Subgroups — C₇×#60646 #13237862

Order 1792.

3250 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#577	C₂	1	4	yes	maximal, complemented
2	C₇×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3154	C₂	1	12	yes	maximal, complemented
5	C₇×#3152	C₂	1	3	yes	maximal, complemented
6	C₇×#3151	C₂	1	3	yes	maximal, complemented
7	C₇×#3147	C₂	1	3	yes	maximal, complemented
8	C₂×C₇×#492	C₂	1	3	yes	maximal, complemented
9	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×2₋¹⁺⁴	C₂²	1	2	yes	—
11	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
12	C₇×#577	—	2	32	no	—
13	C₂×C₇×#137	C₂²	1	12	yes	complemented
14	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	12	yes	complemented
15	C₂×C₇×#135	C₂²	1	12	yes	complemented
16	C₂²×C₇×SD₁₆	C₂²	1	12	yes	complemented
17	C₂×C₇×#131	C₂²	1	2	yes	—
18	C₇×#550	—	2	2	no	—
19	C₇×D₄×Q₈	—	2	2	no	—
20	C₇×#547	—	2	6	no	—
21	C₇×D₄²	—	2	6	no	—
22	C₇×#536	C₂²	1	6	yes	complemented
23	C₇×#535	C₂²	1	6	yes	—
24	C₇×#532	C₂²	1	3	yes	—
25	C₇×#532	C₂²	1	3	yes	complemented
26	C₂×C₇×C₄⋊Q₈	C₂²	1	3	yes	complemented
27	C₂×C₇×#127	C₂²	1	3	yes	—
28	C₄×C₇×#41	C₂²	1	1	yes	characteristic
29	C₇×#497	C₂²	1	12	yes	complemented
30	C₇×#496	C₂²	1	12	yes	complemented
31	C₇×#495	C₂²	1	12	yes	complemented
32	C₇×#494	C₂²	1	3	yes	complemented
33	C₇×#493	C₂²	1	3	yes	complemented
34	C₇×#492	C₂²	1	3	yes	complemented
35	C₇×#492	C₂²	1	6	yes	complemented
36	C₇×#492	C₂²	1	12	yes	complemented
37	C₇×#492	C₂²	1	1	yes	characteristic, complemented
38	C₇×#405	C₂²	1	6	yes	complemented
39	C₄×C₇×M₁₆	C₂²	1	3	yes	complemented
40	C₂×C₄×C₇×C₈	C₂²	1	3	yes	complemented
41	#60646	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₇×2₋¹⁺⁴	—	2	16	no	—
43	C₇×H(5,𝔽₂)	—	2	16	no	—
44	C₂×C₇×#41	—	2	2	no	—
45	C₂×C₇×#41	—	2	6	no	—
46	C₂×C₇×#41	C₂³	1	6	yes	—
47	C₂×C₇×#41	C₂³	1	6	yes	—
48	C₂×C₇×#41	C₂³	1	1	yes	characteristic
49	C₂²×C₇×Q₈	—	2	2	no	—
50	C₂²×C₇×Q₈	C₂³	1	6	yes	—
51	C₂²×C₇×D₄	—	2	6	no	—
52	C₂²×C₇×D₄	—	2	6	no	—
53	C₂²×C₇×D₄	C₂³	1	6	yes	—
54	C₇×#137	—	2	48	no	—
55	C₇×AGL(1,ℤ/8)	—	2	48	no	—
56	C₇×#135	—	2	48	no	—
57	C₂×C₇×Q₁₆	C₂³	1	12	yes	—
58	C₂×C₇×SD₁₆	—	2	48	no	—
59	C₂×C₇×SD₁₆	C₂³	1	12	yes	—
60	C₂×C₇×SD₁₆	C₂³	1	24	yes	—
61	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
62	C₂×C₇×D₈	C₂³	1	12	yes	—
63	C₇×#131	D₄	1	16	yes	complemented
64	C₂×C₇×M₁₆	C₂³	1	6	yes	—
65	C₂²×C₇×C₈	C₂³	1	6	yes	—
66	C₇×C₄⋊Q₈	—	2	6	no	—
67	C₇×C₄⋊Q₈	C₂³	1	3	yes	—
68	C₇×C₄⋊Q₈	C₂³	1	6	yes	—
69	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₇×#127	—	2	6	no	—
71	C₇×#127	C₂³	1	3	yes	—
72	C₇×#127	C₂³	1	6	yes	—
73	C₇×#127	C₂³	1	1	yes	characteristic
74	C₇×#124	C₂³	1	6	yes	—
75	C₇×#124	C₂³	1	6	yes	—
76	C₇×#123	—	2	12	no	—
77	C₇×C₂²⋊Q₈	—	2	12	no	—
78	C₇×#121	—	2	6	no	—
79	C₇×#121	—	2	6	no	—
80	C₇×#121	—	2	12	no	—
81	C₇×#120	—	2	12	no	—
82	C₄×C₇×Q₈	D₄	1	2	yes	—
83	C₄×C₇×D₄	—	2	6	no	—
84	C₄×C₇×D₄	—	2	6	no	—
85	C₄×C₇×D₄	D₄	1	6	yes	—
86	C₇×#117	C₂³	1	3	yes	—
87	C₂×C₇×C₄⋊C₄	—	2	6	no	—
88	C₂×C₄²×C₇	C₂³	1	3	yes	—
89	C₇×#97	C₂³	1	6	yes	—
90	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₄×C₇×C₈	C₂³	1	3	yes	—
92	C₄×C₇×C₈	C₂³	1	6	yes	—
93	C₂×#577	C₂×C₇	1	4	yes	complemented
94	#3499	C₂×C₇	1	1	yes	characteristic, complemented
95	#3498	C₂×C₇	1	1	yes	characteristic, complemented
96	#3154	C₂×C₇	1	12	yes	complemented
97	#3152	C₂×C₇	1	3	yes	complemented
98	#3151	C₂×C₇	1	3	yes	complemented
99	#3147	C₂×C₇	1	3	yes	complemented
100	C₂×#492	C₂×C₇	1	3	yes	complemented
101	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
102	C₂⁴×C₇	—	2	6	no	—
103	C₇×#41	—	2	24	no	—
104	C₇×#41	—	2	24	no	—
105	C₇×#41	—	4	8	no	—
106	C₇×#41	—	4	24	no	—
107	C₇×#41	C₂×D₄	1	8	yes	—
108	C₂×C₇×Q₈	—	2	6	no	—
109	C₂×C₇×Q₈	—	2	24	no	—
110	C₂×C₇×Q₈	—	4	8	no	—
111	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
112	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
113	C₂×C₇×Q₈	C₂⁴	1	6	yes	—
114	C₂×C₇×D₄	—	2	6	no	—
115	C₂×C₇×D₄	—	2	6	no	—
116	C₂×C₇×D₄	—	2	24	no	—
117	C₂×C₇×D₄	—	2	2	no	—
118	C₂×C₇×D₄	—	2	6	no	—
119	C₂×C₇×D₄	—	2	6	no	—
120	C₂×C₇×D₄	—	2	12	no	—
121	C₂×C₇×D₄	—	4	24	no	—
122	C₂×C₇×D₄	—	8	12	no	—
123	C₂×C₇×D₄	C₂×D₄	1	3	yes	—
124	C₂×C₇×D₄	C₂⁴	1	2	yes	—
125	C₂×C₇×D₄	C₂⁴	1	6	yes	—
126	C₂²×C₄×C₇	—	2	6	no	—
127	C₂²×C₄×C₇	—	2	6	no	—
128	C₂²×C₄×C₇	—	2	6	no	—
129	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
130	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
131	C₇×Q₁₆	—	2	24	no	—
132	C₇×SD₁₆	—	2	24	no	—
133	C₇×SD₁₆	—	2	48	no	—
134	C₇×SD₁₆	—	2	8	no	—
135	C₇×D₈	—	2	24	no	—
136	C₇×M₁₆	C₂×D₄	1	24	yes	complemented
137	C₂×C₇×C₈	C₂×D₄	1	24	yes	complemented
138	C₂×C₇×C₈	C₂⁴	1	2	yes	—
139	C₂×C₇×C₈	C₂⁴	1	6	yes	—
140	C₇×C₄⋊C₄	—	2	6	no	—
141	C₇×C₄⋊C₄	—	2	12	no	—
142	C₇×C₄⋊C₄	—	2	2	no	—
143	C₇×C₄⋊C₄	C₂×D₄	1	6	yes	—
144	C₇×C₂²⋊C₄	—	2	12	no	—
145	C₇×C₂²⋊C₄	—	2	12	no	—
146	C₇×C₂²⋊C₄	C₂×D₄	1	6	yes	—
147	C₄²×C₇	C₂×D₄	1	6	yes	—
148	C₄²×C₇	C₂⁴	1	1	yes	characteristic
149	C₄²×C₇	C₂⁴	1	3	yes	—
150	C₂×2₋¹⁺⁴	C₂²×C₇	1	2	yes	—
151	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
152	#577	—	2	32	no	—
153	C₂×#137	C₂²×C₇	1	12	yes	complemented
154	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	12	yes	complemented
155	C₂×#135	C₂²×C₇	1	12	yes	complemented
156	C₂²×SD₁₆	C₂²×C₇	1	12	yes	complemented
157	C₂×#131	C₂²×C₇	1	2	yes	—
158	#550	—	2	2	no	—
159	D₄×Q₈	—	2	2	no	—
160	#547	—	2	6	no	—
161	D₄²	—	2	6	no	—
162	#536	C₂²×C₇	1	6	yes	complemented
163	#535	C₂²×C₇	1	6	yes	—
164	#532	C₂²×C₇	1	3	yes	—
165	#532	C₂²×C₇	1	3	yes	complemented
166	C₂×C₄⋊Q₈	C₂²×C₇	1	3	yes	complemented
167	C₂×#127	C₂²×C₇	1	3	yes	—
168	C₄×#41	C₂²×C₇	1	1	yes	characteristic
169	#497	C₂²×C₇	1	12	yes	complemented
170	#496	C₂²×C₇	1	12	yes	complemented
171	#495	C₂²×C₇	1	12	yes	complemented
172	#494	C₂²×C₇	1	3	yes	complemented
173	#493	C₂²×C₇	1	3	yes	complemented
174	#492	C₂²×C₇	1	3	yes	complemented
175	#492	C₂²×C₇	1	6	yes	complemented
176	#492	C₂²×C₇	1	12	yes	complemented
177	#492	C₂²×C₇	1	1	yes	characteristic, complemented
178	#405	C₂²×C₇	1	6	yes	complemented
179	C₄×M₁₆	C₂²×C₇	1	3	yes	complemented
180	C₂×C₄×C₈	C₂²×C₇	1	3	yes	complemented
181	C₂³×C₇	—	2	2	no	—
182	C₂³×C₇	—	2	6	no	—
183	C₂³×C₇	—	4	12	no	—
184	C₂³×C₇	—	8	12	no	—
185	C₂³×C₇	C₂²×D₄	1	3	yes	—
186	C₇×Q₈	—	2	12	no	—
187	C₇×Q₈	—	2	4	no	—
188	C₇×Q₈	—	4	12	no	—
189	C₇×Q₈	#127	1	4	yes	—
190	C₇×D₄	—	2	4	no	—
191	C₇×D₄	—	2	12	no	—
192	C₇×D₄	—	4	12	no	—
193	C₇×D₄	—	4	12	no	—
194	C₇×D₄	—	4	12	no	—
195	C₇×D₄	—	4	4	no	—
196	C₇×D₄	—	4	12	no	—
197	C₇×D₄	—	8	12	no	—
198	C₇×D₄	#127	1	12	yes	—
199	C₂×C₄×C₇	—	2	12	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	6	no	—
202	C₂×C₄×C₇	—	4	12	no	—
203	C₂×C₄×C₇	—	4	12	no	—
204	C₂×C₄×C₇	—	4	12	no	—
205	C₂×C₄×C₇	C₂²×D₄	1	6	yes	—
206	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
207	C₂×C₄×C₇	C₂²×D₄	1	12	yes	—
208	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
210	C₇×C₈	C₂²×D₄	1	4	yes	—
211	C₇×C₈	C₂²×D₄	1	12	yes	—
212	2₋¹⁺⁴	—	2	16	no	—
213	H(5,𝔽₂)	—	2	16	no	—
214	C₂×#41	—	2	2	no	—
215	C₂×#41	—	2	6	no	—
216	C₂×#41	C₂³×C₇	1	6	yes	—
217	C₂×#41	C₂³×C₇	1	6	yes	—
218	C₂×#41	C₂³×C₇	1	1	yes	characteristic
219	C₂²×Q₈	—	2	2	no	—
220	C₂²×Q₈	C₂³×C₇	1	6	yes	—
221	C₂²×D₄	—	2	6	no	—
222	C₂²×D₄	—	2	6	no	—
223	C₂²×D₄	C₂³×C₇	1	6	yes	—
224	#137	—	2	48	no	—
225	AGL(1,ℤ/8)	—	2	48	no	—
226	#135	—	2	48	no	—
227	C₂×Q₁₆	C₂³×C₇	1	12	yes	—
228	C₂×SD₁₆	—	2	48	no	—
229	C₂×SD₁₆	C₂³×C₇	1	12	yes	—
230	C₂×SD₁₆	C₂³×C₇	1	24	yes	—
231	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
232	C₂×D₈	C₂³×C₇	1	12	yes	—
233	#131	C₇×D₄	1	16	yes	complemented
234	C₂×M₁₆	C₂³×C₇	1	6	yes	—
235	C₂²×C₈	C₂³×C₇	1	6	yes	—
236	C₄⋊Q₈	—	2	6	no	—
237	C₄⋊Q₈	C₂³×C₇	1	3	yes	—
238	C₄⋊Q₈	C₂³×C₇	1	6	yes	—
239	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
240	#127	—	2	6	no	—
241	#127	C₂³×C₇	1	3	yes	—
242	#127	C₂³×C₇	1	6	yes	—
243	#127	C₂³×C₇	1	1	yes	characteristic
244	#124	C₂³×C₇	1	6	yes	—
245	#124	C₂³×C₇	1	6	yes	—
246	#123	—	2	12	no	—
247	C₂²⋊Q₈	—	2	12	no	—
248	#121	—	2	6	no	—
249	#121	—	2	6	no	—
250	#121	—	2	12	no	—
251	#120	—	2	12	no	—
252	C₄×Q₈	C₇×D₄	1	2	yes	—
253	C₄×D₄	—	2	6	no	—
254	C₄×D₄	—	2	6	no	—
255	C₄×D₄	C₇×D₄	1	6	yes	—
256	#117	C₂³×C₇	1	3	yes	—
257	C₂×C₄⋊C₄	—	2	6	no	—
258	C₂×C₄²	C₂³×C₇	1	3	yes	—
259	#97	C₂³×C₇	1	6	yes	—
260	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₇	1	3	yes	—
262	C₄×C₈	C₂³×C₇	1	6	yes	—
263	C₂²×C₇	—	2	6	no	—
264	C₂²×C₇	—	4	2	no	—
265	C₂²×C₇	—	4	6	no	—
266	C₂²×C₇	—	4	12	no	—
267	C₂²×C₇	—	4	4	no	—
268	C₂²×C₇	—	16	12	no	—
269	C₂²×C₇	C₂×#127	1	6	yes	—
270	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
271	C₄×C₇	—	2	6	no	—
272	C₄×C₇	—	4	2	no	—
273	C₄×C₇	—	4	6	no	—
274	C₄×C₇	C₂×#127	1	6	yes	—
275	C₄×C₇	#577	1	4	yes	complemented
276	C₄×C₇	C₂³×D₄	1	2	yes	—
277	C₂⁴	—	2	6	no	—
278	#41	—	2	24	no	—
279	#41	—	2	24	no	—
280	#41	—	4	8	no	—
281	#41	—	4	24	no	—
282	#41	C₂×C₇×D₄	1	8	yes	—
283	C₂×Q₈	—	2	6	no	—
284	C₂×Q₈	—	2	24	no	—
285	C₂×Q₈	—	4	8	no	—
286	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
287	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
288	C₂×Q₈	C₂⁴×C₇	1	6	yes	—
289	C₂×D₄	—	2	6	no	—
290	C₂×D₄	—	2	6	no	—
291	C₂×D₄	—	2	24	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	6	no	—
294	C₂×D₄	—	2	6	no	—
295	C₂×D₄	—	2	12	no	—
296	C₂×D₄	—	4	24	no	—
297	C₂×D₄	—	8	12	no	—
298	C₂×D₄	C₂×C₇×D₄	1	3	yes	—
299	C₂×D₄	C₂⁴×C₇	1	2	yes	—
300	C₂×D₄	C₂⁴×C₇	1	6	yes	—
301	C₂²×C₄	—	2	6	no	—
302	C₂²×C₄	—	2	6	no	—
303	C₂²×C₄	—	2	6	no	—
304	C₂²×C₄	C₂×C₇×D₄	1	6	yes	—
305	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
306	Q₁₆	—	2	24	no	—
307	SD₁₆	—	2	24	no	—
308	SD₁₆	—	2	48	no	—
309	SD₁₆	—	2	8	no	—
310	D₈	—	2	24	no	—
311	M₁₆	C₂×C₇×D₄	1	24	yes	complemented
312	C₂×C₈	C₂×C₇×D₄	1	24	yes	complemented
313	C₂×C₈	C₂⁴×C₇	1	2	yes	—
314	C₂×C₈	C₂⁴×C₇	1	6	yes	—
315	C₄⋊C₄	—	2	6	no	—
316	C₄⋊C₄	—	2	12	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	C₂×C₇×D₄	1	6	yes	—
319	C₂²⋊C₄	—	2	12	no	—
320	C₂²⋊C₄	—	2	12	no	—
321	C₂²⋊C₄	C₂×C₇×D₄	1	6	yes	—
322	C₄²	C₂×C₇×D₄	1	6	yes	—
323	C₄²	C₂⁴×C₇	1	1	yes	characteristic
324	C₄²	C₂⁴×C₇	1	3	yes	—
325	C₂×C₇	—	2	6	no	—
326	C₂×C₇	—	8	2	no	—
327	C₂×C₇	—	8	6	no	—
328	C₂×C₇	C₂²×#127	1	1	yes	characteristic
329	C₂×C₇	C₂×#577	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	6	no	—
332	C₂³	—	4	12	no	—
333	C₂³	—	8	12	no	—
334	C₂³	C₂²×C₇×D₄	1	3	yes	—
335	Q₈	—	2	12	no	—
336	Q₈	—	2	4	no	—
337	Q₈	—	4	12	no	—
338	Q₈	C₇×#127	1	4	yes	—
339	D₄	—	2	4	no	—
340	D₄	—	2	12	no	—
341	D₄	—	4	12	no	—
342	D₄	—	4	12	no	—
343	D₄	—	4	12	no	—
344	D₄	—	4	4	no	—
345	D₄	—	4	12	no	—
346	D₄	—	8	12	no	—
347	D₄	C₇×#127	1	12	yes	—
348	C₂×C₄	—	2	12	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	6	no	—
351	C₂×C₄	—	4	12	no	—
352	C₂×C₄	—	4	12	no	—
353	C₂×C₄	—	4	12	no	—
354	C₂×C₄	C₂²×C₇×D₄	1	6	yes	—
355	C₂×C₄	C₂²×C₇×D₄	1	12	yes	—
356	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
357	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
358	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
359	C₈	C₂²×C₇×D₄	1	4	yes	—
360	C₈	C₂²×C₇×D₄	1	12	yes	—
361	C₇	#60646	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²	—	2	6	no	—
363	C₂²	—	4	12	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	6	no	—
367	C₂²	—	16	12	no	—
368	C₂²	C₂×C₇×#127	1	6	yes	—
369	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
370	C₄	—	2	6	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	6	no	—
373	C₄	C₂×C₇×#127	1	6	yes	—
374	C₄	C₇×#577	1	4	yes	complemented
375	C₄	C₂³×C₇×D₄	1	2	yes	—
376	C₂	—	2	6	no	—
377	C₂	—	8	6	no	—
378	C₂	—	8	2	no	—
379	C₂	C₂²×C₇×#127	1	1	yes	characteristic
380	C₂	C₂×C₇×#577	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. C₂×C₇×#577	C₂	semidirect
2. C₇×#3499	C₂	semidirect
3. C₇×#3498	C₂	semidirect
4. C₇×#3154	C₂	semidirect
5. C₇×#3152	C₂	semidirect
6. C₇×#3151	C₂	semidirect
7. C₇×#3147	C₂	semidirect
8. C₂×C₇×#492	C₂	semidirect
9. C₄×C₇×#131	C₂	semidirect
13. C₂×C₇×#137	C₂²	semidirect
14. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂×C₇×#135	C₂²	semidirect
16. C₂²×C₇×SD₁₆	C₂²	semidirect
22. C₇×#536	C₂²	semidirect
25. C₇×#532	C₂²	semidirect
26. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
29. C₇×#497	C₂²	semidirect
30. C₇×#496	C₂²	semidirect
31. C₇×#495	C₂²	semidirect
32. C₇×#494	C₂²	semidirect
33. C₇×#493	C₂²	semidirect
34. C₇×#492	C₂²	semidirect
35. C₇×#492	C₂²	semidirect
36. C₇×#492	C₂²	semidirect
37. C₇×#492	C₂²	semidirect
38. C₇×#405	C₂²	semidirect
39. C₄×C₇×M₁₆	C₂²	semidirect
40. C₂×C₄×C₇×C₈	C₂²	semidirect
41. #60646	C₇	direct (N × H)
63. C₇×#131	D₄	semidirect
93. C₂×#577	C₂×C₇	semidirect
94. #3499	C₂×C₇	semidirect
95. #3498	C₂×C₇	semidirect
96. #3154	C₂×C₇	semidirect
97. #3152	C₂×C₇	semidirect
98. #3151	C₂×C₇	semidirect
99. #3147	C₂×C₇	semidirect
100. C₂×#492	C₂×C₇	semidirect
101. C₄×#131	C₂×C₇	semidirect
136. C₇×M₁₆	C₂×D₄	semidirect
137. C₂×C₇×C₈	C₂×D₄	semidirect
153. C₂×#137	C₂²×C₇	semidirect
154. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
155. C₂×#135	C₂²×C₇	semidirect
156. C₂²×SD₁₆	C₂²×C₇	semidirect
162. #536	C₂²×C₇	semidirect
165. #532	C₂²×C₇	semidirect
166. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
169. #497	C₂²×C₇	semidirect
170. #496	C₂²×C₇	semidirect
171. #495	C₂²×C₇	semidirect
172. #494	C₂²×C₇	semidirect
173. #493	C₂²×C₇	semidirect
174. #492	C₂²×C₇	semidirect
175. #492	C₂²×C₇	semidirect
176. #492	C₂²×C₇	semidirect
177. #492	C₂²×C₇	semidirect
178. #405	C₂²×C₇	semidirect
179. C₄×M₁₆	C₂²×C₇	semidirect
180. C₂×C₄×C₈	C₂²×C₇	semidirect
233. #131	C₇×D₄	semidirect
275. C₄×C₇	#577	semidirect
311. M₁₆	C₂×C₇×D₄	semidirect
312. C₂×C₈	C₂×C₇×D₄	semidirect
361. C₇	#60646	direct (N × H)
374. C₄	C₇×#577	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#577	2
C₇×#3499	2
C₇×#3498	2
C₇×#3154	2
C₇×#3152	2
C₇×#3151	2
C₇×#3147	2
C₂×C₇×#492	2
C₄×C₇×#131	2
#60646	7

Subgroups — C7×#60646 #13237862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60646 #13237862