Subgroups — #14518815

Order 1944.

714 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758025	C₂	1	1	yes	maximal, characteristic
2	#11758013	C₂	1	2	yes	maximal
3	#10619894	—	3	8	no	maximal
4	C₂×H(5,𝔽₃)	C₂²	1	1	yes	characteristic
5	C₃⋊#1084	—	3	8	no	—
6	C₃⋊#1084	—	6	16	no	—
7	C₃×#1084	D₃	1	8	yes	—
8	Dic₃×H(3,𝔽₃)	—	3	8	no	—
9	H(5,𝔽₃)	Q₈	1	1	yes	characteristic, complemented, Sylow
10	C₃×#627	—	9	16	no	—
11	#6229	—	9	2	no	—
12	C₂×C₃×H(3,𝔽₃)	—	2	16	no	—
13	C₂×C₃×H(3,𝔽₃)	C₂×D₃	1	8	yes	—
14	C₃×C₃⋊Dic₃	—	9	16	no	—
15	C₃×C₃⋊Dic₃	—	18	12	no	—
16	C₃²×Dic₃	—	3	32	no	—
17	C₄×H(3,𝔽₃)	—	9	2	no	—
18	#1084	—	9	2	no	—
19	#1084	—	18	32	no	—
20	#1084	—	18	12	no	—
21	#1084	C₃⋊D₃	1	2	yes	—
22	C₃×H(3,𝔽₃)	—	2	16	no	—
23	C₃×H(3,𝔽₃)	Dic₆	1	8	yes	complemented
24	C₃×Dic₆	—	27	8	no	—
25	#627	—	9	16	no	—
26	C₂×C₃³	—	2	12	no	—
27	C₂×C₃³	D₃²	1	16	yes	—
28	C₂×H(3,𝔽₃)	—	2	12	no	—
29	C₂×H(3,𝔽₃)	—	2	32	no	—
30	C₂×H(3,𝔽₃)	C₂×C₃⋊D₃	1	2	yes	—
31	C₃²×C₄	—	9	8	no	—
32	C₃⋊Dic₃	—	9	16	no	—
33	C₃⋊Dic₃	—	18	12	no	—
34	C₃×Dic₃	—	3	8	no	—
35	C₃×Dic₃	—	9	32	no	—
36	C₃×Dic₃	—	27	8	no	—
37	C₃×Dic₃	—	54	16	no	—
38	C₃³	—	2	12	no	—
39	C₃³	#627	1	16	yes	complemented
40	H(3,𝔽₃)	—	2	12	no	—
41	H(3,𝔽₃)	—	2	32	no	—
42	H(3,𝔽₃)	#634	1	2	yes	—
43	C₃×Q₈	—	81	1	no	—
44	Dic₆	—	27	8	no	—
45	C₂×C₃²	—	2	16	no	—
46	C₂×C₃²	—	9	16	no	—
47	C₂×C₃²	—	18	12	no	—
48	C₂×C₃²	D₃×C₃⋊D₃	1	8	yes	—
49	C₃×C₄	—	9	2	no	—
50	C₃×C₄	—	27	8	no	—
51	C₃×C₄	—	81	1	no	—
52	Dic₃	—	3	8	no	—
53	Dic₃	—	27	8	no	—
54	Dic₃	—	54	16	no	—
55	C₃²	—	2	16	no	—
56	C₃²	—	9	16	no	—
57	C₃²	—	18	12	no	—
58	C₃²	#6293	1	8	yes	—
59	Q₈	—	81	1	no	Sylow
60	C₂×C₃	—	3	8	no	—
61	C₂×C₃	—	6	16	no	—
62	C₂×C₃	C₃⋊D₃²	1	1	yes	characteristic
63	C₄	—	9	2	no	—
64	C₄	—	81	1	no	—
65	C₃	—	3	8	no	—
66	C₃	—	6	16	no	—
67	C₃	#10620153	1	1	yes	characteristic
68	C₂	#11758087	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂×C₃	C₃⋊D₃²
commutator, Fitting, prime radical, cosocle	C₂×H(5,𝔽₃)	C₂²
hypocenter	H(5,𝔽₃)	Q₈
LCS	G ▷ C₂×H(5,𝔽₃) ▷ H(5,𝔽₃)
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
9. H(5,𝔽₃)	Q₈	semidirect
23. C₃×H(3,𝔽₃)	Dic₆	semidirect
39. C₃³	#627	semidirect

Maximal subgroups

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

subgroup	index
#11758025	2
#11758013	2
#10619894	3