Finite Group Databasebeta

← #26124141

Subgroups — #26124141

Order 12032.

1134 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 219 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×#15688986C212yesmaximal
2C2×#15688890C214yesmaximal
3C2×C47×#381C211yesmaximal, characteristic
4C22×C22⋊Dic47C2214yes—
5#15688986—28no—
6C2×C47⋊#95—24no—
7#15688890—28no—
8C24×C4×C47C2211yescharacteristic
9C22×C22⋊C4×C47C2212yes—
10C47×#381—24no—
11C2×#95×C47C414yescomplemented
12C23×Dic47—24no—
13C2×C22⋊Dic47—24no—
14C2×C22⋊Dic47—24no—
15C2×C22⋊Dic47—24no—
16C2×C22⋊Dic47—24no—
17C2×C22⋊Dic47—24no—
18C2×C22⋊Dic47D418yes—
19C47⋊#95—216no—
20C25×C47C2311yescharacteristic
21C23×C4×C47—24no—
22C23×C4×C47—24no—
23C23×C4×C47—24no—
24C23×C4×C47C2×C412yes—
25C23×C4×C47C2×C414yes—
26C23×C4×C47D414yes—
27C2×C22⋊C4×C47—24no—
28C2×C22⋊C4×C47—22no—
29C2×C22⋊C4×C47—22no—
30C2×C22⋊C4×C47—24no—
31#95×C47—28no—
32C24×C47—44no—
33C24×C47C22×C411yescharacteristic
34C24×C47C2×D412yes—
35C24×C47C2×D414yes—
36C24×C47#4114yes—
37C24×C47#4114yes—
38C22×C4×C47—24no—
39C22×C4×C47—28no—
40C22×C4×C47—24no—
41C22×C4×C47—28no—
42C22×C4×C47—28no—
43C22×C4×C47—24no—
44C22×C4×C47—24no—
45C22×C4×C47—28no—
46C22×C4×C47—44no—
47C22×C4×C47—44no—
48C22×C4×C47—44no—
49C22×C4×C47—44no—
50C22×C4×C47—48no—
51C22×C4×C47C22⋊C414yes—
52C22×Dic47—28no—
53C22×Dic47—416no—
54C22×Dic47—44no—
55C22×Dic47—44no—
56C22⋊C4×C47—42no—
57C22⋊C4×C47—44no—
58C22⋊C4×C47—42no—
59C22⋊Dic47—28no—
60C22⋊Dic47—28no—
61C22⋊Dic47—44no—
62C22⋊Dic47—44no—
63C23×C47—28no—
64C23×C47—24no—
65C23×C47—48no—
66C23×C47—48no—
67C23×C47—48no—
68C23×C47C2×C22⋊C411yescharacteristic
69C23×C47#11712yes—
70C23×C47C4×D414yes—
71C23×C47#12012yes—
72C23×C47#12114yes—
73C23×C47#12114yes—
74C23×C47#12312yes—
75C23×C47#12314yes—
76C23×C47#12314yes—
77C23×C47#12414yes—
78C23×C47#12614yes—
79C2×C4×C47—24no—
80C2×C4×C47—28no—
81C2×C4×C47—48no—
82C2×C4×C47—48no—
83C2×C4×C47—48no—
84C2×C4×C47—44no—
85C2×C4×C47—48no—
86C2×C4×C47—88no—
87C2×Dic47—416no—
88C2×Dic47—48no—
89C2×Dic47—88no—
90C2×Dic47—88no—
91#11197—471nomaximal, Sylow
92C22×C47—28no—
93C22×C47—24no—
94C22×C47—24no—
95C22×C47—28no—
96C22×C47—28no—
97C22×C47—24no—
98C22×C47—44no—
99C22×C47—44no—
100C22×C47—44no—
101C22×C47—44no—
102C22×C47#38111yescharacteristic
103C22×C47#38612yes—
104C22×C47#38814yes—
105C22×C47#39414yes—
106C22×C47#39714yes—
107C22×C47#41014yes—
108C4×C47—44no—
109C4×C47—84no—
110Dic47—88no—
111C2×#381—472no—
112C2×#381D4711yescharacteristic
113C2×#342—474no—
114C2×C47—24no—
115C2×C47—24no—
116C2×C47—24no—
117C2×C47#144011yescharacteristic
118C2×C47#182012yes—
119C2×C47#189914yes—
120C24×C4C2×D4711yescharacteristic
121C22×C22⋊C4—474no—
122C22×C22⋊C4C2×D4712yes—
123#381—24no—
124#381—948no—
125C2×#95—944no—
126C2×#95Dic4714yescomplemented
127#342—948no—
128C47#1119711yescharacteristic, complemented, Sylow
129C25C22×D4711yescharacteristic
130C23×C4—24no—
131C23×C4—24no—
132C23×C4—24no—
133C23×C4—944no—
134C23×C4C2×Dic4712yes—
135C23×C4C2×Dic4714yes—
136C23×C4C22⋊D4714yes—
137C2×C22⋊C4—24no—
138C2×C22⋊C4—24no—
139C2×C22⋊C4—22no—
140C2×C22⋊C4—22no—
141C2×C22⋊C4—478no—
142C2×C22⋊C4—944no—
143C2×C22⋊C4—944no—
144C2×C22⋊C4—944no—
145C2×C22⋊C4—944no—
146C2×C22⋊C4—944no—
147#95—28no—
148#95—9416no—
149C24—44no—
150C24#1062535014yes—
151C24D4×D4714yes—
152C24#1062535214yes—
153C24C22×Dic4711yescharacteristic
154C24C2×C22⋊D4712yes—
155C22×C4—24no—
156C22×C4—28no—
157C22×C4—24no—
158C22×C4—28no—
159C22×C4—24no—
160C22×C4—28no—
161C22×C4—24no—
162C22×C4—28no—
163C22×C4—44no—
164C22×C4—44no—
165C22×C4—44no—
166C22×C4—44no—
167C22×C4—48no—
168C22×C4—948no—
169C22×C4—18816no—
170C22×C4—1884no—
171C22×C4—1884no—
172C22×C4C22⋊Dic4714yes—
173C22⋊C4—42no—
174C22⋊C4—44no—
175C22⋊C4—42no—
176C22⋊C4—948no—
177C22⋊C4—948no—
178C22⋊C4—1884no—
179C22⋊C4—1884no—
180C23—24no—
181C23—28no—
182C23—48no—
183C23—48no—
184C23—48no—
185C23C2×C22⋊Dic4711yescharacteristic
186C23#1309398312yes—
187C23D4×Dic4714yes—
188C23#1309399212yes—
189C23#1309399614yes—
190C23#1309399714yes—
191C23#1309400512yes—
192C23#1309400614yes—
193C23#1309400714yes—
194C23#1309401014yes—
195C23#1309401714yes—
196C2×C4—24no—
197C2×C4—28no—
198C2×C4—48no—
199C2×C4—48no—
200C2×C4—48no—
201C2×C4—44no—
202C2×C4—48no—
203C2×C4—88no—
204C2×C4—3768no—
205C2×C4—3768no—
206C2×C4—18816no—
207C2×C4—1888no—
208C22—28no—
209C22—24no—
210C22—28no—
211C22—28no—
212C22—24no—
213C22—24no—
214C22—44no—
215C22—44no—
216C22—44no—
217C22—44no—
218C22#1568898611yescharacteristic
219C22#1568900312yes—
220C22#1568901614yes—
221C22#1568903814yes—
222C22#1568905114yes—
223C22#1568909714yes—
224C4—44no—
225C4—84no—
226C4—3768no—
227C2—24no—
228C2—24no—
229C2—24no—
230C2#2024163711yescharacteristic
231C2#2024346512yes—
232C2#2024384714yes—
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC24×C47C22×C4
FrattiniC25C22×D47
FittingC2×C47×#381C2
socleC23×C47C2×C22⋊C4
prime radical, cosocleC25×C47C23
hypercenterC2×#381D47
hypocenterC47#11197
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
11. C2×#95×C47C4semidirect
126. C2×#95Dic47semidirect
128. C47#11197semidirect

Maximal subgroups

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

subgroupindex
C2×#156889862
C2×#156888902
C2×C47×#3812
#1119747