Finite Group Databasebeta

← #20243324

Subgroups — #20243324

Order 6016.

592 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C23×Dic94C211yesmaximal, characteristic
2C2×#13093949C214yesmaximal, complemented
3#15688983C211yesmaximal, characteristic
4C2×C22⋊C8×C47C211yesmaximal, characteristic
5C22×Dic94—21no—
6C22×Dic94—22no—
7C22×Dic94—28no—
8C22×Dic94C414yescomplemented
9C22×Dic94C2212yes—
10C23×Dic47—21no—
11C2×C4⋊Dic47C2212yes—
12C2×C22⋊Dic47—21no—
13#13093949—28no—
14C47⋊#95—21no—
15C23×C4×C47C2211yescharacteristic
16C22×C8×C47C2212yes—
17C22⋊C8×C47—22no—
18C24×C47D411yescharacteristic
19C22×C4×C47—24no—
20C22×C4×C47C2×C412yes—
21C22×C4×C47D411yescharacteristic
22C22×C4×C47D412yes—
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—28no—
25C22×Dic47—24no—
26C22×Dic47—22no—
27C22×Dic47—22no—
28C2×Dic94—28no—
29C2×Dic94—216no—
30C2×Dic94—24no—
31C2×Dic94—24no—
32C2×Dic94—22no—
33C2×Dic94—216no—
34C2×Dic94C2×C414yes—
35C2×Dic94D418yes—
36C2×C8×C47—24no—
37C2×C8×C47—22no—
38C22⋊Dic47—42no—
39C4⋊Dic47—24no—
40C23×C47—22no—
41C23×C47—22no—
42C23×C47C22⋊C412yes—
43C23×C47SD1612yes—
44C23×C47Q1612yes—
45C23×C47C2×D411yescharacteristic
46C2×C4×C47—22no—
47C2×C4×C47—24no—
48C2×C4×C47—24no—
49C2×C4×C47C22⋊C412yes—
50C2×C4×C47C22×C411yescharacteristic
51C2×C4×C47C2×D414yes—
52C2×C4×C47C2×D411yescharacteristic
53C2×Dic47—216no—
54C2×Dic47—24no—
55C2×Dic47—28no—
56C2×Dic47—42no—
57C2×Dic47—42no—
58C2×Dic47—42no—
59Dic94—216no—
60Dic94—24no—
61Dic94—28no—
62Dic94C22⋊C418yescomplemented
63C8×C47—42no—
64C22×C47—22no—
65C22×C47—22no—
66C22×C47—24no—
67C22×C47—24no—
68C22×C47#10314yescomplemented
69C22×C47C2×C22⋊C411yescharacteristic
70C22×C47#12012yes—
71C22×C47C2×SD1611yescharacteristic
72C22×C47C2×Q1611yescharacteristic
73C22×C47#13712yes—
74C4×C47—22no—
75C4×C47C2×C22⋊C412yes—
76C4×C47#12012yes—
77Dic47—28no—
78Dic47—82no—
79#1787—471nomaximal, Sylow
80C2×C47—24no—
81C2×C47#37911yescharacteristic
82C2×C47C2×#10311yescharacteristic
83C2×C47#41911yescharacteristic
84C2×C47#44812yes—
85C2×C47#45112yes—
86C23×Q8—471no—
87C2×#103—474no—
88C2×C22⋊C8D4711yescharacteristic
89#380—471no—
90C47#178711yescharacteristic, complemented, Sylow
91C22×Q8—474no—
92C22×Q8—472no—
93C22×Q8—948no—
94C22×Q8—941no—
95C22×Q8—942no—
96C23×C4—941no—
97C23×C4C2×D4711yescharacteristic
98C22×C8C2×D4712yes—
99C2×C4⋊C4—472no—
100C2×C22⋊C4—941no—
101#103—948no—
102C22⋊C8—22no—
103#95—941no—
104C24D18811yescharacteristic
105C2×Q8—474no—
106C2×Q8—478no—
107C2×Q8—9416no—
108C2×Q8—948no—
109C2×Q8—9416no—
110C2×Q8—944no—
111C2×Q8—944no—
112C2×Q8—942no—
113C22×C4—24no—
114C22×C4—948no—
115C22×C4—944no—
116C22×C4—942no—
117C22×C4—942no—
118C22×C4C4×D4712yes—
119C22×C4D18811yescharacteristic
120C22×C4C22⋊D4712yes—
121C22×C4C22×D4711yescharacteristic
122C2×C8—24no—
123C2×C8—22no—
124C4⋊C4—944no—
125C22⋊C4—1882no—
126C23—22no—
127C23—22no—
128C23#1062532512yes—
129C23Dic18812yes—
130C23(C2×D47)⋊C412yes—
131C23C2×D18811yescharacteristic
132Q8—478no—
133Q8—9416no—
134Q8—944no—
135Q8—948no—
136C2×C4—22no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—9416no—
140C2×C4—944no—
141C2×C4—948no—
142C2×C4—1882no—
143C2×C4—1882no—
144C2×C4—1882no—
145C2×C4(C2×D47)⋊C412yes—
146C2×C4C2×C4×D4711yescharacteristic
147C2×C4D4×D4714yes—
148C2×C4C2×C22⋊D4711yescharacteristic
149C8—42no—
150C22—22no—
151C22—24no—
152C22—24no—
153C22—22no—
154C22#1309394914yescomplemented
155C22C2×(C2×D47)⋊C411yescharacteristic
156C22#1309399412yes—
157C22C2×#1062532511yescharacteristic
158C22C2×Dic18811yescharacteristic
159C22#1309405712yes—
160C4—22no—
161C4—948no—
162C4—3762no—
163C4C22⋊C4×D4712yes—
164C4#1309399212yes—
165C2—24no—
166C2#1568897811yescharacteristic
167C2C2×#1309394911yescharacteristic
168C2#1568913311yescharacteristic
169C2#1568926412yes—
170C2#1568928112yes—
subgroupG/H
centerC23C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊C8×C47C2
socleC23×C47C2×D4
hypercenterC2×C22⋊C8D47
hypocenterC47#1787
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#13093949C2semidirect
8. C22×Dic94C4semidirect
62. Dic94C22⋊C4semidirect
68. C22×C47#103semidirect
90. C47#1787semidirect
154. C22#13093949semidirect