Group #18070115 — subgroups

Subgroups — #18070115

Order 4864.

136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14561775	C₂	1	1	yes	maximal, characteristic
2	#14561739	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2219	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597276	—	2	1	no	—
5	#11926378	—	2	1	no	—
6	C₂×C₁₉×Q₃₂	C₄	1	1	yes	characteristic
7	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
8	C₁₉×#467	—	2	1	no	—
9	C₁₉×#367	C₄	1	1	yes	characteristic
10	C₁₉×#358	—	2	1	no	—
11	C₂×Q₁₆×C₁₉	—	2	1	no	—
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₁₉×C₂²⋊Q₈	—	4	1	no	—
14	C₂×#64520	—	4	1	no	—
15	C₁₉×Q₃₂	—	4	1	no	—
16	C₁₉×M₃₂	—	4	1	no	—
17	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
19	C₁₉×#107	—	2	1	no	—
20	C₁₉×#103	—	4	1	no	—
21	#10597276	—	2	2	no	—
22	#10597276	—	4	1	no	—
23	C₁₉⋊C₃₂	—	4	1	no	—
24	C₂×Q₈×C₁₉	—	4	1	no	—
25	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
26	Q₁₆×C₁₉	—	4	1	no	—
27	Q₁₆×C₁₉	—	4	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₄⋊C₄×C₁₉	—	4	1	no	—
33	C₄⋊C₄×C₁₉	—	8	1	no	—
34	C₂²⋊C₄×C₁₉	—	8	1	no	—
35	#64520	—	4	2	no	—
36	#64520	—	8	1	no	—
37	C₂×C₁₉⋊C₈	—	8	1	no	—
38	C₁₆×C₁₉	—	2	1	no	—
39	C₁₆×C₁₉	—	2	1	no	—
40	#7425	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	SD₃₂	1	1	yes	characteristic
42	Q₈×C₁₉	—	8	1	no	—
43	Q₈×C₁₉	—	8	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	8	1	no	—
47	C₂×C₄×C₁₉	—	8	1	no	—
48	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
49	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
50	C₈×C₁₉	—	2	1	no	—
51	C₈×C₁₉	#99	1	1	yes	characteristic
52	C₈×C₁₉	#104	1	1	yes	characteristic
53	C₁₉⋊C₈	—	8	2	no	—
54	#2219	D₁₉	1	1	yes	characteristic
55	#1400	—	19	1	no	—
56	#1385	—	19	1	no	—
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	4	1	no	—
59	C₂²×C₁₉	#357	1	1	yes	characteristic
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	—	16	1	no	—
62	C₄×C₁₉	—	16	1	no	—
63	C₄×C₁₉	#327	1	1	yes	characteristic
64	C₄×C₁₉	#360	1	1	yes	characteristic
65	C₂×Q₃₂	Dic₁₉	1	1	yes	characteristic
66	C₂×M₃₂	C₂×D₁₉	1	1	yes	characteristic
67	#467	—	2	1	no	—
68	C₂×#108	—	38	1	no	—
69	M₆₄	—	38	1	no	—
70	#367	Dic₁₉	1	1	yes	characteristic
71	#358	—	2	1	no	—
72	C₂×C₁₉	—	2	1	no	—
73	C₂×C₁₉	—	4	1	no	—
74	C₂×C₁₉	#1347	1	1	yes	characteristic
75	C₂×Q₁₆	—	2	1	no	—
76	C₂×M₁₆	—	76	1	no	—
77	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
78	C₂²⋊Q₈	—	4	1	no	—
79	Q₃₂	—	4	1	no	—
80	M₃₂	—	4	1	no	—
81	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
82	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
83	#108	—	38	2	no	—
84	#108	—	76	1	no	—
85	#107	—	2	1	no	—
86	#103	—	4	1	no	—
87	C₃₂	—	76	1	no	—
88	C₁₉	#7425	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	4	1	no	—
90	C₂²×C₄	#64525	1	1	yes	characteristic
91	Q₁₆	—	4	1	no	—
92	Q₁₆	—	4	1	no	—
93	M₁₆	—	76	2	no	—
94	M₁₆	—	152	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	152	1	no	—
98	C₂×C₈	#64526	1	1	yes	characteristic
99	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
100	C₄⋊C₄	—	4	1	no	—
101	C₄⋊C₄	—	8	1	no	—
102	C₂²⋊C₄	—	8	1	no	—
103	C₁₆	—	2	1	no	—
104	C₁₆	—	2	1	no	—
105	C₂³	#10597284	1	1	yes	characteristic
106	Q₈	—	8	1	no	—
107	Q₈	—	8	1	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	8	1	no	—
111	C₂×C₄	—	8	1	no	—
112	C₂×C₄	#10597283	1	1	yes	characteristic
113	C₂×C₄	#10597289	1	1	yes	characteristic
114	C₈	—	2	1	no	—
115	C₈	—	152	2	no	—
116	C₈	#10597291	1	1	yes	characteristic
117	C₈	#10597294	1	1	yes	characteristic
118	C₂²	—	2	1	no	—
119	C₂²	—	4	1	no	—
120	C₂²	#11926345	1	1	yes	characteristic
121	C₄	—	2	1	no	—
122	C₄	—	16	1	no	—
123	C₄	—	16	1	no	—
124	C₄	#11926278	1	1	yes	characteristic
125	C₄	#11926354	1	1	yes	characteristic
126	C₂	—	2	1	no	—
127	C₂	—	4	1	no	—
128	C₂	#14561644	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561775

C₂

yes

maximal, characteristic

#14561739

C₂

yes

maximal, characteristic

C₁₉×#2219

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926378

—

C₂×C₁₉×Q₃₂

C₄

yes

characteristic

C₂×C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×#467

—

C₁₉×#367

C₄

yes

characteristic

C₁₉×#358

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₂×#64520

—

C₁₉×Q₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×#103

—

#10597276

—

#10597276

—

C₁₉⋊C₃₂

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7425

—

maximal, Sylow

C₂³×C₁₉

SD₃₂

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

#2219

D₁₉

yes

characteristic

#1400

—

#1385

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#357

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×Q₃₂

Dic₁₉

yes

characteristic

C₂×M₃₂

C₂×D₁₉

yes

characteristic

#467

—

C₂×#108

—

M₆₄

—

#367

Dic₁₉

yes

characteristic

#358

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1347

yes

characteristic

C₂×Q₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

—

—

—

—

C₃₂

—

C₁₉

#7425

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

#64525

yes

characteristic

Q₁₆

—

Q₁₆

—

M₁₆

—

M₁₆

—

152

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

152

—

C₂×C₈

#64526

yes

characteristic

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₁₆

—

104

C₁₆

—

105

C₂³

#10597284

yes

characteristic

106

Q₈

—

107

Q₈

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

#10597283

yes

characteristic

113

C₂×C₄

#10597289

yes

characteristic

114

C₈

—

115

C₈

—

152

—

116

C₈

#10597291

yes

characteristic

117

C₈

#10597294

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

#11926345

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#11926278

yes

characteristic

125

C₄

#11926354

yes

characteristic

126

C₂

—

127

C₂

—

128

C₂

#14561644

yes

characteristic

	subgroup	G/H
center	C₂	#14561644
commutator	C₂×C₁₆×C₁₉	C₂×C₄
Frattini	C₂×M₃₂	C₂×D₁₉
Fitting	C₁₉×#2219	C₂
socle	C₂×C₁₉	#1347
prime radical	C₂³×C₁₉	SD₃₂
cosocle	C₂×C₁₉×M₃₂	C₂²
hypercenter	#2219	D₁₉
hypocenter	C₁₉	#7425
LCS	G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #2219

subgroup

G/H

center

C₂

#14561644

commutator

C₂×C₁₆×C₁₉

C₂×C₄

Frattini

C₂×M₃₂

C₂×D₁₉

Fitting

C₁₉×#2219

C₂

socle

C₂×C₁₉

#1347

prime radical

C₂³×C₁₉

SD₃₂

cosocle

C₂×C₁₉×M₃₂

C₂²

D₁₉

C₁₉

G ▷ C₂×C₁₆×C₁₉ ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂ ◁ #2219

N	H ≅ G/N	type
88. C₁₉	#7425	semidirect

H ≅ G/N

type

88. C₁₉

#7425

semidirect

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

subgroup	index
#14561775	2
#14561739	2
C₁₉×#2219	2
#7425	19

subgroup

index

#14561775

#14561739

C₁₉×#2219

#7425

Subgroups — #18070115

Conjugacy classes of subgroups

Complements

Maximal subgroups