Subgroups — D₃×C₁₁×D₁₇₉ #37556408

Order 23628.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₅₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₁×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×D₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×D₁₇₉	—	3	1	no	maximal, Hall
5	C₃×C₁₁×C₁₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₁×C₁₇₉	—	3	1	no	—
7	C₁₁×D₁₇₉	—	3	1	no	—
8	C₁₁×D₁₇₉	D₃	1	1	yes	characteristic, direct product factor
9	D₃×D₁₇₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₁₁×C₁₇₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₅₃₇	C₂×C₁₁	1	1	yes	characteristic, complemented
12	C₃×D₁₇₉	C₂×C₁₁	1	1	yes	characteristic, complemented
13	D₃×C₁₇₉	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₂×D₁₇₉	—	3	1	no	Hall
15	C₃×C₁₇₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇₉	—	3	1	no	—
17	D₁₇₉	—	3	1	no	—
18	D₁₇₉	D₃×C₁₁	1	1	yes	characteristic, direct product factor
19	C₁₇₉	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₃×C₁₁	—	179	1	no	maximal, Hall
21	C₂×C₃×C₁₁	—	179	1	no	—
22	D₃×C₁₁	—	179	1	no	—
23	D₃×C₁₁	D₁₇₉	1	1	yes	characteristic, direct product factor
24	C₂²×C₁₁	—	537	1	no	Hall
25	C₃×C₁₁	C₂×D₁₇₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁	—	3	1	no	—
27	C₂×C₁₁	—	537	1	no	—
28	C₂×C₁₁	—	179	1	no	—
29	C₂×D₃	—	179	1	no	Hall
30	C₁₁	D₃×D₁₇₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	179	1	no	—
32	D₃	—	179	1	no	—
33	D₃	C₁₁×D₁₇₉	1	1	yes	characteristic, direct product factor
34	C₂²	—	537	1	no	Sylow
35	C₃	C₂×C₁₁×D₁₇₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	537	1	no	—
38	C₂	—	179	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₃×D₁₇₉
commutator, cosocle, hypocenter	C₃×C₁₇₉	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₇₉	C₂²
LCS	G ▷ C₃×C₁₇₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₅₃₇	C₂	semidirect
2. D₃×C₁₁×C₁₇₉	C₂	semidirect
3. C₃×C₁₁×D₁₇₉	C₂	semidirect
5. C₃×C₁₁×C₁₇₉	C₂²	semidirect
8. C₁₁×D₁₇₉	D₃	direct (N × H)
9. D₃×D₁₇₉	C₁₁	direct (N × H)
10. C₁₁×C₁₇₉	C₂×D₃	semidirect
11. D₅₃₇	C₂×C₁₁	semidirect
12. C₃×D₁₇₉	C₂×C₁₁	semidirect
13. D₃×C₁₇₉	C₂×C₁₁	semidirect
15. C₃×C₁₇₉	C₂²×C₁₁	semidirect
18. D₁₇₉	D₃×C₁₁	direct (N × H)
19. C₁₇₉	C₂×D₃×C₁₁	semidirect
23. D₃×C₁₁	D₁₇₉	direct (N × H)
25. C₃×C₁₁	C₂×D₁₇₉	semidirect
30. C₁₁	D₃×D₁₇₉	direct (N × H)
33. D₃	C₁₁×D₁₇₉	direct (N × H)
35. C₃	C₂×C₁₁×D₁₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×D₅₃₇	2
D₃×C₁₁×C₁₇₉	2
C₃×C₁₁×D₁₇₉	2
C₂×C₁₁×D₁₇₉	3
D₃×D₁₇₉	11
C₂×D₃×C₁₁	179

Subgroups — D3×C11×D179 #37556408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₁×D₁₇₉ #37556408