Subgroups — C₂×C₂₃⋊C₁₂₈ #19212115

Order 5888.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃⋊C₁₂₈	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₃×C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×C₃₂	C₄	1	1	yes	characteristic
4	C₂₃×C₆₄	C₄	1	1	yes	characteristic
5	C₂₃×C₆₄	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₂₃	C₈	1	1	yes	characteristic
7	C₂₃×C₃₂	C₈	1	1	yes	characteristic
8	C₂₃×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₂₃	C₁₆	1	1	yes	characteristic
10	C₁₆×C₂₃	C₁₆	1	1	yes	characteristic
11	C₁₆×C₂₃	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₂₈	—	23	1	no	maximal, Sylow
13	C₂×C₄×C₂₃	C₃₂	1	1	yes	characteristic
14	C₈×C₂₃	C₃₂	1	1	yes	characteristic
15	C₈×C₂₃	C₂×C₁₆	1	1	yes	characteristic
16	C₂×C₆₄	D₂₃	1	1	yes	characteristic
17	C₁₂₈	—	23	2	no	—
18	C₂²×C₂₃	C₆₄	1	1	yes	characteristic
19	C₄×C₂₃	C₆₄	1	1	yes	characteristic
20	C₄×C₂₃	C₂×C₃₂	1	1	yes	characteristic
21	C₂×C₃₂	Dic₂₃	1	1	yes	characteristic
22	C₆₄	Dic₂₃	1	1	yes	characteristic
23	C₆₄	C₂×D₂₃	1	1	yes	characteristic
24	C₂×C₂₃	C₁₂₈	1	2	yes	complemented
25	C₂×C₂₃	C₂×C₆₄	1	1	yes	characteristic
26	C₂×C₁₆	C₂₃⋊C₈	1	1	yes	characteristic
27	C₃₂	C₂₃⋊C₈	1	1	yes	characteristic
28	C₃₂	C₂×Dic₂₃	1	1	yes	characteristic
29	C₂₃	C₂×C₁₂₈	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₈	C₂₃⋊C₁₆	1	1	yes	characteristic
31	C₁₆	C₂₃⋊C₁₆	1	1	yes	characteristic
32	C₁₆	C₂×C₂₃⋊C₈	1	1	yes	characteristic
33	C₂×C₄	C₂₃⋊C₃₂	1	1	yes	characteristic
34	C₈	C₂₃⋊C₃₂	1	1	yes	characteristic
35	C₈	C₂×C₂₃⋊C₁₆	1	1	yes	characteristic
36	C₂²	C₂₃⋊C₆₄	1	1	yes	characteristic
37	C₄	C₂₃⋊C₆₄	1	1	yes	characteristic
38	C₄	C₂×C₂₃⋊C₃₂	1	1	yes	characteristic
39	C₂	C₂₃⋊C₁₂₈	1	2	yes	direct product factor
40	C₂	C₂×C₂₃⋊C₆₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₆₄	D₂₃
commutator, hypocenter	C₂₃	C₂×C₁₂₈
Frattini	C₆₄	C₂×D₂₃
Fitting	C₂×C₂₃×C₆₄	C₂
socle	C₂²×C₂₃	C₆₄
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. C₂₃⋊C₁₂₈	C₂	direct (N × H)
24. C₂×C₂₃	C₁₂₈	semidirect
29. C₂₃	C₂×C₁₂₈	semidirect
39. C₂	C₂₃⋊C₁₂₈	direct (N × H)

Subgroups — C2×C23⋊C128 #19212115

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₂₃⋊C₁₂₈ #19212115