Subgroups — C₃²×C₁₁×#5997 #34084992

Order 19404.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₁×#5997	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇²×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×C₇⋊D₇	C₂×C₃	1	4	yes	—
5	C₁₁×#5997	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×#5997	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇²×C₁₁	C₃×C₄	1	4	yes	complemented
8	C₃²×C₁₁×D₇	—	14	4	no	—
9	C₁₁×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic
10	C₃²×C₇⋊D₇	C₂×C₁₁	1	1	yes	characteristic
11	C₃²×C₇×C₁₁	—	2	4	no	—
12	C₃×#5997	C₃×C₁₁	1	4	yes	direct product factor
13	C₇²×C₁₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×D₇	—	14	16	no	—
15	C₃²×C₇²	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₄×C₁₁	—	49	1	no	maximal, Hall
17	C₃×C₇⋊D₇	C₂×C₃×C₁₁	1	4	yes	—
18	C₃×C₇×C₁₁	—	2	16	no	—
19	C₂×C₃²×C₁₁	—	49	1	no	—
20	#5997	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₁₁×D₇	—	14	4	no	—
22	C₃×C₇²	C₃×C₄×C₁₁	1	4	yes	complemented
23	C₃×C₄×C₁₁	—	49	4	no	—
24	C₃²×D₇	—	14	4	no	—
25	C₃²×C₁₁	#5997	1	1	yes	characteristic, direct product factor, Hall
26	C₇⋊D₇	C₂×C₃²×C₁₁	1	1	yes	characteristic
27	C₇×C₁₁	—	2	4	no	—
28	C₂×C₃×C₁₁	—	49	4	no	—
29	C₃²×C₇	—	2	4	no	—
30	C₇²	C₃²×C₄×C₁₁	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₁	—	49	1	no	Hall
32	C₃×D₇	—	14	16	no	—
33	C₃²×C₄	—	49	1	no	Hall
34	C₃×C₁₁	C₃×#5997	1	4	yes	direct product factor
35	C₂×C₁₁	—	49	1	no	—
36	C₃×C₇	—	2	16	no	—
37	C₂×C₃²	—	49	1	no	—
38	D₇	—	14	4	no	—
39	C₃×C₄	—	49	4	no	—
40	C₁₁	C₃²×#5997	1	1	yes	characteristic, direct product factor, Sylow
41	C₃²	C₁₁×#5997	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	—	2	4	no	—
43	C₂×C₃	—	49	4	no	—
44	C₄	—	49	1	no	Sylow
45	C₃	C₃×C₁₁×#5997	1	4	yes	direct product factor
46	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₁₁	#5997
commutator, hypocenter	C₇²	C₃²×C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₁	C₄
prime radical	C₃²×C₁₁×C₇⋊D₇	C₂
cosocle	C₇⋊D₇	C₂×C₃²×C₁₁
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃²×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₁×#5997	C₃	direct (N × H)
3. C₃²×C₇²×C₁₁	C₄	semidirect
5. C₁₁×#5997	C₃²	direct (N × H)
6. C₃²×#5997	C₁₁	direct (N × H)
7. C₃×C₇²×C₁₁	C₃×C₄	semidirect
12. C₃×#5997	C₃×C₁₁	direct (N × H)
13. C₇²×C₁₁	C₃²×C₄	semidirect
15. C₃²×C₇²	C₄×C₁₁	semidirect
20. #5997	C₃²×C₁₁	direct (N × H)
22. C₃×C₇²	C₃×C₄×C₁₁	semidirect
25. C₃²×C₁₁	#5997	direct (N × H)
30. C₇²	C₃²×C₄×C₁₁	semidirect
34. C₃×C₁₁	C₃×#5997	direct (N × H)
40. C₁₁	C₃²×#5997	direct (N × H)
41. C₃²	C₁₁×#5997	direct (N × H)
45. C₃	C₃×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
C₃²×C₁₁×C₇⋊D₇	2
C₃×C₁₁×#5997	3
C₃²×#5997	11
C₃²×C₄×C₁₁	49

Subgroups — C32×C11×#5997 #34084992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₁×#5997 #34084992