Subgroups — C₃⋊D₃₇₂₃ #36375262

Order 22338.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₇₂₃	—	3	4	no	maximal
3	C₃×C₁₇×C₇₃	D₃	1	4	yes	complemented
4	D₁₂₄₁	—	9	1	no	Hall
5	C₃⋊D₂₁₉	—	17	1	no	maximal, Hall
6	C₁₇×C₇₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₇₃	D₁₇	1	1	yes	characteristic, complemented, Hall
8	D₂₁₉	—	51	4	no	—
9	C₃⋊D₅₁	—	73	1	no	maximal, Hall
10	C₃×C₇₃	D₅₁	1	4	yes	complemented
11	C₃²×C₁₇	D₇₃	1	1	yes	characteristic, complemented, Hall
12	D₇₃	—	153	1	no	Hall
13	D₅₁	—	219	4	no	—
14	C₇₃	C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₇	D₂₁₉	1	4	yes	complemented
16	D₁₇	—	657	1	no	Hall
17	C₃⋊D₃	—	1241	1	no	Hall
18	C₁₇	C₃⋊D₂₁₉	1	1	yes	characteristic, complemented, Sylow
19	C₃²	D₁₂₄₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	3723	4	no	—
21	C₃	D₃₇₂₃	1	4	yes	complemented
22	C₂	—	11169	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₇×C₇₃	C₂
LCS	G ▷ C₃²×C₁₇×C₇₃
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.