Subgroups — D₃×C₂₉×D₉₃ #44569113

Order 32364.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂₉×D₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×C₃⋊D₉₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×D₉₃	—	3	1	no	maximal
5	D₃×C₂₉×D₃₁	—	3	1	no	maximal
6	C₃²×C₂₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂₉×D₉₃	—	3	1	no	—
8	C₂₉×D₉₃	—	3	1	no	—
9	C₂₉×D₉₃	—	6	1	no	—
10	C₂₉×D₉₃	D₃	1	1	yes	characteristic, direct product factor
11	D₃×C₂₉×C₃₁	D₃	1	1	yes	characteristic, complemented
12	C₃×C₂₉×D₃₁	—	3	1	no	—
13	C₂×C₃×C₂₉×C₃₁	—	3	1	no	—
14	C₂×C₂₉×D₃₁	—	9	1	no	Hall
15	C₃×C₂₉×C₃₁	—	2	1	no	—
16	C₃×C₂₉×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₂₉×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₂₉×C₃₁	—	3	1	no	—
19	C₂₉×D₃₁	—	3	1	no	—
20	C₂₉×D₃₁	—	9	1	no	—
21	D₃×D₉₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	D₃²×C₂₉	—	31	1	no	maximal, Hall
23	C₂₉×C₃₁	D₃²	1	1	yes	characteristic, complemented, Hall
24	C₃⋊D₉₃	C₂×C₂₉	1	1	yes	characteristic, complemented
25	C₃×D₉₃	C₂×C₂₉	1	1	yes	characteristic, complemented
26	C₃×D₃×C₃₁	C₂×C₂₉	1	1	yes	characteristic, complemented
27	C₃⋊D₃×C₂₉	—	31	1	no	—
28	C₃×D₃×C₂₉	—	31	1	no	—
29	C₃×D₃×C₂₉	D₃₁	1	1	yes	characteristic, complemented
30	C₂×D₉₃	—	3	1	no	—
31	D₃×D₃₁	—	3	1	no	—
32	C₂×D₃×C₂₉	—	93	1	no	—
33	C₂×D₃×C₂₉	—	93	1	no	—
34	C₃²×C₃₁	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
35	C₃²×C₂₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₃₁	—	3	1	no	—
37	D₉₃	—	3	1	no	—
38	D₉₃	—	3	1	no	—
39	D₉₃	—	6	1	no	—
40	D₉₃	D₃×C₂₉	1	1	yes	characteristic, direct product factor
41	C₃×D₃₁	—	3	1	no	—
42	D₃×C₃₁	D₃×C₂₉	1	1	yes	characteristic, complemented
43	C₂×C₃×C₂₉	—	3	1	no	—
44	C₂×C₃×C₂₉	—	93	1	no	—
45	D₃×C₂₉	—	31	1	no	—
46	D₃×C₂₉	—	93	1	no	—
47	D₃×C₂₉	—	93	1	no	—
48	D₃×C₂₉	—	186	1	no	—
49	D₃×C₂₉	D₉₃	1	1	yes	characteristic, direct product factor
50	C₂×D₃₁	—	9	1	no	Hall
51	C₂²×C₂₉	—	279	1	no	Hall
52	C₃×C₃₁	—	2	1	no	—
53	C₃×C₃₁	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented
54	C₃×C₃₁	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented
55	C₃×C₂₉	—	2	1	no	—
56	C₃×C₂₉	D₃×D₃₁	1	1	yes	characteristic, complemented
57	C₃×C₂₉	C₂×D₉₃	1	1	yes	characteristic, complemented
58	C₂×C₃₁	—	3	1	no	—
59	D₃₁	—	3	1	no	—
60	D₃₁	—	9	1	no	—
61	C₂×C₂₉	—	3	1	no	—
62	C₂×C₂₉	—	279	1	no	—
63	C₂×C₂₉	—	93	1	no	—
64	D₃²	—	31	1	no	Hall
65	C₃₁	D₃²×C₂₉	1	1	yes	characteristic, complemented, Sylow
66	C₂₉	D₃×D₉₃	1	1	yes	characteristic, direct product factor, Sylow
67	C₃⋊D₃	—	31	1	no	—
68	C₃×D₃	—	31	1	no	—
69	C₃×D₃	C₂₉×D₃₁	1	1	yes	characteristic, complemented
70	C₂×D₃	—	93	1	no	—
71	C₂×D₃	—	93	1	no	—
72	C₃²	C₂×C₂₉×D₃₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	93	1	no	—
75	D₃	—	31	1	no	—
76	D₃	—	93	1	no	—
77	D₃	—	93	1	no	—
78	D₃	—	186	1	no	—
79	D₃	C₂₉×D₉₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	279	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×C₂₉×D₃₁	1	1	yes	characteristic, complemented
83	C₃	C₂×C₂₉×D₉₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	279	1	no	—
86	C₂	—	93	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₃×D₉₃
commutator, cosocle, hypocenter	C₃²×C₃₁	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₂₉×C₃₁	C₂²
LCS	G ▷ C₃²×C₃₁
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₂₉×C₃₁	C₂	semidirect
2. C₃×C₂₉×D₉₃	C₂	semidirect
3. C₂₉×C₃⋊D₉₃	C₂	semidirect
6. C₃²×C₂₉×C₃₁	C₂²	semidirect
10. C₂₉×D₉₃	D₃	direct (N × H)
11. D₃×C₂₉×C₃₁	D₃	semidirect
16. C₃×C₂₉×C₃₁	C₂×D₃	semidirect
17. C₃×C₂₉×C₃₁	C₂×D₃	semidirect
21. D₃×D₉₃	C₂₉	direct (N × H)
23. C₂₉×C₃₁	D₃²	semidirect
24. C₃⋊D₉₃	C₂×C₂₉	semidirect
25. C₃×D₉₃	C₂×C₂₉	semidirect
26. C₃×D₃×C₃₁	C₂×C₂₉	semidirect
29. C₃×D₃×C₂₉	D₃₁	semidirect
34. C₃²×C₃₁	C₂²×C₂₉	semidirect
35. C₃²×C₂₉	C₂×D₃₁	semidirect
40. D₉₃	D₃×C₂₉	direct (N × H)
42. D₃×C₃₁	D₃×C₂₉	semidirect
49. D₃×C₂₉	D₉₃	direct (N × H)
53. C₃×C₃₁	C₂×D₃×C₂₉	semidirect
54. C₃×C₃₁	C₂×D₃×C₂₉	semidirect
56. C₃×C₂₉	D₃×D₃₁	semidirect
57. C₃×C₂₉	C₂×D₉₃	semidirect
65. C₃₁	D₃²×C₂₉	semidirect
66. C₂₉	D₃×D₉₃	direct (N × H)
69. C₃×D₃	C₂₉×D₃₁	semidirect
72. C₃²	C₂×C₂₉×D₃₁	semidirect
79. D₃	C₂₉×D₉₃	direct (N × H)
82. C₃	D₃×C₂₉×D₃₁	semidirect
83. C₃	C₂×C₂₉×D₉₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×C₂₉×C₃₁	2
C₃×C₂₉×D₉₃	2
C₂₉×C₃⋊D₉₃	2
C₂×C₂₉×D₉₃	3
D₃×C₂₉×D₃₁	3
D₃×D₉₃	29
D₃²×C₂₉	31

Subgroups — D3×C29×D93 #44569113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₂₉×D₉₃ #44569113