Subgroups — #14515919

Order 1944.

105 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6861	C₂	1	1	yes	maximal, characteristic
2	#11757289	C₂	1	2	yes	maximal
3	#10619654	C₃	1	1	yes	maximal, characteristic
4	#634⋊C₉	—	3	1	no	maximal
5	C₂×#6861	C₂²	1	1	yes	characteristic
6	C₄×C₃²⋊C₉	—	2	1	no	—
7	C₄×C₃²⋊C₉	D₃	1	1	yes	characteristic
8	C₄×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
9	#66328	C₂×C₃	1	2	yes	—
10	(C₃⋊Dic₃)⋊C₉	—	3	2	no	—
11	#6861	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×#634	—	3	1	no	—
13	C₉×Dic₆	—	9	1	no	—
14	C₃×Dic₁₈	—	9	1	no	—
15	C₂×C₃²⋊C₉	—	2	1	no	—
16	C₂×C₃²⋊C₉	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃²⋊C₉	C₂²×C₃	1	1	yes	characteristic
18	C₃³×C₄	C₃×D₃	1	1	yes	characteristic
19	C₃×C₃⋊Dic₃	—	3	2	no	—
20	C₃×C₄×C₉	—	3	1	no	—
21	C₃×C₄×C₉	—	3	1	no	—
22	C₃×C₄×C₉	—	6	1	no	—
23	C₉×Dic₃	—	9	2	no	—
24	C₃×Dic₉	—	9	2	no	—
25	C₃²⋊C₉	—	2	1	no	—
26	C₃²⋊C₉	Dic₆	1	1	yes	characteristic
27	C₃²⋊C₉	C₃×Q₈	1	1	yes	characteristic
28	#634	—	3	1	no	—
29	C₃×Dic₆	—	9	1	no	—
30	C₃×Dic₆	—	27	1	no	—
31	Q₈×C₉	—	27	1	no	—
32	Dic₁₈	—	9	1	no	—
33	C₂×C₃³	C₂×C₃×D₃	1	1	yes	characteristic
34	C₂×C₃×C₉	—	3	1	no	—
35	C₂×C₃×C₉	—	3	1	no	—
36	C₂×C₃×C₉	—	6	1	no	—
37	C₃²×C₄	—	3	1	no	—
38	C₃²×C₄	—	3	1	no	—
39	C₃²×C₄	—	6	1	no	—
40	C₃²×C₄	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
41	C₃⋊Dic₃	—	3	2	no	—
42	C₃×Dic₃	—	9	2	no	—
43	C₃×Dic₃	—	27	2	no	—
44	C₄×C₉	—	9	1	no	—
45	C₄×C₉	—	9	1	no	—
46	C₄×C₉	—	18	1	no	—
47	C₄×C₉	—	27	2	no	—
48	Dic₉	—	9	2	no	—
49	C₃³	C₃×Dic₆	1	1	yes	characteristic
50	C₃×C₉	—	3	1	no	—
51	C₃×C₉	—	3	1	no	—
52	C₃×C₉	—	6	1	no	—
53	C₃×Q₈	—	27	1	no	—
54	Dic₆	—	9	1	no	—
55	Dic₆	—	27	1	no	—
56	C₂×C₃²	—	3	1	no	—
57	C₂×C₃²	—	3	1	no	—
58	C₂×C₃²	—	6	1	no	—
59	C₂×C₃²	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
60	C₂×C₉	—	9	1	no	—
61	C₂×C₉	—	9	1	no	—
62	C₂×C₉	—	18	1	no	—
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	9	1	no	—
65	C₃×C₄	—	27	2	no	—
66	C₃×C₄	#4176	1	1	yes	characteristic
67	C₃×C₄	#4179	1	1	yes	characteristic
68	Dic₃	—	9	2	no	—
69	Dic₃	—	27	2	no	—
70	C₃²	—	3	1	no	—
71	C₃²	—	3	1	no	—
72	C₃²	—	6	1	no	—
73	C₃²	#634⋊C₃	1	1	yes	characteristic
74	C₉	—	9	1	no	—
75	C₉	—	9	1	no	—
76	C₉	—	18	1	no	—
77	Q₈	—	27	1	no	Sylow
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	—	9	1	no	—
80	C₂×C₃	C₂×#4176	1	1	yes	characteristic
81	C₂×C₃	C₂×#4179	1	1	yes	characteristic
82	C₄	—	27	2	no	—
83	C₄	#92166	1	1	yes	characteristic
84	C₃	—	2	1	no	—
85	C₃	—	9	1	no	—
86	C₃	#10619613	1	1	yes	characteristic
87	C₃	#10619620	1	1	yes	characteristic
88	C₂	C₂×#92166	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×#4179
commutator, cosocle	C₂×C₃²⋊C₉	C₂²×C₃
Frattini, prime radical	C₂×C₃³	C₂×C₃×D₃
Fitting	C₄×#6861	C₂
socle	C₂×C₃²	C₂×(C₃⋊D₃)⋊C₃
hypercenter	C₃×C₄	#4179
hypocenter	C₃²⋊C₉	C₃×Q₈
LCS	G ▷ C₂×C₃²⋊C₉ ▷ C₃²⋊C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
11. #6861	Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6861	2
#11757289	2
#10619654	3
#634⋊C₉	3