Group #14565076 — subgroups

Subgroups — #14565076

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×#107	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×#107	—	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	#2078	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	—	2	1	no	—
51	C₂²×C₁₉	—	2	1	no	—
52	C₂²×C₁₉	#121	1	1	yes	characteristic
53	C₂²×C₁₉	#126	1	2	yes	—
54	C₂×D₁₉	—	4	1	no	—
55	C₂×D₁₉	—	4	1	no	—
56	C₂×D₁₉	—	4	1	no	—
57	C₄×C₁₉	—	8	2	no	—
58	C₄×C₁₉	#123	1	2	yes	—
59	C₄×C₁₉	#123	1	1	yes	characteristic
60	C₄×C₁₉	#124	1	1	yes	characteristic
61	Dic₁₉	—	4	1	no	—
62	C₂×#107	D₁₉	1	1	yes	characteristic, complemented
63	#417	—	19	2	no	—
64	#408	—	19	1	no	—
65	#343	—	19	2	no	—
66	#341	—	19	1	no	—
67	C₂×C₁₉	—	2	2	no	—
68	C₂×C₁₉	#397	1	1	yes	characteristic
69	C₂×C₁₉	#472	1	1	yes	characteristic
70	C₂×C₁₉	#473	1	1	yes	characteristic
71	D₁₉	—	8	1	no	—
72	C₂×#41	—	19	1	no	—
73	C₂×M₁₆	—	19	2	no	—
74	C₂×M₁₆	—	19	1	no	—
75	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
76	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
77	#107	—	2	2	no	—
78	#103	—	38	2	no	—
79	#102	—	38	2	no	—
80	C₂²⋊C₈	—	38	2	no	—
81	C₁₉	#2078	1	1	yes	characteristic, complemented, Sylow
82	#41	—	38	2	no	—
83	#41	—	38	2	no	—
84	C₂×Q₈	—	19	1	no	—
85	C₂×D₄	—	19	1	no	—
86	C₂×D₄	—	38	1	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	—	38	1	no	—
89	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
90	M₁₆	—	38	2	no	—
91	M₁₆	—	38	2	no	—
92	M₁₆	—	38	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	38	2	no	—
95	C₂×C₈	—	38	1	no	—
96	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
97	C₄⋊C₄	—	2	2	no	—
98	C₄⋊C₄	—	2	2	no	—
99	C₂³	—	38	1	no	—
100	C₂³	#64543	1	1	yes	characteristic
101	Q₈	—	38	2	no	—
102	D₄	—	38	2	no	—
103	D₄	—	76	2	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	8	2	no	—
106	C₂×C₄	—	38	1	no	—
107	C₂×C₄	—	76	1	no	—
108	C₂×C₄	—	76	1	no	—
109	C₂×C₄	#64541	1	2	yes	—
110	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
111	C₂×C₄	#64545	1	2	yes	—
112	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	76	1	no	—
115	C₈	—	76	2	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	76	1	no	—
119	C₂²	—	76	1	no	—
120	C₂²	—	76	1	no	—
121	C₂²	#10597344	1	2	yes	—
122	C₂²	#10597384	1	1	yes	characteristic
123	C₄	—	8	2	no	—
124	C₄	—	76	1	no	—
125	C₄	#10597340	1	2	yes	—
126	C₄	#10597375	1	1	yes	characteristic
127	C₄	#10597393	1	1	yes	characteristic
128	C₂	—	2	2	no	—
129	C₂	—	152	1	no	—
130	C₂	#11926470	1	1	yes	characteristic
131	C₂	#11926811	1	1	yes	characteristic
132	C₂	#11926816	1	1	yes	characteristic

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×#107

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×#107

—

(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

—

#2078

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

#126

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#123

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×#107

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

#107

—

#103

—

#102

—

C₂²⋊C₈

—

C₁₉

#2078

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

—

100

C₂³

#64543

yes

characteristic

101

Q₈

—

102

D₄

—

103

D₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

#64541

yes

—

110

C₂×C₄

D₄×D₁₉

yes

characteristic

111

C₂×C₄

#64545

yes

—

112

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

#10597344

yes

—

122

C₂²

#10597384

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

#10597340

yes

—

126

C₄

#10597375

yes

characteristic

127

C₄

#10597393

yes

characteristic

128

C₂

—

129

C₂

—

152

—

130

C₂

#11926470

yes

characteristic

131

C₂

#11926811

yes

characteristic

132

C₂

#11926816

yes

characteristic

	subgroup	G/H
center	C₂²	#10597384
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#107	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂×#64541	C₂²
hypercenter	C₂×#107	D₁₉
hypocenter	C₁₉	#2078
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂²

#10597384

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#107

C₂

C₂²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
3. #11926313	C₂	semidirect
4. #11926309	C₂	semidirect
5. C₂×C₁₉×#107	C₂	semidirect
62. C₂×#107	D₁₉	semidirect
81. C₁₉	#2078	semidirect

H ≅ G/N

type

3. #11926313

C₂

semidirect

4. #11926309

C₂

semidirect

5. C₂×C₁₉×#107

C₂

semidirect

62. C₂×#107

D₁₉

semidirect

81. C₁₉

#2078

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×#107	2
#2078	19

subgroup

index

C₂×C₁₉×#107

Subgroups — #14565076

Conjugacy classes of subgroups

Complements

Maximal subgroups