Subgroups — C₂×C₇×D₁₁₂₁ #44536010

Order 31388.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₉×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₉×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₉×C₅₉	C₂×C₇	1	1	yes	characteristic, complemented
6	D₁₁₂₁	C₂×C₇	1	2	yes	direct product factor
7	C₂×C₇×D₅₉	—	19	1	no	maximal, Hall
8	C₁₉×C₅₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₅₉	D₁₉	1	1	yes	characteristic, complemented
10	C₇×D₅₉	—	19	2	no	—
11	C₂×C₇×D₁₉	—	59	1	no	maximal, Hall
12	C₇×C₅₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₉	D₅₉	1	1	yes	characteristic, complemented
14	C₇×D₁₉	—	59	2	no	—
15	C₂×D₅₉	—	19	1	no	Hall
16	C₇×C₁₉	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅₉	C₇×D₁₉	1	1	yes	characteristic, complemented
18	D₅₉	—	19	2	no	—
19	C₂×D₁₉	—	59	1	no	Hall
20	C₅₉	C₂×C₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₉	C₇×D₅₉	1	1	yes	characteristic, complemented
22	D₁₉	—	59	2	no	—
23	C₂²×C₇	—	1121	1	no	Hall
24	C₁₉	C₂×C₇×D₅₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	—	1121	2	no	—
26	C₂×C₇	D₁₁₂₁	1	1	yes	characteristic, direct product factor
27	C₇	C₂×D₁₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	1121	1	no	Sylow
29	C₂	—	1121	2	no	—
30	C₂	C₇×D₁₁₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₁₂₁
commutator, cosocle, hypocenter	C₁₉×C₅₉	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₉×C₅₉	C₂
LCS	G ▷ C₁₉×C₅₉
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₁₂₁	C₂	direct (N × H)
2. C₂×C₇×C₁₉×C₅₉	C₂	semidirect
3. C₇×C₁₉×C₅₉	C₂²	semidirect
4. C₂×D₁₁₂₁	C₇	direct (N × H)
5. C₂×C₁₉×C₅₉	C₂×C₇	semidirect
6. D₁₁₂₁	C₂×C₇	direct (N × H)
8. C₁₉×C₅₉	C₂²×C₇	semidirect
9. C₂×C₇×C₅₉	D₁₉	semidirect
12. C₇×C₅₉	C₂×D₁₉	semidirect
13. C₂×C₇×C₁₉	D₅₉	semidirect
16. C₇×C₁₉	C₂×D₅₉	semidirect
17. C₂×C₅₉	C₇×D₁₉	semidirect
20. C₅₉	C₂×C₇×D₁₉	semidirect
21. C₂×C₁₉	C₇×D₅₉	semidirect
24. C₁₉	C₂×C₇×D₅₉	semidirect
26. C₂×C₇	D₁₁₂₁	direct (N × H)
27. C₇	C₂×D₁₁₂₁	direct (N × H)
30. C₂	C₇×D₁₁₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₁₁₂₁	2
C₂×C₇×C₁₉×C₅₉	2
C₂×D₁₁₂₁	7
C₂×C₇×D₅₉	19
C₂×C₇×D₁₉	59

Subgroups — C2×C7×D1121 #44536010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₁₁₂₁ #44536010