Subgroups — C₇×#20485 #13197701

Order 1792.

1150 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#405	C₂	1	2	yes	maximal, complemented
4	C₇×#2293	C₂	1	1	yes	maximal, characteristic
5	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1753	C₂	1	2	yes	maximal, complemented
9	C₇×C₈×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₇×#1750	C₂	1	2	yes	maximal, complemented
11	C₄²×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₇×C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₇×#117	C₂²	1	2	yes	—
16	C₇×#436	C₄	1	8	yes	complemented
17	C₇×C₈×D₄	C₄	1	8	yes	complemented
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₇×#405	—	2	8	no	—
23	C₂×C₇×#97	C₂²	1	2	yes	—
24	C₂×C₇×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₇×#390	C₄	1	2	yes	—
33	C₇×#389	C₄	1	2	yes	—
34	C₇×#388	C₄	1	4	yes	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₄³×C₇	C₂²	1	1	yes	characteristic
38	C₇×#336	C₂²	1	2	yes	—
39	C₇×#336	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	#20485	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₇	C₂³	1	2	yes	—
44	C₂×C₇×M₁₆	—	2	4	no	—
45	C₂×C₇×M₁₆	—	2	4	no	—
46	C₂×C₇×M₁₆	C₂×C₄	1	8	yes	—
47	C₂²×C₇×C₈	—	2	4	no	—
48	C₂²×C₇×C₈	—	2	4	no	—
49	C₂²×C₇×C₈	C₂×C₄	1	8	yes	—
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇×C₈	C₂³	1	2	yes	—
53	C₂²×C₇×C₈	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
57	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
58	C₇×#117	—	2	4	no	—
59	C₇×#117	—	2	4	no	—
60	C₂×C₇×C₄⋊C₄	C₂×C₄	1	4	yes	—
61	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
64	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	4	yes	—
65	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
72	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
73	C₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
74	C₇×C₂²⋊C₈	C₂×C₄	1	8	yes	—
75	C₇×C₂²⋊C₈	C₂×C₄	1	8	yes	—
76	C₇×#97	—	2	4	no	—
77	C₇×#97	—	2	4	no	—
78	C₄×C₇×C₈	—	2	4	no	—
79	C₄×C₇×C₈	—	2	2	no	—
80	C₄×C₇×C₈	—	2	2	no	—
81	C₄×C₇×C₈	—	2	2	no	—
82	C₄×C₇×C₈	C₂×C₄	1	4	yes	—
83	C₄×C₇×C₈	C₂×C₄	1	4	yes	—
84	C₄×C₇×C₈	D₄	1	4	yes	complemented
85	C₇×#95	C₂×C₄	1	4	yes	—
86	C₇×#95	C₂×C₄	1	2	yes	—
87	C₂×#436	C₂×C₇	1	1	yes	characteristic
88	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic
89	C₂×#405	C₂×C₇	1	2	yes	complemented
90	#2293	C₂×C₇	1	1	yes	characteristic
91	#1770	C₂×C₇	1	1	yes	characteristic, complemented
92	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
93	#1767	C₂×C₇	1	1	yes	characteristic, complemented
94	#1753	C₂×C₇	1	2	yes	complemented
95	C₈×C₂²⋊C₄	C₂×C₇	1	2	yes	complemented
96	#1750	C₂×C₇	1	2	yes	complemented
97	C₄²×C₈	C₂×C₇	1	1	yes	characteristic, complemented
98	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
99	C₂×C₇×D₄	—	2	4	no	—
100	C₂×C₇×D₄	C₄²	1	4	yes	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	—	2	2	no	—
103	C₂²×C₄×C₇	—	2	2	no	—
104	C₂²×C₄×C₇	—	2	2	no	—
105	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
114	C₇×M₁₆	—	2	16	no	—
115	C₂×C₇×C₈	—	2	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	1	no	—
118	C₂×C₇×C₈	—	2	1	no	—
119	C₂×C₇×C₈	—	2	1	no	—
120	C₂×C₇×C₈	—	2	1	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	2	no	—
123	C₂×C₇×C₈	—	2	16	no	—
124	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
125	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
127	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
128	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
131	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
132	C₂×C₇×C₈	#41	1	2	yes	—
133	C₂×C₇×C₈	#41	1	2	yes	—
134	C₇×C₄⋊C₄	—	2	8	no	—
135	C₇×C₄⋊C₄	—	2	4	no	—
136	C₇×C₄⋊C₄	C₄²	1	4	yes	—
137	C₇×C₂²⋊C₄	—	2	8	no	—
138	C₇×C₂²⋊C₄	—	2	8	no	—
139	C₇×C₂²⋊C₄	C₄²	1	8	yes	—
140	C₄²×C₇	—	2	4	no	—
141	C₄²×C₇	—	2	4	no	—
142	C₄²×C₇	—	2	2	no	—
143	C₄²×C₇	—	2	1	no	—
144	C₄²×C₇	—	2	1	no	—
145	C₄²×C₇	—	2	2	no	—
146	C₄²×C₇	C₂²×C₄	1	2	yes	—
147	C₄²×C₇	C₂²×C₄	1	2	yes	—
148	C₄²×C₇	C₂×D₄	1	2	yes	—
149	C₄²×C₇	#41	1	2	yes	—
150	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
151	C₂³×C₈	C₂²×C₇	1	2	yes	—
152	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
153	C₂×#117	C₂²×C₇	1	2	yes	—
154	#436	C₄×C₇	1	8	yes	complemented
155	C₈×D₄	C₄×C₇	1	8	yes	complemented
156	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
157	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
158	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
159	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
160	#405	—	2	8	no	—
161	C₂×#97	C₂²×C₇	1	2	yes	—
162	C₂×#97	C₂²×C₇	1	2	yes	—
163	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
164	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
166	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
168	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
170	#390	C₄×C₇	1	2	yes	—
171	#389	C₄×C₇	1	2	yes	—
172	#388	C₄×C₇	1	4	yes	—
173	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
174	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
175	C₄³	C₂²×C₇	1	1	yes	characteristic
176	#336	C₂²×C₇	1	2	yes	—
177	#336	C₂²×C₇	1	2	yes	—
178	#336	C₂²×C₇	1	2	yes	—
179	C₂³×C₇	—	2	2	no	—
180	C₂³×C₇	—	2	2	no	—
181	C₂³×C₇	—	2	4	no	—
182	C₂³×C₇	—	2	4	no	—
183	C₂³×C₇	C₂×C₄²	1	4	yes	—
184	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
185	C₇×D₄	—	2	8	no	—
186	C₂×C₄×C₇	—	2	2	no	—
187	C₂×C₄×C₇	—	2	2	no	—
188	C₂×C₄×C₇	—	2	2	no	—
189	C₂×C₄×C₇	—	2	2	no	—
190	C₂×C₄×C₇	—	2	2	no	—
191	C₂×C₄×C₇	—	2	2	no	—
192	C₂×C₄×C₇	—	2	2	no	—
193	C₂×C₄×C₇	—	2	4	no	—
194	C₂×C₄×C₇	—	2	4	no	—
195	C₂×C₄×C₇	—	2	4	no	—
196	C₂×C₄×C₇	—	2	4	no	—
197	C₂×C₄×C₇	—	2	4	no	—
198	C₂×C₄×C₇	—	2	4	no	—
199	C₂×C₄×C₇	—	2	4	no	—
200	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
201	C₂×C₄×C₇	C₂×C₄²	1	4	yes	—
202	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
203	C₂×C₄×C₇	C₄×D₄	1	4	yes	—
204	C₂×C₄×C₇	#131	1	4	yes	—
205	C₂×C₄×C₇	#131	1	4	yes	—
206	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
212	C₇×C₈	—	2	4	no	—
213	C₇×C₈	—	2	4	no	—
214	C₇×C₈	—	2	2	no	—
215	C₇×C₈	—	2	2	no	—
216	C₇×C₈	C₄×D₄	1	4	yes	—
217	C₇×C₈	C₄×D₄	1	4	yes	—
218	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₇	1	2	yes	—
220	C₂×M₁₆	—	2	4	no	—
221	C₂×M₁₆	—	2	4	no	—
222	C₂×M₁₆	C₂×C₄×C₇	1	8	yes	—
223	C₂²×C₈	—	2	4	no	—
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	C₂×C₄×C₇	1	8	yes	—
226	C₂²×C₈	C₂³×C₇	1	2	yes	—
227	C₂²×C₈	C₂³×C₇	1	2	yes	—
228	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
232	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
233	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
234	#117	—	2	4	no	—
235	#117	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₇	1	4	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
240	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	4	yes	—
241	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
242	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
243	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
244	C₂×C₄²	C₂³×C₇	1	2	yes	—
245	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
248	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
249	C₄⋊C₈	C₂×C₄×C₇	1	4	yes	—
250	C₂²⋊C₈	C₂×C₄×C₇	1	8	yes	—
251	C₂²⋊C₈	C₂×C₄×C₇	1	8	yes	—
252	#97	—	2	4	no	—
253	#97	—	2	4	no	—
254	C₄×C₈	—	2	4	no	—
255	C₄×C₈	—	2	2	no	—
256	C₄×C₈	—	2	2	no	—
257	C₄×C₈	—	2	2	no	—
258	C₄×C₈	C₂×C₄×C₇	1	4	yes	—
259	C₄×C₈	C₂×C₄×C₇	1	4	yes	—
260	C₄×C₈	C₇×D₄	1	4	yes	complemented
261	#95	C₂×C₄×C₇	1	4	yes	—
262	#95	C₂×C₄×C₇	1	2	yes	—
263	C₂²×C₇	—	2	4	no	—
264	C₂²×C₇	—	2	4	no	—
265	C₂²×C₇	—	2	4	no	—
266	C₂²×C₇	—	4	4	no	—
267	C₂²×C₇	—	4	4	no	—
268	C₂²×C₇	C₂²×C₄²	1	1	yes	characteristic
269	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂²×C₇	C₄×#41	1	1	yes	characteristic
271	C₂²×C₇	C₂×#131	1	2	yes	—
272	C₂²×C₇	C₂×#131	1	2	yes	—
273	C₄×C₇	—	2	2	no	—
274	C₄×C₇	—	2	4	no	—
275	C₄×C₇	—	2	4	no	—
276	C₄×C₇	—	2	4	no	—
277	C₄×C₇	—	4	4	no	—
278	C₄×C₇	#405	1	4	yes	complemented
279	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
280	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
281	C₄×C₇	C₄×#41	1	1	yes	characteristic
282	C₄×C₇	C₄×#41	1	1	yes	characteristic
283	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	C₄²×C₇	1	4	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
291	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
294	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
295	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
296	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
299	M₁₆	—	2	16	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	16	no	—
309	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
310	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
311	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
312	C₂×C₈	C₂²×C₄×C₇	1	4	yes	—
313	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
314	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
315	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
316	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
317	C₂×C₈	C₇×#41	1	2	yes	—
318	C₂×C₈	C₇×#41	1	2	yes	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	C₄²×C₇	1	4	yes	—
322	C₂²⋊C₄	—	2	8	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	C₄²×C₇	1	8	yes	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	2	no	—
331	C₄²	C₂²×C₄×C₇	1	2	yes	—
332	C₄²	C₂²×C₄×C₇	1	2	yes	—
333	C₄²	C₂×C₇×D₄	1	2	yes	—
334	C₄²	C₇×#41	1	2	yes	—
335	C₂×C₇	—	4	4	no	—
336	C₂×C₇	C₄²×D₄	1	1	yes	characteristic
337	C₂×C₇	C₂×#405	1	1	yes	characteristic
338	C₂×C₇	C₄×#131	1	1	yes	characteristic
339	C₂×C₇	#2931	1	2	yes	—
340	C₂×C₇	#2966	1	2	yes	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	C₂×C₄²×C₇	1	4	yes	—
346	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
347	D₄	—	2	8	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
363	C₂×C₄	C₂×C₄²×C₇	1	4	yes	—
364	C₂×C₄	C₂×C₄²×C₇	1	2	yes	—
365	C₂×C₄	C₄×C₇×D₄	1	4	yes	—
366	C₂×C₄	C₇×#131	1	4	yes	—
367	C₂×C₄	C₇×#131	1	4	yes	—
368	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
369	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
371	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
372	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
373	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
374	C₈	—	2	4	no	—
375	C₈	—	2	4	no	—
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	C₄×C₇×D₄	1	4	yes	—
379	C₈	C₄×C₇×D₄	1	4	yes	—
380	C₇	#20485	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₂²×C₄²×C₇	1	1	yes	characteristic
387	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
388	C₂²	C₄×C₇×#41	1	1	yes	characteristic
389	C₂²	C₂×C₇×#131	1	2	yes	—
390	C₂²	C₂×C₇×#131	1	2	yes	—
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	4	no	—
396	C₄	C₇×#405	1	4	yes	complemented
397	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
398	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
399	C₄	C₄×C₇×#41	1	1	yes	characteristic
400	C₄	C₄×C₇×#41	1	1	yes	characteristic
401	C₂	—	4	4	no	—
402	C₂	C₄²×C₇×D₄	1	1	yes	characteristic
403	C₂	C₂×C₇×#405	1	1	yes	characteristic
404	C₂	C₄×C₇×#131	1	1	yes	characteristic
405	C₂	C₇×#2931	1	2	yes	—
406	C₂	C₇×#2966	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₇×#405	C₂	semidirect
5. C₇×#1770	C₂	semidirect
6. C₇×C₈×C₄⋊C₄	C₂	semidirect
7. C₇×#1767	C₂	semidirect
8. C₇×#1753	C₂	semidirect
9. C₇×C₈×C₂²⋊C₄	C₂	semidirect
10. C₇×#1750	C₂	semidirect
11. C₄²×C₇×C₈	C₂	semidirect
16. C₇×#436	C₄	semidirect
17. C₇×C₈×D₄	C₄	semidirect
41. #20485	C₇	direct (N × H)
84. C₄×C₇×C₈	D₄	semidirect
89. C₂×#405	C₂×C₇	semidirect
91. #1770	C₂×C₇	semidirect
92. C₈×C₄⋊C₄	C₂×C₇	semidirect
93. #1767	C₂×C₇	semidirect
94. #1753	C₂×C₇	semidirect
95. C₈×C₂²⋊C₄	C₂×C₇	semidirect
96. #1750	C₂×C₇	semidirect
97. C₄²×C₈	C₂×C₇	semidirect
154. #436	C₄×C₇	semidirect
155. C₈×D₄	C₄×C₇	semidirect
260. C₄×C₈	C₇×D₄	semidirect
278. C₄×C₇	#405	semidirect
380. C₇	#20485	direct (N × H)
396. C₄	C₇×#405	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#436	2
C₂×C₇×C₈×D₄	2
C₂×C₇×#405	2
C₇×#2293	2
C₇×#1770	2
C₇×C₈×C₄⋊C₄	2
C₇×#1767	2
C₇×#1753	2
C₇×C₈×C₂²⋊C₄	2
C₇×#1750	2
C₄²×C₇×C₈	2
#20485	7

Subgroups — C7×#20485 #13197701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#20485 #13197701