Subgroups — C₇×#17841 #13195057

Order 1792.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2991	C₂	1	1	yes	maximal, characteristic
2	C₇×#2990	C₂	1	1	yes	maximal, characteristic
3	C₇×#2965	C₂	1	1	yes	maximal, characteristic
4	C₇×#1574	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1574	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1572	C₂	1	2	yes	maximal, complemented
7	C₇×#1570	C₂	1	2	yes	maximal, complemented
8	C₇×#1569	C₂	1	2	yes	maximal, complemented
9	C₇×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1565	C₂	1	2	yes	maximal, complemented
11	C₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₇×#41	C₂²	1	1	yes	characteristic
13	C₇×#446	—	2	1	no	—
14	C₇×#446	C₄	1	1	yes	characteristic
15	C₇×#446	C₄	1	1	yes	characteristic
16	C₇×C₈×Q₈	—	2	1	no	—
17	C₇×#436	—	2	1	no	—
18	C₇×#436	—	2	2	no	—
19	C₇×#436	C₄	1	1	yes	characteristic
20	C₇×#436	C₄	1	1	yes	characteristic
21	C₇×#435	—	2	2	no	—
22	C₇×#435	C₄	1	2	yes	—
23	C₇×#435	C₄	1	2	yes	—
24	C₇×C₈×D₄	—	2	1	no	—
25	C₇×#432	C₂²	1	2	yes	—
26	C₇×#431	C₂²	1	1	yes	characteristic
27	C₇×#431	C₂²	1	1	yes	characteristic
28	C₇×#431	C₂²	1	2	yes	—
29	C₇×#431	C₂²	1	2	yes	—
30	C₇×#431	C₂²	1	1	yes	characteristic
31	C₇×#423	C₂²	1	1	yes	characteristic
32	C₇×#423	C₂²	1	1	yes	characteristic
33	C₇×#423	C₂²	1	2	yes	—
34	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
35	C₄×C₇×M₁₆	C₂²	1	2	yes	—
36	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
37	C₇×#335	C₂²	1	1	yes	characteristic
38	C₇×#335	C₂²	1	1	yes	characteristic
39	C₇×#335	C₂²	1	2	yes	—
40	C₇×#335	C₂²	1	2	yes	—
41	C₇×#334	C₂²	1	1	yes	characteristic
42	C₇×#334	C₂²	1	1	yes	characteristic
43	C₇×#334	C₂²	1	2	yes	—
44	C₇×#334	C₂²	1	2	yes	—
45	C₇×#334	C₂²	1	2	yes	—
46	C₇×#334	C₂²	1	2	yes	—
47	#17841	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	Q₈	1	1	yes	characteristic
49	C₂×C₇×M₁₆	—	2	1	no	—
50	C₂×C₇×M₁₆	—	2	2	no	—
51	C₂×C₇×M₁₆	—	2	1	no	—
52	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
54	C₂²×C₇×C₈	—	2	2	no	—
55	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
57	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
58	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
59	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
60	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
61	C₄×C₇×D₄	D₄	1	1	yes	characteristic
62	C₄×C₇×D₄	D₄	1	2	yes	—
63	C₇×#117	Q₈	1	1	yes	characteristic
64	C₇×#117	Q₈	1	2	yes	—
65	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₇	C₂³	1	2	yes	—
67	C₇×C₄⋊C₈	—	2	2	no	—
68	C₇×C₄⋊C₈	—	2	1	no	—
69	C₇×C₄⋊C₈	—	2	1	no	—
70	C₇×C₄⋊C₈	—	2	2	no	—
71	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
72	C₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
73	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₇×C₄⋊C₈	C₂³	1	2	yes	—
77	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₇×C₄⋊C₈	C₂³	1	2	yes	—
79	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₇×C₂²⋊C₈	—	2	1	no	—
82	C₇×C₂²⋊C₈	—	2	2	no	—
83	C₇×C₂²⋊C₈	—	2	1	no	—
84	C₇×C₂²⋊C₈	—	2	2	no	—
85	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
86	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
87	C₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
88	C₇×#97	—	2	2	no	—
89	C₇×#97	C₂×C₄	1	2	yes	—
90	C₇×#97	C₂×C₄	1	2	yes	—
91	C₄×C₇×C₈	—	2	1	no	—
92	C₄×C₇×C₈	—	2	1	no	—
93	C₄×C₇×C₈	—	2	2	no	—
94	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
95	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
97	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
98	C₄×C₇×C₈	C₂³	1	2	yes	—
99	#2991	C₂×C₇	1	1	yes	characteristic
100	#2990	C₂×C₇	1	1	yes	characteristic
101	#2965	C₂×C₇	1	1	yes	characteristic
102	#1574	C₂×C₇	1	1	yes	characteristic, complemented
103	#1574	C₂×C₇	1	1	yes	characteristic, complemented
104	#1572	C₂×C₇	1	2	yes	complemented
105	#1570	C₂×C₇	1	2	yes	complemented
106	#1569	C₂×C₇	1	2	yes	complemented
107	#1566	C₂×C₇	1	1	yes	characteristic, complemented
108	#1565	C₂×C₇	1	2	yes	complemented
109	#1564	C₂×C₇	1	1	yes	characteristic, complemented
110	C₇×#41	—	4	2	no	—
111	C₂×C₇×Q₈	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₇×D₄	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₇×D₄	C₄⋊C₄	1	2	yes	—
114	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
120	C₇×M₁₆	—	2	4	no	—
121	C₇×M₁₆	—	4	2	no	—
122	C₇×M₁₆	—	8	1	no	—
123	C₇×M₁₆	—	8	2	no	—
124	C₇×M₁₆	—	8	1	no	—
125	C₂×C₇×C₈	—	2	2	no	—
126	C₂×C₇×C₈	—	2	1	no	—
127	C₂×C₇×C₈	—	2	1	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	2	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	—	4	1	no	—
133	C₂×C₇×C₈	—	8	2	no	—
134	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
141	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
142	C₇×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
143	C₇×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
144	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
145	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
146	C₇×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
147	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₇	C₂²×C₄	1	2	yes	—
149	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₇	C₂×D₄	1	2	yes	—
151	C₄²×C₇	C₂×Q₈	1	1	yes	characteristic
152	C₄²×C₇	C₂×Q₈	1	2	yes	—
153	C₄²×C₇	C₂⁴	1	1	yes	characteristic
154	C₄×#41	C₂²×C₇	1	1	yes	characteristic
155	#446	—	2	1	no	—
156	#446	C₄×C₇	1	1	yes	characteristic
157	#446	C₄×C₇	1	1	yes	characteristic
158	C₈×Q₈	—	2	1	no	—
159	#436	—	2	1	no	—
160	#436	—	2	2	no	—
161	#436	C₄×C₇	1	1	yes	characteristic
162	#436	C₄×C₇	1	1	yes	characteristic
163	#435	—	2	2	no	—
164	#435	C₄×C₇	1	2	yes	—
165	#435	C₄×C₇	1	2	yes	—
166	C₈×D₄	—	2	1	no	—
167	#432	C₂²×C₇	1	2	yes	—
168	#431	C₂²×C₇	1	1	yes	characteristic
169	#431	C₂²×C₇	1	1	yes	characteristic
170	#431	C₂²×C₇	1	2	yes	—
171	#431	C₂²×C₇	1	2	yes	—
172	#431	C₂²×C₇	1	1	yes	characteristic
173	#423	C₂²×C₇	1	1	yes	characteristic
174	#423	C₂²×C₇	1	1	yes	characteristic
175	#423	C₂²×C₇	1	2	yes	—
176	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
177	C₄×M₁₆	C₂²×C₇	1	2	yes	—
178	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
179	#335	C₂²×C₇	1	1	yes	characteristic
180	#335	C₂²×C₇	1	1	yes	characteristic
181	#335	C₂²×C₇	1	2	yes	—
182	#335	C₂²×C₇	1	2	yes	—
183	#334	C₂²×C₇	1	1	yes	characteristic
184	#334	C₂²×C₇	1	1	yes	characteristic
185	#334	C₂²×C₇	1	2	yes	—
186	#334	C₂²×C₇	1	2	yes	—
187	#334	C₂²×C₇	1	2	yes	—
188	#334	C₂²×C₇	1	2	yes	—
189	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂³×C₇	C₂×C₄⋊C₄	1	2	yes	—
191	C₇×Q₈	—	2	2	no	—
192	C₇×D₄	—	2	2	no	—
193	C₇×D₄	—	4	2	no	—
194	C₂×C₄×C₇	—	2	1	no	—
195	C₂×C₄×C₇	—	2	2	no	—
196	C₂×C₄×C₇	—	2	1	no	—
197	C₂×C₄×C₇	—	2	2	no	—
198	C₂×C₄×C₇	—	2	2	no	—
199	C₂×C₄×C₇	—	2	2	no	—
200	C₂×C₄×C₇	—	2	1	no	—
201	C₂×C₄×C₇	—	2	1	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	4	2	no	—
204	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
205	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
207	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
209	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
213	C₇×C₈	—	2	1	no	—
214	C₇×C₈	—	2	2	no	—
215	C₇×C₈	—	2	1	no	—
216	C₇×C₈	—	2	1	no	—
217	C₇×C₈	—	2	2	no	—
218	C₇×C₈	—	4	1	no	—
219	C₇×C₈	—	4	1	no	—
220	C₇×C₈	—	4	1	no	—
221	C₇×C₈	—	4	2	no	—
222	C₇×C₈	—	4	1	no	—
223	C₇×C₈	—	4	2	no	—
224	C₇×C₈	#131	1	2	yes	—
225	C₂×#41	C₇×Q₈	1	1	yes	characteristic
226	C₂×M₁₆	—	2	1	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	1	no	—
229	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
230	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
233	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
234	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
235	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
236	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
237	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
238	C₄×D₄	C₇×D₄	1	1	yes	characteristic
239	C₄×D₄	C₇×D₄	1	2	yes	—
240	#117	C₇×Q₈	1	1	yes	characteristic
241	#117	C₇×Q₈	1	2	yes	—
242	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₇	1	2	yes	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
249	C₄⋊C₈	C₂×C₄×C₇	1	2	yes	—
250	C₄⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
251	C₄⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
252	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
253	C₄⋊C₈	C₂³×C₇	1	2	yes	—
254	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
255	C₄⋊C₈	C₂³×C₇	1	2	yes	—
256	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
257	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
258	C₂²⋊C₈	—	2	1	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	2	1	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
263	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
264	C₂²⋊C₈	C₂×C₄×C₇	1	2	yes	—
265	#97	—	2	2	no	—
266	#97	C₂×C₄×C₇	1	2	yes	—
267	#97	C₂×C₄×C₇	1	2	yes	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
272	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₇	1	2	yes	—
276	C₂²×C₇	—	2	1	no	—
277	C₂²×C₇	—	2	2	no	—
278	C₂²×C₇	—	2	2	no	—
279	C₂²×C₇	—	2	1	no	—
280	C₂²×C₇	—	2	1	no	—
281	C₂²×C₇	—	2	2	no	—
282	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
283	C₄×C₇	—	2	1	no	—
284	C₄×C₇	—	2	2	no	—
285	C₄×C₇	—	2	2	no	—
286	C₄×C₇	—	2	1	no	—
287	C₄×C₇	—	2	1	no	—
288	C₄×C₇	—	2	2	no	—
289	C₄×C₇	#430	1	2	yes	—
290	C₄×C₇	C₂×#131	1	1	yes	characteristic
291	C₄×C₇	#568	1	1	yes	characteristic
292	C₄×C₇	#577	1	1	yes	characteristic
293	C₄×C₇	#577	1	1	yes	characteristic
294	#41	—	4	2	no	—
295	C₂×Q₈	C₇×C₄⋊C₄	1	1	yes	characteristic
296	C₂×D₄	C₇×C₄⋊C₄	1	1	yes	characteristic
297	C₂×D₄	C₇×C₄⋊C₄	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
300	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
301	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
304	M₁₆	—	2	4	no	—
305	M₁₆	—	4	2	no	—
306	M₁₆	—	8	1	no	—
307	M₁₆	—	8	2	no	—
308	M₁₆	—	8	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	8	2	no	—
318	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
319	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
320	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
321	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
322	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
323	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
324	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
325	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
326	C₄⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
327	C₄⋊C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
328	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
329	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
330	C₂²⋊C₄	C₇×C₄⋊C₄	1	2	yes	—
331	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
332	C₄²	C₂²×C₄×C₇	1	2	yes	—
333	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
334	C₄²	C₂×C₇×D₄	1	2	yes	—
335	C₄²	C₂×C₇×Q₈	1	1	yes	characteristic
336	C₄²	C₂×C₇×Q₈	1	2	yes	—
337	C₄²	C₂⁴×C₇	1	1	yes	characteristic
338	C₂×C₇	—	4	1	no	—
339	C₂×C₇	—	4	2	no	—
340	C₂×C₇	#2906	1	1	yes	characteristic
341	C₂×C₇	#2912	1	1	yes	characteristic
342	C₂×C₇	C₂×#430	1	1	yes	characteristic
343	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
344	C₂³	C₂×C₇×C₄⋊C₄	1	2	yes	—
345	Q₈	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
359	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
361	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
363	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	2	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	2	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	2	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	2	no	—
378	C₈	C₇×#131	1	2	yes	—
379	C₇	#17841	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	C₇×#430	1	2	yes	—
394	C₄	C₂×C₇×#131	1	1	yes	characteristic
395	C₄	C₇×#568	1	1	yes	characteristic
396	C₄	C₇×#577	1	1	yes	characteristic
397	C₄	C₇×#577	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	4	2	no	—
400	C₂	C₇×#2906	1	1	yes	characteristic
401	C₂	C₇×#2912	1	1	yes	characteristic
402	C₂	C₂×C₇×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂²×C₄⋊C₄
prime radical	C₂×C₇×#41	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇×#1574	C₂	semidirect
5. C₇×#1574	C₂	semidirect
6. C₇×#1572	C₂	semidirect
7. C₇×#1570	C₂	semidirect
8. C₇×#1569	C₂	semidirect
9. C₇×#1566	C₂	semidirect
10. C₇×#1565	C₂	semidirect
11. C₇×#1564	C₂	semidirect
47. #17841	C₇	direct (N × H)
102. #1574	C₂×C₇	semidirect
103. #1574	C₂×C₇	semidirect
104. #1572	C₂×C₇	semidirect
105. #1570	C₂×C₇	semidirect
106. #1569	C₂×C₇	semidirect
107. #1566	C₂×C₇	semidirect
108. #1565	C₂×C₇	semidirect
109. #1564	C₂×C₇	semidirect
379. C₇	#17841	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×#2991	2
C₇×#2990	2
C₇×#2965	2
C₇×#1574	2
C₇×#1572	2
C₇×#1570	2
C₇×#1569	2
C₇×#1566	2
C₇×#1565	2
C₇×#1564	2
#17841	7

Subgroups — C7×#17841 #13195057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17841 #13195057