Finite Group Databasebeta

← #26219496

Subgroups — #26219496

Order 12032.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094044C211yesmaximal, characteristic
2C4×#13094030C211yesmaximal, characteristic, complemented
3#20244033C212yesmaximal, complemented
4#20243984C212yesmaximal, complemented
5#20243718C212yesmaximal
6#20243662C212yesmaximal, complemented
7C4×#13093959C211yesmaximal, characteristic, complemented
8C4×#13093950C211yesmaximal, characteristic, complemented
9C4×#13093951C211yesmaximal, characteristic, complemented
10#20243133C211yesmaximal, characteristic, complemented
11C47×#2922C211yesmaximal, characteristic, complemented
12C2×#13094044C2211yescharacteristic
13C2×#13094030C2212yes—
14C4×#10625350C2211yescharacteristic
15C4×#10625337C411yescharacteristic, complemented
16C4×#10625337C411yescharacteristic, complemented
17C4×#10625336C411yescharacteristic, complemented
18C4×#10625336C411yescharacteristic, complemented
19C4×#10625335C411yescharacteristic, complemented
20C4×#10625335C411yescharacteristic, complemented
21C4×#10625334C411yescharacteristic, complemented
22C4×#10625334C411yescharacteristic, complemented
23C2×#13093959C2212yes—
24#15689159C2211yescharacteristic
25C2×#13093951C2212yes—
26C2×#13093950C2212yes—
27#15689119C2211yescharacteristic
28#15689117C2211yescharacteristic
29#15689078C2212yes—
30#15689077—22no—
31C4×#10625329C2211yescharacteristic
32C4×#10625324—21no—
33C2×C4×C47⋊C8C2211yescharacteristic
34C4×C8×D47—21no—
35C42×Dic47C2211yescharacteristic
36#15688887C2212yes—
37#15688884C2212yes—
38#15688882C2212yes—
39#15688877C2212yes—
40#15688877C2212yes—
41C4×#41×C47C2211yescharacteristic
42C47×#433—22no—
43C47×#431—21no—
44C47×#431—21no—
45C47×#424C2212yes—
46C47×#408C2212yes—
47C4×M16×C47C2211yescharacteristic
48C2×C4×C8×C47C2211yescharacteristic
49C2×#10625350C2311yescharacteristic
50#13094044—24no—
51C2×#10625337C2×C411yescharacteristic
52C2×#10625335C2×C411yescharacteristic
53C2×#10625336C2×C411yescharacteristic
54C2×#10625334C2×C411yescharacteristic
55#13094030—24no—
56#13094030—24no—
57C2×#10625329C2312yes—
58C2×#10625324—22no—
59C22×C47⋊C8C2311yescharacteristic
60C22×C47⋊C8C2311yescharacteristic
61C2×C8×D47—22no—
62C4×Dic94C2×C411yescharacteristic
63C4×Dic94C2×C411yescharacteristic
64C4×D188C2×C411yescharacteristic
65C4×D188C2×C411yescharacteristic
66C4×C22⋊D47—21no—
67C4×C22⋊D47—21no—
68#13093983C2311yescharacteristic
69#13093981—21no—
70C2×C4×Dic47—21no—
71C2×C4×Dic47—21no—
72C2×C4×Dic47C2312yes—
73C42×D47—21no—
74#13093959—24no—
75#13093957C2×C411yescharacteristic
76#13093957C2×C411yescharacteristic
77#13093955C2×C411yescharacteristic
78#13093955C2×C411yescharacteristic
79#13093951—24no—
80#13093950—24no—
81#13093948C2×C411yescharacteristic
82#13093948C2×C411yescharacteristic
83#13093947C2×C411yescharacteristic
84#13093947C2×C411yescharacteristic
85#13093945C2×C411yescharacteristic
86#13093945C2×C411yescharacteristic
87#13093944C2×C411yescharacteristic
88#13093944C2×C411yescharacteristic
89#13093935—21no—
90#13093934—22no—
91C4×C47⋊C8—21no—
92C4×C47⋊C8C2×C411yescharacteristic
93C4×C47⋊C8C2×C411yescharacteristic
94C4×C47⋊C8C2×C411yescharacteristic
95C4×C47⋊C8C2×C411yescharacteristic
96C8×Dic47—22no—
97C2×#41×C47C2311yescharacteristic
98C2×M16×C47C2312yes—
99C22×C8×C47C2312yes—
100C4×Q8×C47C2×C411yescharacteristic
101C4×Q8×C47C2×C411yescharacteristic
102C4×D4×C47—21no—
103C4×D4×C47—21no—
104C4×D4×C47C2×C411yescharacteristic
105C4×D4×C47C2×C411yescharacteristic
106#117×C47—21no—
107#117×C47C2311yescharacteristic
108C2×C42×C47—21no—
109C2×C42×C47C2311yescharacteristic
110C4⋊C8×C47—22no—
111C4⋊C8×C47—22no—
112C22⋊C8×C47—22no—
113C22⋊C8×C47—22no—
114#97×C47—21no—
115C4×C8×C47—21no—
116C4×C8×C47D411yescharacteristic
117C4×C8×C47D411yescharacteristic
118C4×C8×C47D412yes—
119#41×C47—22no—
120#41×C47—22no—
121C2×Q8×C47C22×C411yescharacteristic
122C2×D4×C47—21no—
123C2×D4×C47C22×C411yescharacteristic
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47#4111yescharacteristic
128C22×C4×C47#4111yescharacteristic
129C22×C4×C47C2411yescharacteristic
130C2×C22⋊D47—21no—
131C22×Dic47—22no—
132#10625350—22no—
133#10625350#4114yes—
134C2×D188C22×C411yescharacteristic
135C2×C4×D47—21no—
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×Dic94C22×C411yescharacteristic
139M16×C47—22no—
140M16×C47—22no—
141C2×C8×C47—22no—
142C2×C8×C47—22no—
143C2×C8×C47—22no—
144C2×C8×C47C2×D412yes—
145C2×C8×C47C2×D412yes—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47C22×C411yescharacteristic
149C4⋊C4×C47C22×C411yescharacteristic
150C22⋊C4×C47—21no—
151C22⋊C4×C47—21no—
152C22⋊C4×C47—21no—
153C42×C47—21no—
154C42×C47—21no—
155C42×C47—21no—
156C42×C47C22×C411yescharacteristic
157C42×C47C22×C411yescharacteristic
158C42×C47C2×D411yescharacteristic
159C42×C47C2×D411yescharacteristic
160C22⋊Dic47—21no—
161#10625337—22no—
162#10625336—22no—
163#10625335—22no—
164#10625334—22no—
165(C2×D47)⋊C4—21no—
166(C2×D47)⋊C4—21no—
167C4⋊Dic47C22×C411yescharacteristic
168C4⋊Dic47C22×C411yescharacteristic
169Dic47⋊C4—21no—
170Dic47⋊C4—21no—
171C4×Dic47—24no—
172C4×Dic47—21no—
173C4×Dic47—21no—
174C4×Dic47—21no—
175C4×Dic47—22no—
176C4×Dic47—22no—
177C4×Dic47—42no—
178#10625329—22no—
179#10625329#4114yes—
180C2×C47⋊C8—22no—
181C2×C47⋊C8—22no—
182C2×C47⋊C8—22no—
183C2×C47⋊C8C22×C411yescharacteristic
184C2×C47⋊C8C22×C411yescharacteristic
185C2×C47⋊C8C22×C411yescharacteristic
186C2×C47⋊C8C22×C411yescharacteristic
187#10625324—28no—
188C8×D47—28no—
189C23×C47—21no—
190C23×C47C2×#4111yescharacteristic
191C22×D47—21no—
192Q8×C47—21no—
193Q8×C47—21no—
194D4×C47—21no—
195D4×C47—21no—
196D4×C47—42no—
197C2×C4×C47—22no—
198C2×C4×C47—22no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—42no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47C4×D411yescharacteristic
206C2×C4×C47C4×D411yescharacteristic
207C2×C4×C47C4×D411yescharacteristic
208C2×C4×C47C4×D411yescharacteristic
209C2×C4×C47C23×C411yescharacteristic
210C2×C4×C47C22×D411yescharacteristic
211C2×C4×C47C2×#4112yes—
212C2×C4×C47C2×#4112yes—
213C22⋊D47—24no—
214C2×Dic47—21no—
215C2×Dic47—24no—
216C2×Dic47—21no—
217C2×Dic47—21no—
218C2×Dic47—42no—
219C2×Dic47—42no—
220D188—21no—
221D188#11712yes—
222C4×D47—24no—
223C4×D47—42no—
224C4×D47—42no—
225Dic94—21no—
226Dic94#11712yes—
227C8×C47—22no—
228C8×C47—22no—
229C8×C47—42no—
230C47⋊C8—21no—
231C47⋊C8—21no—
232C47⋊C8—21no—
233C47⋊C8—21no—
234C47⋊C8—24no—
235#21137—471nomaximal, Sylow
236C22×C47—21no—
237C22×C47—21no—
238C22×C47—41no—
239C22×C47—41no—
240C22×C47—41no—
241C22×C47C2×C4×D411yescharacteristic
242C22×C47#52912yes—
243C2×D47—22no—
244C2×D47—41no—
245C2×D47—41no—
246C4×C47—21no—
247C4×C47—21no—
248C4×C47—41no—
249C4×C47—41no—
250C4×C47—41no—
251C4×C47#44312yes—
252C4×C47#44412yes—
253C4×C47C2×#11711yescharacteristic
254C4×C47C4×#4111yescharacteristic
255C4×C47#52512yes—
256Dic47—22no—
257Dic47—44no—
258Dic47—41no—
259Dic47—41no—
260C4×#135—471no—
261#2922D4711yescharacteristic, complemented
262C4×#131—471no—
263#1929—472no—
264#1922—472no—
265#1876—472no—
266#1866—472no—
267C4×#108—471no—
268C4×#104—471no—
269C4×#104—471no—
270#1744—471no—
271C2×C47—22no—
272C2×C47—81no—
273C2×C47#229011yescharacteristic
274C2×C47C2×#44311yescharacteristic
275C2×C47C2×#44411yescharacteristic
276D47—42no—
277C2×#135—471no—
278C2×#131—472no—
279C4×#41—471no—
280C4×#41C2×D4711yescharacteristic
281C4×Q16—471no—
282C4×Q16—471no—
283C4×SD16—471no—
284C4×SD16—471no—
285C4×SD16—471no—
286C4×SD16—471no—
287C4×D8—471no—
288C4×D8—471no—
289#433—22no—
290#431—21no—
291#431—21no—
292C2×#108—472no—
293#427—471no—
294#424C2×D4712yes—
295C2×#104—472no—
296C2×#104—472no—
297#416—471no—
298#416—471no—
299#408C2×D4712yes—
300#405—472no—
301#405—942no—
302C4×M16—471no—
303C4×M16—941no—
304C4×M16C2×D4711yescharacteristic
305C2×C4×C8—471no—
306C2×C4×C8—941no—
307C2×C4×C8C2×D4711yescharacteristic
308C43—471no—
309#341—472no—
310#339—472no—
311#339—472no—
312#336—472no—
313#336—472no—
314C47#2113711yescharacteristic, complemented, Sylow
315C2×#41—471no—
316C2×#41C22×D4711yescharacteristic
317#135—944no—
318C2×Q16—471no—
319C2×SD16—471no—
320C2×SD16—471no—
321C2×D8—471no—
322#131—944no—
323#131—944no—
324C2×M16—472no—
325C2×M16—942no—
326C2×M16C22×D4712yes—
327C22×C8—471no—
328C22×C8—471no—
329C22×C8—942no—
330C22×C8C22×D4712yes—
331C4×Q8—471no—
332C4×Q8—471no—
333C4×Q8C4×D4711yescharacteristic
334C4×Q8C4×D4711yescharacteristic
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—471no—
338C4×D4—471no—
339C4×D4—941no—
340C4×D4—941no—
341C4×D4C4×D4711yescharacteristic
342C4×D4C4×D4711yescharacteristic
343#117—21no—
344#117—471no—
345#117—941no—
346#117C22×D4711yescharacteristic
347C2×C42—21no—
348C2×C42—472no—
349C2×C42—941no—
350C2×C42—941no—
351C2×C42—941no—
352C2×C42C22×D4711yescharacteristic
353#108—944no—
354#107—471no—
355#107—471no—
356#106—471no—
357#106—471no—
358C4⋊C8—22no—
359C4⋊C8—22no—
360#104—944no—
361#104—944no—
362#103—471no—
363#103—471no—
364#103—471no—
365#103—471no—
366#102—471no—
367#102—471no—
368#102—471no—
369#102—471no—
370C22⋊C8—22no—
371C22⋊C8—22no—
372#97—21no—
373#97—942no—
374#97—941no—
375C4×C8—21no—
376C4×C8—471no—
377C4×C8—471no—
378C4×C8—471no—
379C4×C8—471no—
380C4×C8—942no—
381C4×C8—941no—
382C4×C8C22⋊D4712yes—
383C4×C8C22⋊D4711yescharacteristic
384C4×C8C22⋊D4711yescharacteristic
385#41—22no—
386#41—22no—
387#41—474no—
388#41—942no—
389C2×Q8—471no—
390C2×Q8C2×C4×D4711yescharacteristic
391C2×D4—21no—
392C2×D4—471no—
393C2×D4—941no—
394C2×D4C2×C4×D4711yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—941no—
399C22×C4—942no—
400C22×C4—941no—
401C22×C4—941no—
402C22×C4#1062535011yescharacteristic
403C22×C4#1062535011yescharacteristic
404C22×C4C23×D4711yescharacteristic
405Q16—942no—
406SD16—942no—
407SD16—942no—
408D8—942no—
409M16—22no—
410M16—22no—
411M16—474no—
412M16—948no—
413M16—942no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—471no—
418C2×C8—471no—
419C2×C8—471no—
420C2×C8—471no—
421C2×C8—948no—
422C2×C8—942no—
423C2×C8—942no—
424C2×C8—942no—
425C2×C8C2×C22⋊D4712yes—
426C2×C8C2×C22⋊D4712yes—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—471no—
430C4⋊C4—471no—
431C4⋊C4—941no—
432C4⋊C4—941no—
433C4⋊C4C2×C4×D4711yescharacteristic
434C4⋊C4C2×C4×D4711yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—941no—
439C22⋊C4—941no—
440C22⋊C4—941no—
441C42—21no—
442C42—21no—
443C42—21no—
444C42—944no—
445C42—941no—
446C42—941no—
447C42—941no—
448C42—942no—
449C42—942no—
450C42—1882no—
451C42C2×C4×D4711yescharacteristic
452C42C2×C4×D4711yescharacteristic
453C42C2×C22⋊D4711yescharacteristic
454C42C2×C22⋊D4711yescharacteristic
455C23—21no—
456C23—941no—
457C23C2×#1062535011yescharacteristic
458Q8—21no—
459Q8—21no—
460Q8—472no—
461Q8—941no—
462D4—21no—
463D4—21no—
464D4—42no—
465D4—472no—
466D4—944no—
467D4—941no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—941no—
477C2×C4—944no—
478C2×C4—944no—
479C2×C4—941no—
480C2×C4—941no—
481C2×C4—1882no—
482C2×C4—1882no—
483C2×C4—1882no—
484C2×C4—1882no—
485C2×C4C4×C22⋊D4711yescharacteristic
486C2×C4C4×C22⋊D4711yescharacteristic
487C2×C4C4×C22⋊D4711yescharacteristic
488C2×C4C4×C22⋊D4711yescharacteristic
489C2×C4C22×C4×D4711yescharacteristic
490C2×C4C22×C22⋊D4711yescharacteristic
491C2×C4#41×D4712yes—
492C2×C4#41×D4712yes—
493C8—22no—
494C8—22no—
495C8—42no—
496C8—941no—
497C8—941no—
498C8—941no—
499C8—941no—
500C8—944no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—942no—
507C22—1881no—
508C22—1881no—
509C22C2×C4×C22⋊D4711yescharacteristic
510C22#1568965112yes—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—41no—
516C4—942no—
517C4—1884no—
518C4—1881no—
519C4—1881no—
520C4#1568923812yes—
521C4#1568924312yes—
522C4#117×D4711yescharacteristic
523C4#1568959111yescharacteristic
524C4#1568963012yes—
525C2—22no—
526C2—81no—
527C2—1882no—
528C2#2024582511yescharacteristic
529C2C2×#1568923811yescharacteristic
530C2C2×#1568924311yescharacteristic
subgroupG/H
centerC42C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2922C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094044C22
cosocleC22×C4×C47C24
hypercenter#2922D47
hypocenterC47#21137
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. C4×#13094030C2semidirect
3. #20244033C2semidirect
4. #20243984C2semidirect
6. #20243662C2semidirect
7. C4×#13093959C2semidirect
8. C4×#13093950C2semidirect
9. C4×#13093951C2semidirect
10. #20243133C2semidirect
11. C47×#2922C2semidirect
15. C4×#10625337C4semidirect
16. C4×#10625337C4semidirect
17. C4×#10625336C4semidirect
18. C4×#10625336C4semidirect
19. C4×#10625335C4semidirect
20. C4×#10625335C4semidirect
21. C4×#10625334C4semidirect
22. C4×#10625334C4semidirect
261. #2922D47semidirect
314. C47#21137semidirect

Maximal subgroups

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

subgroupindex
C4×#130940442
C4×#130940302
#202440332
#202439842
#202437182
#202436622
C4×#130939592
C4×#130939502
C4×#130939512
#202431332
C47×#29222
#2113747