Subgroups — C₃×C₃⋊(C₃⋊D₂₁) #11765821

Order 1134.

380 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₃⋊D₂₁)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₃⋊D₂₁	—	3	13	no	maximal
4	C₃³×C₇	—	2	13	no	—
5	C₃³×C₇	D₃	1	13	yes	complemented
6	C₃³×C₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×C₃⋊(C₃⋊D₃)	—	7	1	no	maximal, Hall
8	C₃⋊D₂₁	—	3	13	no	—
9	C₃×D₂₁	—	9	13	no	—
10	C₃⁴	D₇	1	1	yes	characteristic, complemented, Sylow
11	C₃²×C₇	—	2	52	no	—
12	C₃²×C₇	C₃×D₃	1	13	yes	complemented
13	C₃²×C₇	C₃⋊D₃	1	13	yes	complemented
14	C₃⋊(C₃⋊D₃)	—	7	1	no	—
15	C₃×C₃⋊D₃	—	21	13	no	—
16	D₂₁	—	9	13	no	—
17	C₃×D₇	—	27	1	no	—
18	C₃³	—	2	13	no	—
19	C₃³	C₃×D₇	1	1	yes	characteristic, complemented
20	C₃³	D₂₁	1	13	yes	complemented
21	C₃×C₇	—	2	13	no	—
22	C₃×C₇	C₃×C₃⋊D₃	1	13	yes	complemented
23	C₃×C₇	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
24	C₃⋊D₃	—	21	13	no	—
25	C₃×D₃	—	63	13	no	—
26	D₇	—	27	1	no	Hall
27	C₃²	—	2	52	no	—
28	C₃²	C₃×D₂₁	1	13	yes	complemented
29	C₃²	C₃⋊D₂₁	1	13	yes	complemented
30	C₇	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	189	1	no	—
32	D₃	—	63	13	no	—
33	C₃	—	2	13	no	—
34	C₃	C₃×C₃⋊D₂₁	1	13	yes	complemented
35	C₃	C₃⋊(C₃⋊D₂₁)	1	1	yes	characteristic, direct product factor
36	C₂	—	189	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₃⋊D₂₁)
commutator, cosocle, hypocenter	C₃³×C₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃⁴×C₇	C₂
LCS	G ▷ C₃³×C₇
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.