Subgroups — C₃³×SD₃₂ #11722225

Order 864.

364 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃³×D₈	C₂	1	1	yes	maximal, characteristic
3	C₃³×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×SD₃₂	C₃	1	13	yes	maximal, direct product factor
5	C₃³×Q₈	—	2	1	no	—
6	C₃³×D₄	—	2	1	no	—
7	C₃³×C₈	C₂²	1	1	yes	characteristic
8	C₃²×Q₁₆	C₂×C₃	1	13	yes	complemented
9	C₃²×D₈	C₂×C₃	1	13	yes	—
10	C₃²×C₁₆	C₂×C₃	1	13	yes	complemented
11	C₂²×C₃³	—	4	1	no	—
12	C₃³×C₄	—	4	1	no	—
13	C₃³×C₄	D₄	1	1	yes	characteristic
14	C₃×SD₃₂	C₃²	1	13	yes	direct product factor
15	C₃²×Q₈	—	2	13	no	—
16	C₃²×D₄	—	2	13	no	—
17	C₃²×C₈	C₂²×C₃	1	13	yes	—
18	C₂×C₃³	—	8	1	no	—
19	C₂×C₃³	D₈	1	1	yes	characteristic
20	C₃×Q₁₆	C₂×C₃²	1	13	yes	complemented
21	C₃×D₈	C₂×C₃²	1	13	yes	—
22	C₃×C₁₆	C₂×C₃²	1	13	yes	complemented
23	C₂²×C₃²	—	4	13	no	—
24	C₃²×C₄	—	4	13	no	—
25	C₃²×C₄	C₃×D₄	1	13	yes	—
26	SD₃₂	C₃³	1	1	yes	characteristic, direct product factor, Sylow
27	C₃³	SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
28	C₃×Q₈	—	2	13	no	—
29	C₃×D₄	—	2	13	no	—
30	C₃×C₈	C₂²×C₃²	1	13	yes	—
31	C₂×C₃²	—	8	13	no	—
32	C₂×C₃²	C₃×D₈	1	13	yes	—
33	Q₁₆	C₂×C₃³	1	1	yes	characteristic, complemented
34	D₈	C₂×C₃³	1	1	yes	characteristic
35	C₁₆	C₂×C₃³	1	1	yes	characteristic, complemented
36	C₂²×C₃	—	4	13	no	—
37	C₃×C₄	—	4	13	no	—
38	C₃×C₄	C₃²×D₄	1	13	yes	—
39	C₃²	C₃×SD₃₂	1	13	yes	direct product factor
40	Q₈	—	2	1	no	—
41	D₄	—	2	1	no	—
42	C₈	C₂²×C₃³	1	1	yes	characteristic
43	C₂×C₃	—	8	13	no	—
44	C₂×C₃	C₃²×D₈	1	13	yes	—
45	C₂²	—	4	1	no	—
46	C₄	—	4	1	no	—
47	C₄	C₃³×D₄	1	1	yes	characteristic
48	C₃	C₃²×SD₃₂	1	13	yes	direct product factor
49	C₂	—	8	1	no	—
50	C₂	C₃³×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃³	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₃³
prime radical	C₃³×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ C₃³×C₄ ◁ C₃³×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃³×Q₁₆	C₂	semidirect
3. C₃³×C₁₆	C₂	semidirect
4. C₃²×SD₃₂	C₃	direct (N × H)
8. C₃²×Q₁₆	C₂×C₃	semidirect
10. C₃²×C₁₆	C₂×C₃	semidirect
14. C₃×SD₃₂	C₃²	direct (N × H)
20. C₃×Q₁₆	C₂×C₃²	semidirect
22. C₃×C₁₆	C₂×C₃²	semidirect
26. SD₃₂	C₃³	direct (N × H)
27. C₃³	SD₃₂	direct (N × H)
33. Q₁₆	C₂×C₃³	semidirect
35. C₁₆	C₂×C₃³	semidirect
39. C₃²	C₃×SD₃₂	direct (N × H)
48. C₃	C₃²×SD₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×Q₁₆	2
C₃³×D₈	2
C₃³×C₁₆	2
C₃²×SD₃₂	3

Subgroups — C33×SD32 #11722225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×SD₃₂ #11722225