Subgroups — C₂×C₁₁×D₁₁×C₆₇ #44569849

Order 32428.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₁₁×C₆₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁²×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁×C₆₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₁₁×C₆₇	—	11	1	no	maximal
6	C₂×C₁₁×C₆₇	—	2	5	no	—
7	C₂×C₁₁×C₆₇	—	11	2	no	—
8	C₂×C₁₁×C₆₇	D₁₁	1	1	yes	characteristic, direct product factor
9	C₂×C₁₁×C₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented
10	D₁₁×C₆₇	C₂×C₁₁	1	2	yes	direct product factor
11	C₁₁×C₆₇	—	2	5	no	—
12	C₁₁×C₆₇	C₂×D₁₁	1	1	yes	characteristic, direct product factor
13	C₁₁×C₆₇	C₂²×C₁₁	1	1	yes	characteristic, complemented
14	C₂×C₁₁×D₁₁	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂²×C₆₇	—	11	1	no	Hall
16	C₂×C₁₁²	C₂×C₆₇	1	1	yes	characteristic, complemented
17	C₁₁×D₁₁	C₂×C₆₇	1	2	yes	direct product factor
18	C₂×C₆₇	—	11	2	no	—
19	C₂×C₆₇	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
20	C₁₁²	C₂²×C₆₇	1	1	yes	characteristic, complemented, Sylow
21	C₆₇	C₂×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₁₁	—	11	1	no	—
23	C₂×D₁₁	C₁₁×C₆₇	1	1	yes	characteristic, direct product factor
24	C₂×C₁₁	—	2	5	no	—
25	C₂×C₁₁	—	11	2	no	—
26	C₂×C₁₁	D₁₁×C₆₇	1	1	yes	characteristic, direct product factor
27	C₂×C₁₁	C₂×C₁₁×C₆₇	1	1	yes	characteristic, complemented
28	D₁₁	C₂×C₁₁×C₆₇	1	2	yes	direct product factor
29	C₁₁	—	2	5	no	—
30	C₁₁	C₂²×C₁₁×C₆₇	1	1	yes	characteristic, complemented
31	C₁₁	C₂×D₁₁×C₆₇	1	1	yes	characteristic, direct product factor
32	C₂²	—	11	1	no	Sylow
33	C₂	—	11	2	no	—
34	C₂	C₁₁×D₁₁×C₆₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₆₇	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₁₁×C₆₇
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²×C₆₇	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₁×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₁₁×C₆₇	C₂	direct (N × H)
2. C₂×C₁₁²×C₆₇	C₂	semidirect
3. C₁₁²×C₆₇	C₂²	semidirect
4. C₂×D₁₁×C₆₇	C₁₁	direct (N × H)
8. C₂×C₁₁×C₆₇	D₁₁	direct (N × H)
9. C₂×C₁₁×C₆₇	C₂×C₁₁	semidirect
10. D₁₁×C₆₇	C₂×C₁₁	direct (N × H)
12. C₁₁×C₆₇	C₂×D₁₁	direct (N × H)
13. C₁₁×C₆₇	C₂²×C₁₁	semidirect
14. C₂×C₁₁×D₁₁	C₆₇	direct (N × H)
16. C₂×C₁₁²	C₂×C₆₇	semidirect
17. C₁₁×D₁₁	C₂×C₆₇	direct (N × H)
19. C₂×C₆₇	C₁₁×D₁₁	direct (N × H)
20. C₁₁²	C₂²×C₆₇	semidirect
21. C₆₇	C₂×C₁₁×D₁₁	direct (N × H)
23. C₂×D₁₁	C₁₁×C₆₇	direct (N × H)
26. C₂×C₁₁	D₁₁×C₆₇	direct (N × H)
27. C₂×C₁₁	C₂×C₁₁×C₆₇	semidirect
28. D₁₁	C₂×C₁₁×C₆₇	direct (N × H)
30. C₁₁	C₂²×C₁₁×C₆₇	semidirect
31. C₁₁	C₂×D₁₁×C₆₇	direct (N × H)
34. C₂	C₁₁×D₁₁×C₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₁₁×C₆₇	2
C₂×C₁₁²×C₆₇	2
C₂×D₁₁×C₆₇	11
C₂²×C₁₁×C₆₇	11
C₂×C₁₁×D₁₁	67

Subgroups — C2×C11×D11×C67 #44569849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₁₁×C₆₇ #44569849