Subgroups — #14517229

Order 1944.

221 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
2	#10619584	C₃	1	3	yes	maximal
3	(Q₈⋊C₉)⋊C₉	C₃	1	9	yes	maximal, complemented
4	C₂×#6895	—	4	1	no	maximal
5	C₃²×C₄×C₉	—	3	1	no	—
6	#6895	—	4	1	no	Sylow
7	C₃³×Q₈	C₃²	1	1	yes	characteristic
8	C₃×Q₈×C₉	—	3	3	no	—
9	C₃×Q₈×C₉	C₃²	1	3	yes	—
10	C₃×Q₈⋊C₉	C₃²	1	9	yes	—
11	C₂×C₃²×C₉	A₄	1	1	yes	characteristic
12	C₂×C₉⋊C₉	—	4	9	no	—
13	C₂×C₃²⋊C₉	—	4	3	no	—
14	C₃³×C₄	—	3	1	no	—
15	C₃×C₄×C₉	—	3	9	no	—
16	C₃×C₄×C₉	—	3	3	no	—
17	C₃²×C₉	SL(2,𝔽₃)	1	1	yes	characteristic
18	C₉⋊C₉	—	4	9	no	—
19	C₃²⋊C₉	—	4	3	no	—
20	C₃²×Q₈	—	3	3	no	—
21	C₃²×Q₈	3₋¹⁺²	1	3	yes	—
22	C₃²×Q₈	C₃³	1	1	yes	characteristic
23	Q₈×C₉	—	3	3	no	—
24	Q₈⋊C₉	—	3	9	no	—
25	C₂×C₃³	C₃×A₄	1	1	yes	characteristic
26	C₂×C₃×C₉	—	3	3	no	—
27	C₂×C₃×C₉	—	4	9	no	—
28	C₂×C₃×C₉	C₃×A₄	1	3	yes	—
29	C₃²×C₄	—	3	9	no	—
30	C₃²×C₄	—	3	3	no	—
31	C₃²×C₄	—	3	1	no	—
32	C₄×C₉	—	3	9	no	—
33	C₃³	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	—	4	9	no	—
36	C₃×C₉	C₃×SL(2,𝔽₃)	1	3	yes	—
37	C₃×Q₈	—	3	3	no	—
38	C₃×Q₈	C₃×3₋¹⁺²	1	1	yes	characteristic
39	C₃×Q₈	#737	1	3	yes	—
40	C₂×C₃²	—	3	3	no	—
41	C₂×C₃²	#1094	1	3	yes	—
42	C₂×C₃²	C₃²×A₄	1	1	yes	characteristic
43	C₂×C₉	—	3	3	no	—
44	C₂×C₉	—	12	9	no	—
45	C₃×C₄	—	3	9	no	—
46	C₃×C₄	—	3	3	no	—
47	C₃×C₄	—	3	1	no	—
48	C₃²	—	3	3	no	—
49	C₃²	#6204	1	3	yes	—
50	C₃²	C₃²×SL(2,𝔽₃)	1	1	yes	characteristic
51	C₉	—	3	3	no	—
52	C₉	—	12	9	no	—
53	Q₈	#6895	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃	—	3	3	no	—
55	C₂×C₃	#66436	1	3	yes	—
56	C₂×C₃	C₃×#1094	1	1	yes	characteristic
57	C₄	—	3	1	no	—
58	C₃	—	3	3	no	—
59	C₃	#10619912	1	3	yes	—
60	C₃	C₃×#6204	1	1	yes	characteristic
61	C₂	#11757819	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle	C₂×C₃²	C₃²×A₄
commutator, cosocle	C₃²×Q₈	C₃³
Fitting	C₃²×Q₈×C₉	C₃
prime radical	C₂×C₃³	C₃×A₄
hypercenter	C₂×C₃²×C₉	A₄
hypocenter	Q₈	#6895
LCS	G ▷ C₃²×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃²×C₉

Complements

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

N	H ≅ G/N	type
3. (Q₈⋊C₉)⋊C₉	C₃	semidirect
53. Q₈	#6895	semidirect

Maximal subgroups

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

subgroup	index
C₃²×Q₈×C₉	3
#10619584	3
(Q₈⋊C₉)⋊C₉	3
C₂×#6895	4