Subgroups — #14517554

Order 1944.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6898	C₂	1	1	yes	maximal, characteristic
2	#11757616	C₂	1	2	yes	maximal
3	#10619651	C₃	1	1	yes	maximal, characteristic, complemented
4	#10619590	—	3	4	no	maximal
5	C₂×#6898	C₂²	1	1	yes	characteristic
6	C₄×C₉⋊C₉	—	2	4	no	—
7	C₄×C₃²⋊C₉	D₃	1	4	yes	—
8	C₄×C₉²	C₂×C₃	1	1	yes	characteristic
9	C₉⋊Dic₉	C₂×C₃	1	2	yes	—
10	#66316	—	3	8	no	—
11	#6898	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×#634	—	9	1	no	—
13	#6226	—	3	4	no	—
14	C₂×C₉⋊C₉	—	2	4	no	—
15	C₂×C₃²⋊C₉	C₂×D₃	1	4	yes	—
16	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
17	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
18	C₃×C₃⋊Dic₃	—	9	2	no	—
19	C₃×C₄×C₉	—	2	4	no	—
20	C₃×C₄×C₉	C₃×D₃	1	4	yes	—
21	C₃⋊Dic₉	—	3	8	no	—
22	C₉⋊C₉	—	2	4	no	—
23	C₃²⋊C₉	Dic₆	1	4	yes	—
24	C₉²	C₃×Q₈	1	1	yes	characteristic, complemented
25	#634	—	9	1	no	—
26	C₃×Dic₆	—	27	4	no	—
27	Dic₁₈	—	27	4	no	—
28	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
29	C₂×C₃×C₉	—	2	4	no	—
30	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
31	C₃²×C₄	—	3	4	no	—
32	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
33	C₃⋊Dic₃	—	9	2	no	—
34	C₃×Dic₃	—	27	8	no	—
35	C₄×C₉	—	3	4	no	—
36	C₄×C₉	—	6	4	no	—
37	Dic₉	—	27	8	no	—
38	C₃³	#634	1	1	yes	characteristic
39	C₃×C₉	—	2	4	no	—
40	C₃×C₉	C₃×Dic₆	1	4	yes	—
41	C₃×Q₈	—	81	1	no	—
42	Dic₆	—	27	4	no	—
43	C₂×C₃²	—	3	4	no	—
44	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
45	C₂×C₉	—	3	4	no	—
46	C₂×C₉	—	6	4	no	—
47	C₃×C₄	—	9	1	no	—
48	C₃×C₄	—	81	2	no	—
49	C₃×C₄	#4207	1	4	yes	—
50	Dic₃	—	27	8	no	—
51	C₃²	—	3	4	no	—
52	C₃²	C₃×#634	1	1	yes	characteristic
53	C₉	—	3	4	no	—
54	C₉	—	6	4	no	—
55	Q₈	—	81	1	no	Sylow
56	C₂×C₃	—	9	1	no	—
57	C₂×C₃	C₂×#4207	1	4	yes	—
58	C₄	—	81	2	no	—
59	C₄	#92312	1	1	yes	characteristic
60	C₃	—	9	1	no	—
61	C₃	#10619965	1	4	yes	—
62	C₂	C₂×#92312	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#92312
commutator, cosocle	C₂×C₉²	C₂²×C₃
Frattini, socle	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₄×#6898	C₂
prime radical	C₂×C₃³	C₂×C₃⋊D₃
hypercenter	C₄	#92312
hypocenter	C₉²	C₃×Q₈
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
3. #10619651	C₃	semidirect
11. #6898	Q₈	semidirect
24. C₉²	C₃×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6898	2
#11757616	2
#10619651	3
#10619590	3