Subgroups — C₂×C₃×C₁₉×#64424 #45692577

Order 33516.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×#3861	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₉×#64424	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#64424	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₁₉×#3861	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₉×C₇⋊D₇	C₂×C₃	1	2	yes	complemented
7	C₂×C₁₉×#3861	C₂×C₃	1	3	yes	complemented
8	C₁₉×#64424	C₂×C₃	1	6	yes	direct product factor
9	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₁₉×AGL(1,𝔽₇)	—	7	8	no	maximal
11	C₂×C₁₉×C₇⋊D₇	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₁₉×#3861	C₂²×C₃	1	3	yes	complemented
13	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
14	C₂×C₃×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
15	C₃×C₁₉×AGL(1,𝔽₇)	—	7	16	no	—
16	C₂×C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
17	C₁₉×C₇⋊D₇	C₂×C₃²	1	2	yes	complemented
18	C₂×C₃×#64424	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×D₇×C₁₉	—	7	8	no	—
20	C₂×C₁₉×AGL(1,𝔽₇)	—	7	24	no	—
21	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
22	C₇²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×#3861	C₂×C₁₉	1	1	yes	characteristic, complemented
24	C₃×#64424	C₂×C₁₉	1	2	yes	direct product factor
25	C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	8	yes	complemented
26	C₃×D₇×C₁₉	—	7	16	no	—
27	C₂×C₁₉×ΓL(1,𝔽₈)	—	7	24	no	—
28	C₁₉×AGL(1,𝔽₇)	—	7	48	no	—
29	C₂²×C₃²×C₁₉	—	49	1	no	Hall
30	C₂×C₃×C₇⋊D₇	C₃×C₁₉	1	1	yes	characteristic, complemented
31	C₂×#64424	C₃×C₁₉	1	3	yes	direct product factor
32	C₂×D₇×C₁₉	—	7	8	no	—
33	C₃×#3861	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
34	C₃×C₇×C₁₉	C₂×AGL(1,𝔽₇)	1	8	yes	complemented
35	C₁₉×ΓL(1,𝔽₈)	—	7	24	no	—
36	C₂×C₃²×C₁₉	—	49	2	no	—
37	C₂×C₃²×C₁₉	—	49	1	no	—
38	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
39	C₃×C₇⋊D₇	C₂×C₃×C₁₉	1	2	yes	complemented
40	C₂×#3861	C₂×C₃×C₁₉	1	3	yes	complemented
41	#64424	C₂×C₃×C₁₉	1	6	yes	direct product factor
42	C₂×C₇×C₁₉	C₃×AGL(1,𝔽₇)	1	8	yes	complemented
43	D₇×C₁₉	—	7	16	no	—
44	C₂×C₃×AGL(1,𝔽₇)	—	7	8	no	—
45	C₂²×C₃×C₁₉	—	49	3	no	—
46	C₂²×C₃×C₁₉	—	49	1	no	—
47	C₂×C₇⋊D₇	C₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
48	C₃²×C₁₉	—	49	1	no	Hall
49	C₃×C₇²	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented
50	#3861	C₂²×C₃×C₁₉	1	3	yes	complemented
51	C₇×C₁₉	C₂×C₃×AGL(1,𝔽₇)	1	8	yes	complemented
52	C₂×C₃×ΓL(1,𝔽₈)	—	7	8	no	—
53	C₃×AGL(1,𝔽₇)	—	7	16	no	—
54	C₂×C₃×C₁₉	—	49	6	no	—
55	C₂×C₃×C₁₉	—	49	3	no	—
56	C₂×C₃×C₁₉	—	49	2	no	—
57	C₂×C₃×C₁₉	#64424	1	1	yes	characteristic, direct product factor
58	C₂×C₇²	C₂×C₃²×C₁₉	1	1	yes	characteristic, complemented
59	C₇⋊D₇	C₂×C₃²×C₁₉	1	2	yes	complemented
60	C₂×C₃×D₇	—	7	8	no	—
61	C₂×AGL(1,𝔽₇)	—	7	24	no	—
62	C₂²×C₁₉	—	49	1	no	Hall
63	C₃×ΓL(1,𝔽₈)	—	7	8	no	—
64	C₃×C₁₉	—	49	3	no	—
65	C₃×C₁₉	C₂×#64424	1	1	yes	characteristic, direct product factor
66	C₇²	C₂²×C₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃×C₇	C₁₉×AGL(1,𝔽₇)	1	8	yes	complemented
68	C₃×D₇	—	7	16	no	—
69	C₂×ΓL(1,𝔽₈)	—	7	24	no	—
70	AGL(1,𝔽₇)	—	7	48	no	—
71	C₂×C₁₉	—	49	2	no	—
72	C₂×C₁₉	C₃×#64424	1	1	yes	characteristic, direct product factor
73	C₂²×C₃²	—	49	1	no	Hall
74	C₂×D₇	—	7	8	no	—
75	C₃×C₇	C₂×C₁₉×AGL(1,𝔽₇)	1	8	yes	complemented
76	ΓL(1,𝔽₈)	—	7	24	no	—
77	C₁₉	C₂×C₃×#64424	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×C₃²	—	49	2	no	—
79	C₂×C₃²	—	49	1	no	—
80	C₂×C₇	C₃×C₁₉×AGL(1,𝔽₇)	1	8	yes	complemented
81	D₇	—	7	16	no	—
82	C₂²×C₃	—	49	3	no	—
83	C₂²×C₃	—	49	1	no	—
84	C₃²	—	49	1	no	Sylow
85	C₇	C₂×C₃×C₁₉×AGL(1,𝔽₇)	1	8	yes	complemented
86	C₂×C₃	—	49	6	no	—
87	C₂×C₃	—	49	2	no	—
88	C₂×C₃	—	49	3	no	—
89	C₂×C₃	C₁₉×#64424	1	1	yes	characteristic, direct product factor
90	C₂²	—	49	1	no	Sylow
91	C₃	—	49	3	no	—
92	C₃	C₂×C₁₉×#64424	1	1	yes	characteristic, direct product factor
93	C₂	—	49	2	no	—
94	C₂	C₃×C₁₉×#64424	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	#64424
commutator, cosocle, hypocenter	C₇²	C₂²×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₉×#3861	C₂	semidirect
2. C₃×C₁₉×#64424	C₂	direct (N × H)
3. C₂×C₃×C₁₉×C₇⋊D₇	C₃	semidirect
4. C₂×C₁₉×#64424	C₃	direct (N × H)
5. C₃×C₁₉×#3861	C₂²	semidirect
6. C₃×C₁₉×C₇⋊D₇	C₂×C₃	semidirect
7. C₂×C₁₉×#3861	C₂×C₃	semidirect
8. C₁₉×#64424	C₂×C₃	direct (N × H)
9. C₂×C₃×C₇²×C₁₉	C₂×C₃	semidirect
11. C₂×C₁₉×C₇⋊D₇	C₃²	semidirect
12. C₁₉×#3861	C₂²×C₃	semidirect
13. C₃×C₇²×C₁₉	C₂²×C₃	semidirect
16. C₂×C₇²×C₁₉	C₂×C₃²	semidirect
17. C₁₉×C₇⋊D₇	C₂×C₃²	semidirect
18. C₂×C₃×#64424	C₁₉	direct (N × H)
22. C₇²×C₁₉	C₂²×C₃²	semidirect
23. C₂×C₃×#3861	C₂×C₁₉	semidirect
24. C₃×#64424	C₂×C₁₉	direct (N × H)
25. C₂×C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
30. C₂×C₃×C₇⋊D₇	C₃×C₁₉	semidirect
31. C₂×#64424	C₃×C₁₉	direct (N × H)
33. C₃×#3861	C₂²×C₁₉	semidirect
34. C₃×C₇×C₁₉	C₂×AGL(1,𝔽₇)	semidirect
38. C₂×C₃×C₇²	C₂×C₃×C₁₉	semidirect
39. C₃×C₇⋊D₇	C₂×C₃×C₁₉	semidirect
40. C₂×#3861	C₂×C₃×C₁₉	semidirect
41. #64424	C₂×C₃×C₁₉	direct (N × H)
42. C₂×C₇×C₁₉	C₃×AGL(1,𝔽₇)	semidirect
47. C₂×C₇⋊D₇	C₃²×C₁₉	semidirect
49. C₃×C₇²	C₂²×C₃×C₁₉	semidirect
50. #3861	C₂²×C₃×C₁₉	semidirect
51. C₇×C₁₉	C₂×C₃×AGL(1,𝔽₇)	semidirect
57. C₂×C₃×C₁₉	#64424	direct (N × H)
58. C₂×C₇²	C₂×C₃²×C₁₉	semidirect
59. C₇⋊D₇	C₂×C₃²×C₁₉	semidirect
65. C₃×C₁₉	C₂×#64424	direct (N × H)
66. C₇²	C₂²×C₃²×C₁₉	semidirect
67. C₂×C₃×C₇	C₁₉×AGL(1,𝔽₇)	semidirect
72. C₂×C₁₉	C₃×#64424	direct (N × H)
75. C₃×C₇	C₂×C₁₉×AGL(1,𝔽₇)	semidirect
77. C₁₉	C₂×C₃×#64424	direct (N × H)
80. C₂×C₇	C₃×C₁₉×AGL(1,𝔽₇)	semidirect
85. C₇	C₂×C₃×C₁₉×AGL(1,𝔽₇)	semidirect
89. C₂×C₃	C₁₉×#64424	direct (N × H)
92. C₃	C₂×C₁₉×#64424	direct (N × H)
94. C₂	C₃×C₁₉×#64424	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₉×#3861	2
C₃×C₁₉×#64424	2
C₂×C₃×C₁₉×C₇⋊D₇	3
C₂×C₁₉×#64424	3
C₂×C₃×C₁₉×AGL(1,𝔽₇)	7
C₂×C₃×#64424	19

Subgroups — C2×C3×C19×#64424 #45692577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₉×#64424 #45692577