Subgroups — C₇×#22795 #13200011

Order 1792.

1016 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#431	C₂	1	2	yes	maximal, complemented
2	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#1954	C₂	1	2	yes	maximal
4	C₇×#1923	C₂	1	4	yes	maximal, complemented
5	C₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1797	C₂	1	2	yes	maximal, complemented
7	C₇×C₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
10	C₂×C₄×C₇×D₄	C₄	1	1	yes	characteristic
11	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₇	C₂²	1	2	yes	—
13	C₇×#431	—	2	8	no	—
14	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	—
20	C₂×C₇×C₂²⋊C₈	C₂²	1	4	yes	—
21	C₂×C₄×C₇×C₈	C₂²	1	4	yes	—
22	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
23	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
24	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
25	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×C₇×C₂²⋊C₄	C₄	1	2	yes	—
27	C₄×C₇×C₂²⋊C₄	C₄	1	2	yes	—
28	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₄³×C₇	C₂²	1	1	yes	characteristic
30	C₇×#336	C₂²	1	2	yes	—
31	C₇×#336	C₂²	1	4	yes	—
32	#22795	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₇	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₇	C₂³	1	2	yes	—
37	C₂²×C₇×C₈	C₂³	1	2	yes	—
38	C₂²×C₇×C₈	C₂³	1	4	yes	—
39	C₂²×C₇×C₈	C₂³	1	2	yes	—
40	C₄×C₇×D₄	—	2	4	no	—
41	C₄×C₇×D₄	—	2	2	no	—
42	C₄×C₇×D₄	—	2	2	no	—
43	C₄×C₇×D₄	C₈	1	8	yes	complemented
44	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₇	—	2	4	no	—
51	C₂×C₄²×C₇	—	2	4	no	—
52	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₇	C₂³	1	2	yes	—
60	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
62	C₇×C₄⋊C₈	—	2	4	no	—
63	C₇×C₄⋊C₈	—	2	4	no	—
64	C₇×C₄⋊C₈	—	2	2	no	—
65	C₇×C₄⋊C₈	—	4	2	no	—
66	C₇×C₄⋊C₈	D₄	1	4	yes	complemented
67	C₇×C₂²⋊C₈	—	2	8	no	—
68	C₇×C₂²⋊C₈	—	4	4	no	—
69	C₄×C₇×C₈	—	2	8	no	—
70	C₄×C₇×C₈	—	2	4	no	—
71	C₇×#95	C₂×C₄	1	2	yes	—
72	C₇×#95	C₂×C₄	1	2	yes	—
73	C₇×#95	C₂×C₄	1	2	yes	—
74	C₂×#431	C₂×C₇	1	2	yes	complemented
75	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
76	#1954	C₂×C₇	1	2	yes	—
77	#1923	C₂×C₇	1	4	yes	complemented
78	#1842	C₂×C₇	1	1	yes	characteristic, complemented
79	#1797	C₂×C₇	1	2	yes	complemented
80	C₈×C₄⋊C₄	C₂×C₇	1	2	yes	complemented
81	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
82	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
83	C₂×C₇×D₄	—	2	2	no	—
84	C₂×C₇×D₄	—	2	2	no	—
85	C₂×C₇×D₄	C₂×C₈	1	4	yes	—
86	C₂²×C₄×C₇	—	2	4	no	—
87	C₂²×C₄×C₇	—	2	4	no	—
88	C₂²×C₄×C₇	—	2	4	no	—
89	C₂²×C₄×C₇	—	2	4	no	—
90	C₂²×C₄×C₇	—	2	2	no	—
91	C₂²×C₄×C₇	—	2	2	no	—
92	C₂²×C₄×C₇	—	2	2	no	—
93	C₂²×C₄×C₇	—	2	2	no	—
94	C₂²×C₄×C₇	—	2	2	no	—
95	C₂²×C₄×C₇	—	2	2	no	—
96	C₂²×C₄×C₇	—	4	2	no	—
97	C₂²×C₄×C₇	C₂×C₈	1	8	yes	—
98	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₇×C₈	—	2	2	no	—
109	C₂×C₇×C₈	—	2	2	no	—
110	C₂×C₇×C₈	—	2	4	no	—
111	C₂×C₇×C₈	—	2	2	no	—
112	C₂×C₇×C₈	—	2	4	no	—
113	C₂×C₇×C₈	—	2	2	no	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	—	2	4	no	—
116	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
117	C₇×C₄⋊C₄	—	2	2	no	—
118	C₇×C₄⋊C₄	C₂×C₈	1	4	yes	—
119	C₇×C₄⋊C₄	M₁₆	1	4	yes	—
120	C₇×C₂²⋊C₄	—	2	4	no	—
121	C₇×C₂²⋊C₄	—	2	4	no	—
122	C₇×C₂²⋊C₄	C₂×C₈	1	8	yes	—
123	C₄²×C₇	—	2	4	no	—
124	C₄²×C₇	—	2	4	no	—
125	C₄²×C₇	—	2	2	no	—
126	C₄²×C₇	—	2	2	no	—
127	C₄²×C₇	—	2	2	no	—
128	C₄²×C₇	—	2	2	no	—
129	C₄²×C₇	—	2	1	no	—
130	C₄²×C₇	—	2	1	no	—
131	C₄²×C₇	—	4	1	no	—
132	C₄²×C₇	C₂×C₈	1	4	yes	—
133	C₄²×C₇	C₂×D₄	1	2	yes	—
134	C₄²×C₇	#41	1	2	yes	—
135	C₄²×C₇	#41	1	2	yes	—
136	C₄²×C₇	#41	1	2	yes	—
137	C₂×C₄×D₄	C₄×C₇	1	1	yes	characteristic
138	C₂×C₄×D₄	C₄×C₇	1	1	yes	characteristic
139	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
140	C₂²×C₄²	C₂²×C₇	1	2	yes	—
141	#431	—	2	8	no	—
142	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
143	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
144	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
145	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
146	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
147	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	—
148	C₂×C₂²⋊C₈	C₂²×C₇	1	4	yes	—
149	C₂×C₄×C₈	C₂²×C₇	1	4	yes	—
150	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
151	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
152	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
153	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
154	C₄×C₂²⋊C₄	C₄×C₇	1	2	yes	—
155	C₄×C₂²⋊C₄	C₄×C₇	1	2	yes	—
156	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
157	C₄³	C₂²×C₇	1	1	yes	characteristic
158	#336	C₂²×C₇	1	4	yes	—
159	#336	C₂²×C₇	1	2	yes	—
160	C₂³×C₇	—	2	2	no	—
161	C₂³×C₇	—	2	2	no	—
162	C₂³×C₇	—	2	2	no	—
163	C₂³×C₇	—	2	2	no	—
164	C₂³×C₇	—	2	2	no	—
165	C₂³×C₇	—	2	2	no	—
166	C₂³×C₇	C₂²×C₈	1	4	yes	—
167	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
168	C₇×D₄	—	2	8	no	—
169	C₂×C₄×C₇	—	2	2	no	—
170	C₂×C₄×C₇	—	2	2	no	—
171	C₂×C₄×C₇	—	2	1	no	—
172	C₂×C₄×C₇	—	2	1	no	—
173	C₂×C₄×C₇	—	2	1	no	—
174	C₂×C₄×C₇	—	2	2	no	—
175	C₂×C₄×C₇	—	2	1	no	—
176	C₂×C₄×C₇	—	2	1	no	—
177	C₂×C₄×C₇	—	2	1	no	—
178	C₂×C₄×C₇	—	2	2	no	—
179	C₂×C₄×C₇	—	2	16	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	2	1	no	—
183	C₂×C₄×C₇	—	2	2	no	—
184	C₂×C₄×C₇	—	2	1	no	—
185	C₂×C₄×C₇	—	2	1	no	—
186	C₂×C₄×C₇	—	4	8	no	—
187	C₂×C₄×C₇	—	4	2	no	—
188	C₂×C₄×C₇	—	4	2	no	—
189	C₂×C₄×C₇	—	4	2	no	—
190	C₂×C₄×C₇	—	4	2	no	—
191	C₂×C₄×C₇	#117	1	2	yes	—
192	C₂×C₄×C₇	#117	1	2	yes	—
193	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
196	C₂×C₄×C₇	C₂²×C₈	1	4	yes	—
197	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
198	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
199	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
200	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
201	C₂×C₄×C₇	#131	1	2	yes	—
202	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
208	C₇×C₈	—	2	4	no	—
209	C₇×C₈	—	4	4	no	—
210	C₇×C₈	—	4	2	no	—
211	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
212	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
213	C₂³×C₄	C₂×C₄×C₇	1	2	yes	—
214	C₂³×C₄	C₂³×C₇	1	2	yes	—
215	C₂²×C₈	C₂³×C₇	1	2	yes	—
216	C₂²×C₈	C₂³×C₇	1	4	yes	—
217	C₂²×C₈	C₂³×C₇	1	2	yes	—
218	C₄×D₄	—	2	4	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	C₇×C₈	1	8	yes	complemented
222	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
225	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
227	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
228	C₂×C₄²	—	2	4	no	—
229	C₂×C₄²	—	2	4	no	—
230	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
233	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
234	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₇	1	2	yes	—
238	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
240	C₄⋊C₈	—	2	4	no	—
241	C₄⋊C₈	—	2	4	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	4	2	no	—
244	C₄⋊C₈	C₇×D₄	1	4	yes	complemented
245	C₂²⋊C₈	—	2	8	no	—
246	C₂²⋊C₈	—	4	4	no	—
247	C₄×C₈	—	2	8	no	—
248	C₄×C₈	—	2	4	no	—
249	#95	C₂×C₄×C₇	1	2	yes	—
250	#95	C₂×C₄×C₇	1	2	yes	—
251	#95	C₂×C₄×C₇	1	2	yes	—
252	C₂²×C₇	—	2	4	no	—
253	C₂²×C₇	—	2	4	no	—
254	C₂²×C₇	—	2	4	no	—
255	C₂²×C₇	—	4	2	no	—
256	C₂²×C₇	—	4	2	no	—
257	C₂²×C₇	—	4	2	no	—
258	C₂²×C₇	—	4	2	no	—
259	C₂²×C₇	C₂×#117	1	1	yes	characteristic
260	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
261	C₂²×C₇	#520	1	1	yes	characteristic
262	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
263	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
264	C₂²×C₇	C₂×#131	1	1	yes	characteristic
265	C₂²×C₇	#568	1	1	yes	characteristic
266	C₄×C₇	—	2	2	no	—
267	C₄×C₇	—	2	4	no	—
268	C₄×C₇	—	2	2	no	—
269	C₄×C₇	—	2	4	no	—
270	C₄×C₇	—	2	2	no	—
271	C₄×C₇	—	4	2	no	—
272	C₄×C₇	—	4	1	no	—
273	C₄×C₇	#431	1	4	yes	complemented
274	C₄×C₇	C₈×D₄	1	4	yes	—
275	C₄×C₇	#547	1	1	yes	characteristic
276	C₄×C₇	#550	1	1	yes	characteristic
277	C₄×C₇	#555	1	1	yes	characteristic
278	C₄×C₇	#556	1	1	yes	characteristic
279	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	C₂×C₇×C₈	1	4	yes	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₂×C₇×C₈	1	8	yes	—
295	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	C₂×C₇×C₈	1	4	yes	—
316	C₄⋊C₄	C₇×M₁₆	1	4	yes	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	C₂×C₇×C₈	1	8	yes	—
320	C₄²	—	2	4	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	C₂×C₇×C₈	1	4	yes	—
330	C₄²	C₂×C₇×D₄	1	2	yes	—
331	C₄²	C₇×#41	1	2	yes	—
332	C₄²	C₇×#41	1	2	yes	—
333	C₄²	C₇×#41	1	2	yes	—
334	C₂×C₇	—	4	4	no	—
335	C₂×C₇	#2354	1	1	yes	characteristic
336	C₂×C₇	C₂×#431	1	1	yes	characteristic
337	C₂×C₇	#2925	1	1	yes	characteristic
338	C₂×C₇	C₂×C₈×D₄	1	1	yes	characteristic
339	C₂×C₇	D₄×M₁₆	1	1	yes	characteristic
340	C₂×C₇	#2988	1	1	yes	characteristic
341	C₂×C₇	#2991	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	C₂²×C₇×C₈	1	4	yes	—
349	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
350	D₄	—	2	8	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	16	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	C₇×#117	1	2	yes	—
374	C₂×C₄	C₇×#117	1	2	yes	—
375	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
376	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
377	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
378	C₂×C₄	C₂²×C₇×C₈	1	4	yes	—
379	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
380	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
381	C₂×C₄	C₂×C₇×M₁₆	1	4	yes	—
382	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
383	C₂×C₄	C₇×#131	1	2	yes	—
384	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
385	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
386	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
387	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
388	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
390	C₈	—	2	4	no	—
391	C₈	—	4	4	no	—
392	C₈	—	4	2	no	—
393	C₇	#22795	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	C₂×C₇×#117	1	1	yes	characteristic
402	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
403	C₂²	C₇×#520	1	1	yes	characteristic
404	C₂²	C₂³×C₇×C₈	1	1	yes	characteristic
405	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
406	C₂²	C₂×C₇×#131	1	1	yes	characteristic
407	C₂²	C₇×#568	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	4	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	4	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	2	no	—
415	C₄	C₇×#431	1	4	yes	complemented
416	C₄	C₇×C₈×D₄	1	4	yes	—
417	C₄	C₇×#547	1	1	yes	characteristic
418	C₄	C₇×#550	1	1	yes	characteristic
419	C₄	C₇×#555	1	1	yes	characteristic
420	C₄	C₇×#556	1	1	yes	characteristic
421	C₂	—	4	4	no	—
422	C₂	C₇×#2354	1	1	yes	characteristic
423	C₂	C₂×C₇×#431	1	1	yes	characteristic
424	C₂	C₇×#2925	1	1	yes	characteristic
425	C₂	C₂×C₇×C₈×D₄	1	1	yes	characteristic
426	C₂	C₇×D₄×M₁₆	1	1	yes	characteristic
427	C₂	C₇×#2988	1	1	yes	characteristic
428	C₂	C₇×#2991	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂²	C₂³×C₇×C₈
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×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#431	C₂	semidirect
4. C₇×#1923	C₂	semidirect
5. C₇×#1842	C₂	semidirect
6. C₇×#1797	C₂	semidirect
7. C₇×C₈×C₄⋊C₄	C₂	semidirect
8. C₄×C₇×C₄⋊C₈	C₂	semidirect
32. #22795	C₇	direct (N × H)
43. C₄×C₇×D₄	C₈	semidirect
66. C₇×C₄⋊C₈	D₄	semidirect
74. C₂×#431	C₂×C₇	semidirect
77. #1923	C₂×C₇	semidirect
78. #1842	C₂×C₇	semidirect
79. #1797	C₂×C₇	semidirect
80. C₈×C₄⋊C₄	C₂×C₇	semidirect
81. C₄×C₄⋊C₈	C₂×C₇	semidirect
221. C₄×D₄	C₇×C₈	semidirect
244. C₄⋊C₈	C₇×D₄	semidirect
273. C₄×C₇	#431	semidirect
393. C₇	#22795	direct (N × H)
415. C₄	C₇×#431	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#431	2
C₄²×C₇×D₄	2
C₇×#1954	2
C₇×#1923	2
C₇×#1842	2
C₇×#1797	2
C₇×C₈×C₄⋊C₄	2
C₄×C₇×C₄⋊C₈	2
#22795	7

Subgroups — C7×#22795 #13200011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22795 #13200011