Finite Group Databasebeta

← #25137882

Subgroups — #25137882

Order 11008.

784 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
1C2×#14583205C211yesmaximal, characteristic, complemented
2C2×#14582954C211yesmaximal, characteristic
3#19142904C211yesmaximal, characteristic
4#19137125C211yesmaximal, characteristic
5#19136034C211yesmaximal, characteristic
6#19136024C211yesmaximal, characteristic
7#19135801C211yesmaximal, characteristic
8#19135793C211yesmaximal, characteristic
9#19135551C211yesmaximal, characteristic, complemented
10#19135364C211yesmaximal, characteristic, complemented
11#19135330C211yesmaximal, characteristic, complemented
12#19135285C211yesmaximal, characteristic, complemented
13#19135284C211yesmaximal, characteristic, complemented
14#19134609C211yesmaximal, characteristic, complemented
15C43×#1944C211yesmaximal, characteristic, complemented
16C2×#13063316C2211yescharacteristic
17C2×#13063305C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×C42×D43C2211yescharacteristic
20#14583205—24no—
21#14582954—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582785—21no—
36#14582782—21no—
37#14582781—21no—
38#14582773—21no—
39#14582770—21no—
40#14582770—21no—
41#14582764C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47#14582746—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063316—22no—
68#13063316—22no—
69#13063305—22no—
70#13063305—22no—
71#13063290—22no—
72#13063290—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C42×D43—22no—
91C42×D43—22no—
92#13063258—22no—
93#13063256—22no—
94Dic43⋊C8—22no—
95Dic43⋊C8D414yes—
96#13063250—22no—
97#13063250—22no—
98#13063248—22no—
99#13063248—22no—
100(C2×D43)⋊C8—22no—
101(C2×D43)⋊C8—22no—
102#13063236—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#106×C43—22no—
123#97×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×C4×D43—41no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86#4112yes—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43C2×D412yes—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43#4112yes—
175C42×C43—21no—
176C42×C43—21no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181C4⋊Dic43—24no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43C2×D412yes—
197C4×Dic43#4112yes—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D412yes—
204C23×C43C22×D411yescharacteristic
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43#13712yes—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
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—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C432−1+411yescharacteristic
235C2×C4×C432−1+411yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—21no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43#12112yes—
256C2×Dic43#12112yes—
257C4×D43—44no—
258C4×D43—44no—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263Dic86—22no—
264Dic86—22no—
265Dic86—41no—
266Dic86—41no—
267C8×C43—22no—
268C8×C43—41no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271#24707—431nomaximal, Sylow
272C22×C43C2×#12111yescharacteristic
273C22×C43#52511yescharacteristic
274C22×C43#53611yescharacteristic
275C22×C43C2×#13711yescharacteristic
276C22×C43#57511yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C4×C43—42no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43#54711yescharacteristic
293C4×C43#54811yescharacteristic
294C4×C43#55211yescharacteristic
295C4×C43#55611yescharacteristic
296Dic43—22no—
297Dic43—22no—
298Dic43—42no—
299Dic43—41no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303C2×#479—431no—
304C2×#432—431no—
305#2851—431no—
306C4×C22⋊Q8—431no—
307#2077—431no—
308#2076—431no—
309#2036—431no—
310#2035—431no—
311#1989—431no—
312#1949—431no—
313#1944D4311yescharacteristic, complemented
314#1943—431no—
315#1935—431no—
316#1935—431no—
317#1805—431no—
318C2×C43#241511yescharacteristic
319C2×C43#305411yescharacteristic
320C2×C43#305611yescharacteristic
321C2×C43#311111yescharacteristic
322C2×C43#311711yescharacteristic
323C2×C43#323611yescharacteristic
324C2×C43#324011yescharacteristic
325D43—42no—
326C2×#125—431no—
327C2×C22⋊Q8—431no—
328C2×C4×Q8—431no—
329C22×C42—431no—
330#479—864no—
331#432—864no—
332C2×#107—431no—
333C2×#107C2×D4311yescharacteristic
334C2×#106—431no—
335C2×#106C2×D4311yescharacteristic
336C2×C4⋊C8—431no—
337C2×C4⋊C8—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×#97—431no—
345C2×#97C2×D4311yescharacteristic
346#391—431no—
347#389—431no—
348#389C2×D4311yescharacteristic
349#389C2×D4311yescharacteristic
350#387—861no—
351#387—861no—
352#387—861no—
353#385—861no—
354#385—861no—
355#385—861no—
356#382—431no—
357#380—431no—
358#380—431no—
359#380—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—861no—
362C4×C22⋊C4—861no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340C2×D4311yescharacteristic
370#340C2×D4311yescharacteristic
371C43#2470711yescharacteristic, complemented, Sylow
372C22×Q8—431no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380#125—862no—
381#125—862no—
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C4×Q8—862no—
385C4×Q8—862no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C42—431no—
405C2×C42—431no—
406C2×C42—431no—
407C2×C42—862no—
408C2×C42—862no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42C22×D4311yescharacteristic
412#107—22no—
413#107—862no—
414#106—22no—
415#106—862no—
416C4⋊C8—434no—
417C4⋊C8—862no—
418#103—862no—
419#103—862no—
420#103—862no—
421#103—862no—
422C22⋊C8—862no—
423C22⋊C8—862no—
424#97—22no—
425#97—862no—
426#95—21no—
427#95—21no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437C24—431no—
438C2×Q8—432no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—1721no—
465C22×C4—1721no—
466C22×C4—1721no—
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—432no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8D4×D4312yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—864no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4#1062189812yes—
503C22⋊C4—864no—
504C22⋊C4—1722no—
505C22⋊C4—1722no—
506C22⋊C4—1722no—
507C42—21no—
508C42—21no—
509C42—432no—
510C42—432no—
511C42—862no—
512C42—862no—
513C42—1722no—
514C42—1722no—
515C23—432no—
516C23—861no—
517C23—861no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23C2×D4×D4311yescharacteristic
523Q8—862no—
524Q8—862no—
525Q8—1721no—
526Q8—1721no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—432no—
546C2×C4—432no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—862no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—1724no—
556C2×C4—1724no—
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—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C2×C4#1306337311yescharacteristic
577C2×C4#1306337311yescharacteristic
578C8—22no—
579C8—41no—
580C8—862no—
581C8—1721no—
582C22—862no—
583C22—862no—
584C22—862no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22#121×D4311yescharacteristic
590C22#1458340811yescharacteristic
591C22#1458347411yescharacteristic
592C22#137×D4311yescharacteristic
593C22#1458369511yescharacteristic
594C22#1458369511yescharacteristic
595C22#1458369811yescharacteristic
596C4—42no—
597C4—41no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—862no—
603C4—862no—
604C4—3441no—
605C4—3441no—
606C4—3441no—
607C4—1721no—
608C4—1722no—
609C4#1458355011yescharacteristic
610C4#1458355911yescharacteristic
611C4#1458358111yescharacteristic
612C4#1458362111yescharacteristic
613C2—1722no—
614C2#1913802311yescharacteristic
615C2#1914420211yescharacteristic
616C2#1914422411yescharacteristic
617C2#1914470811yescharacteristic
618C2#1914476411yescharacteristic
619C2#1914580211yescharacteristic
620C2#1914583811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1944C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1944D43
hypocenterC43#24707
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
1. C2×#14583205C2semidirect
9. #19135551C2semidirect
10. #19135364C2semidirect
11. #19135330C2semidirect
12. #19135285C2semidirect
13. #19135284C2semidirect
14. #19134609C2semidirect
15. C43×#1944C2semidirect
313. #1944D43semidirect
371. C43#24707semidirect

Maximal subgroups

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

subgroupindex
C2×#145832052
C2×#145829542
#191429042
#191371252
#191360342
#191360242
#191358012
#191357932
#191355512
#191353642
#191353302
#191352852
#191352842
#191346092
C43×#19442
#2470743