Subgroups — (C₃⋊D₃)⋊D₈₈₉ #44544902

Order 32004.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₆₆₇	C₂	1	2	yes	maximal, complemented
2	C₇×C₃⋊D₃×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×D₈₈₉	—	3	2	no	maximal
4	C₃²×C₇×C₁₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₆₆₇	D₃	1	2	yes	complemented
6	D₃×C₇×C₁₂₇	—	3	2	no	—
7	D₃×C₇×C₁₂₇	—	6	1	no	—
8	C₃×D₈₈₉	—	3	2	no	—
9	(C₃⋊D₃)⋊D₁₂₇	—	7	1	no	maximal, Hall
10	C₂×D₈₈₉	—	9	1	no	Hall
11	C₃×C₇×C₁₂₇	—	2	1	no	—
12	C₃×C₇×C₁₂₇	C₂×D₃	1	2	yes	complemented
13	C₃⋊D₃×C₁₂₇	D₇	1	1	yes	characteristic, complemented
14	C₃×D₃₈₁	—	7	2	no	—
15	C₂×C₇×C₁₂₇	—	9	1	no	—
16	D₈₈₉	—	3	2	no	—
17	D₃×D₁₂₇	—	21	2	no	—
18	C₃²×C₁₂₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
19	C₇×C₁₂₇	D₃²	1	1	yes	characteristic, complemented, Hall
20	D₃₈₁	—	7	2	no	—
21	C₃×D₁₂₇	—	21	2	no	—
22	D₃×C₁₂₇	—	3	2	no	—
23	D₃×C₁₂₇	—	6	1	no	—
24	C₂×D₁₂₇	—	63	1	no	Hall
25	C₃×C₁₂₇	—	2	1	no	—
26	C₃×C₁₂₇	D₃×D₇	1	2	yes	complemented
27	C₂×C₁₂₇	—	9	1	no	—
28	D₁₂₇	—	21	2	no	—
29	(C₃⋊D₃)⋊D₇	—	127	1	no	maximal, Hall
30	C₁₂₇	(C₃⋊D₃)⋊D₇	1	1	yes	characteristic, complemented, Sylow
31	C₇×C₃⋊D₃	D₁₂₇	1	1	yes	characteristic, complemented
32	C₃×D₂₁	—	127	2	no	—
33	D₃×D₇	—	381	2	no	—
34	C₃²×C₇	C₂×D₁₂₇	1	1	yes	characteristic, complemented, Hall
35	D₂₁	—	127	2	no	—
36	C₃×D₇	—	381	2	no	—
37	D₃×C₇	—	3	2	no	—
38	D₃×C₇	—	6	1	no	—
39	D₃²	—	889	1	no	Hall
40	C₂×D₇	—	1143	1	no	Hall
41	C₃×C₇	—	2	1	no	—
42	C₃×C₇	D₃×D₁₂₇	1	2	yes	complemented
43	C₃⋊D₃	D₈₈₉	1	1	yes	characteristic, complemented
44	C₃×D₃	—	889	2	no	—
45	C₂×C₇	—	9	1	no	—
46	D₇	—	381	2	no	—
47	C₂×D₃	—	2667	2	no	—
48	C₃²	C₂×D₈₈₉	1	1	yes	characteristic, complemented, Sylow
49	C₇	(C₃⋊D₃)⋊D₁₂₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	2667	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	889	2	no	—
54	C₂²	—	8001	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₈₈₉	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	2667	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇×C₁₂₇	C₂²
LCS	G ▷ C₃²×C₇×C₁₂₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₆₆₇	C₂	semidirect
2. C₇×C₃⋊D₃×C₁₂₇	C₂	semidirect
4. C₃²×C₇×C₁₂₇	C₂²	semidirect
5. D₂₆₆₇	D₃	semidirect
12. C₃×C₇×C₁₂₇	C₂×D₃	semidirect
13. C₃⋊D₃×C₁₂₇	D₇	semidirect
18. C₃²×C₁₂₇	C₂×D₇	semidirect
19. C₇×C₁₂₇	D₃²	semidirect
26. C₃×C₁₂₇	D₃×D₇	semidirect
30. C₁₂₇	(C₃⋊D₃)⋊D₇	semidirect
31. C₇×C₃⋊D₃	D₁₂₇	semidirect
34. C₃²×C₇	C₂×D₁₂₇	semidirect
42. C₃×C₇	D₃×D₁₂₇	semidirect
43. C₃⋊D₃	D₈₈₉	semidirect
48. C₃²	C₂×D₈₈₉	semidirect
49. C₇	(C₃⋊D₃)⋊D₁₂₇	semidirect
56. C₃	D₃×D₈₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₂₆₆₇	2
C₇×C₃⋊D₃×C₁₂₇	2
D₃×D₈₈₉	3
(C₃⋊D₃)⋊D₁₂₇	7
(C₃⋊D₃)⋊D₇	127

Subgroups — (C3⋊D3)⋊D889 #44544902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊D₈₈₉ #44544902