Subgroups — C₇×#60714 #13237930

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 372 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×#3184	C₂	1	4	yes	maximal, complemented
3	C₇×#3176	C₂	1	8	yes	maximal, complemented
4	C₇×#3169	C₂	1	4	yes	maximal, complemented
5	C₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#493	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3138	C₂	1	2	yes	maximal, complemented
8	C₇×#3058	C₂	1	4	yes	maximal, complemented
9	C₇×#2948	C₂	1	4	yes	maximal, complemented
10	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×D₈	C₂²	1	4	yes	—
12	C₂×C₇×#131	C₂²	1	2	yes	—
13	C₇×#559	—	2	4	no	—
14	C₇×#550	—	2	4	no	—
15	C₇×#546	—	2	8	no	—
16	C₇×#540	C₂²	1	8	yes	complemented
17	C₇×#535	C₂²	1	4	yes	—
18	C₇×#533	C₂²	1	2	yes	—
19	C₇×#532	C₂²	1	8	yes	complemented
20	C₂×C₇×#127	C₂²	1	2	yes	—
21	C₇×#518	C₂²	1	4	yes	—
22	C₄×C₇×#41	C₂²	1	1	yes	characteristic
23	C₇×#500	C₂²	1	2	yes	complemented
24	C₇×#499	C₂²	1	4	yes	complemented
25	C₇×#498	C₂²	1	2	yes	complemented
26	C₇×#493	C₂²	1	2	yes	—
27	C₇×#493	C₂²	1	4	yes	—
28	C₇×#493	C₂²	1	2	yes	—
29	C₇×#490	C₂²	1	8	yes	complemented
30	C₇×#486	C₂²	1	8	yes	complemented
31	C₇×#469	C₂²	1	16	yes	complemented
32	C₇×#466	C₂²	1	16	yes	complemented
33	C₇×#442	C₂²	1	16	yes	complemented
34	C₄×C₇×D₈	C₂²	1	16	yes	complemented
35	C₇×#427	C₂²	1	4	yes	—
36	C₇×#418	C₂²	1	8	yes	—
37	C₇×#405	C₂²	1	2	yes	—
38	C₇×#405	C₂²	1	4	yes	complemented
39	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
41	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
43	#60714	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₇×#41	—	2	8	no	—
45	C₂×C₇×#41	C₂³	1	1	yes	characteristic
46	C₂²×C₇×D₄	—	2	4	no	—
47	C₂²×C₇×D₄	C₂³	1	4	yes	—
48	C₂×C₇×D₈	—	2	16	no	—
49	C₂×C₇×D₈	C₂³	1	8	yes	—
50	C₂×C₇×D₈	C₂³	1	8	yes	—
51	C₇×#131	—	2	8	no	—
52	C₂×C₇×M₁₆	C₂³	1	4	yes	—
53	C₂×C₇×M₁₆	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	4	yes	—
55	C₂²×C₇×C₈	C₂³	1	2	yes	—
56	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
57	C₇×#127	—	2	4	no	—
58	C₇×#127	—	2	4	no	—
59	C₇×#127	C₂³	1	4	yes	—
60	C₇×#127	C₂³	1	4	yes	—
61	C₇×#125	C₂³	1	4	yes	—
62	C₇×#124	—	2	4	no	—
63	C₇×#124	—	2	8	no	—
64	C₇×#123	—	2	16	no	—
65	C₇×C₂²⋊Q₈	—	2	4	no	—
66	C₇×#121	—	2	8	no	—
67	C₇×#121	—	2	16	no	—
68	C₇×#121	C₂³	1	16	yes	—
69	C₇×#120	—	2	8	no	—
70	C₄×C₇×Q₈	—	2	4	no	—
71	C₄×C₇×Q₈	D₄	1	2	yes	—
72	C₄×C₇×D₄	—	2	8	no	—
73	C₄×C₇×D₄	—	2	8	no	—
74	C₄×C₇×D₄	D₄	1	4	yes	—
75	C₄×C₇×D₄	D₄	1	2	yes	—
76	C₄×C₇×D₄	C₂³	1	16	yes	—
77	C₇×#117	C₂³	1	4	yes	—
78	C₇×#117	C₂³	1	1	yes	characteristic
79	C₇×#117	C₂³	1	2	yes	—
80	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂³	1	2	yes	—
83	C₇×#107	C₂³	1	8	yes	—
84	C₇×#106	C₂³	1	8	yes	—
85	C₇×#102	C₂³	1	32	yes	—
86	C₇×#97	C₂³	1	2	yes	—
87	C₇×#97	C₂³	1	4	yes	—
88	C₄×C₇×C₈	C₂³	1	2	yes	—
89	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₇×C₈	C₂³	1	2	yes	—
91	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₇×C₈	C₂³	1	4	yes	—
93	#3508	C₂×C₇	1	2	yes	complemented
94	#3184	C₂×C₇	1	4	yes	complemented
95	#3176	C₂×C₇	1	8	yes	complemented
96	#3169	C₂×C₇	1	4	yes	complemented
97	#3160	C₂×C₇	1	1	yes	characteristic, complemented
98	C₂×#493	C₂×C₇	1	1	yes	characteristic, complemented
99	#3138	C₂×C₇	1	2	yes	complemented
100	#3058	C₂×C₇	1	4	yes	complemented
101	#2948	C₂×C₇	1	4	yes	complemented
102	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
103	C₂⁴×C₇	—	2	4	no	—
104	C₇×#41	—	2	4	no	—
105	C₇×#41	—	8	16	no	—
106	C₂×C₇×Q₈	—	2	4	no	—
107	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
108	C₂×C₇×D₄	—	2	16	no	—
109	C₂×C₇×D₄	—	2	4	no	—
110	C₂×C₇×D₄	—	2	8	no	—
111	C₂×C₇×D₄	—	2	8	no	—
112	C₂×C₇×D₄	—	2	16	no	—
113	C₂×C₇×D₄	—	8	8	no	—
114	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
115	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
116	C₂×C₇×D₄	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₇	—	2	16	no	—
118	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
122	C₇×D₈	—	2	16	no	—
123	C₇×D₈	—	2	16	no	—
124	C₇×M₁₆	—	2	4	no	—
125	C₇×M₁₆	—	2	8	no	—
126	C₂×C₇×C₈	—	2	8	no	—
127	C₂×C₇×C₈	#41	1	8	yes	complemented
128	C₂×C₇×C₈	C₂⁴	1	4	yes	—
129	C₂×C₇×C₈	C₂⁴	1	2	yes	—
130	C₂×C₇×C₈	C₂⁴	1	2	yes	—
131	C₇×C₄⋊C₄	—	2	4	no	—
132	C₇×C₄⋊C₄	—	2	8	no	—
133	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
134	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
135	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
136	C₇×C₂²⋊C₄	—	2	4	no	—
137	C₇×C₂²⋊C₄	—	2	16	no	—
138	C₇×C₂²⋊C₄	—	2	16	no	—
139	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
140	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
141	C₄²×C₇	—	2	4	no	—
142	C₄²×C₇	C₂×D₄	1	4	yes	—
143	C₄²×C₇	C₂×D₄	1	2	yes	—
144	C₄²×C₇	C₂⁴	1	1	yes	characteristic
145	C₄²×C₇	C₂⁴	1	2	yes	—
146	C₄²×C₇	C₂⁴	1	1	yes	characteristic
147	C₂²×D₈	C₂²×C₇	1	4	yes	—
148	C₂×#131	C₂²×C₇	1	2	yes	—
149	#559	—	2	4	no	—
150	#550	—	2	4	no	—
151	#546	—	2	8	no	—
152	#540	C₂²×C₇	1	8	yes	complemented
153	#535	C₂²×C₇	1	4	yes	—
154	#533	C₂²×C₇	1	2	yes	—
155	#532	C₂²×C₇	1	8	yes	complemented
156	C₂×#127	C₂²×C₇	1	2	yes	—
157	#518	C₂²×C₇	1	4	yes	—
158	C₄×#41	C₂²×C₇	1	1	yes	characteristic
159	#500	C₂²×C₇	1	2	yes	complemented
160	#499	C₂²×C₇	1	4	yes	complemented
161	#498	C₂²×C₇	1	2	yes	complemented
162	#493	C₂²×C₇	1	2	yes	—
163	#493	C₂²×C₇	1	4	yes	—
164	#493	C₂²×C₇	1	2	yes	—
165	#490	C₂²×C₇	1	8	yes	complemented
166	#486	C₂²×C₇	1	8	yes	complemented
167	#469	C₂²×C₇	1	16	yes	complemented
168	#466	C₂²×C₇	1	16	yes	complemented
169	#442	C₂²×C₇	1	16	yes	complemented
170	C₄×D₈	C₂²×C₇	1	16	yes	complemented
171	#427	C₂²×C₇	1	4	yes	—
172	#418	C₂²×C₇	1	8	yes	—
173	#405	C₂²×C₇	1	2	yes	—
174	#405	C₂²×C₇	1	4	yes	complemented
175	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
176	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
177	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
179	C₂³×C₇	—	2	8	no	—
180	C₂³×C₇	—	4	8	no	—
181	C₂³×C₇	—	8	8	no	—
182	C₂³×C₇	C₂²×D₄	1	2	yes	—
183	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
184	C₇×Q₈	—	2	2	no	—
185	C₇×Q₈	—	4	8	no	—
186	C₇×D₄	—	2	4	no	—
187	C₇×D₄	—	2	2	no	—
188	C₇×D₄	—	2	16	no	—
189	C₇×D₄	—	4	8	no	—
190	C₇×D₄	—	4	16	no	—
191	C₇×D₄	—	8	8	no	—
192	C₇×D₄	—	8	16	no	—
193	C₂×C₄×C₇	—	2	4	no	—
194	C₂×C₄×C₇	—	2	8	no	—
195	C₂×C₄×C₇	—	2	4	no	—
196	C₂×C₄×C₇	—	2	8	no	—
197	C₂×C₄×C₇	—	8	16	no	—
198	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₇	C₂×#41	1	4	yes	—
204	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
205	C₇×C₈	—	2	4	no	—
206	C₇×C₈	C₂×#41	1	4	yes	—
207	C₇×C₈	C₂×#41	1	4	yes	—
208	C₂×#41	—	2	8	no	—
209	C₂×#41	C₂³×C₇	1	1	yes	characteristic
210	C₂²×D₄	—	2	4	no	—
211	C₂²×D₄	C₂³×C₇	1	4	yes	—
212	C₂×D₈	—	2	16	no	—
213	C₂×D₈	C₂³×C₇	1	8	yes	—
214	C₂×D₈	C₂³×C₇	1	8	yes	—
215	#131	—	2	8	no	—
216	C₂×M₁₆	C₂³×C₇	1	2	yes	—
217	C₂×M₁₆	C₂³×C₇	1	4	yes	—
218	C₂²×C₈	C₂³×C₇	1	4	yes	—
219	C₂²×C₈	C₂³×C₇	1	2	yes	—
220	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
221	#127	—	2	4	no	—
222	#127	—	2	4	no	—
223	#127	C₂³×C₇	1	4	yes	—
224	#127	C₂³×C₇	1	4	yes	—
225	#125	C₂³×C₇	1	4	yes	—
226	#124	—	2	4	no	—
227	#124	—	2	8	no	—
228	#123	—	2	16	no	—
229	C₂²⋊Q₈	—	2	4	no	—
230	#121	—	2	8	no	—
231	#121	—	2	16	no	—
232	#121	C₂³×C₇	1	16	yes	—
233	#120	—	2	8	no	—
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	C₇×D₄	1	2	yes	—
236	C₄×D₄	—	2	8	no	—
237	C₄×D₄	—	2	8	no	—
238	C₄×D₄	C₇×D₄	1	4	yes	—
239	C₄×D₄	C₇×D₄	1	2	yes	—
240	C₄×D₄	C₂³×C₇	1	16	yes	—
241	#117	C₂³×C₇	1	4	yes	—
242	#117	C₂³×C₇	1	1	yes	characteristic
243	#117	C₂³×C₇	1	2	yes	—
244	C₂×C₂²⋊C₄	—	2	8	no	—
245	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₇	1	2	yes	—
247	#107	C₂³×C₇	1	8	yes	—
248	#106	C₂³×C₇	1	8	yes	—
249	#102	C₂³×C₇	1	32	yes	—
250	#97	C₂³×C₇	1	2	yes	—
251	#97	C₂³×C₇	1	4	yes	—
252	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
253	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₇	1	2	yes	—
255	C₄×C₈	C₂³×C₇	1	2	yes	—
256	C₄×C₈	C₂³×C₇	1	4	yes	—
257	C₂²×C₇	—	2	2	no	—
258	C₂²×C₇	—	2	2	no	—
259	C₂²×C₇	—	2	4	no	—
260	C₂²×C₇	—	4	8	no	—
261	C₂²×C₇	—	4	16	no	—
262	C₂²×C₇	—	16	8	no	—
263	C₂²×C₇	#532	1	2	yes	—
264	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
265	C₄×C₇	—	2	2	no	—
266	C₄×C₇	—	2	4	no	—
267	C₄×C₇	—	2	2	no	—
268	C₄×C₇	—	4	8	no	—
269	C₄×C₇	#532	1	2	yes	—
270	C₄×C₇	#576	1	4	yes	—
271	C₄×C₇	C₂²×#41	1	2	yes	—
272	C₂⁴	—	2	4	no	—
273	#41	—	2	4	no	—
274	#41	—	8	16	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
277	C₂×D₄	—	2	16	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	2	8	no	—
281	C₂×D₄	—	2	16	no	—
282	C₂×D₄	—	8	8	no	—
283	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
284	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
285	C₂×D₄	C₂⁴×C₇	1	8	yes	—
286	C₂²×C₄	—	2	16	no	—
287	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
288	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
289	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
291	D₈	—	2	16	no	—
292	D₈	—	2	16	no	—
293	M₁₆	—	2	4	no	—
294	M₁₆	—	2	8	no	—
295	C₂×C₈	—	2	8	no	—
296	C₂×C₈	C₇×#41	1	8	yes	complemented
297	C₂×C₈	C₂⁴×C₇	1	4	yes	—
298	C₂×C₈	C₂⁴×C₇	1	2	yes	—
299	C₂×C₈	C₂⁴×C₇	1	2	yes	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	8	no	—
302	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
303	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
304	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	16	no	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
309	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
310	C₄²	—	2	4	no	—
311	C₄²	C₂×C₇×D₄	1	4	yes	—
312	C₄²	C₂×C₇×D₄	1	2	yes	—
313	C₄²	C₂⁴×C₇	1	1	yes	characteristic
314	C₄²	C₂⁴×C₇	1	2	yes	—
315	C₄²	C₂⁴×C₇	1	1	yes	characteristic
316	C₂×C₇	—	2	2	no	—
317	C₂×C₇	—	4	2	no	—
318	C₂×C₇	—	8	8	no	—
319	C₂×C₇	C₂×#532	1	1	yes	characteristic
320	C₂×C₇	C₂×#576	1	2	yes	—
321	C₂³	—	2	8	no	—
322	C₂³	—	4	8	no	—
323	C₂³	—	8	8	no	—
324	C₂³	C₂²×C₇×D₄	1	2	yes	—
325	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	Q₈	—	4	8	no	—
328	D₄	—	2	4	no	—
329	D₄	—	2	16	no	—
330	D₄	—	2	2	no	—
331	D₄	—	4	8	no	—
332	D₄	—	4	16	no	—
333	D₄	—	8	8	no	—
334	D₄	—	8	16	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	8	16	no	—
340	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
341	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
342	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
343	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
345	C₂×C₄	C₂×C₇×#41	1	4	yes	—
346	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
347	C₈	—	2	4	no	—
348	C₈	C₂×C₇×#41	1	4	yes	—
349	C₈	C₂×C₇×#41	1	4	yes	—
350	C₇	#60714	1	1	yes	characteristic, direct product factor, Sylow
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	4	16	no	—
355	C₂²	—	4	8	no	—
356	C₂²	—	16	8	no	—
357	C₂²	C₇×#532	1	2	yes	—
358	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
359	C₄	—	2	4	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	4	8	no	—
363	C₄	C₇×#532	1	2	yes	—
364	C₄	C₇×#576	1	4	yes	—
365	C₄	C₂²×C₇×#41	1	2	yes	—
366	C₂	—	2	2	no	—
367	C₂	—	4	2	no	—
368	C₂	—	8	8	no	—
369	C₂	C₂×C₇×#532	1	1	yes	characteristic
370	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×#3184	C₂	semidirect
3. C₇×#3176	C₂	semidirect
4. C₇×#3169	C₂	semidirect
5. C₇×#3160	C₂	semidirect
6. C₂×C₇×#493	C₂	semidirect
7. C₇×#3138	C₂	semidirect
8. C₇×#3058	C₂	semidirect
9. C₇×#2948	C₂	semidirect
10. C₄×C₇×#131	C₂	semidirect
16. C₇×#540	C₂²	semidirect
19. C₇×#532	C₂²	semidirect
23. C₇×#500	C₂²	semidirect
24. C₇×#499	C₂²	semidirect
25. C₇×#498	C₂²	semidirect
29. C₇×#490	C₂²	semidirect
30. C₇×#486	C₂²	semidirect
31. C₇×#469	C₂²	semidirect
32. C₇×#466	C₂²	semidirect
33. C₇×#442	C₂²	semidirect
34. C₄×C₇×D₈	C₂²	semidirect
38. C₇×#405	C₂²	semidirect
40. C₄×C₇×M₁₆	C₂²	semidirect
42. C₂×C₄×C₇×C₈	C₂²	semidirect
43. #60714	C₇	direct (N × H)
93. #3508	C₂×C₇	semidirect
94. #3184	C₂×C₇	semidirect
95. #3176	C₂×C₇	semidirect
96. #3169	C₂×C₇	semidirect
97. #3160	C₂×C₇	semidirect
98. C₂×#493	C₂×C₇	semidirect
99. #3138	C₂×C₇	semidirect
100. #3058	C₂×C₇	semidirect
101. #2948	C₂×C₇	semidirect
102. C₄×#131	C₂×C₇	semidirect
127. C₂×C₇×C₈	#41	semidirect
152. #540	C₂²×C₇	semidirect
155. #532	C₂²×C₇	semidirect
159. #500	C₂²×C₇	semidirect
160. #499	C₂²×C₇	semidirect
161. #498	C₂²×C₇	semidirect
165. #490	C₂²×C₇	semidirect
166. #486	C₂²×C₇	semidirect
167. #469	C₂²×C₇	semidirect
168. #466	C₂²×C₇	semidirect
169. #442	C₂²×C₇	semidirect
170. C₄×D₈	C₂²×C₇	semidirect
174. #405	C₂²×C₇	semidirect
176. C₄×M₁₆	C₂²×C₇	semidirect
178. C₂×C₄×C₈	C₂²×C₇	semidirect
296. C₂×C₈	C₇×#41	semidirect
350. C₇	#60714	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×#3184	2
C₇×#3176	2
C₇×#3169	2
C₇×#3160	2
C₂×C₇×#493	2
C₇×#3138	2
C₇×#3058	2
C₇×#2948	2
C₄×C₇×#131	2
#60714	7

Subgroups — C7×#60714 #13237930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60714 #13237930