Finite Group Databasebeta

← #26257576

Subgroups — #26257576

Order 12032.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689404C211yesmaximal, characteristic, complemented
2#20251740C211yesmaximal, characteristic, complemented
3C4×#13093998C211yesmaximal, characteristic
4#20244816C212yesmaximal, complemented
5#20244578C212yesmaximal
6#20244339C211yesmaximal, characteristic, complemented
7#20244152C211yesmaximal, characteristic, complemented
8#20244131C212yesmaximal, complemented
9#20244085C212yesmaximal, complemented
10#20243389C211yesmaximal, characteristic, complemented
11C2×C47×#432C211yesmaximal, characteristic, complemented
12C2×#13094024C2211yescharacteristic
13C2×#13094003—21no—
14C2×#13093998C2211yescharacteristic
15C2×C4×D188C2211yescharacteristic
16C2×C4×C22⋊D47—21no—
17#15689404—24no—
18C2×#13093958C2212yes—
19C2×#13093956C2212yes—
20C2×#13093946C2212yes—
21C2×#13093946C2212yes—
22#15689029—21no—
23#15689025C2211yescharacteristic
24#15689021—21no—
25#15689021C2212yes—
26#15689021C2211yescharacteristic
27#15689014—21no—
28#15689002—21no—
29#15688993C2211yescharacteristic
30#15688983—21no—
31#15688983C2211yescharacteristic
32#15688983C2212yes—
33C4×C4⋊Dic47C2211yescharacteristic
34C4×(C2×D47)⋊C4—21no—
35#15688886C2212yes—
36#15688886C2212yes—
37#15688886C2212yes—
38#15688886C2212yes—
39C22×C42×C47C2211yescharacteristic
40C47×#432—24no—
41C2×C4⋊C8×C47C2211yescharacteristic
42C2×C4⋊C8×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2212yes—
44C2×#97×C47C2212yes—
45C22×Dic94—21no—
46C22×D188C2311yescharacteristic
47C22×C22⋊D47—21no—
48C22×C4×D47—21no—
49#13094024—22no—
50#13094024—22no—
51#13094003—44no—
52#13093998—22no—
53#13093998—22no—
54C4×D188—22no—
55C4×D188—22no—
56C4×C22⋊D47—44no—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47—21no—
59C2×C4⋊Dic47—21no—
60C2×C4⋊Dic47C2311yescharacteristic
61C2×C4⋊Dic47C2312yes—
62C2×C4⋊Dic47C2311yescharacteristic
63C2×C4⋊Dic47C2312yes—
64C2×C4⋊Dic47C2311yescharacteristic
65C2×Dic47⋊C4—21no—
66C2×Dic47⋊C4—22no—
67C2×C22⋊Dic47—22no—
68C2×C22⋊Dic47—21no—
69C2×(C2×D47)⋊C4—21no—
70C2×(C2×D47)⋊C4—21no—
71C2×(C2×D47)⋊C4—21no—
72C2×(C2×D47)⋊C4—21no—
73C2×C4×Dic47—21no—
74#13093958—24no—
75#13093956—24no—
76#13093946—24no—
77#13093946—24no—
78C47⋊#95—21no—
79C47⋊#95—21no—
80C47⋊#95—21no—
81C47⋊#95—22no—
82C47⋊#95—22no—
83C23×C4×C47D411yescharacteristic
84C23×C4×C47D411yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C22×C8×C47C2312yes—
87C22×C8×C47C2312yes—
88C2×C42×C47—22no—
89C2×C42×C47—22no—
90C2×C42×C47D411yescharacteristic
91C2×C42×C47D411yescharacteristic
92C2×C42×C47C2311yescharacteristic
93C2×C42×C47C2311yescharacteristic
94C4⋊C8×C47—22no—
95C4⋊C8×C47D414yescomplemented
96C22⋊C8×C47—24no—
97#97×C47—24no—
98C24×C47C2×D411yescharacteristic
99C23×D47—21no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—41no—
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2411yescharacteristic
118C2×C22⋊D47—24no—
119C2×C22⋊D47—42no—
120C2×C22⋊D47—42no—
121C22×Dic47—21no—
122C22×Dic47—21no—
123C22×Dic47—21no—
124C22×Dic47—22no—
125C22×Dic47—22no—
126C2×D188—21no—
127C2×D188—21no—
128C2×D188—21no—
129C2×D188—21no—
130C2×D188—21no—
131C2×D188#4112yes—
132C2×C4×D47—42no—
133C2×C4×D47—42no—
134C2×C4×D47—42no—
135C2×Dic94—42no—
136C2×Dic94—42no—
137C2×Dic94—42no—
138C2×C8×C47—22no—
139C2×C8×C47—22no—
140C2×C8×C47—22no—
141C2×C8×C47—22no—
142C2×C8×C47—22no—
143C2×C8×C47C2×D414yes—
144C42×C47—22no—
145C42×C47—22no—
146C42×C47—21no—
147C42×C47—21no—
148C42×C47C2×D412yes—
149C42×C47#4112yes—
150C22⋊Dic47—42no—
151C22⋊Dic47—44no—
152(C2×D47)⋊C4—24no—
153(C2×D47)⋊C4—42no—
154(C2×D47)⋊C4—42no—
155(C2×D47)⋊C4—42no—
156C4⋊Dic47—21no—
157C4⋊Dic47—22no—
158C4⋊Dic47—21no—
159C4⋊Dic47—22no—
160C4⋊Dic47—22no—
161C4⋊Dic47—21no—
162C4⋊Dic47—22no—
163C4⋊Dic47—21no—
164C4⋊Dic47—21no—
165C4⋊Dic47—42no—
166C4⋊Dic47—42no—
167C4⋊Dic47—42no—
168C4⋊Dic47#4112yes—
169Dic47⋊C4—42no—
170Dic47⋊C4—44no—
171C4×Dic47—42no—
172C23×C47—21no—
173C23×C47—21no—
174C23×C47—21no—
175C23×C47—21no—
176C23×C47—21no—
177C23×C47—21no—
178C23×C47#13712yes—
179C23×C47C22×D411yescharacteristic
180C22×D47—22no—
181C22×D47—41no—
182C22×D47—41no—
183C22×D47—41no—
184C22×D47—41no—
185C22×D47—41no—
186C22×D47—41no—
187C2×C4×C47—21no—
188C2×C4×C47—21no—
189C2×C4×C47—21no—
190C2×C4×C47—21no—
191C2×C4×C47—21no—
192C2×C4×C47—21no—
193C2×C4×C47—21no—
194C2×C4×C47—21no—
195C2×C4×C47—21no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—44no—
199C2×C4×C47—41no—
200C2×C4×C47—41no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47—44no—
204C2×C4×C47#12112yes—
205C2×C4×C47#12112yes—
206C2×C4×C47AGL(1,ℤ/8)12yes—
207C2×C4×C47AGL(1,ℤ/8)12yes—
208C2×C4×C47C22×D411yescharacteristic
209C2×C4×C47C2×#4111yescharacteristic
210C2×C4×C47C2×#4111yescharacteristic
211C2×C4×C47C2×#4111yescharacteristic
212C2×C4×C472−1+411yescharacteristic
213C2×C4×C472−1+411yescharacteristic
214C22⋊D47—48no—
215C2×Dic47—22no—
216C2×Dic47—41no—
217C2×Dic47—41no—
218C2×Dic47—42no—
219C2×Dic47—41no—
220C2×Dic47—42no—
221C2×Dic47—41no—
222C2×Dic47—41no—
223C2×Dic47—42no—
224C2×Dic47—42no—
225C2×Dic47—41no—
226C2×Dic47—42no—
227C2×Dic47—41no—
228C2×Dic47—42no—
229C2×Dic47—41no—
230D188—22no—
231D188—22no—
232D188—41no—
233D188—41no—
234C4×D47—84no—
235Dic94—84no—
236C8×C47—24no—
237C8×C47—42no—
238#24709—471nomaximal, Sylow
239C22×C47—22no—
240C22×C47—22no—
241C22×C47—22no—
242C22×C47—41no—
243C22×C47—41no—
244C22×C47—41no—
245C22×C47—41no—
246C22×C47C2×#12111yescharacteristic
247C22×C47#52511yescharacteristic
248C22×C47#53611yescharacteristic
249C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C47C2×#13711yescharacteristic
252C22×C47#57511yescharacteristic
253C2×D47—42no—
254C2×D47—42no—
255C2×D47—42no—
256C2×D47—81no—
257C2×D47—81no—
258C2×D47—81no—
259C2×D47—81no—
260C4×C47—22no—
261C4×C47—41no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47#46914yes—
265C4×C47#54711yescharacteristic
266C4×C47#54811yescharacteristic
267C4×C47#55211yescharacteristic
268C4×C47#55611yescharacteristic
269Dic47—42no—
270Dic47—82no—
271Dic47—81no—
272Dic47—82no—
273Dic47—81no—
274C2×#474—471no—
275C2×#432D4711yescharacteristic, complemented
276#2857—471no—
277C4×#121—471no—
278#2076—472no—
279#2034—472no—
280#1988—471no—
281#1948—471no—
282#1944—472no—
283#1936—472no—
284#1802—471no—
285C2×C47—42no—
286C2×C47#241511yescharacteristic
287C2×C47C2×#46911yescharacteristic
288C2×C47#305611yescharacteristic
289C2×C47#311011yescharacteristic
290C2×C47#311511yescharacteristic
291C2×C47#323511yescharacteristic
292C2×C47#323911yescharacteristic
293D47—82no—
294C2×C4⋊Q8—471no—
295C2×C22⋊Q8—941no—
296C2×#121—471no—
297C2×C4×D4—471no—
298C2×C4×D4—941no—
299C22×C42C2×D4711yescharacteristic
300#474—944no—
301#432—24no—
302C2×#107—472no—
303C2×#106—472no—
304C2×C4⋊C8C2×D4711yescharacteristic
305C2×C4⋊C8C2×D4711yescharacteristic
306C2×#102—472no—
307C2×#102—472no—
308C2×C22⋊C8C2×D4712yes—
309C2×#97C2×D4712yes—
310#391—941no—
311#390—471no—
312#389—472no—
313#389—471no—
314#389—941no—
315#388—941no—
316#386—941no—
317#384—471no—
318#380—471no—
319#380—472no—
320#380—941no—
321C4×C4⋊C4—471no—
322C4×C22⋊C4—941no—
323#340—472no—
324#340—472no—
325#340—472no—
326#340—472no—
327C47#2470911yescharacteristic, complemented, Sylow
328C22×Q8—941no—
329C22×D4—471no—
330C22×D4—941no—
331C23×C4—941no—
332C23×C4D18811yescharacteristic
333C23×C4D18811yescharacteristic
334C23×C4C22×D4711yescharacteristic
335C22×C8C22×D4712yes—
336C22×C8C22×D4712yes—
337C4⋊Q8—942no—
338C4⋊Q8—942no—
339C22⋊Q8—1884no—
340#121—942no—
341#121—942no—
342C4×D4—942no—
343C4×D4—942no—
344C4×D4—1884no—
345C2×C4⋊C4—471no—
346C2×C4⋊C4—471no—
347C2×C4⋊C4—472no—
348C2×C4⋊C4—471no—
349C2×C4⋊C4—472no—
350C2×C4⋊C4—941no—
351C2×C4⋊C4—942no—
352C2×C4⋊C4—941no—
353C2×C4⋊C4—941no—
354C2×C4⋊C4—941no—
355C2×C22⋊C4—941no—
356C2×C22⋊C4—941no—
357C2×C22⋊C4—942no—
358C2×C22⋊C4—941no—
359C2×C22⋊C4—941no—
360C2×C22⋊C4—941no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—941no—
364C2×C42D18811yescharacteristic
365C2×C42D18811yescharacteristic
366C2×C42C22×D4711yescharacteristic
367C2×C42C22×D4711yescharacteristic
368#107—944no—
369#106—944no—
370C4⋊C8—22no—
371C4⋊C8C22⋊D4714yescomplemented
372#102—944no—
373#102—944no—
374C22⋊C8—24no—
375#97—24no—
376#95—941no—
377#95—941no—
378#95—941no—
379#95—942no—
380#95—942no—
381C24—941no—
382C24C2×D18811yescharacteristic
383C2×Q8—1882no—
384C2×Q8—1882no—
385C2×Q8—1882no—
386C2×D4—472no—
387C2×D4—944no—
388C2×D4—941no—
389C2×D4—941no—
390C2×D4—941no—
391C2×D4—941no—
392C2×D4—941no—
393C2×D4—1882no—
394C2×D4—1882no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—41no—
407C22×C4—941no—
408C22×C4—941no—
409C22×C4—941no—
410C22×C4—942no—
411C22×C4—942no—
412C22×C4—1882no—
413C22×C4—1882no—
414C22×C4—1882no—
415C22×C4C2×D18811yescharacteristic
416C22×C4C2×D18811yescharacteristic
417C22×C4C2×D18811yescharacteristic
418C22×C4C2×D18811yescharacteristic
419C22×C4C2×D18811yescharacteristic
420C22×C4C23×D4711yescharacteristic
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8C2×C22⋊D4714yes—
427C4⋊C4—472no—
428C4⋊C4—941no—
429C4⋊C4—942no—
430C4⋊C4—941no—
431C4⋊C4—942no—
432C4⋊C4—942no—
433C4⋊C4—941no—
434C4⋊C4—942no—
435C4⋊C4—941no—
436C4⋊C4—941no—
437C4⋊C4—1882no—
438C4⋊C4—1884no—
439C4⋊C4—1882no—
440C4⋊C4—1882no—
441C4⋊C4—1882no—
442C22⋊C4—944no—
443C22⋊C4—1882no—
444C22⋊C4—1882no—
445C22⋊C4—1882no—
446C22⋊C4—1884no—
447C22⋊C4—1882no—
448C42—22no—
449C42—22no—
450C42—21no—
451C42—21no—
452C42—1882no—
453C42#1062535012yes—
454C42C2×C22⋊D4712yes—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—942no—
462C23—1881no—
463C23—1881no—
464C23—1881no—
465C23—1881no—
466C23—1881no—
467C23—1881no—
468C23#1309405712yes—
469C23C22×D18811yescharacteristic
470Q8—3764no—
471D4—942no—
472D4—942no—
473D4—1888no—
474D4—1881no—
475D4—1881no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—44no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—44no—
493C2×C4—942no—
494C2×C4—3764no—
495C2×C4—1881no—
496C2×C4—1882no—
497C2×C4—1882no—
498C2×C4—1881no—
499C2×C4—1882no—
500C2×C4—1881no—
501C2×C4—1882no—
502C2×C4—1881no—
503C2×C4—1882no—
504C2×C4—1881no—
505C2×C4—1882no—
506C2×C4—1881no—
507C2×C4—1881no—
508C2×C4—1881no—
509C2×C4#1309399812yes—
510C2×C4#1309399812yes—
511C2×C4#1309405212yes—
512C2×C4#1309405212yes—
513C2×C4C22×C22⋊D4711yescharacteristic
514C2×C4#41×D4711yescharacteristic
515C2×C4#41×D4711yescharacteristic
516C2×C4C2×#1062535011yescharacteristic
517C2×C4#1309407111yescharacteristic
518C2×C4#1309407111yescharacteristic
519C8—24no—
520C8—42no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—3761no—
529C22—3761no—
530C22—3761no—
531C22—3761no—
532C22—1882no—
533C22—1882no—
534C22—1882no—
535C22C2×#1309399811yescharacteristic
536C22#1568963511yescharacteristic
537C22#1568969911yescharacteristic
538C22C2×#1309405211yescharacteristic
539C22C2×#1309405211yescharacteristic
540C22C2×#1309405711yescharacteristic
541C22#1568992311yescharacteristic
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—3761no—
547C4—3762no—
548C4—3762no—
549C4—3761no—
550C4—1882no—
551C4#1568937614yes—
552C4#1568977211yescharacteristic
553C4#1568978011yescharacteristic
554C4#1568981211yescharacteristic
555C4#1568984111yescharacteristic
556C2—42no—
557C2—3762no—
558C2#2024681111yescharacteristic
559C2C2×#1568937611yescharacteristic
560C2#2025301811yescharacteristic
561C2#2025348811yescharacteristic
562C2#2025354011yescharacteristic
563C2#2025458811yescharacteristic
564C2#2025462011yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#432C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC2×#432D47
hypocenterC47#24709
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#15689404C2semidirect
2. #20251740C2semidirect
4. #20244816C2semidirect
6. #20244339C2semidirect
7. #20244152C2semidirect
8. #20244131C2semidirect
9. #20244085C2semidirect
10. #20243389C2semidirect
11. C2×C47×#432C2semidirect
95. C4⋊C8×C47D4semidirect
275. C2×#432D47semidirect
327. C47#24709semidirect
371. C4⋊C8C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156894042
#202517402
C4×#130939982
#202448162
#202445782
#202443392
#202441522
#202441312
#202440852
#202433892
C2×C47×#4322
#2470947