Finite Group Databasebeta

← #26192585

Subgroups — #26192585

Order 12032.

982 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 179 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#20253768C211yesmaximal, characteristic, complemented
2#20253487C212yesmaximal, complemented
3#20242616C218yesmaximal, complemented
4#20242114C211yesmaximal, characteristic, complemented
5#20241831C212yesmaximal, complemented
6C2×C47×#555C211yesmaximal, characteristic
7#15689680C2211yescharacteristic
8#15689491—22no—
9#15689473C2214yescomplemented
10#15689458—22no—
11#15689403C2214yescomplemented
12#15689328C2214yescomplemented
13#15689274—22no—
14#15689223—24no—
15#15689180C2212yes—
16#15689132—22no—
17C4×#10625329C2211yescharacteristic
18#15688872C2214yescomplemented
19D4⋊(C47⋊C8)C2218yescomplemented
20C47×#555—22no—
21C47×#555—24no—
22C47×#555C2214yes—
23C2×C4⋊Q8×C47C2211yescharacteristic
24C2×#124×C47—22no—
25C2×#121×C47—22no—
26C2×C4×D4×C47C2212yes—
27C2×#117×C47—22no—
28C2×#10625335—24no—
29C2×#10625329—21no—
30#13094024C2312yes—
31#13094016—21no—
32#13094003—22no—
33C4×Dic94—22no—
34#13093983—21no—
35#13093957—24no—
36C4⋊(C47⋊C8)C2314yes—
37#13093948—28no—
38#13093947—24no—
39#13093945—24no—
40C22⋊(C47⋊C8)—22no—
41#13093935—22no—
42#13093935—21no—
43C4×C47⋊C8C2312yes—
44C22×Q8×C47D412yes—
45C22×D4×C47—22no—
46C22×D4×C47D412yes—
47C23×C4×C47—22no—
48C4⋊Q8×C47—22no—
49C4⋊Q8×C47D412yes—
50C4⋊Q8×C47C2312yes—
51#124×C47—28no—
52#124×C47—28no—
53#121×C47—28no—
54#121×C47—28no—
55C4×D4×C47—22no—
56C4×D4×C47—22no—
57C4×D4×C47D414yes—
58C4×D4×C47C2314yes—
59#117×C47—28no—
60#117×C47—28no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47D412yes—
63C2×C22⋊C4×C47—24no—
64C2×C22⋊C4×C47—22no—
65C2×C42×C47—22no—
66C2×C42×C47C2311yescharacteristic
67C24×C47—22no—
68C2×Q8×C47—22no—
69C2×Q8×C47—44no—
70C2×Q8×C47C2×D414yes—
71C2×D4×C47—28no—
72C2×D4×C47—22no—
73C2×D4×C47—44no—
74C2×D4×C47—84no—
75C2×D4×C47C2×D414yes—
76C22×C4×C47—22no—
77C22×C4×C47—22no—
78C22×C4×C47—24no—
79C22×C4×C47—24no—
80C22×C4×C47—48no—
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47C2×D412yes—
83C2×Dic94—22no—
84C4⋊C4×C47—24no—
85C4⋊C4×C47—22no—
86C4⋊C4×C47—24no—
87C4⋊C4×C47C2×D414yes—
88C22⋊C4×C47—216no—
89C22⋊C4×C47—24no—
90C22⋊C4×C47—24no—
91C42×C47—28no—
92C42×C47C2×D411yescharacteristic
93C42×C47C2×D412yes—
94C42×C47C2411yescharacteristic
95C22⋊Dic47—41no—
96#10625335—48no—
97C4⋊Dic47—22no—
98C4⋊Dic47—22no—
99Dic47⋊C4—42no—
100C4×Dic47—41no—
101#10625329—42no—
102C2×C47⋊C8—22no—
103C2×C47⋊C8—24no—
104C23×C47—24no—
105C23×C47—44no—
106C23×C47—44no—
107C23×C47—44no—
108C23×C47#12011yescharacteristic
109Q8×C47—44no—
110Q8×C47—82no—
111D4×C47—24no—
112D4×C47—24no—
113D4×C47—44no—
114D4×C47—88no—
115C2×C4×C47—22no—
116C2×C4×C47—24no—
117C2×C4×C47—24no—
118C2×C4×C47—24no—
119C2×C4×C47—48no—
120C2×C4×C47—44no—
121C2×C4×C47—44no—
122C2×C4×C47—48no—
123C2×C4×C47#12011yescharacteristic
124C2×C4×C47#12012yes—
125C2×C4×C47C22×D411yescharacteristic
126C2×C4×C47C22×D412yes—
127C2×Dic47—42no—
128Dic94—44no—
129C47⋊C8—42no—
130C47⋊C8—44no—
131#18552—471nomaximal, Sylow
132C22×C47—22no—
133C22×C47—44no—
134C22×C47—44no—
135C22×C47—44no—
136C22×C47—88no—
137C22×C47#45512yes—
138C22×C47C2×#12011yescharacteristic
139C4×C47—22no—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—44no—
143C4×C47—44no—
144C4×C47#57514yes—
145Dic47—82no—
146C2×#555D4711yescharacteristic
147#3139—471no—
148#3110—472no—
149#1646—478no—
150#1558—471no—
151#1490—472no—
152C2×C47—22no—
153C2×C47—84no—
154C2×C47#300512yes—
155C2×C47C2×#45511yescharacteristic
156#555—22no—
157#555—24no—
158#555C2×D4714yes—
159#533—471no—
160C2×C4⋊Q8C2×D4711yescharacteristic
161C2×#124—22no—
162C2×#121—22no—
163C2×C4×D4C2×D4712yes—
164C2×#117—22no—
165#491—942no—
166#487—474no—
167#484—942no—
168#474—474no—
169#461—474no—
170#450—942no—
171#440—944no—
172#432—472no—
173#419—942no—
174C4×M16—471no—
175#333—474no—
176D4⋊C8—478no—
177C47#1855211yescharacteristic, complemented, Sylow
178C22×Q8C22⋊D4712yes—
179C22×D4—22no—
180C22×D4C22⋊D4712yes—
181C23×C4—22no—
182C2×SD16—944no—
183C2×M16—941no—
184C4⋊Q8—22no—
185C4⋊Q8—472no—
186C4⋊Q8C22⋊D4712yes—
187C4⋊Q8C22×D4712yes—
188#125—941no—
189#124—28no—
190#124—28no—
191C22⋊Q8—942no—
192#121—28no—
193#121—28no—
194C4×Q8—942no—
195C4×D4—22no—
196C4×D4—22no—
197C4×D4C22⋊D4714yes—
198C4×D4C22×D4714yes—
199#117—28no—
200#117—28no—
201#117—941no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4C22⋊D4712yes—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—22no—
206C2×C42—22no—
207C2×C42C22×D4711yescharacteristic
208#107—944no—
209C4⋊C8—474no—
210#103—948no—
211#103—944no—
212#102—944no—
213C22⋊C8—942no—
214#97—941no—
215#97—942no—
216C4×C8—472no—
217C24—22no—
218C2×Q8—22no—
219C2×Q8—44no—
220C2×Q8—942no—
221C2×Q8C2×C22⋊D4714yes—
222C2×D4—28no—
223C2×D4—22no—
224C2×D4—44no—
225C2×D4—84no—
226C2×D4C2×C22⋊D4714yes—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—48no—
232C22×C4C2×C22⋊D4712yes—
233C22×C4C2×C22⋊D4711yescharacteristic
234SD16—1888no—
235M16—1882no—
236C2×C8—942no—
237C2×C8—944no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—24no—
241C4⋊C4—942no—
242C4⋊C4—942no—
243C4⋊C4—1882no—
244C4⋊C4C2×C22⋊D4714yes—
245C22⋊C4—216no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C22⋊C4—1881no—
249C42—28no—
250C42—1881no—
251C42C2×C22⋊D4711yescharacteristic
252C42C2×C22⋊D4712yes—
253C42C23×D4711yescharacteristic
254C23—24no—
255C23—44no—
256C23—44no—
257C23—44no—
258C23#1309399311yescharacteristic
259Q8—44no—
260Q8—82no—
261Q8—1884no—
262D4—24no—
263D4—24no—
264D4—44no—
265D4—88no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—48no—
274C2×C4—1882no—
275C2×C4#1309399311yescharacteristic
276C2×C4#1309399312yes—
277C2×C4C22×C22⋊D4711yescharacteristic
278C2×C4C22×C22⋊D4712yes—
279C8—1882no—
280C8—1884no—
281C22—22no—
282C22—44no—
283C22—44no—
284C22—44no—
285C22—88no—
286C22#1568930112yes—
287C22C2×#1309399311yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—44no—
292C4—44no—
293C4—3762no—
294C4#1568992114yes—
295C2—22no—
296C2—84no—
297C2#2025263012yes—
298C2C2×#1568930111yescharacteristic
subgroupG/H
centerC22C2×#13093993
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
Fitting, prime radicalC2×C47×#555C2
socleC22×C47C2×#120
hypercenterC2×#555D47
hypocenterC47#18552
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #20253768C2semidirect
2. #20253487C2semidirect
3. #20242616C2semidirect
4. #20242114C2semidirect
5. #20241831C2semidirect
9. #15689473C22semidirect
11. #15689403C22semidirect
12. #15689328C22semidirect
18. #15688872C22semidirect
19. D4⋊(C47⋊C8)C22semidirect
177. C47#18552semidirect

Maximal subgroups

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

subgroupindex
#202537682
#202534872
#202426162
#202421142
#202418312
C2×C47×#5552
#1855247