Subgroups — C₃×D₃₇₃₁ #36375591

Order 22386.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₇₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₅₃₃	—	7	1	no	maximal, Hall
5	C₃×D₂₈₇	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₄₁	D₇	1	1	yes	characteristic, complemented, Hall
7	D₅₃₃	—	7	1	no	Hall
8	C₃×C₇×C₄₁	D₁₃	1	1	yes	characteristic, complemented, Hall
9	D₂₈₇	—	13	1	no	Hall
10	C₃×D₉₁	—	41	1	no	maximal, Hall
11	C₁₃×C₄₁	C₃×D₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₄₁	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₇×C₁₃	D₄₁	1	1	yes	characteristic, complemented, Hall
14	C₃×D₄₁	—	91	1	no	Hall
15	D₉₁	—	41	1	no	Hall
16	C₃×C₄₁	D₉₁	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₃	C₃×D₄₁	1	1	yes	characteristic, complemented, Hall
18	D₄₁	—	91	1	no	Hall
19	C₃×D₁₃	—	287	1	no	Hall
20	C₃×D₇	—	533	1	no	Hall
21	C₄₁	C₃×D₉₁	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₃	D₂₈₇	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	287	1	no	Hall
24	C₃×C₇	D₅₃₃	1	1	yes	characteristic, complemented, Hall
25	D₇	—	533	1	no	Hall
26	C₁₃	C₃×D₂₈₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₅₃₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	3731	1	no	Hall
29	C₃	D₃₇₃₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	3731	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃₇₃₁
commutator, cosocle, hypocenter	C₇×C₁₃×C₄₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₄₁	C₂
LCS	G ▷ C₇×C₁₃×C₄₁
UCS	C₁ ◁ C₃

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.