Subgroups — C₈₉×C₁₁²⋊C₃ #44568161

Order 32307.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₈₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₈₉	—	3	4	no	—
3	C₁₁²⋊C₃	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₈₉	—	121	1	no	maximal, Hall
5	C₁₁²	C₃×C₈₉	1	1	yes	characteristic, complemented, Sylow
6	C₈₉	C₁₁²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
7	C₁₁	—	3	4	no	—
8	C₃	—	121	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₈₉	C₁₁²⋊C₃
commutator, cosocle, hypocenter	C₁₁²	C₃×C₈₉
Frattini	C₁	G
Fitting, socle	C₁₁²×C₈₉	C₃
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₈₉

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.