Subgroups — C₁₁×C₁₃×D₉₁ #39907366

Order 26026.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₃×D₁₃	—	7	1	no	maximal, Hall
3	C₁₃×D₉₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁×D₉₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor
5	C₁₁×C₁₃×D₇	—	13	1	no	maximal
6	C₁₁×C₁₃²	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₃²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₁×C₁₃	—	2	6	no	—
9	C₇×C₁₁×C₁₃	D₁₃	1	1	yes	characteristic, complemented
10	C₇×C₁₁×C₁₃	C₂×C₁₃	1	1	yes	characteristic, complemented
11	C₁₃×D₁₃	—	7	1	no	Hall
12	C₂×C₁₁×C₁₃	—	91	1	no	—
13	C₁₁×D₁₃	—	7	1	no	—
14	D₉₁	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
15	C₁₃×D₇	—	13	1	no	—
16	C₁₃²	C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
17	C₁₁×D₇	—	13	1	no	Hall
18	C₁₁×C₁₃	—	2	6	no	—
19	C₁₁×C₁₃	C₁₃×D₇	1	1	yes	characteristic, complemented
20	C₁₁×C₁₃	D₉₁	1	1	yes	characteristic, direct product factor
21	C₇×C₁₃	—	2	6	no	—
22	C₇×C₁₃	C₁₁×D₁₃	1	1	yes	characteristic, complemented
23	C₇×C₁₃	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
24	C₇×C₁₁	C₁₃×D₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₃	—	91	1	no	—
26	D₁₃	—	7	1	no	—
27	C₂×C₁₁	—	91	1	no	Hall
28	D₇	—	13	1	no	Hall
29	C₁₃	—	2	6	no	—
30	C₁₃	C₁₁×C₁₃×D₇	1	1	yes	characteristic, complemented
31	C₁₃	C₁₁×D₉₁	1	1	yes	characteristic, direct product factor
32	C₁₁	C₁₃×D₉₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₇	C₁₁×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	D₉₁
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₃²	C₂
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×C₁₃²	C₂	semidirect
3. C₁₃×D₉₁	C₁₁	direct (N × H)
4. C₁₁×D₉₁	C₁₃	direct (N × H)
6. C₁₁×C₁₃²	D₇	semidirect
7. C₇×C₁₃²	C₂×C₁₁	semidirect
9. C₇×C₁₁×C₁₃	D₁₃	semidirect
10. C₇×C₁₁×C₁₃	C₂×C₁₃	semidirect
14. D₉₁	C₁₁×C₁₃	direct (N × H)
16. C₁₃²	C₁₁×D₇	semidirect
19. C₁₁×C₁₃	C₁₃×D₇	semidirect
20. C₁₁×C₁₃	D₉₁	direct (N × H)
22. C₇×C₁₃	C₁₁×D₁₃	semidirect
23. C₇×C₁₃	C₂×C₁₁×C₁₃	semidirect
24. C₇×C₁₁	C₁₃×D₁₃	semidirect
30. C₁₃	C₁₁×C₁₃×D₇	semidirect
31. C₁₃	C₁₁×D₉₁	direct (N × H)
32. C₁₁	C₁₃×D₉₁	direct (N × H)
33. C₇	C₁₁×C₁₃×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₁×C₁₃²	2
C₁₁×C₁₃×D₁₃	7
C₁₃×D₉₁	11
C₁₁×D₉₁	13
C₁₁×C₁₃×D₇	13

Subgroups — C11×C13×D91 #39907366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₃×D₉₁ #39907366