Finite Group Databasebeta

← #26114698

Subgroups — #26114698

Order 12032.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244350C211yesmaximal, characteristic
2#20244337C211yesmaximal, characteristic
3#20244147C211yesmaximal, characteristic
4#20243258C211yesmaximal, characteristic
5#20241272C211yesmaximal, characteristic
6#20241222C211yesmaximal, characteristic
7C2×C47×#333C211yesmaximal, characteristic
8C2×#13093958—21no—
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×#13093934—21no—
11C2×C4×C47⋊C8C2211yescharacteristic
12#15688993C2211yescharacteristic
13C4×C4⋊Dic47C2211yescharacteristic
14#15688886—21no—
15#15688885—21no—
16#15688885—21no—
17#15688885—21no—
18#15688885—21no—
19#15688877—21no—
20C2×C4⋊Q8×C47C2211yescharacteristic
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C47×#333C414yescomplemented
24C22×C47⋊C8—21no—
25C22×C47⋊C8D411yescharacteristic
26C22×C47⋊C8D411yescharacteristic
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47D411yescharacteristic
31C2×C4⋊Dic47D411yescharacteristic
32C2×C4×Dic47—21no—
33#13093958—42no—
34C4⋊(C47⋊C8)—21no—
35C4⋊(C47⋊C8)—21no—
36#13093934—42no—
37C4×C47⋊C8—21no—
38C4×C47⋊C8—21no—
39C47⋊#95—21no—
40C22×Q8×C47—21no—
41C22×C8×C47—21no—
42C22×C8×C47—21no—
43C4⋊Q8×C47—21no—
44C4⋊Q8×C47—21no—
45C4⋊Q8×C47—21no—
46C4⋊Q8×C47C2×C412yes—
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C42×C47C2311yescharacteristic
50C4⋊C8×C47—21no—
51C4⋊C8×C47—21no—
52C4⋊C8×C47C2×C412yes—
53C4⋊C8×C47C2×C412yes—
54C2×Q8×C47—22no—
55C2×Q8×C47—41no—
56C2×Q8×C47—81no—
57C2×Q8×C47—81no—
58C22×C4×C47—41no—
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47C2×D411yescharacteristic
61C22×C4×C47#4111yescharacteristic
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—41no—
65C2×C8×C47—22no—
66C2×C8×C47—22no—
67C2×C8×C47—41no—
68C2×C8×C47—41no—
69C2×C8×C47—41no—
70C2×C8×C47—41no—
71C4⋊C4×C47—22no—
72C4⋊C4×C47—22no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C42×C47C22×C411yescharacteristic
76C42×C47#4111yescharacteristic
77C42×C47#4111yescharacteristic
78C42×C47#4111yescharacteristic
79C4⋊Dic47—21no—
80C4⋊Dic47—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—41no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87C4⋊Dic47—81no—
88C4×Dic47—41no—
89C4×Dic47—41no—
90C2×C47⋊C8—21no—
91C2×C47⋊C8—21no—
92C2×C47⋊C8—21no—
93C2×C47⋊C8—21no—
94C2×C47⋊C8—21no—
95C2×C47⋊C8—41no—
96C2×C47⋊C8—41no—
97C2×C47⋊C8—41no—
98C2×C47⋊C8Q1612yes—
99C23×C47#12111yescharacteristic
100Q8×C47—82no—
101Q8×C47—82no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—42no—
105C2×C4×C47—81no—
106C2×C4×C47—81no—
107C2×C4×C47#11711yescharacteristic
108C2×C4×C47C4×D411yescharacteristic
109C2×C4×C47C4×D411yescharacteristic
110C2×C4×C47#12311yescharacteristic
111C2×C4×C47#12411yescharacteristic
112C2×C4×C47#12611yescharacteristic
113C2×C4×C47C2×Q1611yescharacteristic
114C2×C4×C47#13511yescharacteristic
115C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C47#13711yescharacteristic
118C2×C4×C47#13711yescharacteristic
119C2×C4×C47#13711yescharacteristic
120C2×C4×C47#13711yescharacteristic
121C2×Dic47—41no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—81no—
128C2×Dic47—81no—
129C2×Dic47—81no—
130C8×C47—42no—
131C8×C47—42no—
132C47⋊C8—22no—
133C47⋊C8—41no—
134C47⋊C8—81no—
135#9576—471nomaximal, Sylow
136C22×C47#38811yescharacteristic
137C22×C47#46211yescharacteristic
138C22×C47#46311yescharacteristic
139C22×C47#46811yescharacteristic
140C22×C47#47011yescharacteristic
141C22×C47#47111yescharacteristic
142C22×C47#47211yescharacteristic
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—82no—
146C4×C47C4×Q1611yescharacteristic
147C4×C47#44011yescharacteristic
148C4×C47#44011yescharacteristic
149C4×C47#44111yescharacteristic
150C4×C47#48411yescharacteristic
151C4×C47#48511yescharacteristic
152C4×C47#48911yescharacteristic
153C4×C47#49111yescharacteristic
154Dic47—81no—
155Dic47—81no—
156Dic47—161no—
157#1990—471no—
158#1987—471no—
159#1947—471no—
160#1770—471no—
161C2×#333D4711yescharacteristic
162#1296—471no—
163#1277—471no—
164C2×C47#169211yescharacteristic
165C2×C47#169611yescharacteristic
166C2×C47#169711yescharacteristic
167C2×C47#170311yescharacteristic
168C2×C47#192811yescharacteristic
169C2×C47#193111yescharacteristic
170C2×C47#193511yescharacteristic
171C2×C4⋊Q8C2×D4711yescharacteristic
172C2×#107—941no—
173C2×C4⋊C8—471no—
174C2×C4⋊C8C2×D4711yescharacteristic
175C2×C4⋊C8C2×D4711yescharacteristic
176C2×#97—941no—
177C2×C4×C8—471no—
178#384—471no—
179C4×C4⋊C4—471no—
180#340—941no—
181#340—941no—
182#340—941no—
183#340—941no—
184#340—941no—
185#336—941no—
186#333Dic4714yescomplemented
187C47#957611yescharacteristic, complemented, Sylow
188C22×Q8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—471no—
192C22×C8—471no—
193C22×C8—941no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C2×Dic4712yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C42—941no—
206C2×C42C22×D4711yescharacteristic
207#107—1882no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—941no—
211C4⋊C8—941no—
212C4⋊C8C2×Dic4712yes—
213C4⋊C8C2×Dic4712yes—
214#97—1882no—
215C4×C8—941no—
216C4×C8—941no—
217#95—941no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—41no—
223C22×C4—941no—
224C22×C4—941no—
225C22×C4—1881no—
226C22×C4#1062535011yescharacteristic
227C22×C4D4×D4711yescharacteristic
228C22×C4D4×D4711yescharacteristic
229C2×C8—22no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—472no—
236C2×C8—941no—
237C2×C8—941no—
238C2×C8—941no—
239C2×C8—941no—
240C2×C8—941no—
241C2×C8—1881no—
242C2×C8—1881no—
243C2×C8—1881no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—3761no—
253C4⋊C4—1881no—
254C4⋊C4—1881no—
255C4⋊C4—1881no—
256C4⋊C4—1881no—
257C42—1881no—
258C42—1881no—
259C42#1062535011yescharacteristic
260C42#1062535211yescharacteristic
261C42#1062535211yescharacteristic
262C42C22×Dic4711yescharacteristic
263C23#1309399711yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—3761no—
272C2×C4—3761no—
273C2×C4—3761no—
274C2×C4—1881no—
275C2×C4—1881no—
276C2×C4—1881no—
277C2×C4—1881no—
278C2×C4—1881no—
279C2×C4—1881no—
280C2×C4#1309398311yescharacteristic
281C2×C4D4×Dic4711yescharacteristic
282C2×C4D4×Dic4711yescharacteristic
283C2×C4#1309400611yescharacteristic
284C2×C4#1309401011yescharacteristic
285C2×C4#1309401711yescharacteristic
286C2×C4Q16×D4711yescharacteristic
287C2×C4#1309404711yescharacteristic
288C2×C4#1309405111yescharacteristic
289C2×C4#1309405111yescharacteristic
290C2×C4#1309405311yescharacteristic
291C2×C4#1309405311yescharacteristic
292C2×C4#1309405611yescharacteristic
293C2×C4#1309405611yescharacteristic
294C8—42no—
295C8—42no—
296C8—942no—
297C8—3761no—
298C8—1881no—
299C22#1568901611yescharacteristic
300C22#1568933211yescharacteristic
301C22#1568934111yescharacteristic
302C22#1568937211yescharacteristic
303C22#1568938011yescharacteristic
304C22#1568938511yescharacteristic
305C22#1568939211yescharacteristic
306C4—21no—
307C4—21no—
308C4—82no—
309C4—3761no—
310C4—3761no—
311C4—7521no—
312C4Q16×Dic4711yescharacteristic
313C4#1568922411yescharacteristic
314C4#1568922411yescharacteristic
315C4#1568923011yescharacteristic
316C4#1568945711yescharacteristic
317C4#1568946311yescharacteristic
318C4#1568948411yescharacteristic
319C4#1568949011yescharacteristic
320C2#2024289711yescharacteristic
321C2#2024291511yescharacteristic
322C2#2024292411yescharacteristic
323C2#2024296611yescharacteristic
324C2#2024403111yescharacteristic
325C2#2024405211yescharacteristic
326C2#2024408011yescharacteristic
subgroupG/H
centerC23#13093997
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#333C2
socle, prime radicalC23×C47#121
cosocleC2×C42×C47C23
hypercenterC2×#333D47
hypocenterC47#9576
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
23. C47×#333C4semidirect
186. #333Dic47semidirect
187. C47#9576semidirect

Maximal subgroups

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

subgroupindex
#202443502
#202443372
#202441472
#202432582
#202412722
#202412222
C2×C47×#3332
#957647