Subgroups — C₃₇⋊C₃×Dic₄₇ #35229365

Order 20868.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃₇×Dic₄₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₇×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×C₄₇	C₂×C₃	1	1	yes	characteristic
5	C₃₇×C₄₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₄₇	—	37	1	no	maximal, Hall
7	C₄×C₃₇⋊C₃	—	47	1	no	maximal, Hall
8	C₂×C₃×C₄₇	—	37	1	no	—
9	C₂×C₃₇⋊C₃	D₄₇	1	1	yes	characteristic
10	Dic₄₇	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₄×C₃₇	—	47	1	no	Hall
12	C₃×C₄₇	—	37	1	no	Hall
13	C₃₇⋊C₃	Dic₄₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₄₇	C₂×C₃₇⋊C₃	1	1	yes	characteristic
15	C₂×C₃₇	C₃×D₄₇	1	1	yes	characteristic
16	C₄₇	C₄×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	C₃×Dic₄₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1739	1	no	Hall
19	C₂×C₃	—	37	1	no	—
20	C₄	—	47	1	no	Sylow
21	C₃	—	37	1	no	Sylow
22	C₂	D₄₇×C₃₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₄₇×C₃₇⋊C₃
commutator, hypocenter	C₃₇×C₄₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₃₇×C₄₇	C₂×C₃
prime radical	C₂×C₄₇×C₃₇⋊C₃	C₂
LCS	G ▷ C₃₇×C₄₇
UCS	C₁ ◁ C₂

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.