Subgroups — #43246182

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	C₄⋊Dic₈₈₃	C₂	1	1	yes	maximal, characteristic
3	Dic₈₈₃⋊C₄	C₂	1	2	yes	maximal
4	C₄×Dic₈₈₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×C₈₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₈₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₈₈₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₈₈₃	C₂²	1	2	yes	—
9	C₂×C₄×C₈₈₃	C₂²	1	2	yes	—
10	C₂×C₄×C₈₈₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈₈₃	C₂³	1	1	yes	characteristic
12	C₄×C₈₈₃	—	2	2	no	—
13	C₄×C₈₈₃	Q₈	1	2	yes	—
14	Dic₈₈₃	—	2	1	no	—
15	Dic₈₈₃	—	2	1	no	—
16	Dic₈₈₃	—	2	2	no	—
17	C₂×C₈₈₃	C₂×Q₈	1	1	yes	characteristic
18	C₂×C₈₈₃	#41	1	1	yes	characteristic
19	C₂×C₈₈₃	#41	1	1	yes	characteristic
20	C₈₈₃	#125	1	1	yes	characteristic, complemented, Sylow
21	#125	—	883	1	no	maximal, Sylow
22	C₄⋊C₄	—	883	2	no	—
23	C₄⋊C₄	—	883	2	no	—
24	C₄⋊C₄	—	883	1	no	—
25	C₄⋊C₄	D₈₈₃	1	1	yes	characteristic
26	C₄²	—	883	1	no	—
27	C₂×C₄	—	883	1	no	—
28	C₂×C₄	—	883	1	no	—
29	C₂×C₄	—	883	2	no	—
30	C₂×C₄	C₂×D₈₈₃	1	2	yes	—
31	C₂×C₄	C₂×D₈₈₃	1	1	yes	characteristic
32	C₂²	C₂²×D₈₈₃	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	—	1766	1	no	—
35	C₄	—	1766	1	no	—
36	C₄	—	1766	2	no	—
37	C₄	Dic₁₇₆₆	1	2	yes	—
38	C₂	C₂×Dic₁₇₆₆	1	1	yes	characteristic
39	C₂	#28381496	1	1	yes	characteristic
40	C₂	#28381498	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₈₈₃
commutator, socle, prime radical, cosocle	C₂²×C₈₈₃	C₂³
Fitting	C₄⋊C₄×C₈₈₃	C₂
hypercenter	C₄⋊C₄	D₈₈₃
hypocenter	C₈₈₃	#125
LCS	G ▷ C₂²×C₈₈₃ ▷ C₈₈₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

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

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

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