Finite Group Databasebeta

← #20243801

Subgroups — #20243801

Order 6016.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13094005C211yesmaximal, characteristic
2C2×#13093939C211yesmaximal, characteristic
3#15688984C212yesmaximal, complemented
4#15688890C212yesmaximal, complemented
5C47×#518C211yesmaximal, characteristic
6C23×Dic47C2211yescharacteristic
7#13094005—22no—
8#13094005C414yescomplemented
9C2×Dic47⋊C4—21no—
10C2×C22⋊Dic47—21no—
11C2×C22⋊Dic47C2212yes—
12C2×C22⋊Dic47C2211yescharacteristic
13#13093939—22no—
14C47⋊#95—24no—
15C22×D4×C47C2211yescharacteristic
16C4×D4×C47—24no—
17#117×C47—21no—
18C2×C22⋊C4×C47—21no—
19C2×C22⋊C4×C47C2212yes—
20C24×C47D411yescharacteristic
21C24×C47C2311yescharacteristic
22C2×D4×C47—22no—
23C2×D4×C47—22no—
24C2×D4×C47C2×C412yes—
25C2×D4×C47D412yes—
26C22×C4×C47—22no—
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D414yes—
29C22×Dic47—22no—
30C22×Dic47—21no—
31C22×Dic47—21no—
32C22×Dic47—21no—
33C22×Dic47—22no—
34C22×Dic47—22no—
35C22×Dic47C2×C412yescomplemented
36C4⋊C4×C47—22no—
37C22⋊C4×C47—22no—
38C22⋊C4×C47—22no—
39C22⋊C4×C47—22no—
40C42×C47—22no—
41C22⋊Dic47—24no—
42C22⋊Dic47—21no—
43C22⋊Dic47—22no—
44C22⋊Dic47—22no—
45C22⋊Dic47C2×C412yescomplemented
46Dic47⋊C4—24no—
47C23×C47—21no—
48C23×C47—21no—
49C23×C47—42no—
50C23×C47—42no—
51C23×C47C22⋊C412yes—
52C23×C47C22×C411yescharacteristic
53C23×C47C2×D411yescharacteristic
54C23×C47C2×D411yescharacteristic
55C23×C47C2×D412yes—
56C23×C47#4112yes—
57D4×C47—24no—
58D4×C47—24no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—24no—
62C2×C4×C47—44no—
63C2×C4×C47—82no—
64C2×C4×C47C22⋊C412yes—
65C2×Dic47—22no—
66C2×Dic47—22no—
67C2×Dic47—24no—
68C2×Dic47—42no—
69C2×Dic47—41no—
70C2×Dic47—42no—
71C2×Dic47—41no—
72C2×Dic47—44no—
73C2×Dic47—42no—
74C22×C47—24no—
75C22×C47—22no—
76C22×C47—22no—
77C22×C47—41no—
78C22×C47—41no—
79C22×C47—42no—
80C22×C47—42no—
81C22×C47—42no—
82C22×C47—81no—
83C22×C47C2×C22⋊C411yescharacteristic
84C22×C47C4×D412yes—
85C22×C47#12011yescharacteristic
86C22×C47#12112yes—
87C22×C47#12311yescharacteristic
88C4×C47—22no—
89C4×C47—44no—
90Dic47—42no—
91Dic47—42no—
92Dic47—82no—
93#1890—471nomaximal, Sylow
94C2×C47—21no—
95C2×C47—22no—
96C2×C47—21no—
97C2×C47—22no—
98C2×C47—42no—
99C2×C47#38611yescharacteristic
100C2×C47#45812yes—
101C2×#123—471no—
102#518D4711yescharacteristic
103C2×#99—471no—
104#381—472no—
105#342—472no—
106C47#189011yescharacteristic, complemented, Sylow
107C22×D4C2×D4711yescharacteristic
108C23×C4—471no—
109#123—474no—
110#123—942no—
111C4×D4—24no—
112#117—21no—
113C2×C4⋊C4—941no—
114C2×C22⋊C4—21no—
115C2×C22⋊C4—471no—
116C2×C22⋊C4—472no—
117C2×C22⋊C4—941no—
118C2×C22⋊C4C2×D4712yes—
119#99—942no—
120#95—944no—
121C24C22⋊D4711yescharacteristic
122C24C22×D4711yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C4×D4712yes—
126C2×D4D18812yes—
127C22×C4—22no—
128C22×C4—472no—
129C22×C4—941no—
130C22×C4—942no—
131C22×C4—942no—
132C22×C4—941no—
133C22×C4—941no—
134C22×C4—942no—
135C22×C4C22⋊D4711yescharacteristic
136C22×C4C22⋊D4714yes—
137C4⋊C4—22no—
138C4⋊C4—944no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—472no—
143C22⋊C4—944no—
144C22⋊C4—941no—
145C22⋊C4—942no—
146C22⋊C4—942no—
147C42—22no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23(C2×D47)⋊C412yes—
153C23C2×C4×D4711yescharacteristic
154C23C2×D18811yescharacteristic
155C23#1062535012yes—
156C23C2×C22⋊D4711yescharacteristic
157C23C2×C22⋊D4712yes—
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—24no—
163C2×C4—44no—
164C2×C4—82no—
165C2×C4—942no—
166C2×C4—942no—
167C2×C4—944no—
168C2×C4—1884no—
169C2×C4—1882no—
170C2×C4—1882no—
171C2×C4—1881no—
172C2×C4—1882no—
173C2×C4—1881no—
174C2×C4(C2×D47)⋊C412yes—
175C22—24no—
176C22—22no—
177C22—22no—
178C22—41no—
179C22—41no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22C2×(C2×D47)⋊C411yescharacteristic
185C22C4×C22⋊D4712yes—
186C22#1309399311yescharacteristic
187C22#1309399812yes—
188C22#1309400711yescharacteristic
189C4—22no—
190C4—44no—
191C4—3762no—
192C4—1882no—
193C4—1882no—
194C2—22no—
195C2—21no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#1568900211yescharacteristic
200C2#1568931312yes—
subgroupG/H
centerC22#13093993
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC47×#518C2
socleC22×C47#120
hypercenter#518D47
hypocenterC47#1890
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
3. #15688984C2semidirect
4. #15688890C2semidirect
8. #13094005C4semidirect
35. C22×Dic47C2×C4semidirect
45. C22⋊Dic47C2×C4semidirect
106. C47#1890semidirect