Subgroups — C₂³×#6897 #14518565

Order 1944.

800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6897	C₂	1	7	yes	maximal, direct product factor
2	C₂³×C₉⋊C₉	C₃	1	8	yes	maximal, complemented
3	C₂³×C₃²⋊C₉	C₃	1	4	yes	maximal
4	C₂³×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×#6897	C₂²	1	7	yes	direct product factor
6	C₂²×C₉⋊C₉	C₂×C₃	1	56	yes	complemented
7	C₂²×C₃²⋊C₉	C₂×C₃	1	28	yes	—
8	C₂²×C₉²	C₂×C₃	1	7	yes	complemented
9	#6897	C₂³	1	1	yes	characteristic, direct product factor, Sylow
10	C₂³×C₃³	C₃²	1	1	yes	characteristic
11	C₂³×C₃×C₉	C₃²	1	4	yes	—
12	C₂³×C₃×C₉	C₃²	1	8	yes	—
13	C₂×C₉⋊C₉	C₂²×C₃	1	56	yes	complemented
14	C₂×C₃²⋊C₉	C₂²×C₃	1	28	yes	—
15	C₂×C₉²	C₂²×C₃	1	7	yes	complemented
16	C₂²×C₃³	C₂×C₃²	1	7	yes	—
17	C₂²×C₃×C₉	C₂×C₃²	1	28	yes	—
18	C₂²×C₃×C₉	C₂×C₃²	1	56	yes	—
19	C₉⋊C₉	C₂³×C₃	1	8	yes	complemented
20	C₃²⋊C₉	C₂³×C₃	1	4	yes	—
21	C₉²	C₂³×C₃	1	1	yes	characteristic, complemented
22	C₂³×C₃²	—	3	4	no	—
23	C₂³×C₃²	C₃³	1	1	yes	characteristic
24	C₂³×C₉	—	3	4	no	—
25	C₂³×C₉	—	3	8	no	—
26	C₂×C₃³	C₂²×C₃²	1	7	yes	—
27	C₂×C₃×C₉	C₂²×C₃²	1	28	yes	—
28	C₂×C₃×C₉	C₂²×C₃²	1	56	yes	—
29	C₂²×C₃²	—	3	28	no	—
30	C₂²×C₃²	C₂×C₃³	1	7	yes	—
31	C₂²×C₉	—	3	28	no	—
32	C₂²×C₉	—	3	56	no	—
33	C₃³	C₂³×C₃²	1	1	yes	characteristic
34	C₃×C₉	C₂³×C₃²	1	4	yes	—
35	C₃×C₉	C₂³×C₃²	1	8	yes	—
36	C₂³×C₃	—	9	1	no	—
37	C₂³×C₃	#737	1	4	yes	—
38	C₂×C₃²	—	3	28	no	—
39	C₂×C₃²	C₂²×C₃³	1	7	yes	—
40	C₂×C₉	—	3	28	no	—
41	C₂×C₉	—	3	56	no	—
42	C₂²×C₃	—	9	7	no	—
43	C₂²×C₃	C₂×#737	1	28	yes	—
44	C₃²	—	3	4	no	—
45	C₃²	C₂³×C₃³	1	1	yes	characteristic
46	C₉	—	3	4	no	—
47	C₉	—	3	8	no	—
48	C₂³	#6897	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃	—	9	7	no	—
50	C₂×C₃	C₂²×#737	1	28	yes	—
51	C₂²	C₂×#6897	1	7	yes	direct product factor
52	C₃	—	9	1	no	—
53	C₃	C₂³×#737	1	4	yes	—
54	C₂	C₂²×#6897	1	7	yes	direct product factor

	subgroup	G/H
center, socle	C₂³×C₃²	C₃³
commutator, Frattini, cosocle	C₃²	C₂³×C₃³
prime radical	C₂³×C₃³	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#6897	C₂	direct (N × H)
2. C₂³×C₉⋊C₉	C₃	semidirect
4. C₂³×C₉²	C₃	semidirect
5. C₂×#6897	C₂²	direct (N × H)
6. C₂²×C₉⋊C₉	C₂×C₃	semidirect
8. C₂²×C₉²	C₂×C₃	semidirect
9. #6897	C₂³	direct (N × H)
13. C₂×C₉⋊C₉	C₂²×C₃	semidirect
15. C₂×C₉²	C₂²×C₃	semidirect
19. C₉⋊C₉	C₂³×C₃	semidirect
21. C₉²	C₂³×C₃	semidirect
48. C₂³	#6897	direct (N × H)
51. C₂²	C₂×#6897	direct (N × H)
54. C₂	C₂²×#6897	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#6897	2
C₂³×C₉⋊C₉	3
C₂³×C₃²⋊C₉	3
C₂³×C₉²	3

Subgroups — C23×#6897 #14518565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#6897 #14518565