Finite Group Databasebeta

← #26220706

Subgroups — #26220706

Order 12032.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252186C211yesmaximal, characteristic
2#20252037C211yesmaximal, characteristic, complemented
3#20244280C211yesmaximal, characteristic
4#20244275C211yesmaximal, characteristic
5#20244138C211yesmaximal, characteristic, complemented
6#20244133C211yesmaximal, characteristic, complemented
7#20244102C211yesmaximal, characteristic, complemented
8#20244098C211yesmaximal, characteristic, complemented
9#20244095C211yesmaximal, characteristic, complemented
10#20244091C211yesmaximal, characteristic, complemented
11#20243295C211yesmaximal, characteristic, complemented
12C4×#13093950C211yesmaximal, characteristic, complemented
13C4×#13093951C211yesmaximal, characteristic, complemented
14#97×Dic47C211yesmaximal, characteristic, complemented
15C47×#2923C211yesmaximal, characteristic, complemented
16C2×#13094044C2211yescharacteristic
17C4×#10625350C2211yescharacteristic
18#15689233C412yescomplemented
19#15689228C412yescomplemented
20#15689223C412yescomplemented
21#15689221C412yescomplemented
22#15689185—22no—
23#15689178—22no—
24C2×#13093959C2211yescharacteristic
25C2×#13093959C2211yescharacteristic
26#15689159C2211yescharacteristic
27#15689149C2211yescharacteristic
28#15689149C2211yescharacteristic
29C2×#13093951C2211yescharacteristic
30C2×#13093951C2211yescharacteristic
31C2×#13093950C2211yescharacteristic
32C2×#13093950C2211yescharacteristic
33#15689119C2211yescharacteristic
34#15689117C2211yescharacteristic
35#15689089C2211yescharacteristic
36#15689089C2211yescharacteristic
37C4×#10625329C2211yescharacteristic
38C2×#13093935C2211yescharacteristic
39C2×#13093934C2211yescharacteristic
40C2×#13093934C2211yescharacteristic
41C2×C8×Dic47C2211yescharacteristic
42C2×C8×Dic47C2211yescharacteristic
43C42×Dic47C2211yescharacteristic
44#15688887C2211yescharacteristic
45#15688887C2211yescharacteristic
46#15688884C2211yescharacteristic
47#15688884C2211yescharacteristic
48#15688882C2211yescharacteristic
49#15688882C2211yescharacteristic
50C4×#41×C47C2211yescharacteristic
51C47×#433—22no—
52C47×#432—22no—
53C47×#424C2211yescharacteristic
54C47×#424C2211yescharacteristic
55C47×#408C2211yescharacteristic
56C47×#408C2211yescharacteristic
57C4×M16×C47C2211yescharacteristic
58C2×#97×C47C2211yescharacteristic
59C2×#10625350C2311yescharacteristic
60#13094044—22no—
61#13094044—22no—
62C2×#10625337C2×C411yescharacteristic
63C2×#10625335C2×C411yescharacteristic
64C2×#10625336C2×C411yescharacteristic
65C2×#10625334C2×C411yescharacteristic
66C2×#10625329C2311yescharacteristic
67C2×#10625329C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C4×Dic94C2×C412yes—
71C4×D188C2×C412yes—
72C4×C22⋊D47—22no—
73#13093983C2311yescharacteristic
74#13093981—21no—
75C2×C4×Dic47—22no—
76C2×C4×Dic47C2311yescharacteristic
77C2×C4×Dic47C2311yescharacteristic
78C42×D47—21no—
79#13093959—22no—
80#13093959—22no—
81#13093957C2×C412yes—
82#13093955C2×C412yes—
83Dic47⋊C8—22no—
84Dic47⋊C8—22no—
85#13093951—22no—
86#13093951—22no—
87#13093950—22no—
88#13093950—22no—
89#13093948C2×C412yes—
90#13093947C2×C412yes—
91#13093945C2×C412yes—
92#13093944C2×C412yes—
93(C2×D47)⋊C8—22no—
94(C2×D47)⋊C8—22no—
95#13093935—21no—
96#13093935C2×C412yes—
97#13093935C2×C412yes—
98#13093934—22no—
99#13093934—22no—
100C4×C47⋊C8—21no—
101C8×Dic47—22no—
102C8×Dic47—22no—
103C2×#41×C47C2311yescharacteristic
104C2×M16×C47C2311yescharacteristic
105C2×M16×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C4×Q8×C47C2×C412yes—
109C4×D4×C47—22no—
110C4×D4×C47C2×C412yes—
111#117×C47—21no—
112#117×C47C2311yescharacteristic
113C2×C42×C47—21no—
114C2×C42×C47C2311yescharacteristic
115C4⋊C8×C47—22no—
116C4⋊C8×C47—22no—
117C22⋊C8×C47—22no—
118C22⋊C8×C47—22no—
119#97×C47—21no—
120#97×C47D412yes—
121#97×C47D412yes—
122C4×C8×C47—21no—
123#41×C47—21no—
124#41×C47—21no—
125#41×C47—21no—
126#41×C47—21no—
127C2×Q8×C47C22×C411yescharacteristic
128C2×D4×C47—21no—
129C2×D4×C47C22×C411yescharacteristic
130C22×C4×C47—21no—
131C22×C4×C47—22no—
132C22×C4×C47#4112yes—
133C22×C4×C47C2411yescharacteristic
134C2×C22⋊D47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137#10625350—21no—
138#10625350—21no—
139#10625350—21no—
140#10625350—21no—
141C2×D188C22×C411yescharacteristic
142C2×C4×D47—21no—
143C2×C4×D47—22no—
144C2×Dic94C22×C411yescharacteristic
145M16×C47—21no—
146M16×C47—21no—
147M16×C47—21no—
148M16×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47C2×D412yes—
156C2×C8×C47C2×D412yes—
157C4⋊C4×C47—22no—
158C4⋊C4×C47C22×C412yes—
159C22⋊C4×C47—21no—
160C22⋊C4×C47—22no—
161C42×C47—22no—
162C42×C47—21no—
163C42×C47C22×C412yes—
164C42×C47C2×D411yescharacteristic
165C42×C47C2×D411yescharacteristic
166C22⋊Dic47—21no—
167#10625337—22no—
168#10625336—22no—
169#10625335—22no—
170#10625334—22no—
171(C2×D47)⋊C4—22no—
172C4⋊Dic47C22×C412yes—
173Dic47⋊C4—22no—
174C4×Dic47—22no—
175C4×Dic47—21no—
176C4×Dic47—21no—
177C4×Dic47—21no—
178C4×Dic47—44no—
179C4×Dic47#4112yes—
180C4×Dic47#4112yes—
181#10625329—21no—
182#10625329—21no—
183#10625329—21no—
184#10625329—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8C22×C412yes—
190C2×C47⋊C8C22×C411yescharacteristic
191C2×C47⋊C8C22×C411yescharacteristic
192C2×C47⋊C8#4112yes—
193C2×C47⋊C8#4112yes—
194C23×C47—21no—
195C23×C47C2×#4111yescharacteristic
196C22×D47—21no—
197Q8×C47—21no—
198Q8×C47—21no—
199D4×C47—21no—
200D4×C47—21no—
201D4×C47—41no—
202D4×C47—41no—
203C2×C4×C47—22no—
204C2×C4×C47—21no—
205C2×C4×C47—42no—
206C2×C4×C47—41no—
207C2×C4×C47—41no—
208C2×C4×C47—82no—
209C2×C4×C47C4×D412yes—
210C2×C4×C47C4×D412yes—
211C2×C4×C47C23×C411yescharacteristic
212C2×C4×C47C22×D411yescharacteristic
213C2×C4×C47C2×#4111yescharacteristic
214C2×C4×C47C2×#4111yescharacteristic
215C2×C4×C47C2×#4111yescharacteristic
216C2×C4×C47C2×#4111yescharacteristic
217C22⋊D47—41no—
218C22⋊D47—41no—
219C2×Dic47—24no—
220C2×Dic47—22no—
221C2×Dic47—21no—
222C2×Dic47—22no—
223C2×Dic47—22no—
224C2×Dic47—42no—
225D188—21no—
226D188—21no—
227C4×D47—41no—
228C4×D47—41no—
229C4×D47—82no—
230Dic94—21no—
231Dic94—21no—
232C8×C47—22no—
233C8×C47—22no—
234C8×C47—41no—
235C8×C47—41no—
236C47⋊C8—22no—
237C47⋊C8—41no—
238C47⋊C8—41no—
239C47⋊C8#11712yes—
240C47⋊C8#11712yes—
241#21297—471nomaximal, Sylow
242C22×C47—22no—
243C22×C47—42no—
244C22×C47—41no—
245C22×C47C2×C4×D411yescharacteristic
246C22×C47#52911yescharacteristic
247C22×C47#52911yescharacteristic
248C2×D47—42no—
249C2×D47—41no—
250C4×C47—22no—
251C4×C47—22no—
252C4×C47—42no—
253C4×C47—41no—
254C4×C47C2×#11711yescharacteristic
255C4×C47C4×#4111yescharacteristic
256C4×C47#53211yescharacteristic
257C4×C47#53211yescharacteristic
258Dic47—24no—
259Dic47—42no—
260Dic47—42no—
261Dic47—41no—
262#2943—471no—
263#2923—471no—
264#2923D4711yescharacteristic, complemented
265#1975—471no—
266#1974—471no—
267#1946—471no—
268#1945—471no—
269#1938—471no—
270#1938—471no—
271#1937—471no—
272#1937—471no—
273#1778—471no—
274C4×#104—471no—
275C4×#104—471no—
276C4×#97—471no—
277C2×C47—21no—
278C2×C47—21no—
279C2×C47—81no—
280C2×C47#229311yescharacteristic
281C2×C47#295612yes—
282D47—81no—
283C2×#135—471no—
284C4×#41—471no—
285C4×#41C2×D4711yescharacteristic
286#442—472no—
287#441—472no—
288#440—472no—
289#440—472no—
290#433—22no—
291#433—942no—
292#432—22no—
293#432—942no—
294C2×#108—471no—
295C2×#108—471no—
296#427—471no—
297#424—471no—
298#424—471no—
299#424C2×D4711yescharacteristic
300#424C2×D4711yescharacteristic
301C2×#104—471no—
302C2×#104—471no—
303C2×#104—471no—
304C2×#104—471no—
305#416—471no—
306#416—471no—
307#408—471no—
308#408—471no—
309#408C2×D4711yescharacteristic
310#408C2×D4711yescharacteristic
311C4×M16—471no—
312C4×M16C2×D4711yescharacteristic
313C2×#97—471no—
314C2×#97—471no—
315C2×#97—471no—
316C2×#97C2×D4711yescharacteristic
317C2×C4×C8—471no—
318C2×C4×C8—471no—
319C43—471no—
320#341—471no—
321#341—471no—
322#339—471no—
323#339—471no—
324#339—471no—
325#339—471no—
326C47#2129711yescharacteristic, complemented, Sylow
327C2×#41—471no—
328C2×#41C22×D4711yescharacteristic
329#135—942no—
330#135—942no—
331C2×Q16—471no—
332C2×SD16—471no—
333C2×SD16—471no—
334C2×D8—471no—
335C2×M16—471no—
336C2×M16—471no—
337C2×M16C22×D4711yescharacteristic
338C2×M16C22×D4711yescharacteristic
339C22×C8—471no—
340C22×C8—471no—
341C22×C8C22×D4711yescharacteristic
342C22×C8C22×D4711yescharacteristic
343C4×Q8—472no—
344C4×Q8C4×D4712yes—
345C4×D4—22no—
346C4×D4—472no—
347C4×D4—942no—
348C4×D4C4×D4712yes—
349#117—21no—
350#117—471no—
351#117—941no—
352#117C22×D4711yescharacteristic
353C2×C42—21no—
354C2×C42—471no—
355C2×C42—471no—
356C2×C42—941no—
357C2×C42—942no—
358C2×C42C22×D4711yescharacteristic
359#108—942no—
360#108—942no—
361#107—472no—
362#106—472no—
363C4⋊C8—22no—
364C4⋊C8—22no—
365C4⋊C8—942no—
366C4⋊C8—942no—
367#104—942no—
368#104—942no—
369#104—942no—
370#104—942no—
371#103—472no—
372#103—472no—
373#102—472no—
374#102—472no—
375C22⋊C8—22no—
376C22⋊C8—22no—
377C22⋊C8—942no—
378C22⋊C8—942no—
379#97—21no—
380#97—472no—
381#97—472no—
382#97—942no—
383#97—942no—
384#97—941no—
385#97C22⋊D4712yes—
386#97C22⋊D4712yes—
387C4×C8—21no—
388C4×C8—942no—
389C4×C8—942no—
390C4×C8—941no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—941no—
396#41—941no—
397#41—941no—
398#41—941no—
399C2×Q8—471no—
400C2×Q8C2×C4×D4711yescharacteristic
401C2×D4—21no—
402C2×D4—471no—
403C2×D4—941no—
404C2×D4C2×C4×D4711yescharacteristic
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—941no—
408C22×C4—941no—
409C22×C4—942no—
410C22×C4—941no—
411C22×C4#1062535012yes—
412C22×C4C23×D4711yescharacteristic
413Q16—942no—
414SD16—942no—
415SD16—942no—
416D8—942no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—21no—
421M16—941no—
422M16—941no—
423M16—941no—
424M16—941no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—471no—
432C2×C8—471no—
433C2×C8—472no—
434C2×C8—472no—
435C2×C8—472no—
436C2×C8—941no—
437C2×C8—941no—
438C2×C8—941no—
439C2×C8—941no—
440C2×C8C2×C22⋊D4712yes—
441C2×C8C2×C22⋊D4712yes—
442C4⋊C4—22no—
443C4⋊C4—472no—
444C4⋊C4—942no—
445C4⋊C4C2×C4×D4712yes—
446C22⋊C4—21no—
447C22⋊C4—22no—
448C22⋊C4—941no—
449C22⋊C4—942no—
450C42—22no—
451C42—21no—
452C42—472no—
453C42—472no—
454C42—942no—
455C42—941no—
456C42—941no—
457C42—941no—
458C42—1884no—
459C42C2×C4×D4712yes—
460C42C2×C22⋊D4711yescharacteristic
461C42C2×C22⋊D4711yescharacteristic
462C23—21no—
463C23—941no—
464C23C2×#1062535011yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—941no—
468Q8—941no—
469D4—21no—
470D4—21no—
471D4—41no—
472D4—41no—
473D4—941no—
474D4—941no—
475D4—1881no—
476D4—1881no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—82no—
483C2×C4—944no—
484C2×C4—942no—
485C2×C4—942no—
486C2×C4—941no—
487C2×C4—942no—
488C2×C4—3762no—
489C2×C4—1882no—
490C2×C4—1881no—
491C2×C4—1881no—
492C2×C4C4×C22⋊D4712yes—
493C2×C4C4×C22⋊D4712yes—
494C2×C4C22×C4×D4711yescharacteristic
495C2×C4C22×C22⋊D4711yescharacteristic
496C2×C4#41×D4711yescharacteristic
497C2×C4#41×D4711yescharacteristic
498C2×C4#41×D4711yescharacteristic
499C2×C4#41×D4711yescharacteristic
500C8—22no—
501C8—22no—
502C8—41no—
503C8—41no—
504C8—472no—
505C8—472no—
506C8—942no—
507C8—1881no—
508C8—1881no—
509C22—22no—
510C22—41no—
511C22—42no—
512C22—1881no—
513C22—1882no—
514C22C2×C4×C22⋊D4711yescharacteristic
515C22#1568965111yescharacteristic
516C22#1568965111yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—42no—
521C4—944no—
522C4—1882no—
523C4—1881no—
524C4—1882no—
525C4#117×D4711yescharacteristic
526C4#1568959111yescharacteristic
527C4#1568966911yescharacteristic
528C4#1568966911yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—3761no—
533C2#2024584711yescharacteristic
534C2#2025229512yes—
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2923C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094044C22
cosocleC22×C4×C47C24
hypercenter#2923D47
hypocenterC47#21297
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #20252037C2semidirect
5. #20244138C2semidirect
6. #20244133C2semidirect
7. #20244102C2semidirect
8. #20244098C2semidirect
9. #20244095C2semidirect
10. #20244091C2semidirect
11. #20243295C2semidirect
12. C4×#13093950C2semidirect
13. C4×#13093951C2semidirect
14. #97×Dic47C2semidirect
15. C47×#2923C2semidirect
18. #15689233C4semidirect
19. #15689228C4semidirect
20. #15689223C4semidirect
21. #15689221C4semidirect
264. #2923D47semidirect
326. C47#21297semidirect

Maximal subgroups

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

subgroupindex
#202521862
#202520372
#202442802
#202442752
#202441382
#202441332
#202441022
#202440982
#202440952
#202440912
#202432952
C4×#130939502
C4×#130939512
#97×Dic472
C47×#29232
#2129747