Subgroups — SD₆₄×C₂₅₇ #30656241

Order 16448.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₆×C₂₅₇	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₁₆×C₂₅₇	—	2	1	no	—
5	D₈×C₂₅₇	—	2	1	no	—
6	C₁₆×C₂₅₇	C₂²	1	1	yes	characteristic
7	Q₈×C₂₅₇	—	4	1	no	—
8	D₄×C₂₅₇	—	4	1	no	—
9	C₈×C₂₅₇	D₄	1	1	yes	characteristic
10	C₂²×C₂₅₇	—	8	1	no	—
11	C₄×C₂₅₇	—	8	1	no	—
12	C₄×C₂₅₇	D₈	1	1	yes	characteristic
13	C₂×C₂₅₇	—	16	1	no	—
14	C₂×C₂₅₇	D₁₆	1	1	yes	characteristic
15	C₂₅₇	SD₆₄	1	1	yes	characteristic, direct product factor, Sylow
16	SD₆₄	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	Q₃₂	C₂×C₂₅₇	1	1	yes	characteristic, complemented
18	D₁₆	C₂×C₂₅₇	1	1	yes	characteristic
19	C₃₂	C₂×C₂₅₇	1	1	yes	characteristic, complemented
20	Q₁₆	—	2	1	no	—
21	D₈	—	2	1	no	—
22	C₁₆	C₂²×C₂₅₇	1	1	yes	characteristic
23	Q₈	—	4	1	no	—
24	D₄	—	4	1	no	—
25	C₈	D₄×C₂₅₇	1	1	yes	characteristic
26	C₂²	—	8	1	no	—
27	C₄	—	8	1	no	—
28	C₄	D₈×C₂₅₇	1	1	yes	characteristic
29	C₂	—	16	1	no	—
30	C₂	D₁₆×C₂₅₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₅₇	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂²×C₂₅₇
prime radical	D₁₆×C₂₅₇	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₅₇ ◁ C₄×C₂₅₇ ◁ C₈×C₂₅₇ ◁ C₁₆×C₂₅₇ ◁ 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.