Subgroups — D₇₇⋊D₁₀₃ #44540581

Order 31724.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₃×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₇₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₁₁₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₁×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₁₀₃	—	7	1	no	maximal, Hall
6	D₇×D₁₀₃	—	11	1	no	maximal, Hall
7	D₁₁₃₃	D₇	1	1	yes	characteristic, complemented
8	C₁₁×D₁₀₃	—	7	1	no	—
9	D₁₁×C₁₀₃	—	7	1	no	—
10	D₇₂₁	D₁₁	1	1	yes	characteristic, complemented
11	C₇×D₁₀₃	—	11	1	no	—
12	D₇×C₁₀₃	—	11	1	no	—
13	C₁₁×C₁₀₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₀₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₀₃	—	77	1	no	Hall
16	D₇×D₁₁	—	103	1	no	maximal, Hall
17	C₂×C₁₀₃	—	77	1	no	—
18	D₁₀₃	—	7	1	no	—
19	D₁₀₃	—	11	1	no	—
20	D₇₇	D₁₀₃	1	1	yes	characteristic, complemented
21	C₇×D₁₁	—	103	1	no	—
22	C₁₁×D₇	—	103	1	no	—
23	C₁₀₃	D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₇×C₁₁	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₁	—	721	1	no	Hall
26	C₂×D₇	—	1133	1	no	Hall
27	C₂×C₁₁	—	721	1	no	—
28	D₁₁	—	7	1	no	—
29	D₁₁	—	103	1	no	—
30	C₂×C₇	—	1133	1	no	—
31	D₇	—	11	1	no	—
32	D₇	—	103	1	no	—
33	C₁₁	D₇×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
34	C₇	D₁₁×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	7931	1	no	Sylow
36	C₂	—	77	1	no	—
37	C₂	—	1133	1	no	—
38	C₂	—	721	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₀₃×D₇₇	C₂	semidirect
2. C₁₁×D₇₂₁	C₂	semidirect
3. C₇×D₁₁₃₃	C₂	semidirect
4. C₇×C₁₁×C₁₀₃	C₂²	semidirect
7. D₁₁₃₃	D₇	semidirect
10. D₇₂₁	D₁₁	semidirect
13. C₁₁×C₁₀₃	C₂×D₇	semidirect
14. C₇×C₁₀₃	C₂×D₁₁	semidirect
20. D₇₇	D₁₀₃	semidirect
23. C₁₀₃	D₇×D₁₁	semidirect
24. C₇×C₁₁	C₂×D₁₀₃	semidirect
33. C₁₁	D₇×D₁₀₃	semidirect
34. C₇	D₁₁×D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₃×D₇₇	2
C₁₁×D₇₂₁	2
C₇×D₁₁₃₃	2
D₁₁×D₁₀₃	7
D₇×D₁₀₃	11
D₇×D₁₁	103

Subgroups — D77⋊D103 #44540581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₇⋊D₁₀₃ #44540581