Subgroups — C₃×C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃))) #13091722

Order 1458.

36308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁶	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	—	3	121	no	maximal
4	C₃⁵	—	2	121	no	—
5	C₃⁵	D₃	1	121	yes	complemented
6	C₃⁵	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃⋊(C₃⋊(C₃⋊D₃))	—	3	121	no	—
8	C₃×C₃⋊(C₃⋊D₃)	—	9	1210	no	—
9	C₃⁴	—	2	4840	no	—
10	C₃⁴	C₃×D₃	1	121	yes	complemented
11	C₃⁴	C₃⋊D₃	1	1210	yes	complemented
12	C₃⋊(C₃⋊D₃)	—	9	1210	no	—
13	C₃×C₃⋊D₃	—	27	1210	no	—
14	C₃³	—	2	15730	no	—
15	C₃³	C₃×C₃⋊D₃	1	1210	yes	complemented
16	C₃³	C₃⋊(C₃⋊D₃)	1	1210	yes	complemented
17	C₃⋊D₃	—	27	1210	no	—
18	C₃×D₃	—	81	121	no	—
19	C₃²	—	2	4840	no	—
20	C₃²	C₃×C₃⋊(C₃⋊D₃)	1	1210	yes	complemented
21	C₃²	C₃⋊(C₃⋊(C₃⋊D₃))	1	121	yes	complemented
22	C₂×C₃	—	243	1	no	—
23	D₃	—	81	121	no	—
24	C₃	—	2	121	no	—
25	C₃	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	1	121	yes	complemented
26	C₃	C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))	1	1	yes	characteristic, direct product factor
27	C₂	—	243	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₃⋊(C₃⋊(C₃⋊D₃)))
commutator, cosocle, hypocenter	C₃⁵	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃⁶	C₂
LCS	G ▷ C₃⁵
UCS	C₁ ◁ C₃

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.