Subgroups — #14515621

Order 1944.

129 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6857	C₂	1	1	yes	maximal, characteristic
2	C₃×(C₃⋊(C₃⋊C₈))⋊C₃	—	3	1	no	maximal
3	#10619507	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#6857	C₄	1	1	yes	characteristic
5	C₃×C₄×3₋¹⁺²	—	2	1	no	—
6	C₃×C₄×H(3,𝔽₃)	D₃	1	1	yes	characteristic
7	C₄×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
8	#6857	C₈	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₃⋊(C₃⋊C₈)	—	3	1	no	—
10	C₃²×C₃⋊C₈	—	9	1	no	—
11	(C₃⋊(C₃⋊C₈))⋊C₃	—	3	3	no	—
12	C₃×C₉⋊C₈	—	9	1	no	—
13	C₂×C₃×3₋¹⁺²	—	2	1	no	—
14	C₂×C₃×H(3,𝔽₃)	Dic₃	1	1	yes	characteristic
15	C₂×C₃²⋊C₉	C₃×C₄	1	1	yes	characteristic
16	C₃³×C₄	—	3	1	no	—
17	C₃³×C₄	C₃×D₃	1	1	yes	characteristic
18	C₄×3₋¹⁺²	—	6	3	no	—
19	C₄×H(3,𝔽₃)	—	3	3	no	—
20	C₃×C₄×C₉	—	3	1	no	—
21	C₃×C₄×C₉	—	6	1	no	—
22	C₃×3₋¹⁺²	—	2	1	no	—
23	C₃×H(3,𝔽₃)	C₃⋊C₈	1	1	yes	characteristic
24	C₃²⋊C₉	C₃×C₈	1	1	yes	characteristic, complemented
25	C₃²×C₈	—	27	1	no	—
26	C₃⋊(C₃⋊C₈)	—	3	1	no	—
27	C₃×C₃⋊C₈	—	9	3	no	—
28	C₃×C₃⋊C₈	—	9	1	no	—
29	C₃×C₃⋊C₈	—	27	1	no	—
30	C₉⋊C₈	—	9	1	no	—
31	C₂×C₃³	—	3	1	no	—
32	C₂×C₃³	C₃×Dic₃	1	1	yes	characteristic
33	C₂×3₋¹⁺²	—	6	3	no	—
34	C₂×H(3,𝔽₃)	—	3	3	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	3	no	—
39	C₃²×C₄	—	3	1	no	—
40	C₃²×C₄	—	6	1	no	—
41	C₃²×C₄	—	9	1	no	—
42	C₃²×C₄	—	18	1	no	—
43	C₃²×C₄	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
44	C₄×C₉	—	6	3	no	—
45	C₄×C₉	—	9	1	no	—
46	C₃³	—	3	1	no	—
47	C₃³	C₃×C₃⋊C₈	1	1	yes	characteristic
48	3₋¹⁺²	—	6	3	no	—
49	H(3,𝔽₃)	—	3	3	no	—
50	C₃×C₉	—	3	1	no	—
51	C₃×C₉	—	6	1	no	—
52	C₃×C₈	—	27	3	no	—
53	C₃×C₈	—	27	1	no	—
54	C₃⋊C₈	—	9	1	no	—
55	C₃⋊C₈	—	27	1	no	—
56	C₂×C₃²	—	3	1	no	—
57	C₂×C₃²	—	3	3	no	—
58	C₂×C₃²	—	3	1	no	—
59	C₂×C₃²	—	6	1	no	—
60	C₂×C₃²	—	9	1	no	—
61	C₂×C₃²	—	18	1	no	—
62	C₂×C₃²	(C₃⋊Dic₃)⋊C₃	1	1	yes	characteristic
63	C₂×C₉	—	6	3	no	—
64	C₂×C₉	—	9	1	no	—
65	C₃×C₄	—	2	1	no	—
66	C₃×C₄	—	9	1	no	—
67	C₃×C₄	—	9	3	no	—
68	C₃×C₄	#4174	1	1	yes	characteristic
69	C₃×C₄	#4177	1	1	yes	characteristic
70	C₃²	—	3	1	no	—
71	C₃²	—	3	3	no	—
72	C₃²	—	3	1	no	—
73	C₃²	—	6	1	no	—
74	C₃²	—	9	1	no	—
75	C₃²	—	18	1	no	—
76	C₃²	(C₃⋊(C₃⋊C₈))⋊C₃	1	1	yes	characteristic
77	C₉	—	6	3	no	—
78	C₉	—	9	1	no	—
79	C₈	—	27	1	no	Sylow
80	C₂×C₃	—	2	1	no	—
81	C₂×C₃	—	9	1	no	—
82	C₂×C₃	—	9	3	no	—
83	C₂×C₃	#66321	1	1	yes	characteristic
84	C₂×C₃	#66324	1	1	yes	characteristic
85	C₄	#92161	1	1	yes	characteristic
86	C₃	—	2	1	no	—
87	C₃	—	9	1	no	—
88	C₃	—	9	3	no	—
89	C₃	#10619500	1	1	yes	characteristic
90	C₃	#10619503	1	1	yes	characteristic
91	C₂	#11757284	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	#4177
commutator, hypocenter	C₃²⋊C₉	C₃×C₈
Frattini	C₃³×C₄	C₃×D₃
Fitting	C₄×#6857	C₂
socle	C₂×C₃²	(C₃⋊Dic₃)⋊C₃
prime radical	C₂×C₃×H(3,𝔽₃)	Dic₃
cosocle	C₄×C₃²⋊C₉	C₂×C₃
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
3. #10619507	C₃	semidirect
8. #6857	C₈	semidirect
24. C₃²⋊C₉	C₃×C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6857	2
C₃×(C₃⋊(C₃⋊C₈))⋊C₃	3
#10619507	3