Finite Group Databasebeta

← #25104706

Subgroups — #25104706

Order 11008.

826 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583257C211yesmaximal, characteristic
2#19137339C211yesmaximal, characteristic, complemented
3#19137307C211yesmaximal, characteristic
4#19135554C211yesmaximal, characteristic, complemented
5#19135405C211yesmaximal, characteristic
6#19135289C211yesmaximal, characteristic
7#19135286C211yesmaximal, characteristic, complemented
8#19135280C211yesmaximal, characteristic
9#19135269C211yesmaximal, characteristic, complemented
10#19134727C211yesmaximal, characteristic, complemented
11#19134426C211yesmaximal, characteristic, complemented
12C4×#13063248C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic
14#19134283C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19#14583257C418yescomplemented
20C2×#13063250C2211yescharacteristic
21C2×#13063250C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582805—21no—
32#14582804C2211yescharacteristic
33#14582803—21no—
34#14582802C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582787—21no—
38#14582787—21no—
39#14582786—21no—
40#14582783—21no—
41#14582772—21no—
42#14582772—21no—
43#14582768C2211yescharacteristic
44#14582764C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582745C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86—21no—
61C22×Dic86C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063324—22no—
65#13063324C2×C414yescomplemented
66#13063312—22no—
67#13063312C2×C414yes—
68C4×Dic86—22no—
69C4×Dic86—22no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063250—22no—
88#13063250C2×C414yescomplemented
89#13063248—22no—
90#13063248C2×C414yescomplemented
91#13063246—22no—
92#13063246C2×C414yes—
93#13063235—22no—
94#13063235C2×C414yescomplemented
95C4×C43⋊C8—22no—
96C8×Dic43—22no—
97C8×Dic43—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#102×C43—22no—
122#102×C43C2×C414yes—
123#97×C43—22no—
124#95×C43—21no—
125C24×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43C22×C412yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—42no—
136C22×C4×C43—81no—
137C22×C4×C43—81no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—24no—
155C2×Dic86—81no—
156C2×Dic86—81no—
157C2×Dic86C22×C412yes—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C412yes—
163C2×C8×C43#4112yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C412yes—
170C22⋊C4×C43—42no—
171C42×C43—81no—
172C42×C43#4112yes—
173C42×C43#4112yes—
174C22⋊Dic43—24no—
175C22⋊Dic43—24no—
176C22⋊Dic43—81no—
177C22⋊Dic43—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—81no—
184C4⋊Dic43C22×C412yes—
185Dic43⋊C4—24no—
186Dic43⋊C4—42no—
187Dic43⋊C4—81no—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—42no—
193C4×Dic43—81no—
194C4×Dic43C22×C412yes—
195C4×Dic43#4112yes—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C22×C412yes—
201C2×C43⋊C8#4112yes—
202C23×C43—22no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43C22×D411yescharacteristic
210D4×C43—22no—
211D4×C43—22no—
212D4×C43—41no—
213D4×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—84no—
228C2×C4×C43#12412yes—
229C2×C4×C43#12412yes—
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43C4×D412yes—
259C2×Dic43C4×D412yes—
260Dic86—22no—
261Dic86—22no—
262Dic86—41no—
263Dic86—41no—
264Dic86—84no—
265C8×C43—22no—
266C8×C43—22no—
267C43⋊C8—22no—
268C43⋊C8—22no—
269#21654—431nomaximal, Sylow
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43C2×C4×D411yescharacteristic
278C22×C43C2×#12411yescharacteristic
279C22×C43#53211yescharacteristic
280C22×C43#57611yescharacteristic
281C22×C43#57711yescharacteristic
282C22×C43#57711yescharacteristic
283C22×C43#57811yescharacteristic
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—42no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C4×#4111yescharacteristic
290C4×C43C4×#4111yescharacteristic
291C4×C43#52911yescharacteristic
292C4×C43#52911yescharacteristic
293Dic43—22no—
294Dic43—22no—
295Dic43—41no—
296Dic43—41no—
297Dic43—42no—
298Dic43—42no—
299Dic43—81no—
300Dic43—81no—
301C2×#489—431no—
302#2331—431no—
303#2326—431no—
304#1990—431no—
305#1958—431no—
306#1936—431no—
307#1935—431no—
308#1934—431no—
309#1933—431no—
310#1836—431no—
311#1763—431no—
312#1762D4311yescharacteristic
313C4×#103—431no—
314C4×#102—431no—
315#1726—431no—
316C2×C43—82no—
317C2×C43C4×#12411yescharacteristic
318C2×C43#294611yescharacteristic
319C2×C43#294711yescharacteristic
320C2×C43#313611yescharacteristic
321C2×C43#313711yescharacteristic
322C2×C43#317311yescharacteristic
323C2×C43#317511yescharacteristic
324C2×C4⋊Q8—431no—
325C2×#124—431no—
326C2×C4×Q8—431no—
327C2×C4×D4C2×D4311yescharacteristic
328#489—438no—
329C2×#103—431no—
330C2×#103—431no—
331C2×#103—431no—
332C2×#103—431no—
333C2×#102—431no—
334C2×#102—431no—
335C2×#102C2×D4311yescharacteristic
336C2×#102C2×D4311yescharacteristic
337C2×#97—431no—
338C2×#97—431no—
339C2×#97C2×D4311yescharacteristic
340C2×C4×C8—431no—
341C2×C4×C8—431no—
342C2×C4×C8—431no—
343#391—431no—
344#391—861no—
345#391—861no—
346#390—431no—
347#389—431no—
348#389—431no—
349#388—861no—
350#388—861no—
351#387—861no—
352#387—861no—
353#385—861no—
354#385—861no—
355#384—431no—
356#382—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4C2×D4311yescharacteristic
359#376—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368C43#2165411yescharacteristic, complemented, Sylow
369C22×Q8—431no—
370C22×Q8—861no—
371C22×D4C22×D4311yescharacteristic
372C23×C4—21no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8C22×D4311yescharacteristic
376C22×C8C22×D4311yescharacteristic
377C4⋊Q8—434no—
378C4⋊Q8—862no—
379#124—434no—
380#124—862no—
381C4×Q8—862no—
382C4×Q8—862no—
383C4×D4—22no—
384C4×D4—22no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—21no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—861no—
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408#103—434no—
409#103—434no—
410#103—862no—
411#103—862no—
412#102—22no—
413#102—434no—
414#102—862no—
415#102C4×D4314yes—
416#97—22no—
417#97—434no—
418#97—862no—
419C4×C8—862no—
420C4×C8—862no—
421C4×C8—862no—
422#95—21no—
423#95—431no—
424#95—431no—
425#95—431no—
426#95—431no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—21no—
435C2×Q8—432no—
436C2×Q8—864no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—3441no—
443C2×Q8—3441no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×C4×D4312yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4D4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4C23×D4311yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—432no—
472C2×C8—432no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×C4×D4312yes—
478C2×C8#1062189812yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—432no—
485C4⋊C4—864no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—3441no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C4⋊C4—1722no—
496C4⋊C4C2×C4×D4312yes—
497C22⋊C4—42no—
498C22⋊C4—864no—
499C22⋊C4—864no—
500C22⋊C4—3441no—
501C22⋊C4—3441no—
502C42—81no—
503C42—432no—
504C42—432no—
505C42—861no—
506C42—861no—
507C42—3441no—
508C42—1722no—
509C42#1062189812yes—
510C42#1062190012yes—
511C23—22no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23C2×D4×D4311yescharacteristic
519Q8—862no—
520Q8—862no—
521Q8—3444no—
522Q8—1721no—
523Q8—1721no—
524D4—22no—
525D4—22no—
526D4—41no—
527D4—41no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4#1306331112yes—
567C2×C4#1306331112yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4C2×#1062190011yescharacteristic
572C2×C4C2×#1062189811yescharacteristic
573C2×C4C2×#1062189811yescharacteristic
574C8—22no—
575C8—22no—
576C8—862no—
577C8—862no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22C4×D4×D4311yescharacteristic
586C22C2×#1306331111yescharacteristic
587C22#1458344611yescharacteristic
588C22#1458370311yescharacteristic
589C22#1458370911yescharacteristic
590C22#1458370911yescharacteristic
591C22#1458371511yescharacteristic
592C4—22no—
593C4—22no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—862no—
598C4—862no—
599C4—3441no—
600C4—3441no—
601C4—1722no—
602C4—1721no—
603C4—1722no—
604C4—1721no—
605C4C4×#1062190011yescharacteristic
606C4C4×#1062189811yescharacteristic
607C4#1458342711yescharacteristic
608C4#1458342911yescharacteristic
609C2—82no—
610C2C4×#1306331111yescharacteristic
611C2#1914342411yescharacteristic
612C2#1914343511yescharacteristic
613C2#1914494511yescharacteristic
614C2#1914496311yescharacteristic
615C2#1914521011yescharacteristic
616C2#1914523211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#21654
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. #19137339C2semidirect
4. #19135554C2semidirect
7. #19135286C2semidirect
9. #19135269C2semidirect
10. #19134727C2semidirect
11. #19134426C2semidirect
12. C4×#13063248C2semidirect
14. #19134283C2semidirect
19. #14583257C4semidirect
65. #13063324C2×C4semidirect
88. #13063250C2×C4semidirect
90. #13063248C2×C4semidirect
94. #13063235C2×C4semidirect
368. C43#21654semidirect

Maximal subgroups

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

subgroupindex
C2×#145832572
#191373392
#191373072
#191355542
#191354052
#191352892
#191352862
#191352802
#191352692
#191347272
#191344262
C4×#130632482
C4×#130632462
#191342832
C43×#17622
#2165443