Finite Group Databasebeta

← #26186904

Subgroups — #26186904

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#20253984C211yesmaximal, characteristic
2#20252463C211yesmaximal, characteristic, complemented
3#20242300C211yesmaximal, characteristic, complemented
4#20242288C211yesmaximal, characteristic, complemented
5#20242278C211yesmaximal, characteristic, complemented
6#20242271C211yesmaximal, characteristic, complemented
7#20242210C211yesmaximal, characteristic, complemented
8#20242198C211yesmaximal, characteristic, complemented
9C8×#10625336C211yesmaximal, characteristic, complemented
10C8×#10625334C211yesmaximal, characteristic, complemented
11#20242153C211yesmaximal, characteristic, complemented
12#20241848C211yesmaximal, characteristic, complemented
13#20241838C211yesmaximal, characteristic, complemented
14#20241669C211yesmaximal, characteristic, complemented
15C47×#2993C211yesmaximal, characteristic, complemented
16#15689673C2211yescharacteristic
17#15689533C411yescharacteristic
18#15689513C411yescharacteristic
19#15689489C411yescharacteristic
20#15689482C411yescharacteristic
21#15689374C411yescharacteristic
22#15689374C411yescharacteristic
23#15689371C411yescharacteristic
24#15689371C411yescharacteristic
25C4×#10625336C2211yescharacteristic
26C4×#10625336C2211yescharacteristic
27C4×#10625334C2211yescharacteristic
28C4×#10625334C2211yescharacteristic
29#15689202C2211yescharacteristic
30#15689202C2211yescharacteristic
31#15689193—21no—
32#15689193—21no—
33C8×D188C2211yescharacteristic
34C8×D188C2211yescharacteristic
35#15689180C2211yescharacteristic
36#15689088—21no—
37#15689088—21no—
38C4×#10625329C2211yescharacteristic
39C2×C4×C47⋊C8C2211yescharacteristic
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46D4⋊(C47⋊C8)C2211yescharacteristic
47D4⋊(C47⋊C8)C2211yescharacteristic
48#15688850C2211yescharacteristic
49#15688850C2211yescharacteristic
50#15688850C2211yescharacteristic
51#15688850C2211yescharacteristic
52#15688845C2211yescharacteristic
53#15688845C2211yescharacteristic
54C8×C47⋊C8C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C47×#529C2211yescharacteristic
57C47×#446C2211yescharacteristic
58C8×Q8×C47C2211yescharacteristic
59C47×#436—21no—
60C47×#436C2211yescharacteristic
61C47×#435—21no—
62C8×D4×C47C2211yescharacteristic
63C47×#433—21no—
64C47×#431C2211yescharacteristic
65C47×#424—21no—
66C47×#423C2211yescharacteristic
67C2×#10625350—21no—
68C2×#10625336C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625329C2×C411yescharacteristic
73C2×#10625329C2×C411yescharacteristic
74C2×#10625324—21no—
75C2×#10625324—21no—
76C22×C47⋊C8—21no—
77C2×C8×D47—21no—
78C2×C8×D47—21no—
79#13094024C2×C411yescharacteristic
80#13094021C2×C411yescharacteristic
81#13094012—21no—
82#13093998—21no—
83#13093998C2×C411yescharacteristic
84#13093998C2×C411yescharacteristic
85C4×D188—21no—
86C4×D188C2311yescharacteristic
87C4×D188C2311yescharacteristic
88#13093957C2×C411yescharacteristic
89#13093957C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91#13093955C2×C411yescharacteristic
92C4⋊(C47⋊C8)C2311yescharacteristic
93C4⋊(C47⋊C8)C2311yescharacteristic
94#13093948C2×C411yescharacteristic
95#13093948C2×C411yescharacteristic
96#13093945C2×C411yescharacteristic
97#13093945C2×C411yescharacteristic
98#13093944C2×C411yescharacteristic
99#13093944C2×C411yescharacteristic
100#13093944C2×C411yescharacteristic
101#13093944C2×C411yescharacteristic
102C22⋊(C47⋊C8)—21no—
103(C2×D47)⋊C8—21no—
104(C2×D47)⋊C8—21no—
105(C2×D47)⋊C8—21no—
106(C2×D47)⋊C8—21no—
107#13093935—21no—
108#13093935C2×C411yescharacteristic
109#13093935C2×C411yescharacteristic
110C4×C47⋊C8—21no—
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C4×C47⋊C8C2311yescharacteristic
114C4×C47⋊C8C2311yescharacteristic
115C2×M16×C47—21no—
116C2×M16×C47—21no—
117C22×C8×C47—21no—
118#126×C47—21no—
119#125×C47C2×C411yescharacteristic
120#124×C47C2×C411yescharacteristic
121#123×C47—21no—
122C22⋊Q8×C47C2×C411yescharacteristic
123#121×C47C2×C411yescharacteristic
124C4×Q8×C47C2311yescharacteristic
125C4×D4×C47—21no—
126C4×D4×C47C2311yescharacteristic
127#117×C47—21no—
128C2×C42×C47C2311yescharacteristic
129C4⋊C8×C47—21no—
130C4⋊C8×C47—21no—
131C4⋊C8×C47—21no—
132C4⋊C8×C47D411yescharacteristic
133C4⋊C8×C47D411yescharacteristic
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C22⋊C8×C47—21no—
137C22⋊C8×C47—21no—
138C22⋊C8×C47D411yescharacteristic
139C22⋊C8×C47D411yescharacteristic
140#97×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×D4×C47—21no—
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47#4111yescharacteristic
151C2×C22⋊D47—21no—
152C2×C22⋊D47—21no—
153#10625350—81no—
154#10625350—81no—
155C2×D188—21no—
156C2×D188—21no—
157C2×D188C22×C411yescharacteristic
158C2×D188C22×C411yescharacteristic
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×Dic94—21no—
162M16×C47—81no—
163M16×C47—81no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—81no—
167C2×C8×C47C2×D411yescharacteristic
168C2×C8×C47C2×D411yescharacteristic
169C2×C8×C47C2×D411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47C22×C411yescharacteristic
176C4⋊C4×C47C22×C411yescharacteristic
177C22⋊C4×C47—21no—
178C22⋊C4×C47—21no—
179C22⋊C4×C47—21no—
180C22⋊C4×C47—21no—
181C22⋊C4×C47—21no—
182C42×C47—21no—
183C42×C47C22×C411yescharacteristic
184C42×C47C2×D411yescharacteristic
185C42×C47#4111yescharacteristic
186C42×C47C2411yescharacteristic
187#10625336—22no—
188#10625336—22no—
189#10625334—22no—
190#10625334—22no—
191(C2×D47)⋊C4—21no—
192(C2×D47)⋊C4—21no—
193(C2×D47)⋊C4—21no—
194(C2×D47)⋊C4—21no—
195C4⋊Dic47—21no—
196C4⋊Dic47C22×C411yescharacteristic
197C4⋊Dic47C22×C411yescharacteristic
198#10625329—22no—
199#10625329—22no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—42no—
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208C2×C47⋊C8C22×C411yescharacteristic
209#10625324—81no—
210#10625324—81no—
211C8×D47—81no—
212C8×D47—81no—
213C23×C47—21no—
214C23×C47C4×D411yescharacteristic
215C22×D47—21no—
216C22×D47—21no—
217Q8×C47—21no—
218Q8×C47—21no—
219D4×C47—21no—
220D4×C47—21no—
221D4×C47—81no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47C4×D411yescharacteristic
233C2×C4×C47C4×D411yescharacteristic
234C2×C4×C47C4×D411yescharacteristic
235C2×C4×C47C23×C411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C22⋊D47—81no—
239C22⋊D47—81no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242D188—21no—
243D188—21no—
244D188—21no—
245D188—21no—
246D188—81no—
247D188—81no—
248C4×D47—41no—
249C4×D47—41no—
250C4×D47—41no—
251C4×D47—41no—
252Dic94—81no—
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×C47C2×C4×D411yescharacteristic
275C2×D47—41no—
276C2×D47—41no—
277C2×D47—41no—
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×C47—41no—
288C4×C47C2×#13111yescharacteristic
289C4×C47C2×#13111yescharacteristic
290C4×C47#57611yescharacteristic
291C4×C47#57711yescharacteristic
292Dic47—41no—
293Dic47—41no—
294#3171—471no—
295#2993D4711yescharacteristic, complemented
296#2981—471no—
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#293111yescharacteristic
312C2×C47#294611yescharacteristic
313C2×C47#295611yescharacteristic
314D47—81no—
315D47—81no—
316#532—471no—
317#529C2×D4711yescharacteristic
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#446C2×D4711yescharacteristic
327C8×Q8C2×D4711yescharacteristic
328C4×SD16—471no—
329C4×SD16—471no—
330C4×D8—471no—
331C4×D8—471no—
332#436—21no—
333#436—471no—
334#436—471no—
335#436C2×D4711yescharacteristic
336#435—21no—
337#435—941no—
338#435—941no—
339C8×D4—471no—
340C8×D4—471no—
341C8×D4C2×D4711yescharacteristic
342#433—21no—
343#432—471no—
344#431C2×D4711yescharacteristic
345#424—21no—
346#423C2×D4711yescharacteristic
347#408—941no—
348#408—941no—
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—941no—
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—941no—
381C22×C8—941no—
382C22×C8—941no—
383C4⋊Q8—471no—
384#127—471no—
385#126—21no—
386#125C4×D4711yescharacteristic
387#124—941no—
388#124C4×D4711yescharacteristic
389#123—21no—
390C22⋊Q8C4×D4711yescharacteristic
391#121—471no—
392#121—471no—
393#121—941no—
394#121C4×D4711yescharacteristic
395C4×Q8C22×D4711yescharacteristic
396C4×D4—21no—
397C4×D4—471no—
398C4×D4—471no—
399C4×D4—941no—
400C4×D4C22×D4711yescharacteristic
401#117—21no—
402C2×C42C22×D4711yescharacteristic
403#107—471no—
404#107—471no—
405#106—471no—
406#106—471no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8—471no—
411C4⋊C8—471no—
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—941no—
427C22⋊C8—941no—
428C22⋊C8—941no—
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—21no—
438C4×C8—471no—
439C4×C8—471no—
440C4×C8—471no—
441C4×C8—471no—
442C4×C8—941no—
443C4×C8C22×D4711yescharacteristic
444C4×C8C22×D4711yescharacteristic
445#41—3761no—
446#41—3761no—
447C2×Q8—941no—
448C2×Q8C2×C4×D4711yescharacteristic
449C2×D4—21no—
450C2×D4—471no—
451C2×D4—471no—
452C2×D4—941no—
453C2×D4—941no—
454C2×D4—941no—
455C2×D4—941no—
456C2×D4C2×C4×D4711yescharacteristic
457C22×C4—21no—
458C22×C4—941no—
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—471no—
477C2×C8—471no—
478C2×C8—471no—
479C2×C8—471no—
480C2×C8—941no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—3761no—
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—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—471no—
496C4⋊C4—471no—
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—21no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4—941no—
508C22⋊C4—941no—
509C42—21no—
510C42C2×C4×D4711yescharacteristic
511C42#1062535011yescharacteristic
512C42C2×C22⋊D4711yescharacteristic
513C42C23×D4711yescharacteristic
514C23—21no—
515C23—941no—
516C23—941no—
517C23C4×C22⋊D4711yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—3761no—
521D4—21no—
522D4—21no—
523D4—81no—
524D4—941no—
525D4—941no—
526D4—941no—
527D4—941no—
528D4—3761no—
529D4—3761no—
530D4—3761no—
531D4—3761no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—941no—
543C2×C4—941no—
544C2×C4—1881no—
545C2×C4—1881no—
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—1881no—
575C22—1881no—
576C22—1881no—
577C22—1881no—
578C22—1881no—
579C22—1881no—
580C22C2×C4×C22⋊D4711yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—1881no—
589C4—1881no—
590C4#131×D4711yescharacteristic
591C4#131×D4711yescharacteristic
592C4#1568992611yescharacteristic
593C4#1568993111yescharacteristic
594C2—41no—
595C2—81no—
596C2—3761no—
597C2—3761no—
598C2#2025209811yescharacteristic
599C2#2025221611yescharacteristic
600C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2993C2
socleC22×C47C2×C4×D4
prime radical#20253984C2
cosocleC42×C47C24
hypercenter#2993D47
hypocenterC47#17968
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #20252463C2semidirect
3. #20242300C2semidirect
4. #20242288C2semidirect
5. #20242278C2semidirect
6. #20242271C2semidirect
7. #20242210C2semidirect
8. #20242198C2semidirect
9. C8×#10625336C2semidirect
10. C8×#10625334C2semidirect
11. #20242153C2semidirect
12. #20241848C2semidirect
13. #20241838C2semidirect
14. #20241669C2semidirect
15. C47×#2993C2semidirect
295. #2993D47semidirect
367. C47#17968semidirect

Maximal subgroups

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

subgroupindex
#202539842
#202524632
#202423002
#202422882
#202422782
#202422712
#202422102
#202421982
C8×#106253362
C8×#106253342
#202421532
#202418482
#202418382
#202416692
C47×#29932
#1796847