Finite Group Databasebeta

← #20243812

Subgroups — #20243812

Order 6016.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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×C47⋊C8C211yesmaximal, characteristic
2C2×#13093948C212yesmaximal, complemented
3#15688983C211yesmaximal, characteristic
4#15688885C212yesmaximal, complemented
5C2×C22⋊Q8×C47C211yesmaximal, characteristic
6C22×C47⋊C8—22no—
7C22×C47⋊C8—24no—
8C22×C47⋊C8C2212yes—
9C2×C4⋊Dic47C2212yes—
10C2×C22⋊Dic47—21no—
11#13093948—24no—
12C47⋊#95—21no—
13C22×Q8×C47C2211yescharacteristic
14C23×C4×C47C2211yescharacteristic
15C22⋊Q8×C47—22no—
16C22⋊Q8×C47C414yescomplemented
17C2×C4⋊C4×C47—21no—
18C2×C4⋊C4×C47C2211yescharacteristic
19C2×C22⋊C4×C47—21no—
20C24×C47D411yescharacteristic
21C2×Q8×C47—21no—
22C2×Q8×C47—22no—
23C2×Q8×C47—22no—
24C2×Q8×C47C2×C412yes—
25C22×C4×C47—22no—
26C22×C4×C47—22no—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47C2×C412yes—
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D412yes—
32C22×C4×C47C2311yescharacteristic
33C22×Dic47—22no—
34C4⋊C4×C47—24no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47C2×C412yes—
37C22⋊C4×C47—24no—
38C22⋊Dic47—42no—
39C4⋊Dic47—22no—
40C4⋊Dic47—22no—
41C2×C47⋊C8—28no—
42C2×C47⋊C8—22no—
43C2×C47⋊C8—22no—
44C2×C47⋊C8D414yes—
45C23×C47—22no—
46C23×C47—22no—
47C23×C47C22⋊C412yes—
48C23×C47SD1612yes—
49C23×C47Q1612yes—
50C23×C47C2×D411yescharacteristic
51Q8×C47—24no—
52Q8×C47—41no—
53Q8×C47—41no—
54C2×C4×C47—22no—
55C2×C4×C47—24no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—42no—
61C2×C4×C47—42no—
62C2×C4×C47C22⋊C412yes—
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D412yes—
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47#4112yes—
67C2×Dic47—42no—
68C2×Dic47—42no—
69C2×Dic47—42no—
70C47⋊C8—24no—
71C22×C47—22no—
72C22×C47—22no—
73C22×C47—24no—
74C22×C47—24no—
75C22×C47#10314yescomplemented
76C22×C47C2×C22⋊C411yescharacteristic
77C22×C47#12112yes—
78C22×C47C2×SD1611yescharacteristic
79C22×C47C2×Q1611yescharacteristic
80C22×C47#13512yes—
81C4×C47—22no—
82C4×C47—42no—
83C4×C47—42no—
84C4×C47C4×D412yes—
85C4×C47#12011yescharacteristic
86C4×C47#12311yescharacteristic
87Dic47—82no—
88#1892—471nomaximal, Sylow
89C2×C47—24no—
90C2×C47#38611yescharacteristic
91C2×C47C2×#10311yescharacteristic
92C2×C47#41611yescharacteristic
93C2×C47#46512yes—
94C2×C47#46712yes—
95C23×C8—471no—
96C2×C22⋊Q8D4711yescharacteristic
97C2×#103—472no—
98#380—471no—
99#340—472no—
100C47#189211yescharacteristic, complemented, Sylow
101C22×Q8C2×D4711yescharacteristic
102C23×C4C2×D4711yescharacteristic
103C22×C8—472no—
104C22×C8—944no—
105C22×C8—942no—
106C22⋊Q8—22no—
107C22⋊Q8Dic4714yescomplemented
108C2×C4⋊C4—21no—
109C2×C4⋊C4—472no—
110C2×C4⋊C4C2×D4711yescharacteristic
111C2×C22⋊C4—21no—
112C2×C22⋊C4—941no—
113#103—944no—
114#95—941no—
115C24C22⋊D4711yescharacteristic
116C2×Q8—21no—
117C2×Q8—22no—
118C2×Q8—22no—
119C2×Q8C2×Dic4712yes—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—942no—
125C22×C4C2×Dic4712yes—
126C22×C4C22⋊D4711yescharacteristic
127C22×C4C22⋊D4712yes—
128C22×C4C22×D4711yescharacteristic
129C2×C8—474no—
130C2×C8—948no—
131C2×C8—942no—
132C2×C8—942no—
133C4⋊C4—24no—
134C4⋊C4—21no—
135C4⋊C4—942no—
136C4⋊C4—942no—
137C4⋊C4C2×Dic4712yes—
138C22⋊C4—24no—
139C22⋊C4—1882no—
140C23—22no—
141C23—22no—
142C23#1062533612yes—
143C23#1062533712yes—
144C23C22⋊Dic4712yes—
145C23C2×C22⋊D4711yescharacteristic
146Q8—24no—
147Q8—41no—
148Q8—41no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—1882no—
158C2×C4—1882no—
159C2×C4—1882no—
160C2×C4C22⋊Dic4712yes—
161C2×C4D4×D4712yes—
162C2×C4#1062535212yes—
163C2×C4C22×Dic4711yescharacteristic
164C2×C4C2×C22⋊D4711yescharacteristic
165C8—944no—
166C22—22no—
167C22—24no—
168C22—24no—
169C22—22no—
170C22#1309394814yescomplemented
171C22C2×C22⋊Dic4711yescharacteristic
172C22#1309399612yes—
173C22C2×#1062533611yescharacteristic
174C22C2×#1062533711yescharacteristic
175C22#1309404412yes—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—3762no—
180C4D4×Dic4712yes—
181C4#1309399211yescharacteristic
182C4#1309400511yescharacteristic
183C2—24no—
184C2#1568900311yescharacteristic
185C2C2×#1309394811yescharacteristic
186C2#1568911911yescharacteristic
187C2#1568935412yes—
188C2#1568936212yes—
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊Q8×C47C2
socleC23×C47C2×D4
hypercenterC2×C22⋊Q8D47
hypocenterC47#1892
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#13093948C2semidirect
4. #15688885C2semidirect
16. C22⋊Q8×C47C4semidirect
75. C22×C47#103semidirect
100. C47#1892semidirect
107. C22⋊Q8Dic47semidirect
170. C22#13093948semidirect