Subgroups — C₂₉×C₃⋊D₉₃ #30633659

Order 16182.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₉₃	—	3	4	no	maximal
3	C₃×C₂₉×C₃₁	D₃	1	4	yes	complemented
4	C₂₉×D₃₁	—	9	1	no	Hall
5	C₂₉×C₃₁	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₉₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃⋊D₃×C₂₉	—	31	1	no	maximal, Hall
8	C₃²×C₃₁	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₂₉	D₃₁	1	1	yes	characteristic, complemented, Hall
10	D₉₃	—	3	4	no	—
11	D₃×C₂₉	—	93	4	no	—
12	C₃×C₃₁	D₃×C₂₉	1	4	yes	complemented
13	C₃×C₂₉	D₉₃	1	4	yes	complemented
14	D₃₁	—	9	1	no	Hall
15	C₂×C₂₉	—	279	1	no	Hall
16	C₃₁	C₃⋊D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	C₃⋊D₉₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₃⋊D₃	—	31	1	no	Hall
19	C₃²	C₂₉×D₃₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	93	4	no	—
21	C₃	C₂₉×D₉₃	1	4	yes	complemented
22	C₂	—	279	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	C₃⋊D₉₃
commutator, cosocle, hypocenter	C₃²×C₃₁	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₂₉×C₃₁	C₂
LCS	G ▷ C₃²×C₃₁
UCS	C₁ ◁ C₂₉

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.