Subgroups — D₇₇×D₁₀₉ #46777099

Order 33572.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₃₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₉×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₁×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₁×C₁₀₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₁₀₉	—	7	1	no	maximal, Hall
6	D₇×D₁₀₉	—	11	1	no	maximal, Hall
7	D₁₁₉₉	—	7	1	no	—
8	C₁₁×D₁₀₉	D₇	1	1	yes	characteristic, complemented
9	D₁₁×C₁₀₉	—	7	1	no	—
10	D₇₆₃	—	11	1	no	—
11	C₇×D₁₀₉	D₁₁	1	1	yes	characteristic, complemented
12	D₇×C₁₀₉	—	11	1	no	—
13	C₁₁×C₁₀₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₀₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₀₉	—	77	1	no	Hall
16	C₂×D₇₇	—	109	1	no	maximal, Hall
17	C₂×C₁₀₉	—	77	1	no	—
18	D₁₀₉	—	77	1	no	—
19	D₁₀₉	D₇₇	1	1	yes	characteristic, direct product factor
20	C₂×C₇×C₁₁	—	109	1	no	—
21	D₇₇	—	109	1	no	—
22	D₇₇	D₁₀₉	1	1	yes	characteristic, direct product factor
23	C₁₀₉	C₂×D₇₇	1	1	yes	characteristic, complemented, Sylow
24	C₇×C₁₁	C₂×D₁₀₉	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₁	—	763	1	no	Hall
26	C₂×D₇	—	1199	1	no	Hall
27	C₂×C₁₁	—	109	1	no	—
28	D₁₁	—	7	1	no	—
29	D₁₁	—	763	1	no	—
30	C₂×C₇	—	109	1	no	—
31	D₇	—	11	1	no	—
32	D₇	—	1199	1	no	—
33	C₁₁	D₇×D₁₀₉	1	1	yes	characteristic, complemented, Sylow
34	C₇	D₁₁×D₁₀₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8393	1	no	Sylow
36	C₂	—	77	1	no	—
37	C₂	—	109	1	no	—
38	C₂	—	8393	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁×C₁₀₉	C₂²
LCS	G ▷ C₇×C₁₁×C₁₀₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₃₉₃	C₂	semidirect
2. C₁₀₉×D₇₇	C₂	semidirect
3. C₇×C₁₁×D₁₀₉	C₂	semidirect
4. C₇×C₁₁×C₁₀₉	C₂²	semidirect
8. C₁₁×D₁₀₉	D₇	semidirect
11. C₇×D₁₀₉	D₁₁	semidirect
13. C₁₁×C₁₀₉	C₂×D₇	semidirect
14. C₇×C₁₀₉	C₂×D₁₁	semidirect
19. D₁₀₉	D₇₇	direct (N × H)
22. D₇₇	D₁₀₉	direct (N × H)
23. C₁₀₉	C₂×D₇₇	semidirect
24. C₇×C₁₁	C₂×D₁₀₉	semidirect
33. C₁₁	D₇×D₁₀₉	semidirect
34. C₇	D₁₁×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
D₈₃₉₃	2
C₁₀₉×D₇₇	2
C₇×C₁₁×D₁₀₉	2
D₁₁×D₁₀₉	7
D₇×D₁₀₉	11
C₂×D₇₇	109

Subgroups — D77×D109 #46777099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₇×D₁₀₉ #46777099