Subgroups — #34038405

Order 18876.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22628078	C₂	1	1	yes	maximal, characteristic
2	#20262573	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊(C₁₁²⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁⋊D₁₄₃	C₂×C₃	1	1	yes	characteristic
5	C₁₁²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#92150⋊C₃	—	13	1	no	maximal, Hall
7	(C₁₁⋊D₁₁)⋊C₃	—	13	1	no	—
8	#92150	—	13	1	no	Hall
9	C₁₁²⋊C₃	—	13	1	no	Hall
10	D₁₄₃	—	66	2	no	—
11	C₁₁⋊D₁₁	—	13	1	no	—
12	AGL(1,𝔽₁₃)	—	121	1	no	maximal, Hall
13	C₁₁×C₁₃	—	6	2	no	—
14	C₁₁²	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
15	D₁₃⋊C₃	—	121	1	no	—
16	#261	—	121	1	no	Hall
17	C₁₃⋊C₃	—	484	1	no	Hall
18	D₁₃	—	121	1	no	—
19	D₁₁	—	858	2	no	—
20	C₁₃	#92150⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₄	—	1573	1	no	Hall
22	C₁₁	—	6	2	no	—
23	C₂×C₃	—	1573	1	no	—
24	C₄	—	1573	1	no	Sylow
25	C₃	—	6292	1	no	Sylow
26	C₂	—	1573	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁²×C₁₃	C₃×C₄
prime radical	#22628078	C₂
cosocle	C₁₁⋊D₁₄₃	C₂×C₃
LCS	G ▷ C₁₁²×C₁₃
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.