Subgroups — C₁₉⋊C₃×D₆₇⋊C₃ #37523852

Order 22914.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#21439406	C₃	1	1	yes	maximal, characteristic, complemented
3	#21439405	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₉⋊C₃×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₉×D₆₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	#16838390	C₂×C₃	1	1	yes	characteristic, complemented
7	#16838389	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₉×C₆₇⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₉⋊C₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₁₉×D₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₁₉×C₆₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×D₆₇⋊C₃	—	19	1	no	maximal, Hall
13	C₃×C₆₇⋊C₃	—	19	1	no	Hall
14	C₃×D₆₇	—	19	1	no	—
15	D₆₇⋊C₃	—	19	1	no	—
16	D₆₇⋊C₃	—	19	1	no	—
17	D₆₇⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
18	C₂×C₃×C₁₉⋊C₃	—	67	1	no	maximal, Hall
19	C₃×C₆₇	—	19	1	no	—
20	C₆₇⋊C₃	—	19	1	no	—
21	C₆₇⋊C₃	—	19	1	no	—
22	C₆₇⋊C₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
23	C₃×C₁₉⋊C₃	—	67	1	no	Hall
24	D₆₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₁₉	—	67	1	no	—
26	C₂×C₁₉⋊C₃	—	67	1	no	—
27	C₂×C₁₉⋊C₃	—	67	1	no	—
28	C₂×C₁₉⋊C₃	—	201	1	no	—
29	C₆₇	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₁₉	—	67	1	no	—
31	C₁₉⋊C₃	—	67	1	no	—
32	C₁₉⋊C₃	—	67	1	no	—
33	C₁₉⋊C₃	D₆₇⋊C₃	1	1	yes	characteristic, direct product factor
34	C₂×C₁₉	—	201	1	no	Hall
35	C₁₉	C₃×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	—	1273	1	no	Hall
37	C₃²	—	1273	1	no	Sylow
38	C₂×C₃	—	67	1	no	—
39	C₂×C₃	—	3819	1	no	—
40	C₂×C₃	—	1273	1	no	—
41	C₂×C₃	—	1273	1	no	—
42	C₃	—	19	1	no	—
43	C₃	—	67	1	no	—
44	C₃	—	1273	1	no	—
45	C₃	—	1273	1	no	—
46	C₂	—	201	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉×C₆₇	C₂×C₃²
LCS	G ▷ C₁₉×C₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₉⋊C₃×C₆₇⋊C₃	C₂	semidirect
2. #21439406	C₃	semidirect
3. #21439405	C₃	semidirect
4. C₁₉⋊C₃×D₆₇	C₃	semidirect
5. C₁₉×D₆₇⋊C₃	C₃	semidirect
6. #16838390	C₂×C₃	semidirect
7. #16838389	C₂×C₃	semidirect
8. C₁₉×C₆₇⋊C₃	C₂×C₃	semidirect
9. C₁₉⋊C₃×C₆₇	C₂×C₃	semidirect
10. C₁₉×D₆₇	C₃²	semidirect
11. C₁₉×C₆₇	C₂×C₃²	semidirect
17. D₆₇⋊C₃	C₁₉⋊C₃	direct (N × H)
22. C₆₇⋊C₃	C₂×C₁₉⋊C₃	semidirect
24. D₆₇	C₃×C₁₉⋊C₃	semidirect
29. C₆₇	C₂×C₃×C₁₉⋊C₃	semidirect
33. C₁₉⋊C₃	D₆₇⋊C₃	direct (N × H)
35. C₁₉	C₃×D₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₉⋊C₃×C₆₇⋊C₃	2
#21439406	3
#21439405	3
C₁₉⋊C₃×D₆₇	3
C₁₉×D₆₇⋊C₃	3
C₃×D₆₇⋊C₃	19
C₂×C₃×C₁₉⋊C₃	67

Subgroups — C19⋊C3×D67⋊C3 #37523852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊C₃×D₆₇⋊C₃ #37523852