Finite Group Databasebeta

← #26220637

Subgroups — #26220637

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#20246032C211yesmaximal, characteristic, complemented
3#20244263C211yesmaximal, characteristic
4#20244253C211yesmaximal, characteristic
5#20244128C211yesmaximal, characteristic, complemented
6#20244113C211yesmaximal, characteristic, complemented
7#20244088C211yesmaximal, characteristic, complemented
8#20244084C211yesmaximal, characteristic, complemented
9#20244074C211yesmaximal, characteristic, complemented
10#20244070C211yesmaximal, characteristic, complemented
11#20243286C211yesmaximal, characteristic, complemented
12C4×#13093944C211yesmaximal, characteristic, complemented
13C4×#13093945C211yesmaximal, characteristic, complemented
14#20243075C211yesmaximal, characteristic, complemented
15C47×#2319C211yesmaximal, characteristic, complemented
16C22×#10625334C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18#15689233C418yescomplemented
19C2×#13093957C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093945C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093935C2211yescharacteristic
29C2×#13093935C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31C2×C4×C47⋊C8C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33C2×C4×C47⋊C8C2211yescharacteristic
34#15689025C2211yescharacteristic
35#15689025C2211yescharacteristic
36#15689021C2211yescharacteristic
37#15689021C2211yescharacteristic
38#15689012—21no—
39#15689012—21no—
40#15688985—21no—
41#15688982—21no—
42C4×C4⋊Dic47C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49C2×C4×D4×C47C2211yescharacteristic
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#388—21no—
55C47×#388—21no—
56C47×#381—21no—
57C47×#380—21no—
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#376C2211yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C2×#10625334—22no—
63C2×#10625334—22no—
64C2×#10625334C2×C414yes—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C4×D188—22no—
70C4×D188C2×C414yes—
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×C4×Dic47—21no—
82#13093957—22no—
83#13093955—22no—
84#13093955C2×C414yes—
85#13093945—22no—
86#13093945—22no—
87#13093945C2×C414yes—
88#13093944—22no—
89#13093944—22no—
90#13093944C2×C414yes—
91#13093935—22no—
92#13093935—22no—
93#13093935C2×C414yes—
94C4×C47⋊C8—22no—
95C4×C47⋊C8—22no—
96C4×C47⋊C8—22no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C22×D4×C47C2311yescharacteristic
101C23×C4×C47—21no—
102C4×D4×C47—22no—
103C4×D4×C47C2×C414yes—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C42×C47—21no—
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118#95×C47—21no—
119#95×C47—21no—
120#95×C47—21no—
121#95×C47D411yescharacteristic
122#95×C47D411yescharacteristic
123#95×C47D411yescharacteristic
124#95×C47D411yescharacteristic
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×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2411yescharacteristic
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
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—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—81no—
164C4⋊C4×C47—81no—
165C4⋊C4×C47C22×C412yes—
166C22⋊C4×C47—24no—
167C22⋊C4×C47—81no—
168C22⋊C4×C47—81no—
169C22⋊C4×C47—81no—
170C22⋊C4×C47—81no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—81no—
176C42×C47C22×C412yes—
177C42×C47#4112yes—
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⋊Dic47C22×C412yes—
190Dic47⋊C4—81no—
191Dic47⋊C4—81no—
192C4×Dic47—81no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8C22×C412yes—
200C2×C47⋊C8C22×C412yes—
201C2×C47⋊C8#4112yes—
202C2×C47⋊C8#4112yes—
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—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—84no—
250C2×C4×C47C4×D412yes—
251C2×C4×C47C4×D412yes—
252C2×C4×C47C23×C411yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47C2×#4111yescharacteristic
256C2×C4×C47C2×#4111yescharacteristic
257C2×C4×C47C2×#4111yescharacteristic
258C2×Dic47—22no—
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—
272C47⋊C8—22no—
273C47⋊C8—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—41no—
301C4×C47—41no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47—42no—
305C4×C47—81no—
306C4×C47—81no—
307C4×C47C2×#11711yescharacteristic
308C4×C47C4×#4111yescharacteristic
309C4×C47#52911yescharacteristic
310C4×C47#52911yescharacteristic
311Dic47—42no—
312Dic47—81no—
313Dic47—81no—
314C2×#442—471no—
315#2319—471no—
316#2319D4711yescharacteristic, complemented
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×#102—471no—
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×#102—471no—
350C2×#102—471no—
351C2×#97—471no—
352C2×#97—471no—
353C2×#97—471no—
354C2×C4×C8—471no—
355C2×C4×C8—471no—
356C2×C4×C8—471no—
357#390—471no—
358#390—471no—
359#390C2×D4711yescharacteristic
360#390C2×D4711yescharacteristic
361#389—471no—
362#389—471no—
363#389C2×D4711yescharacteristic
364#389C2×D4711yescharacteristic
365#388—21no—
366#388—21no—
367#388—941no—
368#388—941no—
369#381—21no—
370#381—941no—
371#380—21no—
372#380—941no—
373C4×C4⋊C4—471no—
374C4×C4⋊C4C2×D4711yescharacteristic
375#376C2×D4711yescharacteristic
376#340—471no—
377#340—471no—
378#340—471no—
379#340—471no—
380#340—471no—
381#340—471no—
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×C8—471no—
393C22×C8—471no—
394C4×D4—22no—
395C4×D4—474no—
396C4×D4—942no—
397C4×D4C4×D4714yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—471no—
401C2×C4⋊C4—471no—
402C2×C4⋊C4—471no—
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—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
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—941no—
420C2×C42C22×D4711yescharacteristic
421C2×C42C22×D4711yescharacteristic
422C2×C42C22×D4711yescharacteristic
423#107—942no—
424#106—474no—
425#106—942no—
426#102—474no—
427#102—474no—
428#102—942no—
429#102—942no—
430#102—942no—
431#102—942no—
432#97—474no—
433#97—942no—
434#97—942no—
435C4×C8—942no—
436C4×C8—942no—
437C4×C8—942no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—941no—
442#95—941no—
443#95—941no—
444#95C22⋊D4711yescharacteristic
445#95C22⋊D4711yescharacteristic
446#95C22⋊D4711yescharacteristic
447#95C22⋊D4711yescharacteristic
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—941no—
469C22×C4—944no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—3761no—
473C22×C4—3761no—
474C22×C4C2×C22⋊D4711yescharacteristic
475C22×C4C2×C22⋊D4711yescharacteristic
476C22×C4C2×C22⋊D4711yescharacteristic
477C22×C4C2×C22⋊D4711yescharacteristic
478C22×C4C2×C22⋊D4711yescharacteristic
479C22×C4C2×C22⋊D4711yescharacteristic
480C22×C4C23×D4711yescharacteristic
481D8—948no—
482C2×C8—472no—
483C2×C8—472no—
484C2×C8—472no—
485C2×C8—472no—
486C2×C8—472no—
487C2×C8—472no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—472no—
502C4⋊C4—941no—
503C4⋊C4—941no—
504C4⋊C4—941no—
505C4⋊C4—941no—
506C4⋊C4—941no—
507C4⋊C4—3761no—
508C4⋊C4—3761no—
509C4⋊C4C2×C4×D4712yes—
510C22⋊C4—24no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C22⋊C4—944no—
516C22⋊C4—3761no—
517C22⋊C4—3761no—
518C22⋊C4—3761no—
519C22⋊C4—3761no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—81no—
525C42—3761no—
526C42C2×C4×D4712yes—
527C42#1062535012yes—
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—
542C23C22×C22⋊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—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—942no—
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×C4C4×C22⋊D4712yes—
588C2×C4C4×C22⋊D4712yes—
589C2×C4C22×C4×D4711yescharacteristic
590C2×C4#41×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C2×C4#41×D4711yescharacteristic
594C2×C4C2×#1062535011yescharacteristic
595C8—474no—
596C8—942no—
597C8—942no—
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×C4×C22⋊D4711yescharacteristic
614C22#1568966911yescharacteristic
615C22#1568966911yescharacteristic
616C22#1568992611yescharacteristic
617C22#1568992611yescharacteristic
618C22#1568993111yescharacteristic
619C22#1568993411yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—3761no—
630C4—3761no—
631C4—1882no—
632C4#117×D4711yescharacteristic
633C4#1568959111yescharacteristic
634C4#1568965111yescharacteristic
635C4#1568965111yescharacteristic
636C2—82no—
637C2—3762no—
638C2#2024584711yescharacteristic
639C2#2025221611yescharacteristic
640C2#2025222011yescharacteristic
641C2#2025399911yescharacteristic
642C2#2025403211yescharacteristic
643C2#2025406511yescharacteristic
644C2#2025407311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2319C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
cosocleC22×C4×C47C24
hypercenter#2319D47
hypocenterC47#21290
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #20246032C2semidirect
5. #20244128C2semidirect
6. #20244113C2semidirect
7. #20244088C2semidirect
8. #20244084C2semidirect
9. #20244074C2semidirect
10. #20244070C2semidirect
11. #20243286C2semidirect
12. C4×#13093944C2semidirect
13. C4×#13093945C2semidirect
14. #20243075C2semidirect
15. C47×#2319C2semidirect
18. #15689233C4semidirect
316. #2319D47semidirect
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
#202460322
#202442632
#202442532
#202441282
#202441132
#202440882
#202440842
#202440742
#202440702
#202432862
C4×#130939442
C4×#130939452
#202430752
C47×#23192
#2129047