Finite Group Databasebeta

← #26219502

Subgroups — #26219502

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
2#20252030C211yesmaximal, characteristic, complemented
3#20244036C212yesmaximal, complemented
4#20243987C212yesmaximal, complemented
5#20243715C212yesmaximal
6#20243663C212yesmaximal, complemented
7C4×#13093959C211yesmaximal, characteristic, complemented
8C4×#13093950C211yesmaximal, characteristic, complemented
9C4×#13093951C211yesmaximal, characteristic, complemented
10#20243133C211yesmaximal, characteristic, complemented
11C4×#131×C47C211yesmaximal, characteristic, complemented
12C2×#13094044C2211yescharacteristic
13C4×#10625350C2211yescharacteristic
14C4×#10625337C411yescharacteristic, complemented
15C4×#10625337C411yescharacteristic, complemented
16C4×#10625336C411yescharacteristic, complemented
17C4×#10625336C411yescharacteristic, complemented
18C4×#10625335C411yescharacteristic, complemented
19C4×#10625335C411yescharacteristic, complemented
20C4×#10625334C411yescharacteristic, complemented
21C4×#10625334C411yescharacteristic, complemented
22#15689182—22no—
23#15689174—21no—
24#15689174—21no—
25C2×#13093959C2212yes—
26#15689159C2211yescharacteristic
27#15689149C2212yes—
28C2×#13093951C2212yes—
29C2×#13093950C2212yes—
30#15689119C2211yescharacteristic
31#15689117C2211yescharacteristic
32#15689089C2212yes—
33C4×#10625329C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35C42×Dic47C2211yescharacteristic
36#15688887C2212yes—
37#15688884C2212yes—
38#15688882C2212yes—
39#15688877C2212yes—
40#15688877C2212yes—
41C2×#131×C47C2212yes—
42C4×#41×C47C2211yescharacteristic
43C47×#405—22no—
44C47×#405C2212yes—
45C4×M16×C47—21no—
46C4×M16×C47C2211yescharacteristic
47C2×C4×C8×C47—21no—
48C2×C4×C8×C47C2211yescharacteristic
49C2×#10625350C2311yescharacteristic
50#13094044—24no—
51C2×#10625337C2×C411yescharacteristic
52C2×#10625335C2×C411yescharacteristic
53C2×#10625336C2×C411yescharacteristic
54C2×#10625334C2×C411yescharacteristic
55C2×#10625329C2312yes—
56C22×C47⋊C8C2311yescharacteristic
57C22×C47⋊C8C2311yescharacteristic
58C4×Dic94C2×C411yescharacteristic
59C4×Dic94C2×C411yescharacteristic
60C4×D188C2×C411yescharacteristic
61C4×D188C2×C411yescharacteristic
62C4×C22⋊D47—21no—
63C4×C22⋊D47—21no—
64#13093983C2311yescharacteristic
65#13093981—21no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—21no—
68C2×C4×Dic47C2312yes—
69C42×D47—21no—
70#13093959—24no—
71#13093957C2×C411yescharacteristic
72#13093957C2×C411yescharacteristic
73#13093955C2×C411yescharacteristic
74#13093955C2×C411yescharacteristic
75Dic47⋊C8—22no—
76Dic47⋊C8—22no—
77#13093951—24no—
78#13093950—24no—
79#13093948C2×C411yescharacteristic
80#13093948C2×C411yescharacteristic
81#13093947C2×C411yescharacteristic
82#13093947C2×C411yescharacteristic
83#13093945C2×C411yescharacteristic
84#13093945C2×C411yescharacteristic
85#13093944C2×C411yescharacteristic
86#13093944C2×C411yescharacteristic
87(C2×D47)⋊C8—22no—
88(C2×D47)⋊C8—22no—
89#13093935—21no—
90C4×C47⋊C8—21no—
91C4×C47⋊C8C2×C411yescharacteristic
92C4×C47⋊C8C2×C411yescharacteristic
93C4×C47⋊C8C2×C411yescharacteristic
94C4×C47⋊C8C2×C411yescharacteristic
95C2×#41×C47C2311yescharacteristic
96#131×C47—24no—
97#131×C47—24no—
98C2×M16×C47—22no—
99C2×M16×C47C2312yes—
100C22×C8×C47—22no—
101C22×C8×C47C2312yes—
102C4×Q8×C47C2×C411yescharacteristic
103C4×Q8×C47C2×C411yescharacteristic
104C4×D4×C47—21no—
105C4×D4×C47—21no—
106C4×D4×C47C2×C411yescharacteristic
107C4×D4×C47C2×C411yescharacteristic
108#117×C47—21no—
109#117×C47C2311yescharacteristic
110C2×C42×C47—21no—
111C2×C42×C47C2311yescharacteristic
112#97×C47—22no—
113#97×C47—21no—
114C4×C8×C47—22no—
115C4×C8×C47—21no—
116C4×C8×C47D411yescharacteristic
117C4×C8×C47D411yescharacteristic
118C4×C8×C47D412yes—
119#41×C47—22no—
120#41×C47#4114yes—
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—22no—
134C2×D188C22×C411yescharacteristic
135C2×C4×D47—21no—
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×Dic94C22×C411yescharacteristic
139M16×C47—28no—
140M16×C47—22no—
141M16×C47#4114yes—
142C2×C8×C47—28no—
143C2×C8×C47—22no—
144C2×C8×C47—22no—
145C2×C8×C47—22no—
146C2×C8×C47C2×D412yes—
147C2×C8×C47C2×D412yes—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47C22×C411yescharacteristic
151C4⋊C4×C47C22×C411yescharacteristic
152C22⋊C4×C47—21no—
153C22⋊C4×C47—21no—
154C22⋊C4×C47—21no—
155C42×C47—21no—
156C42×C47—21no—
157C42×C47—21no—
158C42×C47C22×C411yescharacteristic
159C42×C47C22×C411yescharacteristic
160C42×C47C2×D411yescharacteristic
161C42×C47C2×D411yescharacteristic
162C22⋊Dic47—21no—
163#10625337—22no—
164#10625336—22no—
165#10625335—22no—
166#10625334—22no—
167(C2×D47)⋊C4—21no—
168(C2×D47)⋊C4—21no—
169C4⋊Dic47C22×C411yescharacteristic
170C4⋊Dic47C22×C411yescharacteristic
171Dic47⋊C4—21no—
172Dic47⋊C4—21no—
173C4×Dic47—24no—
174C4×Dic47—21no—
175C4×Dic47—21no—
176C4×Dic47—21no—
177C4×Dic47—22no—
178C4×Dic47—22no—
179C4×Dic47—42no—
180#10625329—22no—
181#10625329—22no—
182C2×C47⋊C8—22no—
183C2×C47⋊C8—22no—
184C2×C47⋊C8—22no—
185C2×C47⋊C8C22×C411yescharacteristic
186C2×C47⋊C8C22×C411yescharacteristic
187C2×C47⋊C8C22×C411yescharacteristic
188C2×C47⋊C8C22×C411yescharacteristic
189C23×C47—21no—
190C23×C47C2×#4111yescharacteristic
191C22×D47—21no—
192Q8×C47—21no—
193Q8×C47#11712yes—
194D4×C47—24no—
195D4×C47—21no—
196D4×C47#11712yes—
197C2×C4×C47—21no—
198C2×C4×C47—24no—
199C2×C4×C47—22no—
200C2×C4×C47—22no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
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—42no—
214C2×Dic47—24no—
215C2×Dic47—21no—
216C2×Dic47—21no—
217C2×Dic47—21no—
218C2×Dic47—42no—
219C2×Dic47—42no—
220D188—21no—
221D188—21no—
222C4×D47—42no—
223C4×D47—42no—
224C4×D47—42no—
225Dic94—21no—
226Dic94—21no—
227C8×C47—22no—
228C8×C47—24no—
229C8×C47—22no—
230C47⋊C8—21no—
231C47⋊C8—21no—
232C47⋊C8—21no—
233C47⋊C8—21no—
234C47⋊C8—42no—
235#21137—471nomaximal, Sylow
236C22×C47—21no—
237C22×C47—21no—
238C22×C47—22no—
239C22×C47—41no—
240C22×C47—41no—
241C22×C47C2×C4×D411yescharacteristic
242C22×C47#52912yes—
243C2×D47—41no—
244C2×D47—41no—
245C2×D47—41no—
246C4×C47—21no—
247C4×C47—21no—
248C4×C47—22no—
249C4×C47—41no—
250C4×C47—41no—
251C4×C47#44312yes—
252C4×C47#44412yes—
253C4×C47C2×#11711yescharacteristic
254C4×C47C4×#4111yescharacteristic
255C4×C47#52512yes—
256Dic47—44no—
257Dic47—41no—
258Dic47—41no—
259Dic47—41no—
260C4×#135—471no—
261#2922—471no—
262C4×#131D4711yescharacteristic, complemented
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—42no—
273C2×C47#229011yescharacteristic
274C2×C47C2×#44311yescharacteristic
275C2×C47C2×#44411yescharacteristic
276D47—81no—
277C2×#135—471no—
278C2×#131C2×D4712yes—
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—942no—
290#431—941no—
291#431—941no—
292C2×#108—472no—
293#427—471no—
294#424—472no—
295C2×#104—472no—
296C2×#104—472no—
297#416—471no—
298#416—471no—
299#408—472no—
300#405—22no—
301#405C2×D4712yes—
302C4×M16—21no—
303C4×M16—471no—
304C4×M16C2×D4711yescharacteristic
305C2×C4×C8—21no—
306C2×C4×C8—471no—
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—24no—
323#131—24no—
324C2×M16—22no—
325C2×M16—472no—
326C2×M16C22×D4712yes—
327C22×C8—22no—
328C22×C8—471no—
329C22×C8—471no—
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—942no—
359C4⋊C8—942no—
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—942no—
371C22⋊C8—942no—
372#97—22no—
373#97—21no—
374#97—941no—
375C4×C8—22no—
376C4×C8—21no—
377C4×C8—471no—
378C4×C8—471no—
379C4×C8—471no—
380C4×C8—471no—
381C4×C8—941no—
382C4×C8C22⋊D4712yes—
383C4×C8C22⋊D4711yescharacteristic
384C4×C8C22⋊D4711yescharacteristic
385#41—22no—
386#41—942no—
387#41—942no—
388#41#1062535014yes—
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—942no—
399C22×C4—941no—
400C22×C4—941no—
401C22×C4—941no—
402C22×C4#1062535011yescharacteristic
403C22×C4#1062535011yescharacteristic
404C22×C4C23×D4711yescharacteristic
405Q16—942no—
406SD16—942no—
407SD16—942no—
408D8—942no—
409M16—28no—
410M16—22no—
411M16—942no—
412M16—942no—
413M16#1062535014yes—
414C2×C8—28no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—471no—
419C2×C8—471no—
420C2×C8—471no—
421C2×C8—471no—
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—941no—
460Q8—941no—
461Q8#1309398112yes—
462D4—24no—
463D4—21no—
464D4—941no—
465D4—941no—
466D4—1882no—
467D4#1309398112yes—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—944no—
477C2×C4—941no—
478C2×C4—941no—
479C2×C4—941no—
480C2×C4—1882no—
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×C4C2×#1062535012yes—
492C2×C4C2×#1062535012yes—
493C8—22no—
494C8—24no—
495C8—22no—
496C8—941no—
497C8—941no—
498C8—941no—
499C8—941no—
500C8—1882no—
501C22—21no—
502C22—21no—
503C22—22no—
504C22—41no—
505C22—41no—
506C22—1881no—
507C22—1881no—
508C22—1881no—
509C22C2×C4×C22⋊D4711yescharacteristic
510C22#1568965712yes—
511C4—22no—
512C4—21no—
513C4—21no—
514C4—41no—
515C4—41no—
516C4—1884no—
517C4—1881no—
518C4—1881no—
519C4—1881no—
520C4#1568923812yes—
521C4#1568924312yes—
522C4C2×#1309398111yescharacteristic
523C4C4×#1062535011yescharacteristic
524C4#1568963412yes—
525C2—22no—
526C2—42no—
527C2—3761no—
528C2#2024583111yescharacteristic
529C2C2×#1568923811yescharacteristic
530C2C2×#1568924311yescharacteristic
subgroupG/H
centerC42C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#131×C47C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094044C22
cosocleC22×C4×C47C24
hypercenterC4×#131D47
hypocenterC47#21137
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #20252030C2semidirect
3. #20244036C2semidirect
4. #20243987C2semidirect
6. #20243663C2semidirect
7. C4×#13093959C2semidirect
8. C4×#13093950C2semidirect
9. C4×#13093951C2semidirect
10. #20243133C2semidirect
11. C4×#131×C47C2semidirect
14. C4×#10625337C4semidirect
15. C4×#10625337C4semidirect
16. C4×#10625336C4semidirect
17. C4×#10625336C4semidirect
18. C4×#10625335C4semidirect
19. C4×#10625335C4semidirect
20. C4×#10625334C4semidirect
21. C4×#10625334C4semidirect
262. C4×#131D47semidirect
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
#202520302
#202440362
#202439872
#202437152
#202436632
C4×#130939592
C4×#130939502
C4×#130939512
#202431332
C4×#131×C472
#2113747