Subgroups — C₃⋊#22547870 #37562037

Order 23994.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16860688	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#22547870	—	3	1	no	maximal
3	D₃₉₉₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#16860688	—	2	1	no	—
6	#16860688	D₃	1	1	yes	characteristic, complemented
7	D₁₃₃₃	—	3	1	no	Hall
8	C₃₁×C₄₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊(D₄₃⋊C₃)	—	31	1	no	maximal, Hall
10	C₃⋊(D₃₁⋊C₃)	—	43	1	no	maximal, Hall
11	C₃×C₄₃⋊C₃	—	31	1	no	Hall
12	C₃×C₃₁⋊C₃	—	43	1	no	Hall
13	D₁₂₉	—	31	1	no	—
14	D₄₃⋊C₃	—	93	1	no	—
15	D₉₃	—	43	1	no	—
16	D₃₁⋊C₃	—	129	1	no	—
17	C₃×C₄₃	D₃₁⋊C₃	1	1	yes	characteristic, complemented
18	C₄₃⋊C₃	—	31	1	no	—
19	C₄₃⋊C₃	—	62	1	no	—
20	C₃×C₃₁	D₄₃⋊C₃	1	1	yes	characteristic, complemented
21	C₃₁⋊C₃	—	43	1	no	—
22	C₃₁⋊C₃	—	86	1	no	—
23	D₄₃	—	93	1	no	Hall
24	D₃₁	—	129	1	no	Hall
25	C₄₃	C₃⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
26	C₃₁	C₃⋊(D₄₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1333	1	no	Hall
28	C₃²	—	1333	1	no	Sylow
29	C₂×C₃	—	3999	1	no	—
30	D₃	—	1333	1	no	—
31	C₃	—	1333	1	no	—
32	C₃	—	2666	1	no	—
33	C₃	#22547870	1	1	yes	characteristic, complemented
34	C₂	—	3999	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₄₃	C₂×C₃
LCS	G ▷ C₃×C₃₁×C₄₃
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.