Subgroups — C₁₃₇×D₁₂₈ #46856937

Order 35072.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₄×C₁₃₇	C₂	1	2	yes	maximal, complemented
2	C₁₂₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₂×C₁₃₇	—	2	2	no	—
4	C₆₄×C₁₃₇	C₂²	1	1	yes	characteristic
5	D₁₆×C₁₃₇	—	4	2	no	—
6	C₃₂×C₁₃₇	D₄	1	1	yes	characteristic
7	D₈×C₁₃₇	—	8	2	no	—
8	C₁₆×C₁₃₇	D₈	1	1	yes	characteristic
9	D₄×C₁₃₇	—	16	2	no	—
10	C₈×C₁₃₇	D₁₆	1	1	yes	characteristic
11	C₂²×C₁₃₇	—	32	2	no	—
12	C₄×C₁₃₇	D₃₂	1	1	yes	characteristic
13	C₂×C₁₃₇	—	64	2	no	—
14	C₂×C₁₃₇	D₆₄	1	1	yes	characteristic
15	D₁₂₈	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₁₃₇	D₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
17	D₆₄	C₂×C₁₃₇	1	2	yes	complemented
18	C₁₂₈	C₂×C₁₃₇	1	1	yes	characteristic, complemented
19	D₃₂	—	2	2	no	—
20	C₆₄	C₂²×C₁₃₇	1	1	yes	characteristic
21	D₁₆	—	4	2	no	—
22	C₃₂	D₄×C₁₃₇	1	1	yes	characteristic
23	D₈	—	8	2	no	—
24	C₁₆	D₈×C₁₃₇	1	1	yes	characteristic
25	D₄	—	16	2	no	—
26	C₈	D₁₆×C₁₃₇	1	1	yes	characteristic
27	C₂²	—	32	2	no	—
28	C₄	D₃₂×C₁₃₇	1	1	yes	characteristic
29	C₂	—	64	2	no	—
30	C₂	D₆₄×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₇	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₁₃₇
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₇ ◁ C₄×C₁₃₇ ◁ C₈×C₁₃₇ ◁ C₁₆×C₁₃₇ ◁ C₃₂×C₁₃₇ ◁ C₆₄×C₁₃₇ ◁ 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.