Subgroups — C₁₁×SD₃₂ #66919

Order 352.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₁	—	2	1	no	—
5	D₄×C₁₁	—	2	1	no	—
6	C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁	—	4	1	no	—
8	C₄×C₁₁	—	4	1	no	—
9	C₄×C₁₁	D₄	1	1	yes	characteristic
10	SD₃₂	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₁₁	—	8	1	no	—
12	C₂×C₁₁	D₈	1	1	yes	characteristic
13	Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
14	D₈	C₂×C₁₁	1	1	yes	characteristic
15	C₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₁₁	SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
17	Q₈	—	2	1	no	—
18	D₄	—	2	1	no	—
19	C₈	C₂²×C₁₁	1	1	yes	characteristic
20	C₂²	—	4	1	no	—
21	C₄	—	4	1	no	—
22	C₄	D₄×C₁₁	1	1	yes	characteristic
23	C₂	—	8	1	no	—
24	C₂	C₁₁×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₁₁
prime radical	C₁₁×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₈×C₁₁ ◁ 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.