Subgroups — C₂×C₃×Q₃₂ #5381

Order 192.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₁₆	C₂	1	2	yes	maximal
2	C₃×Q₃₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₈	—	2	2	no	—
6	C₃×Q₁₆	—	2	2	no	—
7	C₃×Q₁₆	C₂²	1	4	yes	—
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	C₃×C₁₆	C₂²	1	2	yes	—
10	C₂×Q₁₆	C₂×C₃	1	2	yes	—
11	Q₃₂	C₂×C₃	1	4	yes	direct product factor
12	C₂×C₁₆	C₂×C₃	1	1	yes	characteristic
13	C₃×Q₈	—	2	4	no	—
14	C₃×Q₈	—	4	2	no	—
15	C₂×C₃×C₄	—	4	2	no	—
16	C₂×C₃×C₄	D₄	1	1	yes	characteristic
17	C₃×C₈	D₄	1	1	yes	characteristic
18	C₃×C₈	C₂³	1	1	yes	characteristic
19	C₂×Q₈	—	2	2	no	—
20	Q₁₆	—	2	2	no	—
21	Q₁₆	C₂²×C₃	1	4	yes	—
22	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
23	C₁₆	C₂²×C₃	1	2	yes	—
24	C₂²×C₃	D₈	1	1	yes	characteristic
25	C₃×C₄	—	4	4	no	—
26	C₃×C₄	D₈	1	1	yes	characteristic
27	C₃×C₄	C₂×D₄	1	1	yes	characteristic
28	Q₈	—	2	4	no	—
29	Q₈	—	4	2	no	—
30	C₂×C₄	—	4	2	no	—
31	C₂×C₄	C₃×D₄	1	1	yes	characteristic
32	C₈	C₃×D₄	1	1	yes	characteristic
33	C₈	C₂³×C₃	1	1	yes	characteristic
34	C₂×C₃	Q₃₂	1	2	yes	direct product factor
35	C₂×C₃	C₂×D₈	1	1	yes	characteristic
36	C₂²	C₃×D₈	1	1	yes	characteristic
37	C₄	—	4	4	no	—
38	C₄	C₃×D₈	1	1	yes	characteristic
39	C₄	C₂×C₃×D₄	1	1	yes	characteristic
40	C₃	C₂×Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
41	C₂	C₃×Q₃₂	1	2	yes	direct product factor
42	C₂	C₂×C₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₃
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
2. C₃×Q₃₂	C₂	direct (N × H)
4. C₂×Q₃₂	C₃	direct (N × H)
11. Q₃₂	C₂×C₃	direct (N × H)
34. C₂×C₃	Q₃₂	direct (N × H)
40. C₃	C₂×Q₃₂	direct (N × H)
41. C₂	C₃×Q₃₂	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
C₃×Q₃₂	2
C₂×C₃×C₁₆	2
C₂×Q₃₂	3

Subgroups — C2×C3×Q32 #5381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Q₃₂ #5381