Subgroups — C₃²×D₁₃₃₃ #37562056

Order 23994.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₃₃₃	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₃₁×C₄₃	C₂×C₃	1	4	yes	complemented
4	D₁₃₃₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₃₁×C₄₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃²×D₄₃	—	31	1	no	maximal, Hall
7	C₃²×D₃₁	—	43	1	no	maximal, Hall
8	C₃²×C₄₃	D₃₁	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₃₁	D₄₃	1	1	yes	characteristic, complemented, Hall
10	C₃×D₄₃	—	31	4	no	—
11	C₃×D₃₁	—	43	4	no	—
12	C₃×C₄₃	C₃×D₃₁	1	4	yes	complemented
13	C₃×C₃₁	C₃×D₄₃	1	4	yes	complemented
14	D₄₃	—	31	1	no	Hall
15	D₃₁	—	43	1	no	Hall
16	C₄₃	C₃²×D₃₁	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	C₃²×D₄₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃²	—	1333	1	no	Hall
19	C₃²	D₁₃₃₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	1333	4	no	—
21	C₃	C₃×D₁₃₃₃	1	4	yes	direct product factor
22	C₂	—	1333	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₁₃₃₃
commutator, cosocle, hypocenter	C₃₁×C₄₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₃₁×C₄₃	C₂
LCS	G ▷ C₃₁×C₄₃
UCS	C₁ ◁ C₃²

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.