Group #14565081 — subgroups

Subgroups — #14565081

Order 2432.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926543	C₂	1	2	yes	maximal
2	#11926510	C₂	1	1	yes	maximal, characteristic
3	#11926313	C₂	1	2	yes	maximal, complemented
4	#11926309	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×#64520	C₂²	1	2	yes	—
10	C₂×#64520	C₂²	1	1	yes	characteristic
11	C₁₉×#106	—	2	2	no	—
12	(C₂×D₁₉)⋊C₈	—	2	2	no	—
13	#10597267	—	2	2	no	—
14	#10597266	—	2	2	no	—
15	C₂²×C₄×C₁₉	—	2	2	no	—
16	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×C₂²⋊D₁₉	—	2	1	no	—
18	#64541	—	2	2	no	—
19	#64541	—	2	2	no	—
20	C₂×D₇₆	D₄	1	1	yes	characteristic
21	C₂×C₄×D₁₉	—	2	1	no	—
22	C₂×Dic₃₈	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	D₄	1	2	yes	—
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	#64520	—	2	2	no	—
28	#64520	—	2	2	no	—
29	#64520	—	2	2	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂×C₁₉⋊C₈	—	2	1	no	—
32	C₂³×C₁₉	#41	1	1	yes	characteristic
33	C₂²×D₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	—	8	2	no	—
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	#41	1	2	yes	—
39	C₂×C₄×C₁₉	#41	1	2	yes	—
40	C₂²⋊D₁₉	—	4	2	no	—
41	C₂×Dic₁₉	—	2	1	no	—
42	D₇₆	—	2	2	no	—
43	C₄×D₁₉	—	4	1	no	—
44	C₄×D₁₉	—	4	1	no	—
45	Dic₃₈	—	2	2	no	—
46	C₈×C₁₉	—	2	2	no	—
47	C₁₉⋊C₈	—	4	2	no	—
48	C₁₉⋊C₈	—	4	1	no	—
49	#2079	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	—	2	2	no	—
51	C₂²×C₁₉	#121	1	1	yes	characteristic
52	C₂²×C₁₉	#126	1	2	yes	—
53	C₂×D₁₉	—	4	1	no	—
54	C₂×D₁₉	—	4	2	no	—
55	C₄×C₁₉	—	8	2	no	—
56	C₄×C₁₉	#123	1	2	yes	—
57	C₄×C₁₉	#123	1	1	yes	characteristic
58	C₄×C₁₉	#124	1	1	yes	characteristic
59	Dic₁₉	—	4	1	no	—
60	C₂×#106	D₁₉	1	1	yes	characteristic, complemented
61	#417	—	19	2	no	—
62	#408	—	19	1	no	—
63	#343	—	19	2	no	—
64	#341	—	19	1	no	—
65	C₂×C₁₉	—	2	2	no	—
66	C₂×C₁₉	#397	1	1	yes	characteristic
67	C₂×C₁₉	#471	1	2	yes	—
68	D₁₉	—	8	1	no	—
69	C₂×#41	—	19	1	no	—
70	C₂×M₁₆	—	19	2	no	—
71	C₂×M₁₆	—	19	1	no	—
72	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
73	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
74	#106	—	2	2	no	—
75	#103	—	38	2	no	—
76	#102	—	38	2	no	—
77	C₂²⋊C₈	—	38	2	no	—
78	C₁₉	#2079	1	1	yes	characteristic, complemented, Sylow
79	#41	—	38	2	no	—
80	#41	—	38	2	no	—
81	C₂×Q₈	—	19	1	no	—
82	C₂×D₄	—	19	1	no	—
83	C₂×D₄	—	38	1	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	38	1	no	—
86	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
87	M₁₆	—	38	2	no	—
88	M₁₆	—	38	2	no	—
89	M₁₆	—	38	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	38	2	no	—
92	C₂×C₈	—	38	1	no	—
93	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	—	2	2	no	—
96	C₂³	—	38	1	no	—
97	C₂³	#64543	1	1	yes	characteristic
98	Q₈	—	38	2	no	—
99	D₄	—	38	2	no	—
100	D₄	—	76	2	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	—	8	2	no	—
103	C₂×C₄	—	38	1	no	—
104	C₂×C₄	—	76	1	no	—
105	C₂×C₄	—	76	1	no	—
106	C₂×C₄	#64541	1	2	yes	—
107	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
108	C₂×C₄	#64545	1	2	yes	—
109	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	—	76	1	no	—
112	C₈	—	76	2	no	—
113	C₂²	—	2	2	no	—
114	C₂²	—	76	2	no	—
115	C₂²	—	76	1	no	—
116	C₂²	#10597344	1	2	yes	—
117	C₂²	#10597384	1	1	yes	characteristic
118	C₄	—	8	2	no	—
119	C₄	—	76	1	no	—
120	C₄	#10597340	1	2	yes	—
121	C₄	#10597375	1	1	yes	characteristic
122	C₄	#10597393	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	152	1	no	—
125	C₂	#11926470	1	1	yes	characteristic
126	C₂	#11926804	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926543

C₂

yes

maximal

#11926510

C₂

yes

maximal, characteristic

#11926313

C₂

yes

maximal, complemented

#11926309

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#106

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

characteristic

C₁₉×#106

—

(C₂×D₁₉)⋊C₈

—

#10597267

—

#10597266

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

#64520

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2079

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

#126

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#123

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×#106

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#397

yes

characteristic

C₂×C₁₉

#471

yes

—

D₁₉

—

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

#106

—

#103

—

#102

—

C₂²⋊C₈

—

C₁₉

#2079

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂³

—

C₂³

#64543

yes

characteristic

Q₈

—

D₄

—

100

D₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#64541

yes

—

107

C₂×C₄

D₄×D₁₉

yes

characteristic

108

C₂×C₄

#64545

yes

—

109

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

#10597344

yes

—

117

C₂²

#10597384

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

#10597340

yes

—

121

C₄

#10597375

yes

characteristic

122

C₄

#10597393

yes

characteristic

123

C₂

—

124

C₂

—

152

—

125

C₂

#11926470

yes

characteristic

126

C₂

#11926804

yes

—

	subgroup	G/H
center	C₂²	#10597384
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#106	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂×#64541	C₂²
hypercenter	C₂×#106	D₁₉
hypocenter	C₁₉	#2079
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂²

#10597384

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#106

C₂

C₂²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
3. #11926313	C₂	semidirect
4. #11926309	C₂	semidirect
5. C₂×C₁₉×#106	C₂	semidirect
60. C₂×#106	D₁₉	semidirect
78. C₁₉	#2079	semidirect

H ≅ G/N

type

3. #11926313

C₂

semidirect

4. #11926309

C₂

semidirect

5. C₂×C₁₉×#106

C₂

semidirect

60. C₂×#106

D₁₉

semidirect

78. C₁₉

#2079

semidirect

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

subgroup	index
#11926543	2
#11926510	2
#11926313	2
#11926309	2
C₂×C₁₉×#106	2
#2079	19

subgroup

index

C₂×C₁₉×#106

Subgroups — #14565081

Conjugacy classes of subgroups

Complements

Maximal subgroups