Subgroups — C₁₁₃×SD₂₅₆ #43275572

Order 28928.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁₃×D₆₄	C₂	1	1	yes	maximal, characteristic
3	C₁₁₃×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₆₄×C₁₁₃	—	2	1	no	—
5	D₃₂×C₁₁₃	—	2	1	no	—
6	C₆₄×C₁₁₃	C₂²	1	1	yes	characteristic
7	Q₃₂×C₁₁₃	—	4	1	no	—
8	D₁₆×C₁₁₃	—	4	1	no	—
9	C₃₂×C₁₁₃	D₄	1	1	yes	characteristic
10	Q₁₆×C₁₁₃	—	8	1	no	—
11	D₈×C₁₁₃	—	8	1	no	—
12	C₁₆×C₁₁₃	D₈	1	1	yes	characteristic
13	Q₈×C₁₁₃	—	16	1	no	—
14	D₄×C₁₁₃	—	16	1	no	—
15	C₈×C₁₁₃	D₁₆	1	1	yes	characteristic
16	C₂²×C₁₁₃	—	32	1	no	—
17	C₄×C₁₁₃	—	32	1	no	—
18	C₄×C₁₁₃	D₃₂	1	1	yes	characteristic
19	SD₂₅₆	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂×C₁₁₃	—	64	1	no	—
21	C₂×C₁₁₃	D₆₄	1	1	yes	characteristic
22	Q₁₂₈	C₂×C₁₁₃	1	1	yes	characteristic, complemented
23	D₆₄	C₂×C₁₁₃	1	1	yes	characteristic
24	C₁₂₈	C₂×C₁₁₃	1	1	yes	characteristic, complemented
25	C₁₁₃	SD₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
26	Q₆₄	—	2	1	no	—
27	D₃₂	—	2	1	no	—
28	C₆₄	C₂²×C₁₁₃	1	1	yes	characteristic
29	Q₃₂	—	4	1	no	—
30	D₁₆	—	4	1	no	—
31	C₃₂	D₄×C₁₁₃	1	1	yes	characteristic
32	Q₁₆	—	8	1	no	—
33	D₈	—	8	1	no	—
34	C₁₆	D₈×C₁₁₃	1	1	yes	characteristic
35	Q₈	—	16	1	no	—
36	D₄	—	16	1	no	—
37	C₈	D₁₆×C₁₁₃	1	1	yes	characteristic
38	C₂²	—	32	1	no	—
39	C₄	—	32	1	no	—
40	C₄	D₃₂×C₁₁₃	1	1	yes	characteristic
41	C₂	—	64	1	no	—
42	C₂	C₁₁₃×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁₃	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₁₁₃
prime radical	C₁₁₃×D₆₄	C₂
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁₃ ◁ C₄×C₁₁₃ ◁ C₈×C₁₁₃ ◁ C₁₆×C₁₁₃ ◁ C₃₂×C₁₁₃ ◁ C₆₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁₃×Q₁₂₈	C₂	semidirect
3. C₁₁₃×C₁₂₈	C₂	semidirect
19. SD₂₅₆	C₁₁₃	direct (N × H)
22. Q₁₂₈	C₂×C₁₁₃	semidirect
24. C₁₂₈	C₂×C₁₁₃	semidirect
25. C₁₁₃	SD₂₅₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁₃×Q₁₂₈	2
C₁₁₃×D₆₄	2
C₁₁₃×C₁₂₈	2
SD₂₅₆	113

Subgroups — C113×SD256 #43275572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×SD₂₅₆ #43275572