Subgroups — D₂₁×D₁₂₇⋊C₃ #44544833

Order 32004.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₁×C₁₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊((C₁₂₇⋊C₃)⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₁₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₁×D₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
5	D₇×D₁₂₇⋊C₃	—	3	1	no	maximal
6	C₃×C₇×C₁₂₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	(C₁₂₇⋊C₃)⋊D₇	—	3	1	no	—
8	D₇×C₁₂₇⋊C₃	—	3	1	no	—
9	C₇×D₁₂₇⋊C₃	—	2	1	no	—
10	C₇×D₁₂₇⋊C₃	D₃	1	1	yes	characteristic, complemented
11	D₂₆₆₇	C₂×C₃	1	1	yes	characteristic, complemented
12	D₂₁×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₇×D₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
14	D₃×D₁₂₇⋊C₃	—	7	1	no	maximal, Hall
15	D₇×D₁₂₇	—	3	1	no	Hall
16	C₃×C₇×C₁₂₇	C₂²×C₃	1	1	yes	characteristic, complemented
17	C₇×C₁₂₇⋊C₃	—	2	1	no	—
18	C₇×C₁₂₇⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
19	D₃×C₁₂₇⋊C₃	—	7	1	no	—
20	C₃⋊(D₁₂₇⋊C₃)	—	7	1	no	—
21	C₃×D₁₂₇⋊C₃	D₇	1	1	yes	characteristic, complemented
22	D₈₈₉	—	3	1	no	—
23	C₇×D₁₂₇	C₃×D₃	1	1	yes	characteristic, complemented
24	D₇×C₁₂₇	—	3	1	no	—
25	D₃×D₁₂₇	—	7	1	no	—
26	C₂×D₁₂₇⋊C₃	—	21	1	no	—
27	C₃×C₁₂₇⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₂₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	D₃₈₁	—	7	1	no	—
30	C₃×D₁₂₇	C₃×D₇	1	1	yes	characteristic, complemented
31	D₃×C₁₂₇	—	7	1	no	—
32	C₂×C₁₂₇⋊C₃	—	21	1	no	—
33	D₁₂₇⋊C₃	—	2	1	no	—
34	D₁₂₇⋊C₃	—	21	1	no	—
35	D₁₂₇⋊C₃	D₂₁	1	1	yes	characteristic, direct product factor
36	C₂×D₁₂₇	—	21	1	no	Hall
37	C₃×C₁₂₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented
38	C₁₂₇⋊C₃	—	2	1	no	—
39	C₁₂₇⋊C₃	C₂×D₂₁	1	1	yes	characteristic, complemented
40	C₂×C₁₂₇	—	21	1	no	—
41	D₁₂₇	—	21	1	no	—
42	D₁₂₇	C₃×D₂₁	1	1	yes	characteristic, complemented
43	C₂×C₃×D₂₁	—	127	1	no	maximal, Hall
44	C₁₂₇	C₂×C₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃²×C₇	—	127	1	no	—
46	C₃×D₂₁	—	127	1	no	—
47	C₃×D₂₁	—	127	1	no	—
48	C₂×D₂₁	—	127	1	no	—
49	C₂×C₃×D₇	—	381	1	no	—
50	C₃²×C₇	—	127	1	no	Hall
51	C₂×C₃×C₇	—	127	1	no	—
52	C₂×C₃×C₇	—	127	1	no	—
53	C₂×C₃×C₇	—	254	1	no	—
54	D₂₁	—	127	1	no	—
55	D₂₁	D₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
56	C₃×D₇	—	381	1	no	—
57	C₃×D₇	—	381	1	no	—
58	C₂×C₃×D₃	—	889	1	no	Hall
59	C₂×D₇	—	381	1	no	Hall
60	C₃×C₇	—	127	1	no	—
61	C₃×C₇	—	254	1	no	—
62	C₃×C₇	C₂×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented
63	C₂×C₃²	—	127	1	no	—
64	C₃×D₃	—	889	1	no	—
65	C₃×D₃	—	889	1	no	—
66	C₂×C₇	—	127	1	no	—
67	D₇	—	3	1	no	—
68	D₇	—	381	1	no	—
69	C₂²×C₃	—	2667	1	no	—
70	C₂×D₃	—	889	1	no	—
71	C₃²	—	127	1	no	Sylow
72	C₇	D₃×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	2667	1	no	—
74	C₂×C₃	—	2667	1	no	—
75	C₂×C₃	—	127	1	no	—
76	C₂×C₃	—	127	1	no	—
77	C₂×C₃	—	254	1	no	—
78	D₃	—	7	1	no	—
79	D₃	—	889	1	no	—
80	C₂²	—	2667	1	no	Sylow
81	C₃	—	127	1	no	—
82	C₃	—	254	1	no	—
83	C₃	D₇×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented
84	C₂	—	21	1	no	—
85	C₂	—	2667	1	no	—
86	C₂	—	127	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₂₇	C₂²×C₃
LCS	G ▷ C₃×C₇×C₁₂₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₂₁×C₁₂₇⋊C₃	C₂	semidirect
2. C₃⋊((C₁₂₇⋊C₃)⋊D₇)	C₂	semidirect
3. C₃×C₇×D₁₂₇⋊C₃	C₂	semidirect
4. D₂₁×D₁₂₇	C₃	semidirect
6. C₃×C₇×C₁₂₇⋊C₃	C₂²	semidirect
10. C₇×D₁₂₇⋊C₃	D₃	semidirect
11. D₂₆₆₇	C₂×C₃	semidirect
12. D₂₁×C₁₂₇	C₂×C₃	semidirect
13. C₃×C₇×D₁₂₇	C₂×C₃	semidirect
16. C₃×C₇×C₁₂₇	C₂²×C₃	semidirect
18. C₇×C₁₂₇⋊C₃	C₂×D₃	semidirect
21. C₃×D₁₂₇⋊C₃	D₇	semidirect
23. C₇×D₁₂₇	C₃×D₃	semidirect
27. C₃×C₁₂₇⋊C₃	C₂×D₇	semidirect
28. C₇×C₁₂₇	C₂×C₃×D₃	semidirect
30. C₃×D₁₂₇	C₃×D₇	semidirect
35. D₁₂₇⋊C₃	D₂₁	direct (N × H)
37. C₃×C₁₂₇	C₂×C₃×D₇	semidirect
39. C₁₂₇⋊C₃	C₂×D₂₁	semidirect
42. D₁₂₇	C₃×D₂₁	semidirect
44. C₁₂₇	C₂×C₃×D₂₁	semidirect
55. D₂₁	D₁₂₇⋊C₃	direct (N × H)
62. C₃×C₇	C₂×D₁₂₇⋊C₃	semidirect
72. C₇	D₃×D₁₂₇⋊C₃	semidirect
83. C₃	D₇×D₁₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
D₂₁×C₁₂₇⋊C₃	2
C₃⋊((C₁₂₇⋊C₃)⋊D₇)	2
C₃×C₇×D₁₂₇⋊C₃	2
D₂₁×D₁₂₇	3
D₇×D₁₂₇⋊C₃	3
D₃×D₁₂₇⋊C₃	7
C₂×C₃×D₂₁	127

Subgroups — D21×D127⋊C3 #44544833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₁×D₁₂₇⋊C₃ #44544833