Subgroups — #14515891

Order 1944.

128 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	#10619584	C₃	1	1	yes	maximal, characteristic
3	#10619584	C₃	1	2	yes	maximal
4	C₂×#6858	—	4	1	no	maximal
5	C₃×C₄×3₋¹⁺²	—	3	1	no	—
6	#6858	—	4	1	no	Sylow
7	C₃³×Q₈	C₃²	1	1	yes	characteristic
8	Q₈×3₋¹⁺²	—	3	3	no	—
9	C₃×Q₈×C₉	—	3	1	no	—
10	C₃×Q₈⋊C₉	—	3	1	no	—
11	C₃×Q₈⋊C₉	—	3	2	no	—
12	C₂×C₃×3₋¹⁺²	A₄	1	1	yes	characteristic
13	C₂×C₃²⋊C₉	—	4	2	no	—
14	C₂×C₃²⋊C₉	—	4	1	no	—
15	C₃³×C₄	—	3	1	no	—
16	C₄×3₋¹⁺²	—	3	9	no	—
17	C₃×C₄×C₉	—	3	3	no	—
18	C₃×3₋¹⁺²	SL(2,𝔽₃)	1	1	yes	characteristic
19	C₃²⋊C₉	—	4	2	no	—
20	C₃²⋊C₉	—	4	1	no	—
21	C₃²×Q₈	—	3	1	no	—
22	C₃²×Q₈	—	3	2	no	—
23	C₃²×Q₈	—	3	1	no	—
24	C₃²×Q₈	H(3,𝔽₃)	1	1	yes	characteristic
25	Q₈×C₉	—	3	3	no	—
26	Q₈⋊C₉	—	9	1	no	—
27	Q₈⋊C₉	—	9	2	no	—
28	C₂×C₃³	C₃×A₄	1	1	yes	characteristic
29	C₂×3₋¹⁺²	—	3	3	no	—
30	C₂×C₃×C₉	—	3	1	no	—
31	C₂×C₃×C₉	—	12	2	no	—
32	C₂×C₃×C₉	—	12	1	no	—
33	C₃²×C₄	—	3	1	no	—
34	C₃²×C₄	—	3	3	no	—
35	C₃²×C₄	—	9	1	no	—
36	C₃²×C₄	—	9	2	no	—
37	C₄×C₉	—	3	9	no	—
38	C₃³	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
39	3₋¹⁺²	—	3	3	no	—
40	C₃×C₉	—	3	1	no	—
41	C₃×C₉	—	12	2	no	—
42	C₃×C₉	—	12	1	no	—
43	C₃×Q₈	—	9	1	no	—
44	C₃×Q₈	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
45	C₃×Q₈	#731	1	2	yes	—
46	C₃×Q₈	#733	1	1	yes	characteristic
47	C₂×C₃²	—	3	1	no	—
48	C₂×C₃²	—	3	2	no	—
49	C₂×C₃²	—	3	1	no	—
50	C₂×C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
51	C₂×C₉	—	3	3	no	—
52	C₂×C₉	—	36	2	no	—
53	C₂×C₉	—	36	1	no	—
54	C₃×C₄	—	3	1	no	—
55	C₃×C₄	—	3	2	no	—
56	C₃×C₄	—	3	1	no	—
57	C₃×C₄	—	9	3	no	—
58	C₃²	—	3	1	no	—
59	C₃²	—	3	2	no	—
60	C₃²	—	3	1	no	—
61	C₃²	Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
62	C₉	—	3	3	no	—
63	C₉	—	36	2	no	—
64	C₉	—	36	1	no	—
65	Q₈	#6858	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	9	1	no	—
67	C₂×C₃	#66364	1	1	yes	characteristic
68	C₂×C₃	#66365	1	2	yes	—
69	C₂×C₃	#66368	1	1	yes	characteristic
70	C₄	—	3	1	no	—
71	C₃	—	9	1	no	—
72	C₃	#10619581	1	1	yes	characteristic
73	C₃	#10619582	1	2	yes	—
74	C₃	#10619585	1	1	yes	characteristic
75	C₂	#11757456	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	#6858
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
65. Q₈	#6858	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
#10619584	3
C₂×#6858	4