Subgroups — C₃×C₄×C₃₂ #67956

Order 384.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₂	C₂	1	2	yes	maximal
2	C₃×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₈	C₄	1	1	yes	characteristic
7	C₃×C₃₂	C₄	1	4	yes	direct product factor
8	C₂×C₃₂	C₂×C₃	1	2	yes	—
9	C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×C₈	C₈	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄²	C₈	1	1	yes	characteristic
13	C₃×C₁₆	C₈	1	2	yes	—
14	C₃×C₁₆	C₂×C₄	1	2	yes	—
15	C₂×C₁₆	C₃×C₄	1	1	yes	characteristic
16	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
17	C₄×C₈	C₃×C₄	1	1	yes	characteristic
18	C₃₂	C₃×C₄	1	4	yes	direct product factor
19	C₂×C₃×C₄	C₁₆	1	2	yes	—
20	C₂×C₃×C₄	C₂×C₈	1	1	yes	characteristic
21	C₃×C₈	C₁₆	1	2	yes	—
22	C₃×C₈	C₄²	1	1	yes	characteristic
23	C₃×C₈	C₂×C₈	1	1	yes	characteristic
24	C₂×C₈	C₃×C₈	1	1	yes	characteristic
25	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
26	C₄²	C₃×C₈	1	1	yes	characteristic
27	C₁₆	C₃×C₈	1	2	yes	—
28	C₁₆	C₂×C₃×C₄	1	2	yes	—
29	C₂²×C₃	C₂×C₁₆	1	1	yes	characteristic
30	C₃×C₄	C₃₂	1	4	yes	direct product factor
31	C₃×C₄	C₄×C₈	1	1	yes	characteristic
32	C₃×C₄	C₂×C₁₆	1	1	yes	characteristic
33	C₂×C₄	C₃×C₁₆	1	2	yes	—
34	C₂×C₄	C₂×C₃×C₈	1	1	yes	characteristic
35	C₈	C₃×C₁₆	1	2	yes	—
36	C₈	C₃×C₄²	1	1	yes	characteristic
37	C₈	C₂×C₃×C₈	1	1	yes	characteristic
38	C₂×C₃	C₄×C₁₆	1	1	yes	characteristic
39	C₂×C₃	C₂×C₃₂	1	2	yes	—
40	C₂²	C₂×C₃×C₁₆	1	1	yes	characteristic
41	C₄	C₃×C₃₂	1	4	yes	direct product factor
42	C₄	C₃×C₄×C₈	1	1	yes	characteristic
43	C₄	C₂×C₃×C₁₆	1	1	yes	characteristic
44	C₃	C₄×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×C₄×C₁₆	1	1	yes	characteristic
46	C₂	C₂×C₃×C₃₂	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₆	C₂²×C₃
socle, prime radical	C₂²×C₃	C₂×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₃₂	C₃	direct (N × H)
7. C₃×C₃₂	C₄	direct (N × H)
18. C₃₂	C₃×C₄	direct (N × H)
30. C₃×C₄	C₃₂	direct (N × H)
41. C₄	C₃×C₃₂	direct (N × H)
44. C₃	C₄×C₃₂	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×C₃₂	2
C₃×C₄×C₁₆	2
C₄×C₃₂	3

Subgroups — C3×C4×C32 #67956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₃₂ #67956