Subgroups — C₂×C₁₁×D₆₇₁ #44443261

Order 29524.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₆₇₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁²×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁²×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₆₁	—	11	1	no	maximal
5	C₂×D₆₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₁₁×C₆₁	—	2	5	no	—
7	C₂×C₁₁×C₆₁	D₁₁	1	1	yes	characteristic, complemented
8	C₂×C₁₁×C₆₁	C₂×C₁₁	1	1	yes	characteristic, complemented
9	D₆₇₁	C₂×C₁₁	1	2	yes	direct product factor
10	C₁₁×D₆₁	—	11	2	no	—
11	C₁₁×C₆₁	—	2	5	no	—
12	C₁₁×C₆₁	C₂×D₁₁	1	1	yes	characteristic, complemented
13	C₁₁×C₆₁	C₂²×C₁₁	1	1	yes	characteristic, complemented
14	C₂×C₁₁×D₁₁	—	61	1	no	maximal, Hall
15	C₂×D₆₁	—	11	1	no	Hall
16	C₂×C₁₁²	D₆₁	1	1	yes	characteristic, complemented
17	C₁₁×D₁₁	—	61	2	no	—
18	C₂×C₆₁	C₁₁×D₁₁	1	1	yes	characteristic, complemented
19	D₆₁	—	11	2	no	—
20	C₁₁²	C₂×D₆₁	1	1	yes	characteristic, complemented, Sylow
21	C₆₁	C₂×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₁₁	—	671	1	no	—
23	C₂×D₁₁	—	61	1	no	—
24	C₂×C₁₁	—	2	5	no	—
25	C₂×C₁₁	—	671	2	no	—
26	C₂×C₁₁	C₁₁×D₆₁	1	1	yes	characteristic, complemented
27	C₂×C₁₁	D₆₇₁	1	1	yes	characteristic, direct product factor
28	D₁₁	—	61	2	no	—
29	C₁₁	—	2	5	no	—
30	C₁₁	C₂×D₆₇₁	1	1	yes	characteristic, direct product factor
31	C₁₁	C₂×C₁₁×D₆₁	1	1	yes	characteristic, complemented
32	C₂²	—	671	1	no	Sylow
33	C₂	—	671	2	no	—
34	C₂	C₁₁×D₆₇₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₆₇₁
commutator, cosocle, hypocenter	C₁₁×C₆₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²×C₆₁	C₂
LCS	G ▷ C₁₁×C₆₁
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₆₇₁	C₂	direct (N × H)
2. C₂×C₁₁²×C₆₁	C₂	semidirect
3. C₁₁²×C₆₁	C₂²	semidirect
5. C₂×D₆₇₁	C₁₁	direct (N × H)
7. C₂×C₁₁×C₆₁	D₁₁	semidirect
8. C₂×C₁₁×C₆₁	C₂×C₁₁	semidirect
9. D₆₇₁	C₂×C₁₁	direct (N × H)
12. C₁₁×C₆₁	C₂×D₁₁	semidirect
13. C₁₁×C₆₁	C₂²×C₁₁	semidirect
16. C₂×C₁₁²	D₆₁	semidirect
18. C₂×C₆₁	C₁₁×D₁₁	semidirect
20. C₁₁²	C₂×D₆₁	semidirect
21. C₆₁	C₂×C₁₁×D₁₁	semidirect
26. C₂×C₁₁	C₁₁×D₆₁	semidirect
27. C₂×C₁₁	D₆₇₁	direct (N × H)
30. C₁₁	C₂×D₆₇₁	direct (N × H)
31. C₁₁	C₂×C₁₁×D₆₁	semidirect
34. C₂	C₁₁×D₆₇₁	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×D₆₇₁	2
C₂×C₁₁²×C₆₁	2
C₂×C₁₁×D₆₁	11
C₂×D₆₇₁	11
C₂×C₁₁×D₁₁	61

Subgroups — C2×C11×D671 #44443261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₆₇₁ #44443261