Subgroups — #14516343

Order 1944.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6897	C₂	1	1	yes	maximal, characteristic
2	C₉⋊(C₉⋊C₈)	C₃	1	1	yes	maximal, characteristic, complemented
3	#10619495	—	3	4	no	maximal
4	C₂×#6897	C₄	1	1	yes	characteristic
5	C₄×C₉⋊C₉	—	2	4	no	—
6	C₄×C₃²⋊C₉	D₃	1	4	yes	—
7	C₄×C₉²	C₂×C₃	1	1	yes	characteristic
8	#6897	C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₃⋊(C₃⋊C₈)	—	9	1	no	—
10	C₃⋊(C₉⋊C₈)	—	3	4	no	—
11	C₂×C₉⋊C₉	—	2	4	no	—
12	C₂×C₃²⋊C₉	Dic₃	1	4	yes	—
13	C₂×C₉²	C₃×C₄	1	1	yes	characteristic
14	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
15	C₃×C₄×C₉	—	2	4	no	—
16	C₃×C₄×C₉	C₃×D₃	1	4	yes	—
17	C₉⋊C₉	—	2	4	no	—
18	C₃²⋊C₉	C₃⋊C₈	1	4	yes	—
19	C₉²	C₃×C₈	1	1	yes	characteristic, complemented
20	C₃⋊(C₃⋊C₈)	—	9	1	no	—
21	C₃×C₃⋊C₈	—	27	4	no	—
22	C₉⋊C₈	—	27	4	no	—
23	C₂×C₃³	C₃⋊Dic₃	1	1	yes	characteristic
24	C₂×C₃×C₉	—	2	4	no	—
25	C₂×C₃×C₉	C₃×Dic₃	1	4	yes	—
26	C₃²×C₄	—	3	4	no	—
27	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
28	C₄×C₉	—	3	4	no	—
29	C₄×C₉	—	6	4	no	—
30	C₃³	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
31	C₃×C₉	—	2	4	no	—
32	C₃×C₉	C₃×C₃⋊C₈	1	4	yes	—
33	C₃×C₈	—	81	1	no	—
34	C₃⋊C₈	—	27	4	no	—
35	C₂×C₃²	—	3	4	no	—
36	C₂×C₃²	C₃×C₃⋊Dic₃	1	1	yes	characteristic
37	C₂×C₉	—	3	4	no	—
38	C₂×C₉	—	6	4	no	—
39	C₃×C₄	—	9	1	no	—
40	C₃×C₄	#4207	1	4	yes	—
41	C₃²	—	3	4	no	—
42	C₃²	C₃×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
43	C₉	—	3	4	no	—
44	C₉	—	6	4	no	—
45	C₈	—	81	1	no	Sylow
46	C₂×C₃	—	9	1	no	—
47	C₂×C₃	#66409	1	4	yes	—
48	C₄	#6897⋊C₂	1	1	yes	characteristic
49	C₃	—	9	1	no	—
50	C₃	#10619724	1	4	yes	—
51	C₂	#11757614	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#6897⋊C₂
commutator, hypocenter	C₉²	C₃×C₈
Frattini	C₃²×C₄	C₃×C₃⋊D₃
Fitting	C₄×#6897	C₂
socle	C₂×C₃²	C₃×C₃⋊Dic₃
prime radical	C₂×C₃³	C₃⋊Dic₃
cosocle	C₄×C₉²	C₂×C₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₉⋊(C₉⋊C₈)	C₃	semidirect
8. #6897	C₈	semidirect
19. C₉²	C₃×C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6897	2
C₉⋊(C₉⋊C₈)	3
#10619495	3