Subgroups — #43246183

Order 28256.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₈₈₃	C₂	1	2	yes	maximal
2	Dic₈₈₃⋊C₄	C₂	1	4	yes	maximal
3	C₄²×C₈₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₈₃	C₂²	1	4	yes	—
5	C₂×C₄×C₈₈₃	C₂²	1	2	yes	—
6	C₂×C₄×C₈₈₃	C₂²	1	1	yes	characteristic
7	C₂²×C₈₈₃	C₂³	1	1	yes	characteristic
8	C₄×C₈₈₃	—	2	2	no	—
9	C₄×C₈₈₃	Q₈	1	2	yes	—
10	Dic₈₈₃	—	2	4	no	—
11	C₂×C₈₈₃	C₂×Q₈	1	1	yes	characteristic
12	C₂×C₈₈₃	#41	1	2	yes	—
13	C₈₈₃	#125	1	1	yes	characteristic, complemented, Sylow
14	#125	—	883	1	no	maximal, Sylow
15	C₄⋊C₄	—	883	4	no	—
16	C₄⋊C₄	—	883	2	no	—
17	C₄²	D₈₈₃	1	1	yes	characteristic
18	C₂×C₄	—	883	4	no	—
19	C₂×C₄	C₂×D₈₈₃	1	2	yes	—
20	C₂×C₄	C₂×D₈₈₃	1	1	yes	characteristic
21	C₂²	C₂²×D₈₈₃	1	1	yes	characteristic
22	C₄	—	2	2	no	—
23	C₄	—	1766	4	no	—
24	C₄	Dic₁₇₆₆	1	2	yes	—
25	C₂	C₂×Dic₁₇₆₆	1	1	yes	characteristic
26	C₂	#28381497	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₈₈₃
commutator, socle, prime radical, cosocle	C₂²×C₈₈₃	C₂³
Fitting	C₄²×C₈₈₃	C₂
hypercenter	C₄²	D₈₈₃
hypocenter	C₈₈₃	#125
LCS	G ▷ C₂²×C₈₈₃ ▷ C₈₈₃
UCS	C₁ ◁ C₂² ◁ C₄²

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

N	H ≅ G/N	type
13. C₈₈₃	#125	semidirect

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