Subgroups — D₃×D₂₁×C₁₂₇ #44544896

Order 32004.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₇×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₁×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₁×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₁×C₁₂₇	—	3	1	no	maximal
5	D₃×D₇×C₁₂₇	—	3	1	no	maximal
6	C₃²×C₇×C₁₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₁×C₁₂₇	—	3	1	no	—
8	D₂₁×C₁₂₇	—	3	1	no	—
9	D₂₁×C₁₂₇	—	6	1	no	—
10	D₂₁×C₁₂₇	D₃	1	1	yes	characteristic, direct product factor
11	D₃×C₇×C₁₂₇	D₃	1	1	yes	characteristic, complemented
12	C₃×D₇×C₁₂₇	—	3	1	no	—
13	C₂×C₃×C₇×C₁₂₇	—	3	1	no	—
14	D₃²×C₁₂₇	—	7	1	no	maximal, Hall
15	C₂×D₇×C₁₂₇	—	9	1	no	Hall
16	C₃×C₇×C₁₂₇	—	2	1	no	—
17	C₃×C₇×C₁₂₇	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₇×C₁₂₇	C₂×D₃	1	1	yes	characteristic, complemented
19	C₃⋊D₃×C₁₂₇	—	7	1	no	—
20	C₃×D₃×C₁₂₇	—	7	1	no	—
21	C₃×D₃×C₁₂₇	D₇	1	1	yes	characteristic, complemented
22	C₂×C₇×C₁₂₇	—	3	1	no	—
23	D₇×C₁₂₇	—	3	1	no	—
24	D₇×C₁₂₇	—	9	1	no	—
25	C₂×D₃×C₁₂₇	—	21	1	no	—
26	C₂×D₃×C₁₂₇	—	21	1	no	—
27	C₃²×C₁₂₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₂₇	D₃²	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₁₂₇	—	3	1	no	—
30	C₂×C₃×C₁₂₇	—	21	1	no	—
31	D₃×C₁₂₇	—	7	1	no	—
32	D₃×C₁₂₇	—	21	1	no	—
33	D₃×C₁₂₇	—	21	1	no	—
34	D₃×C₁₂₇	—	42	1	no	—
35	D₃×C₁₂₇	D₂₁	1	1	yes	characteristic, direct product factor
36	C₂²×C₁₂₇	—	63	1	no	Hall
37	C₃×C₁₂₇	—	2	1	no	—
38	C₃×C₁₂₇	D₃×D₇	1	1	yes	characteristic, complemented
39	C₃×C₁₂₇	C₂×D₂₁	1	1	yes	characteristic, complemented
40	C₂×C₁₂₇	—	3	1	no	—
41	C₂×C₁₂₇	—	21	1	no	—
42	C₂×C₁₂₇	—	63	1	no	—
43	D₃×D₂₁	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₁₂₇	D₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃⋊D₂₁	C₂×C₁₂₇	1	1	yes	characteristic, complemented
46	C₃×D₂₁	C₂×C₁₂₇	1	1	yes	characteristic, complemented
47	C₃×D₃×C₇	C₂×C₁₂₇	1	1	yes	characteristic, complemented
48	C₂×D₂₁	—	3	1	no	—
49	D₃×D₇	—	3	1	no	—
50	C₃²×C₇	C₂²×C₁₂₇	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₇	—	3	1	no	—
52	D₂₁	—	3	1	no	—
53	D₂₁	—	3	1	no	—
54	D₂₁	—	6	1	no	—
55	D₂₁	D₃×C₁₂₇	1	1	yes	characteristic, direct product factor
56	C₃×D₇	—	3	1	no	—
57	D₃×C₇	D₃×C₁₂₇	1	1	yes	characteristic, complemented
58	D₃²	—	7	1	no	Hall
59	C₂×D₇	—	9	1	no	Hall
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	C₂×D₃×C₁₂₇	1	1	yes	characteristic, complemented
62	C₃×C₇	C₂×D₃×C₁₂₇	1	1	yes	characteristic, complemented
63	C₃⋊D₃	—	7	1	no	—
64	C₃×D₃	—	7	1	no	—
65	C₃×D₃	D₇×C₁₂₇	1	1	yes	characteristic, complemented
66	C₂×C₇	—	3	1	no	—
67	D₇	—	3	1	no	—
68	D₇	—	9	1	no	—
69	C₂×D₃	—	21	1	no	—
70	C₂×D₃	—	21	1	no	—
71	C₃²	C₂×D₇×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
72	C₇	D₃²×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	21	1	no	—
75	D₃	—	7	1	no	—
76	D₃	—	21	1	no	—
77	D₃	—	21	1	no	—
78	D₃	—	42	1	no	—
79	D₃	D₂₁×C₁₂₇	1	1	yes	characteristic, direct product factor
80	C₂²	—	63	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₇×C₁₂₇	1	1	yes	characteristic, complemented
83	C₃	C₂×D₂₁×C₁₂₇	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	21	1	no	—
86	C₂	—	63	1	no	—

	subgroup	G/H
center, hypercenter	C₁₂₇	D₃×D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₂₇	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₁₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₇×C₁₂₇	C₂	semidirect
2. C₃×D₂₁×C₁₂₇	C₂	semidirect
3. C₃⋊D₂₁×C₁₂₇	C₂	semidirect
6. C₃²×C₇×C₁₂₇	C₂²	semidirect
10. D₂₁×C₁₂₇	D₃	direct (N × H)
11. D₃×C₇×C₁₂₇	D₃	semidirect
17. C₃×C₇×C₁₂₇	C₂×D₃	semidirect
18. C₃×C₇×C₁₂₇	C₂×D₃	semidirect
21. C₃×D₃×C₁₂₇	D₇	semidirect
27. C₃²×C₁₂₇	C₂×D₇	semidirect
28. C₇×C₁₂₇	D₃²	semidirect
35. D₃×C₁₂₇	D₂₁	direct (N × H)
38. C₃×C₁₂₇	D₃×D₇	semidirect
39. C₃×C₁₂₇	C₂×D₂₁	semidirect
43. D₃×D₂₁	C₁₂₇	direct (N × H)
44. C₁₂₇	D₃×D₂₁	direct (N × H)
45. C₃⋊D₂₁	C₂×C₁₂₇	semidirect
46. C₃×D₂₁	C₂×C₁₂₇	semidirect
47. C₃×D₃×C₇	C₂×C₁₂₇	semidirect
50. C₃²×C₇	C₂²×C₁₂₇	semidirect
55. D₂₁	D₃×C₁₂₇	direct (N × H)
57. D₃×C₇	D₃×C₁₂₇	semidirect
61. C₃×C₇	C₂×D₃×C₁₂₇	semidirect
62. C₃×C₇	C₂×D₃×C₁₂₇	semidirect
65. C₃×D₃	D₇×C₁₂₇	semidirect
71. C₃²	C₂×D₇×C₁₂₇	semidirect
72. C₇	D₃²×C₁₂₇	semidirect
79. D₃	D₂₁×C₁₂₇	direct (N × H)
82. C₃	D₃×D₇×C₁₂₇	semidirect
83. C₃	C₂×D₂₁×C₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×C₇×C₁₂₇	2
C₃×D₂₁×C₁₂₇	2
C₃⋊D₂₁×C₁₂₇	2
C₂×D₂₁×C₁₂₇	3
D₃×D₇×C₁₂₇	3
D₃²×C₁₂₇	7
D₃×D₂₁	127

Subgroups — D3×D21×C127 #44544896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₁×C₁₂₇ #44544896