Subgroups — C₃×D₆₉⋊D₃₁ #38787334

Order 25668.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₇₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂₃×D₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃₁×D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₆₉⋊D₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₂₃×D₃₁	—	3	1	no	maximal
6	C₃²×C₂₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃₁×D₆₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂₃×D₉₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₇₁₃	—	2	1	no	—
10	C₃×D₇₁₃	D₃	1	1	yes	characteristic, complemented
11	C₃×D₇₁₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₃₁×D₂₃	—	3	1	no	—
13	C₃×C₂₃×D₃₁	—	3	1	no	—
14	D₂₃×D₃₁	—	3	1	no	Hall
15	C₃×C₂₃×C₃₁	—	2	1	no	—
16	C₃×C₂₃×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₂₃×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented
18	D₇₁₃	C₃×D₃	1	1	yes	characteristic, complemented
19	C₂₃×D₃₁	—	3	1	no	—
20	C₃₁×D₂₃	—	3	1	no	—
21	C₃×D₃×D₃₁	—	23	1	no	maximal, Hall
22	C₃×D₃×D₂₃	—	31	1	no	maximal, Hall
23	C₂₃×C₃₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
24	C₃×D₉₃	D₂₃	1	1	yes	characteristic, complemented
25	C₃×D₃×C₃₁	—	23	1	no	—
26	C₃²×D₃₁	—	23	1	no	—
27	C₃×D₆₉	D₃₁	1	1	yes	characteristic, complemented
28	C₃×D₃×C₂₃	—	31	1	no	—
29	C₃²×D₂₃	—	31	1	no	—
30	C₂×C₃×D₃₁	—	69	1	no	—
31	D₃×D₃₁	—	23	1	no	—
32	C₃²×C₃₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×D₂₃	—	93	1	no	—
34	D₃×D₂₃	—	31	1	no	—
35	C₃²×C₂₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₃₁	—	69	1	no	—
37	D₉₃	C₃×D₂₃	1	1	yes	characteristic, complemented
38	C₃×D₃₁	—	3	1	no	—
39	C₃×D₃₁	—	23	1	no	—
40	C₃×D₃₁	—	23	1	no	—
41	C₃×D₃₁	—	46	1	no	—
42	D₃×C₃₁	—	23	1	no	—
43	C₂×C₃×C₂₃	—	93	1	no	—
44	D₆₉	C₃×D₃₁	1	1	yes	characteristic, complemented
45	C₃×D₂₃	—	3	1	no	—
46	C₃×D₂₃	—	31	1	no	—
47	C₃×D₂₃	—	31	1	no	—
48	C₃×D₂₃	—	62	1	no	—
49	D₃×C₂₃	—	31	1	no	—
50	C₂×D₃₁	—	69	1	no	Hall
51	C₃×C₃₁	—	2	1	no	—
52	C₃×C₃₁	D₃×D₂₃	1	1	yes	characteristic, complemented
53	C₃×C₃₁	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented
54	C₂×D₂₃	—	93	1	no	Hall
55	C₃×C₂₃	—	2	1	no	—
56	C₃×C₂₃	D₃×D₃₁	1	1	yes	characteristic, complemented
57	C₃×C₂₃	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented
58	C₂×C₃₁	—	69	1	no	—
59	D₃₁	—	3	1	no	—
60	D₃₁	—	23	1	no	—
61	C₂×C₂₃	—	93	1	no	—
62	D₂₃	—	3	1	no	—
63	D₂₃	—	31	1	no	—
64	C₂×C₃×D₃	—	713	1	no	Hall
65	C₃₁	C₃×D₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
66	C₂₃	C₃×D₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃²	—	713	1	no	—
68	C₃×D₃	—	23	1	no	—
69	C₃×D₃	—	31	1	no	—
70	C₂²×C₃	—	2139	1	no	—
71	C₂×D₃	—	713	1	no	—
72	C₃²	D₂₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	69	1	no	—
74	C₂×C₃	—	93	1	no	—
75	C₂×C₃	—	1426	1	no	—
76	C₂×C₃	—	713	1	no	—
77	C₂×C₃	—	713	1	no	—
78	D₃	—	23	1	no	—
79	D₃	—	31	1	no	—
80	C₂²	—	2139	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₂₃×D₃₁	1	1	yes	characteristic, complemented
83	C₃	D₆₉⋊D₃₁	1	1	yes	characteristic, direct product factor
84	C₂	—	69	1	no	—
85	C₂	—	93	1	no	—
86	C₂	—	713	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₆₉⋊D₃₁
commutator, cosocle, hypocenter	C₃×C₂₃×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃×C₃₁	C₂²
LCS	G ▷ C₃×C₂₃×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×D₇₁₃	C₂	semidirect
2. C₃×C₂₃×D₉₃	C₂	semidirect
3. C₃×C₃₁×D₆₉	C₂	semidirect
4. D₆₉⋊D₃₁	C₃	direct (N × H)
6. C₃²×C₂₃×C₃₁	C₂²	semidirect
7. C₃₁×D₆₉	C₂×C₃	semidirect
8. C₂₃×D₉₃	C₂×C₃	semidirect
10. C₃×D₇₁₃	D₃	semidirect
11. C₃×D₇₁₃	C₂×C₃	semidirect
16. C₃×C₂₃×C₃₁	C₂×D₃	semidirect
17. C₃×C₂₃×C₃₁	C₂²×C₃	semidirect
18. D₇₁₃	C₃×D₃	semidirect
23. C₂₃×C₃₁	C₂×C₃×D₃	semidirect
24. C₃×D₉₃	D₂₃	semidirect
27. C₃×D₆₉	D₃₁	semidirect
32. C₃²×C₃₁	C₂×D₂₃	semidirect
35. C₃²×C₂₃	C₂×D₃₁	semidirect
37. D₉₃	C₃×D₂₃	semidirect
44. D₆₉	C₃×D₃₁	semidirect
52. C₃×C₃₁	D₃×D₂₃	semidirect
53. C₃×C₃₁	C₂×C₃×D₂₃	semidirect
56. C₃×C₂₃	D₃×D₃₁	semidirect
57. C₃×C₂₃	C₂×C₃×D₃₁	semidirect
65. C₃₁	C₃×D₃×D₂₃	semidirect
66. C₂₃	C₃×D₃×D₃₁	semidirect
72. C₃²	D₂₃×D₃₁	semidirect
82. C₃	C₃×D₂₃×D₃₁	semidirect
83. C₃	D₆₉⋊D₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₇₁₃	2
C₃×C₂₃×D₉₃	2
C₃×C₃₁×D₆₉	2
D₆₉⋊D₃₁	3
C₃×D₂₃×D₃₁	3
C₃×D₃×D₃₁	23
C₃×D₃×D₂₃	31

Subgroups — C3×D69⋊D31 #38787334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₆₉⋊D₃₁ #38787334