Subgroups — C₂×C₁₁×D₅₉₇ #39911087

Order 26268.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₅₉₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×D₁₉₉	—	3	1	no	maximal, Hall
4	C₃×C₁₁×C₁₉₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₁₉₉	D₃	1	1	yes	characteristic, complemented
6	C₁₁×D₁₉₉	—	3	2	no	—
7	C₂×D₅₉₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×C₁₉₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₉₉	C₂×C₁₁	1	1	yes	characteristic, complemented
10	D₅₉₇	C₂×C₁₁	1	2	yes	direct product factor
11	C₂×D₁₉₉	—	3	1	no	Hall
12	C₃×C₁₉₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₉₉	D₃×C₁₁	1	1	yes	characteristic, complemented
14	D₁₉₉	—	3	2	no	—
15	C₁₉₉	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₃×C₁₁	—	199	1	no	maximal, Hall
17	C₂×C₃×C₁₁	D₁₉₉	1	1	yes	characteristic, complemented
18	D₃×C₁₁	—	199	2	no	—
19	C₂²×C₁₁	—	597	1	no	Hall
20	C₃×C₁₁	C₂×D₁₉₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₁	—	597	2	no	—
22	C₂×C₁₁	D₅₉₇	1	1	yes	characteristic, direct product factor
23	C₂×D₃	—	199	1	no	Hall
24	C₁₁	C₂×D₅₉₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	C₁₁×D₁₉₉	1	1	yes	characteristic, complemented
26	D₃	—	199	2	no	—
27	C₂²	—	597	1	no	Sylow
28	C₃	C₂×C₁₁×D₁₉₉	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	597	2	no	—
30	C₂	C₁₁×D₅₉₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₅₉₇
commutator, cosocle, hypocenter	C₃×C₁₉₉	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁×C₁₉₉	C₂
LCS	G ▷ C₃×C₁₉₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₅₉₇	C₂	direct (N × H)
2. C₂×C₃×C₁₁×C₁₉₉	C₂	semidirect
4. C₃×C₁₁×C₁₉₉	C₂²	semidirect
5. C₂×C₁₁×C₁₉₉	D₃	semidirect
7. C₂×D₅₉₇	C₁₁	direct (N × H)
8. C₁₁×C₁₉₉	C₂×D₃	semidirect
9. C₂×C₃×C₁₉₉	C₂×C₁₁	semidirect
10. D₅₉₇	C₂×C₁₁	direct (N × H)
12. C₃×C₁₉₉	C₂²×C₁₁	semidirect
13. C₂×C₁₉₉	D₃×C₁₁	semidirect
15. C₁₉₉	C₂×D₃×C₁₁	semidirect
17. C₂×C₃×C₁₁	D₁₉₉	semidirect
20. C₃×C₁₁	C₂×D₁₉₉	semidirect
22. C₂×C₁₁	D₅₉₇	direct (N × H)
24. C₁₁	C₂×D₅₉₇	direct (N × H)
25. C₂×C₃	C₁₁×D₁₉₉	semidirect
28. C₃	C₂×C₁₁×D₁₉₉	semidirect
30. C₂	C₁₁×D₅₉₇	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×D₅₉₇	2
C₂×C₃×C₁₁×C₁₉₉	2
C₂×C₁₁×D₁₉₉	3
C₂×D₅₉₇	11
C₂×D₃×C₁₁	199

Subgroups — C2×C11×D597 #39911087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₅₉₇ #39911087