Subgroups — #14516146

Order 1944.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₈₁	C₂	1	1	yes	maximal, characteristic
2	C₃⋊Dic₈₁	C₂	1	2	yes	maximal
3	#10619657	—	3	1	no	maximal
4	Dic₁₆₂	—	3	3	no	maximal
5	C₂×C₃×C₈₁	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₂₇	D₃	1	1	yes	characteristic
7	C₃⋊Dic₂₇	—	3	2	no	—
8	C₄×C₈₁	D₃	1	3	yes	—
9	Dic₈₁	—	3	6	no	—
10	C₃×C₈₁	Q₈	1	1	yes	characteristic, complemented, Sylow
11	#6226	—	9	1	no	—
12	Dic₅₄	—	9	2	no	—
13	Dic₅₄	—	9	1	no	—
14	C₂×C₃×C₂₇	C₂×D₃	1	1	yes	characteristic
15	C₂×C₈₁	C₂×D₃	1	3	yes	—
16	C₃×C₄×C₉	D₉	1	1	yes	characteristic
17	C₃⋊Dic₉	—	9	2	no	—
18	C₄×C₂₇	D₉	1	2	yes	—
19	C₄×C₂₇	C₃⋊D₃	1	1	yes	characteristic
20	Dic₂₇	—	9	4	no	—
21	Dic₂₇	—	9	2	no	—
22	C₃×C₂₇	Dic₆	1	1	yes	characteristic
23	C₈₁	Dic₆	1	3	yes	complemented
24	#634	—	27	1	no	—
25	Dic₁₈	—	27	2	no	—
26	Dic₁₈	—	27	1	no	—
27	C₂×C₃×C₉	C₂×D₉	1	1	yes	characteristic
28	C₂×C₂₇	C₂×D₉	1	2	yes	—
29	C₂×C₂₇	C₂×C₃⋊D₃	1	1	yes	characteristic
30	C₃²×C₄	D₂₇	1	1	yes	characteristic
31	C₃⋊Dic₃	—	27	2	no	—
32	C₄×C₉	D₂₇	1	2	yes	—
33	C₄×C₉	C₃⋊D₉	1	1	yes	characteristic
34	Dic₉	—	27	4	no	—
35	Dic₉	—	27	2	no	—
36	C₃×C₉	Dic₁₈	1	1	yes	characteristic
37	C₂₇	Dic₁₈	1	2	yes	—
38	C₂₇	#634	1	1	yes	characteristic
39	Dic₆	—	81	3	no	—
40	Dic₆	—	81	1	no	—
41	C₂×C₃²	C₂×D₂₇	1	1	yes	characteristic
42	C₂×C₉	C₂×D₂₇	1	2	yes	—
43	C₂×C₉	C₂×C₃⋊D₉	1	1	yes	characteristic
44	C₃×C₄	D₈₁	1	3	yes	—
45	C₃×C₄	C₃⋊D₂₇	1	1	yes	characteristic
46	Dic₃	—	81	6	no	—
47	Dic₃	—	81	2	no	—
48	C₃²	Dic₅₄	1	1	yes	characteristic
49	C₉	Dic₅₄	1	2	yes	—
50	C₉	#6226	1	1	yes	characteristic
51	Q₈	—	243	1	no	Sylow
52	C₂×C₃	C₂×D₈₁	1	3	yes	—
53	C₂×C₃	C₂×C₃⋊D₂₇	1	1	yes	characteristic
54	C₄	—	243	2	no	—
55	C₄	C₃⋊D₈₁	1	1	yes	characteristic
56	C₃	Dic₁₆₂	1	3	yes	complemented
57	C₃	#10619657	1	1	yes	characteristic
58	C₂	C₂×C₃⋊D₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₃⋊D₈₁
commutator, cosocle	C₂×C₃×C₈₁	C₂²
Frattini	C₂×C₂₇	C₂×C₃⋊D₃
Fitting	C₃×C₄×C₈₁	C₂
socle, prime radical	C₂×C₃²	C₂×D₂₇
hypercenter	C₄	C₃⋊D₈₁
hypocenter	C₃×C₈₁	Q₈
LCS	G ▷ C₂×C₃×C₈₁ ▷ C₃×C₈₁
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
10. C₃×C₈₁	Q₈	semidirect
23. C₈₁	Dic₆	semidirect
56. C₃	Dic₁₆₂	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₈₁	2
C₃⋊Dic₈₁	2
#10619657	3
Dic₁₆₂	3