Finite Group Databasebeta

← #18070260

Subgroups — #18070260

Order 4864.

162 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C2×#11926374C211yesmaximal, characteristic
2C2×#11926374C211yesmaximal, characteristic
3C2×C19×M64C211yesmaximal, characteristic
4C2×#10597276—21no—
5C2×#10597276—21no—
6#11926374—21no—
7#11926374—21no—
8#11926374C412yes—
9#11926374C412yes—
10C22×C16×C19C2211yescharacteristic
11C19×M64—21no—
12C19×M64C412yes—
13C2×C19×C32—21no—
14C22×C8×C19D411yescharacteristic
15C2×#64520—41no—
16C2×#64520—41no—
17C2×C16×C19C2×C411yescharacteristic
18C2×C16×C19C2×C411yescharacteristic
19C2×C16×C19C2×C411yescharacteristic
20C2×C16×C19D411yescharacteristic
21C2×C16×C19D411yescharacteristic
22C2×C16×C19Q811yescharacteristic
23#10597276—22no—
24#10597276—22no—
25#10597276—41no—
26#10597276—41no—
27C19×C32—22no—
28C22×C4×C19D811yescharacteristic
29C2×C8×C19C22⋊C411yescharacteristic
30C2×C8×C19C22⋊C411yescharacteristic
31C2×C8×C19C4⋊C411yescharacteristic
32C2×C8×C19SD1611yescharacteristic
33C2×C8×C19SD1611yescharacteristic
34C2×C8×C19Q1611yescharacteristic
35#64520—42no—
36#64520—42no—
37#64520—81no—
38#64520—81no—
39C2×C19⋊C8—81no—
40C2×C19⋊C8—81no—
41C16×C19C4211yescharacteristic
42C16×C19C22⋊C411yescharacteristic
43C16×C19C4⋊C411yescharacteristic
44C16×C19C4⋊C411yescharacteristic
45#7479—191nomaximal, Sylow
46C23×C19Q3211yescharacteristic
47C2×C4×C19#10211yescharacteristic
48C2×C4×C19#10211yescharacteristic
49C2×C4×C19#10711yescharacteristic
50C2×C4×C19D1611yescharacteristic
51C2×C4×C19SD3211yescharacteristic
52C2×C4×C19SD3211yescharacteristic
53C8×C19#9511yescharacteristic
54C8×C19#10311yescharacteristic
55C8×C19#10311yescharacteristic
56C8×C19#10611yescharacteristic
57C19⋊C8—82no—
58C19⋊C8—82no—
59C2×M64D1911yescharacteristic
60C2×#368—191no—
61C2×#368—191no—
62C22×C19—41no—
63C22×C19#35811yescharacteristic
64C22×C19#35811yescharacteristic
65C22×C19#36611yescharacteristic
66C4×C19#34011yescharacteristic
67C4×C19#35711yescharacteristic
68C4×C19#35711yescharacteristic
69C4×C19#36711yescharacteristic
70C22×C16C2×D1911yescharacteristic
71C2×#108—381no—
72C2×#108—381no—
73M64—21no—
74M64Dic1912yes—
75C2×C32—21no—
76#368—192no—
77#368—192no—
78#368—381no—
79#368—381no—
80C2×C19—21no—
81C2×C19—21no—
82C2×C19—21no—
83C2×C19#138011yescharacteristic
84C2×M16—761no—
85C2×M16—761no—
86C22×C8D7611yescharacteristic
87C2×C16Dic3811yescharacteristic
88C2×C16C4×D1911yescharacteristic
89C2×C16C4×D1911yescharacteristic
90C2×C16C2×Dic1911yescharacteristic
91C2×C16C22⋊D1911yescharacteristic
92C2×C16C22⋊D1911yescharacteristic
93#108—382no—
94#108—382no—
95#108—761no—
96#108—761no—
97C32—22no—
98C19#747911yescharacteristic, complemented, Sylow
99C22×C4D15211yescharacteristic
100M16—762no—
101M16—762no—
102M16—1521no—
103M16—1521no—
104C2×C8—1521no—
105C2×C8—1521no—
106C2×C8#6451611yescharacteristic
107C2×C8#6451611yescharacteristic
108C2×C8Dic7611yescharacteristic
109C2×C8C4⋊Dic1911yescharacteristic
110C2×C8(C2×D19)⋊C411yescharacteristic
111C2×C8(C2×D19)⋊C411yescharacteristic
112C16C4×Dic1911yescharacteristic
113C16Dic19⋊C411yescharacteristic
114C16Dic19⋊C411yescharacteristic
115C16C22⋊Dic1911yescharacteristic
116C23Dic15211yescharacteristic
117C2×C4D30411yescharacteristic
118C2×C4#1059725711yescharacteristic
119C2×C4#1059725711yescharacteristic
120C2×C4#1059727511yescharacteristic
121C2×C4#1059727811yescharacteristic
122C2×C4#1059727811yescharacteristic
123C8—1522no—
124C8—1522no—
125C8#1059727311yescharacteristic
126C8#1059727311yescharacteristic
127C8#1059727411yescharacteristic
128C8C19⋊#9511yescharacteristic
129C22—41no—
130C22#1192634911yescharacteristic
131C22#1192634911yescharacteristic
132C22#1192637011yescharacteristic
133C4#1192630711yescharacteristic
134C4#1192634611yescharacteristic
135C4#1192634611yescharacteristic
136C4#1192637211yescharacteristic
137C2—21no—
138C2—21no—
139C2—21no—
140C2#1456172711yescharacteristic
subgroupG/H
centerC4#11926346
commutatorC16×C19C42
FrattiniC22×C16C2×D19
FittingC2×C19×M64C2
socleC2×C19#1380
prime radicalC23×C19Q32
cosocleC22×C16×C19C22
hypercenterC2×M64D19
hypocenterC19#7479
LCSG ▷ C16×C19 ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×M64

Complements

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

NH ≅ G/Ntype
98. C19#7479semidirect

Maximal subgroups

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

subgroupindex
C2×#119263742
C2×C19×M642
#747919