Subgroups — C₃²×#1426 #11768475

Order 1152.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₃²×#368	C₂	1	1	yes	maximal, characteristic
3	C₃²×#367	C₂	1	1	yes	maximal, characteristic
4	C₃×#1426	C₃	1	4	yes	maximal, direct product factor
5	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
6	C₃²×#108	—	2	1	no	—
7	C₃²×#107	—	2	1	no	—
8	C₃²×C₃₂	C₄	1	2	yes	complemented
9	C₃×M₆₄	C₂×C₃	1	4	yes	—
10	C₃×#368	C₂×C₃	1	4	yes	—
11	C₃×#367	C₂×C₃	1	4	yes	—
12	C₃²×M₁₆	—	4	1	no	—
13	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
14	C₃²×C₄⋊C₄	—	4	1	no	—
15	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₃²×C₁₆	Q₈	1	1	yes	characteristic
17	#1426	C₃²	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃×C₁₆	C₂²×C₃	1	4	yes	—
19	C₃×#108	—	2	4	no	—
20	C₃×#107	—	2	4	no	—
21	C₃×C₃₂	C₃×C₄	1	8	yes	complemented
22	C₂×C₃²×C₄	—	8	1	no	—
23	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
24	C₃²×C₈	—	8	1	no	—
25	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
26	C₃²×C₈	Q₁₆	1	1	yes	characteristic
27	M₆₄	C₂×C₃²	1	1	yes	characteristic
28	#368	C₂×C₃²	1	1	yes	characteristic
29	#367	C₂×C₃²	1	1	yes	characteristic
30	C₃×M₁₆	—	4	4	no	—
31	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
32	C₃×C₄⋊C₄	—	4	4	no	—
33	C₃×C₁₆	C₂×C₃×C₄	1	4	yes	—
34	C₃×C₁₆	C₃×Q₈	1	4	yes	—
35	C₂²×C₃²	SD₃₂	1	1	yes	characteristic
36	C₃²×C₄	—	16	1	no	—
37	C₃²×C₄	#107	1	1	yes	characteristic
38	C₃²×C₄	SD₃₂	1	1	yes	characteristic
39	C₂×C₁₆	C₂²×C₃²	1	1	yes	characteristic
40	#108	—	2	1	no	—
41	#107	—	2	1	no	—
42	C₃₂	C₃²×C₄	1	2	yes	complemented
43	C₂×C₃×C₄	—	8	4	no	—
44	C₂×C₃×C₄	C₃×D₈	1	4	yes	—
45	C₃×C₈	—	8	4	no	—
46	C₃×C₈	C₃×C₄⋊C₄	1	4	yes	—
47	C₃×C₈	C₃×Q₁₆	1	4	yes	—
48	C₂×C₃²	—	2	1	no	—
49	C₂×C₃²	#367	1	1	yes	characteristic
50	M₁₆	—	4	1	no	—
51	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
52	C₄⋊C₄	—	4	1	no	—
53	C₁₆	C₂×C₃²×C₄	1	1	yes	characteristic
54	C₁₆	C₃²×Q₈	1	1	yes	characteristic
55	C₂²×C₃	C₃×SD₃₂	1	4	yes	—
56	C₃×C₄	—	16	4	no	—
57	C₃×C₄	C₃×#107	1	4	yes	—
58	C₃×C₄	C₃×SD₃₂	1	4	yes	—
59	C₃²	#1426	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₄	—	8	1	no	—
61	C₂×C₄	C₃²×D₈	1	1	yes	characteristic
62	C₈	—	8	1	no	—
63	C₈	C₃²×C₄⋊C₄	1	1	yes	characteristic
64	C₈	C₃²×Q₁₆	1	1	yes	characteristic
65	C₂×C₃	—	2	4	no	—
66	C₂×C₃	C₃×#367	1	4	yes	—
67	C₂²	C₃²×SD₃₂	1	1	yes	characteristic
68	C₄	—	16	1	no	—
69	C₄	C₃²×#107	1	1	yes	characteristic
70	C₄	C₃²×SD₃₂	1	1	yes	characteristic
71	C₃	C₃×#1426	1	4	yes	direct product factor
72	C₂	—	2	1	no	—
73	C₂	C₃²×#367	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃²	#367
commutator	C₁₆	C₂×C₃²×C₄
Frattini, cosocle	C₂×C₁₆	C₂²×C₃²
prime radical	C₂²×C₃²	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ 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
4. C₃×#1426	C₃	direct (N × H)
8. C₃²×C₃₂	C₄	semidirect
17. #1426	C₃²	direct (N × H)
21. C₃×C₃₂	C₃×C₄	semidirect
42. C₃₂	C₃²×C₄	semidirect
59. C₃²	#1426	direct (N × H)
71. C₃	C₃×#1426	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×M₆₄	2
C₃²×#368	2
C₃²×#367	2
C₃×#1426	3

Subgroups — C32×#1426 #11768475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#1426 #11768475