Finite Group Databasebeta

← #26107273

Subgroups — #26107273

Order 12032.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252078C211yesmaximal, characteristic
2#20243166C211yesmaximal, characteristic, complemented
3C22⋊C4×C47⋊C8C211yesmaximal, characteristic, complemented
4#20241877C211yesmaximal, characteristic
5#20241877C211yesmaximal, characteristic
6#20241275C211yesmaximal, characteristic, complemented
7C47×#1297C211yesmaximal, characteristic, complemented
8C2×#13094032C411yescharacteristic, complemented
9C23×C47⋊C8C2211yescharacteristic
10#15689634C2211yescharacteristic
11#15689191—21no—
12#15689191—21no—
13(C22⋊D47)⋊C8—21no—
14(C22⋊D47)⋊C8—21no—
15#15689151C411yescharacteristic, complemented
16#15689091C411yescharacteristic, complemented
17C2×C22⋊(C47⋊C8)C2211yescharacteristic
18C2×C22⋊(C47⋊C8)C2211yescharacteristic
19#15689081C411yescharacteristic, complemented
20C2×#13093935—21no—
21C2×C4×C47⋊C8—21no—
22#15688878—21no—
23#15688878—21no—
24#15688859C412yescomplemented
25#15688859C412yescomplemented
26#15688856C412yescomplemented
27#15688856C412yescomplemented
28C47×#407C2211yescharacteristic
29C4×C22⋊C4×C47C2211yescharacteristic
30C4×C22⋊C4×C47C2211yescharacteristic
31C2×#10625350C2×C411yescharacteristic
32#13094032—42no—
33C2×#10625324—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8—42no—
37C22×C47⋊C8C2×C411yescharacteristic
38C22×C47⋊C8C2×C411yescharacteristic
39C22×C47⋊C8D411yescharacteristic
40C22×C47⋊C8D411yescharacteristic
41C22×C47⋊C8D411yescharacteristic
42C22×C47⋊C8D411yescharacteristic
43C2×C8×D47—21no—
44#13094007—21no—
45#13094003C2×C411yescharacteristic
46#13094003C2×C411yescharacteristic
47#13093998C2×C411yescharacteristic
48#13093998C2×C411yescharacteristic
49#13093993—21no—
50C4×C22⋊D47—21no—
51C4×C22⋊D47—21no—
52#13093983C2×C411yescharacteristic
53Dic47⋊C8—21no—
54Dic47⋊C8—21no—
55C22⋊(C47⋊C8)—21no—
56C22⋊(C47⋊C8)—21no—
57C22⋊(C47⋊C8)C2×C412yes—
58C22⋊(C47⋊C8)C2×C412yes—
59(C2×D47)⋊C8—21no—
60(C2×D47)⋊C8—21no—
61#13093935—42no—
62#13093934—21no—
63C4×C47⋊C8—42no—
64C8×Dic47—21no—
65C23×C4×C47C2311yescharacteristic
66C2×M16×C47C2×C411yescharacteristic
67C2×M16×C47C2×C411yescharacteristic
68C2×C22⋊C4×C47—21no—
69C2×C22⋊C4×C47—21no—
70C2×C42×C47—21no—
71C2×C42×C47—21no—
72C22⋊C8×C47—21no—
73C22⋊C8×C47—21no—
74#95×C47C2×C412yes—
75#95×C47C2×C412yes—
76C24×C47#4111yescharacteristic
77C22×C4×C47—22no—
78C22×C4×C47—22no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47C22×C411yescharacteristic
82C22×C4×C47C22×C411yescharacteristic
83C22×C4×C47C22×C411yescharacteristic
84C22×C4×C47C2×D411yescharacteristic
85C22×C4×C47C2×D411yescharacteristic
86C22×C4×C47#4111yescharacteristic
87C2×C22⋊D47—21no—
88C2×C22⋊D47—21no—
89C2×C22⋊D47—21no—
90#10625350—41no—
91#10625350—41no—
92C2×D188C4211yescharacteristic
93C2×C4×D47—21no—
94C2×Dic94C4211yescharacteristic
95M16×C47—41no—
96M16×C47—41no—
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C22⋊C4×C47—24no—
100C22⋊C4×C47—42no—
101C42×C47—41no—
102C42×C47—41no—
103C42×C47—41no—
104C42×C47—41no—
105C22⋊Dic47—21no—
106C22⋊Dic47—21no—
107C22⋊Dic47—21no—
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4—21no—
110C4⋊Dic47C4211yescharacteristic
111C4⋊Dic47C4211yescharacteristic
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114C4×Dic47—21no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8—22no—
117C2×C47⋊C8—22no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8—41no—
124C2×C47⋊C8—41no—
125C2×C47⋊C8—41no—
126C2×C47⋊C8—41no—
127C2×C47⋊C8C22⋊C411yescharacteristic
128C2×C47⋊C8C22⋊C411yescharacteristic
129C2×C47⋊C8C22⋊C411yescharacteristic
130C2×C47⋊C8C22⋊C411yescharacteristic
131#10625324—42no—
132C8×D47—42no—
133C23×C47—22no—
134C23×C47—22no—
135C23×C47—41no—
136C23×C47#11711yescharacteristic
137C23×C47C4×D411yescharacteristic
138C23×C47C4×D411yescharacteristic
139C22×D47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—24no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—42no—
151C2×C4×C47—42no—
152C2×C4×C47—42no—
153C2×C4×C47—42no—
154C2×C4×C47—42no—
155C2×C4×C47C2×C4211yescharacteristic
156C2×C4×C47C2×C22⋊C411yescharacteristic
157C2×C4×C47C4×D411yescharacteristic
158C2×C4×C47C4×D411yescharacteristic
159C22⋊D47—42no—
160C22⋊D47—42no—
161C22⋊D47—42no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165D188—41no—
166C4×D47—41no—
167C4×D47—41no—
168Dic94—41no—
169C8×C47—41no—
170C8×C47—41no—
171C47⋊C8—21no—
172C47⋊C8—21no—
173C47⋊C8—21no—
174C47⋊C8—42no—
175C47⋊C8—42no—
176C47⋊C8#9912yes—
177#8240—471nomaximal, Sylow
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—44no—
186C22×C47C4×C22⋊C411yescharacteristic
187C22×C47#44312yes—
188C22×C47#44412yes—
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—21no—
195C4×C47—44no—
196C4×C47—82no—
197C4×C47C2×#9911yescharacteristic
198C4×C47#41011yescharacteristic
199Dic47—41no—
200Dic47—41no—
201Dic47—41no—
202#2929—471no—
203#1752—471no—
204C8×C22⋊C4—471no—
205#1501—471no—
206#1501—471no—
207#1298—471no—
208#1297D4711yescharacteristic, complemented
209C2×C47—22no—
210C2×C47—22no—
211C2×C47—41no—
212C2×C47C4×#9911yescharacteristic
213C2×C47#176411yescharacteristic
214C2×C47#176511yescharacteristic
215D47—81no—
216C2×#131—471no—
217C23×C8—471no—
218#525—471no—
219#435—941no—
220#435—941no—
221C8×D4—941no—
222C8×D4—941no—
223#424—471no—
224#408—471no—
225#407C2×D4711yescharacteristic
226C2×C22⋊C8—471no—
227C2×C22⋊C8—471no—
228#405—471no—
229C2×#97—941no—
230C2×C4×C8—941no—
231C4×C22⋊C4C2×D4711yescharacteristic
232C4×C22⋊C4C2×D4711yescharacteristic
233#336—941no—
234#336—941no—
235#328—472no—
236#328—472no—
237#327—472no—
238#327—472no—
239C47#824011yescharacteristic, complemented, Sylow
240C2×#41—471no—
241C23×C4C22×D4711yescharacteristic
242#131—1882no—
243C2×M16—941no—
244C2×M16C4×D4711yescharacteristic
245C2×M16C4×D4711yescharacteristic
246C22×C8—471no—
247C22×C8—471no—
248C22×C8—471no—
249C22×C8—471no—
250C22×C8—471no—
251C22×C8—471no—
252C22×C8—941no—
253C22×C8—941no—
254C22×C8—941no—
255C22×C8—1882no—
256#123—941no—
257C22⋊Q8—471no—
258C22⋊Q8—471no—
259#121—471no—
260#121—471no—
261#120—941no—
262C4×D4—941no—
263C4×D4—941no—
264#117—471no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C42—21no—
268C2×C42—21no—
269C4⋊C8—941no—
270C4⋊C8—941no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—472no—
274C22⋊C8—472no—
275C22⋊C8—941no—
276C22⋊C8—941no—
277C22⋊C8—941no—
278C22⋊C8—941no—
279#97—941no—
280#97—1882no—
281C4×C8—941no—
282C4×C8—1882no—
283#95C4×D4712yes—
284#95C4×D4712yes—
285C24#1062535211yescharacteristic
286#41—1881no—
287#41—1881no—
288C2×Q8—471no—
289C2×D4—471no—
290C2×D4—941no—
291C2×D4—941no—
292C2×D4—941no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—941no—
298C22×C4C2×C4×D4711yescharacteristic
299C22×C4C2×C4×D4711yescharacteristic
300C22×C4C2×C4×D4711yescharacteristic
301C22×C4D4×D4711yescharacteristic
302C22×C4D4×D4711yescharacteristic
303C22×C4#1062535411yescharacteristic
304M16—41no—
305M16—41no—
306M16—1882no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—471no—
310C2×C8—471no—
311C2×C8—471no—
312C2×C8—471no—
313C2×C8—942no—
314C2×C8—942no—
315C2×C8—942no—
316C2×C8—942no—
317C2×C8—942no—
318C2×C8—1882no—
319C2×C8—1881no—
320C2×C8—1881no—
321C2×C8—1881no—
322C2×C8—1881no—
323C2×C8—1881no—
324C2×C8—1881no—
325C2×C8—1881no—
326C4⋊C4—471no—
327C4⋊C4—471no—
328C4⋊C4—941no—
329C4⋊C4—941no—
330C22⋊C4—24no—
331C22⋊C4—42no—
332C22⋊C4—941no—
333C22⋊C4—941no—
334C22⋊C4—941no—
335C22⋊C4—941no—
336C22⋊C4—941no—
337C42—41no—
338C42—41no—
339C42—41no—
340C42—41no—
341C42—941no—
342C23—22no—
343C23—22no—
344C23—41no—
345C23—941no—
346C23#1309398211yescharacteristic
347C23(C22⋊D47)⋊C411yescharacteristic
348C23(C22⋊D47)⋊C411yescharacteristic
349Q8—1881no—
350D4—1881no—
351D4—1882no—
352D4—1882no—
353D4—1882no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—1881no—
373C2×C4—1881no—
374C2×C4C42×D4711yescharacteristic
375C2×C4C22⋊C4×D4711yescharacteristic
376C2×C4#1309398611yescharacteristic
377C2×C4#1309398611yescharacteristic
378C8—41no—
379C8—41no—
380C8—472no—
381C8—941no—
382C8—941no—
383C8—941no—
384C8—1882no—
385C8—1882no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—1881no—
395C22—1881no—
396C22—1881no—
397C22#1568897011yescharacteristic
398C22#1568923712yes—
399C22#1568924212yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—82no—
405C4—1881no—
406C4—1881no—
407C4—1881no—
408C4#99×D4711yescharacteristic
409C4#1568909511yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—3761no—
414C2#2024317511yescharacteristic
415C2#2024322211yescharacteristic
416C2#2024322911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1297C2
socleC22×C47C4×C22⋊C4
prime radical#15689634C22
cosocleC23×C4×C47C23
hypercenter#1297D47
hypocenterC47#8240
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #20243166C2semidirect
3. C22⋊C4×C47⋊C8C2semidirect
6. #20241275C2semidirect
7. C47×#1297C2semidirect
8. C2×#13094032C4semidirect
15. #15689151C4semidirect
16. #15689091C4semidirect
19. #15689081C4semidirect
24. #15688859C4semidirect
25. #15688859C4semidirect
26. #15688856C4semidirect
27. #15688856C4semidirect
208. #1297D47semidirect
239. C47#8240semidirect

Maximal subgroups

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

subgroupindex
#202520782
#202431662
C22⋊C4×C47⋊C82
#202418772
#202412752
C47×#12972
#824047