Subgroups — C₂×C₃×#19150312 #45692575

Order 33516.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#14584116	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#19150312	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₇²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#19150312	C₃	1	3	yes	maximal, direct product factor
5	C₃×#14584116	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇²×D₁₉	C₂×C₃	1	2	yes	complemented
7	C₂×#14584116	C₂×C₃	1	3	yes	complemented
8	#19150312	C₂×C₃	1	6	yes	direct product factor
9	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×#11716322	—	7	8	no	maximal
11	C₂×C₇²×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
12	#14584116	C₂²×C₃	1	3	yes	complemented
13	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
14	C₂×C₃×#87705	—	7	8	no	—
15	C₃×#11716322	—	7	16	no	—
16	C₂×C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
17	C₇²×D₁₉	C₂×C₃²	1	2	yes	complemented
18	C₂²×C₃×#3861	—	19	1	no	maximal, Hall
19	C₂×C₃×C₇×D₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
20	C₂×#11716322	—	7	24	no	—
21	C₃×#87705	—	7	8	no	—
22	C₇²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×#3861	—	19	2	no	—
24	C₂×C₃×#3861	—	19	1	no	—
25	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
26	C₃×C₇×D₁₉	C₂×ΓL(1,𝔽₈)	1	16	yes	complemented
27	C₂×#87705	—	7	24	no	—
28	#11716322	—	7	48	no	—
29	C₂×C₃×D₁₉⋊C₃	—	49	1	no	Hall
30	C₂²×C₃×C₇²	—	19	1	no	—
31	C₂²×#3861	—	19	3	no	—
32	C₂×C₇×D₁₉	C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
33	C₃×#3861	—	19	1	no	Hall
34	C₃×C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	8	yes	complemented
35	#87705	—	7	24	no	—
36	C₂×C₃×C₁₉⋊C₃	—	49	1	no	—
37	C₃×D₁₉⋊C₃	—	49	2	no	—
38	C₂×C₃×C₇²	—	19	2	no	—
39	C₂×C₃×C₇²	D₁₉⋊C₃	1	1	yes	characteristic, complemented
40	C₂×#3861	—	19	6	no	—
41	C₂×#3861	—	19	3	no	—
42	C₂×C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
43	C₇×D₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	16	yes	complemented
44	C₂²×C₃×ΓL(1,𝔽₈)	—	133	8	no	—
45	C₂×C₃×D₁₉	#3861	1	1	yes	characteristic, complemented
46	C₂×D₁₉⋊C₃	—	49	3	no	—
47	C₂²×C₇²	—	19	1	no	Hall
48	C₃×C₁₉⋊C₃	—	49	1	no	Hall
49	C₃×C₇²	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented
50	#3861	—	19	3	no	—
51	C₇×C₁₉	C₂²×C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
52	C₂×C₃×ΓL(1,𝔽₈)	—	133	16	no	—
53	C₂×C₃×ΓL(1,𝔽₈)	—	133	8	no	—
54	C₂×C₃×C₁₉	C₂×#3861	1	1	yes	characteristic, complemented
55	C₃×D₁₉	C₂×#3861	1	2	yes	complemented
56	C₂×C₁₉⋊C₃	—	49	3	no	—
57	D₁₉⋊C₃	—	49	6	no	—
58	C₂×C₇²	—	19	2	no	—
59	C₂×C₇²	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
60	C₂²×C₃×C₇	—	19	8	no	—
61	C₂²×ΓL(1,𝔽₈)	—	133	24	no	—
62	C₂×D₁₉	C₃×#3861	1	1	yes	characteristic, complemented, Hall
63	C₃×ΓL(1,𝔽₈)	—	133	8	no	—
64	C₃×C₁₉	C₂²×#3861	1	1	yes	characteristic, complemented
65	C₁₉⋊C₃	—	49	3	no	—
66	C₇²	C₂×C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃×C₇	—	19	16	no	—
68	C₂×C₃×C₇	#11716322	1	8	yes	complemented
69	C₂×ΓL(1,𝔽₈)	—	133	48	no	—
70	C₂×ΓL(1,𝔽₈)	—	133	24	no	—
71	C₂×C₁₉	C₂×C₃×#3861	1	1	yes	characteristic, complemented
72	D₁₉	C₂×C₃×#3861	1	2	yes	complemented
73	C₂²×C₃²	—	931	1	no	Hall
74	C₂²×C₇	—	19	8	no	—
75	C₃×C₇	C₂×#11716322	1	8	yes	complemented
76	ΓL(1,𝔽₈)	—	133	24	no	—
77	C₁₉	C₂²×C₃×#3861	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₃²	—	931	2	no	—
79	C₂×C₃²	—	931	1	no	—
80	C₂×C₇	—	19	16	no	—
81	C₂×C₇	C₃×#11716322	1	8	yes	complemented
82	C₂²×C₃	—	19	1	no	—
83	C₂²×C₃	—	931	3	no	—
84	C₃²	—	931	1	no	Sylow
85	C₇	C₂×C₃×#11716322	1	8	yes	complemented
86	C₂×C₃	—	19	2	no	—
87	C₂×C₃	—	931	6	no	—
88	C₂×C₃	—	931	3	no	—
89	C₂×C₃	#19150312	1	1	yes	characteristic, direct product factor
90	C₂²	—	19	1	no	Sylow
91	C₃	—	931	3	no	—
92	C₃	C₂×#19150312	1	1	yes	characteristic, direct product factor
93	C₂	—	19	2	no	—
94	C₂	C₃×#19150312	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#19150312
commutator, cosocle, hypocenter	C₇²×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#14584116	C₂	semidirect
2. C₃×#19150312	C₂	direct (N × H)
3. C₂×C₃×C₇²×D₁₉	C₃	semidirect
4. C₂×#19150312	C₃	direct (N × H)
5. C₃×#14584116	C₂²	semidirect
6. C₃×C₇²×D₁₉	C₂×C₃	semidirect
7. C₂×#14584116	C₂×C₃	semidirect
8. #19150312	C₂×C₃	direct (N × H)
9. C₂×C₃×C₇²×C₁₉	C₂×C₃	semidirect
11. C₂×C₇²×D₁₉	C₃²	semidirect
12. #14584116	C₂²×C₃	semidirect
13. C₃×C₇²×C₁₉	C₂²×C₃	semidirect
16. C₂×C₇²×C₁₉	C₂×C₃²	semidirect
17. C₇²×D₁₉	C₂×C₃²	semidirect
19. C₂×C₃×C₇×D₁₉	ΓL(1,𝔽₈)	semidirect
22. C₇²×C₁₉	C₂²×C₃²	semidirect
25. C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
26. C₃×C₇×D₁₉	C₂×ΓL(1,𝔽₈)	semidirect
32. C₂×C₇×D₁₉	C₃×ΓL(1,𝔽₈)	semidirect
34. C₃×C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	semidirect
39. C₂×C₃×C₇²	D₁₉⋊C₃	semidirect
42. C₂×C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
43. C₇×D₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
45. C₂×C₃×D₁₉	#3861	semidirect
49. C₃×C₇²	C₂×D₁₉⋊C₃	semidirect
51. C₇×C₁₉	C₂²×C₃×ΓL(1,𝔽₈)	semidirect
54. C₂×C₃×C₁₉	C₂×#3861	semidirect
55. C₃×D₁₉	C₂×#3861	semidirect
59. C₂×C₇²	C₃×D₁₉⋊C₃	semidirect
62. C₂×D₁₉	C₃×#3861	semidirect
64. C₃×C₁₉	C₂²×#3861	semidirect
66. C₇²	C₂×C₃×D₁₉⋊C₃	semidirect
68. C₂×C₃×C₇	#11716322	semidirect
71. C₂×C₁₉	C₂×C₃×#3861	semidirect
72. D₁₉	C₂×C₃×#3861	semidirect
75. C₃×C₇	C₂×#11716322	semidirect
77. C₁₉	C₂²×C₃×#3861	semidirect
81. C₂×C₇	C₃×#11716322	semidirect
85. C₇	C₂×C₃×#11716322	semidirect
89. C₂×C₃	#19150312	direct (N × H)
92. C₃	C₂×#19150312	direct (N × H)
94. C₂	C₃×#19150312	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×#14584116	2
C₃×#19150312	2
C₂×C₃×C₇²×D₁₉	3
C₂×#19150312	3
C₂×C₃×#11716322	7
C₂²×C₃×#3861	19

Subgroups — C2×C3×#19150312 #45692575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#19150312 #45692575