Subgroups — C₂³×#733⋊C₂ #13048202

Order 1296.

871 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#733	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#733⋊C₂	C₂	1	14	yes	maximal, direct product factor
3	C₂³×AGL(1,ℤ/9)	—	3	3	no	maximal
4	C₂³×C₃×D₉	—	3	1	no	maximal
5	C₂²×#733	C₂²	1	7	yes	complemented
6	C₂×#733⋊C₂	C₂²	1	28	yes	direct product factor
7	C₂³×3₋¹⁺²	D₃	1	3	yes	—
8	C₂³×C₃×C₉	D₃	1	1	yes	characteristic
9	C₂²×AGL(1,ℤ/9)	—	3	42	no	—
10	C₂²×C₃×D₉	—	3	14	no	—
11	C₂×#733	C₂³	1	7	yes	complemented
12	#733⋊C₂	C₂³	1	8	yes	direct product factor
13	C₂³×C₃×D₃	—	9	1	no	—
14	C₂³×D₉	—	3	1	no	—
15	C₂³×D₉	—	3	3	no	—
16	C₂²×3₋¹⁺²	C₂×D₃	1	21	yes	—
17	C₂²×C₃×C₉	C₂×D₃	1	7	yes	—
18	C₂×AGL(1,ℤ/9)	—	3	84	no	—
19	C₂×C₃×D₉	—	3	28	no	—
20	#733	C₂⁴	1	1	yes	characteristic, complemented, Sylow
21	C₂³×C₃²	C₃⋊D₃	1	1	yes	characteristic
22	C₂²×C₃×D₃	—	9	14	no	—
23	C₂³×C₉	—	3	1	no	—
24	C₂³×C₉	—	3	3	no	—
25	C₂²×D₉	—	3	14	no	—
26	C₂²×D₉	—	3	42	no	—
27	C₂×3₋¹⁺²	C₂²×D₃	1	21	yes	—
28	C₂×C₃×C₉	C₂²×D₃	1	7	yes	—
29	AGL(1,ℤ/9)	—	3	24	no	—
30	C₃×D₉	—	3	8	no	—
31	C₂⁴×C₃	—	27	1	no	—
32	C₂³×D₃	—	9	1	no	—
33	C₂²×C₃²	C₂×C₃⋊D₃	1	7	yes	—
34	C₂×C₃×D₃	—	9	28	no	—
35	C₂²×C₉	—	3	7	no	—
36	C₂²×C₉	—	3	21	no	—
37	C₂×D₉	—	3	28	no	—
38	C₂×D₉	—	3	84	no	—
39	3₋¹⁺²	C₂³×D₃	1	3	yes	—
40	C₃×C₉	C₂³×D₃	1	1	yes	characteristic
41	C₂³×C₃	—	3	1	no	—
42	C₂³×C₃	—	27	14	no	—
43	C₂³×C₃	#272	1	1	yes	characteristic
44	C₂²×D₃	—	9	14	no	—
45	C₂×C₃²	C₂²×C₃⋊D₃	1	7	yes	—
46	C₃×D₃	—	9	8	no	—
47	C₂×C₉	—	3	7	no	—
48	C₂×C₉	—	3	21	no	—
49	D₉	—	3	8	no	—
50	D₉	—	3	24	no	—
51	C₂⁴	—	27	1	no	Sylow
52	C₂²×C₃	—	3	7	no	—
53	C₂²×C₃	—	27	28	no	—
54	C₂²×C₃	C₂×#272	1	7	yes	—
55	C₂×D₃	—	9	28	no	—
56	C₃²	C₂³×C₃⋊D₃	1	1	yes	characteristic
57	C₉	—	3	1	no	—
58	C₉	—	3	3	no	—
59	C₂³	—	27	14	no	—
60	C₂³	#733⋊C₂	1	1	yes	characteristic, direct product factor
61	C₂×C₃	—	3	7	no	—
62	C₂×C₃	—	27	8	no	—
63	C₂×C₃	C₂²×#272	1	7	yes	—
64	D₃	—	9	8	no	—
65	C₂²	—	27	28	no	—
66	C₂²	C₂×#733⋊C₂	1	7	yes	direct product factor
67	C₃	—	3	1	no	—
68	C₃	C₂³×#272	1	1	yes	characteristic
69	C₂	—	27	8	no	—
70	C₂	C₂²×#733⋊C₂	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	#733⋊C₂
commutator, cosocle, hypocenter	#733	C₂⁴
Frattini	C₃²	C₂³×C₃⋊D₃
Fitting	C₂³×#733	C₂
socle	C₂³×C₃	#272
LCS	G ▷ #733
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂³×#733	C₂	semidirect
2. C₂²×#733⋊C₂	C₂	direct (N × H)
5. C₂²×#733	C₂²	semidirect
6. C₂×#733⋊C₂	C₂²	direct (N × H)
11. C₂×#733	C₂³	semidirect
12. #733⋊C₂	C₂³	direct (N × H)
20. #733	C₂⁴	semidirect
60. C₂³	#733⋊C₂	direct (N × H)
66. C₂²	C₂×#733⋊C₂	direct (N × H)
70. C₂	C₂²×#733⋊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
C₂³×#733	2
C₂²×#733⋊C₂	2
C₂³×AGL(1,ℤ/9)	3
C₂³×C₃×D₉	3

Subgroups — C23×#733⋊C2 #13048202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#733⋊C₂ #13048202