Subgroups — C₁₁×D₁₂₈ #14584744

Order 2816.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₆₄	C₂	1	2	yes	maximal, complemented
2	C₁₁×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₃₂	—	2	2	no	—
4	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
5	C₁₁×D₁₆	—	4	2	no	—
6	C₁₁×C₃₂	D₄	1	1	yes	characteristic
7	D₁₂₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₁₁×D₈	—	8	2	no	—
9	C₁₁×C₁₆	D₈	1	1	yes	characteristic
10	D₆₄	C₂×C₁₁	1	2	yes	complemented
11	C₁₂₈	C₂×C₁₁	1	1	yes	characteristic, complemented
12	D₄×C₁₁	—	16	2	no	—
13	C₈×C₁₁	D₁₆	1	1	yes	characteristic
14	D₃₂	—	2	2	no	—
15	C₆₄	C₂²×C₁₁	1	1	yes	characteristic
16	C₂²×C₁₁	—	32	2	no	—
17	C₄×C₁₁	D₃₂	1	1	yes	characteristic
18	D₁₆	—	4	2	no	—
19	C₃₂	D₄×C₁₁	1	1	yes	characteristic
20	C₂×C₁₁	—	64	2	no	—
21	C₂×C₁₁	D₆₄	1	1	yes	characteristic
22	D₈	—	8	2	no	—
23	C₁₆	C₁₁×D₈	1	1	yes	characteristic
24	C₁₁	D₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
25	D₄	—	16	2	no	—
26	C₈	C₁₁×D₁₆	1	1	yes	characteristic
27	C₂²	—	32	2	no	—
28	C₄	C₁₁×D₃₂	1	1	yes	characteristic
29	C₂	—	64	2	no	—
30	C₂	C₁₁×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₁₁
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₈×C₁₁ ◁ C₁₁×C₁₆ ◁ C₁₁×C₃₂ ◁ C₁₁×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.