Subgroups — #66941

Order 352.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₂	C₂	1	2	yes	maximal
2	C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	Dic₁₁⋊C₄	C₂	1	2	yes	maximal
5	C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₁	C₂²	1	2	yes	—
9	C₂×Dic₁₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₁	C₂²	1	1	yes	characteristic
11	Dic₂₂	—	2	4	no	—
12	C₂²×C₁₁	C₂³	1	1	yes	characteristic
13	C₄×C₁₁	—	2	2	no	—
14	C₄×C₁₁	Q₈	1	2	yes	complemented
15	Dic₁₁	—	2	2	no	—
16	Dic₁₁	D₄	1	2	yes	—
17	Dic₁₁	Q₈	1	2	yes	complemented
18	C₄⋊Q₈	—	11	1	no	maximal, Sylow
19	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
20	C₂×C₁₁	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₁₁	C₂×Q₈	1	1	yes	characteristic
22	C₂×Q₈	—	11	2	no	—
23	C₄⋊C₄	—	11	2	no	—
24	C₄⋊C₄	—	11	1	no	—
25	C₄⋊C₄	D₁₁	1	1	yes	characteristic
26	C₄²	—	11	1	no	—
27	C₁₁	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	22	4	no	—
29	C₂×C₄	—	11	1	no	—
30	C₂×C₄	—	11	1	no	—
31	C₂×C₄	—	11	2	no	—
32	C₂×C₄	C₂×D₁₁	1	2	yes	—
33	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
34	C₂²	C₂²×D₁₁	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	11	2	no	—
37	C₄	—	11	2	no	—
38	C₄	—	22	2	no	—
39	C₄	Dic₂₂	1	2	yes	complemented
40	C₂	C₂×Dic₂₂	1	1	yes	characteristic
41	C₂	D₄×D₁₁	1	1	yes	characteristic
42	C₂	Q₈×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₁
commutator, socle, prime radical, cosocle	C₂²×C₁₁	C₂³
Fitting	C₁₁×C₄⋊C₄	C₂
hypercenter	C₄⋊C₄	D₁₁
hypocenter	C₁₁	C₄⋊Q₈
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

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.