Subgroups — #46782503

Order 33664.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30681896	C₂	1	3	yes	maximal
2	#30681695	C₂	1	3	yes	maximal
3	#338×C₂₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₂₆₃⋊C₈	C₂²	1	1	yes	characteristic
5	#22554429	C₂²	1	3	yes	—
6	#22554380	C₄	1	6	yes	complemented
7	C₈×Dic₂₆₃	C₄	1	6	yes	complemented
8	C₂×M₁₆×C₂₆₃	C₂²	1	3	yes	—
9	C₂×C₂₆₃⋊C₈	C₂×C₄	1	3	yes	—
10	C₂×C₂₆₃⋊C₈	C₂×C₄	1	3	yes	—
11	C₄⋊Dic₂₆₃	—	2	3	no	—
12	C₂²⋊Dic₂₆₃	—	2	3	no	—
13	C₄×Dic₂₆₃	C₂×C₄	1	6	yes	—
14	C₂²×C₄×C₂₆₃	C₂³	1	1	yes	characteristic
15	M₁₆×C₂₆₃	—	2	6	no	—
16	C₂×C₈×C₂₆₃	C₂×C₄	1	6	yes	—
17	C₂×Dic₂₆₃	—	2	6	no	—
18	C₂₆₃⋊C₈	C₄²	1	1	yes	characteristic
19	C₂₆₃⋊C₈	C₄²	1	3	yes	—
20	C₂³×C₂₆₃	#41	1	1	yes	characteristic
21	C₂×C₄×C₂₆₃	C₂²×C₄	1	3	yes	—
22	C₂×C₄×C₂₆₃	#41	1	3	yes	—
23	C₈×C₂₆₃	—	2	6	no	—
24	C₂²×C₂₆₃	—	4	1	no	—
25	C₂²×C₂₆₃	#117	1	3	yes	—
26	C₄×C₂₆₃	C₂×C₄²	1	1	yes	characteristic
27	C₄×C₂₆₃	#117	1	3	yes	—
28	Dic₂₆₃	—	4	6	no	—
29	C₂×C₂₆₃	—	2	3	no	—
30	C₂×C₂₆₃	#376	1	1	yes	characteristic
31	C₂₆₃	#1747	1	1	yes	characteristic, complemented, Sylow
32	#1747	—	263	1	no	maximal, Sylow
33	#405	—	263	3	no	—
34	#338	D₂₆₃	1	1	yes	characteristic
35	H(3,ℤ/4)	—	263	3	no	—
36	C₂×M₁₆	C₂×D₂₆₃	1	3	yes	—
37	C₂²×C₈	—	263	1	no	—
38	#117	—	263	3	no	—
39	#97	—	263	6	no	—
40	C₄×C₈	—	263	6	no	—
41	C₂²×C₄	C₂²×D₂₆₃	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	263	3	no	—
44	C₂×C₈	—	263	3	no	—
45	C₂×C₈	C₄×D₂₆₃	1	6	yes	—
46	C₄⋊C₄	—	526	3	no	—
47	C₂²⋊C₄	—	526	3	no	—
48	C₄²	—	263	6	no	—
49	C₂³	#16862377	1	1	yes	characteristic
50	C₂×C₄	—	526	6	no	—
51	C₂×C₄	C₂×C₄×D₂₆₃	1	3	yes	—
52	C₂×C₄	#16862375	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	263	1	no	—
55	C₈	—	263	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#22554428	1	3	yes	—
58	C₄	—	1052	6	no	—
59	C₄	C₄²×D₂₆₃	1	1	yes	characteristic
60	C₄	#22554426	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#30681783	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₂₆₃
commutator	C₄×C₂₆₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₆₃
Fitting	#338×C₂₆₃	C₂
socle	C₂×C₂₆₃	#376
prime radical	C₂³×C₂₆₃	#41
cosocle	C₂²×C₄×C₂₆₃	C₂³
hypercenter	#338	D₂₆₃
hypocenter	C₂₆₃	#1747
LCS	G ▷ C₄×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
6. #22554380	C₄	semidirect
7. C₈×Dic₂₆₃	C₄	semidirect
31. C₂₆₃	#1747	semidirect

Maximal subgroups

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

subgroup	index
#30681896	2
#30681695	2
#338×C₂₆₃	2
#1747	263