Subgroups — C₃×#19104944⋊C₂ #44535702

Order 31356.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19104944	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#19104948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#19104952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₃×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented
5	#19104944⋊C₂	C₃	1	3	yes	maximal, direct product factor
6	C₃×#14579731	C₂²	1	1	yes	characteristic, complemented, Hall
7	#19104952	C₂×C₃	1	3	yes	complemented
8	#19104948	C₂×C₃	1	3	yes	complemented
9	#19104944	C₂×C₃	1	3	yes	complemented
10	C₃×D₈₇₁	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×D₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₁₃×D₆₇	C₂×C₃	1	1	yes	characteristic, complemented
13	D₁₃×D₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented
15	#14579731	C₂²×C₃	1	3	yes	complemented
16	C₂×C₃×D₆₇⋊C₃	—	13	1	no	maximal, Hall
17	D₈₇₁	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₁₃×D₆₇	C₂×C₃²	1	1	yes	characteristic, complemented
19	D₁₃×C₆₇	C₂×C₃²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₆₇⋊C₃	—	13	1	no	—
21	C₃×D₆₇⋊C₃	—	13	1	no	—
22	C₃×D₆₇⋊C₃	—	13	1	no	—
23	C₁₃×C₆₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×D₆₇	—	13	1	no	—
25	C₂×D₆₇⋊C₃	—	13	3	no	—
26	C₃×C₆₇⋊C₃	—	13	1	no	Hall
27	C₂×C₃×D₁₃⋊C₃	—	67	1	no	maximal, Hall
28	C₂×C₃×C₆₇	—	13	1	no	—
29	C₃×D₆₇	—	13	1	no	—
30	C₃×D₆₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₂×C₆₇⋊C₃	—	13	3	no	—
32	D₆₇⋊C₃	—	13	3	no	—
33	D₆₇⋊C₃	—	13	3	no	—
34	C₂×D₆₇	—	13	1	no	Hall
35	C₂×C₃×C₁₃⋊C₃	—	67	1	no	—
36	C₃×D₁₃⋊C₃	—	67	1	no	—
37	C₃×D₁₃⋊C₃	—	67	1	no	—
38	C₃×C₆₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
39	C₆₇⋊C₃	—	13	3	no	—
40	C₂×C₃×D₁₃	—	67	1	no	—
41	C₂×D₁₃⋊C₃	—	67	3	no	—
42	C₂×C₆₇	—	13	1	no	—
43	D₆₇	—	13	1	no	—
44	D₆₇	C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented
45	C₃×C₁₃⋊C₃	—	67	1	no	Hall
46	C₂×C₃×C₁₃	—	67	1	no	—
47	C₃×D₁₃	—	67	1	no	—
48	C₃×D₁₃	D₆₇⋊C₃	1	1	yes	characteristic, complemented
49	C₂×C₁₃⋊C₃	—	67	3	no	—
50	D₁₃⋊C₃	—	67	3	no	—
51	D₁₃⋊C₃	—	67	3	no	—
52	C₆₇	C₂×C₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
53	C₂×D₁₃	—	67	1	no	Hall
54	C₃×C₁₃	C₂×D₆₇⋊C₃	1	1	yes	characteristic, complemented
55	C₁₃⋊C₃	—	67	3	no	—
56	C₂²×C₃²	—	871	1	no	Hall
57	C₂×C₁₃	—	67	1	no	—
58	D₁₃	—	67	1	no	—
59	D₁₃	C₃×D₆₇⋊C₃	1	1	yes	characteristic, complemented
60	C₂×C₃²	—	871	1	no	—
61	C₂×C₃²	—	871	1	no	—
62	C₂×C₃²	—	871	1	no	—
63	C₁₃	C₂×C₃×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₃	—	871	1	no	—
65	C₂²×C₃	—	871	3	no	—
66	C₃²	—	871	1	no	Sylow
67	C₂×C₃	—	13	1	no	—
68	C₂×C₃	—	67	1	no	—
69	C₂×C₃	—	871	3	no	—
70	C₂×C₃	—	871	3	no	—
71	C₂×C₃	—	871	3	no	—
72	C₂×C₃	—	871	1	no	—
73	C₂²	—	871	1	no	Sylow
74	C₃	—	871	3	no	—
75	C₃	#19104944⋊C₂	1	1	yes	characteristic, direct product factor
76	C₂	—	13	1	no	—
77	C₂	—	67	1	no	—
78	C₂	—	871	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#19104944⋊C₂
commutator, cosocle, hypocenter	C₁₃×C₆₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₆₇	C₂²×C₃
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#19104944	C₂	semidirect
2. C₃×#19104948	C₂	semidirect
3. C₃×#19104952	C₂	semidirect
4. C₃×D₁₃×D₆₇	C₃	semidirect
5. #19104944⋊C₂	C₃	direct (N × H)
6. C₃×#14579731	C₂²	semidirect
7. #19104952	C₂×C₃	semidirect
8. #19104948	C₂×C₃	semidirect
9. #19104944	C₂×C₃	semidirect
10. C₃×D₈₇₁	C₂×C₃	semidirect
11. C₃×D₁₃×C₆₇	C₂×C₃	semidirect
12. C₃×C₁₃×D₆₇	C₂×C₃	semidirect
13. D₁₃×D₆₇	C₃²	semidirect
14. C₃×C₁₃×C₆₇	C₂²×C₃	semidirect
15. #14579731	C₂²×C₃	semidirect
17. D₈₇₁	C₂×C₃²	semidirect
18. C₁₃×D₆₇	C₂×C₃²	semidirect
19. D₁₃×C₆₇	C₂×C₃²	semidirect
23. C₁₃×C₆₇	C₂²×C₃²	semidirect
30. C₃×D₆₇	D₁₃⋊C₃	semidirect
38. C₃×C₆₇	C₂×D₁₃⋊C₃	semidirect
44. D₆₇	C₃×D₁₃⋊C₃	semidirect
48. C₃×D₁₃	D₆₇⋊C₃	semidirect
52. C₆₇	C₂×C₃×D₁₃⋊C₃	semidirect
54. C₃×C₁₃	C₂×D₆₇⋊C₃	semidirect
59. D₁₃	C₃×D₆₇⋊C₃	semidirect
63. C₁₃	C₂×C₃×D₆₇⋊C₃	semidirect
75. C₃	#19104944⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#19104944	2
C₃×#19104948	2
C₃×#19104952	2
C₃×D₁₃×D₆₇	3
#19104944⋊C₂	3
C₂×C₃×D₆₇⋊C₃	13
C₂×C₃×D₁₃⋊C₃	67

Subgroups — C3×#19104944⋊C2 #44535702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#19104944⋊C₂ #44535702