Subgroups — C₁₁⋊#14555575 #37563528

Order 24156.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃⋊D₃×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₁×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₁×C₆₁	—	6	2	no	—
4	Dic₆₇₁	—	9	1	no	maximal, Hall
5	#14555575	—	11	1	no	maximal, Hall
6	C₃×C₁₁×C₆₁	—	2	2	no	—
7	C₂×C₁₁×C₆₁	—	9	1	no	—
8	C₃⋊D₃×C₆₁	D₁₁	1	1	yes	characteristic
9	C₁₁×C₆₁	#157	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₆₁	Dic₁₁	1	1	yes	characteristic, complemented, Hall
11	C₁₁⋊#157	—	61	1	no	maximal, Hall
12	D₃×C₆₁	—	6	2	no	—
13	Dic₆₁	—	99	1	no	Hall
14	C₁₁×C₃⋊D₃	D₆₁	1	1	yes	characteristic
15	C₃×C₆₁	—	2	2	no	—
16	C₂×C₆₁	—	9	1	no	—
17	C₃²×C₁₁	Dic₆₁	1	1	yes	characteristic, complemented, Hall
18	D₃×C₁₁	—	6	2	no	—
19	C₆₁	C₁₁⋊#157	1	1	yes	characteristic, complemented, Sylow
20	Dic₁₁	—	549	1	no	Hall
21	#157	—	671	1	no	Hall
22	C₃×C₁₁	—	2	2	no	—
23	C₂×C₁₁	—	9	1	no	—
24	C₃⋊D₃	D₆₇₁	1	1	yes	characteristic
25	C₁₁	#14555575	1	1	yes	characteristic, complemented, Sylow
26	C₃²	Dic₆₇₁	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	6039	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₁×C₆₁	C₄
prime radical, cosocle	C₁₁×C₃⋊D₃×C₆₁	C₂
LCS	G ▷ C₃²×C₁₁×C₆₁
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.