Subgroups — C₇×#60490 #13237706

Order 1792.

2178 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#518	C₂	1	1	yes	maximal, characteristic
3	C₇×#3081	C₂	1	16	yes	maximal, complemented
4	C₇×#3077	C₂	1	8	yes	maximal, complemented
5	C₇×#2911	C₂	1	2	yes	maximal, complemented
6	C₇×#2905	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#418	C₂	1	2	yes	maximal
8	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
9	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
10	C₇×#544	—	2	2	no	—
11	C₇×#544	C₂²	1	8	yes	complemented
12	C₇×#543	—	2	2	no	—
13	C₇×#533	—	2	4	no	—
14	C₇×#533	C₂²	1	4	yes	complemented
15	C₇×#518	—	2	4	no	—
16	C₇×#518	C₂²	1	8	yes	—
17	C₂×C₄×C₇×D₄	—	2	2	no	—
18	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
19	C₂×C₇×#117	C₂²	1	1	yes	characteristic
20	C₂×C₇×#117	C₂²	1	2	yes	—
21	C₂×C₇×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₇×C₂²⋊C₄	—	2	2	no	—
23	C₇×#478	C₂²	1	32	yes	complemented
24	C₇×#476	C₂²	1	16	yes	complemented
25	C₇×#474	C₂²	1	16	yes	complemented
26	C₇×#428	C₂²	1	8	yes	complemented
27	C₇×#428	C₂²	1	8	yes	complemented
28	C₇×#427	C₂²	1	8	yes	complemented
29	C₇×#424	C₂²	1	8	yes	complemented
30	C₇×#423	C₂²	1	4	yes	complemented
31	C₇×#418	C₂²	1	8	yes	—
32	C₇×#418	C₂²	1	8	yes	—
33	C₂×C₇×#102	C₂²	1	8	yes	—
34	#60490	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂⁵×C₇	—	2	1	no	—
36	C₂²×C₇×D₄	—	2	1	no	—
37	C₂²×C₇×D₄	—	2	2	no	—
38	C₂²×C₇×D₄	—	2	4	no	—
39	C₂²×C₇×D₄	Q₈	1	8	yes	complemented
40	C₂²×C₇×D₄	C₂³	1	2	yes	—
41	C₂²×C₇×D₄	C₂³	1	4	yes	—
42	C₂³×C₄×C₇	—	2	4	no	—
43	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
44	C₂×C₇×M₁₆	—	2	8	no	—
45	C₂×C₇×M₁₆	C₂³	1	4	yes	—
46	C₂×C₇×M₁₆	C₂³	1	4	yes	—
47	C₂²×C₇×C₈	C₂³	1	4	yes	—
48	C₇×C₄⋊Q₈	—	2	8	no	—
49	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
50	C₇×#125	—	2	8	no	—
51	C₇×#125	C₂³	1	8	yes	complemented
52	C₇×C₂²⋊Q₈	—	2	8	no	—
53	C₇×C₂²⋊Q₈	—	2	16	no	—
54	C₄×C₇×Q₈	—	2	8	no	—
55	C₄×C₇×D₄	—	2	16	no	—
56	C₄×C₇×D₄	—	2	8	no	—
57	C₄×C₇×D₄	C₂³	1	16	yes	—
58	C₇×#117	—	2	2	no	—
59	C₇×#117	—	2	2	no	—
60	C₇×#117	—	2	2	no	—
61	C₇×#117	D₄	1	4	yes	—
62	C₇×#117	C₂³	1	4	yes	—
63	C₇×#117	C₂³	1	4	yes	—
64	C₇×#117	C₂³	1	4	yes	—
65	C₇×#117	C₂³	1	4	yes	—
66	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
72	C₂×C₇×C₂²⋊C₄	—	2	16	no	—
73	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
74	C₂×C₄²×C₇	—	2	1	no	—
75	C₂×C₄²×C₇	—	2	2	no	—
76	C₂×C₄²×C₇	C₂³	1	2	yes	—
77	C₇×#107	C₂³	1	16	yes	complemented
78	C₇×#106	C₂³	1	16	yes	complemented
79	C₇×C₄⋊C₈	C₂³	1	16	yes	complemented
80	C₇×#102	C₂³	1	32	yes	—
81	#3458	C₂×C₇	1	1	yes	characteristic, complemented
82	C₂×#518	C₂×C₇	1	1	yes	characteristic
83	#3081	C₂×C₇	1	16	yes	complemented
84	#3077	C₂×C₇	1	8	yes	complemented
85	#2911	C₂×C₇	1	2	yes	complemented
86	#2905	C₂×C₇	1	1	yes	characteristic, complemented
87	C₂×#418	C₂×C₇	1	2	yes	—
88	C₂⁴×C₇	—	2	2	no	—
89	C₂⁴×C₇	—	2	8	no	—
90	C₂⁴×C₇	—	2	4	no	—
91	C₂⁴×C₇	—	8	4	no	—
92	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
93	C₂×C₇×Q₈	—	2	8	no	—
94	C₂×C₇×D₄	—	2	8	no	—
95	C₂×C₇×D₄	—	2	16	no	—
96	C₂×C₇×D₄	—	2	2	no	—
97	C₂×C₇×D₄	—	2	4	no	—
98	C₂×C₇×D₄	—	2	8	no	—
99	C₂×C₇×D₄	—	2	4	no	—
100	C₂×C₇×D₄	C₂×Q₈	1	8	yes	—
101	C₂×C₇×D₄	C₂×Q₈	1	16	yes	—
102	C₂×C₇×D₄	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₇	—	2	2	no	—
104	C₂²×C₄×C₇	—	2	4	no	—
105	C₂²×C₄×C₇	—	2	16	no	—
106	C₂²×C₄×C₇	—	8	8	no	—
107	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
111	C₂²×C₄×C₇	#41	1	4	yes	—
112	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
114	C₇×M₁₆	—	2	8	no	—
115	C₇×M₁₆	—	2	8	no	—
116	C₂×C₇×C₈	—	2	8	no	—
117	C₂×C₇×C₈	C₂⁴	1	8	yes	—
118	C₇×C₄⋊C₄	—	2	2	no	—
119	C₇×C₄⋊C₄	—	2	4	no	—
120	C₇×C₄⋊C₄	—	2	8	no	—
121	C₇×C₄⋊C₄	—	2	16	no	—
122	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
123	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
124	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
125	C₇×C₂²⋊C₄	—	2	4	no	—
126	C₇×C₂²⋊C₄	—	2	4	no	—
127	C₇×C₂²⋊C₄	—	2	4	no	—
128	C₇×C₂²⋊C₄	—	2	16	no	—
129	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
130	C₄²×C₇	—	2	4	no	—
131	C₄²×C₇	—	2	4	no	—
132	C₄²×C₇	—	2	4	no	—
133	C₄²×C₇	C₂×D₄	1	4	yes	—
134	C₄²×C₇	C₂⁴	1	4	yes	—
135	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
136	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
137	#544	—	2	2	no	—
138	#544	C₂²×C₇	1	8	yes	complemented
139	#543	—	2	2	no	—
140	#533	—	2	4	no	—
141	#533	C₂²×C₇	1	4	yes	complemented
142	#518	—	2	4	no	—
143	#518	C₂²×C₇	1	8	yes	—
144	C₂×C₄×D₄	—	2	2	no	—
145	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
146	C₂×#117	C₂²×C₇	1	2	yes	—
147	C₂×#117	C₂²×C₇	1	1	yes	characteristic
148	C₂×#117	C₂²×C₇	1	1	yes	characteristic
149	C₂²×C₂²⋊C₄	—	2	2	no	—
150	#478	C₂²×C₇	1	32	yes	complemented
151	#476	C₂²×C₇	1	16	yes	complemented
152	#474	C₂²×C₇	1	16	yes	complemented
153	#428	C₂²×C₇	1	8	yes	complemented
154	#428	C₂²×C₇	1	8	yes	complemented
155	#427	C₂²×C₇	1	8	yes	complemented
156	#424	C₂²×C₇	1	8	yes	complemented
157	#423	C₂²×C₇	1	4	yes	complemented
158	#418	C₂²×C₇	1	8	yes	—
159	#418	C₂²×C₇	1	8	yes	—
160	C₂×#102	C₂²×C₇	1	8	yes	—
161	C₂³×C₇	—	2	8	no	—
162	C₂³×C₇	—	2	4	no	—
163	C₂³×C₇	—	2	16	no	—
164	C₂³×C₇	—	4	2	no	—
165	C₂³×C₇	—	4	8	no	—
166	C₂³×C₇	—	8	8	no	—
167	C₂³×C₇	—	8	16	no	—
168	C₂³×C₇	C₂²⋊Q₈	1	4	yes	—
169	C₂³×C₇	C₂²×D₄	1	2	yes	—
170	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
171	C₇×Q₈	—	8	8	no	—
172	C₇×D₄	—	2	8	no	—
173	C₇×D₄	—	2	16	no	—
174	C₇×D₄	—	2	4	no	—
175	C₇×D₄	C₂²×Q₈	1	8	yes	—
176	C₂×C₄×C₇	—	2	4	no	—
177	C₂×C₄×C₇	—	2	8	no	—
178	C₂×C₄×C₇	—	4	4	no	—
179	C₂×C₄×C₇	—	4	4	no	—
180	C₂×C₄×C₇	—	8	16	no	—
181	C₂×C₄×C₇	—	8	4	no	—
182	C₂×C₄×C₇	C₂²⋊Q₈	1	4	yes	—
183	C₂×C₄×C₇	C₂²⋊Q₈	1	8	yes	—
184	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
185	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
188	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
189	C₂×C₄×C₇	C₂×#41	1	4	yes	—
190	C₂×C₄×C₇	C₂×#41	1	2	yes	—
191	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
192	C₇×C₈	—	2	8	no	—
193	C₂⁵	—	2	1	no	—
194	C₂²×D₄	—	2	1	no	—
195	C₂²×D₄	—	2	2	no	—
196	C₂²×D₄	—	2	4	no	—
197	C₂²×D₄	C₇×Q₈	1	8	yes	complemented
198	C₂²×D₄	C₂³×C₇	1	2	yes	—
199	C₂²×D₄	C₂³×C₇	1	4	yes	—
200	C₂³×C₄	—	2	4	no	—
201	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
202	C₂×M₁₆	—	2	8	no	—
203	C₂×M₁₆	C₂³×C₇	1	4	yes	—
204	C₂×M₁₆	C₂³×C₇	1	4	yes	—
205	C₂²×C₈	C₂³×C₇	1	4	yes	—
206	C₄⋊Q₈	—	2	8	no	—
207	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
208	#125	—	2	8	no	—
209	#125	C₂³×C₇	1	8	yes	complemented
210	C₂²⋊Q₈	—	2	8	no	—
211	C₂²⋊Q₈	—	2	16	no	—
212	C₄×Q₈	—	2	8	no	—
213	C₄×D₄	—	2	16	no	—
214	C₄×D₄	—	2	8	no	—
215	C₄×D₄	C₂³×C₇	1	16	yes	—
216	#117	—	2	2	no	—
217	#117	—	2	2	no	—
218	#117	—	2	2	no	—
219	#117	C₇×D₄	1	4	yes	—
220	#117	C₂³×C₇	1	4	yes	—
221	#117	C₂³×C₇	1	4	yes	—
222	#117	C₂³×C₇	1	4	yes	—
223	#117	C₂³×C₇	1	4	yes	—
224	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
225	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₂²⋊C₄	—	2	2	no	—
229	C₂×C₂²⋊C₄	—	2	4	no	—
230	C₂×C₂²⋊C₄	—	2	16	no	—
231	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	C₂³×C₇	1	2	yes	—
235	#107	C₂³×C₇	1	16	yes	complemented
236	#106	C₂³×C₇	1	16	yes	complemented
237	C₄⋊C₈	C₂³×C₇	1	16	yes	complemented
238	#102	C₂³×C₇	1	32	yes	—
239	C₂²×C₇	—	2	2	no	—
240	C₂²×C₇	—	2	4	no	—
241	C₂²×C₇	—	2	8	no	—
242	C₂²×C₇	—	4	4	no	—
243	C₂²×C₇	—	4	16	no	—
244	C₂²×C₇	—	4	8	no	—
245	C₂²×C₇	—	8	16	no	—
246	C₂²×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
247	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
248	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
249	C₄×C₇	—	2	8	no	—
250	C₄×C₇	—	4	4	no	—
251	C₄×C₇	—	4	8	no	—
252	C₄×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
253	C₄×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
254	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
255	C₄×C₇	C₂²×#41	1	1	yes	characteristic
256	C₂⁴	—	2	2	no	—
257	C₂⁴	—	2	8	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	8	4	no	—
260	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
261	C₂×Q₈	—	2	8	no	—
262	C₂×D₄	—	2	8	no	—
263	C₂×D₄	—	2	16	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	C₂×C₇×Q₈	1	8	yes	—
269	C₂×D₄	C₂×C₇×Q₈	1	16	yes	—
270	C₂×D₄	C₂⁴×C₇	1	4	yes	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	16	no	—
274	C₂²×C₄	—	8	8	no	—
275	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
276	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
278	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
279	C₂²×C₄	C₇×#41	1	4	yes	—
280	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
282	M₁₆	—	2	8	no	—
283	M₁₆	—	2	8	no	—
284	C₂×C₈	—	2	8	no	—
285	C₂×C₈	C₂⁴×C₇	1	8	yes	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
291	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
292	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	2	4	no	—
296	C₂²⋊C₄	—	2	16	no	—
297	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
298	C₄²	—	2	4	no	—
299	C₄²	—	2	4	no	—
300	C₄²	—	2	4	no	—
301	C₄²	C₂×C₇×D₄	1	4	yes	—
302	C₄²	C₂⁴×C₇	1	4	yes	—
303	C₂×C₇	—	2	2	no	—
304	C₂×C₇	—	2	4	no	—
305	C₂×C₇	—	4	8	no	—
306	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
307	C₂×C₇	#3585	1	2	yes	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	8	no	—
310	C₂³	—	2	16	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	8	8	no	—
314	C₂³	—	8	16	no	—
315	C₂³	C₇×C₂²⋊Q₈	1	4	yes	—
316	C₂³	C₂²×C₇×D₄	1	2	yes	—
317	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
318	Q₈	—	8	8	no	—
319	D₄	—	2	4	no	—
320	D₄	—	2	8	no	—
321	D₄	—	2	16	no	—
322	D₄	C₂²×C₇×Q₈	1	8	yes	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	8	16	no	—
328	C₂×C₄	—	8	4	no	—
329	C₂×C₄	C₇×C₂²⋊Q₈	1	4	yes	—
330	C₂×C₄	C₇×C₂²⋊Q₈	1	8	yes	—
331	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
332	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
333	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
334	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
335	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
336	C₂×C₄	C₂×C₇×#41	1	4	yes	—
337	C₂×C₄	C₂×C₇×#41	1	2	yes	—
338	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
339	C₈	—	2	8	no	—
340	C₇	#60490	1	1	yes	characteristic, direct product factor, Sylow
341	C₂²	—	2	2	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	16	no	—
346	C₂²	—	4	8	no	—
347	C₂²	—	8	16	no	—
348	C₂²	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
349	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
350	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
351	C₄	—	2	8	no	—
352	C₄	—	4	4	no	—
353	C₄	—	4	8	no	—
354	C₄	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
355	C₄	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
356	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
357	C₄	C₂²×C₇×#41	1	1	yes	characteristic
358	C₂	—	2	2	no	—
359	C₂	—	2	4	no	—
360	C₂	—	4	8	no	—
361	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
362	C₂	C₇×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂³×C₇×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3458	C₂	semidirect
3. C₇×#3081	C₂	semidirect
4. C₇×#3077	C₂	semidirect
5. C₇×#2911	C₂	semidirect
6. C₇×#2905	C₂	semidirect
11. C₇×#544	C₂²	semidirect
14. C₇×#533	C₂²	semidirect
23. C₇×#478	C₂²	semidirect
24. C₇×#476	C₂²	semidirect
25. C₇×#474	C₂²	semidirect
26. C₇×#428	C₂²	semidirect
27. C₇×#428	C₂²	semidirect
28. C₇×#427	C₂²	semidirect
29. C₇×#424	C₂²	semidirect
30. C₇×#423	C₂²	semidirect
34. #60490	C₇	direct (N × H)
39. C₂²×C₇×D₄	Q₈	semidirect
49. C₇×C₄⋊Q₈	C₂³	semidirect
51. C₇×#125	C₂³	semidirect
77. C₇×#107	C₂³	semidirect
78. C₇×#106	C₂³	semidirect
79. C₇×C₄⋊C₈	C₂³	semidirect
81. #3458	C₂×C₇	semidirect
83. #3081	C₂×C₇	semidirect
84. #3077	C₂×C₇	semidirect
85. #2911	C₂×C₇	semidirect
86. #2905	C₂×C₇	semidirect
138. #544	C₂²×C₇	semidirect
141. #533	C₂²×C₇	semidirect
150. #478	C₂²×C₇	semidirect
151. #476	C₂²×C₇	semidirect
152. #474	C₂²×C₇	semidirect
153. #428	C₂²×C₇	semidirect
154. #428	C₂²×C₇	semidirect
155. #427	C₂²×C₇	semidirect
156. #424	C₂²×C₇	semidirect
157. #423	C₂²×C₇	semidirect
197. C₂²×D₄	C₇×Q₈	semidirect
207. C₄⋊Q₈	C₂³×C₇	semidirect
209. #125	C₂³×C₇	semidirect
235. #107	C₂³×C₇	semidirect
236. #106	C₂³×C₇	semidirect
237. C₄⋊C₈	C₂³×C₇	semidirect
340. C₇	#60490	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×#3458	2
C₂×C₇×#518	2
C₇×#3081	2
C₇×#3077	2
C₇×#2911	2
C₇×#2905	2
C₂×C₇×#418	2
#60490	7

Subgroups — C7×#60490 #13237706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60490 #13237706