Finite Group Databasebeta

← #26228580

Subgroups — #26228580

Order 12032.

648 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253174C211yesmaximal, characteristic
2#20252321C211yesmaximal, characteristic, complemented
3#20252031C211yesmaximal, characteristic
4#20244330C211yesmaximal, characteristic, complemented
5#20244160C211yesmaximal, characteristic, complemented
6#20244133C211yesmaximal, characteristic, complemented
7#20244092C211yesmaximal, characteristic
8#20244091C211yesmaximal, characteristic
9#20244035C211yesmaximal, characteristic
10#20244034C211yesmaximal, characteristic
11#20243990C211yesmaximal, characteristic, complemented
12#20243989C211yesmaximal, characteristic, complemented
13#20243407C211yesmaximal, characteristic
14C8×Dic47⋊C4C211yesmaximal, characteristic, complemented
15C47×#1945C211yesmaximal, characteristic, complemented
16#15689676C2211yescharacteristic
17#15689591C2211yescharacteristic
18#15689433C411yescharacteristic, complemented
19#15689429C411yescharacteristic, complemented
20#15689426C411yescharacteristic, complemented
21#15689422C411yescharacteristic, complemented
22#15689417C411yescharacteristic, complemented
23#15689412C411yescharacteristic, complemented
24#15689407C411yescharacteristic, complemented
25#15689402C411yescharacteristic, complemented
26#15689252—21no—
27#15689252—21no—
28#15689247—21no—
29#15689247—21no—
30#15689183—21no—
31#15689183—21no—
32#15689175—21no—
33#15689175—21no—
34C2×#13093959C2211yescharacteristic
35#15689159C2211yescharacteristic
36#15689150C2211yescharacteristic
37#15689149C2211yescharacteristic
38#15689146C2211yescharacteristic
39C2×Dic47⋊C8C2211yescharacteristic
40C2×#13093952C2211yescharacteristic
41C2×#13093950C2211yescharacteristic
42#15689120C2211yescharacteristic
43#15689117C2211yescharacteristic
44#15689091C2211yescharacteristic
45#15689089C2211yescharacteristic
46#15689081C2211yescharacteristic
47#15689079C2211yescharacteristic
48M16×Dic47C2211yescharacteristic
49C2×C8×Dic47C2211yescharacteristic
50C2×C8×Dic47C2211yescharacteristic
51C4×Dic47⋊C4C2211yescharacteristic
52#15688888C2211yescharacteristic
53#15688887C2211yescharacteristic
54#15688884C2211yescharacteristic
55#15688883C2211yescharacteristic
56#15688882C2211yescharacteristic
57#15688882C2211yescharacteristic
58#15688878C2211yescharacteristic
59#15688877C2211yescharacteristic
60C2×#108×C47C2211yescharacteristic
61C47×#427C2211yescharacteristic
62C47×#424C2211yescharacteristic
63C47×#424C2211yescharacteristic
64C2×C4×C8×C47C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#339C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68C2×#10625329C2311yescharacteristic
69C2×#10625329C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72#13094023C2×C411yescharacteristic
73#13094023C2×C411yescharacteristic
74#13094015C2×C411yescharacteristic
75#13094015C2×C411yescharacteristic
76#13094001—21no—
77#13094001—21no—
78C4×Dic94—21no—
79C4×Dic94—21no—
80#13093989C2×C411yescharacteristic
81#13093989C2×C411yescharacteristic
82#13093986C2×C411yescharacteristic
83#13093986C2×C411yescharacteristic
84(C22⋊D47)⋊C4—21no—
85(C22⋊D47)⋊C4—21no—
86#13093983C2311yescharacteristic
87#13093981—21no—
88C2×Dic47⋊C4—21no—
89C2×C4×Dic47C2311yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91C42×D47—21no—
92#13093959—41no—
93#13093957C2×C411yescharacteristic
94#13093957C2×C411yescharacteristic
95#13093955C2×C411yescharacteristic
96#13093955C2×C411yescharacteristic
97C4⋊(C47⋊C8)—21no—
98C4⋊(C47⋊C8)—21no—
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8C2×C411yescharacteristic
104Dic47⋊C8C2×C411yescharacteristic
105Dic47⋊C8C2×C411yescharacteristic
106Dic47⋊C8C2×C411yescharacteristic
107#13093952—41no—
108#13093950—41no—
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093947C2×C411yescharacteristic
112#13093947C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114#13093946C2×C411yescharacteristic
115#13093944C2×C411yescharacteristic
116#13093944C2×C411yescharacteristic
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121#13093935—21no—
122#13093934—21no—
123#13093934—21no—
124C4×C47⋊C8—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47—41no—
128C8×Dic47D411yescharacteristic
129C8×Dic47D411yescharacteristic
130C8×Dic47D411yescharacteristic
131C8×Dic47D411yescharacteristic
132C47⋊#95—21no—
133C2×M16×C47C2311yescharacteristic
134C2×M16×C47C2311yescharacteristic
135C22×C8×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137#117×C47C2311yescharacteristic
138#117×C47C2311yescharacteristic
139C2×C42×C47C2311yescharacteristic
140#108×C47—41no—
141#107×C47C2×C411yescharacteristic
142#107×C47C2×C411yescharacteristic
143#106×C47C2×C411yescharacteristic
144#106×C47C2×C411yescharacteristic
145C4⋊C8×C47—21no—
146C4⋊C8×C47—21no—
147C4⋊C8×C47—21no—
148C4⋊C8×C47—21no—
149C4×C8×C47—41no—
150C22×C4×C47—21no—
151C22×C4×C47C2411yescharacteristic
152C2×C22⋊D47—21no—
153C22×Dic47—21no—
154C22×Dic47#4111yescharacteristic
155C22×Dic47#4111yescharacteristic
156#10625350—21no—
157#10625350—21no—
158#10625350—21no—
159#10625350—21no—
160C2×D188C22×C411yescharacteristic
161C2×C4×D47—21no—
162C2×C4×D47—21no—
163C2×C4×D47—21no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94C22×C411yescharacteristic
167M16×C47—21no—
168M16×C47—21no—
169M16×C47—21no—
170M16×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47C22×C411yescharacteristic
178C2×C8×C47C22×C411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C4⋊C4×C47C22×C411yescharacteristic
182C4⋊C4×C47C22×C411yescharacteristic
183C4⋊C4×C47C22×C411yescharacteristic
184C4⋊C4×C47C22×C411yescharacteristic
185C22⋊C4×C47—21no—
186C22⋊C4×C47—21no—
187C42×C47—21no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C22⋊Dic47—21no—
192(C2×D47)⋊C4—21no—
193(C2×D47)⋊C4—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—21no—
196C4⋊Dic47C22×C411yescharacteristic
197C4⋊Dic47C22×C411yescharacteristic
198Dic47⋊C4—24no—
199Dic47⋊C4—21no—
200Dic47⋊C4—21no—
201Dic47⋊C4—21no—
202Dic47⋊C4—21no—
203Dic47⋊C4—21no—
204Dic47⋊C4—21no—
205C4×Dic47—21no—
206C4×Dic47—21no—
207C4×Dic47—21no—
208C4×Dic47—21no—
209C4×Dic47—21no—
210C4×Dic47C22×C411yescharacteristic
211C4×Dic47C22×C411yescharacteristic
212C4×Dic47C2×D411yescharacteristic
213C4×Dic47C2×D411yescharacteristic
214#10625329—21no—
215#10625329—21no—
216#10625329—21no—
217#10625329—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8C22×C411yescharacteristic
225C2×C47⋊C8C22×C411yescharacteristic
226C2×C47⋊C8C2×D411yescharacteristic
227C2×C47⋊C8C2×D411yescharacteristic
228C23×C47C2×#4111yescharacteristic
229C22×D47—21no—
230C2×C4×C47—22no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47C23×C411yescharacteristic
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47H(5,𝔽2)11yescharacteristic
240C2×C4×C472−1+411yescharacteristic
241C2×C4×C472−1+411yescharacteristic
242C2×C4×C472−1+411yescharacteristic
243C22⋊D47—41no—
244C22⋊D47—41no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47C4×D411yescharacteristic
254C2×Dic47C4×D411yescharacteristic
255C2×Dic47C4×D411yescharacteristic
256C2×Dic47C4×D411yescharacteristic
257D188—21no—
258D188—21no—
259C4×D47—42no—
260C4×D47—41no—
261C4×D47—41no—
262C4×D47—42no—
263Dic94—21no—
264Dic94—21no—
265Dic94—42no—
266Dic94—42no—
267C8×C47—21no—
268C8×C47—21no—
269C8×C47—21no—
270C8×C47—21no—
271C8×C47—41no—
272C8×C47—41no—
273C47⋊C8—21no—
274C47⋊C8—21no—
275C47⋊C8—21no—
276C47⋊C8—21no—
277C47⋊C8—41no—
278C47⋊C8—41no—
279#22130—471nomaximal, Sylow
280C22×C47—21no—
281C22×C47—21no—
282C22×C47C2×C4×D411yescharacteristic
283C22×C47#54111yescharacteristic
284C22×C47#54211yescharacteristic
285C2×D47—41no—
286C2×D47—41no—
287C2×D47—41no—
288C4×C47—42no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47#51911yescharacteristic
294C4×C47#52011yescharacteristic
295C4×C47#53611yescharacteristic
296C4×C47#53711yescharacteristic
297Dic47—21no—
298Dic47—21no—
299Dic47—21no—
300Dic47—42no—
301Dic47—41no—
302Dic47—41no—
303Dic47—41no—
304Dic47#44312yes—
305#3076—471no—
306#2960—471no—
307#2922—471no—
308#1986—471no—
309#1950—471no—
310#1945—471no—
311#1945D4711yescharacteristic, complemented
312#1937—471no—
313#1937—471no—
314#1929—471no—
315#1929—471no—
316#1922—471no—
317#1922—471no—
318#1806—471no—
319C8×C4⋊C4—471no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47#232311yescharacteristic
323C2×C47C2×#44311yescharacteristic
324C2×C47#295511yescharacteristic
325D47—81no—
326#533—471no—
327C4×#41—471no—
328#479—471no—
329#479—471no—
330#478—471no—
331#478—471no—
332#477—471no—
333#476—471no—
334#475—471no—
335#474—471no—
336#446—941no—
337#446—941no—
338C8×Q8—941no—
339C8×Q8—941no—
340#433—941no—
341#433—941no—
342#431—941no—
343#431—941no—
344C2×#108—471no—
345C2×#108C2×D4711yescharacteristic
346#427—471no—
347#427C2×D4711yescharacteristic
348#424—471no—
349#424—471no—
350#424C2×D4711yescharacteristic
351#424C2×D4711yescharacteristic
352#423—471no—
353C2×C4⋊C8—471no—
354C2×#104—471no—
355C2×#104—471no—
356#416—471no—
357#416—471no—
358#408—471no—
359#408—471no—
360#405—471no—
361#405—471no—
362C4×M16—471no—
363C2×C4×C8—471no—
364C2×C4×C8—471no—
365C2×C4×C8C2×D4711yescharacteristic
366C4×C4⋊C4—471no—
367#341—471no—
368#341—471no—
369#339—471no—
370#339—471no—
371#339—471no—
372#339—471no—
373#339C2×D4711yescharacteristic
374#339C2×D4711yescharacteristic
375#336—471no—
376#336—471no—
377C47#2213011yescharacteristic, complemented, Sylow
378C2×#41—471no—
379C2×M16—471no—
380C2×M16—471no—
381C2×M16C22×D4711yescharacteristic
382C2×M16C22×D4711yescharacteristic
383C22×C8—471no—
384C22×C8—471no—
385C22×C8C22×D4711yescharacteristic
386C22×C8C22×D4711yescharacteristic
387C4⋊Q8—471no—
388C4⋊Q8—471no—
389#125—471no—
390#125—471no—
391C22⋊Q8—941no—
392C22⋊Q8—941no—
393C4×Q8—471no—
394C4×Q8—471no—
395C4×Q8—941no—
396C4×Q8—941no—
397C4×D4—471no—
398C4×D4—471no—
399C4×D4—941no—
400C4×D4—941no—
401#117—471no—
402#117—941no—
403#117C22×D4711yescharacteristic
404#117C22×D4711yescharacteristic
405C2×C4⋊C4—941no—
406C2×C42—471no—
407C2×C42—471no—
408C2×C42—941no—
409C2×C42C22×D4711yescharacteristic
410#108—41no—
411#108—1881no—
412#107—471no—
413#107—471no—
414#107C4×D4711yescharacteristic
415#107C4×D4711yescharacteristic
416#106—471no—
417#106—471no—
418#106C4×D4711yescharacteristic
419#106C4×D4711yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—471no—
425C4⋊C8—471no—
426C4⋊C8—471no—
427C4⋊C8—471no—
428C4⋊C8—941no—
429C4⋊C8—941no—
430C4⋊C8—941no—
431C4⋊C8—941no—
432C4⋊C8—941no—
433C4⋊C8—941no—
434#104—1881no—
435#104—1881no—
436#103—471no—
437#103—471no—
438#103—471no—
439#103—471no—
440#102—471no—
441#102—471no—
442#102—471no—
443#102—471no—
444C22⋊C8—941no—
445C22⋊C8—941no—
446C22⋊C8—941no—
447C22⋊C8—941no—
448#97—941no—
449#97—941no—
450#97—941no—
451C4×C8—41no—
452C4×C8—471no—
453C4×C8—471no—
454C4×C8—471no—
455C4×C8—471no—
456C4×C8—941no—
457C4×C8—941no—
458C4×C8—941no—
459C4×C8—1881no—
460#95—941no—
461#41—941no—
462#41—941no—
463#41—941no—
464#41—941no—
465C2×Q8—471no—
466C2×Q8—941no—
467C2×Q8—941no—
468C2×D4—471no—
469C2×D4—941no—
470C22×C4—21no—
471C22×C4—471no—
472C22×C4—471no—
473C22×C4—941no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4C23×D4711yescharacteristic
478M16—21no—
479M16—21no—
480M16—21no—
481M16—21no—
482M16—941no—
483M16—941no—
484M16—941no—
485M16—941no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—471no—
493C2×C8—471no—
494C2×C8—471no—
495C2×C8—471no—
496C2×C8—941no—
497C2×C8—941no—
498C2×C8—941no—
499C2×C8—941no—
500C2×C8—941no—
501C2×C8—941no—
502C2×C8C2×C4×D4711yescharacteristic
503C2×C8C2×C4×D4711yescharacteristic
504C2×C8D4×D4711yescharacteristic
505C2×C8D4×D4711yescharacteristic
506C4⋊C4—471no—
507C4⋊C4—471no—
508C4⋊C4—941no—
509C4⋊C4—941no—
510C4⋊C4—941no—
511C4⋊C4—941no—
512C4⋊C4—941no—
513C4⋊C4—941no—
514C4⋊C4—941no—
515C4⋊C4—941no—
516C4⋊C4—944no—
517C4⋊C4C2×C4×D4711yescharacteristic
518C4⋊C4C2×C4×D4711yescharacteristic
519C4⋊C4C2×C4×D4711yescharacteristic
520C4⋊C4C2×C4×D4711yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—941no—
524C22⋊C4—941no—
525C22⋊C4—941no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—471no—
531C42—471no—
532C42—471no—
533C42—471no—
534C42—941no—
535C42—941no—
536C42—941no—
537C42—941no—
538C42—941no—
539C23—941no—
540C23#41×D4711yescharacteristic
541Q8—941no—
542Q8—941no—
543Q8—1882no—
544Q8—1882no—
545D4—941no—
546D4—941no—
547D4—1881no—
548D4—1881no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—471no—
557C2×C4—471no—
558C2×C4—471no—
559C2×C4—471no—
560C2×C4—942no—
561C2×C4—942no—
562C2×C4—941no—
563C2×C4—941no—
564C2×C4—941no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4—1881no—
571C2×C4—1881no—
572C2×C4C22×C4×D4711yescharacteristic
573C2×C4C2×D4×D4711yescharacteristic
574C2×C4#1309406911yescharacteristic
575C2×C4#1309407111yescharacteristic
576C2×C4#1309407211yescharacteristic
577C2×C4#1309407211yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—941no—
585C8—941no—
586C8—941no—
587C8—941no—
588C8—1881no—
589C8—1881no—
590C22—21no—
591C22—21no—
592C22—1881no—
593C22—1881no—
594C22—1881no—
595C22C4×D4×D4711yescharacteristic
596C22#1568973211yescharacteristic
597C22#1568974311yescharacteristic
598C4—42no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—472no—
604C4—941no—
605C4—941no—
606C4—941no—
607C4—1882no—
608C4—1881no—
609C4—1881no—
610C4—1881no—
611C4#1568959911yescharacteristic
612C4#1568960411yescharacteristic
613C4#1568969811yescharacteristic
614C4#1568970011yescharacteristic
615C2—21no—
616C2—21no—
617C2—3761no—
618C2#2024606511yescharacteristic
619C2#443×D4711yescharacteristic
620C2#2025228611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1945C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C23
cosocleC22×C4×C47C24
hypercenter#1945D47
hypocenterC47#22130
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

Complements

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

NH ≅ G/Ntype
2. #20252321C2semidirect
4. #20244330C2semidirect
5. #20244160C2semidirect
6. #20244133C2semidirect
11. #20243990C2semidirect
12. #20243989C2semidirect
14. C8×Dic47⋊C4C2semidirect
15. C47×#1945C2semidirect
18. #15689433C4semidirect
19. #15689429C4semidirect
20. #15689426C4semidirect
21. #15689422C4semidirect
22. #15689417C4semidirect
23. #15689412C4semidirect
24. #15689407C4semidirect
25. #15689402C4semidirect
311. #1945D47semidirect
377. C47#22130semidirect

Maximal subgroups

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

subgroupindex
#202531742
#202523212
#202520312
#202443302
#202441602
#202441332
#202440922
#202440912
#202440352
#202440342
#202439902
#202439892
#202434072
C8×Dic47⋊C42
C47×#19452
#2213047