Subgroups — C₂²×C₁₇×C₁₈₁⋊C₃ #49147377

Order 36924.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₁₈₁⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₇×C₁₈₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₁₈₁⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₇×C₁₈₁	C₂×C₃	1	3	yes	complemented
5	C₁₇×C₁₈₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₁₈₁⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₈₁⋊C₃	C₂×C₁₇	1	3	yes	direct product factor
8	C₂²×C₁₈₁	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₈₁⋊C₃	C₂²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₈₁	C₂×C₃×C₁₇	1	3	yes	complemented
11	C₂²×C₃×C₁₇	—	181	1	no	maximal, Hall
12	C₁₈₁	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₇	—	181	3	no	—
14	C₂²×C₁₇	C₁₈₁⋊C₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₇	—	181	1	no	Hall
16	C₂×C₁₇	C₂×C₁₈₁⋊C₃	1	3	yes	direct product factor
17	C₁₇	C₂²×C₁₈₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₃	—	181	1	no	Hall
19	C₂×C₃	—	181	3	no	—
20	C₂²	C₁₇×C₁₈₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	181	1	no	Sylow
22	C₂	C₂×C₁₇×C₁₈₁⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₁₇	C₁₈₁⋊C₃
commutator, cosocle, hypocenter	C₁₈₁	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂²×C₁₇×C₁₈₁	C₃
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₂²×C₁₇

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.