Subgroups — C₇×#17959 #13195175

Order 1792.

630 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3168	C₂	1	1	yes	maximal, characteristic
2	C₇×#2966	C₂	1	2	yes	maximal, complemented
3	C₇×#1591	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1590	C₂	1	2	yes	maximal, complemented
5	C₇×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×C₈×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₇×C₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1494	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#529	C₂²	1	2	yes	—
13	C₇×#499	C₄	1	1	yes	characteristic
14	C₇×#495	C₄	1	1	yes	characteristic
15	C₇×#488	C₄	1	2	yes	—
16	C₇×#467	C₄	1	1	yes	characteristic
17	C₇×#466	C₄	1	1	yes	characteristic
18	C₇×#465	C₄	1	2	yes	—
19	C₇×#446	C₂²	1	2	yes	—
20	C₇×C₈×Q₈	C₂²	1	2	yes	—
21	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
23	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
24	C₇×#436	C₂²	1	2	yes	—
25	C₇×#435	—	2	2	no	—
26	C₇×C₈×D₄	—	2	2	no	—
27	C₇×C₈×D₄	C₂²	1	2	yes	—
28	C₇×#433	—	2	2	no	—
29	C₇×#432	C₂²	1	2	yes	—
30	C₇×#405	—	2	2	no	—
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
34	C₇×#335	C₂²	1	1	yes	characteristic
35	C₇×#335	C₂²	1	1	yes	characteristic
36	C₇×#334	C₂²	1	2	yes	—
37	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₇×D₄⋊C₈	C₂²	1	2	yes	—
40	C₇×D₄⋊C₈	C₂²	1	2	yes	—
41	C₇×C₈²	C₂²	1	1	yes	characteristic
42	C₇×C₈²	C₂²	1	1	yes	characteristic
43	C₇×C₈²	C₂²	1	1	yes	characteristic
44	C₇×C₈²	C₂²	1	1	yes	characteristic
45	#17959	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
47	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₇×M₁₆	—	2	2	no	—
50	C₂²×C₇×C₈	—	2	1	no	—
51	C₂²×C₇×C₈	—	2	2	no	—
52	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
55	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
56	C₇×#126	—	2	2	no	—
57	C₇×#125	C₂×C₄	1	2	yes	—
58	C₇×#124	C₂×C₄	1	2	yes	—
59	C₇×#123	—	2	2	no	—
60	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
61	C₇×#121	C₂×C₄	1	2	yes	—
62	C₄×C₇×Q₈	C₂³	1	2	yes	—
63	C₄×C₇×D₄	—	2	2	no	—
64	C₄×C₇×D₄	C₂³	1	2	yes	—
65	C₇×#117	—	2	2	no	—
66	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
67	C₇×#107	C₂×C₄	1	1	yes	characteristic
68	C₇×#107	C₂×C₄	1	1	yes	characteristic
69	C₇×#106	C₂×C₄	1	2	yes	—
70	C₇×C₄⋊C₈	—	2	2	no	—
71	C₇×C₄⋊C₈	—	2	2	no	—
72	C₇×C₄⋊C₈	C₂³	1	2	yes	—
73	C₇×C₄⋊C₈	C₂³	1	2	yes	—
74	C₇×#103	C₂×C₄	1	2	yes	—
75	C₇×#103	C₂×C₄	1	2	yes	—
76	C₇×#102	C₂×C₄	1	2	yes	—
77	C₇×#102	C₂×C₄	1	2	yes	—
78	C₇×C₂²⋊C₈	—	2	2	no	—
79	C₇×C₂²⋊C₈	—	2	2	no	—
80	C₇×C₂²⋊C₈	—	2	2	no	—
81	C₇×#97	—	2	2	no	—
82	C₇×#97	—	2	2	no	—
83	C₄×C₇×C₈	—	2	2	no	—
84	C₄×C₇×C₈	—	2	1	no	—
85	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
86	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
87	C₄×C₇×C₈	D₄	1	1	yes	characteristic
88	C₄×C₇×C₈	D₄	1	1	yes	characteristic
89	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
95	#3168	C₂×C₇	1	1	yes	characteristic
96	#2966	C₂×C₇	1	2	yes	complemented
97	#1591	C₂×C₇	1	1	yes	characteristic, complemented
98	#1590	C₂×C₇	1	2	yes	complemented
99	#1589	C₂×C₇	1	1	yes	characteristic, complemented
100	C₈×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
101	C₈×SD₁₆	C₂×C₇	1	2	yes	complemented
102	C₈×D₈	C₂×C₇	1	1	yes	characteristic, complemented
103	#1568	C₂×C₇	1	1	yes	characteristic, complemented
104	#1494	C₂×C₇	1	2	yes	complemented
105	C₂×C₈²	C₂×C₇	1	1	yes	characteristic, complemented
106	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
107	C₂×C₇×D₄	—	2	2	no	—
108	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₇	—	2	2	no	—
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	#41	1	1	yes	characteristic
113	C₇×Q₁₆	—	2	2	no	—
114	C₇×SD₁₆	—	2	4	no	—
115	C₇×D₈	—	2	2	no	—
116	C₇×M₁₆	—	4	4	no	—
117	C₂×C₇×C₈	—	2	4	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	—	2	1	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	2	no	—
123	C₂×C₇×C₈	—	2	2	no	—
124	C₂×C₇×C₈	—	2	2	no	—
125	C₂×C₇×C₈	—	2	2	no	—
126	C₂×C₇×C₈	—	4	4	no	—
127	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
132	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	—	2	2	no	—
138	C₇×C₄⋊C₄	—	2	2	no	—
139	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
141	C₇×C₂²⋊C₄	—	2	2	no	—
142	C₇×C₂²⋊C₄	—	2	2	no	—
143	C₇×C₂²⋊C₄	—	2	2	no	—
144	C₇×C₂²⋊C₄	—	2	2	no	—
145	C₇×C₂²⋊C₄	—	2	2	no	—
146	C₄²×C₇	—	2	2	no	—
147	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₇	#41	1	1	yes	characteristic
150	C₄²×C₇	C₂⁴	1	1	yes	characteristic
151	#529	C₂²×C₇	1	2	yes	—
152	#499	C₄×C₇	1	1	yes	characteristic
153	#495	C₄×C₇	1	1	yes	characteristic
154	#488	C₄×C₇	1	2	yes	—
155	#467	C₄×C₇	1	1	yes	characteristic
156	#466	C₄×C₇	1	1	yes	characteristic
157	#465	C₄×C₇	1	2	yes	—
158	#446	C₂²×C₇	1	2	yes	—
159	C₈×Q₈	C₂²×C₇	1	2	yes	—
160	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
161	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
162	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
163	#436	C₂²×C₇	1	2	yes	—
164	#435	—	2	2	no	—
165	C₈×D₄	—	2	2	no	—
166	C₈×D₄	C₂²×C₇	1	2	yes	—
167	#433	—	2	2	no	—
168	#432	C₂²×C₇	1	2	yes	—
169	#405	—	2	2	no	—
170	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
171	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
172	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
173	#335	C₂²×C₇	1	1	yes	characteristic
174	#335	C₂²×C₇	1	1	yes	characteristic
175	#334	C₂²×C₇	1	2	yes	—
176	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
177	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
178	D₄⋊C₈	C₂²×C₇	1	2	yes	—
179	D₄⋊C₈	C₂²×C₇	1	2	yes	—
180	C₈²	C₂²×C₇	1	1	yes	characteristic
181	C₈²	C₂²×C₇	1	1	yes	characteristic
182	C₈²	C₂²×C₇	1	1	yes	characteristic
183	C₈²	C₂²×C₇	1	1	yes	characteristic
184	C₂³×C₇	—	2	2	no	—
185	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
186	C₇×Q₈	—	2	2	no	—
187	C₇×Q₈	—	2	2	no	—
188	C₇×D₄	—	2	2	no	—
189	C₇×D₄	—	2	2	no	—
190	C₇×D₄	—	4	4	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	1	no	—
193	C₂×C₄×C₇	—	2	1	no	—
194	C₂×C₄×C₇	—	2	1	no	—
195	C₂×C₄×C₇	—	2	1	no	—
196	C₂×C₄×C₇	—	2	2	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	4	2	no	—
200	C₂×C₄×C₇	—	4	2	no	—
201	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
207	C₇×C₈	—	2	2	no	—
208	C₇×C₈	—	2	2	no	—
209	C₇×C₈	—	2	1	no	—
210	C₇×C₈	—	2	1	no	—
211	C₇×C₈	—	2	1	no	—
212	C₇×C₈	—	2	1	no	—
213	C₇×C₈	—	4	2	no	—
214	C₇×C₈	—	4	2	no	—
215	C₇×C₈	#131	1	2	yes	—
216	C₇×C₈	#131	1	2	yes	—
217	C₇×C₈	#135	1	2	yes	—
218	C₇×C₈	#135	1	2	yes	—
219	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
220	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
221	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
226	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
227	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
228	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
229	#126	—	2	2	no	—
230	#125	C₂×C₄×C₇	1	2	yes	—
231	#124	C₂×C₄×C₇	1	2	yes	—
232	#123	—	2	2	no	—
233	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
234	#121	C₂×C₄×C₇	1	2	yes	—
235	C₄×Q₈	C₂³×C₇	1	2	yes	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	C₂³×C₇	1	2	yes	—
238	#117	—	2	2	no	—
239	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
240	#107	C₂×C₄×C₇	1	1	yes	characteristic
241	#107	C₂×C₄×C₇	1	1	yes	characteristic
242	#106	C₂×C₄×C₇	1	2	yes	—
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	C₂³×C₇	1	2	yes	—
246	C₄⋊C₈	C₂³×C₇	1	2	yes	—
247	#103	C₂×C₄×C₇	1	2	yes	—
248	#103	C₂×C₄×C₇	1	2	yes	—
249	#102	C₂×C₄×C₇	1	2	yes	—
250	#102	C₂×C₄×C₇	1	2	yes	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	2	2	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	#97	—	2	2	no	—
255	#97	—	2	2	no	—
256	C₄×C₈	—	2	2	no	—
257	C₄×C₈	—	2	1	no	—
258	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
259	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
260	C₄×C₈	C₇×D₄	1	1	yes	characteristic
261	C₄×C₈	C₇×D₄	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
266	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
268	C₂²×C₇	—	2	1	no	—
269	C₂²×C₇	—	2	1	no	—
270	C₂²×C₇	—	4	2	no	—
271	C₂²×C₇	—	4	2	no	—
272	C₂²×C₇	—	4	2	no	—
273	C₂²×C₇	#443	1	2	yes	—
274	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
275	C₄×C₇	—	2	1	no	—
276	C₄×C₇	—	2	1	no	—
277	C₄×C₇	—	2	1	no	—
278	C₄×C₇	—	2	1	no	—
279	C₄×C₇	—	4	2	no	—
280	C₄×C₇	—	4	2	no	—
281	C₄×C₇	—	4	2	no	—
282	C₄×C₇	C₂×#131	1	1	yes	characteristic
283	C₄×C₇	C₂×#131	1	1	yes	characteristic
284	C₄×C₇	C₂×#135	1	1	yes	characteristic
285	C₄×C₇	C₂×#135	1	1	yes	characteristic
286	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
292	C₂²×C₄	C₇×#41	1	1	yes	characteristic
293	Q₁₆	—	2	2	no	—
294	SD₁₆	—	2	4	no	—
295	D₈	—	2	2	no	—
296	M₁₆	—	4	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	4	no	—
307	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
308	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
309	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
310	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
311	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
312	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
313	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
314	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
320	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
328	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
329	C₄²	C₇×#41	1	1	yes	characteristic
330	C₄²	C₂⁴×C₇	1	1	yes	characteristic
331	C₂×C₇	—	2	2	no	—
332	C₂×C₇	—	8	2	no	—
333	C₂×C₇	#2931	1	1	yes	characteristic
334	C₂×C₇	C₄×#135	1	1	yes	characteristic
335	C₂×C₇	C₂×#443	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
338	Q₈	—	2	2	no	—
339	Q₈	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	2	no	—
342	D₄	—	4	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
354	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
355	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
356	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
358	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₈	C₇×#131	1	2	yes	—
368	C₈	C₇×#131	1	2	yes	—
369	C₈	C₇×#135	1	2	yes	—
370	C₈	C₇×#135	1	2	yes	—
371	C₇	#17959	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	C₇×#443	1	2	yes	—
378	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	C₂×C₇×#131	1	1	yes	characteristic
387	C₄	C₂×C₇×#131	1	1	yes	characteristic
388	C₄	C₂×C₇×#135	1	1	yes	characteristic
389	C₄	C₂×C₇×#135	1	1	yes	characteristic
390	C₂	—	2	2	no	—
391	C₂	—	8	2	no	—
392	C₂	C₇×#2931	1	1	yes	characteristic
393	C₂	C₄×C₇×#135	1	1	yes	characteristic
394	C₂	C₂×C₇×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇×C₈	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇×C₈ ◁ C₂×C₄×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2966	C₂	semidirect
3. C₇×#1591	C₂	semidirect
4. C₇×#1590	C₂	semidirect
5. C₇×#1589	C₂	semidirect
6. C₇×C₈×Q₁₆	C₂	semidirect
7. C₇×C₈×SD₁₆	C₂	semidirect
8. C₇×C₈×D₈	C₂	semidirect
9. C₇×#1568	C₂	semidirect
10. C₇×#1494	C₂	semidirect
11. C₂×C₇×C₈²	C₂	semidirect
45. #17959	C₇	direct (N × H)
96. #2966	C₂×C₇	semidirect
97. #1591	C₂×C₇	semidirect
98. #1590	C₂×C₇	semidirect
99. #1589	C₂×C₇	semidirect
100. C₈×Q₁₆	C₂×C₇	semidirect
101. C₈×SD₁₆	C₂×C₇	semidirect
102. C₈×D₈	C₂×C₇	semidirect
103. #1568	C₂×C₇	semidirect
104. #1494	C₂×C₇	semidirect
105. C₂×C₈²	C₂×C₇	semidirect
371. C₇	#17959	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×#3168	2
C₇×#2966	2
C₇×#1591	2
C₇×#1590	2
C₇×#1589	2
C₇×C₈×Q₁₆	2
C₇×C₈×SD₁₆	2
C₇×C₈×D₈	2
C₇×#1568	2
C₇×#1494	2
C₂×C₇×C₈²	2
#17959	7

Subgroups — C7×#17959 #13195175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17959 #13195175