Subgroups — C₂²×C₃×C₃₂ #72971

Order 384.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₃₂	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₈	C₄	1	1	yes	characteristic
5	C₂×C₃×C₁₆	C₄	1	3	yes	—
6	C₂×C₃×C₁₆	C₂²	1	3	yes	—
7	C₃×C₃₂	C₂²	1	4	yes	direct product factor
8	C₂²×C₁₆	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃₂	C₂×C₃	1	6	yes	direct product factor
10	C₂²×C₃×C₄	C₈	1	1	yes	characteristic
11	C₂×C₃×C₈	C₈	1	3	yes	—
12	C₂×C₃×C₈	C₂×C₄	1	3	yes	—
13	C₃×C₁₆	C₂×C₄	1	3	yes	—
14	C₃×C₁₆	C₂³	1	1	yes	characteristic
15	C₂²×C₈	C₃×C₄	1	1	yes	characteristic
16	C₂×C₁₆	C₃×C₄	1	3	yes	—
17	C₂×C₁₆	C₂²×C₃	1	3	yes	—
18	C₃₂	C₂²×C₃	1	4	yes	direct product factor
19	C₂³×C₃	C₁₆	1	1	yes	characteristic
20	C₂×C₃×C₄	C₁₆	1	3	yes	—
21	C₂×C₃×C₄	C₂×C₈	1	3	yes	—
22	C₃×C₈	C₂×C₈	1	3	yes	—
23	C₃×C₈	C₂²×C₄	1	1	yes	characteristic
24	C₂²×C₄	C₃×C₈	1	1	yes	characteristic
25	C₂×C₈	C₃×C₈	1	3	yes	—
26	C₂×C₈	C₂×C₃×C₄	1	3	yes	—
27	C₁₆	C₂×C₃×C₄	1	3	yes	—
28	C₁₆	C₂³×C₃	1	1	yes	characteristic
29	C₂²×C₃	C₃₂	1	4	yes	direct product factor
30	C₂²×C₃	C₂×C₁₆	1	3	yes	—
31	C₃×C₄	C₂×C₁₆	1	3	yes	—
32	C₃×C₄	C₂²×C₈	1	1	yes	characteristic
33	C₂³	C₃×C₁₆	1	1	yes	characteristic
34	C₂×C₄	C₃×C₁₆	1	3	yes	—
35	C₂×C₄	C₂×C₃×C₈	1	3	yes	—
36	C₈	C₂×C₃×C₈	1	3	yes	—
37	C₈	C₂²×C₃×C₄	1	1	yes	characteristic
38	C₂×C₃	C₂×C₃₂	1	6	yes	direct product factor
39	C₂×C₃	C₂²×C₁₆	1	1	yes	characteristic
40	C₂²	C₃×C₃₂	1	4	yes	direct product factor
41	C₂²	C₂×C₃×C₁₆	1	3	yes	—
42	C₄	C₂×C₃×C₁₆	1	3	yes	—
43	C₄	C₂²×C₃×C₈	1	1	yes	characteristic
44	C₃	C₂²×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₂×C₃×C₃₂	1	6	yes	direct product factor
46	C₂	C₂²×C₃×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂³×C₃
socle, prime radical	C₂³×C₃	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₃₂	C₂	direct (N × H)
3. C₂²×C₃₂	C₃	direct (N × H)
7. C₃×C₃₂	C₂²	direct (N × H)
9. C₂×C₃₂	C₂×C₃	direct (N × H)
18. C₃₂	C₂²×C₃	direct (N × H)
29. C₂²×C₃	C₃₂	direct (N × H)
38. C₂×C₃	C₂×C₃₂	direct (N × H)
40. C₂²	C₃×C₃₂	direct (N × H)
44. C₃	C₂²×C₃₂	direct (N × H)
45. C₂	C₂×C₃×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
C₂²×C₃×C₁₆	2
C₂×C₃×C₃₂	2
C₂²×C₃₂	3

Subgroups — C22×C3×C32 #72971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₃₂ #72971