Finite Group Databasebeta

← #26120098

Subgroups — #26120098

Order 12032.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689329C211yesmaximal, characteristic
2#20244349C211yesmaximal, characteristic, complemented
3#20244182C211yesmaximal, characteristic
4#20243389C211yesmaximal, characteristic
5C2×#15688870C211yesmaximal, characteristic, complemented
6#20241272C211yesmaximal, characteristic, complemented
7C2×C47×#335C211yesmaximal, characteristic, complemented
8C22×#10625325—21no—
9C2×#13094024C2211yescharacteristic
10C2×C4×D188C2211yescharacteristic
11#15689329—22no—
12#15689329—22no—
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14C2×#13093949—21no—
15C2×#13093946—21no—
16C2×(C2×D47)⋊C8—21no—
17C2×(C2×D47)⋊C8—21no—
18#15688993C2211yescharacteristic
19#15688886—21no—
20#15688886—21no—
21#15688886—21no—
22#15688870—22no—
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4×C8×C47C2211yescharacteristic
26C47×#335—22no—
27C22×Dic94—21no—
28C22×D188D411yescharacteristic
29C22×C4×D47—21no—
30C2×#10625325—24no—
31C2×#10625325—42no—
32C2×#10625325—42no—
33C22×C47⋊C8—21no—
34#13094024—21no—
35#13094024—21no—
36#13094024—21no—
37#13094024D412yes—
38C4×D188—21no—
39C4×D188—21no—
40C4×D188—21no—
41C4×D188—21no—
42C2×C4⋊Dic47—21no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47D411yescharacteristic
48C2×(C2×D47)⋊C4—21no—
49C4⋊(C47⋊C8)—21no—
50C4⋊(C47⋊C8)—21no—
51#13093949—24no—
52#13093946—42no—
53(C2×D47)⋊C8—42no—
54(C2×D47)⋊C8—42no—
55C22×C8×C47—21no—
56C22×C8×C47—21no—
57C22×C8×C47D411yescharacteristic
58C22×C8×C47D411yescharacteristic
59C2×C42×C47C2311yescharacteristic
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47—21no—
63C4⋊C8×C47D412yes—
64C4×C8×C47—21no—
65C4×C8×C47—21no—
66C23×D47—21no—
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47#4111yescharacteristic
70C22×Dic47—21no—
71C22×Dic47—41no—
72C22×Dic47—41no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188—21no—
77C2×D188—21no—
78C2×D188D812yes—
79C2×C4×D47—41no—
80C2×C4×D47—41no—
81C2×C4×D47—41no—
82C2×C4×D47—41no—
83C2×C4×D47—41no—
84C2×C4×D47—41no—
85C2×Dic94—22no—
86C2×Dic94—41no—
87C2×Dic94—41no—
88C2×Dic94—41no—
89C2×Dic94—41no—
90C2×Dic94—41no—
91C2×C8×C47—21no—
92C2×C8×C47—21no—
93C2×C8×C47—22no—
94C2×C8×C47—21no—
95C2×C8×C47—21no—
96C2×C8×C47—21no—
97C2×C8×C47—41no—
98C2×C8×C47—41no—
99C2×C8×C47—41no—
100C2×C8×C47—41no—
101C2×C8×C47—41no—
102C2×C8×C47SD1612yescomplemented
103C42×C47C2×D411yescharacteristic
104C42×C47C2×D411yescharacteristic
105C42×C47#4111yescharacteristic
106C42×C47#4111yescharacteristic
107(C2×D47)⋊C4—41no—
108(C2×D47)⋊C4—41no—
109C4⋊Dic47—21no—
110C4⋊Dic47—22no—
111C4⋊Dic47—22no—
112C4⋊Dic47—21no—
113C4⋊Dic47—41no—
114C4⋊Dic47—41no—
115C4⋊Dic47—41no—
116C4⋊Dic47—41no—
117C4⋊Dic47—41no—
118C4⋊Dic47—41no—
119C4⋊Dic47—81no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123#10625325—48no—
124C23×C47#12111yescharacteristic
125C22×D47—22no—
126C22×D47—41no—
127C22×D47—41no—
128C22×D47—41no—
129C22×D47—41no—
130C22×D47—41no—
131C22×D47—41no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47#12011yescharacteristic
135C2×C4×C47#12111yescharacteristic
136C2×C4×C47#12111yescharacteristic
137C2×C4×C47#12311yescharacteristic
138C2×C4×C47#12311yescharacteristic
139C2×C4×C47#12411yescharacteristic
140C2×C4×C47C2×D811yescharacteristic
141C2×C4×C47C2×SD1611yescharacteristic
142C2×C4×C47#13511yescharacteristic
143C2×C4×C47#13511yescharacteristic
144C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C47#13711yescharacteristic
147C2×C4×C47#13711yescharacteristic
148C2×Dic47—42no—
149C2×Dic47—41no—
150C2×Dic47—41no—
151C2×Dic47—41no—
152C2×Dic47—81no—
153C2×Dic47—81no—
154C2×Dic47—81no—
155C2×Dic47—81no—
156C2×Dic47—81no—
157D188—22no—
158D188—22no—
159D188—41no—
160D188—41no—
161C4×D47—81no—
162C4×D47—81no—
163C4×D47—81no—
164C4×D47—81no—
165Dic94—42no—
166Dic94—42no—
167Dic94—81no—
168Dic94—81no—
169C8×C47—22no—
170C8×C47—42no—
171C8×C47—41no—
172C8×C47—81no—
173C47⋊C8—81no—
174#10476—471nomaximal, Sylow
175C22×C47#39411yescharacteristic
176C22×C47#46111yescharacteristic
177C22×C47#46311yescharacteristic
178C22×C47#46611yescharacteristic
179C22×C47#46811yescharacteristic
180C22×C47#47111yescharacteristic
181C22×C47#47311yescharacteristic
182C2×D47—42no—
183C2×D47—42no—
184C2×D47—42no—
185C2×D47—81no—
186C2×D47—81no—
187C2×D47—81no—
188C2×D47—81no—
189C4×C47—21no—
190C4×C47—21no—
191C4×C47#44711yescharacteristic
192C4×C47#45211yescharacteristic
193C4×C47#46011yescharacteristic
194C4×C47#46411yescharacteristic
195C4×C47#46511yescharacteristic
196C4×C47#46811yescharacteristic
197C4×C47#48011yescharacteristic
198C4×C47#48211yescharacteristic
199Dic47—81no—
200Dic47—82no—
201Dic47—161no—
202C2×#461—471no—
203#1990—471no—
204#1954—471no—
205#1802—471no—
206C2×#335D4711yescharacteristic, complemented
207C2×#332—471no—
208#1296—471no—
209C2×C47#167311yescharacteristic
210C2×C47#168111yescharacteristic
211C2×C47#169111yescharacteristic
212C2×C47#169911yescharacteristic
213C2×C47#203311yescharacteristic
214C2×C47#205211yescharacteristic
215C2×C47#205511yescharacteristic
216D47—82no—
217C22×SD16—941no—
218C2×C4⋊Q8—471no—
219C2×C4×D4—471no—
220#461—942no—
221#461—942no—
222C2×C4⋊C8—471no—
223C2×C4⋊C8C2×D4711yescharacteristic
224C2×C4⋊C8C2×D4711yescharacteristic
225C2×#103—941no—
226C2×#102—941no—
227C2×C22⋊C8—941no—
228C2×C22⋊C8—941no—
229C2×C4×C8C2×D4711yescharacteristic
230#384—471no—
231#340—941no—
232#340—941no—
233#340—941no—
234#335—22no—
235#332—942no—
236C47#1047611yescharacteristic, complemented, Sylow
237C22×Q8—941no—
238C22×D4—471no—
239C23×C4—941no—
240C2×SD16—944no—
241C2×SD16—1882no—
242C2×SD16—1882no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—941no—
246C22×C8D18811yescharacteristic
247C22×C8D18811yescharacteristic
248C4⋊Q8—472no—
249C4⋊Q8—941no—
250C4⋊Q8—941no—
251C4⋊Q8—941no—
252C4×D4—941no—
253C4×D4—941no—
254C4×D4—941no—
255C4×D4—941no—
256C2×C4⋊C4—471no—
257C2×C4⋊C4—941no—
258C2×C4⋊C4—941no—
259C2×C4⋊C4—941no—
260C2×C4⋊C4—941no—
261C2×C4⋊C4—941no—
262C2×C22⋊C4—941no—
263C2×C42C22×D4711yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—941no—
268C4⋊C8—941no—
269C4⋊C8C22⋊D4712yes—
270#103—944no—
271#102—1882no—
272C22⋊C8—1882no—
273C22⋊C8—1882no—
274C4×C8—21no—
275C4×C8—21no—
276C24—941no—
277C2×Q8—942no—
278C2×Q8—1881no—
279C2×Q8—1881no—
280C2×Q8—1881no—
281C2×Q8—1881no—
282C2×Q8—1881no—
283C2×D4—472no—
284C2×D4—941no—
285C2×D4—941no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—941no—
289C22×C4—941no—
290C22×C4—1881no—
291C22×C4—1881no—
292C22×C4—1881no—
293C22×C4—1881no—
294C22×C4—1881no—
295C22×C4—1881no—
296C22×C4—1881no—
297C22×C4—1881no—
298C22×C4C2×D18811yescharacteristic
299C22×C4D4×D4711yescharacteristic
300C22×C4#1062535411yescharacteristic
301SD16—1888no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—22no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—1881no—
314C2×C8—1881no—
315C2×C8—1881no—
316C2×C8#1062532512yescomplemented
317C4⋊C4—941no—
318C4⋊C4—942no—
319C4⋊C4—941no—
320C4⋊C4—942no—
321C4⋊C4—3761no—
322C4⋊C4—1881no—
323C4⋊C4—1881no—
324C4⋊C4—1881no—
325C4⋊C4—1881no—
326C4⋊C4—1881no—
327C4⋊C4—1881no—
328C22⋊C4—1881no—
329C22⋊C4—1881no—
330C42#1062535011yescharacteristic
331C42D4×D4711yescharacteristic
332C42#1062535411yescharacteristic
333C42C2×C22⋊D4711yescharacteristic
334C23—942no—
335C23—1881no—
336C23—1881no—
337C23—1881no—
338C23—1881no—
339C23—1881no—
340C23—1881no—
341C23#1309399911yescharacteristic
342Q8—3761no—
343Q8—3761no—
344Q8—1882no—
345Q8—1882no—
346D4—942no—
347D4—942no—
348D4—1881no—
349D4—1881no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—3761no—
353C2×C4—3761no—
354C2×C4—3761no—
355C2×C4—3761no—
356C2×C4—3761no—
357C2×C4—3761no—
358C2×C4—3761no—
359C2×C4—3761no—
360C2×C4—3761no—
361C2×C4—1881no—
362C2×C4—1882no—
363C2×C4—1881no—
364C2×C4—1881no—
365C2×C4#1309399211yescharacteristic
366C2×C4#1309399811yescharacteristic
367C2×C4#1309399911yescharacteristic
368C2×C4#1309400911yescharacteristic
369C2×C4#1309400911yescharacteristic
370C2×C4#1309401311yescharacteristic
371C2×C4D8×D4711yescharacteristic
372C2×C4C2×#1062532511yescharacteristic
373C2×C4#1309404611yescharacteristic
374C2×C4#1309404711yescharacteristic
375C2×C4#1309404811yescharacteristic
376C2×C4#1309405211yescharacteristic
377C2×C4#1309405611yescharacteristic
378C2×C4#1309405711yescharacteristic
379C8—22no—
380C8—42no—
381C8—41no—
382C8—81no—
383C8—3761no—
384C22—3761no—
385C22—3761no—
386C22—3761no—
387C22—3761no—
388C22—1882no—
389C22—1882no—
390C22—1882no—
391C22#1568904011yescharacteristic
392C22#1568932911yescharacteristic
393C22#1568933911yescharacteristic
394C22#1568936011yescharacteristic
395C22#1568937011yescharacteristic
396C22#1568938711yescharacteristic
397C22#1568939911yescharacteristic
398C4—21no—
399C4—21no—
400C4—3762no—
401C4—3761no—
402C4—7521no—
403C4#1568925511yescharacteristic
404C4#1568928411yescharacteristic
405C4#1568932411yescharacteristic
406C4#1568934611yescharacteristic
407C4#1568935211yescharacteristic
408C4#1568936911yescharacteristic
409C4#1568943811yescharacteristic
410C4#1568945011yescharacteristic
411C2—3762no—
412C2#2024277811yescharacteristic
413C2#2024282611yescharacteristic
414C2#2024288811yescharacteristic
415C2#2024293611yescharacteristic
416C2#2024457211yescharacteristic
417C2#2024468911yescharacteristic
418C2#2024470611yescharacteristic
subgroupG/H
centerC23#13093999
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC2×C47×#335C2
socleC23×C47#121
prime radicalC22×D188D4
hypercenterC2×#335D47
hypocenterC47#10476
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #20244349C2semidirect
5. C2×#15688870C2semidirect
6. #20241272C2semidirect
7. C2×C47×#335C2semidirect
102. C2×C8×C47SD16semidirect
206. C2×#335D47semidirect
236. C47#10476semidirect
316. C2×C8#10625325semidirect

Maximal subgroups

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

subgroupindex
C2×#156893292
#202443492
#202441822
#202433892
C2×#156888702
#202412722
C2×C47×#3352
#1047647