Subgroups — C₃×(C₁₁⋊C₅)⋊#5997 #44568584

Order 32340.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁⋊C₅×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	(C₁₁⋊C₅)⋊#5997	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇²×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁⋊#5997	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₁⋊C₅×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	C₇²×C₁₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₃×D₇×C₁₁⋊C₅	—	14	4	no	—
10	C₁₁⋊#5997	C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇²×C₁₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₇⋊D₇	—	11	1	no	—
13	C₃×C₇×C₁₁⋊C₅	—	2	4	no	—
14	C₁₁×C₇⋊D₇	C₂×C₃×C₅	1	1	yes	characteristic
15	C₅×#5997	—	11	1	no	Hall
16	D₇×C₁₁⋊C₅	—	14	4	no	—
17	C₃×C₅×C₇²	—	11	1	no	Hall
18	C₃×Dic₁₁⋊C₅	—	49	1	no	maximal, Hall
19	C₃×#5997	—	55	1	no	Hall
20	C₇²×C₁₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
21	C₅×C₇⋊D₇	—	11	1	no	—
22	C₃×C₁₁×D₇	—	14	4	no	—
23	C₇×C₁₁⋊C₅	—	2	4	no	—
24	C₂×C₃×C₁₁⋊C₅	—	49	1	no	—
25	C₃×C₇⋊D₇	AGL(1,𝔽₁₁)	1	1	yes	characteristic
26	C₅×C₇²	—	11	1	no	Hall
27	C₃×C₇×C₁₁	—	2	4	no	—
28	Dic₁₁⋊C₅	—	49	1	no	Hall
29	C₃×C₅×D₇	—	154	4	no	—
30	#5997	—	55	1	no	Hall
31	C₃×C₁₁⋊C₅	#5997	1	1	yes	characteristic, complemented, Hall
32	C₁₁×D₇	—	14	4	no	—
33	C₃×C₇²	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
34	C₃×Dic₁₁	—	49	1	no	Hall
35	C₂×C₁₁⋊C₅	—	49	1	no	—
36	C₃×C₅×C₇	—	22	4	no	—
37	C₇⋊D₇	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
38	C₇×C₁₁	—	2	4	no	—
39	C₅×D₇	—	154	4	no	—
40	C₂×C₃×C₁₁	—	49	1	no	—
41	C₃×C₄×C₅	—	539	1	no	Hall
42	C₁₁⋊C₅	C₃×#5997	1	1	yes	characteristic, complemented, Hall
43	C₇²	C₃×Dic₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
44	Dic₁₁	—	49	1	no	Hall
45	C₃×D₇	—	14	4	no	—
46	C₅×C₇	—	22	4	no	—
47	C₃×C₁₁	C₅×#5997	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₅	—	539	1	no	—
49	C₂×C₁₁	—	49	1	no	—
50	C₃×C₇	—	2	4	no	—
51	C₄×C₅	—	539	1	no	Hall
52	C₃×C₅	—	11	1	no	Hall
53	D₇	—	14	4	no	—
54	C₃×C₄	—	2695	1	no	Hall
55	C₁₁	C₃×C₅×#5997	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	539	1	no	—
57	C₇	—	2	4	no	—
58	C₂×C₃	—	49	1	no	—
59	C₅	—	11	1	no	Sylow
60	C₄	—	2695	1	no	Sylow
61	C₃	(C₁₁⋊C₅)⋊#5997	1	1	yes	characteristic, direct product factor, Sylow
62	C₂	—	49	1	no	—

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

Complements

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

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

Subgroups — C3×(C11⋊C5)⋊#5997 #44568584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₁₁⋊C₅)⋊#5997 #44568584