Subgroups — #21463225⋊C₃ #37555207

Order 23532.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃⋊(D₃₇⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	#21463225	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅₃×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₉₆₁	C₂×C₃	1	1	yes	characteristic
5	C₃₇×C₅₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#6157	—	37	1	no	maximal, Hall
7	#3866⋊C₃	—	53	1	no	maximal, Hall
8	C₃×D₅₃	—	37	1	no	—
9	D₃₇⋊C₃	—	53	1	no	—
10	#6157	—	37	1	no	Hall
11	C₃×C₅₃	—	148	1	no	Hall
12	#3866	—	53	1	no	Hall
13	C₃₇⋊C₃	#6157	1	1	yes	characteristic, complemented, Hall
14	D₅₃	—	37	1	no	—
15	D₃₇	—	53	1	no	—
16	C₅₃	#3866⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	C₃×#6157	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1961	1	no	Hall
19	C₂×C₃	—	1961	1	no	—
20	C₄	—	1961	1	no	Sylow
21	C₃	—	148	1	no	Sylow
22	C₂	—	1961	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃₇×C₅₃	C₃×C₄
prime radical	C₅₃⋊(D₃₇⋊C₃)	C₂
cosocle	D₁₉₆₁	C₂×C₃
LCS	G ▷ C₃₇×C₅₃
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.