Finite Group Databasebeta

← #26371416

Subgroups — #26371416

Order 12032.

534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20254047C211yesmaximal, characteristic, complemented
2#20245590C211yesmaximal, characteristic, complemented
3#20245585C211yesmaximal, characteristic, complemented
4#20245552C211yesmaximal, characteristic, complemented
5#20245545C211yesmaximal, characteristic, complemented
6#20245438C211yesmaximal, characteristic, complemented
7#20245433C211yesmaximal, characteristic, complemented
8#20245328C211yesmaximal, characteristic
9#20245328C211yesmaximal, characteristic
10#20245257C211yesmaximal, characteristic, complemented
11#20245252C211yesmaximal, characteristic, complemented
12C4×#13093970C211yesmaximal, characteristic, complemented
13C4×#13093968C211yesmaximal, characteristic, complemented
14#20245195C211yesmaximal, characteristic, complemented
15C47×#2951C211yesmaximal, characteristic
16#15689735—21no—
17C2×#13093970C2211yescharacteristic
18C2×#13093970C2211yescharacteristic
19C2×#13093968C2211yescharacteristic
20C2×#13093968C2211yescharacteristic
21#15689525C2211yescharacteristic
22#15689503C2211yescharacteristic
23#15689492—21no—
24#15689381—21no—
25#15689364C2211yescharacteristic
26#15689364C2211yescharacteristic
27#15689231—21no—
28C4×Dic188C2211yescharacteristic
29C4×Dic188C2211yescharacteristic
30#15688950C2211yescharacteristic
31#15688950C2211yescharacteristic
32#15688948C2211yescharacteristic
33#15688948C2211yescharacteristic
34C4⋊(C47⋊C16)C2211yescharacteristic
35C4⋊(C47⋊C16)C2211yescharacteristic
36#15688927C2211yescharacteristic
37#15688927C2211yescharacteristic
38#15688926C2211yescharacteristic
39#15688926C2211yescharacteristic
40#15688926C2211yescharacteristic
41#15688926C2211yescharacteristic
42#15688924C2211yescharacteristic
43#15688924C2211yescharacteristic
44C22⋊(C47⋊C16)C2211yescharacteristic
45C22⋊(C47⋊C16)C2211yescharacteristic
46#15688899C2211yescharacteristic
47C4×C47⋊C16C2211yescharacteristic
48C2×#135×C47C2211yescharacteristic
49C47×#520—21no—
50C47×#440—21no—
51C47×#440—21no—
52C4×Q16×C47C2211yescharacteristic
53C4×Q16×C47C2211yescharacteristic
54C4×D8×C47C2211yescharacteristic
55C4×D8×C47C2211yescharacteristic
56C2×#107×C47C2211yescharacteristic
57C47×#417—21no—
58C47×#405C2211yescharacteristic
59C2×Dic188—21no—
60C2×Dic188C2311yescharacteristic
61C2×Dic188C2311yescharacteristic
62#13094024—21no—
63#13094017—41no—
64#13094017—41no—
65#13094016—21no—
66#13094014—41no—
67#13094014—41no—
68#13094003—21no—
69#13094003—21no—
70C4×Dic94—21no—
71C4×Dic94—21no—
72#13093970—22no—
73#13093970—22no—
74#13093968—22no—
75#13093968—22no—
76C2×C47⋊C16C2311yescharacteristic
77C2×C47⋊C16C2311yescharacteristic
78C2×C47⋊C16C2311yescharacteristic
79C2×C47⋊C16C2311yescharacteristic
80#13093958C2311yescharacteristic
81#13093958C2311yescharacteristic
82#13093956—21no—
83#13093949—21no—
84#13093949—21no—
85#13093949—21no—
86#13093949—21no—
87C2×#41×C47—21no—
88#135×C47—22no—
89#135×C47—22no—
90C2×Q16×C47C2311yescharacteristic
91C2×SD16×C47—21no—
92C2×D8×C47C2311yescharacteristic
93C2×M16×C47D411yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C4×Q8×C47—21no—
96C4×Q8×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47—41no—
100C4×D4×C47—41no—
101#117×C47—41no—
102#117×C47D411yescharacteristic
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—41no—
105#107×C47—21no—
106#107×C47C2311yescharacteristic
107#107×C47C2311yescharacteristic
108#103×C47—21no—
109#103×C47—21no—
110#102×C47—21no—
111#102×C47—21no—
112#97×C47D411yescharacteristic
113#97×C47D411yescharacteristic
114C4×C8×C47C2311yescharacteristic
115C4×C8×C47C2311yescharacteristic
116#41×C47—24no—
117#41×C47—42no—
118C2×Q8×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47—41no—
124C22×C4×C47—41no—
125C22×C4×C47C2×D411yescharacteristic
126C2×Dic94—21no—
127C2×Dic94—21no—
128Q16×C47—21no—
129Q16×C47#4112yes—
130SD16×C47—24no—
131D8×C47—21no—
132D8×C47#4112yes—
133M16×C47—41no—
134C2×C8×C47—21no—
135C2×C8×C47—21no—
136C2×C8×C47C2×D411yescharacteristic
137C2×C8×C47C2×D411yescharacteristic
138C2×C8×C47C2×D411yescharacteristic
139C2×C8×C47C2411yescharacteristic
140C4⋊C4×C47—21no—
141C4⋊C4×C47—21no—
142C4⋊C4×C47—41no—
143C4⋊C4×C47—41no—
144C4⋊C4×C47—41no—
145C4⋊C4×C47D811yescharacteristic
146C4⋊C4×C47D811yescharacteristic
147C22⋊C4×C47—41no—
148C22⋊C4×C47—41no—
149C22⋊C4×C47D811yescharacteristic
150C22⋊C4×C47D811yescharacteristic
151C42×C47—41no—
152C42×C47—41no—
153C42×C47C2×D411yescharacteristic
154C42×C47C2×D411yescharacteristic
155C22⋊Dic47—41no—
156C22⋊Dic47—41no—
157C4⋊Dic47—21no—
158C4⋊Dic47—21no—
159C4⋊Dic47—41no—
160C4⋊Dic47—41no—
161Dic47⋊C4—41no—
162Dic47⋊C4—41no—
163Dic47⋊C4—41no—
164Dic47⋊C4—41no—
165Dic47⋊C4—41no—
166Dic47⋊C4—41no—
167C4×Dic47—41no—
168C4×Dic47—41no—
169Dic188—21no—
170Dic188—21no—
171Dic188—21no—
172Dic188—21no—
173Dic188—42no—
174C47⋊C16—21no—
175C47⋊C16—21no—
176C47⋊C16—21no—
177C47⋊C16—21no—
178C23×C47—41no—
179C23×C47C2×D811yescharacteristic
180Q8×C47—22no—
181Q8×C47—41no—
182D4×C47—22no—
183D4×C47—44no—
184D4×C47—41no—
185C2×C4×C47—21no—
186C2×C4×C47—21no—
187C2×C4×C47—44no—
188C2×C4×C47—41no—
189C2×C4×C47—41no—
190C2×C4×C47—41no—
191C2×C4×C47—161no—
192C2×C4×C47—161no—
193C2×C4×C47—161no—
194C2×C4×C47C2×D811yescharacteristic
195C2×C4×C47C2×D811yescharacteristic
196C2×C4×C47C2×D811yescharacteristic
197C2×C4×C47C2×D811yescharacteristic
198C2×C4×C47C2×D811yescharacteristic
199C2×C4×C47C22×D411yescharacteristic
200C2×Dic47—41no—
201C2×Dic47—41no—
202C2×Dic47—41no—
203C2×Dic47—41no—
204Dic94—41no—
205Dic94—41no—
206Dic94—41no—
207Dic94—41no—
208C8×C47—21no—
209C8×C47—21no—
210C8×C47—21no—
211C8×C47C2×#4111yescharacteristic
212C8×C47C2×#4111yescharacteristic
213#33680—471nomaximal, Sylow
214C22×C47—21no—
215C22×C47—21no—
216C22×C47—21no—
217C22×C47—42no—
218C22×C47—81no—
219C22×C47—81no—
220C22×C47C22×D811yescharacteristic
221C4×C47—21no—
222C4×C47—21no—
223C4×C47—21no—
224C4×C47—21no—
225C4×C47—21no—
226C4×C47—42no—
227C4×C47—81no—
228C4×C47—81no—
229C4×C47#52511yescharacteristic
230C4×C47#57511yescharacteristic
231Dic47—81no—
232Dic47—81no—
233Dic47—81no—
234Dic47—81no—
235#3177—471no—
236#2951D4711yescharacteristic
237#2236—471no—
238#2235—471no—
239#2229—471no—
240#2228—471no—
241#2209—471no—
242#2208—471no—
243#2189—471no—
244#2189—471no—
245#2176—471no—
246#2175—471no—
247C4×Q32—471no—
248C4×SD32—471no—
249#2164—471no—
250C2×C47—41no—
251C2×C47—82no—
252C2×C47#310011yescharacteristic
253C2×C47#341611yescharacteristic
254C2×C47#341711yescharacteristic
255C2×#135C2×D4711yescharacteristic
256#541—941no—
257#520—21no—
258C2×Q32—471no—
259C2×Q32—471no—
260C2×SD32—471no—
261C2×SD32—471no—
262#499—471no—
263#494—471no—
264#491—941no—
265#470—941no—
266#467—471no—
267#467—471no—
268#441—941no—
269#440—21no—
270#440—21no—
271C4×Q16—471no—
272C4×Q16—471no—
273C4×Q16C2×D4711yescharacteristic
274C4×Q16C2×D4711yescharacteristic
275C4×D8C2×D4711yescharacteristic
276C4×D8C2×D4711yescharacteristic
277C2×#107C2×D4711yescharacteristic
278#417—21no—
279#405C2×D4711yescharacteristic
280#367—471no—
281#367—471no—
282#366—471no—
283#366—471no—
284C4⋊C16—471no—
285C4⋊C16—471no—
286#358—471no—
287#358—471no—
288#358—471no—
289#358—471no—
290#358—471no—
291#358—471no—
292#357—471no—
293#357—471no—
294C22⋊C16—471no—
295C22⋊C16—471no—
296#346—471no—
297C4×C16—471no—
298C47#3368011yescharacteristic, complemented, Sylow
299C2×#41—21no—
300#135—22no—
301#135—22no—
302C2×Q16—471no—
303C2×Q16—471no—
304C2×Q16—941no—
305C2×Q16C22×D4711yescharacteristic
306C2×SD16—21no—
307C2×D8C22×D4711yescharacteristic
308C2×M16C22⋊D4711yescharacteristic
309C22×C8C22×D4711yescharacteristic
310C4⋊Q8—941no—
311#126—1881no—
312#126—1881no—
313#125—941no—
314#125—1881no—
315#125—1881no—
316C22⋊Q8—941no—
317C22⋊Q8—941no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—941no—
321C4×Q8—941no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—41no—
325C4×D4—41no—
326#117—41no—
327#117C22⋊D4711yescharacteristic
328C2×C4⋊C4—21no—
329C2×C4⋊C4—41no—
330Q32—942no—
331Q32—942no—
332SD32—942no—
333SD32—942no—
334C2×C16—471no—
335C2×C16—471no—
336C2×C16—471no—
337C2×C16—471no—
338#107—21no—
339#107—471no—
340#107—471no—
341#107C22×D4711yescharacteristic
342#107C22×D4711yescharacteristic
343#106—941no—
344#103—21no—
345#103—21no—
346#103—941no—
347#103—941no—
348#103—941no—
349#103—941no—
350#102—21no—
351#102—21no—
352#97C22⋊D4711yescharacteristic
353#97C22⋊D4711yescharacteristic
354C4×C8C22×D4711yescharacteristic
355C4×C8C22×D4711yescharacteristic
356#41—24no—
357#41—42no—
358C2×Q8—21no—
359C2×Q8—941no—
360C2×Q8—941no—
361C2×D4—21no—
362C2×D4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C2×C22⋊D4711yescharacteristic
368Q16—21no—
369Q16—941no—
370Q16—941no—
371Q16—941no—
372Q16—941no—
373Q16—1882no—
374Q16#1062535012yes—
375SD16—24no—
376D8—21no—
377D8#1062535012yes—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D4711yescharacteristic
382C2×C8C2×C22⋊D4711yescharacteristic
383C2×C8C2×C22⋊D4711yescharacteristic
384C2×C8C23×D4711yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—941no—
391C4⋊C4—941no—
392C4⋊C4—1881no—
393C4⋊C4—1881no—
394C4⋊C4—1881no—
395C4⋊C4—1881no—
396C4⋊C4—1881no—
397C4⋊C4—1881no—
398C4⋊C4—1881no—
399C4⋊C4—1881no—
400C4⋊C4#1062533411yescharacteristic
401C4⋊C4#1062533411yescharacteristic
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—1881no—
405C22⋊C4—1881no—
406C22⋊C4#1062533411yescharacteristic
407C22⋊C4#1062533411yescharacteristic
408C42—41no—
409C42—41no—
410C42—1881no—
411C42—1881no—
412C42C2×C22⋊D4711yescharacteristic
413C42C2×C22⋊D4711yescharacteristic
414C16—941no—
415C16—941no—
416C16—941no—
417C16—941no—
418C23—41no—
419C23C2×#1062533411yescharacteristic
420Q8—22no—
421Q8—41no—
422Q8—1881no—
423Q8—1881no—
424Q8—1881no—
425Q8—1881no—
426D4—22no—
427D4—44no—
428D4—41no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—44no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—161no—
436C2×C4—161no—
437C2×C4—161no—
438C2×C4—1881no—
439C2×C4—1881no—
440C2×C4—1881no—
441C2×C4—1881no—
442C2×C4C2×#1062533411yescharacteristic
443C2×C4C2×#1062533411yescharacteristic
444C2×C4C2×#1062533411yescharacteristic
445C2×C4C2×#1062533411yescharacteristic
446C2×C4C2×#1062533411yescharacteristic
447C2×C4C22×C22⋊D4711yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8C2×#1062535011yescharacteristic
452C8C2×#1062535011yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22C22×#1062533411yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—81no—
467C4—81no—
468C4—3761no—
469C4—3761no—
470C4—3761no—
471C4—3761no—
472C4#1568963411yescharacteristic
473C4#1568992111yescharacteristic
474C2—41no—
475C2—82no—
476C2#2025338811yescharacteristic
477C2#2025653511yescharacteristic
478C2#2025653911yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2951C2
socleC22×C47C22×D8
prime radicalC2×#135×C47C22
hypercenter#2951D47
hypocenterC47#33680
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #20254047C2semidirect
2. #20245590C2semidirect
3. #20245585C2semidirect
4. #20245552C2semidirect
5. #20245545C2semidirect
6. #20245438C2semidirect
7. #20245433C2semidirect
10. #20245257C2semidirect
11. #20245252C2semidirect
12. C4×#13093970C2semidirect
13. C4×#13093968C2semidirect
14. #20245195C2semidirect
298. C47#33680semidirect

Maximal subgroups

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

subgroupindex
#202540472
#202455902
#202455852
#202455522
#202455452
#202454382
#202454332
#202453282
#202452572
#202452522
C4×#130939702
C4×#130939682
#202451952
C47×#29512
#3368047