Subgroups — #14515751

Order 1944.

145 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92204	C₂	1	1	yes	maximal, characteristic
2	#11757290	C₂	1	2	yes	maximal, complemented
3	#4169⋊C₄	—	3	2	no	maximal
4	C₂×#6862	C₂²	1	1	yes	characteristic
5	#92204	C₄	1	2	yes	complemented
6	C₂×#4169	—	3	2	no	—
7	C₂×#4169	—	6	1	no	—
8	#66328	D₃	1	2	yes	—
9	(C₃⋊Dic₃)⋊C₉	—	3	2	no	—
10	#6862	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
11	#6294	—	9	1	no	—
12	(C₃⋊D₉)⋊C₄	—	9	2	no	—
13	C₂×C₃²⋊C₉	—	2	1	no	—
14	C₂×C₃²⋊C₉	C₂×D₃	1	2	yes	—
15	#4169	—	3	4	no	—
16	#4169	—	6	2	no	—
17	C₂×C₃×C₃⋊D₃	—	9	1	no	—
18	C₃×C₃⋊Dic₃	—	3	2	no	—
19	C₂×C₃⋊D₉	—	3	2	no	—
20	C₂×C₃⋊D₉	—	6	1	no	—
21	C₉×Dic₃	—	9	2	no	—
22	C₃×Dic₉	—	9	2	no	—
23	C₃²⋊C₉	—	2	1	no	—
24	C₃²⋊C₉	C₄×D₃	1	2	yes	—
25	#624	—	27	1	no	—
26	D₃×Dic₃	—	27	2	no	—
27	C₄×D₉	—	27	2	no	—
28	C₂×C₃³	D₃²	1	1	yes	characteristic
29	C₃×C₃⋊D₃	—	9	2	no	—
30	C₂×C₃×C₉	—	3	2	no	—
31	C₂×C₃×C₉	—	6	1	no	—
32	C₃⋊D₉	—	3	4	no	—
33	C₃⋊D₉	—	6	2	no	—
34	C₂×C₃⋊D₃	—	9	1	no	—
35	C₂×C₃×D₃	—	27	2	no	—
36	C₂×C₃×D₃	—	54	1	no	—
37	C₃⋊Dic₃	—	3	2	no	—
38	C₃×Dic₃	—	9	2	no	—
39	C₃×Dic₃	—	27	2	no	—
40	C₂×D₉	—	27	2	no	—
41	C₂×D₉	—	54	1	no	—
42	C₄×C₉	—	27	2	no	—
43	Dic₉	—	9	2	no	—
44	C₃³	#624	1	1	yes	characteristic
45	C₃×C₉	—	3	2	no	—
46	C₃×C₉	—	6	1	no	—
47	C₂×Dic₃	—	81	1	no	—
48	C₄×D₃	—	81	2	no	—
49	C₂×C₃²	—	3	2	no	—
50	C₂×C₃²	—	6	1	no	—
51	C₂×C₃²	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
52	C₃⋊D₃	—	9	2	no	—
53	C₃×D₃	—	27	4	no	—
54	C₃×D₃	—	54	2	no	—
55	C₂×C₉	—	9	2	no	—
56	C₂×C₉	—	18	1	no	—
57	D₉	—	27	4	no	—
58	D₉	—	54	2	no	—
59	C₂²×C₃	—	81	1	no	—
60	C₂×D₃	—	27	2	no	—
61	C₂×D₃	—	54	1	no	—
62	C₃×C₄	—	27	2	no	—
63	Dic₃	—	9	2	no	—
64	Dic₃	—	27	2	no	—
65	C₃²	—	3	2	no	—
66	C₃²	—	6	1	no	—
67	C₃²	#6199	1	1	yes	characteristic
68	C₉	—	9	2	no	—
69	C₉	—	18	1	no	—
70	C₂×C₄	—	243	1	no	Sylow
71	C₂×C₃	—	2	1	no	—
72	C₂×C₃	—	9	1	no	—
73	C₂×C₃	—	81	2	no	—
74	C₂×C₃	#4176⋊C₂	1	2	yes	—
75	D₃	—	27	4	no	—
76	D₃	—	54	2	no	—
77	C₂²	—	81	1	no	—
78	C₄	—	27	2	no	—
79	C₃	—	2	1	no	—
80	C₃	—	9	1	no	—
81	C₃	#4184⋊C₄	1	2	yes	—
82	C₂	—	81	2	no	—
83	C₂	#92167⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#92167⋊C₂
commutator, hypocenter	#6862	C₂×C₄
Frattini	C₂×C₃³	D₃²
Fitting, cosocle	C₂×#6862	C₂²
socle	C₂×C₃²	((C₃⋊D₃)⋊C₃)⋊C₂
prime radical	C₂×#92204	C₂
LCS	G ▷ #6862
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. #11757290	C₂	semidirect
5. #92204	C₄	semidirect
10. #6862	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#92204	2
#11757290	2
#4169⋊C₄	3