Subgroups — C₃₇⋊C₃×D₁₄₁ #44531076

Order 31302.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₇×C₃₇⋊C₃	—	3	1	no	maximal
3	C₃₇×D₁₄₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃₇×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₄₇×C₃₇⋊C₃	—	2	1	no	—
6	C₄₇×C₃₇⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₃₇×D₄₇	—	3	1	no	Hall
8	C₃₇×C₄₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₁₄₁	—	37	1	no	maximal, Hall
10	D₃×C₃₇⋊C₃	—	47	1	no	maximal, Hall
11	C₃²×C₄₇	—	37	1	no	Hall
12	C₃×C₃₇⋊C₃	D₄₇	1	1	yes	characteristic, complemented, Hall
13	D₁₄₁	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
14	C₃×D₄₇	—	111	1	no	—
15	D₃×C₃₇	—	47	1	no	—
16	C₂×C₃₇⋊C₃	—	141	1	no	—
17	C₃×C₄₇	—	37	1	no	—
18	C₃×C₄₇	—	74	1	no	—
19	C₃×C₄₇	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
20	C₃×C₃₇	C₃×D₄₇	1	1	yes	characteristic, complemented
21	C₃₇⋊C₃	—	2	1	no	—
22	C₃₇⋊C₃	D₁₄₁	1	1	yes	characteristic, direct product factor
23	D₄₇	—	3	1	no	Hall
24	C₂×C₃₇	—	141	1	no	Hall
25	C₄₇	D₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₃₇	C₃×D₁₄₁	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1739	1	no	Hall
28	C₃²	—	37	1	no	Sylow
29	C₂×C₃	—	5217	1	no	—
30	D₃	—	47	1	no	—
31	C₃	—	37	1	no	—
32	C₃	—	74	1	no	—
33	C₃	D₄₇×C₃₇⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	141	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₇×C₄₇	C₂×C₃
LCS	G ▷ C₃×C₃₇×C₄₇
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.