Subgroups — #46782357

Order 33664.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30682343	C₂	1	2	yes	maximal
2	#30682289	C₂	1	4	yes	maximal
3	C₈²×C₂₆₃	C₂	1	1	yes	maximal, characteristic
4	#22554470	C₂²	1	4	yes	—
5	#22554404	—	2	4	no	—
6	#22554395	—	2	8	no	—
7	C₄×C₈×C₂₆₃	C₂²	1	2	yes	—
8	C₄×C₈×C₂₆₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₂₆	—	2	4	no	—
10	C₄⋊Dic₂₆₃	—	2	4	no	—
11	C₄⋊Dic₂₆₃	—	2	4	no	—
12	C₂×C₈×C₂₆₃	D₄	1	4	yes	—
13	C₂×C₈×C₂₆₃	D₄	1	2	yes	—
14	C₄²×C₂₆₃	C₂³	1	1	yes	characteristic
15	Dic₅₂₆	—	4	8	no	—
16	C₂×Dic₂₆₃	—	4	4	no	—
17	C₂×C₄×C₂₆₃	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₆₃	C₂×D₄	1	2	yes	—
19	C₈×C₂₆₃	—	2	4	no	—
20	C₈×C₂₆₃	Q₁₆	1	4	yes	—
21	C₂²×C₂₆₃	#127	1	1	yes	characteristic
22	C₄×C₂₆₃	C₂×Q₁₆	1	2	yes	—
23	C₄×C₂₆₃	#135	1	4	yes	—
24	Dic₂₆₃	—	8	4	no	—
25	C₂×C₂₆₃	#494	1	1	yes	characteristic
26	C₂×C₂₆₃	#495	1	2	yes	—
27	C₂₆₃	#1710	1	1	yes	characteristic, complemented, Sylow
28	#1710	—	263	1	no	maximal, Sylow
29	#500	—	263	2	no	—
30	#487	—	263	4	no	—
31	C₈²	D₂₆₃	1	1	yes	characteristic
32	C₄⋊Q₈	—	263	4	no	—
33	#107	—	526	4	no	—
34	#103	—	526	8	no	—
35	C₄×C₈	C₂×D₂₆₃	1	2	yes	—
36	C₄×C₈	C₂×D₂₆₃	1	1	yes	characteristic
37	C₂×Q₈	—	526	4	no	—
38	C₂×C₈	D₁₀₅₂	1	4	yes	—
39	C₂×C₈	D₁₀₅₂	1	2	yes	—
40	C₄⋊C₄	—	526	4	no	—
41	C₄⋊C₄	—	526	4	no	—
42	C₄²	C₂²×D₂₆₃	1	1	yes	characteristic
43	Q₈	—	1052	8	no	—
44	C₂×C₄	—	1052	4	no	—
45	C₂×C₄	C₂×D₁₀₅₂	1	1	yes	characteristic
46	C₂×C₄	C₂×D₁₀₅₂	1	2	yes	—
47	C₈	—	2	4	no	—
48	C₈	Dic₁₀₅₂	1	4	yes	—
49	C₂²	#22554467	1	1	yes	characteristic
50	C₄	—	2104	4	no	—
51	C₄	C₂×Dic₁₀₅₂	1	2	yes	—
52	C₄	#22554492	1	4	yes	—
53	C₂	#30682318	1	1	yes	characteristic
54	C₂	#30682322	1	2	yes	—

	subgroup	G/H
center	C₂²	#22554467
commutator, cosocle	C₄²×C₂₆₃	C₂³
Frattini	C₄²	C₂²×D₂₆₃
Fitting	C₈²×C₂₆₃	C₂
socle, prime radical	C₂²×C₂₆₃	#127
hypercenter	C₈²	D₂₆₃
hypocenter	C₂₆₃	#1710
LCS	G ▷ C₄²×C₂₆₃ ▷ C₂²×C₂₆₃ ▷ C₂₆₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
27. C₂₆₃	#1710	semidirect

Maximal subgroups

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

subgroup	index
#30682343	2
#30682289	2
C₈²×C₂₆₃	2
#1710	263