Subgroups — #14518813

Order 1944.

836 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92392	C₂	1	2	yes	maximal, complemented
2	#11758025	C₂	1	1	yes	maximal, characteristic, complemented
3	#10619891	—	3	8	no	maximal
4	C₂×H(5,𝔽₃)	C₂²	1	1	yes	characteristic
5	#92392	—	2	2	no	—
6	C₂×C₃×#272	D₃	1	8	yes	complemented
7	C₂×D₃×H(3,𝔽₃)	—	3	8	no	—
8	C₃⋊#1084	—	3	8	no	—
9	C₃⋊#1084	—	6	16	no	—
10	H(5,𝔽₃)	D₄	1	1	yes	characteristic, complemented, Sylow
11	C₃×#625	—	9	16	no	—
12	#6235	—	9	2	no	—
13	C₂×C₃×H(3,𝔽₃)	—	2	16	no	—
14	C₂×C₃×H(3,𝔽₃)	C₂×D₃	1	8	yes	—
15	C₃×#272	—	2	8	no	—
16	D₃×H(3,𝔽₃)	—	6	8	no	—
17	C₂×C₃²×D₃	—	3	32	no	—
18	C₃×C₃⋊Dic₃	—	9	16	no	—
19	C₃×C₃⋊Dic₃	—	18	12	no	—
20	C₂²×H(3,𝔽₃)	—	9	2	no	—
21	C₂×#272	C₃⋊D₃	1	2	yes	—
22	#1084	—	9	2	no	—
23	#1084	—	18	32	no	—
24	#1084	—	18	12	no	—
25	C₃×H(3,𝔽₃)	—	2	16	no	—
26	C₃×H(3,𝔽₃)	#67	1	8	yes	complemented
27	C₃×#67	—	27	8	no	—
28	#625	—	9	16	no	—
29	C₂×C₃³	—	2	12	no	—
30	C₂×C₃³	D₃²	1	16	yes	—
31	C₃²×D₃	—	6	32	no	—
32	C₂×H(3,𝔽₃)	—	2	12	no	—
33	C₂×H(3,𝔽₃)	—	2	32	no	—
34	C₂×H(3,𝔽₃)	—	18	2	no	—
35	C₂×H(3,𝔽₃)	C₂×C₃⋊D₃	1	2	yes	—
36	#272	—	2	2	no	—
37	C₂²×C₃²	—	9	8	no	—
38	C₂×C₃×D₃	—	3	8	no	—
39	C₂×C₃×D₃	—	9	32	no	—
40	C₃⋊Dic₃	—	9	16	no	—
41	C₃⋊Dic₃	—	18	12	no	—
42	C₃×Dic₃	—	27	8	no	—
43	C₃×Dic₃	—	54	16	no	—
44	C₃³	—	2	12	no	—
45	C₃³	#625	1	16	yes	complemented
46	H(3,𝔽₃)	—	2	12	no	—
47	H(3,𝔽₃)	—	2	32	no	—
48	H(3,𝔽₃)	#638	1	2	yes	—
49	C₃×D₄	—	81	1	no	—
50	#67	—	27	8	no	—
51	C₂×C₃²	—	2	16	no	—
52	C₂×C₃²	—	9	16	no	—
53	C₂×C₃²	—	18	12	no	—
54	C₂×C₃²	—	18	8	no	—
55	C₂×C₃²	D₃×C₃⋊D₃	1	8	yes	—
56	C₃×D₃	—	6	8	no	—
57	C₃×D₃	—	18	32	no	—
58	C₂²×C₃	—	9	2	no	—
59	C₂²×C₃	—	27	8	no	—
60	C₂×D₃	—	3	8	no	—
61	C₃×C₄	—	81	1	no	—
62	Dic₃	—	27	8	no	—
63	Dic₃	—	54	16	no	—
64	C₃²	—	2	16	no	—
65	C₃²	—	9	16	no	—
66	C₃²	—	18	12	no	—
67	C₃²	#6290	1	8	yes	—
68	D₄	—	81	1	no	Sylow
69	C₂×C₃	—	3	8	no	—
70	C₂×C₃	—	6	16	no	—
71	C₂×C₃	—	18	2	no	—
72	C₂×C₃	—	54	8	no	—
73	C₂×C₃	C₃⋊D₃²	1	1	yes	characteristic
74	D₃	—	6	8	no	—
75	C₂²	—	9	2	no	—
76	C₄	—	81	1	no	—
77	C₃	—	3	8	no	—
78	C₃	—	6	16	no	—
79	C₃	#10620151	1	1	yes	characteristic
80	C₂	—	18	2	no	—
81	C₂	#11758087	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂×C₃	C₃⋊D₃²
commutator, Fitting, cosocle	C₂×H(5,𝔽₃)	C₂²
hypocenter	H(5,𝔽₃)	D₄
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
1. C₂×#92392	C₂	semidirect
2. #11758025	C₂	semidirect
6. C₂×C₃×#272	D₃	semidirect
10. H(5,𝔽₃)	D₄	semidirect
26. C₃×H(3,𝔽₃)	#67	semidirect
45. C₃³	#625	semidirect

Maximal subgroups

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

subgroup	index
C₂×#92392	2
#11758025	2
#10619891	3