Finite Group Databasebeta

← #26220641

Subgroups — #26220641

Order 12032.

862 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689233C211yesmaximal, characteristic
2#20246031C211yesmaximal, characteristic, complemented
3#20246026C211yesmaximal, characteristic, complemented
4#20244261C211yesmaximal, characteristic
5#20244251C211yesmaximal, characteristic
6#20244130C211yesmaximal, characteristic, complemented
7#20244115C211yesmaximal, characteristic, complemented
8#20244086C211yesmaximal, characteristic, complemented
9#20244082C211yesmaximal, characteristic, complemented
10#20244072C211yesmaximal, characteristic, complemented
11#20244068C211yesmaximal, characteristic, complemented
12#20243286C211yesmaximal, characteristic, complemented
13C4×#13093946C211yesmaximal, characteristic, complemented
14#20243074C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C22×#10625334C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18#15689233C418yescomplemented
19C2×#13093957C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093946C2211yescharacteristic
23C2×#13093946C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093935C2211yescharacteristic
27C2×#13093934C2211yescharacteristic
28C2×#13093934C2211yescharacteristic
29C2×C8×Dic47C2211yescharacteristic
30C2×C8×Dic47C2211yescharacteristic
31#15689026C2211yescharacteristic
32#15689026C2211yescharacteristic
33#15689024C2211yescharacteristic
34#15689024C2211yescharacteristic
35#15689022C2211yescharacteristic
36#15689022C2211yescharacteristic
37#15689019C2211yescharacteristic
38#15689019C2211yescharacteristic
39#15689016—21no—
40#15689016—21no—
41#15689014—21no—
42#15689014—21no—
43#15688986—21no—
44#15688985—21no—
45#15688983—21no—
46#15688982—21no—
47C4×C4⋊Dic47C2211yescharacteristic
48#15688969C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C2×#102×C47C2211yescharacteristic
55C2×#102×C47C2211yescharacteristic
56C2×C4×C8×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C2×#10625334—22no—
63C2×#10625334—22no—
64C2×#10625334C2×C414yes—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C4×D188—22no—
68C4×D188C2×C414yes—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
76C2×C22⋊Dic47—21no—
77C2×C22⋊Dic47—21no—
78C2×C22⋊Dic47—21no—
79C2×C22⋊Dic47—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×(C2×D47)⋊C4—21no—
84C2×(C2×D47)⋊C4—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47C2311yescharacteristic
87C2×C4×Dic47C2311yescharacteristic
88#13093957—22no—
89#13093955—22no—
90#13093955C2×C414yes—
91#13093946—22no—
92#13093946—22no—
93#13093945C2×C414yes—
94#13093944C2×C414yes—
95#13093935C2×C414yes—
96#13093934—22no—
97#13093934—22no—
98C8×Dic47—22no—
99C8×Dic47—22no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95D411yescharacteristic
106C47⋊#95D411yescharacteristic
107C47⋊#95D411yescharacteristic
108C47⋊#95D411yescharacteristic
109C22×D4×C47C2311yescharacteristic
110C23×C4×C47—21no—
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C4×D4×C47—22no—
114C4×D4×C47C2×C414yes—
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C22⋊C4×C47—21no—
119C2×C42×C47—21no—
120C2×C42×C47C2311yescharacteristic
121#102×C47—22no—
122#102×C47—22no—
123C4×C8×C47—22no—
124#95×C47—21no—
125C24×C47—21no—
126C23×D47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47C22×C412yes—
133C22×C4×C47—21no—
134C22×C4×C47—24no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—81no—
138C22×C4×C47—81no—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2411yescharacteristic
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47C2×D411yescharacteristic
146C22×Dic47C2×D411yescharacteristic
147C22×Dic47C2×D411yescharacteristic
148C22×Dic47C2×D411yescharacteristic
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188C22×C412yes—
155C2×C4×D47—24no—
156C2×C4×D47—81no—
157C2×C4×D47—81no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47#4112yes—
163C2×C8×C47#4112yes—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47C22×C412yes—
170C22⋊C4×C47—24no—
171C42×C47—81no—
172C42×C47C22×C412yes—
173C42×C47#4112yes—
174C22⋊Dic47—81no—
175C22⋊Dic47—81no—
176C22⋊Dic47—81no—
177C22⋊Dic47—81no—
178#10625334—28no—
179(C2×D47)⋊C4—24no—
180(C2×D47)⋊C4—81no—
181(C2×D47)⋊C4—81no—
182(C2×D47)⋊C4—81no—
183(C2×D47)⋊C4—81no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47—21no—
189C4⋊Dic47—81no—
190C4⋊Dic47—81no—
191C4⋊Dic47C22×C412yes—
192Dic47⋊C4—81no—
193Dic47⋊C4—81no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196C4×Dic47—21no—
197C4×Dic47—21no—
198C4×Dic47—81no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8C22×C412yes—
202C2×C47⋊C8C22×C412yes—
203C2×C47⋊C8#4112yes—
204C2×C47⋊C8#4112yes—
205C23×C47—22no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47C22×D411yescharacteristic
213C22×D47—22no—
214C22×D47—41no—
215C22×D47—41no—
216C22×D47—41no—
217C22×D47—41no—
218C22×D47—41no—
219C22×D47—41no—
220D4×C47—22no—
221D4×C47—22no—
222D4×C47—41no—
223D4×C47—41no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—22no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—84no—
238C2×C4×C47C4×D412yes—
239C2×C4×C47C4×D412yes—
240C2×C4×C47C23×C411yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×Dic47—22no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—21no—
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—21no—
255C2×Dic47—21no—
256C2×Dic47—21no—
257C2×Dic47—21no—
258C2×Dic47—21no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267D188—22no—
268D188—22no—
269D188—41no—
270D188—41no—
271C4×D47—84no—
272C8×C47—22no—
273C8×C47—22no—
274C47⋊C8—22no—
275C47⋊C8#11714yes—
276#21290—471nomaximal, Sylow
277C22×C47—42no—
278C22×C47—42no—
279C22×C47—42no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47C2×C4×D411yescharacteristic
285C22×C47#53211yescharacteristic
286C22×C47#53211yescharacteristic
287C22×C47#57611yescharacteristic
288C22×C47#57611yescharacteristic
289C22×C47#57711yescharacteristic
290C22×C47#57711yescharacteristic
291C2×D47—42no—
292C2×D47—42no—
293C2×D47—42no—
294C2×D47—81no—
295C2×D47—81no—
296C2×D47—81no—
297C2×D47—81no—
298C4×C47—22no—
299C4×C47—22no—
300C4×C47—42no—
301C4×C47—81no—
302C4×C47—81no—
303C4×C47C2×#11711yescharacteristic
304C4×C47C4×#4111yescharacteristic
305C4×C47#52911yescharacteristic
306C4×C47#52911yescharacteristic
307Dic47—41no—
308Dic47—41no—
309Dic47—41no—
310Dic47—41no—
311Dic47—42no—
312Dic47—81no—
313Dic47—81no—
314C2×#442—471no—
315#2319—471no—
316#2319—471no—
317#1972—471no—
318#1970—471no—
319#1944—471no—
320#1941—471no—
321#1936—471no—
322#1936—471no—
323#1934—471no—
324#1934—471no—
325#1776—471no—
326C4×#102—471no—
327C4×#102D4711yescharacteristic, complemented
328#1726—471no—
329C2×C47—82no—
330C2×C47#229311yescharacteristic
331C2×C47#294611yescharacteristic
332C2×C47#294611yescharacteristic
333C2×C47#317311yescharacteristic
334C2×C47#317611yescharacteristic
335C2×C47#317911yescharacteristic
336C2×C47#317911yescharacteristic
337D47—82no—
338C22×D8—471no—
339C2×C4×D4—471no—
340C2×C4×D4C2×D4711yescharacteristic
341#442—478no—
342C2×#107—471no—
343C2×#106—471no—
344C2×#106—471no—
345C2×#102—471no—
346C2×#102—471no—
347C2×#102—471no—
348C2×#102—471no—
349C2×#102C2×D4711yescharacteristic
350C2×#102C2×D4711yescharacteristic
351C2×#97—471no—
352C2×#97—471no—
353C2×#97—471no—
354C2×C4×C8—471no—
355C2×C4×C8—471no—
356C2×C4×C8C2×D4711yescharacteristic
357#390—471no—
358#390—471no—
359#390—471no—
360#390—471no—
361#389—471no—
362#389—471no—
363#389—471no—
364#389—471no—
365#388—941no—
366#388—941no—
367#388—941no—
368#388—941no—
369#381—941no—
370#381—941no—
371#380—941no—
372#380—941no—
373C4×C4⋊C4—471no—
374C4×C4⋊C4C2×D4711yescharacteristic
375#376—471no—
376#340—471no—
377#340—471no—
378#340—471no—
379#340—471no—
380#340C2×D4711yescharacteristic
381#340C2×D4711yescharacteristic
382C47#2129011yescharacteristic, complemented, Sylow
383C22×D4—471no—
384C22×D4C22×D4711yescharacteristic
385C23×C4—21no—
386C23×C4—941no—
387C2×D8—474no—
388C2×D8—942no—
389C2×D8—942no—
390C22×C8—471no—
391C22×C8—471no—
392C22×C8C22×D4711yescharacteristic
393C22×C8C22×D4711yescharacteristic
394C4×D4—22no—
395C4×D4—474no—
396C4×D4—942no—
397C4×D4C4×D4714yes—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—471no—
400C2×C4⋊C4—471no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4—941no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4C22×D4711yescharacteristic
406C2×C4⋊C4C22×D4711yescharacteristic
407C2×C4⋊C4C22×D4711yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—941no—
410C2×C22⋊C4—941no—
411C2×C22⋊C4—941no—
412C2×C22⋊C4—941no—
413C2×C22⋊C4—941no—
414C2×C22⋊C4—941no—
415C2×C22⋊C4—941no—
416C2×C22⋊C4—941no—
417C2×C22⋊C4—941no—
418C2×C42—21no—
419C2×C42—471no—
420C2×C42—471no—
421C2×C42—941no—
422C2×C42C22×D4711yescharacteristic
423#107—942no—
424#106—474no—
425#106—942no—
426#102—22no—
427#102—22no—
428#102—474no—
429#102—474no—
430#102—942no—
431#102—942no—
432#97—474no—
433#97—942no—
434#97—942no—
435C4×C8—22no—
436C4×C8—942no—
437C4×C8—942no—
438#95—21no—
439#95—471no—
440#95—471no—
441#95—471no—
442#95—471no—
443#95—941no—
444#95—941no—
445#95—941no—
446#95—941no—
447#95—941no—
448C24—21no—
449C24—941no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—472no—
456C2×D4—941no—
457C2×D4—941no—
458C2×D4—941no—
459C2×D4—941no—
460C2×D4—941no—
461C2×D4C2×C4×D4712yes—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—81no—
467C22×C4—81no—
468C22×C4—471no—
469C22×C4—471no—
470C22×C4—471no—
471C22×C4—471no—
472C22×C4—941no—
473C22×C4—944no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—3761no—
477C22×C4—3761no—
478C22×C4D4×D4711yescharacteristic
479C22×C4D4×D4711yescharacteristic
480C22×C4C23×D4711yescharacteristic
481D8—948no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—472no—
487C2×C8—472no—
488C2×C8—472no—
489C2×C8—472no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8#1062535012yes—
493C2×C8#1062535012yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—472no—
500C4⋊C4—941no—
501C4⋊C4—941no—
502C4⋊C4—941no—
503C4⋊C4—941no—
504C4⋊C4—941no—
505C4⋊C4—3761no—
506C4⋊C4—3761no—
507C4⋊C4—3761no—
508C4⋊C4—3761no—
509C4⋊C4C2×C4×D4712yes—
510C22⋊C4—24no—
511C22⋊C4—944no—
512C22⋊C4—3761no—
513C22⋊C4—3761no—
514C22⋊C4—3761no—
515C22⋊C4—3761no—
516C22⋊C4—3761no—
517C22⋊C4—3761no—
518C22⋊C4—3761no—
519C22⋊C4—3761no—
520C42—81no—
521C42—941no—
522C42—941no—
523C42—941no—
524C42—941no—
525C42—3761no—
526C42C2×C4×D4712yes—
527C42#1062535212yes—
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—942no—
536C23—1881no—
537C23—1881no—
538C23—1881no—
539C23—1881no—
540C23—1881no—
541C23—1881no—
542C23C2×D4×D4711yescharacteristic
543D4—22no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—942no—
548D4—942no—
549D4—1881no—
550D4—1881no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4—942no—
566C2×C4—941no—
567C2×C4—941no—
568C2×C4—941no—
569C2×C4—941no—
570C2×C4—941no—
571C2×C4—941no—
572C2×C4—941no—
573C2×C4—941no—
574C2×C4—941no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—941no—
578C2×C4—3764no—
579C2×C4—1881no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1881no—
584C2×C4—1881no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4(C22⋊D47)⋊C412yes—
588C2×C4(C22⋊D47)⋊C412yes—
589C2×C4C22×C4×D4711yescharacteristic
590C2×C4#41×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4C2×#1062535211yescharacteristic
593C2×C4C2×#1062535011yescharacteristic
594C2×C4C2×#1062535011yescharacteristic
595C8—22no—
596C8—22no—
597C8—474no—
598C8—942no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—3761no—
607C22—3761no—
608C22—3761no—
609C22—3761no—
610C22—1882no—
611C22—1882no—
612C22—1882no—
613C22C2×(C22⋊D47)⋊C411yescharacteristic
614C22#1568967011yescharacteristic
615C22#1568967011yescharacteristic
616C22#1568992411yescharacteristic
617C22#1568992511yescharacteristic
618C22#1568992911yescharacteristic
619C22#1568993011yescharacteristic
620C4—22no—
621C4—22no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—3761no—
626C4—3761no—
627C4—1881no—
628C4—1882no—
629C4—1881no—
630C4—1881no—
631C4—1881no—
632C4#117×D4711yescharacteristic
633C4C4×#1062535011yescharacteristic
634C4#1568965311yescharacteristic
635C4#1568965311yescharacteristic
636C2—82no—
637C2—3762no—
638C2#2024585111yescharacteristic
639C2#2025221411yescharacteristic
640C2#2025222311yescharacteristic
641C2#2025400111yescharacteristic
642C2#2025403411yescharacteristic
643C2#2025406711yescharacteristic
644C2#2025407511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#102×C47C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
cosocleC22×C4×C47C24
hypercenterC4×#102D47
hypocenterC47#21290
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #20246031C2semidirect
3. #20246026C2semidirect
6. #20244130C2semidirect
7. #20244115C2semidirect
8. #20244086C2semidirect
9. #20244082C2semidirect
10. #20244072C2semidirect
11. #20244068C2semidirect
12. #20243286C2semidirect
13. C4×#13093946C2semidirect
14. #20243074C2semidirect
15. C4×#102×C47C2semidirect
18. #15689233C4semidirect
327. C4×#102D47semidirect
382. C47#21290semidirect

Maximal subgroups

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

subgroupindex
C2×#156892332
#202460312
#202460262
#202442612
#202442512
#202441302
#202441152
#202440862
#202440822
#202440722
#202440682
#202432862
C4×#130939462
#202430742
C4×#102×C472
#2129047