Finite Group Databasebeta

← #26316595

Subgroups — #26316595

Order 12032.

642 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251749C211yesmaximal, characteristic
2#125×Dic47C211yesmaximal, characteristic
3#20244892C212yesmaximal
4#20244885C212yesmaximal
5#20244358C211yesmaximal, characteristic
6#20243969C212yesmaximal
7#20243962C212yesmaximal
8#20243554C211yesmaximal, characteristic
9#20243522C211yesmaximal, characteristic
10#20243242C211yesmaximal, characteristic
11C47×#1992C211yesmaximal, characteristic
12C2×#13094015—21no—
13C2×#13093957C2212yes—
14C2×#13093955C2212yes—
15C2×Dic47⋊C8C2212yes—
16C2×#13093935C2211yescharacteristic
17#15689022—21no—
18#15689022C2212yes—
19#15689022C2211yescharacteristic
20#15689022C2211yescharacteristic
21#15689019—21no—
22#15689019C2212yes—
23#15689009—21no—
24#15689009—21no—
25#15688993C2211yescharacteristic
26#15688989C2211yescharacteristic
27#15688988—21no—
28C4⋊C4×Dic47—21no—
29C4⋊C4×Dic47—21no—
30C4⋊C4×Dic47C2211yescharacteristic
31C4⋊C4×Dic47C2211yescharacteristic
32C42×Dic47C2211yescharacteristic
33#15688886C2212yes—
34#15688886C2212yes—
35#15688885C2212yes—
36#15688885C2212yes—
37#15688877C2212yes—
38C2×#125×C47C2211yescharacteristic
39C2×#97×C47C2211yescharacteristic
40C47×#384C2211yescharacteristic
41C47×#340C2212yes—
42C47×#340C2212yes—
43C22×C47⋊C8C2312yes—
44#13094015—44no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—21no—
48C2×C4⋊Dic47—21no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47C2311yescharacteristic
51C2×C4⋊Dic47C2311yescharacteristic
52C2×C4⋊Dic47C2312yes—
53C2×Dic47⋊C4—22no—
54C2×C4×Dic47—21no—
55C2×C4×Dic47—21no—
56C2×C4×Dic47D411yescharacteristic
57C2×C4×Dic47D411yescharacteristic
58C2×C4×Dic47D411yescharacteristic
59C2×C4×Dic47D411yescharacteristic
60C2×C4×Dic47C2311yescharacteristic
61C2×C4×Dic47C2311yescharacteristic
62#13093957—24no—
63#13093955—24no—
64Dic47⋊C8—24no—
65#13093935—22no—
66C47⋊#95—21no—
67C47⋊#95—21no—
68C47⋊#95—21no—
69C47⋊#95—21no—
70C47⋊#95—21no—
71C47⋊#95—21no—
72C47⋊#95—22no—
73C47⋊#95—22no—
74C22×C8×C47C2312yes—
75#125×C47—22no—
76#125×C47Q814yes—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47C2312yes—
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C4⋊C4×C47C2311yescharacteristic
84C2×C42×C47C2311yescharacteristic
85#97×C47—22no—
86C22×C4×C47—21no—
87C22×C4×C47—21no—
88C22×C4×C47—22no—
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47C2411yescharacteristic
92C22×Dic47—21no—
93C22×Dic47—21no—
94C22×Dic47—22no—
95C22×Dic47C2×D411yescharacteristic
96C22×Dic47C2×D411yescharacteristic
97C22×Dic47C2×D411yescharacteristic
98C22×Dic47C2×D411yescharacteristic
99C2×C8×C47—22no—
100C2×C8×C47—22no—
101C2×C8×C47—22no—
102C4⋊C4×C47—24no—
103C4⋊C4×C47—24no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—21no—
106C4⋊C4×C47—22no—
107C4⋊C4×C47—22no—
108C4⋊C4×C47—42no—
109C4⋊C4×C47—42no—
110C4⋊C4×C47C2×Q812yes—
111C4⋊C4×C47C2×Q812yes—
112C42×C47C2×Q812yes—
113C42×C47#4112yes—
114C4⋊Dic47—22no—
115C4⋊Dic47—22no—
116C4⋊Dic47—24no—
117C4⋊Dic47—42no—
118C4⋊Dic47—42no—
119C4⋊Dic47—42no—
120C4⋊Dic47—44no—
121C4⋊Dic47—42no—
122Dic47⋊C4—44no—
123C4×Dic47—22no—
124C4×Dic47—22no—
125C4×Dic47—22no—
126C4×Dic47—22no—
127C4×Dic47—41no—
128C4×Dic47—41no—
129C4×Dic47—42no—
130C4×Dic47—42no—
131C2×C47⋊C8—22no—
132C2×C47⋊C8—22no—
133C2×C47⋊C8#4114yes—
134C23×C47C22×D411yescharacteristic
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—22no—
140C2×C4×C47—22no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47—42no—
148C2×C4×C47C22⋊Q812yes—
149C2×C4×C47C22⋊Q812yes—
150C2×C4×C47C22×Q811yescharacteristic
151C2×C4×C47C2×#4112yes—
152C2×C4×C47C2×#4111yescharacteristic
153C2×C4×C472−1+412yes—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—41no—
165C2×Dic47—41no—
166C2×Dic47—42no—
167C2×Dic47—41no—
168C2×Dic47—42no—
169C2×Dic47—41no—
170C2×Dic47—41no—
171C2×Dic47—41no—
172C2×Dic47—42no—
173C2×Dic47AGL(1,ℤ/8)12yes—
174C2×Dic47#13712yes—
175C8×C47—42no—
176C47⋊C8—24no—
177#29183—471nomaximal, Sylow
178C22×C47C2×C22⋊Q811yescharacteristic
179C22×C47#53211yescharacteristic
180C22×C47#53611yescharacteristic
181C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
182C22×C47C2×#13711yescharacteristic
183C22×C47#57511yescharacteristic
184C22×C47#57511yescharacteristic
185C4×C47—22no—
186C4×C47—22no—
187C4×C47—42no—
188C4×C47—42no—
189C4×C47—82no—
190C4×C47#55212yes—
191C4×C47#55712yes—
192Dic47—22no—
193Dic47—22no—
194Dic47—41no—
195Dic47—41no—
196Dic47—81no—
197Dic47—81no—
198Dic47—82no—
199#2859—471no—
200C4×#125—471no—
201#2088—472no—
202#2087—472no—
203#1992—471no—
204#1992D4711yescharacteristic
205#1919—472no—
206#1918—472no—
207#1847—471no—
208#1836—471no—
209#1767—471no—
210C2×C47#256511yescharacteristic
211C2×C47#307911yescharacteristic
212C2×C47#308011yescharacteristic
213C2×C47#317111yescharacteristic
214C2×C47#318111yescharacteristic
215C2×C47#323411yescharacteristic
216C2×C47#323711yescharacteristic
217C2×#125—941no—
218C2×#125C2×D4711yescharacteristic
219C2×#107—472no—
220C2×#106—472no—
221C2×C4⋊C8—472no—
222C2×#97—471no—
223C2×#97C2×D4711yescharacteristic
224#389—471no—
225#389—471no—
226#389—472no—
227#389—472no—
228#389—941no—
229#389—941no—
230#387—941no—
231#387—941no—
232#384—471no—
233#384C2×D4711yescharacteristic
234#382—471no—
235#382—941no—
236C4×C4⋊C4—471no—
237C4×C4⋊C4—471no—
238C4×C4⋊C4—941no—
239C4×C4⋊C4—941no—
240C43—471no—
241#340—472no—
242#340—472no—
243#340—472no—
244#340—472no—
245#340C2×D4712yes—
246#340C2×D4712yes—
247#336—472no—
248C47#2918311yescharacteristic, complemented, Sylow
249C22×C8—472no—
250C22×C8C22×D4712yes—
251#125—22no—
252#125—1884no—
253#125Dic9414yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—472no—
259C2×C4⋊C4—471no—
260C2×C4⋊C4—471no—
261C2×C4⋊C4—942no—
262C2×C4⋊C4—942no—
263C2×C4⋊C4—941no—
264C2×C4⋊C4—941no—
265C2×C4⋊C4—941no—
266C2×C4⋊C4—941no—
267C2×C4⋊C4C22×D4712yes—
268C2×C4⋊C4C22×D4711yescharacteristic
269C2×C4⋊C4C22×D4711yescharacteristic
270C2×C42—471no—
271C2×C42—471no—
272C2×C42—471no—
273C2×C42—471no—
274C2×C42—471no—
275C2×C42—471no—
276C2×C42—941no—
277C2×C42—941no—
278C2×C42C22×D4711yescharacteristic
279#107—944no—
280#106—944no—
281C4⋊C8—944no—
282#97—22no—
283#97—942no—
284#95—941no—
285#95—941no—
286#95—941no—
287#95—941no—
288#95—942no—
289#95—942no—
290#95—941no—
291#95—941no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—471no—
296C22×C4—471no—
297C22×C4—471no—
298C22×C4—471no—
299C22×C4—941no—
300C22×C4—941no—
301C22×C4—942no—
302C22×C4D4×D4711yescharacteristic
303C22×C4D4×D4711yescharacteristic
304C22×C4C23×D4711yescharacteristic
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—474no—
309C2×C8—942no—
310C2×C8—942no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—942no—
320C4⋊C4—942no—
321C4⋊C4—944no—
322C4⋊C4—1882no—
323C4⋊C4—1882no—
324C4⋊C4—1882no—
325C4⋊C4—1884no—
326C4⋊C4—1884no—
327C4⋊C4—1882no—
328C4⋊C4C2×Dic9412yes—
329C4⋊C4C2×Dic9412yes—
330C42—942no—
331C42—942no—
332C42—942no—
333C42—942no—
334C42—1881no—
335C42—1881no—
336C42—1882no—
337C42—1882no—
338C42C2×Dic9412yes—
339C42#1062535212yes—
340C23C2×D4×D4711yescharacteristic
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—472no—
355C2×C4—472no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—1881no—
367C2×C4—1882no—
368C2×C4—1881no—
369C2×C4—1881no—
370C2×C4—1881no—
371C2×C4—1882no—
372C2×C4—1881no—
373C2×C4—1881no—
374C2×C4—1882no—
375C2×C4#1309400112yes—
376C2×C4#1309400112yes—
377C2×C4C22×Dic9411yescharacteristic
378C2×C4#41×D4712yes—
379C2×C4C2×#1062535211yescharacteristic
380C2×C4#1309407212yes—
381C8—42no—
382C8—944no—
383C22C2×#1309400111yescharacteristic
384C22#1568967211yescharacteristic
385C22#1568969811yescharacteristic
386C22AGL(1,ℤ/8)×D4711yescharacteristic
387C22#137×D4711yescharacteristic
388C22#1568991911yescharacteristic
389C22#1568992211yescharacteristic
390C4—22no—
391C4—22no—
392C4—42no—
393C4—42no—
394C4—82no—
395C4—942no—
396C4—942no—
397C4—3761no—
398C4—3762no—
399C4—3761no—
400C4—1881no—
401C4—1881no—
402C4#1568980712yes—
403C4#1568984912yes—
404C2#2024858211yescharacteristic
405C2#2025319911yescharacteristic
406C2#2025320811yescharacteristic
407C2#2025398211yescharacteristic
408C2#2025409611yescharacteristic
409C2#2025457911yescharacteristic
410C2#2025460311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#1992C2
socle, prime radicalC23×C47C22×D4
hypercenter#1992D47
hypocenterC47#29183
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
248. C47#29183semidirect

Maximal subgroups

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

subgroupindex
#202517492
#125×Dic472
#202448922
#202448852
#202443582
#202439692
#202439622
#202435542
#202435222
#202432422
C47×#19922
#2918347