Subgroups — C₂×C₁₀₃×D₇₇ #44540587

Order 31724.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×D₇₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₁×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁×C₁₀₃	—	7	1	no	maximal, Hall
5	C₂×D₇×C₁₀₃	—	11	1	no	maximal, Hall
6	C₂×C₁₁×C₁₀₃	D₇	1	1	yes	characteristic, complemented
7	D₁₁×C₁₀₃	—	7	2	no	—
8	C₂×C₇×C₁₀₃	D₁₁	1	1	yes	characteristic, complemented
9	D₇×C₁₀₃	—	11	2	no	—
10	C₁₁×C₁₀₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₀₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₁₀₃	—	77	1	no	Hall
13	C₂×D₇₇	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₀₃	—	77	2	no	—
15	C₂×C₁₀₃	D₇₇	1	1	yes	characteristic, direct product factor
16	C₂×C₇×C₁₁	C₂×C₁₀₃	1	1	yes	characteristic, complemented
17	D₇₇	C₂×C₁₀₃	1	2	yes	direct product factor
18	C₁₀₃	C₂×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₇×C₁₁	C₂²×C₁₀₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₁	—	7	1	no	Hall
21	C₂×D₇	—	11	1	no	Hall
22	C₂×C₁₁	D₇×C₁₀₃	1	1	yes	characteristic, complemented
23	D₁₁	—	7	2	no	—
24	C₂×C₇	D₁₁×C₁₀₃	1	1	yes	characteristic, complemented
25	D₇	—	11	2	no	—
26	C₁₁	C₂×D₇×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₂×D₁₁×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	77	1	no	Sylow
29	C₂	—	77	2	no	—
30	C₂	C₁₀₃×D₇₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₀₃	D₇₇
commutator, cosocle, hypocenter	C₇×C₁₁	C₂²×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₁₀₃	C₂
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂×C₁₀₃

Complements

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

N	H ≅ G/N	type
1. C₁₀₃×D₇₇	C₂	direct (N × H)
2. C₂×C₇×C₁₁×C₁₀₃	C₂	semidirect
3. C₇×C₁₁×C₁₀₃	C₂²	semidirect
6. C₂×C₁₁×C₁₀₃	D₇	semidirect
8. C₂×C₇×C₁₀₃	D₁₁	semidirect
10. C₁₁×C₁₀₃	C₂×D₇	semidirect
11. C₇×C₁₀₃	C₂×D₁₁	semidirect
13. C₂×D₇₇	C₁₀₃	direct (N × H)
15. C₂×C₁₀₃	D₇₇	direct (N × H)
16. C₂×C₇×C₁₁	C₂×C₁₀₃	semidirect
17. D₇₇	C₂×C₁₀₃	direct (N × H)
18. C₁₀₃	C₂×D₇₇	direct (N × H)
19. C₇×C₁₁	C₂²×C₁₀₃	semidirect
22. C₂×C₁₁	D₇×C₁₀₃	semidirect
24. C₂×C₇	D₁₁×C₁₀₃	semidirect
26. C₁₁	C₂×D₇×C₁₀₃	semidirect
27. C₇	C₂×D₁₁×C₁₀₃	semidirect
30. C₂	C₁₀₃×D₇₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₃×D₇₇	2
C₂×C₇×C₁₁×C₁₀₃	2
C₂×D₁₁×C₁₀₃	7
C₂×D₇×C₁₀₃	11
C₂×D₇₇	103

Subgroups — C2×C103×D77 #44540587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₃×D₇₇ #44540587