Subgroups — C₃×#41⋊C₉ #88690

Order 432.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#41	C₃	1	1	yes	maximal, characteristic
3	#41⋊C₉	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₄×C₉	—	4	1	no	maximal
5	C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
6	C₃²×D₄	—	3	1	no	—
7	C₂×C₃²×C₄	—	3	1	no	—
8	Q₈⋊C₉	C₂×C₃	1	3	yes	complemented
9	C₂×C₃×C₉	—	4	1	no	—
10	C₃×#41	C₉	1	3	yes	complemented
11	C₃×#41	C₃²	1	1	yes	characteristic
12	C₂²×C₃²	—	3	1	no	—
13	C₃²×C₄	—	3	1	no	—
14	C₃²×C₄	A₄	1	1	yes	characteristic
15	C₄×C₉	—	4	3	no	—
16	C₃×C₉	—	4	1	no	Sylow
17	C₃×Q₈	C₂×C₉	1	3	yes	—
18	C₃×Q₈	C₂×C₃²	1	1	yes	characteristic
19	C₃×D₄	—	3	3	no	—
20	C₃×D₄	—	3	1	no	—
21	C₂×C₃×C₄	—	3	3	no	—
22	C₂×C₃×C₄	—	3	1	no	—
23	C₂×C₃²	—	6	1	no	—
24	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
25	C₂×C₉	—	4	3	no	—
26	#41	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₃	—	3	3	no	—
28	C₂²×C₃	—	3	1	no	—
29	C₃×C₄	—	3	3	no	—
30	C₃×C₄	—	3	1	no	—
31	C₃×C₄	C₂²⋊C₉	1	3	yes	—
32	C₃×C₄	C₃×A₄	1	1	yes	characteristic
33	C₃²	#41⋊C₃	1	1	yes	characteristic
34	C₉	—	4	3	no	—
35	Q₈	C₂×C₃×C₉	1	1	yes	characteristic
36	D₄	—	3	1	no	—
37	C₂×C₄	—	3	1	no	—
38	C₂×C₃	—	6	3	no	—
39	C₂×C₃	—	6	1	no	—
40	C₂×C₃	C₂×C₂²⋊C₉	1	3	yes	—
41	C₂×C₃	C₂×C₃×A₄	1	1	yes	characteristic
42	C₂²	—	3	1	no	—
43	C₄	—	3	1	no	—
44	C₄	C₃×C₂²⋊C₉	1	1	yes	characteristic
45	C₃	#41⋊C₉	1	3	yes	direct product factor
46	C₃	C₃×#41⋊C₃	1	1	yes	characteristic
47	C₂	—	6	1	no	—
48	C₂	C₂×C₃×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₄	A₄
commutator, hypocenter	Q₈	C₂×C₃×C₉
Frattini	C₂×C₃	C₂×C₃×A₄
Fitting, prime radical	C₃²×#41	C₃
socle	C₂×C₃²	C₂×A₄
cosocle	C₃×Q₈	C₂×C₃²
LCS	G ▷ Q₈
UCS	C₁ ◁ C₃²×C₄

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈⋊C₉	C₂	semidirect
3. #41⋊C₉	C₃	direct (N × H)
8. Q₈⋊C₉	C₂×C₃	semidirect
10. C₃×#41	C₉	semidirect
26. #41	C₃×C₉	semidirect
45. C₃	#41⋊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
C₃×Q₈⋊C₉	2
C₃²×#41	3
#41⋊C₉	3
C₃×C₄×C₉	4

Subgroups — C3×#41⋊C9 #88690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41⋊C₉ #88690