Subgroups — C₃²×C₈²⋊C₃ #13145746

Order 1728.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₈²	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₈²⋊C₃	C₃	1	12	yes	maximal, direct product factor
3	C₃²×C₄²⋊C₃	—	4	1	no	maximal
4	C₃²×C₄×C₈	—	3	1	no	—
5	C₃×C₈²	C₃²	1	4	yes	complemented
6	C₈²⋊C₃	C₃²	1	9	yes	direct product factor
7	C₂×C₃²×C₈	—	3	2	no	—
8	C₃²×C₄²	A₄	1	1	yes	characteristic
9	C₃×C₄²⋊C₃	—	4	12	no	—
10	C₃²×A₄	—	16	1	no	—
11	C₃×C₄×C₈	—	3	4	no	—
12	C₂×C₃²×C₄	—	3	1	no	—
13	C₃²×C₈	—	3	4	no	—
14	C₈²	C₃³	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃×C₈	—	3	8	no	—
16	C₃×C₄²	C₃×A₄	1	4	yes	—
17	C₄²⋊C₃	—	4	9	no	—
18	C₂²×C₃²	C₄²⋊C₃	1	1	yes	characteristic
19	C₃×A₄	—	16	12	no	—
20	C₃²×C₄	—	3	2	no	—
21	C₄×C₈	—	3	1	no	—
22	C₃³	—	64	1	no	Sylow
23	C₂×C₃×C₄	—	3	4	no	—
24	C₃×C₈	—	3	16	no	—
25	C₂×C₃²	—	3	1	no	—
26	C₂×C₈	—	3	2	no	—
27	C₄²	C₃²×A₄	1	1	yes	characteristic
28	C₂²×C₃	C₃×C₄²⋊C₃	1	4	yes	—
29	A₄	—	16	9	no	—
30	C₃×C₄	—	3	8	no	—
31	C₃²	—	64	12	no	—
32	C₃²	C₈²⋊C₃	1	1	yes	characteristic, direct product factor
33	C₂×C₄	—	3	1	no	—
34	C₈	—	3	4	no	—
35	C₂×C₃	—	3	4	no	—
36	C₂²	C₃²×C₄²⋊C₃	1	1	yes	characteristic
37	C₄	—	3	2	no	—
38	C₃	—	64	9	no	—
39	C₃	C₃×C₈²⋊C₃	1	4	yes	direct product factor
40	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	C₈²⋊C₃
commutator, cosocle, hypocenter	C₈²	C₃³
Frattini	C₄²	C₃²×A₄
Fitting	C₃²×C₈²	C₃
socle	C₂²×C₃²	C₄²⋊C₃
LCS	G ▷ C₈²
UCS	C₁ ◁ C₃²

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.