Subgroups — C₃³×C₄⋊C₄ #88867

Order 432.

364 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄	C₂	1	2	yes	maximal
2	C₂×C₃³×C₄	C₂	1	1	yes	maximal, characteristic
3	C₃²×C₄⋊C₄	C₃	1	13	yes	maximal, direct product factor
4	C₂²×C₃³	C₂²	1	1	yes	characteristic
5	C₃³×C₄	—	2	2	no	—
6	C₃³×C₄	C₄	1	2	yes	complemented
7	C₂×C₃²×C₄	C₂×C₃	1	26	yes	—
8	C₂×C₃²×C₄	C₂×C₃	1	13	yes	—
9	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
10	C₂×C₃³	D₄	1	1	yes	characteristic
11	C₂×C₃³	Q₈	1	1	yes	characteristic
12	C₃×C₄⋊C₄	C₃²	1	13	yes	direct product factor
13	C₂²×C₃²	C₂²×C₃	1	13	yes	—
14	C₃²×C₄	—	2	26	no	—
15	C₃²×C₄	C₃×C₄	1	26	yes	complemented
16	C₃³	C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃×C₄	C₂×C₃²	1	26	yes	—
18	C₂×C₃×C₄	C₂×C₃²	1	13	yes	—
19	C₂×C₃²	C₂×C₃×C₄	1	13	yes	—
20	C₂×C₃²	C₃×D₄	1	13	yes	—
21	C₂×C₃²	C₃×Q₈	1	13	yes	—
22	C₄⋊C₄	C₃³	1	1	yes	characteristic, direct product factor, Sylow
23	C₂²×C₃	C₂²×C₃²	1	13	yes	—
24	C₃×C₄	—	2	26	no	—
25	C₃×C₄	C₃²×C₄	1	26	yes	complemented
26	C₃²	C₃×C₄⋊C₄	1	13	yes	direct product factor
27	C₂×C₄	C₂×C₃³	1	2	yes	—
28	C₂×C₄	C₂×C₃³	1	1	yes	characteristic
29	C₂×C₃	C₂×C₃²×C₄	1	13	yes	—
30	C₂×C₃	C₃²×D₄	1	13	yes	—
31	C₂×C₃	C₃²×Q₈	1	13	yes	—
32	C₂²	C₂²×C₃³	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	C₃³×C₄	1	2	yes	complemented
35	C₃	C₃²×C₄⋊C₄	1	13	yes	direct product factor
36	C₂	C₂×C₃³×C₄	1	1	yes	characteristic
37	C₂	C₃³×D₄	1	1	yes	characteristic
38	C₂	C₃³×Q₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃³	C₂²
commutator	C₂	C₂×C₃³×C₄
Frattini, cosocle	C₂²	C₂²×C₃³
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
3. C₃²×C₄⋊C₄	C₃	direct (N × H)
6. C₃³×C₄	C₄	semidirect
12. C₃×C₄⋊C₄	C₃²	direct (N × H)
15. C₃²×C₄	C₃×C₄	semidirect
16. C₃³	C₄⋊C₄	direct (N × H)
22. C₄⋊C₄	C₃³	direct (N × H)
25. C₃×C₄	C₃²×C₄	semidirect
26. C₃²	C₃×C₄⋊C₄	direct (N × H)
34. C₄	C₃³×C₄	semidirect
35. C₃	C₃²×C₄⋊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
C₂×C₃³×C₄	2
C₃²×C₄⋊C₄	3

Subgroups — C33×C4⋊C4 #88867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₄⋊C₄ #88867