Subgroups — C₂×C₇×D₁₁₁₉ #44531313

Order 31332.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₁₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₃₇₃	—	3	1	no	maximal, Hall
4	C₃×C₇×C₃₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₃₇₃	D₃	1	1	yes	characteristic, complemented
6	C₇×D₃₇₃	—	3	2	no	—
7	C₂×D₁₁₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₃₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₃₇₃	C₂×C₇	1	1	yes	characteristic, complemented
10	D₁₁₁₉	C₂×C₇	1	2	yes	direct product factor
11	C₂×D₃₇₃	—	3	1	no	Hall
12	C₃×C₃₇₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃₇₃	D₃×C₇	1	1	yes	characteristic, complemented
14	D₃₇₃	—	3	2	no	—
15	C₃₇₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₃×C₇	—	373	1	no	maximal, Hall
17	C₂×C₃×C₇	D₃₇₃	1	1	yes	characteristic, complemented
18	D₃×C₇	—	373	2	no	—
19	C₂²×C₇	—	1119	1	no	Hall
20	C₃×C₇	C₂×D₃₇₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇	—	1119	2	no	—
22	C₂×C₇	D₁₁₁₉	1	1	yes	characteristic, direct product factor
23	C₂×D₃	—	373	1	no	Hall
24	C₇	C₂×D₁₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃	C₇×D₃₇₃	1	1	yes	characteristic, complemented
26	D₃	—	373	2	no	—
27	C₂²	—	1119	1	no	Sylow
28	C₃	C₂×C₇×D₃₇₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	1119	2	no	—
30	C₂	C₇×D₁₁₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₁₁₉
commutator, cosocle, hypocenter	C₃×C₃₇₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₃₇₃	C₂
LCS	G ▷ C₃×C₃₇₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₁₁₉	C₂	direct (N × H)
2. C₂×C₃×C₇×C₃₇₃	C₂	semidirect
4. C₃×C₇×C₃₇₃	C₂²	semidirect
5. C₂×C₇×C₃₇₃	D₃	semidirect
7. C₂×D₁₁₁₉	C₇	direct (N × H)
8. C₇×C₃₇₃	C₂×D₃	semidirect
9. C₂×C₃×C₃₇₃	C₂×C₇	semidirect
10. D₁₁₁₉	C₂×C₇	direct (N × H)
12. C₃×C₃₇₃	C₂²×C₇	semidirect
13. C₂×C₃₇₃	D₃×C₇	semidirect
15. C₃₇₃	C₂×D₃×C₇	semidirect
17. C₂×C₃×C₇	D₃₇₃	semidirect
20. C₃×C₇	C₂×D₃₇₃	semidirect
22. C₂×C₇	D₁₁₁₉	direct (N × H)
24. C₇	C₂×D₁₁₁₉	direct (N × H)
25. C₂×C₃	C₇×D₃₇₃	semidirect
28. C₃	C₂×C₇×D₃₇₃	semidirect
30. C₂	C₇×D₁₁₁₉	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×D₁₁₁₉	2
C₂×C₃×C₇×C₃₇₃	2
C₂×C₇×D₃₇₃	3
C₂×D₁₁₁₉	7
C₂×D₃×C₇	373

Subgroups — C2×C7×D1119 #44531313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₁₁₁₉ #44531313