Subgroups — C₃³×Q₈⋊C₉ #14518869

Order 1944.

1400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×Q₈	C₃	1	1	yes	maximal, characteristic
2	C₃²×Q₈⋊C₉	C₃	1	39	yes	maximal, direct product factor
3	C₂×C₃³×C₉	—	4	1	no	maximal
4	C₃⁴×C₄	—	3	1	no	—
5	C₃³×C₉	—	4	1	no	Sylow
6	C₃³×Q₈	C₉	1	27	yes	complemented
7	C₃³×Q₈	C₃²	1	13	yes	—
8	C₃×Q₈⋊C₉	C₃²	1	117	yes	direct product factor
9	C₂×C₃⁴	A₄	1	1	yes	characteristic
10	C₂×C₃²×C₉	—	4	39	no	—
11	C₃³×C₄	—	3	27	no	—
12	C₃³×C₄	—	3	13	no	—
13	C₃⁴	SL(2,𝔽₃)	1	1	yes	characteristic
14	C₃²×C₉	—	4	39	no	—
15	C₃²×Q₈	C₃×C₉	1	117	yes	complemented
16	C₃²×Q₈	C₃³	1	13	yes	—
17	Q₈⋊C₉	C₃³	1	27	yes	direct product factor
18	C₂×C₃³	C₂²⋊C₉	1	27	yes	—
19	C₂×C₃³	C₃×A₄	1	13	yes	—
20	C₂×C₃×C₉	—	4	117	no	—
21	C₃²×C₄	—	3	117	no	—
22	C₃²×C₄	—	3	13	no	—
23	C₃³	Q₈⋊C₉	1	27	yes	direct product factor
24	C₃³	C₃×SL(2,𝔽₃)	1	13	yes	—
25	C₃×C₉	—	4	117	no	—
26	C₃×Q₈	C₃²×C₉	1	39	yes	complemented
27	C₃×Q₈	C₃⁴	1	1	yes	characteristic
28	C₂×C₃²	C₃×C₂²⋊C₉	1	117	yes	—
29	C₂×C₃²	C₃²×A₄	1	13	yes	—
30	C₂×C₉	—	4	27	no	—
31	C₃×C₄	—	3	39	no	—
32	C₃×C₄	—	3	1	no	—
33	C₃²	C₃×Q₈⋊C₉	1	117	yes	direct product factor
34	C₃²	C₃²×SL(2,𝔽₃)	1	13	yes	—
35	C₉	—	4	27	no	—
36	Q₈	C₃³×C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃	C₃²×C₂²⋊C₉	1	39	yes	—
38	C₂×C₃	C₃³×A₄	1	1	yes	characteristic
39	C₄	—	3	1	no	—
40	C₃	C₃²×Q₈⋊C₉	1	39	yes	direct product factor
41	C₃	C₃³×SL(2,𝔽₃)	1	1	yes	characteristic
42	C₂	C₃³×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical, hypercenter	C₂×C₃⁴	A₄
commutator, hypocenter	Q₈	C₃³×C₉
Frattini	C₂×C₃	C₃³×A₄
Fitting	C₃⁴×Q₈	C₃
cosocle	C₃×Q₈	C₃⁴
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂×C₃⁴

Complements

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

N	H ≅ G/N	type
2. C₃²×Q₈⋊C₉	C₃	direct (N × H)
6. C₃³×Q₈	C₉	semidirect
8. C₃×Q₈⋊C₉	C₃²	direct (N × H)
15. C₃²×Q₈	C₃×C₉	semidirect
17. Q₈⋊C₉	C₃³	direct (N × H)
23. C₃³	Q₈⋊C₉	direct (N × H)
26. C₃×Q₈	C₃²×C₉	semidirect
33. C₃²	C₃×Q₈⋊C₉	direct (N × H)
36. Q₈	C₃³×C₉	semidirect
40. C₃	C₃²×Q₈⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁴×Q₈	3
C₃²×Q₈⋊C₉	3
C₂×C₃³×C₉	4

Subgroups — C33×Q8⋊C9 #14518869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×Q₈⋊C₉ #14518869