Subgroups — C₇×#61011 #13238227

Order 1792.

1896 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3508	C₂	1	2	yes	maximal, complemented
2	C₇×#3259	C₂	1	4	yes	maximal, complemented
3	C₇×#3228	C₂	1	4	yes	maximal, complemented
4	C₇×#3205	C₂	1	4	yes	maximal, complemented
5	C₇×#3199	C₂	1	4	yes	maximal, complemented
6	C₇×#3184	C₂	1	2	yes	maximal, complemented
7	C₇×#3169	C₂	1	2	yes	maximal, complemented
8	C₇×#3122	C₂	1	8	yes	maximal, complemented
9	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#559	—	2	4	no	—
11	C₇×#550	—	2	4	no	—
12	C₇×#546	—	2	4	no	—
13	C₇×#546	—	2	4	no	—
14	C₇×#540	C₂²	1	4	yes	—
15	C₇×#540	C₂²	1	4	yes	complemented
16	C₇×#535	C₂²	1	4	yes	—
17	C₇×#533	C₂²	1	2	yes	complemented
18	C₇×#532	C₂²	1	4	yes	—
19	C₇×#532	C₂²	1	4	yes	complemented
20	C₂×C₇×#127	C₂²	1	2	yes	complemented
21	C₇×#518	C₂²	1	4	yes	complemented
22	C₄×C₇×#41	C₂²	1	1	yes	characteristic
23	C₇×#500	C₂²	1	2	yes	complemented
24	C₇×#498	C₂²	1	2	yes	complemented
25	C₇×#493	C₂²	1	2	yes	—
26	C₇×#493	C₂²	1	2	yes	—
27	C₇×#486	C₂²	1	4	yes	complemented
28	C₇×#486	C₂²	1	4	yes	complemented
29	C₇×#482	C₂²	1	16	yes	complemented
30	C₇×#478	C₂²	1	16	yes	complemented
31	C₇×#469	C₂²	1	8	yes	complemented
32	C₇×#466	C₂²	1	8	yes	complemented
33	C₇×#459	C₂²	1	16	yes	complemented
34	C₇×#447	C₂²	1	16	yes	complemented
35	C₇×#442	C₂²	1	8	yes	complemented
36	C₄×C₇×D₈	C₂²	1	8	yes	complemented
37	C₇×#433	C₂²	1	4	yes	complemented
38	C₇×#431	C₂²	1	4	yes	complemented
39	C₇×#424	C₂²	1	2	yes	complemented
40	C₇×#408	C₂²	1	2	yes	—
41	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
43	#61011	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₇×#41	—	2	4	no	—
45	C₂×C₇×#41	—	2	4	no	—
46	C₂×C₇×#41	C₂³	1	1	yes	characteristic
47	C₂²×C₇×D₄	—	2	4	no	—
48	C₂²×C₇×D₄	C₂³	1	4	yes	—
49	C₂×C₇×D₈	C₂³	1	8	yes	—
50	C₂×C₇×D₈	C₂³	1	8	yes	—
51	C₂×C₇×M₁₆	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	2	yes	—
53	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
54	C₇×#127	—	2	4	no	—
55	C₇×#127	—	2	4	no	—
56	C₇×#127	C₂³	1	4	yes	—
57	C₇×#127	C₂³	1	4	yes	—
58	C₇×#125	C₂³	1	4	yes	—
59	C₇×#124	—	2	4	no	—
60	C₇×#124	—	2	4	no	—
61	C₇×#124	—	2	4	no	—
62	C₇×#123	—	2	8	no	—
63	C₇×#123	—	2	8	no	—
64	C₇×C₂²⋊Q₈	—	2	4	no	—
65	C₇×#121	—	2	4	no	—
66	C₇×#121	—	2	4	no	—
67	C₇×#121	—	2	8	no	—
68	C₇×#121	—	2	8	no	—
69	C₇×#121	C₂³	1	8	yes	—
70	C₇×#121	C₂³	1	8	yes	—
71	C₇×#120	—	2	4	no	—
72	C₇×#120	—	2	4	no	—
73	C₄×C₇×Q₈	—	2	4	no	—
74	C₄×C₇×Q₈	D₄	1	2	yes	—
75	C₄×C₇×D₄	—	2	8	no	—
76	C₄×C₇×D₄	—	2	4	no	—
77	C₄×C₇×D₄	—	2	4	no	—
78	C₄×C₇×D₄	D₄	1	2	yes	—
79	C₄×C₇×D₄	D₄	1	4	yes	—
80	C₄×C₇×D₄	C₂³	1	8	yes	—
81	C₄×C₇×D₄	C₂³	1	8	yes	—
82	C₇×#117	C₂³	1	4	yes	—
83	C₇×#117	C₂³	1	2	yes	—
84	C₇×#117	C₂³	1	1	yes	characteristic
85	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
86	C₂×C₄²×C₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
88	C₇×#107	C₂³	1	8	yes	—
89	C₇×#106	C₂³	1	8	yes	—
90	C₇×C₄⋊C₈	C₂³	1	8	yes	—
91	C₇×#102	C₂³	1	16	yes	—
92	C₇×#102	C₂³	1	16	yes	—
93	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
94	C₇×#97	C₂³	1	2	yes	—
95	C₄×C₇×C₈	C₂³	1	2	yes	—
96	C₄×C₇×C₈	C₂³	1	2	yes	—
97	C₄×C₇×C₈	C₂³	1	2	yes	—
98	#3508	C₂×C₇	1	2	yes	complemented
99	#3259	C₂×C₇	1	4	yes	complemented
100	#3228	C₂×C₇	1	4	yes	complemented
101	#3205	C₂×C₇	1	4	yes	complemented
102	#3199	C₂×C₇	1	4	yes	complemented
103	#3184	C₂×C₇	1	2	yes	complemented
104	#3169	C₂×C₇	1	2	yes	complemented
105	#3122	C₂×C₇	1	8	yes	complemented
106	#2922	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂⁴×C₇	—	2	4	no	—
108	C₇×#41	—	4	2	no	—
109	C₇×#41	—	8	8	no	—
110	C₇×#41	—	8	8	no	—
111	C₂×C₇×Q₈	—	2	4	no	—
112	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
113	C₂×C₇×D₄	—	2	8	no	—
114	C₂×C₇×D₄	—	2	8	no	—
115	C₂×C₇×D₄	—	2	4	no	—
116	C₂×C₇×D₄	—	2	4	no	—
117	C₂×C₇×D₄	—	2	4	no	—
118	C₂×C₇×D₄	—	2	8	no	—
119	C₂×C₇×D₄	—	4	8	no	—
120	C₂×C₇×D₄	—	8	8	no	—
121	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
122	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
123	C₂×C₇×D₄	C₂⁴	1	8	yes	—
124	C₂²×C₄×C₇	—	2	8	no	—
125	C₂²×C₄×C₇	—	2	8	no	—
126	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
130	C₇×D₈	—	4	8	no	—
131	C₇×D₈	—	4	8	no	—
132	C₇×M₁₆	—	4	2	no	—
133	C₂×C₇×C₈	—	4	2	no	—
134	C₂×C₇×C₈	C₂⁴	1	4	yes	—
135	C₂×C₇×C₈	C₂⁴	1	4	yes	—
136	C₇×C₄⋊C₄	—	2	4	no	—
137	C₇×C₄⋊C₄	—	2	8	no	—
138	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
139	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
140	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
141	C₇×C₂²⋊C₄	—	2	4	no	—
142	C₇×C₂²⋊C₄	—	2	8	no	—
143	C₇×C₂²⋊C₄	—	2	8	no	—
144	C₇×C₂²⋊C₄	—	2	8	no	—
145	C₇×C₂²⋊C₄	—	2	8	no	—
146	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
147	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
148	C₄²×C₇	—	2	4	no	—
149	C₄²×C₇	C₂×D₄	1	2	yes	—
150	C₄²×C₇	C₂×D₄	1	4	yes	—
151	C₄²×C₇	C₂⁴	1	1	yes	characteristic
152	C₄²×C₇	C₂⁴	1	1	yes	characteristic
153	C₄²×C₇	C₂⁴	1	2	yes	—
154	#559	—	2	4	no	—
155	#550	—	2	4	no	—
156	#546	—	2	4	no	—
157	#546	—	2	4	no	—
158	#540	C₂²×C₇	1	4	yes	—
159	#540	C₂²×C₇	1	4	yes	complemented
160	#535	C₂²×C₇	1	4	yes	—
161	#533	C₂²×C₇	1	2	yes	complemented
162	#532	C₂²×C₇	1	4	yes	—
163	#532	C₂²×C₇	1	4	yes	complemented
164	C₂×#127	C₂²×C₇	1	2	yes	complemented
165	#518	C₂²×C₇	1	4	yes	complemented
166	C₄×#41	C₂²×C₇	1	1	yes	characteristic
167	#500	C₂²×C₇	1	2	yes	complemented
168	#498	C₂²×C₇	1	2	yes	complemented
169	#493	C₂²×C₇	1	2	yes	—
170	#493	C₂²×C₇	1	2	yes	—
171	#486	C₂²×C₇	1	4	yes	complemented
172	#486	C₂²×C₇	1	4	yes	complemented
173	#482	C₂²×C₇	1	16	yes	complemented
174	#478	C₂²×C₇	1	16	yes	complemented
175	#469	C₂²×C₇	1	8	yes	complemented
176	#466	C₂²×C₇	1	8	yes	complemented
177	#459	C₂²×C₇	1	16	yes	complemented
178	#447	C₂²×C₇	1	16	yes	complemented
179	#442	C₂²×C₇	1	8	yes	complemented
180	C₄×D₈	C₂²×C₇	1	8	yes	complemented
181	#433	C₂²×C₇	1	4	yes	complemented
182	#431	C₂²×C₇	1	4	yes	complemented
183	#424	C₂²×C₇	1	2	yes	complemented
184	#408	C₂²×C₇	1	2	yes	—
185	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
186	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
187	C₂³×C₇	—	2	8	no	—
188	C₂³×C₇	—	4	8	no	—
189	C₂³×C₇	—	8	8	no	—
190	C₂³×C₇	C₂²×D₄	1	2	yes	—
191	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
192	C₇×Q₈	—	4	1	no	—
193	C₇×Q₈	—	4	8	no	—
194	C₇×D₄	—	2	16	no	—
195	C₇×D₄	—	4	2	no	—
196	C₇×D₄	—	4	1	no	—
197	C₇×D₄	—	4	8	no	—
198	C₇×D₄	—	4	8	no	—
199	C₇×D₄	—	4	8	no	—
200	C₇×D₄	—	8	8	no	—
201	C₇×D₄	—	8	8	no	—
202	C₇×D₄	—	8	8	no	—
203	C₂×C₄×C₇	—	2	8	no	—
204	C₂×C₄×C₇	—	2	4	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	4	no	—
207	C₂×C₄×C₇	—	2	8	no	—
208	C₂×C₄×C₇	—	8	8	no	—
209	C₂×C₄×C₇	—	8	8	no	—
210	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
214	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
216	C₇×C₈	—	2	4	no	—
217	C₇×C₈	—	2	4	no	—
218	C₂×#41	—	2	4	no	—
219	C₂×#41	—	2	4	no	—
220	C₂×#41	C₂³×C₇	1	1	yes	characteristic
221	C₂²×D₄	—	2	4	no	—
222	C₂²×D₄	C₂³×C₇	1	4	yes	—
223	C₂×D₈	C₂³×C₇	1	8	yes	—
224	C₂×D₈	C₂³×C₇	1	8	yes	—
225	C₂×M₁₆	C₂³×C₇	1	2	yes	—
226	C₂²×C₈	C₂³×C₇	1	2	yes	—
227	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
228	#127	—	2	4	no	—
229	#127	—	2	4	no	—
230	#127	C₂³×C₇	1	4	yes	—
231	#127	C₂³×C₇	1	4	yes	—
232	#125	C₂³×C₇	1	4	yes	—
233	#124	—	2	4	no	—
234	#124	—	2	4	no	—
235	#124	—	2	4	no	—
236	#123	—	2	8	no	—
237	#123	—	2	8	no	—
238	C₂²⋊Q₈	—	2	4	no	—
239	#121	—	2	4	no	—
240	#121	—	2	4	no	—
241	#121	—	2	8	no	—
242	#121	—	2	8	no	—
243	#121	C₂³×C₇	1	8	yes	—
244	#121	C₂³×C₇	1	8	yes	—
245	#120	—	2	4	no	—
246	#120	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	C₇×D₄	1	2	yes	—
249	C₄×D₄	—	2	8	no	—
250	C₄×D₄	—	2	4	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	C₇×D₄	1	2	yes	—
253	C₄×D₄	C₇×D₄	1	4	yes	—
254	C₄×D₄	C₂³×C₇	1	8	yes	—
255	C₄×D₄	C₂³×C₇	1	8	yes	—
256	#117	C₂³×C₇	1	4	yes	—
257	#117	C₂³×C₇	1	2	yes	—
258	#117	C₂³×C₇	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	8	no	—
260	C₂×C₄²	C₂³×C₇	1	2	yes	—
261	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
262	#107	C₂³×C₇	1	8	yes	—
263	#106	C₂³×C₇	1	8	yes	—
264	C₄⋊C₈	C₂³×C₇	1	8	yes	—
265	#102	C₂³×C₇	1	16	yes	—
266	#102	C₂³×C₇	1	16	yes	—
267	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
268	#97	C₂³×C₇	1	2	yes	—
269	C₄×C₈	C₂³×C₇	1	2	yes	—
270	C₄×C₈	C₂³×C₇	1	2	yes	—
271	C₄×C₈	C₂³×C₇	1	2	yes	—
272	C₂²×C₇	—	2	2	no	—
273	C₂²×C₇	—	2	1	no	—
274	C₂²×C₇	—	2	2	no	—
275	C₂²×C₇	—	2	4	no	—
276	C₂²×C₇	—	4	8	no	—
277	C₂²×C₇	—	4	8	no	—
278	C₂²×C₇	—	4	8	no	—
279	C₂²×C₇	—	16	8	no	—
280	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
281	C₄×C₇	—	2	2	no	—
282	C₄×C₇	—	2	1	no	—
283	C₄×C₇	—	2	2	no	—
284	C₄×C₇	—	2	4	no	—
285	C₄×C₇	—	4	8	no	—
286	C₄×C₇	#576	1	4	yes	—
287	C₄×C₇	#585	1	2	yes	—
288	C₂⁴	—	2	4	no	—
289	#41	—	4	2	no	—
290	#41	—	8	8	no	—
291	#41	—	8	8	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
294	C₂×D₄	—	2	8	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	4	8	no	—
301	C₂×D₄	—	8	8	no	—
302	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
303	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
304	C₂×D₄	C₂⁴×C₇	1	8	yes	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
308	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
309	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
311	D₈	—	4	8	no	—
312	D₈	—	4	8	no	—
313	M₁₆	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	C₂⁴×C₇	1	4	yes	—
316	C₂×C₈	C₂⁴×C₇	1	4	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
320	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
321	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	2	8	no	—
325	C₂²⋊C₄	—	2	8	no	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
328	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
329	C₄²	—	2	4	no	—
330	C₄²	C₂×C₇×D₄	1	2	yes	—
331	C₄²	C₂×C₇×D₄	1	4	yes	—
332	C₄²	C₂⁴×C₇	1	1	yes	characteristic
333	C₄²	C₂⁴×C₇	1	1	yes	characteristic
334	C₄²	C₂⁴×C₇	1	2	yes	—
335	C₂×C₇	—	4	1	no	—
336	C₂×C₇	—	4	2	no	—
337	C₂×C₇	—	8	8	no	—
338	C₂×C₇	#3449	1	1	yes	characteristic
339	C₂×C₇	C₂×#576	1	2	yes	—
340	C₂³	—	2	8	no	—
341	C₂³	—	4	8	no	—
342	C₂³	—	8	8	no	—
343	C₂³	C₂²×C₇×D₄	1	2	yes	—
344	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
345	Q₈	—	4	1	no	—
346	Q₈	—	4	8	no	—
347	D₄	—	2	16	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	8	no	—
353	D₄	—	8	8	no	—
354	D₄	—	8	8	no	—
355	D₄	—	8	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	8	8	no	—
362	C₂×C₄	—	8	8	no	—
363	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
364	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
366	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
367	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
368	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	—	2	4	no	—
371	C₇	#61011	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	2	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	4	8	no	—
377	C₂²	—	4	8	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	16	8	no	—
380	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	8	no	—
386	C₄	C₇×#576	1	4	yes	—
387	C₄	C₇×#585	1	2	yes	—
388	C₂	—	4	2	no	—
389	C₂	—	4	1	no	—
390	C₂	—	8	8	no	—
391	C₂	C₇×#3449	1	1	yes	characteristic
392	C₂	C₂×C₇×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3508	C₂	semidirect
2. C₇×#3259	C₂	semidirect
3. C₇×#3228	C₂	semidirect
4. C₇×#3205	C₂	semidirect
5. C₇×#3199	C₂	semidirect
6. C₇×#3184	C₂	semidirect
7. C₇×#3169	C₂	semidirect
8. C₇×#3122	C₂	semidirect
9. C₇×#2922	C₂	semidirect
15. C₇×#540	C₂²	semidirect
17. C₇×#533	C₂²	semidirect
19. C₇×#532	C₂²	semidirect
20. C₂×C₇×#127	C₂²	semidirect
21. C₇×#518	C₂²	semidirect
23. C₇×#500	C₂²	semidirect
24. C₇×#498	C₂²	semidirect
27. C₇×#486	C₂²	semidirect
28. C₇×#486	C₂²	semidirect
29. C₇×#482	C₂²	semidirect
30. C₇×#478	C₂²	semidirect
31. C₇×#469	C₂²	semidirect
32. C₇×#466	C₂²	semidirect
33. C₇×#459	C₂²	semidirect
34. C₇×#447	C₂²	semidirect
35. C₇×#442	C₂²	semidirect
36. C₄×C₇×D₈	C₂²	semidirect
37. C₇×#433	C₂²	semidirect
38. C₇×#431	C₂²	semidirect
39. C₇×#424	C₂²	semidirect
41. C₄×C₇×M₁₆	C₂²	semidirect
42. C₂×C₄×C₇×C₈	C₂²	semidirect
43. #61011	C₇	direct (N × H)
98. #3508	C₂×C₇	semidirect
99. #3259	C₂×C₇	semidirect
100. #3228	C₂×C₇	semidirect
101. #3205	C₂×C₇	semidirect
102. #3199	C₂×C₇	semidirect
103. #3184	C₂×C₇	semidirect
104. #3169	C₂×C₇	semidirect
105. #3122	C₂×C₇	semidirect
106. #2922	C₂×C₇	semidirect
159. #540	C₂²×C₇	semidirect
161. #533	C₂²×C₇	semidirect
163. #532	C₂²×C₇	semidirect
164. C₂×#127	C₂²×C₇	semidirect
165. #518	C₂²×C₇	semidirect
167. #500	C₂²×C₇	semidirect
168. #498	C₂²×C₇	semidirect
171. #486	C₂²×C₇	semidirect
172. #486	C₂²×C₇	semidirect
173. #482	C₂²×C₇	semidirect
174. #478	C₂²×C₇	semidirect
175. #469	C₂²×C₇	semidirect
176. #466	C₂²×C₇	semidirect
177. #459	C₂²×C₇	semidirect
178. #447	C₂²×C₇	semidirect
179. #442	C₂²×C₇	semidirect
180. C₄×D₈	C₂²×C₇	semidirect
181. #433	C₂²×C₇	semidirect
182. #431	C₂²×C₇	semidirect
183. #424	C₂²×C₇	semidirect
185. C₄×M₁₆	C₂²×C₇	semidirect
186. C₂×C₄×C₈	C₂²×C₇	semidirect
371. C₇	#61011	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×#3508	2
C₇×#3259	2
C₇×#3228	2
C₇×#3205	2
C₇×#3199	2
C₇×#3184	2
C₇×#3169	2
C₇×#3122	2
C₇×#2922	2
#61011	7

Subgroups — C7×#61011 #13238227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61011 #13238227