Subgroups — #1143⋊C₉ #11758849

Order 1008.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊(D₇⋊C₉)	C₂	1	1	yes	maximal, characteristic
3	(C₇⋊C₈)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1143	C₃	1	1	yes	maximal, characteristic
5	C₂×D₇⋊C₉	—	2	1	no	—
6	C₄×C₇⋊C₉	—	2	1	no	—
7	C₄×C₇⋊C₉	C₂²	1	1	yes	characteristic
8	C₃×C₇×Q₈	C₂×C₃	1	1	yes	characteristic
9	C₃×D₂₈	C₂×C₃	1	1	yes	characteristic
10	C₃×C₇⋊C₈	C₂×C₃	1	1	yes	characteristic
11	C₉×SD₁₆	—	7	1	no	maximal, Hall
12	C₂×C₇⋊C₉	D₄	1	1	yes	characteristic
13	D₇⋊C₉	—	4	1	no	—
14	#1143	C₉	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×D₇	—	2	1	no	—
16	C₃×C₄×C₇	—	2	1	no	—
17	C₃×C₄×C₇	C₂²×C₃	1	1	yes	characteristic
18	Q₈×C₉	—	7	1	no	—
19	D₄×C₉	—	7	1	no	—
20	C₈×C₉	—	7	1	no	—
21	C₇⋊C₉	SD₁₆	1	1	yes	characteristic, complemented, Hall
22	C₇×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
23	D₂₈	C₂×C₉	1	1	yes	characteristic
24	C₇⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
25	C₃×SD₁₆	—	7	1	no	—
26	C₂×C₃×C₇	C₃×D₄	1	1	yes	characteristic
27	C₃×D₇	—	4	1	no	—
28	C₂²×C₉	—	14	1	no	—
29	C₄×C₉	—	7	1	no	—
30	C₄×C₉	—	14	1	no	—
31	C₂×D₇	—	2	1	no	—
32	C₄×C₇	—	2	1	no	—
33	C₄×C₇	C₂²×C₉	1	1	yes	characteristic
34	C₃×Q₈	AGL(1,𝔽₇)	1	1	yes	characteristic
35	C₃×D₄	—	7	1	no	—
36	C₃×C₈	—	7	1	no	—
37	C₃×C₇	C₃×SD₁₆	1	1	yes	characteristic
38	C₂×C₉	—	7	1	no	—
39	C₂×C₉	—	28	1	no	—
40	SD₁₆	—	7	1	no	Sylow
41	C₂×C₇	D₄×C₉	1	1	yes	characteristic
42	D₇	—	4	1	no	—
43	C₂²×C₃	—	14	1	no	—
44	C₃×C₄	—	2	1	no	—
45	C₃×C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
46	C₉	—	7	1	no	Sylow
47	Q₈	D₇⋊C₉	1	1	yes	characteristic, complemented
48	D₄	—	7	1	no	—
49	C₈	—	7	1	no	—
50	C₇	C₉×SD₁₆	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	28	1	no	—
52	C₂×C₃	(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic
53	C₂²	—	14	1	no	—
54	C₄	—	2	1	no	—
55	C₄	C₂×D₇⋊C₉	1	1	yes	characteristic
56	C₃	#1143⋊C₃	1	1	yes	characteristic
57	C₂	—	28	1	no	—
58	C₂	(C₂²⋊D₇)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	(C₂²⋊D₇)⋊C₃
commutator	C₄×C₇	C₂²×C₉
Frattini	C₃×C₄	C₂×AGL(1,𝔽₇)
Fitting	C₃×C₇×Q₈	C₂×C₃
socle	C₂×C₃×C₇	C₃×D₄
prime radical	C₃×D₂₈	C₂×C₃
cosocle	C₃×C₄×C₇	C₂²×C₃
hypercenter	C₃×Q₈	AGL(1,𝔽₇)
hypocenter	C₇	C₉×SD₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. Q₈×C₇⋊C₉	C₂	semidirect
3. (C₇⋊C₈)⋊C₉	C₂	semidirect
14. #1143	C₉	semidirect
21. C₇⋊C₉	SD₁₆	semidirect
22. C₇×Q₈	C₂×C₉	semidirect
24. C₇⋊C₈	C₂×C₉	semidirect
47. Q₈	D₇⋊C₉	semidirect
50. C₇	C₉×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₇⋊C₉	2
C₄⋊(D₇⋊C₉)	2
(C₇⋊C₈)⋊C₉	2
C₃×#1143	3
C₉×SD₁₆	7

Subgroups — #1143⋊C9 #11758849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1143⋊C₉ #11758849