Subgroups — D₂₃×C₁₂₈ #19212114

Order 5888.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₂₃⋊C₁₂₈	C₂	semidirect
3. C₂₃×C₁₂₈	C₂	semidirect
19. C₁₂₈	D₂₃	direct (N × H)
27. D₂₃	C₁₂₈	direct (N × H)
31. C₂₃	C₂×C₁₂₈	semidirect

Subgroups — D23×C128 #19212114

Conjugacy classes of subgroups

Complements

Subgroups — D₂₃×C₁₂₈ #19212114