Subgroups — C₃×C₅×C₁₁⋊#5997 #44568803

Order 32340.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁⋊#5997	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇²×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁⋊#5997	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₁×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	C₃×C₁₁×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic
7	C₃×C₅×#5997	—	11	1	no	maximal, Hall
8	C₅×C₇²×C₁₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₁₁×D₇	—	14	4	no	—
10	C₁₁⋊#5997	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇²×C₁₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₇⋊D₇	D₁₁	1	1	yes	characteristic
13	C₃×C₅×C₇×C₁₁	—	2	4	no	—
14	C₁₁×C₇⋊D₇	C₂×C₃×C₅	1	1	yes	characteristic
15	C₅×#5997	—	11	1	no	Hall
16	C₅×C₁₁×D₇	—	14	4	no	—
17	C₃×C₅×C₇²	Dic₁₁	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×Dic₁₁	—	49	1	no	maximal, Hall
19	C₃×#5997	—	11	1	no	Hall
20	C₇²×C₁₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
21	C₅×C₇⋊D₇	C₃×D₁₁	1	1	yes	characteristic
22	C₃×C₁₁×D₇	—	14	4	no	—
23	C₅×C₇×C₁₁	—	2	4	no	—
24	C₂×C₃×C₅×C₁₁	—	49	1	no	—
25	C₃×C₇⋊D₇	C₅×D₁₁	1	1	yes	characteristic
26	C₅×C₇²	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
27	C₃×C₇×C₁₁	—	2	4	no	—
28	C₅×Dic₁₁	—	49	1	no	Hall
29	C₃×C₅×D₇	—	14	4	no	—
30	#5997	—	11	1	no	Hall
31	C₃×C₅×C₁₁	#5997	1	1	yes	characteristic, complemented, Hall
32	C₁₁×D₇	—	14	4	no	—
33	C₃×C₇²	C₅×Dic₁₁	1	1	yes	characteristic, complemented, Hall
34	C₃×Dic₁₁	—	49	1	no	Hall
35	C₂×C₅×C₁₁	—	49	1	no	—
36	C₃×C₅×C₇	—	2	4	no	—
37	C₇⋊D₇	C₃×C₅×D₁₁	1	1	yes	characteristic
38	C₇×C₁₁	—	2	4	no	—
39	C₅×D₇	—	14	4	no	—
40	C₂×C₃×C₁₁	—	49	1	no	—
41	C₃×C₄×C₅	—	539	1	no	Hall
42	C₅×C₁₁	C₃×#5997	1	1	yes	characteristic, complemented, Hall
43	C₇²	C₃×C₅×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
44	Dic₁₁	—	49	1	no	Hall
45	C₃×D₇	—	14	4	no	—
46	C₅×C₇	—	2	4	no	—
47	C₃×C₁₁	C₅×#5997	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₅	—	49	1	no	—
49	C₂×C₁₁	—	49	1	no	—
50	C₃×C₇	—	2	4	no	—
51	C₄×C₅	—	539	1	no	Hall
52	C₃×C₅	C₁₁⋊#5997	1	1	yes	characteristic, direct product factor, Hall
53	D₇	—	14	4	no	—
54	C₃×C₄	—	539	1	no	Hall
55	C₁₁	C₃×C₅×#5997	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	49	1	no	—
57	C₇	—	2	4	no	—
58	C₂×C₃	—	49	1	no	—
59	C₅	C₃×C₁₁⋊#5997	1	1	yes	characteristic, direct product factor, Sylow
60	C₄	—	539	1	no	Sylow
61	C₃	C₅×C₁₁⋊#5997	1	1	yes	characteristic, direct product factor, Sylow
62	C₂	—	49	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	C₁₁⋊#5997
commutator, hypocenter	C₇²×C₁₁	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₁	C₄
prime radical	C₃×C₅×C₁₁×C₇⋊D₇	C₂
cosocle	C₁₁×C₇⋊D₇	C₂×C₃×C₅
LCS	G ▷ C₇²×C₁₁
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁⋊#5997	C₃	direct (N × H)
3. C₃×C₅×C₇²×C₁₁	C₄	semidirect
4. C₃×C₁₁⋊#5997	C₅	direct (N × H)
8. C₅×C₇²×C₁₁	C₃×C₄	semidirect
10. C₁₁⋊#5997	C₃×C₅	direct (N × H)
11. C₃×C₇²×C₁₁	C₄×C₅	semidirect
17. C₃×C₅×C₇²	Dic₁₁	semidirect
20. C₇²×C₁₁	C₃×C₄×C₅	semidirect
26. C₅×C₇²	C₃×Dic₁₁	semidirect
31. C₃×C₅×C₁₁	#5997	semidirect
33. C₃×C₇²	C₅×Dic₁₁	semidirect
42. C₅×C₁₁	C₃×#5997	semidirect
43. C₇²	C₃×C₅×Dic₁₁	semidirect
47. C₃×C₁₁	C₅×#5997	semidirect
52. C₃×C₅	C₁₁⋊#5997	direct (N × H)
55. C₁₁	C₃×C₅×#5997	semidirect
59. C₅	C₃×C₁₁⋊#5997	direct (N × H)
61. C₃	C₅×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
C₃×C₅×C₁₁×C₇⋊D₇	2
C₅×C₁₁⋊#5997	3
C₃×C₁₁⋊#5997	5
C₃×C₅×#5997	11
C₃×C₅×Dic₁₁	49

Subgroups — C3×C5×C11⋊#5997 #44568803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₁⋊#5997 #44568803