Finite Group Databasebeta

← #26113738

Subgroups — #26113738

Order 12032.

526 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 103 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#20248768C211yesmaximal, characteristic
2#20241907C212yesmaximal
3#20241718C211yesmaximal, characteristic
4#20241274C212yesmaximal
5C47×#2313C211yesmaximal, characteristic
6C2×#13094003C2211yescharacteristic
7#15689087C2212yes—
8#15689053C412yescomplemented
9#15689043C412yescomplemented
10#15689018—22no—
11#15688996—21no—
12#15688996—21no—
13C4×C22⋊Dic47C2211yescharacteristic
14#15688859—24no—
15#15688849—22no—
16C22×C4⋊C4×C47C2211yescharacteristic
17C47×#387—24no—
18C47×#381—21no—
19C47×#380—21no—
20C4×C22⋊C4×C47C2212yes—
21C22×Dic94C2×C411yescharacteristic
22C2×#10625329—22no—
23#13094003—22no—
24#13094003—22no—
25C2×C4⋊Dic47C2×C411yescharacteristic
26C2×Dic47⋊C4—22no—
27C2×Dic47⋊C4—21no—
28C2×Dic47⋊C4—22no—
29C2×C22⋊Dic47—21no—
30C2×C22⋊Dic47—21no—
31C2×C4×Dic47—21no—
32C22⋊(C47⋊C8)—22no—
33C22⋊(C47⋊C8)—22no—
34C47⋊#95—22no—
35C47⋊#95—22no—
36C47⋊#95C2×C412yes—
37C23×C4×C47D411yescharacteristic
38C23×C4×C47D411yescharacteristic
39C23×C4×C47C2311yescharacteristic
40C2×C4⋊C4×C47—22no—
41C2×C4⋊C4×C47—22no—
42C2×C4⋊C4×C47—22no—
43C2×C4⋊C4×C47C2×C412yes—
44C2×C4⋊C4×C47D412yes—
45C2×C22⋊C4×C47—22no—
46C2×C42×C47—22no—
47#95×C47—22no—
48#95×C47—24no—
49#95×C47D414yes—
50C24×C47C2×D411yescharacteristic
51C22×C4×C47—21no—
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47—24no—
56C22×C4×C47—42no—
57C22×C4×C47—81no—
58C22×C4×C47—81no—
59C22×C4×C47C22⋊C412yes—
60C22×C4×C47C22⋊C412yes—
61C22×C4×C47C22×C411yescharacteristic
62C22×C4×C47C2×D412yes—
63C22×C4×C47C2×D411yescharacteristic
64C22×C4×C47#4112yes—
65C22×Dic47—22no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C2×Dic94—22no—
69C2×Dic94—81no—
70C4⋊C4×C47—24no—
71C4⋊C4×C47—24no—
72C4⋊C4×C47—82no—
73C22⋊C4×C47—44no—
74C42×C47—82no—
75C22⋊Dic47—24no—
76C22⋊Dic47—41no—
77C22⋊Dic47—41no—
78C4⋊Dic47—22no—
79Dic47⋊C4—44no—
80Dic47⋊C4—42no—
81Dic47⋊C4—82no—
82C4×Dic47—81no—
83#10625329—82no—
84C2×C47⋊C8—42no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—41no—
88C23×C47C2×C22⋊C411yescharacteristic
89C23×C47#12011yescharacteristic
90C23×C47#12311yescharacteristic
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—42no—
96C2×C4×C47—41no—
97C2×C4×C47—42no—
98C2×C4×C47—41no—
99C2×C4×C47—42no—
100C2×C4×C47—42no—
101C2×C4×C47—42no—
102C2×C4×C47—42no—
103C2×C4×C47—44no—
104C2×C4×C47—44no—
105C2×C4×C47—44no—
106C2×C4×C47—81no—
107C2×C4×C47C4×D412yes—
108C2×C4×C47#12112yes—
109C2×Dic47—24no—
110C2×Dic47—42no—
111C2×Dic47—42no—
112C2×Dic47—42no—
113C2×Dic47—41no—
114C2×Dic47—41no—
115C2×Dic47—42no—
116Dic94—82no—
117C47⋊C8—82no—
118#9412—471nomaximal, Sylow
119C22×C47—21no—
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—44no—
127C22×C47#38611yescharacteristic
128C22×C47#42112yes—
129C22×C47#45612yes—
130C4×C47—22no—
131C4×C47—22no—
132C4×C47—42no—
133C4×C47—42no—
134C4×C47—84no—
135Dic47—44no—
136Dic47—81no—
137Dic47—81no—
138#2583—471no—
139#2313D4711yescharacteristic
140#1508—472no—
141#1463—471no—
142#1297—472no—
143C2×C47—22no—
144C2×C47—22no—
145C2×C47—41no—
146C2×C47#188611yescharacteristic
147C2×C47#189711yescharacteristic
148C2×C47#191311yescharacteristic
149C2×C22⋊Q8—471no—
150C22×C4⋊C4C2×D4711yescharacteristic
151#407—472no—
152#398—472no—
153#395—472no—
154#389—942no—
155#387—24no—
156#385—941no—
157#385—941no—
158#381—21no—
159#380—21no—
160C4×C22⋊C4—471no—
161C4×C22⋊C4C2×D4712yes—
162#328—944no—
163#324—942no—
164C47#941211yescharacteristic, complemented, Sylow
165C22×Q8—471no—
166C23×C4C22⋊D4711yescharacteristic
167C23×C4C22⋊D4711yescharacteristic
168C23×C4C22×D4711yescharacteristic
169C2×M16—942no—
170C22⋊Q8—942no—
171C22⋊Q8—942no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—471no—
176C2×C4⋊C4—942no—
177C2×C4⋊C4—942no—
178C2×C4⋊C4—941no—
179C2×C4⋊C4C4×D4712yes—
180C2×C4⋊C4D18812yes—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—941no—
183C2×C22⋊C4—941no—
184C2×C42—22no—
185C2×C42—941no—
186C22⋊C8—942no—
187C22⋊C8—942no—
188#95—22no—
189#95—24no—
190#95—472no—
191#95—942no—
192#95—942no—
193#95C22⋊D4714yes—
194C24C2×C22⋊D4711yescharacteristic
195C2×Q8—942no—
196C2×Q8—3761no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—24no—
202C22×C4—42no—
203C22×C4—81no—
204C22×C4—81no—
205C22×C4—942no—
206C22×C4—941no—
207C22×C4—941no—
208C22×C4(C2×D47)⋊C412yes—
209C22×C4(C2×D47)⋊C412yes—
210C22×C4C2×C4×D4711yescharacteristic
211C22×C4C2×D18811yescharacteristic
212C22×C4#1062535012yes—
213C22×C4C2×C22⋊D4712yes—
214M16—3762no—
215C2×C8—1882no—
216C4⋊C4—24no—
217C4⋊C4—24no—
218C4⋊C4—82no—
219C4⋊C4—942no—
220C4⋊C4—3762no—
221C4⋊C4—1884no—
222C4⋊C4—1882no—
223C22⋊C4—44no—
224C22⋊C4—944no—
225C22⋊C4—1881no—
226C22⋊C4—1881no—
227C42—82no—
228C42—3761no—
229C23—22no—
230C23—22no—
231C23—41no—
232C23C2×(C2×D47)⋊C411yescharacteristic
233C23#1309399311yescharacteristic
234C23#1309400711yescharacteristic
235Q8—3762no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—44no—
249C2×C4—44no—
250C2×C4—44no—
251C2×C4—81no—
252C2×C4—944no—
253C2×C4—1882no—
254C2×C4—1881no—
255C2×C4—1881no—
256C2×C4—1882no—
257C2×C4—1882no—
258C2×C4—1882no—
259C2×C4C4×C22⋊D4712yes—
260C2×C4#1309399812yes—
261C8—3762no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22#1568900211yescharacteristic
271C22#1568914112yes—
272C22#1568930612yes—
273C4—22no—
274C4—22no—
275C4—42no—
276C4—42no—
277C4—84no—
278C4—3761no—
279C4—3761no—
280C4—1884no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2#2024378111yescharacteristic
285C2#2024383611yescharacteristic
286C2#2024393011yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2313C2
socleC22×C47#386
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenter#2313D47
hypocenterC47#9412
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
8. #15689053C4semidirect
9. #15689043C4semidirect
164. C47#9412semidirect

Maximal subgroups

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

subgroupindex
#202487682
#202419072
#202417182
#202412742
C47×#23132
#941247