Subgroups — C₃×C₃⋊(C₁₁⋊#5997) #34085013

Order 19404.

152 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	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₁⋊#5997	—	3	1	no	maximal
4	C₃²×C₇²×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇⋊D₇	—	2	1	no	—
6	C₃×C₁₁×C₇⋊D₇	D₃	1	1	yes	characteristic
7	C₃×C₁₁×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
8	C₁₁⋊#5997	—	3	1	no	Hall
9	C₃×C₃⋊#5997	—	11	1	no	maximal, Hall
10	C₃×C₇²×C₁₁	—	2	1	no	—
11	C₃×C₇²×C₁₁	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇²×C₁₁	C₃×C₄	1	1	yes	characteristic, complemented
13	C₃²×C₁₁×D₇	—	14	4	no	—
14	C₁₁×C₇⋊D₇	C₃×D₃	1	1	yes	characteristic
15	C₃²×C₇⋊D₇	D₁₁	1	1	yes	characteristic
16	C₃²×C₇×C₁₁	—	2	4	no	—
17	C₃⋊#5997	—	11	1	no	—
18	C₃×#5997	—	33	1	no	—
19	C₇²×C₁₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₁×D₇	—	14	4	no	—
21	C₃×C₁₁×D₇	—	14	4	no	—
22	C₃×C₁₁×D₇	—	14	8	no	—
23	C₃²×C₇²	Dic₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×Dic₃₃	—	49	1	no	maximal, Hall
25	C₃×C₇⋊D₇	—	2	1	no	—
26	C₃×C₇⋊D₇	C₃×D₁₁	1	1	yes	characteristic
27	C₃×C₇⋊D₇	D₃₃	1	1	yes	characteristic
28	C₃×C₇×C₁₁	—	2	8	no	—
29	C₃×C₇×C₁₁	—	2	4	no	—
30	C₃×C₇×C₁₁	—	2	4	no	—
31	C₂×C₃²×C₁₁	—	49	1	no	—
32	#5997	—	33	1	no	Hall
33	C₁₁×D₇	—	14	4	no	—
34	C₃×C₇²	—	2	1	no	—
35	C₃×C₇²	C₃×Dic₁₁	1	1	yes	characteristic, complemented
36	C₃×C₇²	Dic₃₃	1	1	yes	characteristic, complemented
37	Dic₃₃	—	49	1	no	—
38	C₃×Dic₁₁	—	147	1	no	—
39	C₃²×D₇	—	14	4	no	—
40	C₃²×C₁₁	#5997	1	1	yes	characteristic, complemented, Hall
41	C₇⋊D₇	C₃×D₃₃	1	1	yes	characteristic
42	C₇×C₁₁	—	2	4	no	—
43	C₂×C₃×C₁₁	—	49	1	no	—
44	C₂×C₃×C₁₁	—	49	1	no	—
45	C₂×C₃×C₁₁	—	98	1	no	—
46	C₃²×C₇	—	2	4	no	—
47	C₇²	C₃×Dic₃₃	1	1	yes	characteristic, complemented, Sylow
48	Dic₁₁	—	147	1	no	Hall
49	C₃×D₇	—	14	4	no	—
50	C₃×D₇	—	14	4	no	—
51	C₃×D₇	—	14	8	no	—
52	C₃×Dic₃	—	539	1	no	Hall
53	C₃×C₁₁	—	2	1	no	—
54	C₃×C₁₁	C₃×#5997	1	1	yes	characteristic, complemented
55	C₃×C₁₁	C₃⋊#5997	1	1	yes	characteristic, complemented
56	C₂×C₁₁	—	49	1	no	—
57	C₃×C₇	—	2	8	no	—
58	C₃×C₇	—	2	4	no	—
59	C₃×C₇	—	2	4	no	—
60	C₂×C₃²	—	49	1	no	—
61	D₇	—	14	4	no	—
62	C₃×C₄	—	1617	1	no	—
63	Dic₃	—	539	1	no	—
64	C₁₁	C₃×C₃⋊#5997	1	1	yes	characteristic, complemented, Sylow
65	C₃²	C₁₁⋊#5997	1	1	yes	characteristic, complemented, Sylow
66	C₇	—	2	4	no	—
67	C₂×C₃	—	49	1	no	—
68	C₂×C₃	—	49	1	no	—
69	C₂×C₃	—	98	1	no	—
70	C₄	—	1617	1	no	Sylow
71	C₃	—	2	1	no	—
72	C₃	C₃×C₁₁⋊#5997	1	1	yes	characteristic, complemented
73	C₃	C₃⋊(C₁₁⋊#5997)	1	1	yes	characteristic, direct product factor
74	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₁₁⋊#5997)
commutator, hypocenter	C₃×C₇²×C₁₁	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₁	C₄
prime radical	C₃²×C₁₁×C₇⋊D₇	C₂
cosocle	C₃×C₁₁×C₇⋊D₇	C₂×C₃
LCS	G ▷ C₃×C₇²×C₁₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₁₁⋊#5997)	C₃	direct (N × H)
4. C₃²×C₇²×C₁₁	C₄	semidirect
11. C₃×C₇²×C₁₁	Dic₃	semidirect
12. C₃×C₇²×C₁₁	C₃×C₄	semidirect
19. C₇²×C₁₁	C₃×Dic₃	semidirect
23. C₃²×C₇²	Dic₁₁	semidirect
35. C₃×C₇²	C₃×Dic₁₁	semidirect
36. C₃×C₇²	Dic₃₃	semidirect
40. C₃²×C₁₁	#5997	semidirect
47. C₇²	C₃×Dic₃₃	semidirect
54. C₃×C₁₁	C₃×#5997	semidirect
55. C₃×C₁₁	C₃⋊#5997	semidirect
64. C₁₁	C₃×C₃⋊#5997	semidirect
65. C₃²	C₁₁⋊#5997	semidirect
72. C₃	C₃×C₁₁⋊#5997	semidirect
73. 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
C₃×C₁₁⋊#5997	3
C₃×C₃⋊#5997	11
C₃×Dic₃₃	49

Subgroups — C3×C3⋊(C11⋊#5997) #34085013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊(C₁₁⋊#5997) #34085013