Subgroups — D₆₄×C₂₂₃ #43250444

Order 28544.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₂×C₂₂₃	C₂	1	2	yes	maximal, complemented
2	C₆₄×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×C₂₂₃	—	2	2	no	—
4	C₃₂×C₂₂₃	C₂²	1	1	yes	characteristic
5	D₈×C₂₂₃	—	4	2	no	—
6	C₁₆×C₂₂₃	D₄	1	1	yes	characteristic
7	D₄×C₂₂₃	—	8	2	no	—
8	C₈×C₂₂₃	D₈	1	1	yes	characteristic
9	C₂²×C₂₂₃	—	16	2	no	—
10	C₄×C₂₂₃	D₁₆	1	1	yes	characteristic
11	C₂×C₂₂₃	—	32	2	no	—
12	C₂×C₂₂₃	D₃₂	1	1	yes	characteristic
13	C₂₂₃	D₆₄	1	1	yes	characteristic, direct product factor, Sylow
14	D₆₄	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	D₃₂	C₂×C₂₂₃	1	2	yes	complemented
16	C₆₄	C₂×C₂₂₃	1	1	yes	characteristic, complemented
17	D₁₆	—	2	2	no	—
18	C₃₂	C₂²×C₂₂₃	1	1	yes	characteristic
19	D₈	—	4	2	no	—
20	C₁₆	D₄×C₂₂₃	1	1	yes	characteristic
21	D₄	—	8	2	no	—
22	C₈	D₈×C₂₂₃	1	1	yes	characteristic
23	C₂²	—	16	2	no	—
24	C₄	D₁₆×C₂₂₃	1	1	yes	characteristic
25	C₂	—	32	2	no	—
26	C₂	D₃₂×C₂₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₂₃	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₂₂₃
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₂₃ ◁ C₄×C₂₂₃ ◁ C₈×C₂₂₃ ◁ C₁₆×C₂₂₃ ◁ C₃₂×C₂₂₃ ◁ 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.