Subgroups — #1712⋊C₉ #11919335

Order 1152.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#1712	C₃	1	1	yes	maximal, characteristic
3	#127⋊C₉	—	4	1	no	maximal
4	C₃×#493	—	3	1	no	—
5	C₃×#493	—	3	1	no	—
6	C₃×C₈²	C₂×C₃	1	1	yes	characteristic
7	C₄²⋊C₉	—	4	1	no	—
8	#1712	C₉	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₃×D₈	—	6	2	no	—
10	C₂×C₃×D₈	—	6	2	no	—
11	C₃×#127	—	3	1	no	—
12	C₃×#127	A₄	1	1	yes	characteristic
13	C₃×C₄×C₈	—	3	1	no	—
14	C₂×C₂²⋊C₉	—	16	1	no	—
15	#493	—	3	1	no	—
16	#493	—	3	1	no	—
17	C₈²	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×C₃×D₄	—	6	1	no	—
19	C₂×C₃×D₄	—	6	1	no	—
20	C₂×C₃×D₄	—	6	2	no	—
21	C₃×D₈	—	12	4	no	—
22	C₃×D₈	—	12	4	no	—
23	C₂×C₃×C₈	—	3	2	no	—
24	C₃×C₄²	C₂×A₄	1	1	yes	characteristic
25	C₂²⋊C₉	—	16	1	no	—
26	C₂×D₈	—	6	2	no	—
27	C₂×D₈	—	6	2	no	—
28	#127	—	3	1	no	—
29	#127	C₂²⋊C₉	1	1	yes	characteristic
30	C₄×C₈	—	3	1	no	—
31	C₂³×C₃	—	4	1	no	—
32	C₂³×C₃	—	12	1	no	—
33	C₃×D₄	—	12	2	no	—
34	C₃×D₄	—	12	2	no	—
35	C₃×D₄	—	12	4	no	—
36	C₂×C₃×C₄	—	3	1	no	—
37	C₃×C₈	—	3	4	no	—
38	C₂×C₉	—	64	1	no	—
39	C₂×D₄	—	6	1	no	—
40	C₂×D₄	—	6	1	no	—
41	C₂×D₄	—	6	2	no	—
42	D₈	—	12	4	no	—
43	D₈	—	12	4	no	—
44	C₂×C₈	—	3	2	no	—
45	C₄²	C₂×C₂²⋊C₉	1	1	yes	characteristic
46	C₂²×C₃	—	24	1	no	—
47	C₂²×C₃	—	24	1	no	—
48	C₂²×C₃	—	24	2	no	—
49	C₂²×C₃	#127⋊C₃	1	1	yes	characteristic
50	C₃×C₄	—	3	2	no	—
51	C₉	—	64	1	no	Sylow
52	C₂³	—	4	1	no	—
53	C₂³	—	12	1	no	—
54	D₄	—	12	2	no	—
55	D₄	—	12	2	no	—
56	D₄	—	12	4	no	—
57	C₂×C₄	—	3	1	no	—
58	C₈	—	3	4	no	—
59	C₂×C₃	—	3	1	no	—
60	C₂×C₃	—	16	1	no	—
61	C₂×C₃	—	48	1	no	—
62	C₂²	—	24	1	no	—
63	C₂²	—	24	1	no	—
64	C₂²	—	24	2	no	—
65	C₂²	#127⋊C₉	1	1	yes	characteristic
66	C₄	—	3	2	no	—
67	C₃	#1712⋊C₃	1	1	yes	characteristic
68	C₂	—	3	1	no	—
69	C₂	—	16	1	no	—
70	C₂	—	48	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#1712⋊C₃
commutator, hypocenter	C₈²	C₂×C₉
Frattini	C₃×C₄²	C₂×A₄
Fitting, prime radical	C₃×#1712	C₃
socle	C₂²×C₃	#127⋊C₃
cosocle	C₃×C₈²	C₂×C₃
LCS	G ▷ C₈²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₈²⋊C₉	C₂	semidirect
8. #1712	C₉	semidirect
17. C₈²	C₂×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₈²⋊C₉	2
C₃×#1712	3
#127⋊C₉	4

Subgroups — #1712⋊C9 #11919335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1712⋊C₉ #11919335