Subgroups — C₃²×D₇×C₂₅₇ #44569221

Order 32382.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₇×C₂₅₇	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₂₅₇	C₂×C₃	1	4	yes	complemented
4	C₂×C₃²×C₂₅₇	—	7	1	no	maximal, Hall
5	D₇×C₂₅₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₂₅₇	D₇	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₂₅₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₂₅₇	—	7	4	no	—
9	C₃×C₂₅₇	C₃×D₇	1	4	yes	direct product factor
10	C₂×C₂₅₇	—	7	1	no	Hall
11	C₂₅₇	C₃²×D₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₃²×D₇	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₇	C₂×C₂₅₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₇	C₃×C₂₅₇	1	4	yes	direct product factor
15	C₃×C₇	C₂×C₃×C₂₅₇	1	4	yes	complemented
16	C₂×C₃²	—	7	1	no	Hall
17	D₇	C₃²×C₂₅₇	1	1	yes	characteristic, direct product factor, Hall
18	C₃²	D₇×C₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₇	C₂×C₃²×C₂₅₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	7	4	no	—
21	C₃	C₃×D₇×C₂₅₇	1	4	yes	direct product factor
22	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₂₅₇	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃²×C₂₅₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₅₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃²×C₂₅₇

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.