Subgroups — C₃²×C₄₇×C₁₁⋊C₅ #37551601

Order 23265.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×C₁₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₁₁×C₄₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₇×C₁₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃²×C₅×C₄₇	—	11	1	no	maximal, Hall
5	C₃×C₁₁×C₄₇	C₃×C₅	1	4	yes	complemented
6	C₃×C₅×C₄₇	—	11	4	no	—
7	C₁₁×C₄₇	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₁₁⋊C₅	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃²×C₄₇	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₄₇	—	11	1	no	Hall
11	C₃×C₁₁⋊C₅	C₃×C₄₇	1	4	yes	direct product factor
12	C₃×C₄₇	C₃×C₁₁⋊C₅	1	4	yes	direct product factor
13	C₃²×C₁₁	C₅×C₄₇	1	1	yes	characteristic, complemented, Hall
14	C₁₁⋊C₅	C₃²×C₄₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄₇	C₃²×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₃²×C₅	—	11	1	no	Hall
17	C₃×C₁₁	C₃×C₅×C₄₇	1	4	yes	complemented
18	C₃×C₅	—	11	4	no	—
19	C₁₁	C₃²×C₅×C₄₇	1	1	yes	characteristic, complemented, Sylow
20	C₃²	C₄₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	—	11	1	no	Sylow
22	C₃	C₃×C₄₇×C₁₁⋊C₅	1	4	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃²×C₄₇	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₃²×C₅×C₄₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₄₇	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃²×C₄₇

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.