Subgroups — C₃×#68062 #11782589

Order 1152.

597 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#4695	C₂	1	6	yes	maximal, complemented
2	C₃²×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#1712	—	3	1	no	maximal
4	#68062	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃×D₂₄	—	2	12	no	—
6	C₃×#874	C₂²	1	4	yes	—
7	C₃²×C₄×C₈	C₂²	1	3	yes	—
8	C₃×#493	—	3	6	no	—
9	#4695	C₂×C₃	1	6	yes	complemented
10	C₃×C₈²	—	2	1	no	—
11	C₃×C₈²	D₃	1	1	yes	characteristic, complemented
12	C₃×C₈²	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₃×D₁₂	—	2	12	no	—
14	C₂×C₃²×C₈	D₄	1	6	yes	—
15	C₃²×C₄²	C₂³	1	1	yes	characteristic
16	C₃×D₂₄	—	4	24	no	—
17	#1712	—	3	1	no	Sylow
18	C₂×C₃×D₈	—	6	12	no	—
19	C₃×#127	—	3	4	no	—
20	C₂×D₂₄	—	2	12	no	—
21	#874	C₂²×C₃	1	4	yes	—
22	C₃×C₄×C₈	—	2	3	no	—
23	C₃×C₄×C₈	C₂×D₃	1	3	yes	—
24	C₃×C₄×C₈	C₂²×C₃	1	3	yes	—
25	C₂²×C₃×D₃	—	4	4	no	—
26	C₂×C₃²×C₄	C₂×D₄	1	3	yes	—
27	C₃×D₁₂	—	4	24	no	—
28	C₃²×C₈	D₈	1	12	yes	complemented
29	#493	—	3	6	no	—
30	C₈²	C₃×D₃	1	1	yes	characteristic, complemented
31	C₂×C₃×D₄	—	6	12	no	—
32	C₂×D₁₂	—	2	12	no	—
33	C₃×D₈	—	12	24	no	—
34	C₂×C₃×C₈	—	2	6	no	—
35	C₂×C₃×C₈	D₁₂	1	6	yes	—
36	C₂×C₃×C₈	C₃×D₄	1	6	yes	—
37	C₃×C₄²	—	2	1	no	—
38	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
39	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
40	D₂₄	—	4	24	no	—
41	C₂²×C₃²	#127	1	1	yes	characteristic
42	C₂×C₃×D₃	—	8	12	no	—
43	C₃²×C₄	C₂×D₈	1	6	yes	—
44	C₂×D₈	—	6	12	no	—
45	#127	—	3	4	no	—
46	C₄×C₈	C₂×C₃×D₃	1	3	yes	—
47	C₂³×C₃	—	12	4	no	—
48	C₂²×D₃	—	4	4	no	—
49	C₃×D₄	—	12	24	no	—
50	C₂×C₃×C₄	—	2	3	no	—
51	C₂×C₃×C₄	C₂×D₁₂	1	3	yes	—
52	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
53	D₁₂	—	4	24	no	—
54	C₃×C₈	—	2	12	no	—
55	C₃×C₈	D₂₄	1	12	yes	complemented
56	C₃×C₈	C₃×D₈	1	12	yes	complemented
57	C₂×C₃²	#493	1	3	yes	—
58	C₃×D₃	—	16	4	no	—
59	C₂×D₄	—	6	12	no	—
60	D₈	—	12	24	no	—
61	C₂×C₈	C₃×D₁₂	1	6	yes	—
62	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
63	C₂²×C₃	—	2	1	no	—
64	C₂²×C₃	—	24	12	no	—
65	C₂²×C₃	#874	1	1	yes	characteristic
66	C₂²×C₃	C₃×#127	1	1	yes	characteristic
67	C₂×D₃	—	8	12	no	—
68	C₃×C₄	—	2	6	no	—
69	C₃×C₄	C₂×D₂₄	1	6	yes	—
70	C₃×C₄	C₂×C₃×D₈	1	6	yes	—
71	C₃²	#1712	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	12	4	no	—
73	D₄	—	12	24	no	—
74	C₂×C₄	C₂×C₃×D₁₂	1	3	yes	—
75	C₈	C₃×D₂₄	1	12	yes	complemented
76	C₂×C₃	—	2	3	no	—
77	C₂×C₃	—	48	4	no	—
78	C₂×C₃	#4695	1	3	yes	—
79	C₂×C₃	C₃×#493	1	3	yes	—
80	D₃	—	16	4	no	—
81	C₂²	—	24	12	no	—
82	C₂²	C₃×#874	1	1	yes	characteristic
83	C₄	C₂×C₃×D₂₄	1	6	yes	—
84	C₃	—	2	1	no	—
85	C₃	#68062	1	1	yes	characteristic, direct product factor
86	C₃	C₃×#1712	1	1	yes	characteristic, complemented
87	C₂	—	48	4	no	—
88	C₂	C₃×#4695	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	#874
commutator, cosocle	C₃×C₄²	C₂³×C₃
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×C₈²	C₂
socle	C₂²×C₃²	#127
hypercenter	C₃×C₈²	D₃
hypocenter	C₃	C₃×#1712
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₈²

Complements

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

N	H ≅ G/N	type
1. C₃×#4695	C₂	semidirect
2. C₃²×C₈²	C₂	semidirect
4. #68062	C₃	direct (N × H)
9. #4695	C₂×C₃	semidirect
11. C₃×C₈²	D₃	semidirect
12. C₃×C₈²	C₂×C₃	semidirect
28. C₃²×C₈	D₈	semidirect
30. C₈²	C₃×D₃	semidirect
55. C₃×C₈	D₂₄	semidirect
56. C₃×C₈	C₃×D₈	semidirect
71. C₃²	#1712	semidirect
75. C₈	C₃×D₂₄	semidirect
85. C₃	#68062	direct (N × H)
86. C₃	C₃×#1712	semidirect

Maximal subgroups

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

subgroup	index
C₃×#4695	2
C₃²×C₈²	2
C₃×#1712	3
#68062	3

Subgroups — C3×#68062 #11782589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#68062 #11782589