Subgroups — C₃⋊(C₇⋊#11924078) #37590039

Order 24612.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₂₉₃	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#11924078	—	3	1	no	maximal, Hall
3	C₃×C₇×C₂₉₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×D₂₉₃	D₃	1	1	yes	characteristic
5	C₃⋊#11924078	—	7	1	no	maximal, Hall
6	C₇×C₂₉₃	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₃×D₂₉₃	D₇	1	1	yes	characteristic
8	#11924078	—	21	1	no	Hall
9	C₃×C₂₉₃	Dic₇	1	1	yes	characteristic, complemented, Hall
10	D₂₉₃	D₂₁	1	1	yes	characteristic
11	C₂₉₃	Dic₂₁	1	1	yes	characteristic, complemented, Sylow
12	Dic₂₁	—	293	1	no	maximal, Hall
13	C₂×C₃×C₇	—	293	1	no	—
14	Dic₇	—	879	1	no	Hall
15	C₃×C₇	#11924078	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇	—	293	1	no	—
17	Dic₃	—	2051	1	no	Hall
18	C₇	C₃⋊#11924078	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	293	1	no	—
20	C₄	—	6153	1	no	Sylow
21	C₃	C₇⋊#11924078	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	293	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₇×C₂₉₃	C₄
prime radical, cosocle	C₃×C₇×D₂₉₃	C₂
LCS	G ▷ C₃×C₇×C₂₉₃
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.