Finite Group Databasebeta

← #18069466

Subgroups — #18069466

Order 4864.

262 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10597274C211yesmaximal, characteristic
2#14562383C211yesmaximal, characteristic
3C4×C19×M32C211yesmaximal, characteristic
4#11926597—21no—
5C2×#10597274C412yes—
6C4×C4⋊Dic19—21no—
7#11926307—21no—
8#11926297C412yescomplemented
9#11926295—21no—
10C2×C19×M32—21no—
11C2×C4×C8×C19C2211yescharacteristic
12C19×#346C412yescomplemented
13C4×C16×C19—21no—
14C22×C8×C19C2×C411yescharacteristic
15C22×C8×C19D411yescharacteristic
16C2×C42×C19D411yescharacteristic
17C2×C4⋊Dic19—22no—
18C2×C4×Dic19—41no—
19C19×M32—24no—
20C2×C16×C19—22no—
21C4×C8×C19C2×C411yescharacteristic
22C4×C8×C19C2×C411yescharacteristic
23C4×C8×C19D411yescharacteristic
24C4×C8×C19Q811yescharacteristic
25C19⋊#95—41no—
26C22⋊(C19⋊C8)—41no—
27#10597274—22no—
28#10597274C814yescomplemented
29C4⋊(C19⋊C8)—22no—
30C4×C19⋊C8—41no—
31C22×C4×C19C22⋊C411yescharacteristic
32C22×C4×C19D811yescharacteristic
33C22×C4×C19SD1611yescharacteristic
34C22×Dic19—42no—
35C2×C8×C19—22no—
36C2×C8×C19C4211yescharacteristic
37C2×C8×C19C22⋊C411yescharacteristic
38C2×C8×C19C4⋊C411yescharacteristic
39C2×C8×C19C4⋊C411yescharacteristic
40C2×C8×C19C2×C812yes—
41C2×C8×C19M1612yes—
42C42×C19C22⋊C411yescharacteristic
43C42×C19C4⋊C411yescharacteristic
44C42×C19SD1611yescharacteristic
45C42×C19Q1611yescharacteristic
46C4⋊Dic19—24no—
47C4⋊Dic19—42no—
48C4×Dic19—82no—
49C2×C19⋊C8—42no—
50C16×C19—24no—
51#7175—191nomaximal, Sylow
52C23×C19#10211yescharacteristic
53C2×C4×C19—22no—
54C2×C4×C19—41no—
55C2×C4×C19#9511yescharacteristic
56C2×C4×C19C22⋊C812yes—
57C2×C4×C19#10211yescharacteristic
58C2×C4×C19#10311yescharacteristic
59C2×C4×C19#10311yescharacteristic
60C2×C4×C19#10412yes—
61C2×C4×C19#10611yescharacteristic
62C2×C4×C19#10711yescharacteristic
63C2×Dic19—44no—
64C2×Dic19—82no—
65C2×Dic19—82no—
66C8×C19—21no—
67C8×C19—21no—
68C8×C19C4×C811yescharacteristic
69C8×C19#9711yescharacteristic
70C8×C19C4⋊C812yes—
71C19⋊C8—82no—
72C4×M32D1911yescharacteristic
73C4×#106—191no—
74#1564—191no—
75C22×C19—21no—
76C22×C19—21no—
77C22×C19D4⋊C812yes—
78C22×C19#34011yescharacteristic
79C4×C19—21no—
80C4×C19—21no—
81C4×C19—21no—
82C4×C19Q8⋊C812yes—
83C4×C19#33611yescharacteristic
84C4×C19#33911yescharacteristic
85C4×C19#36012yes—
86Dic19—84no—
87C2×M32—21no—
88#431—381no—
89C2×#106—192no—
90C2×C4×C8C2×D1911yescharacteristic
91C4×C4⋊C4—381no—
92#346Dic1912yescomplemented
93C4×C16—21no—
94#340—381no—
95#335—192no—
96#334—381no—
97C2×C19—22no—
98C2×C19#127911yescharacteristic
99C2×C19#138611yescharacteristic
100C2×C19#138911yescharacteristic
101C22×C8C4×D1911yescharacteristic
102C22×C8C22⋊D1911yescharacteristic
103C2×C4⋊C4—382no—
104C2×C42—761no—
105C2×C42D7611yescharacteristic
106M32—24no—
107C2×C16—22no—
108#106—194no—
109#106—382no—
110C4⋊C8—382no—
111C22⋊C8—761no—
112C4×C8—761no—
113C4×C8Dic3811yescharacteristic
114C4×C8C4×D1911yescharacteristic
115C4×C8C2×Dic1911yescharacteristic
116C4×C8C22⋊D1911yescharacteristic
117#95—761no—
118C19#717511yescharacteristic, complemented, Sylow
119C22×C4—762no—
120C22×C4#6451611yescharacteristic
121C22×C4D15211yescharacteristic
122C22×C4(C2×D19)⋊C411yescharacteristic
123C2×C8—22no—
124C2×C8—762no—
125C2×C8C8×D1912yes—
126C2×C8#6451512yes—
127C2×C8C4×Dic1911yescharacteristic
128C2×C8Dic19⋊C411yescharacteristic
129C2×C8Dic19⋊C411yescharacteristic
130C2×C8C22⋊Dic1911yescharacteristic
131C4⋊C4—384no—
132C4⋊C4—762no—
133C42—1522no—
134C42#6451611yescharacteristic
135C42Dic7611yescharacteristic
136C42C4⋊Dic1911yescharacteristic
137C42(C2×D19)⋊C411yescharacteristic
138C16—24no—
139C23#1059727811yescharacteristic
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—764no—
143C2×C4—1522no—
144C2×C4—1522no—
145C2×C4#1059726212yes—
146C2×C4#1059727311yescharacteristic
147C2×C4#1059727311yescharacteristic
148C2×C4#1059727411yescharacteristic
149C2×C4#1059727511yescharacteristic
150C2×C4(C2×D19)⋊C812yes—
151C2×C4#1059727811yescharacteristic
152C2×C4C19⋊#9511yescharacteristic
153C8—21no—
154C8—21no—
155C8—1522no—
156C8C8×Dic1911yescharacteristic
157C8Dic19⋊C812yes—
158C8#1059727211yescharacteristic
159C22—21no—
160C22—21no—
161C22#1192627312yes—
162C22#1192630711yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—1524no—
167C4#1192627612yes—
168C4#1192629811yescharacteristic
169C4#1192630411yescharacteristic
170C4#1192635512yes—
171C2—22no—
172C2#1456147511yescharacteristic
173C2#1456174111yescharacteristic
174C2#1456175011yescharacteristic
subgroupG/H
centerC2×C4#10597278
commutatorC8×C19C4×C8
FrattiniC2×C4×C8C2×D19
FittingC4×C19×M32C2
socleC22×C19#340
prime radicalC23×C19#102
cosocleC2×C4×C8×C19C22
hypercenterC4×M32D19
hypocenterC19#7175
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×M32

Complements

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

NH ≅ G/Ntype
8. #11926297C4semidirect
12. C19×#346C4semidirect
28. #10597274C8semidirect
92. #346Dic19semidirect
118. C19#7175semidirect

Maximal subgroups

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

subgroupindex
C4×#105972742
#145623832
C4×C19×M322
#717519