Subgroups — #66922

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	C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₁	C₂	1	4	yes	maximal
4	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₁	C₂²	1	2	yes	—
6	C₂×Dic₁₁	C₂²	1	4	yes	—
7	Dic₂₂	—	2	4	no	—
8	C₂²×C₁₁	C₂³	1	1	yes	characteristic
9	C₄×C₁₁	D₄	1	2	yes	—
10	C₄×C₁₁	Q₈	1	4	yes	complemented
11	Dic₁₁	—	2	4	no	—
12	C₄⋊Q₈	—	11	1	no	maximal, Sylow
13	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
14	C₂×C₁₁	C₂×Q₈	1	2	yes	—
15	C₂×Q₈	—	11	2	no	—
16	C₄⋊C₄	—	11	4	no	—
17	C₄²	D₁₁	1	1	yes	characteristic
18	C₁₁	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
19	Q₈	—	22	4	no	—
20	C₂×C₄	—	11	4	no	—
21	C₂×C₄	C₂×D₁₁	1	2	yes	—
22	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
23	C₂²	C₂²×D₁₁	1	1	yes	characteristic
24	C₄	—	22	4	no	—
25	C₄	Dic₂₂	1	4	yes	complemented
26	C₄	D₄₄	1	2	yes	—
27	C₂	C₂×Dic₂₂	1	2	yes	—
28	C₂	C₂×D₄₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₁
commutator, socle, prime radical, cosocle	C₂²×C₁₁	C₂³
Fitting	C₄²×C₁₁	C₂
hypercenter	C₄²	D₁₁
hypocenter	C₁₁	C₄⋊Q₈
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄²

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.