
254	C₄×C₇	—	2	1	no	—
255	C₄×C₇	—	2	1	no	—
256	C₄×C₇	—	4	4	no	—
257	C₄×C₇	—	8	2	no	—
258	C₄×C₇	#444	1	2	yes	complemented
259	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
260	C₄×C₇	#518	1	1	yes	characteristic
261	C₄×C₇	D₄²	1	1	yes	characteristic
262	C₄×C₇	#550	1	1	yes	characteristic
263	#41	—	2	4	no	—
264	#41	—	2	4	no	—
265	#41	—	2	4	no	—
266	#41	—	2	4	no	—
267	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	C₇×#41	1	1	yes	characteristic
275	C₂²×C₄	C₇×#41	1	1	yes	characteristic
276	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
277	Q₁₆	—	2	4	no	—
278	Q₁₆	—	4	2	no	—
279	SD₁₆	—	2	8	no	—
280	SD₁₆	—	4	4	no	—
281	D₈	—	2	4	no	—
282	D₈	—	4	2	no	—
283	M₁₆	—	2	2	no	—
284	M₁₆	—	2	2	no	—
285	M₁₆	—	2	2	no	—
286	M₁₆	—	4	8	no	—
287	M₁₆	C₂×C₇×D₄	1	4	yes	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	4	8	no	—
295	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
296	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
297	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
298	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
299	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
300	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
301	C₂×C₈	C₇×#41	1	2	yes	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
310	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
311	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
312	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
313	C₂×C₇	—	2	1	no	—
314	C₂×C₇	—	2	1	no	—
315	C₂×C₇	—	8	4	no	—
316	C₂×C₇	#2366	1	1	yes	characteristic
317	C₂×C₇	C₂×#444	1	1	yes	characteristic
318	C₂×C₇	#2957	1	1	yes	characteristic
319	C₂³	—	2	4	no	—
320	C₂³	C₂×C₇×#41	1	1	yes	characteristic
321	Q₈	—	2	4	no	—
322	Q₈	—	2	4	no	—
323	D₄	—	2	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	8	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
338	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
339	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
340	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
341	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
344	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
345	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
347	C₈	—	2	1	no	—
348	C₈	—	2	1	no	—
349	C₈	—	2	4	no	—
350	C₈	—	2	4	no	—
351	C₈	—	4	2	no	—
352	C₈	C₄×C₇×D₄	1	2	yes	—
353	C₈	C₄×C₇×D₄	1	2	yes	—
354	C₇	#23180	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	4	4	no	—
360	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
361	C₂²	C₇×#550	1	1	yes	characteristic
362	C₂²	C₇×#559	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	4	no	—
367	C₄	—	8	2	no	—
368	C₄	C₇×#444	1	2	yes	complemented
369	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
370	C₄	C₇×#518	1	1	yes	characteristic
371	C₄	C₇×D₄²	1	1	yes	characteristic
372	C₄	C₇×#550	1	1	yes	characteristic
373	C₂	—	2	1	no	—
374	C₂	—	2	1	no	—
375	C₂	—	8	4	no	—
376	C₂	C₇×#2366	1	1	yes	characteristic
377	C₂	C₂×C₇×#444	1	1	yes	characteristic
378	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×#444	C₂	semidirect
3. C₇×#2935	C₂	semidirect
4. C₇×#1980	C₂	semidirect
5. C₇×#1975	C₂	semidirect
6. C₇×#1876	C₂	semidirect
7. C₄×C₇×#108	C₂	semidirect
8. C₇×#1770	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. #23180	C₇	direct (N × H)
66. C₇×#108	D₄	semidirect
82. C₂×#444	C₂×C₇	semidirect
83. #2935	C₂×C₇	semidirect
84. #1980	C₂×C₇	semidirect
85. #1975	C₂×C₇	semidirect
86. #1876	C₂×C₇	semidirect
87. C₄×#108	C₂×C₇	semidirect
88. #1770	C₂×C₇	semidirect
143. #495	C₄×C₇	semidirect
144. #495	C₄×C₇	semidirect
145. #494	C₄×C₇	semidirect
146. #493	C₄×C₇	semidirect
147. #492	C₄×C₇	semidirect
230. #108	C₇×D₄	semidirect
258. C₄×C₇	#444	semidirect
354. C₇	#23180	direct (N × H)
368. C₄	C₇×#444	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×#444	2
C₇×#2935	2
C₇×#1980	2
C₇×#1975	2
C₇×#1876	2
C₄×C₇×#108	2
C₇×#1770	2
#23180	7

Subgroups — C7×#23180 #13200396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23180 #13200396