Subgroups — C₇×#22633 #13199849

Order 1792.

700 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2283	C₂	1	1	yes	maximal, characteristic
2	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1924	C₂	1	2	yes	maximal
5	C₇×#1923	C₂	1	2	yes	maximal
6	C₇×#1832	C₂	1	2	yes	maximal, complemented
7	C₇×#1797	C₂	1	1	yes	maximal, characteristic
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×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₇×#1746	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₇×#383	C₄	1	2	yes	—
25	C₇×#382	C₄	1	1	yes	characteristic
26	C₇×#382	C₄	1	1	yes	characteristic
27	C₇×#381	C₄	1	2	yes	—
28	C₇×#380	C₄	1	1	yes	characteristic
29	C₇×#380	C₄	1	1	yes	characteristic
30	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₇×#376	C₂²	1	2	yes	—
34	C₇×#336	C₂²	1	1	yes	characteristic
35	C₇×#336	C₂²	1	2	yes	—
36	C₇×#336	C₂²	1	2	yes	—
37	C₇×#336	C₂²	1	2	yes	—
38	C₇×#336	C₂²	1	1	yes	characteristic
39	C₇×#336	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	#22633	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₇×C₈	C₂³	1	2	yes	—
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₇	—	2	2	no	—
58	C₂×C₄²×C₇	—	2	2	no	—
59	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₇	C₂³	1	2	yes	—
63	C₂×C₄²×C₇	C₂³	1	2	yes	—
64	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
65	C₇×C₄⋊C₈	—	2	2	no	—
66	C₇×C₄⋊C₈	—	2	2	no	—
67	C₇×C₄⋊C₈	—	4	2	no	—
68	C₇×C₄⋊C₈	—	4	2	no	—
69	C₇×C₂²⋊C₈	—	2	2	no	—
70	C₇×C₂²⋊C₈	—	2	2	no	—
71	C₇×C₂²⋊C₈	—	4	2	no	—
72	C₇×#97	—	2	4	no	—
73	C₄×C₇×C₈	—	2	4	no	—
74	C₄×C₇×C₈	—	2	2	no	—
75	C₄×C₇×C₈	—	2	2	no	—
76	C₇×#95	C₂×C₄	1	2	yes	—
77	C₇×#95	C₂×C₄	1	2	yes	—
78	C₇×#95	C₂×C₄	1	2	yes	—
79	C₇×#95	C₂×C₄	1	2	yes	—
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	C₇×#95	C₂×C₄	1	2	yes	—
84	#2283	C₂×C₇	1	1	yes	characteristic
85	#1939	C₂×C₇	1	1	yes	characteristic, complemented
86	#1939	C₂×C₇	1	1	yes	characteristic, complemented
87	#1924	C₂×C₇	1	2	yes	—
88	#1923	C₂×C₇	1	2	yes	—
89	#1832	C₂×C₇	1	2	yes	complemented
90	#1797	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	C₄×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic
94	#1746	C₂×C₇	1	2	yes	complemented
95	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
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	—	2	2	no	—
101	C₂²×C₄×C₇	—	2	1	no	—
102	C₂²×C₄×C₇	—	2	1	no	—
103	C₂²×C₄×C₇	—	2	1	no	—
104	C₂²×C₄×C₇	—	2	1	no	—
105	C₂²×C₄×C₇	—	2	1	no	—
106	C₂²×C₄×C₇	—	2	1	no	—
107	C₂²×C₄×C₇	—	4	1	no	—
108	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
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	—	2	2	no	—
140	C₇×C₂²⋊C₄	—	2	4	no	—
141	C₇×C₂²⋊C₄	—	4	2	no	—
142	C₄²×C₇	—	2	2	no	—
143	C₄²×C₇	—	2	2	no	—
144	C₄²×C₇	—	2	2	no	—
145	C₄²×C₇	—	2	2	no	—
146	C₄²×C₇	—	2	1	no	—
147	C₄²×C₇	—	2	1	no	—
148	C₄²×C₇	—	2	2	no	—
149	C₄²×C₇	—	2	2	no	—
150	C₄²×C₇	#41	1	2	yes	—
151	C₄²×C₇	#41	1	2	yes	—
152	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
153	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
154	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
155	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
156	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
157	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
158	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
159	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
160	C₂×#97	C₂²×C₇	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
162	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
163	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
164	#383	C₄×C₇	1	2	yes	—
165	#382	C₄×C₇	1	1	yes	characteristic
166	#382	C₄×C₇	1	1	yes	characteristic
167	#381	C₄×C₇	1	2	yes	—
168	#380	C₄×C₇	1	1	yes	characteristic
169	#380	C₄×C₇	1	1	yes	characteristic
170	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
172	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
173	#376	C₂²×C₇	1	2	yes	—
174	#336	C₂²×C₇	1	2	yes	—
175	#336	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	#336	C₂²×C₇	1	2	yes	—
180	#336	C₂²×C₇	1	1	yes	characteristic
181	C₂³×C₇	—	2	1	no	—
182	C₂³×C₇	—	2	1	no	—
183	C₂³×C₇	—	2	1	no	—
184	C₂³×C₇	—	2	1	no	—
185	C₂³×C₇	—	2	1	no	—
186	C₂³×C₇	—	2	1	no	—
187	C₂³×C₇	#131	1	2	yes	—
188	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₇	—	2	1	no	—
190	C₂×C₄×C₇	—	2	1	no	—
191	C₂×C₄×C₇	—	2	1	no	—
192	C₂×C₄×C₇	—	2	1	no	—
193	C₂×C₄×C₇	—	2	1	no	—
194	C₂×C₄×C₇	—	2	2	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	1	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	2	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	1	no	—
212	C₂×C₄×C₇	—	4	4	no	—
213	C₂×C₄×C₇	—	4	1	no	—
214	C₂×C₄×C₇	—	4	1	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	no	—
217	C₂×C₄×C₇	—	4	4	no	—
218	C₂×C₄×C₇	#117	1	2	yes	—
219	C₂×C₄×C₇	#117	1	2	yes	—
220	C₂×C₄×C₇	#131	1	2	yes	—
221	C₂×C₄×C₇	#131	1	2	yes	—
222	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
228	C₇×C₈	—	2	2	no	—
229	C₇×C₈	—	2	2	no	—
230	C₇×C₈	—	4	1	no	—
231	C₇×C₈	—	4	1	no	—
232	C₇×C₈	—	4	2	no	—
233	C₇×C₈	—	4	2	no	—
234	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
235	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₇	1	2	yes	—
240	C₂²×C₈	C₂³×C₇	1	2	yes	—
241	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
248	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
252	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₇	1	2	yes	—
255	C₂×C₄²	C₂³×C₇	1	2	yes	—
256	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	4	2	no	—
260	C₄⋊C₈	—	4	2	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	4	2	no	—
264	#97	—	2	4	no	—
265	C₄×C₈	—	2	4	no	—
266	C₄×C₈	—	2	2	no	—
267	C₄×C₈	—	2	2	no	—
268	#95	C₂×C₄×C₇	1	2	yes	—
269	#95	C₂×C₄×C₇	1	2	yes	—
270	#95	C₂×C₄×C₇	1	2	yes	—
271	#95	C₂×C₄×C₇	1	2	yes	—
272	#95	C₂×C₄×C₇	1	2	yes	—
273	#95	C₂×C₄×C₇	1	2	yes	—
274	#95	C₂×C₄×C₇	1	2	yes	—
275	#95	C₂×C₄×C₇	1	2	yes	—
276	C₂²×C₇	—	2	2	no	—
277	C₂²×C₇	—	2	2	no	—
278	C₂²×C₇	—	2	2	no	—
279	C₂²×C₇	—	4	1	no	—
280	C₂²×C₇	—	4	1	no	—
281	C₂²×C₇	—	4	1	no	—
282	C₂²×C₇	—	4	1	no	—
283	C₂²×C₇	C₂×#117	1	1	yes	characteristic
284	C₂²×C₇	C₄×#41	1	1	yes	characteristic
285	C₂²×C₇	#520	1	1	yes	characteristic
286	C₂²×C₇	C₂×#131	1	1	yes	characteristic
287	C₂²×C₇	C₂×#131	1	1	yes	characteristic
288	C₂²×C₇	C₂×#131	1	1	yes	characteristic
289	C₂²×C₇	#568	1	1	yes	characteristic
290	C₄×C₇	—	2	2	no	—
291	C₄×C₇	—	4	1	no	—
292	C₄×C₇	—	4	1	no	—
293	C₄×C₇	—	4	1	no	—
294	C₄×C₇	—	4	2	no	—
295	C₄×C₇	—	4	2	no	—
296	C₄×C₇	—	4	2	no	—
297	C₄×C₇	—	4	2	no	—
298	C₄×C₇	#433	1	4	yes	—
299	C₄×C₇	#552	1	1	yes	characteristic
300	C₄×C₇	#552	1	1	yes	characteristic
301	C₄×C₇	#555	1	1	yes	characteristic
302	C₄×C₇	#555	1	1	yes	characteristic
303	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
320	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
321	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
322	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
323	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	C₇×#41	1	2	yes	—
343	C₂×C₈	C₇×#41	1	2	yes	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	C₇×#41	1	2	yes	—
359	C₄²	C₇×#41	1	2	yes	—
360	C₂×C₇	—	4	2	no	—
361	C₂×C₇	#2346	1	1	yes	characteristic
362	C₂×C₇	C₂×#433	1	1	yes	characteristic
363	C₂×C₇	#2924	1	1	yes	characteristic
364	C₂×C₇	#2966	1	1	yes	characteristic
365	C₂×C₇	#2969	1	1	yes	characteristic
366	C₂×C₇	#2993	1	1	yes	characteristic
367	C₂×C₇	#2994	1	1	yes	characteristic
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	C₇×#131	1	2	yes	—
375	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₇×#117	1	2	yes	—
406	C₂×C₄	C₇×#117	1	2	yes	—
407	C₂×C₄	C₇×#131	1	2	yes	—
408	C₂×C₄	C₇×#131	1	2	yes	—
409	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
410	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
411	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
412	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
413	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₇	#22633	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	C₂×C₇×#117	1	1	yes	characteristic
430	C₂²	C₄×C₇×#41	1	1	yes	characteristic
431	C₂²	C₇×#520	1	1	yes	characteristic
432	C₂²	C₂×C₇×#131	1	1	yes	characteristic
433	C₂²	C₂×C₇×#131	1	1	yes	characteristic
434	C₂²	C₂×C₇×#131	1	1	yes	characteristic
435	C₂²	C₇×#568	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	1	no	—
444	C₄	C₇×#433	1	4	yes	—
445	C₄	C₇×#552	1	1	yes	characteristic
446	C₄	C₇×#552	1	1	yes	characteristic
447	C₄	C₇×#555	1	1	yes	characteristic
448	C₄	C₇×#555	1	1	yes	characteristic
449	C₂	—	4	2	no	—
450	C₂	C₇×#2346	1	1	yes	characteristic
451	C₂	C₂×C₇×#433	1	1	yes	characteristic
452	C₂	C₇×#2924	1	1	yes	characteristic
453	C₂	C₇×#2966	1	1	yes	characteristic
454	C₂	C₇×#2969	1	1	yes	characteristic
455	C₂	C₇×#2993	1	1	yes	characteristic
456	C₂	C₇×#2994	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	C₂⁴×C₇	C₂²×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
2. C₇×#1939	C₂	semidirect
3. C₇×#1939	C₂	semidirect
6. C₇×#1832	C₂	semidirect
8. C₇×#1770	C₂	semidirect
9. C₇×C₈×C₄⋊C₄	C₂	semidirect
11. C₇×#1746	C₂	semidirect
41. #22633	C₇	direct (N × H)
85. #1939	C₂×C₇	semidirect
86. #1939	C₂×C₇	semidirect
89. #1832	C₂×C₇	semidirect
91. #1770	C₂×C₇	semidirect
92. C₈×C₄⋊C₄	C₂×C₇	semidirect
94. #1746	C₂×C₇	semidirect
421. C₇	#22633	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×#2283	2
C₇×#1939	2
C₇×#1924	2
C₇×#1923	2
C₇×#1832	2
C₇×#1797	2
C₇×#1770	2
C₇×C₈×C₄⋊C₄	2
C₄×C₇×C₂²⋊C₈	2
C₇×#1746	2
#22633	7

Subgroups — C7×#22633 #13199849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22633 #13199849