Subgroups — C₂×C₃×SD₃₂ #5380

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₃×SD₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×SD₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₈	—	2	1	no	—
7	C₂×C₃×D₄	—	2	1	no	—
8	C₃×Q₁₆	—	2	1	no	—
9	C₃×Q₁₆	C₂²	1	2	yes	complemented
10	C₃×D₈	—	2	1	no	—
11	C₃×D₈	C₂²	1	2	yes	—
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₁₆	C₂²	1	2	yes	complemented
14	C₂×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×D₈	C₂×C₃	1	1	yes	characteristic
16	SD₃₂	C₂×C₃	1	4	yes	direct product factor
17	C₂×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂³×C₃	—	4	1	no	—
19	C₃×Q₈	—	2	2	no	—
20	C₃×Q₈	—	4	1	no	—
21	C₃×D₄	—	2	2	no	—
22	C₃×D₄	—	4	1	no	—
23	C₂×C₃×C₄	—	4	1	no	—
24	C₂×C₃×C₄	D₄	1	1	yes	characteristic
25	C₃×C₈	D₄	1	1	yes	characteristic
26	C₃×C₈	C₂³	1	1	yes	characteristic
27	C₂×Q₈	—	2	1	no	—
28	C₂×D₄	—	2	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	C₂²×C₃	1	2	yes	complemented
31	D₈	—	2	1	no	—
32	D₈	C₂²×C₃	1	2	yes	—
33	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
34	C₁₆	C₂²×C₃	1	2	yes	complemented
35	C₂²×C₃	—	4	2	no	—
36	C₂²×C₃	—	8	2	no	—
37	C₂²×C₃	D₈	1	1	yes	characteristic
38	C₃×C₄	—	4	2	no	—
39	C₃×C₄	D₈	1	1	yes	characteristic
40	C₃×C₄	C₂×D₄	1	1	yes	characteristic
41	C₂³	—	4	1	no	—
42	Q₈	—	2	2	no	—
43	Q₈	—	4	1	no	—
44	D₄	—	2	2	no	—
45	D₄	—	4	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	C₃×D₄	1	1	yes	characteristic
48	C₈	C₃×D₄	1	1	yes	characteristic
49	C₈	C₂³×C₃	1	1	yes	characteristic
50	C₂×C₃	—	8	2	no	—
51	C₂×C₃	SD₃₂	1	2	yes	direct product factor
52	C₂×C₃	C₂×D₈	1	1	yes	characteristic
53	C₂²	—	4	2	no	—
54	C₂²	—	8	2	no	—
55	C₂²	C₃×D₈	1	1	yes	characteristic
56	C₄	—	4	2	no	—
57	C₄	C₃×D₈	1	1	yes	characteristic
58	C₄	C₂×C₃×D₄	1	1	yes	characteristic
59	C₃	C₂×SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
60	C₂	—	8	2	no	—
61	C₂	C₃×SD₃₂	1	2	yes	direct product factor
62	C₂	C₂×C₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₃
prime radical	C₂×C₃×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₁₆	C₂	semidirect
3. C₃×SD₃₂	C₂	direct (N × H)
4. C₂×C₃×C₁₆	C₂	semidirect
5. C₂×SD₃₂	C₃	direct (N × H)
9. C₃×Q₁₆	C₂²	semidirect
13. C₃×C₁₆	C₂²	semidirect
14. C₂×Q₁₆	C₂×C₃	semidirect
16. SD₃₂	C₂×C₃	direct (N × H)
17. C₂×C₁₆	C₂×C₃	semidirect
30. Q₁₆	C₂²×C₃	semidirect
34. C₁₆	C₂²×C₃	semidirect
51. C₂×C₃	SD₃₂	direct (N × H)
59. C₃	C₂×SD₃₂	direct (N × H)
61. C₂	C₃×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
C₂×C₃×Q₁₆	2
C₂×C₃×D₈	2
C₃×SD₃₂	2
C₂×C₃×C₁₆	2
C₂×SD₃₂	3

Subgroups — C2×C3×SD32 #5380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×SD₃₂ #5380