Subgroups — C₃²×#1425 #11768474

Order 1152.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃²×#368	C₂	1	2	yes	maximal
3	C₃×#1425	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
5	C₃²×#108	—	2	2	no	—
6	C₃²×C₃₂	C₄	1	2	yes	—
7	C₂×C₃×C₃₂	C₂×C₃	1	4	yes	—
8	C₃×#368	C₂×C₃	1	8	yes	—
9	C₃²×M₁₆	—	4	2	no	—
10	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
11	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₃²×C₁₆	Q₈	1	1	yes	characteristic
13	#1425	C₃²	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₃×C₁₆	C₂²×C₃	1	4	yes	—
15	C₃×#108	—	2	8	no	—
16	C₃×C₃₂	C₃×C₄	1	8	yes	—
17	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
18	C₃²×C₈	—	8	2	no	—
19	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
20	C₃²×C₈	Q₁₆	1	1	yes	characteristic
21	C₂×C₃₂	C₂×C₃²	1	1	yes	characteristic
22	#368	C₂×C₃²	1	2	yes	—
23	C₃×M₁₆	—	4	8	no	—
24	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
25	C₃×C₁₆	C₂×C₃×C₄	1	4	yes	—
26	C₃×C₁₆	C₃×Q₈	1	4	yes	—
27	C₂²×C₃²	Q₃₂	1	1	yes	characteristic
28	C₃²×C₄	#107	1	1	yes	characteristic
29	C₃²×C₄	D₁₆	1	1	yes	characteristic
30	C₂×C₁₆	C₂²×C₃²	1	1	yes	characteristic
31	#108	—	2	2	no	—
32	C₃₂	C₃²×C₄	1	2	yes	—
33	C₂×C₃×C₄	C₃×D₈	1	4	yes	—
34	C₃×C₈	—	8	8	no	—
35	C₃×C₈	C₃×C₄⋊C₄	1	4	yes	—
36	C₃×C₈	C₃×Q₁₆	1	4	yes	—
37	C₂×C₃²	—	2	1	no	—
38	C₂×C₃²	#366	1	1	yes	characteristic
39	M₁₆	—	4	2	no	—
40	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
41	C₁₆	C₂×C₃²×C₄	1	1	yes	characteristic
42	C₁₆	C₃²×Q₈	1	1	yes	characteristic
43	C₂²×C₃	C₃×Q₃₂	1	4	yes	—
44	C₃×C₄	C₃×#107	1	4	yes	—
45	C₃×C₄	C₃×D₁₆	1	4	yes	—
46	C₃²	#1425	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₄	C₃²×D₈	1	1	yes	characteristic
48	C₈	—	8	2	no	—
49	C₈	C₃²×C₄⋊C₄	1	1	yes	characteristic
50	C₈	C₃²×Q₁₆	1	1	yes	characteristic
51	C₂×C₃	—	2	4	no	—
52	C₂×C₃	C₃×#366	1	4	yes	—
53	C₂²	C₃²×Q₃₂	1	1	yes	characteristic
54	C₄	C₃²×#107	1	1	yes	characteristic
55	C₄	C₃²×D₁₆	1	1	yes	characteristic
56	C₃	C₃×#1425	1	4	yes	direct product factor
57	C₂	—	2	1	no	—
58	C₂	C₃²×#366	1	1	yes	characteristic

	subgroup	G/H
center	C₃²×C₄	D₁₆
commutator	C₁₆	C₂×C₃²×C₄
Frattini, cosocle	C₂×C₁₆	C₂²×C₃²
socle	C₂×C₃²	#366
prime radical	C₂²×C₃²	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃²×C₄ ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×C₈ ◁ C₂×C₃²×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#1425	C₃	direct (N × H)
13. #1425	C₃²	direct (N × H)
46. C₃²	#1425	direct (N × H)
56. C₃	C₃×#1425	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×C₃²×C₃₂	2
C₃²×#368	2
C₃×#1425	3

Subgroups — C32×#1425 #11768474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1425 #11768474