Subgroups — C₇×#22836 #13200052

Order 1792.

752 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2293	C₂	1	1	yes	maximal, characteristic
2	C₇×#1954	C₂	1	1	yes	maximal, characteristic
3	C₇×#1954	C₂	1	1	yes	maximal, characteristic
4	C₇×#1924	C₂	1	2	yes	maximal, complemented
5	C₇×#1923	C₂	1	2	yes	maximal, complemented
6	C₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1818	C₂	1	2	yes	maximal, complemented
8	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1750	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₇×#117	C₂²	1	2	yes	—
14	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₇×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
26	C₇×#390	C₄	1	1	yes	characteristic
27	C₇×#390	C₄	1	1	yes	characteristic
28	C₇×#389	C₄	1	1	yes	characteristic
29	C₇×#389	C₄	1	1	yes	characteristic
30	C₇×#388	C₄	1	2	yes	—
31	C₇×#388	C₄	1	2	yes	—
32	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₄³×C₇	C₂²	1	1	yes	characteristic
35	C₇×#336	C₂²	1	1	yes	characteristic
36	C₇×#336	C₂²	1	2	yes	—
37	C₇×#336	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	#22836	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	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇×C₈	C₂³	1	2	yes	—
47	C₂²×C₇×C₈	C₂³	1	2	yes	—
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₄×C₇×D₄	—	2	2	no	—
51	C₄×C₇×D₄	—	2	2	no	—
52	C₇×#117	—	4	2	no	—
53	C₇×#117	—	4	2	no	—
54	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
72	C₇×C₄⋊C₈	—	2	2	no	—
73	C₇×C₄⋊C₈	—	2	2	no	—
74	C₇×C₄⋊C₈	—	2	2	no	—
75	C₇×C₄⋊C₈	—	2	2	no	—
76	C₇×C₂²⋊C₈	—	2	4	no	—
77	C₇×C₂²⋊C₈	—	2	4	no	—
78	C₇×C₂²⋊C₈	—	4	2	no	—
79	C₇×C₂²⋊C₈	—	4	2	no	—
80	C₇×#97	—	4	2	no	—
81	C₄×C₇×C₈	—	2	2	no	—
82	C₄×C₇×C₈	—	2	2	no	—
83	C₄×C₇×C₈	—	4	2	no	—
84	C₇×#95	C₂×C₄	1	2	yes	—
85	C₇×#95	C₂×C₄	1	2	yes	—
86	C₇×#95	C₂×C₄	1	2	yes	—
87	#2293	C₂×C₇	1	1	yes	characteristic
88	#1954	C₂×C₇	1	1	yes	characteristic
89	#1954	C₂×C₇	1	1	yes	characteristic
90	#1924	C₂×C₇	1	2	yes	complemented
91	#1923	C₂×C₇	1	2	yes	complemented
92	#1831	C₂×C₇	1	1	yes	characteristic, complemented
93	#1818	C₂×C₇	1	2	yes	complemented
94	#1770	C₂×C₇	1	1	yes	characteristic, complemented
95	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
96	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
97	#1750	C₂×C₇	1	2	yes	complemented
98	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
99	C₂×C₇×D₄	—	2	2	no	—
100	C₂×C₇×D₄	—	2	2	no	—
101	C₂×C₇×D₄	—	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	—	2	2	no	—
106	C₂²×C₄×C₇	—	2	2	no	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂²×C₄	1	2	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	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	1	no	—
122	C₂×C₇×C₈	—	2	1	no	—
123	C₂×C₇×C₈	—	2	1	no	—
124	C₂×C₇×C₈	—	2	2	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	2	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	—	2	2	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	—	2	1	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	#41	1	2	yes	—
135	C₂×C₇×C₈	#41	1	2	yes	—
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	—	4	2	no	—
140	C₇×C₄⋊C₄	—	4	2	no	—
141	C₇×C₂²⋊C₄	—	2	4	no	—
142	C₇×C₂²⋊C₄	—	2	4	no	—
143	C₇×C₂²⋊C₄	—	4	2	no	—
144	C₇×C₂²⋊C₄	—	4	2	no	—
145	C₇×C₂²⋊C₄	—	4	2	no	—
146	C₄²×C₇	—	2	2	no	—
147	C₄²×C₇	—	2	2	no	—
148	C₄²×C₇	—	2	2	no	—
149	C₄²×C₇	—	2	1	no	—
150	C₄²×C₇	—	2	1	no	—
151	C₄²×C₇	—	2	2	no	—
152	C₄²×C₇	—	2	2	no	—
153	C₄²×C₇	—	2	1	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	—	4	1	no	—
156	C₄²×C₇	#41	1	2	yes	—
157	C₄²×C₇	#41	1	2	yes	—
158	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
159	C₂×#117	C₂²×C₇	1	2	yes	—
160	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
161	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
163	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
164	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
165	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
166	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
167	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
168	C₂×#97	C₂²×C₇	1	2	yes	—
169	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
170	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
171	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
172	#390	C₄×C₇	1	1	yes	characteristic
173	#390	C₄×C₇	1	1	yes	characteristic
174	#389	C₄×C₇	1	1	yes	characteristic
175	#389	C₄×C₇	1	1	yes	characteristic
176	#388	C₄×C₇	1	2	yes	—
177	#388	C₄×C₇	1	2	yes	—
178	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
179	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
180	C₄³	C₂²×C₇	1	1	yes	characteristic
181	#336	C₂²×C₇	1	1	yes	characteristic
182	#336	C₂²×C₇	1	2	yes	—
183	#336	C₂²×C₇	1	2	yes	—
184	#336	C₂²×C₇	1	2	yes	—
185	#336	C₂²×C₇	1	2	yes	—
186	#336	C₂²×C₇	1	1	yes	characteristic
187	C₂³×C₇	—	2	2	no	—
188	C₂³×C₇	—	2	2	no	—
189	C₂³×C₇	—	2	2	no	—
190	C₂³×C₇	—	2	2	no	—
191	C₂³×C₇	—	2	2	no	—
192	C₂³×C₇	—	2	2	no	—
193	C₂³×C₇	—	2	2	no	—
194	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
195	C₇×D₄	—	4	4	no	—
196	C₂×C₄×C₇	—	2	1	no	—
197	C₂×C₄×C₇	—	2	1	no	—
198	C₂×C₄×C₇	—	2	1	no	—
199	C₂×C₄×C₇	—	2	1	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	1	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	2	1	no	—
204	C₂×C₄×C₇	—	2	1	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	1	no	—
211	C₂×C₄×C₇	—	2	1	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	2	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	2	no	—
218	C₂×C₄×C₇	—	4	2	no	—
219	C₂×C₄×C₇	—	4	2	no	—
220	C₂×C₄×C₇	—	4	2	no	—
221	C₂×C₄×C₇	—	4	2	no	—
222	C₂×C₄×C₇	#117	1	2	yes	—
223	C₂×C₄×C₇	#117	1	2	yes	—
224	C₂×C₄×C₇	#131	1	2	yes	—
225	C₂×C₄×C₇	#131	1	2	yes	—
226	C₂×C₄×C₇	#131	1	2	yes	—
227	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
233	C₇×C₈	—	2	2	no	—
234	C₇×C₈	—	2	2	no	—
235	C₇×C₈	—	4	1	no	—
236	C₇×C₈	—	4	1	no	—
237	C₇×C₈	—	4	2	no	—
238	C₇×C₈	—	4	2	no	—
239	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₇	1	2	yes	—
241	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₇	1	2	yes	—
244	C₂²×C₈	C₂³×C₇	1	2	yes	—
245	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	2	no	—
249	#117	—	4	2	no	—
250	#117	—	4	2	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
255	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
258	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
259	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
261	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
263	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
264	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₇	1	2	yes	—
267	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	4	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	4	2	no	—
276	C₂²⋊C₈	—	4	2	no	—
277	#97	—	4	2	no	—
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	4	2	no	—
281	#95	C₂×C₄×C₇	1	2	yes	—
282	#95	C₂×C₄×C₇	1	2	yes	—
283	#95	C₂×C₄×C₇	1	2	yes	—
284	C₂²×C₇	—	4	2	no	—
285	C₂²×C₇	—	4	2	no	—
286	C₂²×C₇	—	4	2	no	—
287	C₂²×C₇	—	4	2	no	—
288	C₂²×C₇	—	4	2	no	—
289	C₂²×C₇	—	4	2	no	—
290	C₂²×C₇	—	4	2	no	—
291	C₂²×C₇	C₂×#117	1	1	yes	characteristic
292	C₂²×C₇	C₄×#41	1	1	yes	characteristic
293	C₂²×C₇	#518	1	1	yes	characteristic
294	C₂²×C₇	C₂×#131	1	1	yes	characteristic
295	C₂²×C₇	C₂×#131	1	1	yes	characteristic
296	C₂²×C₇	C₂×#131	1	1	yes	characteristic
297	C₂²×C₇	#568	1	1	yes	characteristic
298	C₄×C₇	—	2	2	no	—
299	C₄×C₇	—	2	2	no	—
300	C₄×C₇	—	4	2	no	—
301	C₄×C₇	—	4	1	no	—
302	C₄×C₇	—	4	1	no	—
303	C₄×C₇	—	4	2	no	—
304	C₄×C₇	—	4	1	no	—
305	C₄×C₇	—	4	2	no	—
306	C₄×C₇	#433	1	4	yes	—
307	C₄×C₇	#553	1	1	yes	characteristic
308	C₄×C₇	#553	1	1	yes	characteristic
309	C₄×C₇	#559	1	1	yes	characteristic
310	C₄×C₇	#559	1	1	yes	characteristic
311	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
322	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
323	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
325	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	C₇×#41	1	2	yes	—
348	C₂×C₈	C₇×#41	1	2	yes	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	4	1	no	—
369	C₄²	C₇×#41	1	2	yes	—
370	C₄²	C₇×#41	1	2	yes	—
371	C₂×C₇	—	8	2	no	—
372	C₂×C₇	#2357	1	1	yes	characteristic
373	C₂×C₇	C₂×#433	1	1	yes	characteristic
374	C₂×C₇	#2925	1	1	yes	characteristic
375	C₂×C₇	#2966	1	1	yes	characteristic
376	C₂×C₇	#2969	1	1	yes	characteristic
377	C₂×C₇	#2979	1	1	yes	characteristic
378	C₂×C₇	#2981	1	1	yes	characteristic
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
387	D₄	—	4	4	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	C₇×#117	1	2	yes	—
415	C₂×C₄	C₇×#117	1	2	yes	—
416	C₂×C₄	C₇×#131	1	2	yes	—
417	C₂×C₄	C₇×#131	1	2	yes	—
418	C₂×C₄	C₇×#131	1	2	yes	—
419	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
422	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
423	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	2	2	no	—
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₇	#22836	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	C₂×C₇×#117	1	1	yes	characteristic
440	C₂²	C₄×C₇×#41	1	1	yes	characteristic
441	C₂²	C₇×#518	1	1	yes	characteristic
442	C₂²	C₂×C₇×#131	1	1	yes	characteristic
443	C₂²	C₂×C₇×#131	1	1	yes	characteristic
444	C₂²	C₂×C₇×#131	1	1	yes	characteristic
445	C₂²	C₇×#568	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	C₇×#433	1	4	yes	—
455	C₄	C₇×#553	1	1	yes	characteristic
456	C₄	C₇×#553	1	1	yes	characteristic
457	C₄	C₇×#559	1	1	yes	characteristic
458	C₄	C₇×#559	1	1	yes	characteristic
459	C₂	—	8	2	no	—
460	C₂	C₇×#2357	1	1	yes	characteristic
461	C₂	C₂×C₇×#433	1	1	yes	characteristic
462	C₂	C₇×#2925	1	1	yes	characteristic
463	C₂	C₇×#2966	1	1	yes	characteristic
464	C₂	C₇×#2969	1	1	yes	characteristic
465	C₂	C₇×#2979	1	1	yes	characteristic
466	C₂	C₇×#2981	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₇×#1924	C₂	semidirect
5. C₇×#1923	C₂	semidirect
6. C₇×#1831	C₂	semidirect
7. C₇×#1818	C₂	semidirect
8. C₇×#1770	C₂	semidirect
9. C₇×C₈×C₄⋊C₄	C₂	semidirect
10. C₄×C₇×C₄⋊C₈	C₂	semidirect
11. C₇×#1750	C₂	semidirect
41. #22836	C₇	direct (N × H)
90. #1924	C₂×C₇	semidirect
91. #1923	C₂×C₇	semidirect
92. #1831	C₂×C₇	semidirect
93. #1818	C₂×C₇	semidirect
94. #1770	C₂×C₇	semidirect
95. C₈×C₄⋊C₄	C₂×C₇	semidirect
96. C₄×C₄⋊C₈	C₂×C₇	semidirect
97. #1750	C₂×C₇	semidirect
431. C₇	#22836	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×#2293	2
C₇×#1954	2
C₇×#1924	2
C₇×#1923	2
C₇×#1831	2
C₇×#1818	2
C₇×#1770	2
C₇×C₈×C₄⋊C₄	2
C₄×C₇×C₄⋊C₈	2
C₇×#1750	2
#22836	7

Subgroups — C7×#22836 #13200052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22836 #13200052