Subgroups — C₂×C₁₁×#3874 #15693174

Order 3300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3874	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₅×C₁₁	—	3	1	no	maximal, Hall
4	C₁₁×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₁₁	D₃	1	1	yes	characteristic, complemented
6	C₅×D₅×C₁₁	—	3	2	no	—
7	C₂×#3874	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅²×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₅×C₁₁	—	15	1	no	—
10	C₂×D₅×C₁₁	—	3	1	no	—
11	C₂×C₅²⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented
12	#3874	C₂×C₁₁	1	2	yes	direct product factor
13	C₂×D₃×C₁₁	—	25	1	no	maximal, Hall
14	C₂×C₅×C₁₁	—	3	1	no	—
15	C₂×C₅×C₁₁	—	3	1	no	—
16	C₂×C₅×C₁₁	—	15	2	no	—
17	D₅×C₁₁	—	3	2	no	—
18	C₂×C₅×D₅	—	3	1	no	Hall
19	C₅²⋊C₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₁	—	25	1	no	—
21	D₃×C₁₁	—	25	2	no	—
22	C₅×C₁₁	—	3	1	no	—
23	C₅×C₁₁	—	3	1	no	—
24	C₂×C₅²	D₃×C₁₁	1	1	yes	characteristic, complemented
25	C₅×D₅	—	3	2	no	—
26	C₂²×C₁₁	—	15	1	no	Hall
27	C₃×C₁₁	—	25	1	no	Hall
28	C₅²	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₁	—	15	2	no	—
30	C₂×C₁₁	#3874	1	1	yes	characteristic, direct product factor
31	C₂²×C₅	—	15	1	no	—
32	C₂×D₅	—	3	1	no	—
33	C₂×D₃	—	25	1	no	Hall
34	C₁₁	C₂×#3874	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₅	—	3	1	no	—
36	C₂×C₅	—	3	1	no	—
37	C₂×C₅	—	15	2	no	—
38	D₅	—	3	2	no	—
39	C₂×C₃	—	25	1	no	—
40	D₃	—	25	2	no	—
41	C₅	—	3	1	no	—
42	C₅	—	3	1	no	—
43	C₂²	—	15	1	no	Sylow
44	C₃	—	25	1	no	Sylow
45	C₂	—	15	2	no	—
46	C₂	C₁₁×#3874	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₁	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×C₅²⋊C₃	C₂	semidirect
2. C₁₁×#3874	C₂	direct (N × H)
4. C₁₁×C₅²⋊C₃	C₂²	semidirect
5. C₂×C₅²×C₁₁	D₃	semidirect
7. C₂×#3874	C₁₁	direct (N × H)
8. C₅²×C₁₁	C₂×D₃	semidirect
11. C₂×C₅²⋊C₃	C₂×C₁₁	semidirect
12. #3874	C₂×C₁₁	direct (N × H)
19. C₅²⋊C₃	C₂²×C₁₁	semidirect
24. C₂×C₅²	D₃×C₁₁	semidirect
28. C₅²	C₂×D₃×C₁₁	semidirect
30. C₂×C₁₁	#3874	direct (N × H)
34. C₁₁	C₂×#3874	direct (N × H)
46. C₂	C₁₁×#3874	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×C₁₁×C₅²⋊C₃	2
C₁₁×#3874	2
C₂×C₅×D₅×C₁₁	3
C₂×#3874	11
C₂×D₃×C₁₁	25

Subgroups — C2×C11×#3874 #15693174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3874 #15693174