Subgroups — D₃₃⋊D₁₂₇ #30660932

Order 16764.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₃×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₃₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₁₂₇	—	3	1	no	maximal, Hall
5	C₃×C₁₁×C₁₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₃₉₇	D₃	1	1	yes	characteristic, complemented
7	C₁₁×D₁₂₇	—	3	1	no	—
8	D₁₁×C₁₂₇	—	3	1	no	—
9	D₃×D₁₂₇	—	11	1	no	maximal, Hall
10	C₁₁×C₁₂₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃₈₁	D₁₁	1	1	yes	characteristic, complemented
12	C₃×D₁₂₇	—	11	1	no	—
13	D₃×C₁₂₇	—	11	1	no	—
14	C₂×D₁₂₇	—	33	1	no	Hall
15	C₃×C₁₂₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₂₇	—	33	1	no	—
17	D₁₂₇	—	3	1	no	—
18	D₁₂₇	—	11	1	no	—
19	D₃×D₁₁	—	127	1	no	maximal, Hall
20	C₁₂₇	D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
21	D₃₃	D₁₂₇	1	1	yes	characteristic, complemented
22	C₃×D₁₁	—	127	1	no	—
23	D₃×C₁₁	—	127	1	no	—
24	C₂×D₁₁	—	381	1	no	Hall
25	C₃×C₁₁	C₂×D₁₂₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁	—	381	1	no	—
27	D₁₁	—	3	1	no	—
28	D₁₁	—	127	1	no	—
29	C₂×D₃	—	1397	1	no	Hall
30	C₁₁	D₃×D₁₂₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	1397	1	no	—
32	D₃	—	11	1	no	—
33	D₃	—	127	1	no	—
34	C₂²	—	4191	1	no	Sylow
35	C₃	D₁₁×D₁₂₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	33	1	no	—
37	C₂	—	1397	1	no	—
38	C₂	—	381	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₂₇	C₂²
LCS	G ▷ C₃×C₁₁×C₁₂₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃₃×C₁₂₇	C₂	semidirect
2. C₁₁×D₃₈₁	C₂	semidirect
3. C₃×D₁₃₉₇	C₂	semidirect
5. C₃×C₁₁×C₁₂₇	C₂²	semidirect
6. D₁₃₉₇	D₃	semidirect
10. C₁₁×C₁₂₇	C₂×D₃	semidirect
11. D₃₈₁	D₁₁	semidirect
15. C₃×C₁₂₇	C₂×D₁₁	semidirect
20. C₁₂₇	D₃×D₁₁	semidirect
21. D₃₃	D₁₂₇	semidirect
25. C₃×C₁₁	C₂×D₁₂₇	semidirect
30. C₁₁	D₃×D₁₂₇	semidirect
35. C₃	D₁₁×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
D₃₃×C₁₂₇	2
C₁₁×D₃₈₁	2
C₃×D₁₃₉₇	2
D₁₁×D₁₂₇	3
D₃×D₁₂₇	11
D₃×D₁₁	127

Subgroups — D33⋊D127 #30660932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₃⋊D₁₂₇ #30660932