Subgroups — #20259722⋊D₃ #49149558

Order 36972.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊#20259714	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊#20259718	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#20259722	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉⋊D₇₉	C₃	1	1	yes	maximal, characteristic, complemented
5	#20259714⋊C₂	—	3	1	no	maximal
6	C₃×#15690494	C₂²	1	1	yes	characteristic, complemented, Hall
7	#20259722	—	2	1	no	—
8	#20259722	D₃	1	1	yes	characteristic, complemented
9	#20259718	—	3	1	no	—
10	#20259714	—	3	1	no	—
11	D₃₉×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₁₃×D₂₃₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×D₁₀₂₇	C₂×C₃	1	1	yes	characteristic, complemented
14	D₁₃×D₇₉	—	3	1	no	Hall
15	C₃×C₁₃×C₇₉	C₂²×C₃	1	1	yes	characteristic, complemented
16	#15690494	—	2	1	no	—
17	#15690494	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃×D₇₉⋊C₃	—	13	1	no	maximal, Hall
19	D₁₀₂₇	C₃×D₃	1	1	yes	characteristic, complemented
20	C₁₃×D₇₉	—	3	1	no	—
21	D₁₃×C₇₉	—	3	1	no	—
22	C₃⋊(D₇₉⋊C₃)	—	13	1	no	—
23	D₃×C₇₉⋊C₃	—	13	1	no	—
24	C₃×D₇₉⋊C₃	—	13	1	no	—
25	C₁₃×C₇₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	D₃×D₇₉	—	13	1	no	—
27	C₂×D₇₉⋊C₃	—	39	1	no	—
28	C₃×C₇₉⋊C₃	—	13	1	no	Hall
29	D₂₃₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
30	C₃×D₇₉	—	13	1	no	—
31	D₃×C₇₉	—	13	1	no	—
32	C₂×C₇₉⋊C₃	—	39	1	no	—
33	D₇₉⋊C₃	—	13	1	no	—
34	D₇₉⋊C₃	—	26	1	no	—
35	D₇₉⋊C₃	—	39	1	no	—
36	D₃×D₁₃⋊C₃	—	79	1	no	maximal, Hall
37	C₂×D₇₉	—	39	1	no	Hall
38	C₃×C₇₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
39	C₇₉⋊C₃	—	13	1	no	—
40	C₇₉⋊C₃	—	26	1	no	—
41	C₃⋊(D₁₃⋊C₃)	—	79	1	no	—
42	D₃×C₁₃⋊C₃	—	79	1	no	—
43	C₃×D₁₃⋊C₃	—	79	1	no	—
44	C₂×C₇₉	—	39	1	no	—
45	D₇₉	—	3	1	no	—
46	D₇₉	—	13	1	no	—
47	D₃×D₁₃	—	79	1	no	—
48	C₂×D₁₃⋊C₃	—	237	1	no	—
49	C₃×C₁₃⋊C₃	—	79	1	no	Hall
50	C₇₉	D₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	D₃₉	D₇₉⋊C₃	1	1	yes	characteristic, complemented
52	C₃×D₁₃	—	79	1	no	—
53	D₃×C₁₃	—	79	1	no	—
54	C₂×C₁₃⋊C₃	—	237	1	no	—
55	D₁₃⋊C₃	—	79	1	no	—
56	D₁₃⋊C₃	—	158	1	no	—
57	D₁₃⋊C₃	—	237	1	no	—
58	C₂×D₁₃	—	237	1	no	Hall
59	C₃×C₁₃	C₂×D₇₉⋊C₃	1	1	yes	characteristic, complemented
60	C₁₃⋊C₃	—	79	1	no	—
61	C₁₃⋊C₃	—	158	1	no	—
62	C₂×C₃×D₃	—	1027	1	no	Hall
63	C₂×C₁₃	—	237	1	no	—
64	D₁₃	—	3	1	no	—
65	D₁₃	—	79	1	no	—
66	C₂×C₃²	—	1027	1	no	—
67	C₃×D₃	—	1027	1	no	—
68	C₃×D₃	—	1027	1	no	—
69	C₁₃	D₃×D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	3081	1	no	—
71	C₂×D₃	—	1027	1	no	—
72	C₃²	—	1027	1	no	Sylow
73	C₂×C₃	—	1027	1	no	—
74	C₂×C₃	—	1027	1	no	—
75	C₂×C₃	—	2054	1	no	—
76	C₂×C₃	—	3081	1	no	—
77	C₂×C₃	—	3081	1	no	—
78	D₃	—	13	1	no	—
79	D₃	—	79	1	no	—
80	C₂²	—	3081	1	no	Sylow
81	C₃	—	1027	1	no	—
82	C₃	—	2054	1	no	—
83	C₃	#20259714⋊C₂	1	1	yes	characteristic, complemented
84	C₂	—	1027	1	no	—
85	C₂	—	39	1	no	—
86	C₂	—	237	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₇₉	C₂²×C₃
LCS	G ▷ C₃×C₁₃×C₇₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊#20259714	C₂	semidirect
2. C₃⋊#20259718	C₂	semidirect
3. C₃×#20259722	C₂	semidirect
4. D₃₉⋊D₇₉	C₃	semidirect
6. C₃×#15690494	C₂²	semidirect
8. #20259722	D₃	semidirect
11. D₃₉×C₇₉	C₂×C₃	semidirect
12. C₁₃×D₂₃₇	C₂×C₃	semidirect
13. C₃×D₁₀₂₇	C₂×C₃	semidirect
15. C₃×C₁₃×C₇₉	C₂²×C₃	semidirect
17. #15690494	C₂×D₃	semidirect
19. D₁₀₂₇	C₃×D₃	semidirect
25. C₁₃×C₇₉	C₂×C₃×D₃	semidirect
29. D₂₃₇	D₁₃⋊C₃	semidirect
38. C₃×C₇₉	C₂×D₁₃⋊C₃	semidirect
50. C₇₉	D₃×D₁₃⋊C₃	semidirect
51. D₃₉	D₇₉⋊C₃	semidirect
59. C₃×C₁₃	C₂×D₇₉⋊C₃	semidirect
69. C₁₃	D₃×D₇₉⋊C₃	semidirect
83. C₃	#20259714⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊#20259714	2
C₃⋊#20259718	2
C₃×#20259722	2
D₃₉⋊D₇₉	3
#20259714⋊C₂	3
D₃×D₇₉⋊C₃	13
D₃×D₁₃⋊C₃	79

Subgroups — #20259722⋊D3 #49149558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #20259722⋊D₃ #49149558