Subgroups — C₉×C₁₁×#5997 #34084705

Order 19404.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₁×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₁×#5997	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₉×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
5	C₁₁×#5997	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×#5997	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇²×C₁₁	C₃×C₄	1	1	yes	characteristic
8	C₉×C₁₁×D₇	—	14	4	no	—
9	C₁₁×C₇⋊D₇	C₂×C₉	1	1	yes	characteristic
10	C₉×C₇⋊D₇	C₂×C₁₁	1	1	yes	characteristic
11	C₇×C₉×C₁₁	—	2	4	no	—
12	C₃×#5997	C₃×C₁₁	1	1	yes	characteristic
13	C₇²×C₁₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×D₇	—	14	4	no	—
15	C₇²×C₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₄×C₉×C₁₁	—	49	1	no	maximal, Hall
17	C₃×C₇⋊D₇	C₂×C₃×C₁₁	1	1	yes	characteristic
18	C₃×C₇×C₁₁	—	2	4	no	—
19	C₂×C₉×C₁₁	—	49	1	no	—
20	#5997	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₁₁×D₇	—	14	4	no	—
22	C₃×C₇²	C₃×C₄×C₁₁	1	1	yes	characteristic
23	C₃×C₄×C₁₁	—	49	1	no	—
24	C₉×D₇	—	14	4	no	—
25	C₉×C₁₁	#5997	1	1	yes	characteristic, direct product factor, Hall
26	C₇⋊D₇	C₂×C₉×C₁₁	1	1	yes	characteristic
27	C₇×C₁₁	—	2	4	no	—
28	C₂×C₃×C₁₁	—	49	1	no	—
29	C₇×C₉	—	2	4	no	—
30	C₇²	C₄×C₉×C₁₁	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₁	—	49	1	no	Hall
32	C₃×D₇	—	14	4	no	—
33	C₄×C₉	—	49	1	no	Hall
34	C₃×C₁₁	C₃×#5997	1	1	yes	characteristic
35	C₂×C₁₁	—	49	1	no	—
36	C₃×C₇	—	2	4	no	—
37	C₂×C₉	—	49	1	no	—
38	D₇	—	14	4	no	—
39	C₃×C₄	—	49	1	no	—
40	C₁₁	C₉×#5997	1	1	yes	characteristic, direct product factor, Sylow
41	C₉	C₁₁×#5997	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	—	2	4	no	—
43	C₂×C₃	—	49	1	no	—
44	C₄	—	49	1	no	Sylow
45	C₃	C₃×C₁₁×#5997	1	1	yes	characteristic
46	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₁₁	#5997
commutator, hypocenter	C₇²	C₄×C₉×C₁₁
Frattini	C₃	C₃×C₁₁×#5997
Fitting	C₇²×C₉×C₁₁	C₄
socle	C₃×C₇²×C₁₁	C₃×C₄
prime radical	C₃×C₁₁×C₇⋊D₇	C₂×C₃
cosocle	C₃×C₇⋊D₇	C₂×C₃×C₁₁
LCS	G ▷ C₇²
UCS	C₁ ◁ C₉×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₇²×C₉×C₁₁	C₄	semidirect
5. C₁₁×#5997	C₉	direct (N × H)
6. C₉×#5997	C₁₁	direct (N × H)
13. C₇²×C₁₁	C₄×C₉	semidirect
15. C₇²×C₉	C₄×C₁₁	semidirect
20. #5997	C₉×C₁₁	direct (N × H)
25. C₉×C₁₁	#5997	direct (N × H)
30. C₇²	C₄×C₉×C₁₁	semidirect
40. C₁₁	C₉×#5997	direct (N × H)
41. C₉	C₁₁×#5997	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₁₁×C₇⋊D₇	2
C₃×C₁₁×#5997	3
C₉×#5997	11
C₄×C₉×C₁₁	49

Subgroups — C9×C11×#5997 #34084705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₁₁×#5997 #34084705