Finite Group Databasebeta

← #26228601

Subgroups — #26228601

Order 12032.

628 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#20253170C211yesmaximal, characteristic
2#20252037C211yesmaximal, characteristic
3#20244333C211yesmaximal, characteristic, complemented
4#20244161C211yesmaximal, characteristic, complemented
5#20244138C211yesmaximal, characteristic, complemented
6#20244133C211yesmaximal, characteristic, complemented
7#20244098C211yesmaximal, characteristic
8#20244091C211yesmaximal, characteristic
9#20244036C211yesmaximal, characteristic
10#20244036C211yesmaximal, characteristic
11#20243987C211yesmaximal, characteristic, complemented
12#20243987C211yesmaximal, characteristic, complemented
13#20243405C211yesmaximal, characteristic
14#20243260C211yesmaximal, characteristic, complemented
15C47×#2961C211yesmaximal, characteristic, complemented
16C4×#10625350C2211yescharacteristic
17#15689427C411yescharacteristic, complemented
18#15689427C411yescharacteristic, complemented
19#15689420C411yescharacteristic, complemented
20#15689420C411yescharacteristic, complemented
21#15689415C411yescharacteristic, complemented
22#15689410C411yescharacteristic, complemented
23#15689405C411yescharacteristic, complemented
24#15689400C411yescharacteristic, complemented
25#15689185—21no—
26#15689185—21no—
27#15689178—21no—
28#15689178—21no—
29C2×#13093959C2211yescharacteristic
30C2×#13093959C2211yescharacteristic
31#15689159C2211yescharacteristic
32#15689159C2211yescharacteristic
33#15689149C2211yescharacteristic
34#15689149C2211yescharacteristic
35C2×C4⋊(C47⋊C8)C2211yescharacteristic
36C2×#13093950C2211yescharacteristic
37C2×#13093950C2211yescharacteristic
38#15689117C2211yescharacteristic
39#15689117C2211yescharacteristic
40#15689089C2211yescharacteristic
41#15689089C2211yescharacteristic
42C4×#10625329C2211yescharacteristic
43C2×#13093934C2211yescharacteristic
44C2×C8×Dic47C2211yescharacteristic
45C4×C4⋊Dic47C2211yescharacteristic
46#15688887C2211yescharacteristic
47#15688887C2211yescharacteristic
48#15688884C2211yescharacteristic
49#15688884C2211yescharacteristic
50#15688882C2211yescharacteristic
51#15688882C2211yescharacteristic
52#15688882C2211yescharacteristic
53#15688882C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C47×#533C2211yescharacteristic
57C47×#446—21no—
58C47×#446—21no—
59C47×#446—21no—
60C47×#446—21no—
61C47×#424C2211yescharacteristic
62C47×#424C2211yescharacteristic
63C47×#423C2211yescharacteristic
64C47×#405C2211yescharacteristic
65C47×#405C2211yescharacteristic
66C2×#97×C47C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68C2×#10625329C2311yescharacteristic
69C2×#10625329C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C4×Dic94C2×C411yescharacteristic
73C4×Dic94C2×C411yescharacteristic
74C4×D188C2×C411yescharacteristic
75C4×D188C2×C411yescharacteristic
76C4×C22⋊D47—21no—
77C4×C22⋊D47—21no—
78#13093983C2311yescharacteristic
79#13093981—21no—
80C2×C4⋊Dic47—21no—
81C2×C4×Dic47C2311yescharacteristic
82C2×C4×Dic47C2311yescharacteristic
83C42×D47—21no—
84#13093959—41no—
85#13093959—41no—
86#13093957C2×C411yescharacteristic
87#13093957C2×C411yescharacteristic
88#13093957C2×C411yescharacteristic
89#13093957C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91#13093955C2×C411yescharacteristic
92#13093955C2×C411yescharacteristic
93#13093955C2×C411yescharacteristic
94C4⋊(C47⋊C8)C2×C411yescharacteristic
95C4⋊(C47⋊C8)C2×C411yescharacteristic
96C4⋊(C47⋊C8)C2×C411yescharacteristic
97C4⋊(C47⋊C8)C2×C411yescharacteristic
98Dic47⋊C8—21no—
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102#13093950—41no—
103#13093950—41no—
104#13093947C2×C411yescharacteristic
105#13093947C2×C411yescharacteristic
106#13093947C2×C411yescharacteristic
107#13093947C2×C411yescharacteristic
108#13093944C2×C411yescharacteristic
109#13093944C2×C411yescharacteristic
110#13093944C2×C411yescharacteristic
111#13093944C2×C411yescharacteristic
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8—21no—
116#13093935—21no—
117#13093934—41no—
118C4×C47⋊C8—21no—
119C8×Dic47—41no—
120C47⋊#95—21no—
121C2×M16×C47C2311yescharacteristic
122C2×M16×C47C2311yescharacteristic
123C22×C8×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125C4⋊Q8×C47C2×C411yescharacteristic
126C4⋊Q8×C47C2×C411yescharacteristic
127#125×C47C2×C411yescharacteristic
128#125×C47C2×C411yescharacteristic
129C22⋊Q8×C47—21no—
130C22⋊Q8×C47—21no—
131C4×Q8×C47—21no—
132C4×Q8×C47—21no—
133#117×C47C2311yescharacteristic
134#117×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47—21no—
138C4⋊C8×C47—21no—
139C4⋊C8×C47—21no—
140C4⋊C8×C47—21no—
141C4⋊C8×C47—21no—
142#97×C47—21no—
143#97×C47—21no—
144#97×C47D411yescharacteristic
145#97×C47D411yescharacteristic
146#97×C47D411yescharacteristic
147#97×C47D411yescharacteristic
148C4×C8×C47—21no—
149C4×C8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C22×C4×C47#4111yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C22×C4×C47C2411yescharacteristic
155C2×C22⋊D47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158#10625350—21no—
159#10625350—21no—
160#10625350—21no—
161#10625350—21no—
162C2×D188C22×C411yescharacteristic
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×C4×D47—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×C47C2×D411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47C22×C411yescharacteristic
188C4⋊C4×C47C22×C411yescharacteristic
189C4⋊C4×C47C22×C411yescharacteristic
190C4⋊C4×C47C22×C411yescharacteristic
191C22⋊C4×C47—21no—
192C22⋊C4×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47C22×C411yescharacteristic
196C42×C47C22×C411yescharacteristic
197C42×C47C2×D411yescharacteristic
198C42×C47C2×D411yescharacteristic
199C22⋊Dic47—21no—
200(C2×D47)⋊C4—21no—
201(C2×D47)⋊C4—21no—
202C4⋊Dic47—42no—
203C4⋊Dic47C22×C411yescharacteristic
204C4⋊Dic47C22×C411yescharacteristic
205Dic47⋊C4—21no—
206Dic47⋊C4—21no—
207C4×Dic47—21no—
208C4×Dic47—21no—
209C4×Dic47—21no—
210C4×Dic47—21no—
211C4×Dic47—21no—
212C4×Dic47—21no—
213C4×Dic47—21no—
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⋊C8C22×C411yescharacteristic
227C2×C47⋊C8C22×C411yescharacteristic
228C23×C47C2×#4111yescharacteristic
229C22×D47—21no—
230Q8×C47—81no—
231Q8×C47—81no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47C4×D411yescharacteristic
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47C23×C411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47H(5,𝔽2)11yescharacteristic
245C2×C4×C472−1+411yescharacteristic
246C2×C4×C472−1+411yescharacteristic
247C2×C4×C472−1+411yescharacteristic
248C22⋊D47—41no—
249C22⋊D47—41no—
250C2×Dic47—22no—
251C2×Dic47—21no—
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259D188—21no—
260D188—21no—
261C4×D47—41no—
262C4×D47—41no—
263C4×D47—81no—
264C4×D47—81no—
265Dic94—21no—
266Dic94—21no—
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#22132—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—21no—
289C4×C47—21no—
290C4×C47—21no—
291C4×C47—21no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47#51911yescharacteristic
297C4×C47#52011yescharacteristic
298C4×C47#53611yescharacteristic
299C4×C47#53711yescharacteristic
300Dic47—42no—
301Dic47—41no—
302Dic47—41no—
303Dic47—41no—
304Dic47—81no—
305#3076—471no—
306#2961D4711yescharacteristic, complemented
307#2923—471no—
308#1986—471no—
309#1950—471no—
310#1946—471no—
311#1945—471no—
312#1938—471no—
313#1937—471no—
314#1929—471no—
315#1929—471no—
316#1922—471no—
317#1922—471no—
318#1806—471no—
319#1771—471no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47#232311yescharacteristic
323C2×C47#295611yescharacteristic
324C2×C47#295711yescharacteristic
325D47—81no—
326#533C2×D4711yescharacteristic
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—21no—
337#446—21no—
338#446—21no—
339#446—21no—
340#433—941no—
341#433—941no—
342#432—941no—
343#432—941no—
344C2×#108—471no—
345C2×#108—471no—
346#427—471no—
347#427—471no—
348#424—471no—
349#424—471no—
350#424C2×D4711yescharacteristic
351#424C2×D4711yescharacteristic
352#423C2×D4711yescharacteristic
353C2×C4⋊C8—471no—
354C2×#104—471no—
355C2×#104—471no—
356#416—471no—
357#416—471no—
358#408—471no—
359#408—471no—
360#405C2×D4711yescharacteristic
361#405C2×D4711yescharacteristic
362C4×M16—471no—
363C2×#97—471no—
364C2×#97C2×D4711yescharacteristic
365C2×C4×C8—471no—
366C4×C4⋊C4—471no—
367#341—471no—
368#341—471no—
369#339—471no—
370#339—471no—
371#339—471no—
372#339—471no—
373#339—471no—
374#339—471no—
375#336—471no—
376#336—471no—
377C47#2213211yescharacteristic, 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⋊Q8C4×D4711yescharacteristic
388C4⋊Q8C4×D4711yescharacteristic
389#125C4×D4711yescharacteristic
390#125C4×D4711yescharacteristic
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—471no—
396C4×Q8—471no—
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—1881no—
411#108—1881no—
412#107—471no—
413#107—471no—
414#107—471no—
415#107—471no—
416#106—471no—
417#106—471no—
418#106—471no—
419#106—471no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8—21no—
426C4⋊C8—471no—
427C4⋊C8—471no—
428C4⋊C8—471no—
429C4⋊C8—471no—
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—21no—
449#97—21no—
450#97—941no—
451#97—1881no—
452#97C22⋊D4711yescharacteristic
453#97C22⋊D4711yescharacteristic
454#97C22⋊D4711yescharacteristic
455#97C22⋊D4711yescharacteristic
456C4×C8—21no—
457C4×C8—21no—
458C4×C8—941no—
459C4×C8—1881no—
460#95—941no—
461#41—941no—
462#41—941no—
463#41—941no—
464#41—941no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—471no—
468C2×D4—471no—
469C2×D4—941no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—941no—
473C22×C4—941no—
474C22×C4—941no—
475C22×C4#1062535011yescharacteristic
476C22×C4#1062535011yescharacteristic
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×C22⋊D4711yescharacteristic
503C2×C8C2×C22⋊D4711yescharacteristic
504C2×C8C2×C22⋊D4711yescharacteristic
505C2×C8C2×C22⋊D4711yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—471no—
513C4⋊C4—471no—
514C4⋊C4—941no—
515C4⋊C4—941no—
516C4⋊C4—1882no—
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—941no—
529C42—941no—
530C42—941no—
531C42—941no—
532C42—941no—
533C42—941no—
534C42—941no—
535C42C2×C4×D4711yescharacteristic
536C42C2×C4×D4711yescharacteristic
537C42C2×C22⋊D4711yescharacteristic
538C42C2×C22⋊D4711yescharacteristic
539C23—941no—
540C23C2×#1062535011yescharacteristic
541Q8—81no—
542Q8—81no—
543Q8—941no—
544Q8—941no—
545D4—941no—
546D4—941no—
547D4—1881no—
548D4—1881no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—942no—
556C2×C4—941no—
557C2×C4—941no—
558C2×C4—941no—
559C2×C4—3761no—
560C2×C4—3761no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4C4×C22⋊D4711yescharacteristic
569C2×C4C4×C22⋊D4711yescharacteristic
570C2×C4C4×C22⋊D4711yescharacteristic
571C2×C4C4×C22⋊D4711yescharacteristic
572C2×C4C22×C4×D4711yescharacteristic
573C2×C4C22×C22⋊D4711yescharacteristic
574C2×C4#1309407011yescharacteristic
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—
595C22C2×C4×C22⋊D4711yescharacteristic
596C22#1568973111yescharacteristic
597C22#1568974511yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—3761no—
607C4—1882no—
608C4—1881no—
609C4—1881no—
610C4—1881no—
611C4#1568959911yescharacteristic
612C4#1568960511yescharacteristic
613C4#1568969711yescharacteristic
614C4#1568970111yescharacteristic
615C2—21no—
616C2—21no—
617C2—3761no—
618C2#2024606411yescharacteristic
619C2#2025229511yescharacteristic
620C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2961C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C23
cosocleC22×C4×C47C24
hypercenter#2961D47
hypocenterC47#22132
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #20244333C2semidirect
4. #20244161C2semidirect
5. #20244138C2semidirect
6. #20244133C2semidirect
11. #20243987C2semidirect
12. #20243987C2semidirect
14. #20243260C2semidirect
15. C47×#2961C2semidirect
17. #15689427C4semidirect
18. #15689427C4semidirect
19. #15689420C4semidirect
20. #15689420C4semidirect
21. #15689415C4semidirect
22. #15689410C4semidirect
23. #15689405C4semidirect
24. #15689400C4semidirect
306. #2961D47semidirect
377. C47#22132semidirect

Maximal subgroups

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

subgroupindex
#202531702
#202520372
#202443332
#202441612
#202441382
#202441332
#202440982
#202440912
#202440362
#202439872
#202434052
#202432602
C47×#29612
#2213247