Subgroups — #1658⋊C₉ #11919329

Order 1152.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#564⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#1658	C₃	1	1	yes	maximal, characteristic
3	#127⋊C₉	—	4	1	no	maximal
4	C₃×#564	C₂×C₃	1	1	yes	characteristic
5	C₃×#490	—	3	1	no	—
6	C₃×#330	—	3	1	no	—
7	C₄²⋊C₉	—	4	1	no	—
8	C₄²⋊C₉	—	8	2	no	—
9	#1658	C₉	1	1	yes	characteristic, complemented, Sylow
10	C₃×#127	A₄	1	1	yes	characteristic
11	C₃×#125	—	3	1	no	—
12	C₃×#125	—	6	2	no	—
13	C₃×#102	—	6	2	no	—
14	C₃×#97	—	3	1	no	—
15	C₂×C₂²⋊C₉	—	16	1	no	—
16	#564	C₂×C₉	1	1	yes	characteristic, complemented
17	#490	—	3	1	no	—
18	#330	—	3	1	no	—
19	C₂×C₃×D₄	—	6	1	no	—
20	C₂×C₃×C₈	—	6	1	no	—
21	C₃×C₄⋊C₄	—	3	2	no	—
22	C₃×C₄⋊C₄	—	6	2	no	—
23	C₃×C₄⋊C₄	—	6	2	no	—
24	C₃×C₄²	—	2	2	no	—
25	C₃×C₄²	C₂×A₄	1	1	yes	characteristic
26	C₂²⋊C₉	—	16	1	no	—
27	#127	C₂²⋊C₉	1	1	yes	characteristic
28	#125	—	3	1	no	—
29	#125	—	6	2	no	—
30	#102	—	6	2	no	—
31	#97	—	3	1	no	—
32	C₂³×C₃	—	4	1	no	—
33	C₃×D₄	—	12	2	no	—
34	C₂×C₃×C₄	—	3	1	no	—
35	C₂×C₃×C₄	—	6	2	no	—
36	C₃×C₈	—	12	1	no	—
37	C₂×C₉	—	64	1	no	—
38	C₂×D₄	—	6	1	no	—
39	C₂×C₈	—	6	1	no	—
40	C₄⋊C₄	—	3	2	no	—
41	C₄⋊C₄	—	6	2	no	—
42	C₄⋊C₄	—	6	2	no	—
43	C₄²	—	2	2	no	—
44	C₄²	C₂×C₂²⋊C₉	1	1	yes	characteristic
45	C₂²×C₃	—	24	1	no	—
46	C₂²×C₃	#120⋊C₃	1	1	yes	characteristic
47	C₃×C₄	—	6	1	no	—
48	C₃×C₄	—	12	2	no	—
49	C₉	—	64	1	no	Sylow
50	C₂³	—	4	1	no	—
51	D₄	—	12	2	no	—
52	C₂×C₄	—	3	1	no	—
53	C₂×C₄	—	6	2	no	—
54	C₈	—	12	1	no	—
55	C₂×C₃	—	3	1	no	—
56	C₂×C₃	—	16	1	no	—
57	C₂²	—	24	1	no	—
58	C₂²	#120⋊C₉	1	1	yes	characteristic
59	C₄	—	6	1	no	—
60	C₄	—	12	2	no	—
61	C₃	#1658⋊C₃	1	1	yes	characteristic
62	C₂	—	3	1	no	—
63	C₂	—	16	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#1658⋊C₃
commutator, hypocenter	#564	C₂×C₉
Frattini	C₃×C₄²	C₂×A₄
Fitting	C₃×#1658	C₃
socle	C₂²×C₃	#120⋊C₃
prime radical	C₃×#127	A₄
cosocle	C₃×#564	C₂×C₃
LCS	G ▷ #564
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #564⋊C₉	C₂	semidirect
9. #1658	C₉	semidirect
16. #564	C₂×C₉	semidirect

Maximal subgroups

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

subgroup	index
#564⋊C₉	2
C₃×#1658	3
#127⋊C₉	4

Subgroups — #1658⋊C9 #11919329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1658⋊C₉ #11919329