Subgroups — C₃⋊(C₄₁⋊(D₃₁⋊C₃)) #37504263

Order 22878.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁⋊(D₃₁⋊C₃)	—	3	1	no	maximal
3	D₃₈₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃₁×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
5	C₄₁×C₃₁⋊C₃	—	2	1	no	—
6	C₄₁×C₃₁⋊C₃	D₃	1	1	yes	characteristic, complemented
7	D₁₂₇₁	—	3	1	no	Hall
8	C₃₁×C₄₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₁₂₃	—	31	1	no	maximal, Hall
10	C₃⋊(D₃₁⋊C₃)	—	41	1	no	maximal, Hall
11	C₃²×C₄₁	—	62	1	no	Hall
12	C₃×C₃₁⋊C₃	D₄₁	1	1	yes	characteristic, complemented, Hall
13	D₁₂₃	—	31	1	no	—
14	C₃×D₄₁	—	93	1	no	—
15	D₉₃	—	41	1	no	—
16	D₃₁⋊C₃	—	123	1	no	—
17	C₃×C₄₁	—	62	1	no	—
18	C₃×C₄₁	—	62	1	no	—
19	C₃×C₄₁	D₃₁⋊C₃	1	1	yes	characteristic, complemented
20	C₃×C₃₁	C₃×D₄₁	1	1	yes	characteristic, complemented
21	C₃₁⋊C₃	—	2	1	no	—
22	C₃₁⋊C₃	D₁₂₃	1	1	yes	characteristic, complemented
23	D₄₁	—	93	1	no	Hall
24	D₃₁	—	123	1	no	Hall
25	C₄₁	C₃⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
26	C₃₁	C₃×D₁₂₃	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1271	1	no	Hall
28	C₃²	—	62	1	no	Sylow
29	C₂×C₃	—	3813	1	no	—
30	D₃	—	1271	1	no	—
31	C₃	—	62	1	no	—
32	C₃	—	62	1	no	—
33	C₃	C₄₁⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented
34	C₂	—	3813	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₄₁	C₂×C₃
LCS	G ▷ C₃×C₃₁×C₄₁
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.