Subgroups — C₇×#22830 #13200046

Order 1792.

716 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₇×#1985	C₂	1	2	yes	maximal
3	C₇×#1917	C₂	1	2	yes	maximal
4	C₇×#1916	C₂	1	2	yes	maximal
5	C₇×#1839	C₂	1	1	yes	maximal, characteristic
6	C₇×#1839	C₂	1	1	yes	maximal, characteristic
7	C₇×#1831	C₂	1	1	yes	maximal, characteristic
8	C₇×#1771	C₂	1	2	yes	maximal
9	C₇×#1767	C₂	1	1	yes	maximal, characteristic
10	C₇×#1745	C₂	1	1	yes	maximal, characteristic
11	C₇×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₇×Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×C₇×Q₈	C₄	1	1	yes	characteristic
14	C₂×C₄×C₇×Q₈	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×#97	C₂²	1	2	yes	—
18	C₂×C₇×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
20	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
22	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
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	C₄	1	1	yes	characteristic
26	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄³×C₇	C₂²	1	1	yes	characteristic
30	C₄³×C₇	C₂²	1	1	yes	characteristic
31	C₄³×C₇	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	2	yes	—
36	C₇×#336	C₂²	1	1	yes	characteristic
37	C₇×#336	C₂²	1	1	yes	characteristic
38	C₇×#336	C₂²	1	1	yes	characteristic
39	C₇×#336	C₂²	1	1	yes	characteristic
40	C₇×#336	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	#22830	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₇×C₈	C₂³	1	2	yes	—
46	C₂²×C₇×C₈	C₂³	1	2	yes	—
47	C₂²×C₇×C₈	C₂³	1	2	yes	—
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₄×C₇×Q₈	—	2	4	no	—
50	C₄×C₇×Q₈	—	2	4	no	—
51	C₄×C₇×Q₈	—	2	2	no	—
52	C₄×C₇×Q₈	—	2	2	no	—
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×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	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×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
81	C₇×C₄⋊C₈	—	2	4	no	—
82	C₇×C₄⋊C₈	—	2	4	no	—
83	C₇×#97	—	2	4	no	—
84	C₇×#97	—	2	4	no	—
85	C₄×C₇×C₈	—	2	4	no	—
86	C₇×#95	C₂×C₄	1	1	yes	characteristic
87	C₇×#95	C₂×C₄	1	1	yes	characteristic
88	C₇×#95	C₂×C₄	1	1	yes	characteristic
89	C₇×#95	C₂×C₄	1	1	yes	characteristic
90	C₇×#95	C₂×C₄	1	1	yes	characteristic
91	C₇×#95	C₂×C₄	1	1	yes	characteristic
92	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic
93	#1985	C₂×C₇	1	2	yes	—
94	#1917	C₂×C₇	1	2	yes	—
95	#1916	C₂×C₇	1	2	yes	—
96	#1839	C₂×C₇	1	1	yes	characteristic
97	#1839	C₂×C₇	1	1	yes	characteristic
98	#1831	C₂×C₇	1	1	yes	characteristic
99	#1771	C₂×C₇	1	2	yes	—
100	#1767	C₂×C₇	1	1	yes	characteristic
101	#1745	C₂×C₇	1	1	yes	characteristic
102	#1744	C₂×C₇	1	1	yes	characteristic
103	C₂×C₇×Q₈	—	2	2	no	—
104	C₂×C₇×Q₈	—	2	2	no	—
105	C₂×C₇×Q₈	—	2	2	no	—
106	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
125	C₂×C₇×C₈	—	2	2	no	—
126	C₂×C₇×C₈	—	2	2	no	—
127	C₂×C₇×C₈	—	2	2	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	#41	1	4	yes	—
133	C₇×C₄⋊C₄	—	2	2	no	—
134	C₇×C₄⋊C₄	—	2	2	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
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×C₄⋊C₄	—	2	2	no	—
141	C₇×C₄⋊C₄	M₁₆	1	4	yes	—
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	2	no	—
147	C₄²×C₇	—	2	2	no	—
148	C₄²×C₇	—	2	2	no	—
149	C₄²×C₇	—	2	2	no	—
150	C₄²×C₇	—	2	2	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	—	2	1	no	—
156	C₄²×C₇	—	2	1	no	—
157	C₄²×C₇	—	2	2	no	—
158	C₄²×C₇	—	4	1	no	—
159	C₄²×C₇	—	4	1	no	—
160	C₄²×C₇	—	4	1	no	—
161	C₄²×C₇	M₁₆	1	4	yes	—
162	C₄²×C₇	#41	1	2	yes	—
163	C₄²×C₇	#41	1	2	yes	—
164	C₂×C₄×Q₈	C₄×C₇	1	1	yes	characteristic
165	C₂×C₄×Q₈	C₄×C₇	1	1	yes	characteristic
166	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
168	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
169	C₂×#97	C₂²×C₇	1	2	yes	—
170	C₂×#97	C₂²×C₇	1	2	yes	—
171	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
172	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
173	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
174	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
175	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
176	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
177	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
178	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
179	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
180	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
181	C₄³	C₂²×C₇	1	1	yes	characteristic
182	C₄³	C₂²×C₇	1	1	yes	characteristic
183	C₄³	C₂²×C₇	1	1	yes	characteristic
184	#336	C₂²×C₇	1	1	yes	characteristic
185	#336	C₂²×C₇	1	1	yes	characteristic
186	#336	C₂²×C₇	1	2	yes	—
187	#336	C₂²×C₇	1	1	yes	characteristic
188	#336	C₂²×C₇	1	2	yes	—
189	#336	C₂²×C₇	1	2	yes	—
190	#336	C₂²×C₇	1	2	yes	—
191	#336	C₂²×C₇	1	2	yes	—
192	#336	C₂²×C₇	1	2	yes	—
193	#336	C₂²×C₇	1	2	yes	—
194	#336	C₂²×C₇	1	1	yes	characteristic
195	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
196	C₇×Q₈	—	2	8	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	1	no	—
201	C₂×C₄×C₇	—	2	1	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	1	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	1	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	1	no	—
225	C₂×C₄×C₇	—	2	1	no	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	1	no	—
229	C₂×C₄×C₇	—	2	1	no	—
230	C₂×C₄×C₇	#117	1	2	yes	—
231	C₂×C₄×C₇	#117	1	2	yes	—
232	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
233	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
234	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
235	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
236	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
237	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
238	C₂×C₄×C₇	#131	1	2	yes	—
239	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₇	C₂×#41	1	2	yes	—
241	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
243	C₇×C₈	—	2	4	no	—
244	C₇×C₈	—	4	2	no	—
245	C₇×C₈	—	4	2	no	—
246	C₇×C₈	—	4	2	no	—
247	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₇	1	2	yes	—
249	C₂²×C₈	C₂³×C₇	1	2	yes	—
250	C₂²×C₈	C₂³×C₇	1	2	yes	—
251	C₂²×C₈	C₂³×C₇	1	2	yes	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
265	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
267	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
269	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
270	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
271	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
272	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
273	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
274	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
275	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
276	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
284	C₄⋊C₈	—	2	4	no	—
285	C₄⋊C₈	—	2	4	no	—
286	#97	—	2	4	no	—
287	#97	—	2	4	no	—
288	C₄×C₈	—	2	4	no	—
289	#95	C₂×C₄×C₇	1	1	yes	characteristic
290	#95	C₂×C₄×C₇	1	1	yes	characteristic
291	#95	C₂×C₄×C₇	1	1	yes	characteristic
292	#95	C₂×C₄×C₇	1	1	yes	characteristic
293	#95	C₂×C₄×C₇	1	1	yes	characteristic
294	#95	C₂×C₄×C₇	1	1	yes	characteristic
295	C₂²×C₇	C₂×#117	1	1	yes	characteristic
296	C₂²×C₇	C₄×#41	1	1	yes	characteristic
297	C₂²×C₇	#519	1	1	yes	characteristic
298	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
299	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
300	C₂²×C₇	C₂×#131	1	1	yes	characteristic
301	C₂²×C₇	#568	1	1	yes	characteristic
302	C₄×C₇	—	2	2	no	—
303	C₄×C₇	—	2	2	no	—
304	C₄×C₇	—	2	2	no	—
305	C₄×C₇	—	2	2	no	—
306	C₄×C₇	—	2	2	no	—
307	C₄×C₇	—	2	2	no	—
308	C₄×C₇	—	2	2	no	—
309	C₄×C₇	—	2	2	no	—
310	C₄×C₇	—	2	2	no	—
311	C₄×C₇	—	4	1	no	—
312	C₄×C₇	—	4	1	no	—
313	C₄×C₇	—	4	1	no	—
314	C₄×C₇	—	4	1	no	—
315	C₄×C₇	—	4	1	no	—
316	C₄×C₇	#552	1	2	yes	—
317	C₄×C₇	#556	1	2	yes	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
322	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
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	C₂²×C₄×C₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
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	2	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	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	C₇×#41	1	4	yes	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	C₇×M₁₆	1	4	yes	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	4	1	no	—
374	C₄²	—	4	1	no	—
375	C₄²	—	4	1	no	—
376	C₄²	C₇×M₁₆	1	4	yes	—
377	C₄²	C₇×#41	1	2	yes	—
378	C₄²	C₇×#41	1	2	yes	—
379	C₂×C₇	#2356	1	1	yes	characteristic
380	C₂×C₇	#2920	1	1	yes	characteristic
381	C₂×C₇	#2925	1	1	yes	characteristic
382	C₂×C₇	#2965	1	1	yes	characteristic
383	C₂×C₇	#2970	1	1	yes	characteristic
384	C₂×C₇	#2983	1	1	yes	characteristic
385	C₂×C₇	#2984	1	1	yes	characteristic
386	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
387	Q₈	—	2	8	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	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	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	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	C₇×#117	1	2	yes	—
422	C₂×C₄	C₇×#117	1	2	yes	—
423	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
424	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
425	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
426	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
427	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
428	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
429	C₂×C₄	C₇×#131	1	2	yes	—
430	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
431	C₂×C₄	C₂×C₇×#41	1	2	yes	—
432	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
433	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
434	C₈	—	2	4	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₇	#22830	1	1	yes	characteristic, direct product factor, Sylow
439	C₂²	C₂×C₇×#117	1	1	yes	characteristic
440	C₂²	C₄×C₇×#41	1	1	yes	characteristic
441	C₂²	C₇×#519	1	1	yes	characteristic
442	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
443	C₂²	C₂²×C₇×M₁₆	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	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	C₇×#552	1	2	yes	—
461	C₄	C₇×#556	1	2	yes	—
462	C₂	C₇×#2356	1	1	yes	characteristic
463	C₂	C₇×#2920	1	1	yes	characteristic
464	C₂	C₇×#2925	1	1	yes	characteristic
465	C₂	C₇×#2965	1	1	yes	characteristic
466	C₂	C₇×#2970	1	1	yes	characteristic
467	C₂	C₇×#2983	1	1	yes	characteristic
468	C₂	C₇×#2984	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle, prime radical	C₂³×C₇	C₂³×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
43. #22830	C₇	direct (N × H)
438. C₇	#22830	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×C₇×Q₈	2
C₇×#1985	2
C₇×#1917	2
C₇×#1916	2
C₇×#1839	2
C₇×#1831	2
C₇×#1771	2
C₇×#1767	2
C₇×#1745	2
C₇×#1744	2
#22830	7

Subgroups — C7×#22830 #13200046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22830 #13200046