Subgroups — C₃³×C₂²⋊C₄ #88866

Order 432.

476 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×C₄	C₂	1	2	yes	maximal, complemented
3	C₃²×C₂²⋊C₄	C₃	1	13	yes	maximal, direct product factor
4	C₂²×C₃³	—	2	2	no	—
5	C₂²×C₃³	C₄	1	2	yes	complemented
6	C₂²×C₃³	C₂²	1	1	yes	characteristic
7	C₃³×C₄	—	2	2	no	—
8	C₂³×C₃²	C₂×C₃	1	13	yes	—
9	C₂×C₃²×C₄	C₂×C₃	1	26	yes	complemented
10	C₂×C₃³	—	2	2	no	—
11	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃³	D₄	1	2	yes	—
13	C₃×C₂²⋊C₄	C₃²	1	13	yes	direct product factor
14	C₂²×C₃²	—	2	26	no	—
15	C₂²×C₃²	C₃×C₄	1	26	yes	complemented
16	C₂²×C₃²	C₂²×C₃	1	13	yes	—
17	C₃²×C₄	—	2	26	no	—
18	C₃³	C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
19	C₂³×C₃	C₂×C₃²	1	13	yes	—
20	C₂×C₃×C₄	C₂×C₃²	1	26	yes	complemented
21	C₂×C₃²	—	2	26	no	—
22	C₂×C₃²	C₂×C₃×C₄	1	13	yes	—
23	C₂×C₃²	C₃×D₄	1	26	yes	—
24	C₂²⋊C₄	C₃³	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃	—	2	26	no	—
26	C₂²×C₃	C₃²×C₄	1	26	yes	complemented
27	C₂²×C₃	C₂²×C₃²	1	13	yes	—
28	C₃×C₄	—	2	26	no	—
29	C₃²	C₃×C₂²⋊C₄	1	13	yes	direct product factor
30	C₂³	C₂×C₃³	1	1	yes	characteristic
31	C₂×C₄	C₂×C₃³	1	2	yes	complemented
32	C₂×C₃	—	2	26	no	—
33	C₂×C₃	C₂×C₃²×C₄	1	13	yes	—
34	C₂×C₃	C₃²×D₄	1	26	yes	—
35	C₂²	—	2	2	no	—
36	C₂²	C₃³×C₄	1	2	yes	complemented
37	C₂²	C₂²×C₃³	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₃	C₃²×C₂²⋊C₄	1	13	yes	direct product factor
40	C₂	—	2	2	no	—
41	C₂	C₂×C₃³×C₄	1	1	yes	characteristic
42	C₂	C₃³×D₄	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃³	C₂²
commutator	C₂	C₂×C₃³×C₄
Frattini, cosocle	C₂²	C₂²×C₃³
prime radical	C₂³×C₃³	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃³ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₃³×C₄	C₂	semidirect
3. C₃²×C₂²⋊C₄	C₃	direct (N × H)
5. C₂²×C₃³	C₄	semidirect
9. C₂×C₃²×C₄	C₂×C₃	semidirect
13. C₃×C₂²⋊C₄	C₃²	direct (N × H)
15. C₂²×C₃²	C₃×C₄	semidirect
18. C₃³	C₂²⋊C₄	direct (N × H)
20. C₂×C₃×C₄	C₂×C₃²	semidirect
24. C₂²⋊C₄	C₃³	direct (N × H)
26. C₂²×C₃	C₃²×C₄	semidirect
29. C₃²	C₃×C₂²⋊C₄	direct (N × H)
31. C₂×C₄	C₂×C₃³	semidirect
36. C₂²	C₃³×C₄	semidirect
39. C₃	C₃²×C₂²⋊C₄	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃³	2
C₂×C₃³×C₄	2
C₃²×C₂²⋊C₄	3

Subgroups — C33×C22⋊C4 #88866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₂²⋊C₄ #88866