Subgroups — C₂×C₃×D₃₂ #72974

Order 384.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₃×D₃₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×D₈	—	2	2	no	—
6	C₃×D₁₆	—	2	2	no	—
7	C₃×D₁₆	C₂²	1	4	yes	complemented
8	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₃×C₃₂	C₂²	1	2	yes	complemented
10	C₂×D₁₆	C₂×C₃	1	2	yes	complemented
11	D₃₂	C₂×C₃	1	4	yes	direct product factor
12	C₂×C₃₂	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₃×D₄	—	4	2	no	—
14	C₃×D₈	—	2	4	no	—
15	C₃×D₈	—	4	2	no	—
16	C₂×C₃×C₈	D₄	1	1	yes	characteristic
17	C₃×C₁₆	D₄	1	1	yes	characteristic
18	C₃×C₁₆	C₂³	1	1	yes	characteristic
19	C₂×D₈	—	2	2	no	—
20	D₁₆	—	2	2	no	—
21	D₁₆	C₂²×C₃	1	4	yes	complemented
22	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
23	C₃₂	C₂²×C₃	1	2	yes	complemented
24	C₂³×C₃	—	8	2	no	—
25	C₃×D₄	—	4	4	no	—
26	C₃×D₄	—	8	2	no	—
27	C₂×C₃×C₄	D₈	1	1	yes	characteristic
28	C₃×C₈	D₈	1	1	yes	characteristic
29	C₃×C₈	C₂×D₄	1	1	yes	characteristic
30	C₂×D₄	—	4	2	no	—
31	D₈	—	2	4	no	—
32	D₈	—	4	2	no	—
33	C₂×C₈	C₃×D₄	1	1	yes	characteristic
34	C₁₆	C₃×D₄	1	1	yes	characteristic
35	C₁₆	C₂³×C₃	1	1	yes	characteristic
36	C₂²×C₃	—	8	4	no	—
37	C₂²×C₃	—	16	4	no	—
38	C₂²×C₃	D₁₆	1	1	yes	characteristic
39	C₃×C₄	D₁₆	1	1	yes	characteristic
40	C₃×C₄	C₂×D₈	1	1	yes	characteristic
41	C₂³	—	8	2	no	—
42	D₄	—	4	4	no	—
43	D₄	—	8	2	no	—
44	C₂×C₄	C₃×D₈	1	1	yes	characteristic
45	C₈	C₃×D₈	1	1	yes	characteristic
46	C₈	C₂×C₃×D₄	1	1	yes	characteristic
47	C₂×C₃	—	16	4	no	—
48	C₂×C₃	D₃₂	1	2	yes	direct product factor
49	C₂×C₃	C₂×D₁₆	1	1	yes	characteristic
50	C₂²	—	8	4	no	—
51	C₂²	—	16	4	no	—
52	C₂²	C₃×D₁₆	1	1	yes	characteristic
53	C₄	C₃×D₁₆	1	1	yes	characteristic
54	C₄	C₂×C₃×D₈	1	1	yes	characteristic
55	C₃	C₂×D₃₂	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	16	4	no	—
57	C₂	C₃×D₃₂	1	2	yes	direct product factor
58	C₂	C₂×C₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₁₆	C₂	semidirect
2. C₃×D₃₂	C₂	direct (N × H)
3. C₂×C₃×C₃₂	C₂	semidirect
4. C₂×D₃₂	C₃	direct (N × H)
7. C₃×D₁₆	C₂²	semidirect
9. C₃×C₃₂	C₂²	semidirect
10. C₂×D₁₆	C₂×C₃	semidirect
11. D₃₂	C₂×C₃	direct (N × H)
12. C₂×C₃₂	C₂×C₃	semidirect
21. D₁₆	C₂²×C₃	semidirect
23. C₃₂	C₂²×C₃	semidirect
48. C₂×C₃	D₃₂	direct (N × H)
55. C₃	C₂×D₃₂	direct (N × H)
57. C₂	C₃×D₃₂	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×C₃×D₁₆	2
C₃×D₃₂	2
C₂×C₃×C₃₂	2
C₂×D₃₂	3

Subgroups — C2×C3×D32 #72974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃₂ #72974