Group #18076348 — subgroups

Subgroups — #18076348

Order 4864.

338 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 163 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	#14563807	C₂	1	1	yes	maximal, characteristic
2	#14562390	C₂	1	4	yes	maximal
3	C₂×#11926265	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1848	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597276	—	2	2	no	—
6	#11926568	C₂²	1	2	yes	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	#11926294	—	2	8	no	—
9	#11926265	C₄	1	4	yes	—
10	C₂×C₁₉×#108	—	2	2	no	—
11	C₁₉×#423	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₁₉	—	2	2	no	—
14	C₂²×C₈×C₁₉	D₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
16	C₂×#64520	—	2	2	no	—
17	C₂²×C₁₉⋊C₈	Q₈	1	4	yes	—
18	C₁₉×#108	—	4	4	no	—
19	C₁₉×C₄⋊C₈	—	2	4	no	—
20	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₉	Q₈	1	2	yes	—
22	#10597276	—	4	4	no	—
23	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
24	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
25	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
26	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
28	M₁₆×C₁₉	—	4	4	no	—
29	C₂×C₈×C₁₉	—	4	2	no	—
30	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
31	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
32	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
33	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
34	C₄²×C₁₉	C₂×D₄	1	2	yes	—
35	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
36	#64520	—	4	4	no	—
37	C₂×C₁₉⋊C₈	—	4	4	no	—
38	C₂×C₁₉⋊C₈	—	4	2	no	—
39	C₂×C₁₉⋊C₈	C₄⋊C₄	1	8	yes	—
40	#8825	—	19	1	no	maximal, Sylow
41	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
47	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
48	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
49	C₈×C₁₉	—	8	2	no	—
50	C₈×C₁₉	#106	1	8	yes	—
51	C₁₉⋊C₈	—	2	8	no	—
52	C₁₉⋊C₈	—	8	2	no	—
53	#1848	—	19	1	no	—
54	#1848	D₁₉	1	1	yes	characteristic
55	#1566	—	19	4	no	—
56	C₂×#322	—	19	1	no	—
57	C₂²×C₁₉	—	2	2	no	—
58	C₂²×C₁₉	#384	1	1	yes	characteristic
59	C₂²×C₁₉	#498	1	2	yes	—
60	C₄×C₁₉	—	2	2	no	—
61	C₄×C₁₉	C₂×#106	1	2	yes	—
62	C₄×C₁₉	#430	1	4	yes	—
63	C₄×C₁₉	#492	1	1	yes	characteristic
64	C₄×C₁₉	#492	1	1	yes	characteristic
65	C₂×#108	—	2	2	no	—
66	C₂×#108	—	38	2	no	—
67	#423	—	19	2	no	—
68	#423	C₂×D₁₉	1	2	yes	—
69	C₂×C₄×C₈	—	19	2	no	—
70	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
71	#334	—	38	8	no	—
72	#322	—	19	4	no	—
73	C₂×C₁₉	—	2	2	no	—
74	C₂×C₁₉	#1844	1	1	yes	characteristic
75	C₂×C₁₉	#1849	1	2	yes	—
76	C₂×M₁₆	—	2	2	no	—
77	C₂×M₁₆	—	38	2	no	—
78	C₂²×C₈	—	19	4	no	—
79	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
80	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
81	#108	—	4	4	no	—
82	#108	—	76	4	no	—
83	C₄⋊C₈	—	2	4	no	—
84	C₄⋊C₈	—	38	4	no	—
85	C₄×C₈	—	19	4	no	—
86	C₄×C₈	—	19	4	no	—
87	C₄×C₈	Dic₃₈	1	2	yes	—
88	C₄×C₈	C₄×D₁₉	1	2	yes	—
89	C₁₉	#8825	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
91	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
92	M₁₆	—	4	4	no	—
93	M₁₆	—	76	4	no	—
94	C₂×C₈	—	4	2	no	—
95	C₂×C₈	—	19	8	no	—
96	C₂×C₈	—	76	4	no	—
97	C₂×C₈	—	76	2	no	—
98	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
99	C₂×C₈	#64526	1	4	yes	—
100	C₂×C₈	#64527	1	4	yes	—
101	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
102	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
103	C₄²	D₄×D₁₉	1	2	yes	—
104	C₂³	#10597390	1	1	yes	characteristic
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	#10597334	1	2	yes	—
107	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
108	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
109	C₂×C₄	C₂×#64526	1	2	yes	—
110	C₂×C₄	#10597386	1	1	yes	characteristic
111	C₂×C₄	C₂×#64527	1	2	yes	—
112	C₈	—	8	2	no	—
113	C₈	—	38	8	no	—
114	C₈	—	152	2	no	—
115	C₈	#10597265	1	8	yes	—
116	C₂²	—	2	2	no	—
117	C₂²	#11926413	1	1	yes	characteristic
118	C₂²	#11926940	1	2	yes	—
119	C₄	—	2	2	no	—
120	C₄	C₂×#10597265	1	2	yes	—
121	C₄	#11926591	1	4	yes	—
122	C₄	#11926916	1	1	yes	characteristic
123	C₄	#11926918	1	1	yes	characteristic
124	C₂	—	2	2	no	—
125	C₂	#14563791	1	1	yes	characteristic
126	C₂	#14563808	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563807

C₂

yes

maximal, characteristic

#14562390

C₂

yes

maximal

C₂×#11926265

C₂

yes

maximal, characteristic

C₁₉×#1848

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926568

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926294

—

#11926265

C₄

yes

—

C₂×C₁₉×#108

—

C₁₉×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

Q₈

yes

—

C₁₉×#108

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×Q₈

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

#8825

—

maximal, Sylow

C₂³×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#127

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

#106

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1848

—

#1848

D₁₉

yes

characteristic

#1566

—

C₂×#322

—

C₂²×C₁₉

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#498

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×#106

yes

—

C₄×C₁₉

#430

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

—

C₂×D₁₉

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#334

—

#322

—

C₂×C₁₉

—

C₂×C₁₉

#1844

yes

characteristic

C₂×C₁₉

#1849

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₃₈

yes

—

C₄×C₈

C₄×D₁₉

yes

—

C₁₉

#8825

yes

characteristic, complemented, Sylow

C₂²×C₄

Q₈×D₁₉

yes

—

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₉⋊C₄

yes

—

C₂×C₈

#64526

yes

—

100

C₂×C₈

#64527

yes

—

101

C₄²

C₂×Dic₃₈

yes

characteristic

102

C₄²

C₂×C₄×D₁₉

yes

characteristic

103

C₄²

D₄×D₁₉

yes

—

104

C₂³

#10597390

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

#10597334

yes

—

107

C₂×C₄

C₄⋊C₄×D₁₉

yes

—

108

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

109

C₂×C₄

C₂×#64526

yes

—

110

C₂×C₄

#10597386

yes

characteristic

111

C₂×C₄

C₂×#64527

yes

—

112

C₈

—

113

C₈

—

114

C₈

—

152

—

115

C₈

#10597265

yes

—

116

C₂²

—

117

C₂²

#11926413

yes

characteristic

118

C₂²

#11926940

yes

—

119

C₄

—

120

C₄

C₂×#10597265

yes

—

121

C₄

#11926591

yes

—

122

C₄

#11926916

yes

characteristic

123

C₄

#11926918

yes

characteristic

124

C₂

—

125

C₂

#14563791

yes

characteristic

126

C₂

#14563808

yes

—

	subgroup	G/H
center	C₂×C₄	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1848	C₂
socle	C₂²×C₁₉	#384
prime radical	C₂³×C₁₉	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1848	D₁₉
hypocenter	C₁₉	#8825
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂×C₄

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1848

C₂

socle

C₂²×C₁₉

#384

prime radical

C₂³×C₁₉

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
89. C₁₉	#8825	semidirect

H ≅ G/N

type

89. C₁₉

#8825

semidirect

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

subgroup	index
#14563807	2
#14562390	2
C₂×#11926265	2
C₁₉×#1848	2
#8825	19

subgroup

index

C₁₉×#1848

Subgroups — #18076348

Conjugacy classes of subgroups

Complements

Maximal subgroups