Subgroups — C₂₃×SD₁₂₈ #15669049

Order 2944.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×D₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×Q₃₂	—	2	1	no	—
5	C₂₃×D₁₆	—	2	1	no	—
6	C₂₃×C₃₂	C₂²	1	1	yes	characteristic
7	Q₁₆×C₂₃	—	4	1	no	—
8	D₈×C₂₃	—	4	1	no	—
9	C₁₆×C₂₃	D₄	1	1	yes	characteristic
10	Q₈×C₂₃	—	8	1	no	—
11	D₄×C₂₃	—	8	1	no	—
12	C₈×C₂₃	D₈	1	1	yes	characteristic
13	SD₁₂₈	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂²×C₂₃	—	16	1	no	—
15	C₄×C₂₃	—	16	1	no	—
16	C₄×C₂₃	D₁₆	1	1	yes	characteristic
17	Q₆₄	C₂×C₂₃	1	1	yes	characteristic, complemented
18	D₃₂	C₂×C₂₃	1	1	yes	characteristic
19	C₆₄	C₂×C₂₃	1	1	yes	characteristic, complemented
20	C₂×C₂₃	—	32	1	no	—
21	C₂×C₂₃	D₃₂	1	1	yes	characteristic
22	Q₃₂	—	2	1	no	—
23	D₁₆	—	2	1	no	—
24	C₃₂	C₂²×C₂₃	1	1	yes	characteristic
25	C₂₃	SD₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
26	Q₁₆	—	4	1	no	—
27	D₈	—	4	1	no	—
28	C₁₆	D₄×C₂₃	1	1	yes	characteristic
29	Q₈	—	8	1	no	—
30	D₄	—	8	1	no	—
31	C₈	D₈×C₂₃	1	1	yes	characteristic
32	C₂²	—	16	1	no	—
33	C₄	—	16	1	no	—
34	C₄	C₂₃×D₁₆	1	1	yes	characteristic
35	C₂	—	32	1	no	—
36	C₂	C₂₃×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₂₃
prime radical	C₂₃×D₃₂	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₄×C₂₃ ◁ C₈×C₂₃ ◁ C₁₆×C₂₃ ◁ C₂₃×C₃₂ ◁ G

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

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