Subgroups — #1274×C₂₆₃ #46778243

Order 33664.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431×C₂₆₃	C₂	1	2	yes	maximal
2	#376×C₂₆₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₂₆₃	C₄	1	2	yes	—
4	C₂×C₄²×C₂₆₃	C₂²	1	1	yes	characteristic
5	C₄⋊C₈×C₂₆₃	—	2	2	no	—
6	C₂²⋊C₈×C₂₆₃	—	2	2	no	—
7	C₄×C₈×C₂₆₃	C₄	1	4	yes	complemented
8	#95×C₂₆₃	—	2	2	no	—
9	C₂²×C₄×C₂₆₃	—	2	2	no	—
10	C₂²×C₄×C₂₆₃	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄×C₂₆₃	D₄	1	2	yes	—
12	C₂×C₈×C₂₆₃	—	2	4	no	—
13	C₄²×C₂₆₃	—	2	2	no	—
14	C₄²×C₂₆₃	C₈	1	4	yes	complemented
15	C₄²×C₂₆₃	C₂×C₄	1	2	yes	—
16	C₄²×C₂₆₃	D₄	1	1	yes	characteristic
17	C₄²×C₂₆₃	Q₈	1	1	yes	characteristic
18	C₂³×C₂₆₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₂₆₃	—	2	4	no	—
20	C₂×C₄×C₂₆₃	—	4	2	no	—
21	C₂×C₄×C₂₆₃	—	4	4	no	—
22	C₂×C₄×C₂₆₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₂₆₃	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₂₆₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₂₆₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₆₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₂₆₃	M₁₆	1	2	yes	—
28	C₈×C₂₆₃	—	4	4	no	—
29	C₂²×C₂₆₃	—	2	2	no	—
30	C₂²×C₂₆₃	#95	1	1	yes	characteristic
31	C₂²×C₂₆₃	C₂²⋊C₈	1	2	yes	—
32	C₄×C₂₆₃	—	2	2	no	—
33	C₄×C₂₆₃	—	2	2	no	—
34	C₄×C₂₆₃	—	4	4	no	—
35	C₄×C₂₆₃	C₄×C₈	1	1	yes	characteristic
36	C₄×C₂₆₃	#97	1	1	yes	characteristic
37	C₄×C₂₆₃	C₄⋊C₈	1	2	yes	—
38	C₂×C₂₆₃	—	2	2	no	—
39	C₂×C₂₆₃	#336	1	1	yes	characteristic
40	C₂×C₂₆₃	H(3,ℤ/4)	1	2	yes	—
41	C₂₆₃	#1274	1	1	yes	characteristic, direct product factor, Sylow
42	#1274	C₂₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	#431	C₂×C₂₆₃	1	2	yes	—
44	#376	C₂×C₂₆₃	1	1	yes	characteristic
45	C₂×C₄²	C₄×C₂₆₃	1	2	yes	—
46	C₂×C₄²	C₂²×C₂₆₃	1	1	yes	characteristic
47	C₄⋊C₈	—	2	2	no	—
48	C₂²⋊C₈	—	2	2	no	—
49	C₄×C₈	C₄×C₂₆₃	1	4	yes	complemented
50	#95	—	2	2	no	—
51	C₂²×C₄	—	2	2	no	—
52	C₂²×C₄	C₂×C₄×C₂₆₃	1	1	yes	characteristic
53	C₂²×C₄	D₄×C₂₆₃	1	2	yes	—
54	C₂×C₈	—	2	4	no	—
55	C₄²	—	2	2	no	—
56	C₄²	C₈×C₂₆₃	1	4	yes	complemented
57	C₄²	C₂×C₄×C₂₆₃	1	2	yes	—
58	C₄²	D₄×C₂₆₃	1	1	yes	characteristic
59	C₄²	Q₈×C₂₆₃	1	1	yes	characteristic
60	C₂³	C₂²⋊C₄×C₂₆₃	1	1	yes	characteristic
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	—	4	2	no	—
63	C₂×C₄	—	4	4	no	—
64	C₂×C₄	C₄²×C₂₆₃	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊C₄×C₂₆₃	1	2	yes	—
66	C₂×C₄	C₄⋊C₄×C₂₆₃	1	2	yes	—
67	C₂×C₄	C₄⋊C₄×C₂₆₃	1	1	yes	characteristic
68	C₂×C₄	C₂×C₈×C₂₆₃	1	2	yes	—
69	C₂×C₄	M₁₆×C₂₆₃	1	2	yes	—
70	C₈	—	4	4	no	—
71	C₂²	—	2	2	no	—
72	C₂²	#95×C₂₆₃	1	1	yes	characteristic
73	C₂²	C₂²⋊C₈×C₂₆₃	1	2	yes	—
74	C₄	—	2	2	no	—
75	C₄	—	2	2	no	—
76	C₄	—	4	4	no	—
77	C₄	C₄×C₈×C₂₆₃	1	1	yes	characteristic
78	C₄	#97×C₂₆₃	1	1	yes	characteristic
79	C₄	C₄⋊C₈×C₂₆₃	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	#336×C₂₆₃	1	1	yes	characteristic
82	C₂	H(3,ℤ/4)×C₂₆₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₆₃	C₄²
commutator	C₄	C₄×C₈×C₂₆₃
Frattini, cosocle	C₂×C₄²	C₂²×C₂₆₃
socle	C₂²×C₂₆₃	#95
prime radical	C₂³×C₂₆₃	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₆₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₄×C₈×C₂₆₃	C₄	semidirect
14. C₄²×C₂₆₃	C₈	semidirect
41. C₂₆₃	#1274	direct (N × H)
42. #1274	C₂₆₃	direct (N × H)
49. C₄×C₈	C₄×C₂₆₃	semidirect
56. C₄²	C₈×C₂₆₃	semidirect

Maximal subgroups

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

subgroup	index
#431×C₂₆₃	2
#376×C₂₆₃	2
#1274	263

Subgroups — #1274×C263 #46778243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1274×C₂₆₃ #46778243