Subgroups — C₇×#22702 #13199918

Order 1792.

888 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#435	C₂	1	2	yes	maximal
2	C₇×#2293	C₂	1	1	yes	maximal, characteristic
3	C₇×#1940	C₂	1	2	yes	maximal, complemented
4	C₇×#1851	C₂	1	2	yes	maximal, complemented
5	C₇×#1850	C₂	1	2	yes	maximal, complemented
6	C₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1798	C₂	1	2	yes	maximal, complemented
8	C₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1729	C₂	1	2	yes	maximal, complemented
10	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
11	C₂³×C₇×C₈	C₂²	1	2	yes	—
12	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₇×#117	C₂²	1	2	yes	—
14	C₇×#435	—	2	8	no	—
15	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
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	2	yes	—
19	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×#97	C₂²	1	2	yes	—
22	C₇×#390	C₄	1	1	yes	characteristic
23	C₇×#390	C₄	1	1	yes	characteristic
24	C₇×#389	C₄	1	1	yes	characteristic
25	C₇×#389	C₄	1	1	yes	characteristic
26	C₇×#388	C₄	1	2	yes	—
27	C₇×#388	C₄	1	2	yes	—
28	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₄³×C₇	C₂²	1	1	yes	characteristic
31	C₇×#336	C₂²	1	1	yes	characteristic
32	C₇×#336	C₂²	1	2	yes	—
33	C₇×#336	C₂²	1	2	yes	—
34	C₇×#336	C₂²	1	2	yes	—
35	C₇×#336	C₂²	1	1	yes	characteristic
36	C₇×#336	C₂²	1	1	yes	characteristic
37	C₇×#336	C₂²	1	1	yes	characteristic
38	#22702	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₇	C₂³	1	2	yes	—
41	C₂×C₇×M₁₆	—	2	4	no	—
42	C₂×C₇×M₁₆	—	2	4	no	—
43	C₂×C₇×M₁₆	—	4	2	no	—
44	C₂²×C₇×C₈	—	2	4	no	—
45	C₂²×C₇×C₈	—	2	4	no	—
46	C₂²×C₇×C₈	—	4	2	no	—
47	C₂²×C₇×C₈	C₂³	1	2	yes	—
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	C₂³	1	2	yes	—
51	C₄×C₇×D₄	D₄	1	4	yes	—
52	C₄×C₇×D₄	Q₈	1	4	yes	—
53	C₇×#117	—	4	2	no	—
54	C₇×#117	—	4	2	no	—
55	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	C₇×C₄⋊C₈	—	2	4	no	—
74	C₇×C₄⋊C₈	—	2	4	no	—
75	C₇×C₄⋊C₈	—	4	2	no	—
76	C₇×C₄⋊C₈	—	4	2	no	—
77	C₇×C₂²⋊C₈	—	2	4	no	—
78	C₇×C₂²⋊C₈	—	2	4	no	—
79	C₇×#97	—	2	4	no	—
80	C₇×#95	C₂×C₄	1	2	yes	—
81	C₇×#95	C₂×C₄	1	2	yes	—
82	C₇×#95	C₂×C₄	1	2	yes	—
83	C₂×#435	C₂×C₇	1	2	yes	—
84	#2293	C₂×C₇	1	1	yes	characteristic
85	#1940	C₂×C₇	1	2	yes	complemented
86	#1851	C₂×C₇	1	2	yes	complemented
87	#1850	C₂×C₇	1	2	yes	complemented
88	#1831	C₂×C₇	1	1	yes	characteristic, complemented
89	#1798	C₂×C₇	1	2	yes	complemented
90	#1767	C₂×C₇	1	1	yes	characteristic, complemented
91	#1729	C₂×C₇	1	2	yes	complemented
92	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
93	C₂×C₇×D₄	—	4	1	no	—
94	C₂×C₇×D₄	—	4	1	no	—
95	C₂×C₇×D₄	C₄⋊C₄	1	4	yes	—
96	C₂²×C₄×C₇	—	2	2	no	—
97	C₂²×C₄×C₇	—	2	2	no	—
98	C₂²×C₄×C₇	—	2	2	no	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
111	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
112	C₇×M₁₆	—	4	8	no	—
113	C₂×C₇×C₈	—	2	2	no	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	—	2	2	no	—
116	C₂×C₇×C₈	—	2	2	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	2	2	no	—
119	C₂×C₇×C₈	—	2	2	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	—	4	8	no	—
125	C₂×C₇×C₈	#41	1	4	yes	—
126	C₇×C₄⋊C₄	—	4	1	no	—
127	C₇×C₄⋊C₄	—	4	1	no	—
128	C₇×C₄⋊C₄	—	4	2	no	—
129	C₇×C₄⋊C₄	—	4	2	no	—
130	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
131	C₇×C₂²⋊C₄	—	2	4	no	—
132	C₇×C₂²⋊C₄	—	4	2	no	—
133	C₇×C₂²⋊C₄	—	4	2	no	—
134	C₇×C₂²⋊C₄	—	4	2	no	—
135	C₇×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
136	C₄²×C₇	—	2	2	no	—
137	C₄²×C₇	—	2	2	no	—
138	C₄²×C₇	—	2	2	no	—
139	C₄²×C₇	—	2	2	no	—
140	C₄²×C₇	—	2	2	no	—
141	C₄²×C₇	—	4	1	no	—
142	C₄²×C₇	—	4	1	no	—
143	C₄²×C₇	—	4	1	no	—
144	C₄²×C₇	C₂×D₄	1	2	yes	—
145	C₄²×C₇	C₂×Q₈	1	2	yes	—
146	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
147	C₂³×C₈	C₂²×C₇	1	2	yes	—
148	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
149	C₂×#117	C₂²×C₇	1	2	yes	—
150	#435	—	2	8	no	—
151	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
152	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
153	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
154	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
155	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
156	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
157	C₂×#97	C₂²×C₇	1	2	yes	—
158	#390	C₄×C₇	1	1	yes	characteristic
159	#390	C₄×C₇	1	1	yes	characteristic
160	#389	C₄×C₇	1	1	yes	characteristic
161	#389	C₄×C₇	1	1	yes	characteristic
162	#388	C₄×C₇	1	2	yes	—
163	#388	C₄×C₇	1	2	yes	—
164	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
165	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
166	C₄³	C₂²×C₇	1	1	yes	characteristic
167	#336	C₂²×C₇	1	1	yes	characteristic
168	#336	C₂²×C₇	1	2	yes	—
169	#336	C₂²×C₇	1	1	yes	characteristic
170	#336	C₂²×C₇	1	1	yes	characteristic
171	#336	C₂²×C₇	1	2	yes	—
172	#336	C₂²×C₇	1	2	yes	—
173	#336	C₂²×C₇	1	1	yes	characteristic
174	C₂³×C₇	—	2	2	no	—
175	C₂³×C₇	—	2	2	no	—
176	C₂³×C₇	—	2	2	no	—
177	C₂³×C₇	—	2	2	no	—
178	C₂³×C₇	—	2	2	no	—
179	C₂³×C₇	—	2	2	no	—
180	C₂³×C₇	C₂×C₄⋊C₄	1	4	yes	—
181	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
182	C₇×D₄	—	4	4	no	—
183	C₂×C₄×C₇	—	2	1	no	—
184	C₂×C₄×C₇	—	2	2	no	—
185	C₂×C₄×C₇	—	2	2	no	—
186	C₂×C₄×C₇	—	2	1	no	—
187	C₂×C₄×C₇	—	2	1	no	—
188	C₂×C₄×C₇	—	2	1	no	—
189	C₂×C₄×C₇	—	2	1	no	—
190	C₂×C₄×C₇	—	2	1	no	—
191	C₂×C₄×C₇	—	2	4	no	—
192	C₂×C₄×C₇	—	2	4	no	—
193	C₂×C₄×C₇	—	2	4	no	—
194	C₂×C₄×C₇	—	2	4	no	—
195	C₂×C₄×C₇	—	2	1	no	—
196	C₂×C₄×C₇	—	2	1	no	—
197	C₂×C₄×C₇	—	2	1	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	2	no	—
202	C₂×C₄×C₇	—	2	1	no	—
203	C₂×C₄×C₇	—	2	1	no	—
204	C₂×C₄×C₇	—	2	1	no	—
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	2	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
211	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
212	C₂×C₄×C₇	C₂×C₄⋊C₄	1	4	yes	—
213	C₂×C₄×C₇	#131	1	2	yes	—
214	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₇	C₂×#41	1	2	yes	—
217	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
218	C₇×C₈	—	2	4	no	—
219	C₇×C₈	—	4	2	no	—
220	C₇×C₈	—	4	2	no	—
221	C₇×C₈	—	4	2	no	—
222	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₇	1	2	yes	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	4	2	no	—
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	4	2	no	—
230	C₂²×C₈	C₂³×C₇	1	2	yes	—
231	C₂²×C₈	C₂³×C₇	1	2	yes	—
232	C₂²×C₈	C₂³×C₇	1	2	yes	—
233	C₂²×C₈	C₂³×C₇	1	2	yes	—
234	C₄×D₄	C₇×D₄	1	4	yes	—
235	C₄×D₄	C₇×Q₈	1	4	yes	—
236	#117	—	4	2	no	—
237	#117	—	4	2	no	—
238	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
245	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
247	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
248	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
249	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
250	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₇	1	2	yes	—
254	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
256	C₄⋊C₈	—	2	4	no	—
257	C₄⋊C₈	—	2	4	no	—
258	C₄⋊C₈	—	4	2	no	—
259	C₄⋊C₈	—	4	2	no	—
260	C₂²⋊C₈	—	2	4	no	—
261	C₂²⋊C₈	—	2	4	no	—
262	#97	—	2	4	no	—
263	#95	C₂×C₄×C₇	1	2	yes	—
264	#95	C₂×C₄×C₇	1	2	yes	—
265	#95	C₂×C₄×C₇	1	2	yes	—
266	C₂²×C₇	—	2	4	no	—
267	C₂²×C₇	—	2	4	no	—
268	C₂²×C₇	—	2	4	no	—
269	C₂²×C₇	—	4	2	no	—
270	C₂²×C₇	—	4	2	no	—
271	C₂²×C₇	—	4	2	no	—
272	C₂²×C₇	—	4	2	no	—
273	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×C₇	C₄×#41	1	1	yes	characteristic
275	C₂²×C₇	#518	1	1	yes	characteristic
276	C₂²×C₇	C₂×#131	1	1	yes	characteristic
277	C₂²×C₇	#568	1	1	yes	characteristic
278	C₂²×C₇	#568	1	1	yes	characteristic
279	C₂²×C₇	#568	1	1	yes	characteristic
280	C₄×C₇	—	2	4	no	—
281	C₄×C₇	—	2	2	no	—
282	C₄×C₇	—	2	2	no	—
283	C₄×C₇	—	2	2	no	—
284	C₄×C₇	—	4	1	no	—
285	C₄×C₇	—	4	1	no	—
286	C₄×C₇	—	4	2	no	—
287	C₄×C₇	—	4	1	no	—
288	C₄×C₇	—	4	2	no	—
289	C₄×C₇	#546	1	2	yes	—
290	C₄×C₇	#554	1	2	yes	—
291	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	C₇×C₄⋊C₄	1	4	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
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	C₂²×C₄×C₇	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
309	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
310	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
311	M₁₆	—	4	8	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	8	no	—
324	C₂×C₈	C₇×#41	1	4	yes	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	C₇×C₄⋊C₄	1	8	yes	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	1	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	C₂×C₇×D₄	1	2	yes	—
344	C₄²	C₂×C₇×Q₈	1	2	yes	—
345	C₂×C₇	—	4	4	no	—
346	C₂×C₇	#2349	1	1	yes	characteristic
347	C₂×C₇	#2905	1	1	yes	characteristic
348	C₂×C₇	#2906	1	1	yes	characteristic
349	C₂×C₇	#2967	1	1	yes	characteristic
350	C₂×C₇	#2968	1	1	yes	characteristic
351	C₂×C₇	#2980	1	1	yes	characteristic
352	C₂×C₇	#2981	1	1	yes	characteristic
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	C₂×C₇×C₄⋊C₄	1	4	yes	—
360	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
361	D₄	—	4	4	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
390	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
391	C₂×C₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
392	C₂×C₄	C₇×#131	1	2	yes	—
393	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
395	C₂×C₄	C₂×C₇×#41	1	2	yes	—
396	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
397	C₈	—	2	4	no	—
398	C₈	—	4	2	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₇	#22702	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
410	C₂²	C₄×C₇×#41	1	1	yes	characteristic
411	C₂²	C₇×#518	1	1	yes	characteristic
412	C₂²	C₂×C₇×#131	1	1	yes	characteristic
413	C₂²	C₇×#568	1	1	yes	characteristic
414	C₂²	C₇×#568	1	1	yes	characteristic
415	C₂²	C₇×#568	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	4	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	2	no	—
425	C₄	C₇×#546	1	2	yes	—
426	C₄	C₇×#554	1	2	yes	—
427	C₂	—	4	4	no	—
428	C₂	C₇×#2349	1	1	yes	characteristic
429	C₂	C₇×#2905	1	1	yes	characteristic
430	C₂	C₇×#2906	1	1	yes	characteristic
431	C₂	C₇×#2967	1	1	yes	characteristic
432	C₂	C₇×#2968	1	1	yes	characteristic
433	C₂	C₇×#2980	1	1	yes	characteristic
434	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
3. C₇×#1940	C₂	semidirect
4. C₇×#1851	C₂	semidirect
5. C₇×#1850	C₂	semidirect
6. C₇×#1831	C₂	semidirect
7. C₇×#1798	C₂	semidirect
8. C₇×#1767	C₂	semidirect
9. C₇×#1729	C₂	semidirect
38. #22702	C₇	direct (N × H)
85. #1940	C₂×C₇	semidirect
86. #1851	C₂×C₇	semidirect
87. #1850	C₂×C₇	semidirect
88. #1831	C₂×C₇	semidirect
89. #1798	C₂×C₇	semidirect
90. #1767	C₂×C₇	semidirect
91. #1729	C₂×C₇	semidirect
401. C₇	#22702	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#435	2
C₇×#2293	2
C₇×#1940	2
C₇×#1851	2
C₇×#1850	2
C₇×#1831	2
C₇×#1798	2
C₇×#1767	2
C₇×#1729	2
#22702	7

Subgroups — C7×#22702 #13199918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22702 #13199918