Subgroups — C₁₁²×#1039⋊C₃ #49137293

Order 36300.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁²×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁²×#1039	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅²×C₁₁²	C₂×C₃	1	1	yes	characteristic
5	C₁₁×#1039⋊C₃	C₁₁	1	12	yes	maximal, direct product factor
6	C₅²×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₁₁²×Dic₅	—	15	2	no	—
8	C₂×C₁₁×C₅²⋊C₃	C₂×C₁₁	1	12	yes	—
9	C₃×C₄×C₁₁²	—	25	1	no	maximal, Hall
10	C₂×C₅×C₁₁²	—	3	2	no	—
11	C₁₁×#1039	C₃×C₁₁	1	12	yes	complemented
12	C₁₁×C₅²⋊C₃	C₄×C₁₁	1	12	yes	complemented
13	C₂×C₃×C₁₁²	—	25	1	no	—
14	C₅×C₁₁²	—	3	2	no	—
15	C₂×C₅²×C₁₁	C₂×C₃×C₁₁	1	12	yes	—
16	C₄×C₁₁²	—	25	1	no	Hall
17	C₃×C₁₁²	—	25	1	no	Hall
18	#1039⋊C₃	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
19	C₅²×C₁₁	C₃×C₄×C₁₁	1	12	yes	complemented
20	C₂×C₁₁²	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
21	C₁₁×Dic₅	—	15	24	no	—
22	C₂×C₅²⋊C₃	C₂×C₁₁²	1	1	yes	characteristic
23	C₃×C₄×C₁₁	—	25	12	no	—
24	C₁₁²	#1039⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅×C₁₁	—	3	24	no	—
26	#1039	C₃×C₁₁²	1	1	yes	characteristic, complemented, Hall
27	C₅²⋊C₃	C₄×C₁₁²	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₁	—	25	12	no	—
29	C₅×C₁₁	—	3	24	no	—
30	C₂×C₅²	C₂×C₃×C₁₁²	1	1	yes	characteristic
31	C₄×C₁₁	—	25	12	no	—
32	C₃×C₁₁	—	25	12	no	—
33	C₅²	C₃×C₄×C₁₁²	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₁₁	C₁₁×(C₅⋊D₅)⋊C₃	1	12	yes	—
35	Dic₅	—	15	2	no	—
36	C₃×C₄	—	25	1	no	Hall
37	C₁₁	C₁₁×#1039⋊C₃	1	12	yes	direct product factor
38	C₂×C₅	—	3	2	no	—
39	C₂×C₃	—	25	1	no	—
40	C₅	—	3	2	no	—
41	C₄	—	25	1	no	Sylow
42	C₃	—	25	1	no	Sylow
43	C₂	C₁₁²×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁²	(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²	C₃×C₄×C₁₁²
Frattini	C₂	C₁₁²×(C₅⋊D₅)⋊C₃
Fitting, socle	C₂×C₅²×C₁₁²	C₂×C₃
prime radical	C₂×C₁₁²×C₅²⋊C₃	C₂
cosocle	C₂×C₅²	C₂×C₃×C₁₁²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₁₁²

Complements

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

N	H ≅ G/N	type
2. C₁₁²×#1039	C₃	semidirect
3. C₁₁²×C₅²⋊C₃	C₄	semidirect
5. C₁₁×#1039⋊C₃	C₁₁	direct (N × H)
6. C₅²×C₁₁²	C₃×C₄	semidirect
11. C₁₁×#1039	C₃×C₁₁	semidirect
12. C₁₁×C₅²⋊C₃	C₄×C₁₁	semidirect
18. #1039⋊C₃	C₁₁²	direct (N × H)
19. C₅²×C₁₁	C₃×C₄×C₁₁	semidirect
24. C₁₁²	#1039⋊C₃	direct (N × H)
26. #1039	C₃×C₁₁²	semidirect
27. C₅²⋊C₃	C₄×C₁₁²	semidirect
33. C₅²	C₃×C₄×C₁₁²	semidirect
37. C₁₁	C₁₁×#1039⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁²×C₅²⋊C₃	2
C₁₁²×#1039	3
C₁₁×#1039⋊C₃	11
C₃×C₄×C₁₁²	25

Subgroups — C112×#1039⋊C3 #49137293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁²×#1039⋊C₃ #49137293