Subgroups — #2845⋊C₉ #11919661

Order 1152.

139 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
2	C₂×C₄²⋊C₉	—	4	1	no	maximal
3	#95⋊C₉	—	4	4	no	maximal
4	C₃×#398	—	3	4	no	—
5	C₃×#382	—	3	1	no	—
6	C₄²⋊C₉	—	4	1	no	—
7	#2845	C₉	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₄⋊C₄	—	3	2	no	—
9	C₂×C₃×C₄⋊C₄	—	3	4	no	—
10	C₂×C₃×C₄²	A₄	1	1	yes	characteristic
11	C₃×#95	—	3	4	no	—
12	C₃×#95	A₄	1	4	yes	—
13	C₂×C₂²⋊C₉	—	16	1	no	—
14	#398	—	3	4	no	—
15	#382	—	3	1	no	—
16	C₂²×C₃×C₄	—	3	1	no	—
17	C₂²×C₃×C₄	—	3	4	no	—
18	C₃×C₄⋊C₄	—	12	2	no	—
19	C₃×C₄⋊C₄	—	12	4	no	—
20	C₃×C₄²	—	3	1	no	—
21	C₃×C₄²	SL(2,𝔽₃)	1	1	yes	characteristic
22	C₂²⋊C₉	—	16	1	no	—
23	C₂×C₄⋊C₄	—	3	2	no	—
24	C₂×C₄⋊C₄	—	3	4	no	—
25	C₂×C₄²	C₂²⋊C₉	1	1	yes	characteristic
26	#95	—	3	4	no	—
27	#95	C₂²⋊C₉	1	4	yes	—
28	C₂³×C₃	C₂²⋊A₄	1	1	yes	characteristic
29	C₂×C₃×C₄	—	3	1	no	—
30	C₂×C₃×C₄	—	3	1	no	—
31	C₂×C₃×C₄	—	6	1	no	—
32	C₂×C₃×C₄	—	6	1	no	—
33	C₂×C₃×C₄	—	6	4	no	—
34	C₂×C₃×C₄	—	6	4	no	—
35	C₂×C₃×C₄	—	6	4	no	—
36	C₂×C₉	—	64	1	no	—
37	C₂²×C₄	—	3	1	no	—
38	C₂²×C₄	—	3	4	no	—
39	C₄⋊C₄	—	12	2	no	—
40	C₄⋊C₄	—	12	4	no	—
41	C₄²	—	3	1	no	—
42	C₄²	Q₈⋊C₉	1	1	yes	characteristic
43	C₂²×C₃	—	3	1	no	—
44	C₂²×C₃	—	3	1	no	—
45	C₂²×C₃	C₂²⋊SL(2,𝔽₃)	1	1	yes	characteristic
46	C₃×C₄	—	6	1	no	—
47	C₃×C₄	—	6	1	no	—
48	C₃×C₄	—	12	4	no	—
49	C₉	—	64	1	no	Sylow
50	C₂³	C₂²⋊(C₂²⋊C₉)	1	1	yes	characteristic
51	C₂×C₄	—	3	1	no	—
52	C₂×C₄	—	3	1	no	—
53	C₂×C₄	—	6	1	no	—
54	C₂×C₄	—	6	1	no	—
55	C₂×C₄	—	6	4	no	—
56	C₂×C₄	—	6	4	no	—
57	C₂×C₄	—	6	4	no	—
58	C₂×C₃	—	3	1	no	—
59	C₂×C₃	—	3	1	no	—
60	C₂×C₃	#564⋊C₃	1	1	yes	characteristic
61	C₂²	—	3	1	no	—
62	C₂²	—	3	1	no	—
63	C₂²	C₂²⋊(Q₈⋊C₉)	1	1	yes	characteristic
64	C₄	—	6	1	no	—
65	C₄	—	6	1	no	—
66	C₄	—	12	4	no	—
67	C₃	#2845⋊C₃	1	1	yes	characteristic
68	C₂	—	3	1	no	—
69	C₂	—	3	1	no	—
70	C₂	#564⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#564⋊C₃
commutator, hypocenter	#2845	C₉
Frattini, socle, prime radical	C₂³×C₃	C₂²⋊A₄
Fitting, cosocle	C₃×#2845	C₃
LCS	G ▷ #2845
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
7. #2845	C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×#2845	3
C₂×C₄²⋊C₉	4
#95⋊C₉	4

Subgroups — #2845⋊C9 #11919661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2845⋊C₉ #11919661