Subgroups — C₄₁×D₁₂₈ #23783752

Order 10496.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×D₆₄	C₂	1	2	yes	maximal, complemented
2	C₄₁×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×D₃₂	—	2	2	no	—
4	C₄₁×C₆₄	C₂²	1	1	yes	characteristic
5	D₁₆×C₄₁	—	4	2	no	—
6	C₃₂×C₄₁	D₄	1	1	yes	characteristic
7	D₈×C₄₁	—	8	2	no	—
8	C₁₆×C₄₁	D₈	1	1	yes	characteristic
9	D₄×C₄₁	—	16	2	no	—
10	C₈×C₄₁	D₁₆	1	1	yes	characteristic
11	D₁₂₈	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₄₁	—	32	2	no	—
13	C₄×C₄₁	D₃₂	1	1	yes	characteristic
14	D₆₄	C₂×C₄₁	1	2	yes	complemented
15	C₁₂₈	C₂×C₄₁	1	1	yes	characteristic, complemented
16	C₂×C₄₁	—	64	2	no	—
17	C₂×C₄₁	D₆₄	1	1	yes	characteristic
18	D₃₂	—	2	2	no	—
19	C₆₄	C₂²×C₄₁	1	1	yes	characteristic
20	C₄₁	D₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
21	D₁₆	—	4	2	no	—
22	C₃₂	D₄×C₄₁	1	1	yes	characteristic
23	D₈	—	8	2	no	—
24	C₁₆	D₈×C₄₁	1	1	yes	characteristic
25	D₄	—	16	2	no	—
26	C₈	D₁₆×C₄₁	1	1	yes	characteristic
27	C₂²	—	32	2	no	—
28	C₄	C₄₁×D₃₂	1	1	yes	characteristic
29	C₂	—	64	2	no	—
30	C₂	C₄₁×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₄₁
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₄×C₄₁ ◁ C₈×C₄₁ ◁ C₁₆×C₄₁ ◁ C₃₂×C₄₁ ◁ C₄₁×C₆₄ ◁ 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.