Subgroups — C₇×#60676 #13237892

Order 1792.

1998 conjugacy classes of subgroups.

The subgroup lattice has 400 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	2	yes	maximal, complemented
2	C₇×#3172	C₂	1	8	yes	maximal, complemented
3	C₇×#3171	C₂	1	8	yes	maximal, complemented
4	C₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3135	C₂	1	2	yes	maximal, complemented
7	C₇×#3054	C₂	1	4	yes	maximal, complemented
8	C₄×C₇×#135	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#135	C₂²	1	4	yes	—
11	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
12	C₇×#533	C₂²	1	4	yes	—
13	C₇×#533	C₂²	1	2	yes	—
14	C₇×#532	C₂²	1	2	yes	—
15	C₇×#532	C₂²	1	4	yes	—
16	C₇×#529	—	2	4	no	—
17	C₇×#529	—	2	4	no	—
18	C₇×#529	C₂²	1	8	yes	—
19	C₇×#525	—	2	4	no	—
20	C₇×#525	C₂²	1	4	yes	—
21	C₄×C₇×#41	—	2	4	no	—
22	C₄×C₇×#41	C₂²	1	4	yes	—
23	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
24	C₇×#501	C₂²	1	8	yes	complemented
25	C₇×#497	C₂²	1	4	yes	complemented
26	C₇×#496	C₂²	1	4	yes	complemented
27	C₇×#491	C₂²	1	4	yes	complemented
28	C₇×#490	C₂²	1	4	yes	complemented
29	C₇×#489	C₂²	1	8	yes	complemented
30	C₇×#470	C₂²	1	8	yes	—
31	C₇×#469	C₂²	1	8	yes	—
32	C₇×#468	C₂²	1	16	yes	—
33	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
34	C₄×C₇×SD₁₆	C₂²	1	16	yes	complemented
35	C₄×C₇×D₈	C₂²	1	8	yes	complemented
36	C₇×#427	C₂²	1	4	yes	—
37	C₇×#416	C₂²	1	8	yes	—
38	C₄×C₇×M₁₆	C₂²	1	8	yes	—
39	C₂×C₇×#97	C₂²	1	1	yes	characteristic
40	C₂×C₇×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
42	#60676	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₇×#41	—	2	4	no	—
44	C₂×C₇×#41	C₂³	1	4	yes	—
45	C₂³×C₄×C₇	D₄	1	2	yes	—
46	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
47	C₇×#135	—	2	16	no	—
48	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
49	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
50	C₂×C₇×D₈	C₂³	1	4	yes	—
51	C₂×C₇×M₁₆	—	2	8	no	—
52	C₂×C₇×M₁₆	C₂³	1	8	yes	—
53	C₂²×C₇×C₈	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	2	yes	—
55	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
57	C₇×#127	C₂³	1	2	yes	—
58	C₇×#126	—	2	8	no	—
59	C₇×#125	—	2	4	no	—
60	C₇×#125	C₂³	1	4	yes	—
61	C₇×#124	—	2	4	no	—
62	C₇×#124	C₂³	1	4	yes	—
63	C₇×#123	—	2	8	no	—
64	C₇×#123	—	2	4	no	—
65	C₇×C₂²⋊Q₈	—	2	4	no	—
66	C₇×C₂²⋊Q₈	—	2	4	no	—
67	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
68	C₇×#121	—	2	4	no	—
69	C₇×#121	—	2	4	no	—
70	C₇×#121	C₂³	1	8	yes	—
71	C₇×#120	—	2	4	no	—
72	C₄×C₇×Q₈	—	2	4	no	—
73	C₄×C₇×Q₈	—	2	4	no	—
74	C₄×C₇×Q₈	C₂³	1	8	yes	—
75	C₄×C₇×D₄	—	2	8	no	—
76	C₄×C₇×D₄	—	2	8	no	—
77	C₄×C₇×D₄	—	2	8	no	—
78	C₄×C₇×D₄	—	2	4	no	—
79	C₄×C₇×D₄	—	2	4	no	—
80	C₄×C₇×D₄	C₂³	1	8	yes	—
81	C₇×#117	—	2	4	no	—
82	C₇×#117	—	2	8	no	—
83	C₇×#117	—	2	4	no	—
84	C₇×#117	C₂³	1	4	yes	—
85	C₂×C₄²×C₇	—	2	4	no	—
86	C₂×C₄²×C₇	D₄	1	2	yes	—
87	C₂×C₄²×C₇	D₄	1	2	yes	—
88	C₂×C₄²×C₇	D₄	1	2	yes	—
89	C₂×C₄²×C₇	C₂³	1	4	yes	—
90	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
92	C₇×#107	C₂³	1	8	yes	—
93	C₇×#106	C₂³	1	8	yes	—
94	C₇×#103	C₂³	1	16	yes	—
95	C₇×#102	C₂³	1	16	yes	—
96	C₇×#97	C₂³	1	4	yes	—
97	C₇×#97	C₂³	1	4	yes	—
98	C₄×C₇×C₈	C₂³	1	8	yes	—
99	#3444	C₂×C₇	1	2	yes	complemented
100	#3172	C₂×C₇	1	8	yes	complemented
101	#3171	C₂×C₇	1	8	yes	complemented
102	#3162	C₂×C₇	1	1	yes	characteristic, complemented
103	#3150	C₂×C₇	1	1	yes	characteristic, complemented
104	#3135	C₂×C₇	1	2	yes	complemented
105	#3054	C₂×C₇	1	4	yes	complemented
106	C₄×#135	C₂×C₇	1	4	yes	complemented
107	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
109	C₇×#41	—	2	16	no	—
110	C₇×#41	—	4	16	no	—
111	C₂×C₇×Q₈	—	2	4	no	—
112	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
113	C₂×C₇×D₄	—	2	4	no	—
114	C₂×C₇×D₄	—	2	8	no	—
115	C₂×C₇×D₄	—	2	4	no	—
116	C₂×C₇×D₄	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	—	2	8	no	—
120	C₂²×C₄×C₇	—	4	4	no	—
121	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
129	C₇×Q₁₆	—	2	8	no	—
130	C₇×SD₁₆	—	2	16	no	—
131	C₇×D₈	—	2	8	no	—
132	C₇×M₁₆	—	2	16	no	—
133	C₂×C₇×C₈	—	2	4	no	—
134	C₂×C₇×C₈	#41	1	8	yes	complemented
135	C₂×C₇×C₈	C₂⁴	1	4	yes	—
136	C₂×C₇×C₈	C₂⁴	1	4	yes	—
137	C₇×C₄⋊C₄	—	2	4	no	—
138	C₇×C₄⋊C₄	—	2	4	no	—
139	C₇×C₄⋊C₄	—	2	8	no	—
140	C₇×C₄⋊C₄	—	2	8	no	—
141	C₇×C₄⋊C₄	—	2	8	no	—
142	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
143	C₇×C₂²⋊C₄	—	2	8	no	—
144	C₇×C₂²⋊C₄	—	2	4	no	—
145	C₇×C₂²⋊C₄	—	2	8	no	—
146	C₇×C₂²⋊C₄	—	2	8	no	—
147	C₇×C₂²⋊C₄	—	2	8	no	—
148	C₄²×C₇	—	2	8	no	—
149	C₄²×C₇	—	2	4	no	—
150	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₇	C₂×D₄	1	4	yes	—
152	C₄²×C₇	C₂×D₄	1	2	yes	—
153	C₄²×C₇	C₂×D₄	1	4	yes	—
154	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₇	C₂⁴	1	2	yes	—
156	C₄²×C₇	C₂⁴	1	2	yes	—
157	C₂×#135	C₂²×C₇	1	4	yes	—
158	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
159	#533	C₂²×C₇	1	4	yes	—
160	#533	C₂²×C₇	1	2	yes	—
161	#532	C₂²×C₇	1	2	yes	—
162	#532	C₂²×C₇	1	4	yes	—
163	#529	—	2	4	no	—
164	#529	—	2	4	no	—
165	#529	C₂²×C₇	1	8	yes	—
166	#525	—	2	4	no	—
167	#525	C₂²×C₇	1	4	yes	—
168	C₄×#41	—	2	4	no	—
169	C₄×#41	C₂²×C₇	1	4	yes	—
170	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
171	#501	C₂²×C₇	1	8	yes	complemented
172	#497	C₂²×C₇	1	4	yes	complemented
173	#496	C₂²×C₇	1	4	yes	complemented
174	#491	C₂²×C₇	1	4	yes	complemented
175	#490	C₂²×C₇	1	4	yes	complemented
176	#489	C₂²×C₇	1	8	yes	complemented
177	#470	C₂²×C₇	1	8	yes	—
178	#469	C₂²×C₇	1	8	yes	—
179	#468	C₂²×C₇	1	16	yes	—
180	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
181	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
182	C₄×D₈	C₂²×C₇	1	8	yes	complemented
183	#427	C₂²×C₇	1	4	yes	—
184	#416	C₂²×C₇	1	8	yes	—
185	C₄×M₁₆	C₂²×C₇	1	8	yes	—
186	C₂×#97	C₂²×C₇	1	1	yes	characteristic
187	C₂×#97	C₂²×C₇	1	1	yes	characteristic
188	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
189	C₂³×C₇	—	2	2	no	—
190	C₂³×C₇	—	2	4	no	—
191	C₂³×C₇	—	4	2	no	—
192	C₂³×C₇	C₂²×D₄	1	2	yes	—
193	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
194	C₇×Q₈	—	2	8	no	—
195	C₇×Q₈	—	4	8	no	—
196	C₇×D₄	—	2	8	no	—
197	C₇×D₄	—	4	8	no	—
198	C₇×D₄	—	4	16	no	—
199	C₇×D₄	—	4	8	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	4	no	—
202	C₂×C₄×C₇	—	2	4	no	—
203	C₂×C₄×C₇	—	2	8	no	—
204	C₂×C₄×C₇	—	2	4	no	—
205	C₂×C₄×C₇	—	2	4	no	—
206	C₂×C₄×C₇	—	2	8	no	—
207	C₂×C₄×C₇	—	4	4	no	—
208	C₂×C₄×C₇	—	4	2	no	—
209	C₂×C₄×C₇	—	4	8	no	—
210	C₂×C₄×C₇	—	4	16	no	—
211	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
215	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₇	C₂×#41	1	4	yes	—
217	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
218	C₇×C₈	—	2	4	no	—
219	C₇×C₈	C₂×#41	1	8	yes	—
220	C₂×#41	—	2	4	no	—
221	C₂×#41	C₂³×C₇	1	4	yes	—
222	C₂³×C₄	C₇×D₄	1	2	yes	—
223	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
224	#135	—	2	16	no	—
225	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
226	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
227	C₂×D₈	C₂³×C₇	1	4	yes	—
228	C₂×M₁₆	—	2	8	no	—
229	C₂×M₁₆	C₂³×C₇	1	8	yes	—
230	C₂²×C₈	C₂³×C₇	1	2	yes	—
231	C₂²×C₈	C₂³×C₇	1	2	yes	—
232	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
233	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
234	#127	C₂³×C₇	1	2	yes	—
235	#126	—	2	8	no	—
236	#125	—	2	4	no	—
237	#125	C₂³×C₇	1	4	yes	—
238	#124	—	2	4	no	—
239	#124	C₂³×C₇	1	4	yes	—
240	#123	—	2	8	no	—
241	#123	—	2	4	no	—
242	C₂²⋊Q₈	—	2	4	no	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
245	#121	—	2	4	no	—
246	#121	—	2	4	no	—
247	#121	C₂³×C₇	1	8	yes	—
248	#120	—	2	4	no	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	C₂³×C₇	1	8	yes	—
252	C₄×D₄	—	2	8	no	—
253	C₄×D₄	—	2	8	no	—
254	C₄×D₄	—	2	8	no	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	C₂³×C₇	1	8	yes	—
258	#117	—	2	4	no	—
259	#117	—	2	8	no	—
260	#117	—	2	4	no	—
261	#117	C₂³×C₇	1	4	yes	—
262	C₂×C₄²	—	2	4	no	—
263	C₂×C₄²	C₇×D₄	1	2	yes	—
264	C₂×C₄²	C₇×D₄	1	2	yes	—
265	C₂×C₄²	C₇×D₄	1	2	yes	—
266	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₇	1	4	yes	—
268	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
269	#107	C₂³×C₇	1	8	yes	—
270	#106	C₂³×C₇	1	8	yes	—
271	#103	C₂³×C₇	1	16	yes	—
272	#102	C₂³×C₇	1	16	yes	—
273	#97	C₂³×C₇	1	4	yes	—
274	#97	C₂³×C₇	1	4	yes	—
275	C₄×C₈	C₂³×C₇	1	8	yes	—
276	C₂²×C₇	—	2	2	no	—
277	C₂²×C₇	—	2	2	no	—
278	C₂²×C₇	—	2	4	no	—
279	C₂²×C₇	—	4	4	no	—
280	C₂²×C₇	—	4	4	no	—
281	C₂²×C₇	—	4	8	no	—
282	C₂²×C₇	#532	1	2	yes	—
283	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
284	C₄×C₇	—	2	2	no	—
285	C₄×C₇	—	2	2	no	—
286	C₄×C₇	—	2	4	no	—
287	C₄×C₇	—	4	4	no	—
288	C₄×C₇	—	4	8	no	—
289	C₄×C₇	#532	1	2	yes	—
290	C₄×C₇	#575	1	4	yes	—
291	C₄×C₇	C₂²×#41	1	2	yes	—
292	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
293	#41	—	2	16	no	—
294	#41	—	4	16	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	C₂⁴×C₇	1	4	yes	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
306	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
308	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
309	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
310	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
313	Q₁₆	—	2	8	no	—
314	SD₁₆	—	2	16	no	—
315	D₈	—	2	8	no	—
316	M₁₆	—	2	16	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	C₇×#41	1	8	yes	complemented
319	C₂×C₈	C₂⁴×C₇	1	4	yes	—
320	C₂×C₈	C₂⁴×C₇	1	4	yes	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	2	8	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₄²	—	2	8	no	—
333	C₄²	—	2	4	no	—
334	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
335	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
336	C₄²	C₂×C₇×D₄	1	4	yes	—
337	C₄²	C₂×C₇×D₄	1	2	yes	—
338	C₄²	C₂×C₇×D₄	1	4	yes	—
339	C₄²	C₂⁴×C₇	1	2	yes	—
340	C₄²	C₂⁴×C₇	1	2	yes	—
341	C₂×C₇	—	2	2	no	—
342	C₂×C₇	—	4	2	no	—
343	C₂×C₇	—	8	4	no	—
344	C₂×C₇	C₂×#532	1	1	yes	characteristic
345	C₂×C₇	C₂×#575	1	2	yes	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	4	2	no	—
349	C₂³	C₂²×C₇×D₄	1	2	yes	—
350	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
351	Q₈	—	2	8	no	—
352	Q₈	—	4	8	no	—
353	D₄	—	2	8	no	—
354	D₄	—	4	8	no	—
355	D₄	—	4	16	no	—
356	D₄	—	4	8	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	16	no	—
368	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
369	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
370	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
371	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
373	C₂×C₄	C₂×C₇×#41	1	4	yes	—
374	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	C₂×C₇×#41	1	8	yes	—
377	C₇	#60676	1	1	yes	characteristic, direct product factor, Sylow
378	C₂²	—	2	2	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	8	no	—
383	C₂²	—	4	4	no	—
384	C₂²	C₇×#532	1	2	yes	—
385	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
386	C₄	—	2	4	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	8	no	—
390	C₄	—	4	4	no	—
391	C₄	C₇×#532	1	2	yes	—
392	C₄	C₇×#575	1	4	yes	—
393	C₄	C₂²×C₇×#41	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	4	2	no	—
396	C₂	—	8	4	no	—
397	C₂	C₂×C₇×#532	1	1	yes	characteristic
398	C₂	C₂×C₇×#575	1	2	yes	—

	subgroup	G/H
center	C₄²×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3444	C₂	semidirect
2. C₇×#3172	C₂	semidirect
3. C₇×#3171	C₂	semidirect
4. C₇×#3162	C₂	semidirect
5. C₇×#3150	C₂	semidirect
6. C₇×#3135	C₂	semidirect
7. C₇×#3054	C₂	semidirect
8. C₄×C₇×#135	C₂	semidirect
9. C₂×C₄×C₇×M₁₆	C₂	semidirect
24. C₇×#501	C₂²	semidirect
25. C₇×#497	C₂²	semidirect
26. C₇×#496	C₂²	semidirect
27. C₇×#491	C₂²	semidirect
28. C₇×#490	C₂²	semidirect
29. C₇×#489	C₂²	semidirect
33. C₄×C₇×Q₁₆	C₂²	semidirect
34. C₄×C₇×SD₁₆	C₂²	semidirect
35. C₄×C₇×D₈	C₂²	semidirect
42. #60676	C₇	direct (N × H)
99. #3444	C₂×C₇	semidirect
100. #3172	C₂×C₇	semidirect
101. #3171	C₂×C₇	semidirect
102. #3162	C₂×C₇	semidirect
103. #3150	C₂×C₇	semidirect
104. #3135	C₂×C₇	semidirect
105. #3054	C₂×C₇	semidirect
106. C₄×#135	C₂×C₇	semidirect
107. C₂×C₄×M₁₆	C₂×C₇	semidirect
134. C₂×C₇×C₈	#41	semidirect
171. #501	C₂²×C₇	semidirect
172. #497	C₂²×C₇	semidirect
173. #496	C₂²×C₇	semidirect
174. #491	C₂²×C₇	semidirect
175. #490	C₂²×C₇	semidirect
176. #489	C₂²×C₇	semidirect
180. C₄×Q₁₆	C₂²×C₇	semidirect
181. C₄×SD₁₆	C₂²×C₇	semidirect
182. C₄×D₈	C₂²×C₇	semidirect
318. C₂×C₈	C₇×#41	semidirect
377. C₇	#60676	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×#3172	2
C₇×#3171	2
C₇×#3162	2
C₇×#3150	2
C₇×#3135	2
C₇×#3054	2
C₄×C₇×#135	2
C₂×C₄×C₇×M₁₆	2
#60676	7

Subgroups — C7×#60676 #13237892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60676 #13237892