Subgroups — #1711⋊C₉ #11919333

Order 1152.

78 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×#1711	C₃	1	1	yes	maximal, characteristic
3	#127⋊C₉	—	4	1	no	maximal
4	C₃×#487	—	3	1	no	—
5	C₃×#486	—	3	1	no	—
6	C₃×C₈²	C₂×C₃	1	1	yes	characteristic
7	C₄²⋊C₉	—	4	1	no	—
8	#1711	C₉	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₄⋊Q₈	—	3	1	no	—
10	C₃×#127	A₄	1	1	yes	characteristic
11	C₃×#103	—	6	2	no	—
12	C₃×#102	—	6	2	no	—
13	C₃×C₄×C₈	—	3	1	no	—
14	C₂×C₂²⋊C₉	—	16	1	no	—
15	#487	—	3	1	no	—
16	#486	—	3	1	no	—
17	C₈²	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×C₃×Q₈	—	6	1	no	—
19	C₂×C₃×D₄	—	6	1	no	—
20	C₂×C₃×C₈	—	3	2	no	—
21	C₃×C₄⋊C₄	—	6	1	no	—
22	C₃×C₄⋊C₄	—	6	1	no	—
23	C₃×C₄²	C₂×A₄	1	1	yes	characteristic
24	C₂²⋊C₉	—	16	1	no	—
25	C₄⋊Q₈	—	3	1	no	—
26	#127	C₂²⋊C₉	1	1	yes	characteristic
27	#103	—	6	2	no	—
28	#102	—	6	2	no	—
29	C₄×C₈	—	3	1	no	—
30	C₂³×C₃	—	4	1	no	—
31	C₃×Q₈	—	12	2	no	—
32	C₃×D₄	—	12	2	no	—
33	C₂×C₃×C₄	—	3	1	no	—
34	C₂×C₃×C₄	—	12	1	no	—
35	C₃×C₈	—	6	2	no	—
36	C₂×C₉	—	64	1	no	—
37	C₂×Q₈	—	6	1	no	—
38	C₂×D₄	—	6	1	no	—
39	C₂×C₈	—	3	2	no	—
40	C₄⋊C₄	—	6	1	no	—
41	C₄⋊C₄	—	6	1	no	—
42	C₄²	C₂×C₂²⋊C₉	1	1	yes	characteristic
43	C₂²×C₃	—	24	1	no	—
44	C₂²×C₃	#127⋊C₃	1	1	yes	characteristic
45	C₃×C₄	—	3	2	no	—
46	C₃×C₄	—	24	1	no	—
47	C₉	—	64	1	no	Sylow
48	C₂³	—	4	1	no	—
49	Q₈	—	12	2	no	—
50	D₄	—	12	2	no	—
51	C₂×C₄	—	3	1	no	—
52	C₂×C₄	—	12	1	no	—
53	C₈	—	6	2	no	—
54	C₂×C₃	—	3	1	no	—
55	C₂×C₃	—	16	1	no	—
56	C₂²	—	24	1	no	—
57	C₂²	#127⋊C₉	1	1	yes	characteristic
58	C₄	—	3	2	no	—
59	C₄	—	24	1	no	—
60	C₃	#1711⋊C₃	1	1	yes	characteristic
61	C₂	—	3	1	no	—
62	C₂	—	16	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#1711⋊C₃
commutator, hypocenter	C₈²	C₂×C₉
Frattini	C₃×C₄²	C₂×A₄
Fitting	C₃×#1711	C₃
socle	C₂²×C₃	#127⋊C₃
prime radical	C₃×#127	A₄
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. #1711	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×#1711	3
#127⋊C₉	4

Subgroups — #1711⋊C9 #11919333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1711⋊C₉ #11919333