Finite Group Databasebeta

← #26186908

Subgroups — #26186908

Order 12032.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253977C211yesmaximal, characteristic
2#20252539C211yesmaximal, characteristic, complemented
3#20242300C211yesmaximal, characteristic, complemented
4#20242290C211yesmaximal, characteristic, complemented
5#20242276C211yesmaximal, characteristic, complemented
6#20242271C211yesmaximal, characteristic, complemented
7#20242210C211yesmaximal, characteristic, complemented
8#20242200C211yesmaximal, characteristic, complemented
9C8×#10625335C211yesmaximal, characteristic, complemented
10C8×#10625334C211yesmaximal, characteristic, complemented
11#20242156C211yesmaximal, characteristic, complemented
12#20241846C211yesmaximal, characteristic, complemented
13#20241839C211yesmaximal, characteristic, complemented
14#20241669C211yesmaximal, characteristic, complemented
15C47×#2981C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689529C411yescharacteristic
18#15689510C411yescharacteristic
19#15689487C411yescharacteristic
20#15689485C411yescharacteristic
21#15689374C411yescharacteristic
22#15689374C411yescharacteristic
23#15689367C411yescharacteristic
24#15689367C411yescharacteristic
25#15689253C2211yescharacteristic
26C8×Dic94C2211yescharacteristic
27C4×#10625335C2211yescharacteristic
28C4×#10625335C2211yescharacteristic
29C4×#10625334C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689202C2211yescharacteristic
32#15689198—21no—
33#15689197—21no—
34C8×D188C2211yescharacteristic
35#15689183—21no—
36#15689148—21no—
37#15689147C2211yescharacteristic
38C4×#10625329C2211yescharacteristic
39C2×C4×C47⋊C8C2211yescharacteristic
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44#15688853C2211yescharacteristic
45#15688853C2211yescharacteristic
46D4⋊(C47⋊C8)C2211yescharacteristic
47D4⋊(C47⋊C8)C2211yescharacteristic
48D4⋊(C47⋊C8)C2211yescharacteristic
49D4⋊(C47⋊C8)C2211yescharacteristic
50#15688850C2211yescharacteristic
51#15688850C2211yescharacteristic
52#15688845C2211yescharacteristic
53#15688845C2211yescharacteristic
54C8×C47⋊C8C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C47×#532C2211yescharacteristic
57C47×#436C2211yescharacteristic
58C47×#436C2211yescharacteristic
59C47×#435—21no—
60C47×#435—21no—
61C8×D4×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#432C2211yescharacteristic
64C47×#431C2211yescharacteristic
65C47×#408—21no—
66C47×#408—21no—
67C2×#10625335C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625334C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625329C2×C411yescharacteristic
73C2×#10625329C2×C411yescharacteristic
74C2×#10625324—21no—
75C22×C47⋊C8—21no—
76C2×C8×D47—21no—
77#13094018—21no—
78#13094016C2×C411yescharacteristic
79#13094012C2×C411yescharacteristic
80#13094007—21no—
81#13094003C2×C411yescharacteristic
82#13093998C2×C411yescharacteristic
83C4×Dic94C2311yescharacteristic
84C4×D188C2311yescharacteristic
85C4×C22⋊D47—21no—
86#13093981—21no—
87#13093957C2×C411yescharacteristic
88#13093957C2×C411yescharacteristic
89#13093955C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91C4⋊(C47⋊C8)—21no—
92C4⋊(C47⋊C8)C2311yescharacteristic
93C4⋊(C47⋊C8)C2311yescharacteristic
94Dic47⋊C8—21no—
95Dic47⋊C8—21no—
96#13093947C2×C411yescharacteristic
97#13093947C2×C411yescharacteristic
98#13093945C2×C411yescharacteristic
99#13093945C2×C411yescharacteristic
100#13093945C2×C411yescharacteristic
101#13093945C2×C411yescharacteristic
102#13093944C2×C411yescharacteristic
103#13093944C2×C411yescharacteristic
104(C2×D47)⋊C8—21no—
105(C2×D47)⋊C8—21no—
106#13093935C2×C411yescharacteristic
107#13093935C2×C411yescharacteristic
108#13093934—21no—
109C4×C47⋊C8—21no—
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C4×C47⋊C8C2311yescharacteristic
114C8×Dic47—21no—
115C2×#41×C47—21no—
116C2×M16×C47—21no—
117C2×M16×C47—21no—
118C22×C8×C47—21no—
119C22×C8×C47—21no—
120C4⋊Q8×C47C2×C411yescharacteristic
121#127×C47C2×C411yescharacteristic
122#124×C47—21no—
123#121×C47—21no—
124#121×C47C2×C411yescharacteristic
125#121×C47C2×C411yescharacteristic
126C4×D4×C47—21no—
127C4×D4×C47C2311yescharacteristic
128C4×D4×C47C2311yescharacteristic
129C2×C42×C47C2311yescharacteristic
130C4⋊C8×C47D411yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136C22⋊C8×C47—21no—
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C22⋊C8×C47D411yescharacteristic
140C22⋊C8×C47D411yescharacteristic
141#97×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—81no—
145#41×C47—81no—
146C2×Q8×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47C22×C411yescharacteristic
152C2×D4×C47C22×C411yescharacteristic
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47#4111yescharacteristic
158C2×C22⋊D47—21no—
159C2×D188C22×C411yescharacteristic
160C2×C4×D47—21no—
161C2×Dic94C22×C411yescharacteristic
162M16×C47—81no—
163M16×C47—81no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—81no—
167C2×C8×C47—81no—
168C2×C8×C47C2×D411yescharacteristic
169C2×C8×C47C2×D411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C22⋊C4×C47—21no—
176C22⋊C4×C47—21no—
177C22⋊C4×C47—21no—
178C22⋊C4×C47—21no—
179C42×C47C22×C411yescharacteristic
180C42×C47C2×D411yescharacteristic
181C42×C47#4111yescharacteristic
182C42×C47C2411yescharacteristic
183C22⋊Dic47—21no—
184#10625335—22no—
185#10625335—22no—
186#10625334—22no—
187#10625334—22no—
188(C2×D47)⋊C4—21no—
189(C2×D47)⋊C4—21no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—21no—
192C4⋊Dic47C22×C411yescharacteristic
193C4⋊Dic47C22×C411yescharacteristic
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196Dic47⋊C4—21no—
197Dic47⋊C4—21no—
198C4×Dic47—21no—
199#10625329—22no—
200#10625329—22no—
201#10625329—81no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—42no—
207C2×C47⋊C8C22×C411yescharacteristic
208C2×C47⋊C8C22×C411yescharacteristic
209C2×C47⋊C8C22×C411yescharacteristic
210C2×C47⋊C8C22×C411yescharacteristic
211#10625324—81no—
212C8×D47—81no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47C4×D411yescharacteristic
216C22×D47—21no—
217Q8×C47—81no—
218D4×C47—21no—
219D4×C47—21no—
220D4×C47—21no—
221D4×C47—21no—
222D4×C47—81no—
223D4×C47—81no—
224D4×C47—81no—
225D4×C47—81no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47C4×D411yescharacteristic
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C23×C411yescharacteristic
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C22⋊D47—81no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247D188—21no—
248D188—21no—
249C4×D47—41no—
250C4×D47—41no—
251Dic94—21no—
252Dic94—21no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—41no—
258C8×C47—41no—
259C47⋊C8—22no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—41no—
263C47⋊C8—41no—
264C47⋊C8—41no—
265C47⋊C8#13112yes—
266C47⋊C8#13112yes—
267#17968—471nomaximal, Sylow
268C22×C47—21no—
269C22×C47—21no—
270C22×C47—21no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47C2×C4×D411yescharacteristic
278C2×D47—41no—
279C2×D47—41no—
280C2×D47—41no—
281C4×C47—21no—
282C4×C47—21no—
283C4×C47—21no—
284C4×C47—21no—
285C4×C47—41no—
286C4×C47—41no—
287C4×C47C2×#13111yescharacteristic
288C4×C47C2×#13111yescharacteristic
289C4×C47#57611yescharacteristic
290C4×C47#57711yescharacteristic
291Dic47—41no—
292Dic47—41no—
293Dic47—41no—
294#3171—471no—
295#2993—471no—
296#2981D4711yescharacteristic, complemented
297#1594—471no—
298#1592—471no—
299#1590—471no—
300#1589—471no—
301#1580—471no—
302SD16⋊C8—471no—
303C8×SD16—471no—
304C8×D8—471no—
305#1569—471no—
306#1494—471no—
307#1492—471no—
308C8×M16—471no—
309C2×C47—41no—
310C2×C47—81no—
311C2×C47—81no—
312C2×C47#293111yescharacteristic
313C2×C47#294611yescharacteristic
314C2×C47#295611yescharacteristic
315D47—81no—
316#532C2×D4711yescharacteristic
317#529—471no—
318#501—471no—
319#496—471no—
320#490—471no—
321#489—471no—
322#469—471no—
323#469—471no—
324#468—471no—
325#468—471no—
326#446—471no—
327C8×Q8—471no—
328C4×SD16—471no—
329C4×SD16—471no—
330C4×D8—471no—
331C4×D8—471no—
332#436—471no—
333#436—941no—
334#436C2×D4711yescharacteristic
335#436C2×D4711yescharacteristic
336#435—21no—
337#435—21no—
338#435—941no—
339C8×D4—471no—
340C8×D4C2×D4711yescharacteristic
341C8×D4C2×D4711yescharacteristic
342#433—941no—
343#432C2×D4711yescharacteristic
344#431C2×D4711yescharacteristic
345#424—941no—
346#423—471no—
347#408—21no—
348#408—21no—
349C4×M16—471no—
350C2×C4×C8—471no—
351#335—471no—
352#335—471no—
353#334—471no—
354#334—471no—
355Q8⋊C8—471no—
356Q8⋊C8—471no—
357D4⋊C8—471no—
358D4⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363#322—471no—
364#322—471no—
365C82—471no—
366C82—471no—
367C47#1796811yescharacteristic, complemented, Sylow
368C2×#41—21no—
369C2×SD16—471no—
370C2×SD16—471no—
371C2×D8—471no—
372C2×D8—471no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—471no—
376C2×M16—471no—
377C2×M16—941no—
378C2×M16—941no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—941no—
382C22×C8—941no—
383C4⋊Q8C4×D4711yescharacteristic
384#127C4×D4711yescharacteristic
385#126—941no—
386#125—471no—
387#124—21no—
388#124—471no—
389#123—941no—
390C22⋊Q8—471no—
391#121—21no—
392#121—471no—
393#121C4×D4711yescharacteristic
394#121C4×D4711yescharacteristic
395C4×Q8—471no—
396C4×D4—21no—
397C4×D4—471no—
398C4×D4—941no—
399C4×D4C22×D4711yescharacteristic
400C4×D4C22×D4711yescharacteristic
401#117—941no—
402C2×C42C22×D4711yescharacteristic
403#107—471no—
404#107—471no—
405#106—471no—
406#106—471no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—941no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8C22⋊D4711yescharacteristic
413C4⋊C8C22⋊D4711yescharacteristic
414C4⋊C8C22×D4711yescharacteristic
415C4⋊C8C22×D4711yescharacteristic
416#103—471no—
417#103—471no—
418#102—471no—
419#102—471no—
420#102—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—941no—
430C22⋊C8—941no—
431C22⋊C8C22⋊D4711yescharacteristic
432C22⋊C8C22⋊D4711yescharacteristic
433#97—21no—
434#97—471no—
435#97—471no—
436#97—941no—
437C4×C8—471no—
438C4×C8—471no—
439C4×C8—471no—
440C4×C8—471no—
441C4×C8—941no—
442C4×C8—941no—
443C4×C8C22×D4711yescharacteristic
444C4×C8C22×D4711yescharacteristic
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—471no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—471no—
454C2×D4—941no—
455C2×D4C2×C4×D4711yescharacteristic
456C2×D4C2×C4×D4711yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—941no—
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4#1062535011yescharacteristic
462C22×C4C2×C22⋊D4711yescharacteristic
463SD16—942no—
464SD16—942no—
465D8—942no—
466D8—942no—
467M16—81no—
468M16—81no—
469M16—942no—
470M16—942no—
471M16—3761no—
472M16—3761no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—471no—
478C2×C8—471no—
479C2×C8—471no—
480C2×C8—471no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—941no—
485C2×C8—3761no—
486C2×C8—1882no—
487C2×C8C2×C22⋊D4711yescharacteristic
488C2×C8C2×C22⋊D4711yescharacteristic
489C2×C8C2×C22⋊D4711yescharacteristic
490C2×C8C2×C22⋊D4711yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—471no—
493C4⋊C4—471no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4C2×C4×D4711yescharacteristic
499C4⋊C4C2×C4×D4711yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—941no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4—941no—
508C22⋊C4—941no—
509C42—941no—
510C42C2×C4×D4711yescharacteristic
511C42#1062535011yescharacteristic
512C42C2×C22⋊D4711yescharacteristic
513C42C23×D4711yescharacteristic
514C23—21no—
515C23—21no—
516C23—941no—
517C23C4×C22⋊D4711yescharacteristic
518Q8—81no—
519Q8—941no—
520Q8—941no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—941no—
530D4—941no—
531D4—3761no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—941no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4C4×C22⋊D4711yescharacteristic
549C2×C4C4×C22⋊D4711yescharacteristic
550C2×C4C4×C22⋊D4711yescharacteristic
551C2×C4C22×C4×D4711yescharacteristic
552C2×C4C22×C22⋊D4711yescharacteristic
553C2×C4C2×#1062535011yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—472no—
561C8—472no—
562C8—942no—
563C8—941no—
564C8—941no—
565C8—1881no—
566C8—1881no—
567C8—1881no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—1881no—
578C22—1881no—
579C22—1881no—
580C22C2×C4×C22⋊D4711yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—1881no—
588C4—1881no—
589C4—1881no—
590C4#131×D4711yescharacteristic
591C4#131×D4711yescharacteristic
592C4#1568992611yescharacteristic
593C4#1568993411yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—3761no—
598C2#2025209811yescharacteristic
599C2#2025222011yescharacteristic
600C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2981C2
socleC22×C47C2×C4×D4
prime radical#20253977C2
cosocleC42×C47C24
hypercenter#2981D47
hypocenterC47#17968
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #20252539C2semidirect
3. #20242300C2semidirect
4. #20242290C2semidirect
5. #20242276C2semidirect
6. #20242271C2semidirect
7. #20242210C2semidirect
8. #20242200C2semidirect
9. C8×#10625335C2semidirect
10. C8×#10625334C2semidirect
11. #20242156C2semidirect
12. #20241846C2semidirect
13. #20241839C2semidirect
14. #20241669C2semidirect
15. C47×#2981C2semidirect
296. #2981D47semidirect
367. C47#17968semidirect

Maximal subgroups

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

subgroupindex
#202539772
#202525392
#202423002
#202422902
#202422762
#202422712
#202422102
#202422002
C8×#106253352
C8×#106253342
#202421562
#202418462
#202418392
#202416692
C47×#29812
#1796847