Subgroups — #14518812

Order 1944.

1068 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92404	C₂	1	1	yes	maximal, characteristic
2	#11758013	C₂	1	2	yes	maximal, complemented
3	#10619890	—	3	8	no	maximal
4	C₂×H(5,𝔽₃)	C₂²	1	1	yes	characteristic
5	#92404	C₄	1	2	yes	complemented
6	C₂×C₃⋊#272	—	3	8	no	—
7	C₂×C₃⋊#272	—	6	16	no	—
8	C₃×#1084	D₃	1	8	yes	complemented
9	Dic₃×H(3,𝔽₃)	—	3	8	no	—
10	H(5,𝔽₃)	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₃×#624	—	9	16	no	—
12	C₄×#272	—	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	—	3	16	no	—
16	C₃⋊#272	—	6	32	no	—
17	C₂×C₃×C₃⋊D₃	—	9	16	no	—
18	C₂×C₃×C₃⋊D₃	—	18	12	no	—
19	C₃²×Dic₃	—	3	32	no	—
20	C₂×#272	—	9	2	no	—
21	C₂×#272	—	18	32	no	—
22	C₂×#272	—	18	12	no	—
23	C₄×H(3,𝔽₃)	—	9	2	no	—
24	#1084	C₃⋊D₃	1	2	yes	complemented
25	C₃×H(3,𝔽₃)	—	2	16	no	—
26	C₃×H(3,𝔽₃)	C₄×D₃	1	8	yes	complemented
27	C₃×C₄×D₃	—	27	8	no	—
28	#624	—	9	16	no	—
29	C₂×C₃³	—	2	12	no	—
30	C₂×C₃³	D₃²	1	16	yes	—
31	C₃×C₃⋊D₃	—	9	32	no	—
32	C₃×C₃⋊D₃	—	18	24	no	—
33	C₂×H(3,𝔽₃)	—	2	12	no	—
34	C₂×H(3,𝔽₃)	—	2	32	no	—
35	C₂×H(3,𝔽₃)	C₂×C₃⋊D₃	1	2	yes	—
36	#272	—	9	4	no	—
37	#272	—	18	64	no	—
38	#272	—	18	24	no	—
39	C₂×C₃⋊D₃	—	9	16	no	—
40	C₂×C₃⋊D₃	—	18	12	no	—
41	C₂×C₃×D₃	—	27	8	no	—
42	C₂×C₃×D₃	—	54	16	no	—
43	C₃²×C₄	—	9	8	no	—
44	C₃×Dic₃	—	3	8	no	—
45	C₃×Dic₃	—	9	32	no	—
46	C₃³	—	2	12	no	—
47	C₃³	#624	1	16	yes	complemented
48	H(3,𝔽₃)	—	2	12	no	—
49	H(3,𝔽₃)	—	2	32	no	—
50	H(3,𝔽₃)	C₄×C₃⋊D₃	1	2	yes	—
51	C₂×C₃×C₄	—	81	1	no	—
52	C₄×D₃	—	27	8	no	—
53	C₂×C₃²	—	2	16	no	—
54	C₂×C₃²	—	9	16	no	—
55	C₂×C₃²	—	18	12	no	—
56	C₂×C₃²	D₃×C₃⋊D₃	1	8	yes	—
57	C₃⋊D₃	—	9	32	no	—
58	C₃⋊D₃	—	18	24	no	—
59	C₃×D₃	—	27	16	no	—
60	C₃×D₃	—	54	32	no	—
61	C₂²×C₃	—	81	1	no	—
62	C₂×D₃	—	27	8	no	—
63	C₂×D₃	—	54	16	no	—
64	C₃×C₄	—	9	2	no	—
65	C₃×C₄	—	27	8	no	—
66	Dic₃	—	3	8	no	—
67	C₃²	—	2	16	no	—
68	C₃²	—	9	16	no	—
69	C₃²	—	18	12	no	—
70	C₃²	#6289	1	8	yes	—
71	C₂×C₄	—	81	1	no	Sylow
72	C₂×C₃	—	3	8	no	—
73	C₂×C₃	—	6	16	no	—
74	C₂×C₃	—	81	2	no	—
75	C₂×C₃	C₃⋊D₃²	1	1	yes	characteristic
76	D₃	—	27	16	no	—
77	D₃	—	54	32	no	—
78	C₂²	—	81	1	no	—
79	C₄	—	9	2	no	—
80	C₃	—	3	8	no	—
81	C₃	—	6	16	no	—
82	C₃	#10620150	1	1	yes	characteristic
83	C₂	—	81	2	no	—
84	C₂	#11758087	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂×C₃	C₃⋊D₃²
commutator, hypocenter	H(5,𝔽₃)	C₂×C₄
Fitting, cosocle	C₂×H(5,𝔽₃)	C₂²
prime radical	C₂×#92404	C₂
LCS	G ▷ H(5,𝔽₃)
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. #11758013	C₂	semidirect
5. #92404	C₄	semidirect
8. C₃×#1084	D₃	semidirect
10. H(5,𝔽₃)	C₂×C₄	semidirect
24. #1084	C₃⋊D₃	semidirect
26. C₃×H(3,𝔽₃)	C₄×D₃	semidirect
47. C₃³	#624	semidirect

Maximal subgroups

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

subgroup	index
C₂×#92404	2
#11758013	2
#10619890	3