Subgroups — #37590607

Order 24684.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×(C₁₁⋊D₁₁)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#22551741	—	3	1	no	maximal, Hall
3	C₁₇×C₁₁²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic
5	C₁₁²×C₁₇	Dic₃	1	1	yes	characteristic, complemented, Hall
6	#13089721	—	17	1	no	maximal, Hall
7	(C₁₁⋊D₁₁)⋊C₃	D₁₇	1	1	yes	characteristic
8	#92150	—	51	1	no	Hall
9	C₁₇×D₁₁	—	66	2	no	—
10	C₁₁²⋊C₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
11	C₁₁⋊D₁₁	D₅₁	1	1	yes	characteristic
12	Dic₅₁	—	121	1	no	maximal, Hall
13	C₁₁×C₁₇	—	6	2	no	—
14	C₁₁²	Dic₅₁	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃×C₁₇	—	121	1	no	—
16	Dic₁₇	—	363	1	no	Hall
17	C₃×C₁₇	—	484	1	no	Hall
18	C₂×C₁₇	—	121	1	no	—
19	D₁₁	—	66	2	no	—
20	C₁₇	#13089721	1	1	yes	characteristic, complemented, Sylow
21	Dic₃	—	2057	1	no	Hall
22	C₁₁	—	6	2	no	—
23	C₂×C₃	—	121	1	no	—
24	C₄	—	6171	1	no	Sylow
25	C₃	—	484	1	no	Sylow
26	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₁₇×C₁₁²⋊C₃	C₄
Fitting, socle	C₁₁²×C₁₇	Dic₃
prime radical, cosocle	C₁₇×(C₁₁⋊D₁₁)⋊C₃	C₂
LCS	G ▷ C₁₇×C₁₁²⋊C₃
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.