Subgroups — C₂×C₅×C₁₁×C₆₇⋊C₃ #36348608

Order 22110.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₁×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₁₁×C₆₇⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₆₇⋊C₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₅×C₆₇⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₆₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₆₇⋊C₃	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₁₁×C₆₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₆₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₂×C₆₇⋊C₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₆₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₅×C₁₁	—	67	1	no	maximal, Hall
14	C₆₇⋊C₃	C₂×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅×C₁₁	—	67	1	no	Hall
16	C₂×C₆₇	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₁	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₆₇	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃×C₁₁	—	67	1	no	Hall
20	C₅×C₁₁	C₂×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₁	—	67	1	no	Hall
22	C₂×C₃×C₅	—	67	1	no	Hall
23	C₂×C₁₁	C₅×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₅	—	67	1	no	Hall
25	C₁₁	C₂×C₅×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₅	C₁₁×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	—	67	1	no	Hall
28	C₅	C₂×C₁₁×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	67	1	no	Sylow
30	C₂	C₅×C₁₁×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁	C₆₇⋊C₃
commutator, cosocle, hypocenter	C₆₇	C₂×C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₆₇	C₃
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₆₇⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₁₁×C₆₇	C₃	semidirect
3. C₂×C₁₁×C₆₇⋊C₃	C₅	direct (N × H)
4. C₅×C₁₁×C₆₇	C₂×C₃	semidirect
5. C₁₁×C₆₇⋊C₃	C₂×C₅	direct (N × H)
6. C₂×C₅×C₆₇⋊C₃	C₁₁	direct (N × H)
7. C₂×C₁₁×C₆₇	C₃×C₅	semidirect
8. C₅×C₆₇⋊C₃	C₂×C₁₁	direct (N × H)
9. C₁₁×C₆₇	C₂×C₃×C₅	semidirect
10. C₂×C₅×C₆₇	C₃×C₁₁	semidirect
11. C₂×C₆₇⋊C₃	C₅×C₁₁	direct (N × H)
12. C₅×C₆₇	C₂×C₃×C₁₁	semidirect
14. C₆₇⋊C₃	C₂×C₅×C₁₁	direct (N × H)
16. C₂×C₆₇	C₃×C₅×C₁₁	semidirect
17. C₂×C₅×C₁₁	C₆₇⋊C₃	direct (N × H)
18. C₆₇	C₂×C₃×C₅×C₁₁	semidirect
20. C₅×C₁₁	C₂×C₆₇⋊C₃	direct (N × H)
23. C₂×C₁₁	C₅×C₆₇⋊C₃	direct (N × H)
25. C₁₁	C₂×C₅×C₆₇⋊C₃	direct (N × H)
26. C₂×C₅	C₁₁×C₆₇⋊C₃	direct (N × H)
28. C₅	C₂×C₁₁×C₆₇⋊C₃	direct (N × H)
30. C₂	C₅×C₁₁×C₆₇⋊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
C₅×C₁₁×C₆₇⋊C₃	2
C₂×C₅×C₁₁×C₆₇	3
C₂×C₁₁×C₆₇⋊C₃	5
C₂×C₅×C₆₇⋊C₃	11
C₂×C₃×C₅×C₁₁	67

Subgroups — C2×C5×C11×C67⋊C3 #36348608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₁×C₆₇⋊C₃ #36348608