Subgroups — SD₃₂×C₇₅₇ #37564260

Order 24224.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×C₇₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×C₇₅₇	C₂	1	1	yes	maximal, characteristic
3	C₁₆×C₇₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₇₅₇	—	2	1	no	—
5	D₄×C₇₅₇	—	2	1	no	—
6	C₈×C₇₅₇	C₂²	1	1	yes	characteristic
7	C₂²×C₇₅₇	—	4	1	no	—
8	C₄×C₇₅₇	—	4	1	no	—
9	C₄×C₇₅₇	D₄	1	1	yes	characteristic
10	C₂×C₇₅₇	—	8	1	no	—
11	C₂×C₇₅₇	D₈	1	1	yes	characteristic
12	C₇₅₇	SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
13	SD₃₂	C₇₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	Q₁₆	C₂×C₇₅₇	1	1	yes	characteristic, complemented
15	D₈	C₂×C₇₅₇	1	1	yes	characteristic
16	C₁₆	C₂×C₇₅₇	1	1	yes	characteristic, complemented
17	Q₈	—	2	1	no	—
18	D₄	—	2	1	no	—
19	C₈	C₂²×C₇₅₇	1	1	yes	characteristic
20	C₂²	—	4	1	no	—
21	C₄	—	4	1	no	—
22	C₄	D₄×C₇₅₇	1	1	yes	characteristic
23	C₂	—	8	1	no	—
24	C₂	D₈×C₇₅₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇₅₇	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₇₅₇
prime radical	D₈×C₇₅₇	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₅₇ ◁ C₄×C₇₅₇ ◁ C₈×C₇₅₇ ◁ 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.