Finite Group Databasebeta

← #26109619

Subgroups — #26109619

Order 12032.

830 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 147 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
1#20243298C212yesmaximal
2#20241231C214yesmaximal, complemented
3C2×C47×#380C211yesmaximal, characteristic
4C2×C22⋊(C47⋊C8)—22no—
5C2×C22⋊(C47⋊C8)—22no—
6C2×C22⋊(C47⋊C8)C2214yes—
7C24×C4×C47C2211yescharacteristic
8C22×C4⋊C4×C47C412yes—
9C22×C22⋊C4×C47C412yes—
10C47×#380—22no—
11C47×#380—22no—
12C2×#95×C47C2212yes—
13C22×C47⋊C8—24no—
14C22⋊(C47⋊C8)—28no—
15C22⋊(C47⋊C8)—44no—
16C22⋊(C47⋊C8)—44no—
17C25×C47C2×C411yescharacteristic
18C23×C4×C47—24no—
19C23×C4×C47—44no—
20C23×C4×C47C2×C411yescharacteristic
21C23×C4×C47C2×C414yes—
22C23×C4×C47D412yes—
23C23×C4×C47D412yes—
24C23×C4×C47C2311yescharacteristic
25C2×C4⋊C4×C47—22no—
26C2×C4⋊C4×C47—22no—
27C2×C4⋊C4×C47—44no—
28C2×C22⋊C4×C47—22no—
29C2×C22⋊C4×C47—22no—
30C2×C22⋊C4×C47—44no—
31#95×C47—24no—
32C24×C47—22no—
33C24×C47—22no—
34C24×C47—22no—
35C24×C47—24no—
36C24×C47—42no—
37C24×C47C22⋊C411yescharacteristic
38C24×C47C22⋊C411yescharacteristic
39C24×C47C22×C411yescharacteristic
40C22×C4×C47—22no—
41C22×C4×C47—24no—
42C22×C4×C47—24no—
43C22×C4×C47—24no—
44C22×C4×C47—24no—
45C22×C4×C47—24no—
46C22×C4×C47—24no—
47C22×C4×C47—28no—
48C22×C4×C47—42no—
49C22×C4×C47—42no—
50C22×C4×C47—42no—
51C22×C4×C47—416no—
52C22×C4×C47—44no—
53C22×C4×C47—44no—
54C22×C4×C47C22⋊C412yes—
55C22×C4×C47C2×D412yes—
56C22×C4×C47#4114yes—
57C4⋊C4×C47—44no—
58C4⋊C4×C47—44no—
59C22⋊C4×C47—44no—
60C22⋊C4×C47—44no—
61C2×C47⋊C8—44no—
62C2×C47⋊C8—44no—
63C2×C47⋊C8—44no—
64C23×C47—22no—
65C23×C47—21no—
66C23×C47—21no—
67C23×C47—28no—
68C23×C47—21no—
69C23×C47—21no—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47—21no—
75C23×C47—21no—
76C23×C47—48no—
77C23×C47—48no—
78C23×C47—44no—
79C23×C47—44no—
80C23×C47#10012yes—
81C23×C47#10112yes—
82C23×C47C2×C22⋊C411yescharacteristic
83C23×C47#11712yes—
84C23×C47#13114yes—
85C2×C4×C47—28no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—44no—
91C2×C4×C47—48no—
92C2×C4×C47—48no—
93C2×C4×C47—44no—
94C2×C4×C47—44no—
95C2×C4×C47—44no—
96C2×C4×C47—88no—
97C2×C4×C47#9914yes—
98C2×C4×C47#12314yes—
99C47⋊C8—84no—
100#8704—471nomaximal, Sylow
101C22×C47—22no—
102C22×C47—22no—
103C22×C47—24no—
104C22×C47—24no—
105C22×C47—22no—
106C22×C47—22no—
107C22×C47—24no—
108C22×C47—24no—
109C22×C47—416no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47—41no—
113C22×C47—41no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47#38111yescharacteristic
117C22×C47#40812yes—
118C22×C47C2×#9912yes—
119C22×C47C2×#10011yescharacteristic
120C22×C47C2×#10111yescharacteristic
121C22×C47#43314yes—
122C4×C47—24no—
123C4×C47—24no—
124C4×C47—84no—
125C2×#380D4711yescharacteristic
126#1779—472no—
127#1280—474no—
128C2×C47—24no—
129C2×C47—42no—
130C2×C47—42no—
131C2×C47#147112yes—
132C2×C47#147212yes—
133C2×C47#181811yescharacteristic
134C2×C47#181911yescharacteristic
135C2×C47#182111yescharacteristic
136C24×C4C2×D4711yescharacteristic
137C22×C4⋊C4Dic4712yes—
138C22×C22⋊C4Dic4712yes—
139C2×C22⋊C8—474no—
140C2×C22⋊C8—942no—
141C2×C22⋊C8—942no—
142#380—22no—
143#380—22no—
144C2×#95C2×D4712yes—
145C47#870411yescharacteristic, complemented, Sylow
146C25C2×Dic4711yescharacteristic
147C23×C4—24no—
148C23×C4—44no—
149C23×C4C2×Dic4711yescharacteristic
150C23×C4C2×Dic4714yes—
151C23×C4C22⋊D4712yes—
152C23×C4C22⋊D4712yes—
153C23×C4C22×D4711yescharacteristic
154C22×C8—944no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—44no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—44no—
161C22⋊C8—948no—
162C22⋊C8—1884no—
163C22⋊C8—1884no—
164#95—24no—
165C24—22no—
166C24—22no—
167C24—22no—
168C24—24no—
169C24—42no—
170C24C22⋊Dic4711yescharacteristic
171C24C22⋊Dic4711yescharacteristic
172C24C22×Dic4711yescharacteristic
173C22×C4—22no—
174C22×C4—24no—
175C22×C4—24no—
176C22×C4—24no—
177C22×C4—24no—
178C22×C4—24no—
179C22×C4—24no—
180C22×C4—28no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—416no—
185C22×C4—44no—
186C22×C4—44no—
187C22×C4C22⋊Dic4712yes—
188C22×C4#1062535014yes—
189C22×C4C2×C22⋊D4712yes—
190C2×C8—1884no—
191C2×C8—1884no—
192C2×C8—1884no—
193C4⋊C4—44no—
194C4⋊C4—44no—
195C22⋊C4—44no—
196C22⋊C4—44no—
197C23—22no—
198C23—21no—
199C23—21no—
200C23—28no—
201C23—21no—
202C23—21no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—21no—
208C23—21no—
209C23—48no—
210C23—48no—
211C23—44no—
212C23—44no—
213C23#1309394112yes—
214C23#1309394312yes—
215C23C2×C22⋊Dic4711yescharacteristic
216C23#1309398312yes—
217C23#1309403114yes—
218C2×C4—28no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—44no—
224C2×C4—48no—
225C2×C4—48no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—44no—
229C2×C4—88no—
230C2×C4#1309393914yes—
231C2×C4#1309400714yes—
232C8—3764no—
233C22—22no—
234C22—22no—
235C22—24no—
236C22—24no—
237C22—22no—
238C22—22no—
239C22—24no—
240C22—24no—
241C22—416no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—42no—
247C22—42no—
248C22#1568898611yescharacteristic
249C22#1568909012yes—
250C22C2×#1309393912yes—
251C22C2×#1309394111yescharacteristic
252C22C2×#1309394311yescharacteristic
253C22#1568918414yes—
254C4—24no—
255C4—24no—
256C4—84no—
257C2—24no—
258C2—42no—
259C2—42no—
260C2#2024174812yes—
261C2#2024175212yes—
262C2#2024345911yescharacteristic
263C2#2024346211yescharacteristic
264C2#2024346811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#380C2
socleC23×C47C2×C22⋊C4
prime radicalC25×C47C2×C4
cosocleC23×C4×C47C23
hypercenterC2×#380D47
hypocenterC47#8704
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #20241231C2semidirect
145. C47#8704semidirect

Maximal subgroups

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

subgroupindex
#202432982
#202412312
C2×C47×#3802
#870447