Finite Group Databasebeta

← #26190330

Subgroups — #26190330

Order 12032.

908 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256793C211yesmaximal, characteristic
2#20254532C212yesmaximal, complemented
3#20242395C214yesmaximal, complemented
4#20242378C214yesmaximal
5#20241951C212yesmaximal, complemented
6#20241702C211yesmaximal, characteristic
7C47×#2621C211yesmaximal, characteristic
8#15689754—21no—
9#15689754C2212yes—
10#15689751—22no—
11#15689751—22no—
12#15689749—21no—
13#15689749C2212yes—
14#15689680—21no—
15#15689680C2212yes—
16#15689676—24no—
17C2×#13093983—21no—
18#15689519—22no—
19#15689475—22no—
20#15689453C2218yes—
21#15689405—24no—
22#15689176C2212yes—
23#15688859C2218yes—
24#15688849C2212yes—
25#15688847C2212yes—
26C2×C4⋊Q8×C47C2211yescharacteristic
27C2×C22⋊Q8×C47—21no—
28C2×#117×C47C2211yescharacteristic
29C47×#398—21no—
30C47×#398C2212yes—
31C47×#397—21no—
32C47×#397C2212yes—
33C47×#391—21no—
34C47×#382C2211yescharacteristic
35#13094024—21no—
36#13094024—21no—
37#13094024D412yes—
38#13094024D412yes—
39#13094023—24no—
40#13094023—24no—
41#13094016—22no—
42#13094016—22no—
43#13094015—24no—
44#13094015—24no—
45#13094003—22no—
46#13094003—22no—
47#13094003—22no—
48#13094003C2314yes—
49#13094001—24no—
50#13094001—24no—
51#13094001—24no—
52#13094001—24no—
53C4×Dic94—22no—
54C4×Dic94—22no—
55C4×Dic94—22no—
56C4×Dic94D414yes—
57#13093983—22no—
58#13093983—22no—
59#13093983—22no—
60#13093983—22no—
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47—21no—
63C2×C22⋊Dic47—22no—
64C2×C4×Dic47—22no—
65#13093955—28no—
66C4⋊(C47⋊C8)—22no—
67#13093947—28no—
68C22⋊(C47⋊C8)C2314yes—
69C4×C47⋊C8—22no—
70C22×Q8×C47—21no—
71C23×C4×C47D411yescharacteristic
72C4⋊Q8×C47—22no—
73C4⋊Q8×C47—22no—
74C22⋊Q8×C47—44no—
75#117×C47—22no—
76#117×C47—22no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47D411yescharacteristic
81C2×C4⋊C4×C47C2312yes—
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C22⋊C4×C47—22no—
84C2×C22⋊C4×C47D411yescharacteristic
85C2×C22⋊C4×C47C2311yescharacteristic
86C2×C42×C47D411yescharacteristic
87C2×C42×C47C2311yescharacteristic
88#95×C47—21no—
89#95×C47—22no—
90#95×C47—22no—
91#95×C47C2312yes—
92C24×C47C2×D411yescharacteristic
93C2×Q8×C47—41no—
94C2×Q8×C47—41no—
95C2×Q8×C47—42no—
96C2×Q8×C47—42no—
97C22×C4×C47—21no—
98C22×C4×C47—21no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47SD1614yes—
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×D411yescharacteristic
108C22×C4×C47C2411yescharacteristic
109C22×Dic47—22no—
110C22×Dic47—22no—
111C2×Dic94—22no—
112C2×Dic94—22no—
113C2×Dic94—22no—
114C2×Dic94C2×D414yes—
115C4⋊C4×C47—22no—
116C4⋊C4×C47—22no—
117C4⋊C4×C47—24no—
118C4⋊C4×C47—42no—
119C4⋊C4×C47—42no—
120C4⋊C4×C47—44no—
121C22⋊C4×C47—22no—
122C22⋊C4×C47—22no—
123C22⋊C4×C47—44no—
124C42×C47—21no—
125C42×C47—21no—
126C42×C47C2×D412yes—
127C42×C47C2×D412yes—
128C22⋊Dic47—24no—
129C22⋊Dic47—24no—
130C4⋊Dic47—22no—
131C4⋊Dic47—22no—
132C4⋊Dic47—22no—
133C4⋊Dic47—22no—
134C4⋊Dic47—22no—
135C4⋊Dic47—22no—
136C4⋊Dic47—22no—
137C4⋊Dic47C2×D414yes—
138Dic47⋊C4—24no—
139Dic47⋊C4—24no—
140Dic47⋊C4—24no—
141Dic47⋊C4—24no—
142C4×Dic47—24no—
143C4×Dic47—24no—
144C2×C47⋊C8—24no—
145C23×C47—21no—
146C23×C47—21no—
147C23×C47—41no—
148C23×C47—41no—
149C23×C47C2×SD1612yes—
150C23×C47C22×D411yescharacteristic
151Q8×C47—82no—
152Q8×C47—82no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—24no—
156C2×C4×C47—24no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—41no—
160C2×C4×C47—41no—
161C2×C4×C47—41no—
162C2×C4×C47—41no—
163C2×C4×C47—42no—
164C2×C4×C47—42no—
165C2×C4×C47—42no—
166C2×C4×C47—42no—
167C2×C4×C47—42no—
168C2×C4×C47—42no—
169C2×C4×C47#12012yes—
170C2×C4×C47#12011yescharacteristic
171C2×C4×C47#12011yescharacteristic
172C2×C4×C47C2×SD1612yes—
173C2×C4×C47C2×SD1612yes—
174C2×C4×C47#13712yes—
175C2×C4×C47C22×D412yes—
176C2×Dic47—24no—
177C2×Dic47—24no—
178C2×Dic47—82no—
179C2×Dic47—82no—
180Dic94—44no—
181Dic94—82no—
182Dic94—82no—
183Dic94—82no—
184C47⋊C8—44no—
185#18310—471nomaximal, Sylow
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—22no—
189C22×C47—42no—
190C22×C47—41no—
191C22×C47—41no—
192C22×C47—81no—
193C22×C47C2×#12011yescharacteristic
194C22×C47C22×SD1611yescharacteristic
195C22×C47C2×#13711yescharacteristic
196C4×C47—22no—
197C4×C47—22no—
198C4×C47—22no—
199C4×C47—41no—
200C4×C47—41no—
201C4×C47—82no—
202C4×C47—82no—
203C4×C47#44812yes—
204C4×C47#44812yes—
205Dic47—44no—
206Dic47—44no—
207#3458—471no—
208#3229—472no—
209#2621D4711yescharacteristic
210#1611—474no—
211#1608—474no—
212#1518—472no—
213#1458—471no—
214C2×C47—21no—
215C2×C47—21no—
216C2×C47—42no—
217C2×C47C2×#44811yescharacteristic
218C2×C47#302211yescharacteristic
219C2×C47#302811yescharacteristic
220#544—472no—
221#544—942no—
222#544—942no—
223#544—941no—
224#543—472no—
225#543—941no—
226#533—472no—
227#533—944no—
228#533—941no—
229C2×C4⋊Q8C2×D4711yescharacteristic
230C2×C22⋊Q8—21no—
231C2×#117—941no—
232C2×#117C2×D4711yescharacteristic
233#498—942no—
234#487—942no—
235#483—478no—
236#475—944no—
237#431—472no—
238#398—21no—
239#398C2×D4712yes—
240#397—21no—
241#397C2×D4712yes—
242#391—21no—
243#382C2×D4711yescharacteristic
244#328—478no—
245#324—472no—
246#323—472no—
247C47#1831011yescharacteristic, complemented, Sylow
248C22×Q8—21no—
249C23×C4C22⋊D4711yescharacteristic
250C4⋊Q8—22no—
251C4⋊Q8—22no—
252C4⋊Q8—472no—
253C4⋊Q8—472no—
254C4⋊Q8—941no—
255C4⋊Q8—941no—
256C4⋊Q8—944no—
257C4⋊Q8—944no—
258#125—942no—
259#125—944no—
260#125—944no—
261#125—942no—
262C22⋊Q8—44no—
263C22⋊Q8—474no—
264C22⋊Q8—944no—
265C22⋊Q8—944no—
266C22⋊Q8—944no—
267C22⋊Q8—944no—
268C22⋊Q8—942no—
269C22⋊Q8—942no—
270C22⋊Q8—942no—
271C4×Q8—474no—
272C4×Q8—942no—
273C4×Q8—942no—
274C4×Q8—942no—
275#117—22no—
276#117—22no—
277#117—942no—
278#117—942no—
279#117—942no—
280#117—942no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—941no—
285C2×C4⋊C4—941no—
286C2×C4⋊C4C22⋊D4711yescharacteristic
287C2×C4⋊C4C22×D4712yes—
288C2×C4⋊C4C22×D4711yescharacteristic
289C2×C22⋊C4—22no—
290C2×C22⋊C4—942no—
291C2×C22⋊C4C22⋊D4711yescharacteristic
292C2×C22⋊C4C22×D4711yescharacteristic
293C2×C42—942no—
294C2×C42C22⋊D4711yescharacteristic
295C2×C42C22×D4711yescharacteristic
296#106—948no—
297C4⋊C8—942no—
298#103—948no—
299C22⋊C8—474no—
300C4×C8—942no—
301#95—21no—
302#95—22no—
303#95—22no—
304#95C22×D4712yes—
305C24C2×C22⋊D4711yescharacteristic
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—42no—
309C2×Q8—42no—
310C2×Q8—474no—
311C2×Q8—942no—
312C2×Q8—942no—
313C2×Q8—942no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—942no—
320C22×C4—942no—
321C22×C4#1062533514yes—
322C22×C4C2×C22⋊D4711yescharacteristic
323C22×C4C2×C22⋊D4711yescharacteristic
324C22×C4C2×C22⋊D4711yescharacteristic
325C22×C4C2×C22⋊D4711yescharacteristic
326C22×C4C2×C22⋊D4711yescharacteristic
327C22×C4C23×D4711yescharacteristic
328C2×C8—944no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—44no—
335C4⋊C4—474no—
336C4⋊C4—944no—
337C4⋊C4—944no—
338C4⋊C4—942no—
339C4⋊C4—942no—
340C4⋊C4—942no—
341C4⋊C4—942no—
342C4⋊C4—944no—
343C4⋊C4—942no—
344C4⋊C4—942no—
345C4⋊C4—942no—
346C4⋊C4—944no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—44no—
350C22⋊C4—944no—
351C22⋊C4—944no—
352C42—21no—
353C42—21no—
354C42—944no—
355C42—944no—
356C42D4×D4712yes—
357C42D4×D4712yes—
358C23—21no—
359C23—21no—
360C23—41no—
361C23—41no—
362C23C2×#1062533512yes—
363C23C22×C22⋊D4711yescharacteristic
364Q8—82no—
365Q8—82no—
366Q8—3762no—
367Q8—3762no—
368Q8—3762no—
369Q8—1884no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—944no—
387C2×C4—944no—
388C2×C4—3762no—
389C2×C4—3762no—
390C2×C4#1309399212yes—
391C2×C4#1309399211yescharacteristic
392C2×C4#1309399211yescharacteristic
393C2×C4C2×#1062533512yes—
394C2×C4C2×#1062533512yes—
395C2×C4#1309405412yes—
396C2×C4C2×D4×D4712yes—
397C8—1884no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—42no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22C2×#1309399211yescharacteristic
406C22C22×#1062533511yescharacteristic
407C22C2×#1309405411yescharacteristic
408C4—22no—
409C4—22no—
410C4—22no—
411C4—41no—
412C4—41no—
413C4—82no—
414C4—82no—
415C4—1884no—
416C4—1884no—
417C4#1568926112yes—
418C4#1568926112yes—
419C2—21no—
420C2—21no—
421C2—42no—
422C2C2×#1568926111yescharacteristic
423C2#2025276611yescharacteristic
424C2#2025279311yescharacteristic
subgroupG/H
centerC22C2×#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2621C2
socleC22×C47C2×#120
prime radicalC24×C47C2×D4
hypercenter#2621D47
hypocenterC47#18310
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2621

Complements

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

NH ≅ G/Ntype
2. #20254532C2semidirect
3. #20242395C2semidirect
5. #20241951C2semidirect
247. C47#18310semidirect

Maximal subgroups

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

subgroupindex
#202567932
#202545322
#202423952
#202423782
#202419512
#202417022
C47×#26212
#1831047