Subgroups — #14515890

Order 1944.

143 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₃×#6204	C₃	1	1	yes	maximal, characteristic
3	#10619584	C₃	1	1	yes	maximal, characteristic
4	#10619584	C₃	1	1	yes	maximal, characteristic
5	C₂×#6860	—	4	1	no	maximal
6	C₃×C₄×3₋¹⁺²	—	3	1	no	—
7	#6860	—	4	1	no	Sylow
8	C₃³×Q₈	C₃²	1	1	yes	characteristic
9	Q₈×3₋¹⁺²	—	3	3	no	—
10	C₃×Q₈×C₉	—	3	1	no	—
11	#6204	—	3	3	no	—
12	C₃×Q₈⋊C₉	—	3	1	no	—
13	C₃×Q₈⋊C₉	—	3	1	no	—
14	C₃×Q₈⋊C₉	—	3	1	no	—
15	C₂×C₃×3₋¹⁺²	—	4	1	no	—
16	C₂×C₃×3₋¹⁺²	A₄	1	1	yes	characteristic
17	C₂×C₃²⋊C₉	—	4	1	no	—
18	C₂×C₃²⋊C₉	—	4	1	no	—
19	C₃³×C₄	—	3	1	no	—
20	C₄×3₋¹⁺²	—	3	9	no	—
21	C₃×C₄×C₉	—	3	3	no	—
22	C₃×3₋¹⁺²	—	4	1	no	—
23	C₃×3₋¹⁺²	SL(2,𝔽₃)	1	1	yes	characteristic
24	C₃²⋊C₉	—	4	1	no	—
25	C₃²⋊C₉	—	4	1	no	—
26	C₃²×Q₈	—	3	1	no	—
27	C₃²×Q₈	—	3	1	no	—
28	C₃²×Q₈	—	3	2	no	—
29	C₃²×Q₈	H(3,𝔽₃)	1	1	yes	characteristic
30	Q₈×C₉	—	3	3	no	—
31	Q₈⋊C₉	—	3	3	no	—
32	Q₈⋊C₉	—	9	1	no	—
33	Q₈⋊C₉	—	9	1	no	—
34	C₂×C₃³	C₃×A₄	1	1	yes	characteristic
35	C₂×3₋¹⁺²	—	3	3	no	—
36	C₂×3₋¹⁺²	—	12	3	no	—
37	C₂×C₃×C₉	—	3	1	no	—
38	C₂×C₃×C₉	—	12	1	no	—
39	C₂×C₃×C₉	—	12	1	no	—
40	C₂×C₃×C₉	—	12	1	no	—
41	C₃²×C₄	—	3	1	no	—
42	C₃²×C₄	—	3	3	no	—
43	C₃²×C₄	—	9	2	no	—
44	C₃²×C₄	—	9	1	no	—
45	C₄×C₉	—	3	9	no	—
46	C₃³	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
47	3₋¹⁺²	—	3	3	no	—
48	3₋¹⁺²	—	12	3	no	—
49	C₃×C₉	—	3	1	no	—
50	C₃×C₉	—	12	1	no	—
51	C₃×C₉	—	12	1	no	—
52	C₃×C₉	—	12	1	no	—
53	C₃×Q₈	—	9	1	no	—
54	C₃×Q₈	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
55	C₃×Q₈	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
56	C₃×Q₈	#733	1	2	yes	—
57	C₂×C₃²	—	3	2	no	—
58	C₂×C₃²	—	3	1	no	—
59	C₂×C₃²	—	3	1	no	—
60	C₂×C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
61	C₂×C₉	—	3	3	no	—
62	C₂×C₉	—	12	3	no	—
63	C₂×C₉	—	36	1	no	—
64	C₂×C₉	—	36	1	no	—
65	C₃×C₄	—	3	2	no	—
66	C₃×C₄	—	3	1	no	—
67	C₃×C₄	—	3	1	no	—
68	C₃×C₄	—	9	3	no	—
69	C₃²	—	3	2	no	—
70	C₃²	—	3	1	no	—
71	C₃²	—	3	1	no	—
72	C₃²	Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
73	C₉	—	3	3	no	—
74	C₉	—	12	3	no	—
75	C₉	—	36	1	no	—
76	C₉	—	36	1	no	—
77	Q₈	#6860	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₃	—	9	1	no	—
79	C₂×C₃	#66364	1	2	yes	—
80	C₂×C₃	#66366	1	1	yes	characteristic
81	C₂×C₃	#66368	1	1	yes	characteristic
82	C₄	—	3	1	no	—
83	C₃	—	9	1	no	—
84	C₃	#10619581	1	2	yes	—
85	C₃	#10619583	1	1	yes	characteristic
86	C₃	#10619585	1	1	yes	characteristic
87	C₂	#11757455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃²	C₂²⋊H(3,𝔽₃)
commutator, cosocle	C₃³×Q₈	C₃²
Frattini, prime radical	C₂×C₃³	C₃×A₄
Fitting	C₃×Q₈×3₋¹⁺²	C₃
hypercenter	C₂×C₃×3₋¹⁺²	A₄
hypocenter	Q₈	#6860
LCS	G ▷ C₃³×Q₈ ▷ C₃²×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃³ ◁ C₂×C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
77. Q₈	#6860	semidirect

Maximal subgroups

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

subgroup	index
C₃×Q₈×3₋¹⁺²	3
C₃×#6204	3
#10619584	3
C₂×#6860	4