Subgroups — C₃×#2845⋊C₃ #11919660

Order 1152.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2845	C₃	1	1	yes	maximal, characteristic, complemented
2	#2845⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₄²⋊C₃	—	4	1	no	maximal
4	C₃×#95⋊C₃	—	4	4	no	maximal
5	C₃×#398	—	3	4	no	—
6	C₃×#382	—	3	1	no	—
7	C₃×C₄²⋊C₃	—	4	1	no	—
8	#2845	C₃²	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₃×C₄⋊C₄	—	3	2	no	—
10	C₂×C₃×C₄⋊C₄	—	3	4	no	—
11	C₂×C₃×C₄²	A₄	1	1	yes	characteristic
12	C₂×C₄²⋊C₃	—	4	3	no	—
13	C₃×#95	—	3	4	no	—
14	C₃×#95	A₄	1	4	yes	—
15	#95⋊C₃	—	4	12	no	—
16	C₂×C₃×A₄	—	16	1	no	—
17	#398	—	3	4	no	—
18	#382	—	3	1	no	—
19	C₂²×C₃×C₄	—	3	1	no	—
20	C₂²×C₃×C₄	—	3	4	no	—
21	C₃×C₄⋊C₄	—	12	2	no	—
22	C₃×C₄⋊C₄	—	12	4	no	—
23	C₃×C₄²	—	3	1	no	—
24	C₃×C₄²	SL(2,𝔽₃)	1	1	yes	characteristic
25	C₄²⋊C₃	—	4	3	no	—
26	C₃×A₄	—	16	1	no	—
27	C₂×C₄⋊C₄	—	3	2	no	—
28	C₂×C₄⋊C₄	—	3	4	no	—
29	C₂×C₄²	C₃×A₄	1	1	yes	characteristic
30	#95	—	3	4	no	—
31	#95	C₃×A₄	1	4	yes	—
32	C₂³×C₃	C₂²⋊A₄	1	1	yes	characteristic
33	C₂×A₄	—	16	3	no	—
34	C₂×C₃×C₄	—	3	1	no	—
35	C₂×C₃×C₄	—	3	1	no	—
36	C₂×C₃×C₄	—	6	1	no	—
37	C₂×C₃×C₄	—	6	1	no	—
38	C₂×C₃×C₄	—	6	4	no	—
39	C₂×C₃×C₄	—	6	4	no	—
40	C₂×C₃×C₄	—	6	4	no	—
41	C₂×C₃²	—	64	1	no	—
42	C₂²×C₄	—	3	1	no	—
43	C₂²×C₄	—	3	4	no	—
44	C₄⋊C₄	—	12	2	no	—
45	C₄⋊C₄	—	12	4	no	—
46	C₄²	—	3	1	no	—
47	C₄²	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
48	C₂²×C₃	—	3	1	no	—
49	C₂²×C₃	—	3	1	no	—
50	C₂²×C₃	C₂²⋊SL(2,𝔽₃)	1	1	yes	characteristic
51	A₄	—	16	3	no	—
52	C₃×C₄	—	6	1	no	—
53	C₃×C₄	—	6	1	no	—
54	C₃×C₄	—	12	4	no	—
55	C₃²	—	64	1	no	Sylow
56	C₂³	C₃×C₂²⋊A₄	1	1	yes	characteristic
57	C₂×C₄	—	3	1	no	—
58	C₂×C₄	—	3	1	no	—
59	C₂×C₄	—	6	1	no	—
60	C₂×C₄	—	6	1	no	—
61	C₂×C₄	—	6	4	no	—
62	C₂×C₄	—	6	4	no	—
63	C₂×C₄	—	6	4	no	—
64	C₂×C₃	—	3	1	no	—
65	C₂×C₃	—	3	1	no	—
66	C₂×C₃	—	64	3	no	—
67	C₂×C₃	#564⋊C₃	1	1	yes	characteristic
68	C₂²	—	3	1	no	—
69	C₂²	—	3	1	no	—
70	C₂²	C₃×C₂²⋊SL(2,𝔽₃)	1	1	yes	characteristic
71	C₄	—	6	1	no	—
72	C₄	—	6	1	no	—
73	C₄	—	12	4	no	—
74	C₃	—	64	3	no	—
75	C₃	#2845⋊C₃	1	1	yes	characteristic, direct product factor
76	C₂	—	3	1	no	—
77	C₂	—	3	1	no	—
78	C₂	C₃×#564⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#564⋊C₃
commutator, cosocle, hypocenter	#2845	C₃²
Frattini	C₂³	C₃×C₂²⋊A₄
Fitting	C₃×#2845	C₃
socle	C₂³×C₃	C₂²⋊A₄
LCS	G ▷ #2845
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#2845	C₃	semidirect
2. #2845⋊C₃	C₃	direct (N × H)
8. #2845	C₃²	semidirect
75. C₃	#2845⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#2845	3
#2845⋊C₃	3
C₂×C₃×C₄²⋊C₃	4
C₃×#95⋊C₃	4

Subgroups — C3×#2845⋊C3 #11919660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2845⋊C₃ #11919660