Subgroups — D₁₁² #92151

Order 484.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₁₁	C₂	1	2	yes	maximal, complemented
3	C₁₁²	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂×D₁₁	—	11	2	no	maximal
5	C₂×C₁₁	—	11	2	no	—
6	D₁₁	—	11	2	no	—
7	D₁₁	—	22	5	no	—
8	D₁₁	D₁₁	1	2	yes	direct product factor
9	C₁₁	—	2	5	no	—
10	C₁₁	C₂×D₁₁	1	2	yes	complemented
11	C₂²	—	121	1	no	Sylow
12	C₂	—	11	2	no	—
13	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²	C₂²
LCS	G ▷ C₁₁²
UCS	C₁

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.