Subgroups — #66943

Order 352.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₁₁	C₂	1	2	yes	maximal
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	1	yes	characteristic
9	C₂×Dic₁₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₁	C₂²	1	2	yes	—
11	C₂²×C₁₁	C₂³	1	1	yes	characteristic
12	C₄×C₁₁	—	2	2	no	—
13	C₄×C₁₁	Q₈	1	2	yes	—
14	Dic₁₁	—	2	1	no	—
15	Dic₁₁	—	2	1	no	—
16	Dic₁₁	—	2	2	no	—
17	#125	—	11	1	no	maximal, Sylow
18	C₂×C₁₁	C₂×Q₈	1	1	yes	characteristic
19	C₂×C₁₁	#41	1	1	yes	characteristic
20	C₂×C₁₁	#41	1	1	yes	characteristic
21	C₄⋊C₄	—	11	2	no	—
22	C₄⋊C₄	—	11	2	no	—
23	C₄⋊C₄	—	11	1	no	—
24	C₄⋊C₄	D₁₁	1	1	yes	characteristic
25	C₄²	—	11	1	no	—
26	C₁₁	#125	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₄	—	11	1	no	—
28	C₂×C₄	—	11	1	no	—
29	C₂×C₄	—	11	2	no	—
30	C₂×C₄	C₂×D₁₁	1	2	yes	—
31	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
32	C₂²	C₂²×D₁₁	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	—	22	1	no	—
35	C₄	—	22	1	no	—
36	C₄	—	22	2	no	—
37	C₄	Dic₂₂	1	2	yes	—
38	C₂	C₂×Dic₂₂	1	1	yes	characteristic
39	C₂	#4341	1	1	yes	characteristic
40	C₂	#4343	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	#125
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
26. C₁₁	#125	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.