Subgroups — C₇×#22133 #13199349

Order 1792.

1010 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic
4	C₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1954	C₂	1	2	yes	maximal, complemented
6	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1923	C₂	1	2	yes	maximal, complemented
8	C₇×#1869	C₂	1	2	yes	maximal, complemented
9	C₇×#1850	C₂	1	2	yes	maximal, complemented
10	C₇×#1797	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₇×C₈	C₂²	1	2	yes	—
13	C₂×C₇×#121	C₄	1	1	yes	characteristic
14	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
16	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
17	C₇×C₈×D₄	—	2	4	no	—
18	C₇×#431	—	2	4	no	—
19	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
32	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
33	C₇×#390	C₄	1	1	yes	characteristic
34	C₇×#389	C₄	1	1	yes	characteristic
35	C₇×#388	C₄	1	2	yes	—
36	C₇×#386	C₄	1	2	yes	—
37	C₇×#380	C₄	1	1	yes	characteristic
38	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	#22133	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₇	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	—	2	4	no	—
51	C₂²×C₇×C₈	—	4	2	no	—
52	C₂²×C₇×C₈	—	4	2	no	—
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇×C₈	C₂³	1	2	yes	—
55	C₂²×C₇×C₈	C₂³	1	2	yes	—
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₇×#121	C₈	1	8	yes	complemented
60	C₄×C₇×D₄	—	2	2	no	—
61	C₄×C₇×D₄	—	2	2	no	—
62	C₄×C₇×D₄	—	4	2	no	—
63	C₄×C₇×D₄	—	4	2	no	—
64	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₇	—	2	2	no	—
74	C₂×C₄²×C₇	—	2	2	no	—
75	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	2	yes	—
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×C₄⋊C₈	—	2	2	no	—
82	C₇×C₄⋊C₈	—	2	2	no	—
83	C₇×C₄⋊C₈	—	2	2	no	—
84	C₇×C₄⋊C₈	—	4	2	no	—
85	C₇×C₂²⋊C₈	—	2	2	no	—
86	C₇×C₂²⋊C₈	—	2	2	no	—
87	C₇×C₂²⋊C₈	—	2	4	no	—
88	C₇×C₂²⋊C₈	—	4	2	no	—
89	C₇×C₂²⋊C₈	—	4	2	no	—
90	C₇×C₂²⋊C₈	—	4	2	no	—
91	C₄×C₇×C₈	—	2	2	no	—
92	C₄×C₇×C₈	—	4	2	no	—
93	C₄×C₇×C₈	D₄	1	4	yes	complemented
94	C₇×#95	C₂×C₄	1	2	yes	—
95	C₇×#95	C₂×C₄	1	2	yes	—
96	C₇×#95	C₂×C₄	1	2	yes	—
97	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
98	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
99	C₄×#121	C₂×C₇	1	1	yes	characteristic
100	#1954	C₂×C₇	1	1	yes	characteristic, complemented
101	#1954	C₂×C₇	1	2	yes	complemented
102	#1939	C₂×C₇	1	1	yes	characteristic, complemented
103	#1923	C₂×C₇	1	2	yes	complemented
104	#1869	C₂×C₇	1	2	yes	complemented
105	#1850	C₂×C₇	1	2	yes	complemented
106	#1797	C₂×C₇	1	1	yes	characteristic, complemented
107	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
109	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₇×D₄	—	2	2	no	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	4	2	no	—
113	C₂×C₇×D₄	—	4	2	no	—
114	C₂×C₇×D₄	C₂×C₈	1	4	yes	—
115	C₂×C₇×D₄	C₂×C₈	1	8	yes	complemented
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	2	no	—
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	2	1	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	1	no	—
127	C₂²×C₄×C₇	—	2	1	no	—
128	C₂²×C₄×C₇	—	2	2	no	—
129	C₂²×C₄×C₇	—	2	1	no	—
130	C₂²×C₄×C₇	—	2	2	no	—
131	C₂²×C₄×C₇	—	4	1	no	—
132	C₂²×C₄×C₇	—	4	1	no	—
133	C₂²×C₄×C₇	C₂×C₈	1	4	yes	complemented
134	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
143	C₂×C₇×C₈	—	2	1	no	—
144	C₂×C₇×C₈	—	2	1	no	—
145	C₂×C₇×C₈	—	2	1	no	—
146	C₂×C₇×C₈	—	2	1	no	—
147	C₂×C₇×C₈	—	2	1	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	2	no	—
150	C₂×C₇×C₈	—	2	2	no	—
151	C₂×C₇×C₈	—	2	2	no	—
152	C₂×C₇×C₈	—	2	1	no	—
153	C₂×C₇×C₈	—	2	1	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	—	2	2	no	—
156	C₂×C₇×C₈	—	2	1	no	—
157	C₂×C₇×C₈	—	2	2	no	—
158	C₂×C₇×C₈	—	2	1	no	—
159	C₂×C₇×C₈	—	4	8	no	—
160	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
161	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	—	2	2	no	—
164	C₇×C₄⋊C₄	—	4	2	no	—
165	C₇×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
166	C₇×C₂²⋊C₄	—	2	4	no	—
167	C₇×C₂²⋊C₄	—	4	2	no	—
168	C₇×C₂²⋊C₄	—	4	2	no	—
169	C₇×C₂²⋊C₄	—	4	2	no	—
170	C₇×C₂²⋊C₄	C₂×C₈	1	8	yes	complemented
171	C₄²×C₇	—	2	2	no	—
172	C₄²×C₇	—	2	2	no	—
173	C₄²×C₇	—	2	1	no	—
174	C₄²×C₇	—	2	1	no	—
175	C₄²×C₇	—	2	2	no	—
176	C₄²×C₇	—	2	2	no	—
177	C₄²×C₇	C₂×D₄	1	2	yes	—
178	C₄²×C₇	#41	1	2	yes	—
179	C₂³×C₈	C₂²×C₇	1	2	yes	—
180	C₂×#121	C₄×C₇	1	1	yes	characteristic
181	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
182	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
183	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
184	C₈×D₄	—	2	4	no	—
185	#431	—	2	4	no	—
186	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
192	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
193	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
194	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
195	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
200	#390	C₄×C₇	1	1	yes	characteristic
201	#389	C₄×C₇	1	1	yes	characteristic
202	#388	C₄×C₇	1	2	yes	—
203	#386	C₄×C₇	1	2	yes	—
204	#380	C₄×C₇	1	1	yes	characteristic
205	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
206	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
207	#336	C₂²×C₇	1	2	yes	—
208	#336	C₂²×C₇	1	2	yes	—
209	#336	C₂²×C₇	1	2	yes	—
210	C₂³×C₇	—	2	2	no	—
211	C₂³×C₇	—	2	1	no	—
212	C₂³×C₇	—	2	1	no	—
213	C₂³×C₇	—	2	2	no	—
214	C₂³×C₇	—	2	1	no	—
215	C₂³×C₇	—	2	2	no	—
216	C₂³×C₇	—	2	1	no	—
217	C₂³×C₇	—	2	2	no	—
218	C₂³×C₇	—	2	2	no	—
219	C₂³×C₇	—	2	1	no	—
220	C₂³×C₇	—	2	1	no	—
221	C₂³×C₇	—	2	2	no	—
222	C₂³×C₇	C₂²×C₈	1	4	yes	—
223	C₂³×C₇	C₂²×C₈	1	2	yes	—
224	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
225	C₇×D₄	—	2	8	no	—
226	C₇×D₄	—	4	8	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	1	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	8	no	—
234	C₂×C₄×C₇	—	2	1	no	—
235	C₂×C₄×C₇	—	2	1	no	—
236	C₂×C₄×C₇	—	2	2	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	2	1	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	1	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	1	no	—
244	C₂×C₄×C₇	—	2	2	no	—
245	C₂×C₄×C₇	—	2	1	no	—
246	C₂×C₄×C₇	—	4	4	no	—
247	C₂×C₄×C₇	—	4	2	no	—
248	C₂×C₄×C₇	—	4	1	no	—
249	C₂×C₄×C₇	—	4	1	no	—
250	C₂×C₄×C₇	—	4	2	no	—
251	C₂×C₄×C₇	—	4	1	no	—
252	C₂×C₄×C₇	—	4	2	no	—
253	C₂×C₄×C₇	—	4	1	no	—
254	C₂×C₄×C₇	—	4	2	no	—
255	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
256	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
258	C₂×C₄×C₇	C₂²×C₈	1	4	yes	—
259	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
260	C₂×C₄×C₇	#131	1	2	yes	—
261	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
267	C₇×C₈	—	2	2	no	—
268	C₇×C₈	—	2	2	no	—
269	C₇×C₈	—	4	1	no	—
270	C₇×C₈	—	4	2	no	—
271	C₇×C₈	—	4	1	no	—
272	C₇×C₈	—	4	2	no	—
273	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
274	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
275	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
276	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₇	1	2	yes	—
278	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
279	C₂²×C₈	—	2	4	no	—
280	C₂²×C₈	—	4	2	no	—
281	C₂²×C₈	—	4	2	no	—
282	C₂²×C₈	C₂³×C₇	1	2	yes	—
283	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₇	1	2	yes	—
285	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
288	#121	C₇×C₈	1	8	yes	complemented
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	4	2	no	—
292	C₄×D₄	—	4	2	no	—
293	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
296	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
301	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
305	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₇	1	2	yes	—
307	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	4	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	2	4	no	—
317	C₂²⋊C₈	—	4	2	no	—
318	C₂²⋊C₈	—	4	2	no	—
319	C₂²⋊C₈	—	4	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	4	2	no	—
322	C₄×C₈	C₇×D₄	1	4	yes	complemented
323	#95	C₂×C₄×C₇	1	2	yes	—
324	#95	C₂×C₄×C₇	1	2	yes	—
325	#95	C₂×C₄×C₇	1	2	yes	—
326	C₂²×C₇	—	2	2	no	—
327	C₂²×C₇	—	2	4	no	—
328	C₂²×C₇	—	2	2	no	—
329	C₂²×C₇	—	2	4	no	—
330	C₂²×C₇	—	2	4	no	—
331	C₂²×C₇	—	2	2	no	—
332	C₂²×C₇	—	4	2	no	—
333	C₂²×C₇	—	4	1	no	—
334	C₂²×C₇	—	4	1	no	—
335	C₂²×C₇	—	4	2	no	—
336	C₂²×C₇	—	4	1	no	—
337	C₂²×C₇	—	4	2	no	—
338	C₂²×C₇	—	4	1	no	—
339	C₂²×C₇	—	4	2	no	—
340	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
341	C₂²×C₇	#518	1	1	yes	characteristic
342	C₂²×C₇	#520	1	1	yes	characteristic
343	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
344	C₂²×C₇	C₂×#131	1	1	yes	characteristic
345	C₂²×C₇	#568	1	1	yes	characteristic
346	C₂²×C₇	#568	1	1	yes	characteristic
347	C₄×C₇	—	2	2	no	—
348	C₄×C₇	—	2	2	no	—
349	C₄×C₇	—	2	4	no	—
350	C₄×C₇	—	4	1	no	—
351	C₄×C₇	—	4	2	no	—
352	C₄×C₇	—	4	1	no	—
353	C₄×C₇	—	4	2	no	—
354	C₄×C₇	C₈×D₄	1	4	yes	—
355	C₄×C₇	#535	1	1	yes	characteristic
356	C₄×C₇	#537	1	1	yes	characteristic
357	C₄×C₇	#540	1	1	yes	characteristic
358	C₄×C₇	#542	1	1	yes	characteristic
359	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
360	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	C₂×C₇×C₈	1	4	yes	—
366	C₂×D₄	C₂×C₇×C₈	1	8	yes	complemented
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	C₂×C₇×C₈	1	4	yes	complemented
385	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
387	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
388	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
392	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	4	8	no	—
411	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
412	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	C₂×C₇×C₈	1	4	yes	complemented
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	C₂×C₇×C₈	1	8	yes	complemented
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	C₂×C₇×D₄	1	2	yes	—
429	C₄²	C₇×#41	1	2	yes	—
430	C₂×C₇	—	4	2	no	—
431	C₂×C₇	—	4	4	no	—
432	C₂×C₇	#2324	1	1	yes	characteristic
433	C₂×C₇	C₂×C₈×D₄	1	1	yes	characteristic
434	C₂×C₇	#2930	1	1	yes	characteristic
435	C₂×C₇	#2972	1	1	yes	characteristic
436	C₂×C₇	#2981	1	1	yes	characteristic
437	C₂×C₇	#2988	1	1	yes	characteristic
438	C₂×C₇	#2993	1	1	yes	characteristic
439	C₂³	—	2	2	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	2	no	—
451	C₂³	C₂²×C₇×C₈	1	4	yes	—
452	C₂³	C₂²×C₇×C₈	1	2	yes	—
453	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
454	D₄	—	2	8	no	—
455	D₄	—	4	8	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
485	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
486	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
487	C₂×C₄	C₂²×C₇×C₈	1	4	yes	—
488	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
489	C₂×C₄	C₇×#131	1	2	yes	—
490	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
491	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
492	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
493	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
495	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	2	2	no	—
498	C₈	—	4	1	no	—
499	C₈	—	4	2	no	—
500	C₈	—	4	1	no	—
501	C₈	—	4	2	no	—
502	C₇	#22133	1	1	yes	characteristic, direct product factor, Sylow
503	C₂²	—	2	2	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
518	C₂²	C₇×#518	1	1	yes	characteristic
519	C₂²	C₇×#520	1	1	yes	characteristic
520	C₂²	C₂³×C₇×C₈	1	1	yes	characteristic
521	C₂²	C₂×C₇×#131	1	1	yes	characteristic
522	C₂²	C₇×#568	1	1	yes	characteristic
523	C₂²	C₇×#568	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	4	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	2	no	—
531	C₄	C₇×C₈×D₄	1	4	yes	—
532	C₄	C₇×#535	1	1	yes	characteristic
533	C₄	C₇×#537	1	1	yes	characteristic
534	C₄	C₇×#540	1	1	yes	characteristic
535	C₄	C₇×#542	1	1	yes	characteristic
536	C₂	—	4	2	no	—
537	C₂	—	4	4	no	—
538	C₂	C₇×#2324	1	1	yes	characteristic
539	C₂	C₂×C₇×C₈×D₄	1	1	yes	characteristic
540	C₂	C₇×#2930	1	1	yes	characteristic
541	C₂	C₇×#2972	1	1	yes	characteristic
542	C₂	C₇×#2981	1	1	yes	characteristic
543	C₂	C₇×#2988	1	1	yes	characteristic
544	C₂	C₇×#2993	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	C₂×C₇×#121	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×C₈×D₄	C₂	semidirect
2. C₂×C₇×#431	C₂	semidirect
4. C₇×#1954	C₂	semidirect
5. C₇×#1954	C₂	semidirect
6. C₇×#1939	C₂	semidirect
7. C₇×#1923	C₂	semidirect
8. C₇×#1869	C₂	semidirect
9. C₇×#1850	C₂	semidirect
10. C₇×#1797	C₂	semidirect
11. C₇×C₈×C₄⋊C₄	C₂	semidirect
43. #22133	C₇	direct (N × H)
59. C₇×#121	C₈	semidirect
93. C₄×C₇×C₈	D₄	semidirect
97. C₂×C₈×D₄	C₂×C₇	semidirect
98. C₂×#431	C₂×C₇	semidirect
100. #1954	C₂×C₇	semidirect
101. #1954	C₂×C₇	semidirect
102. #1939	C₂×C₇	semidirect
103. #1923	C₂×C₇	semidirect
104. #1869	C₂×C₇	semidirect
105. #1850	C₂×C₇	semidirect
106. #1797	C₂×C₇	semidirect
107. C₈×C₄⋊C₄	C₂×C₇	semidirect
115. C₂×C₇×D₄	C₂×C₈	semidirect
133. C₂²×C₄×C₇	C₂×C₈	semidirect
165. C₇×C₄⋊C₄	C₂×C₈	semidirect
170. C₇×C₂²⋊C₄	C₂×C₈	semidirect
288. #121	C₇×C₈	semidirect
322. C₄×C₈	C₇×D₄	semidirect
366. C₂×D₄	C₂×C₇×C₈	semidirect
384. C₂²×C₄	C₂×C₇×C₈	semidirect
416. C₄⋊C₄	C₂×C₇×C₈	semidirect
421. C₂²⋊C₄	C₂×C₇×C₈	semidirect
502. C₇	#22133	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×C₈×D₄	2
C₂×C₇×#431	2
C₄×C₇×#121	2
C₇×#1954	2
C₇×#1939	2
C₇×#1923	2
C₇×#1869	2
C₇×#1850	2
C₇×#1797	2
C₇×C₈×C₄⋊C₄	2
#22133	7

Subgroups — C7×#22133 #13199349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22133 #13199349