Subgroups — C₂×C₃×#19149507 #45684348

Order 33174.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19149507	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×#19149507	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₁₉×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×C₉₇	C₂×C₃	1	1	yes	characteristic, complemented
5	#19149507	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₁₉×C₉₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₁₉×C₉₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₉₇⋊C₃	—	19	1	no	maximal, Hall
9	C₃×C₉₇⋊C₃	—	19	1	no	Hall
10	C₂×C₃×C₉₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented
11	C₂×C₉₇⋊C₃	—	19	3	no	—
12	C₂×C₃×C₁₉⋊C₃	—	97	1	no	maximal, Hall
13	C₃×C₉₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
14	C₉₇⋊C₃	—	19	3	no	—
15	C₂×C₉₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₉⋊C₃	—	97	1	no	Hall
17	C₂×C₃×C₁₉	C₉₇⋊C₃	1	1	yes	characteristic, complemented
18	C₂×C₁₉⋊C₃	—	97	3	no	—
19	C₉₇	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₁₉	C₂×C₉₇⋊C₃	1	1	yes	characteristic, complemented
21	C₁₉⋊C₃	—	97	3	no	—
22	C₂×C₁₉	C₃×C₉₇⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₁₉	C₂×C₃×C₉₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃²	—	1843	1	no	Hall
25	C₃²	—	1843	1	no	Sylow
26	C₂×C₃	—	1843	3	no	—
27	C₂×C₃	#19149507	1	1	yes	characteristic, direct product factor
28	C₃	—	1843	3	no	—
29	C₃	C₂×#19149507	1	1	yes	characteristic, direct product factor
30	C₂	C₃×#19149507	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	#19149507
commutator, cosocle, hypocenter	C₁₉×C₉₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₉₇	C₃
LCS	G ▷ C₁₉×C₉₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#19149507	C₂	direct (N × H)
2. C₂×#19149507	C₃	direct (N × H)
3. C₂×C₃×C₁₉×C₉₇	C₃	semidirect
4. C₃×C₁₉×C₉₇	C₂×C₃	semidirect
5. #19149507	C₂×C₃	direct (N × H)
6. C₂×C₁₉×C₉₇	C₃²	semidirect
7. C₁₉×C₉₇	C₂×C₃²	semidirect
10. C₂×C₃×C₉₇	C₁₉⋊C₃	semidirect
13. C₃×C₉₇	C₂×C₁₉⋊C₃	semidirect
15. C₂×C₉₇	C₃×C₁₉⋊C₃	semidirect
17. C₂×C₃×C₁₉	C₉₇⋊C₃	semidirect
19. C₉₇	C₂×C₃×C₁₉⋊C₃	semidirect
20. C₃×C₁₉	C₂×C₉₇⋊C₃	semidirect
22. C₂×C₁₉	C₃×C₉₇⋊C₃	semidirect
23. C₁₉	C₂×C₃×C₉₇⋊C₃	semidirect
27. C₂×C₃	#19149507	direct (N × H)
29. C₃	C₂×#19149507	direct (N × H)
30. C₂	C₃×#19149507	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×#19149507	2
C₂×#19149507	3
C₂×C₃×C₁₉×C₉₇	3
C₂×C₃×C₉₇⋊C₃	19
C₂×C₃×C₁₉⋊C₃	97

Subgroups — C2×C3×#19149507 #45684348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#19149507 #45684348