Finite Group Databasebeta

← #25073320

Subgroups — #25073320

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145619C211yesmaximal, characteristic, complemented
2#19145142C211yesmaximal, characteristic, complemented
3C2×#14583179C211yesmaximal, characteristic, complemented
4#19133879C212yesmaximal, complemented
5#19133865C212yesmaximal, complemented
6#19133844C212yesmaximal, complemented
7#19133830C212yesmaximal, complemented
8#19133295C211yesmaximal, characteristic, complemented
9#19133038C211yesmaximal, characteristic, complemented
10#19133008C211yesmaximal, characteristic, complemented
11C43×#3520C211yesmaximal, characteristic
12C2×#13063325C2211yescharacteristic
13#14583309—22no—
14#14583302C2212yescomplemented
15#14583295C2212yescomplemented
16#14583294—21no—
17#14583269—21no—
18#14583179—21no—
19#14583179—21no—
20#14583179C2212yes—
21#14583179C2212yes—
22#14583109C2212yescomplemented
23#14583104C2212yescomplemented
24#14583054—21no—
25#14583037—21no—
26#14582956C2211yescharacteristic
27#14582942—22no—
28C2×#13063258—21no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063246—21no—
31C4×#10621877C2211yescharacteristic
32#14582645C2212yescomplemented
33#14582645C2212yescomplemented
34Q8⋊(C43⋊C8)C2212yescomplemented
35D4⋊(C43⋊C8)C2212yes—
36D4⋊(C43⋊C8)C2212yes—
37D4⋊(C43⋊C8)C2212yescomplemented
38C43×#556C2211yescharacteristic
39C43×#554—21no—
40C43×#552—21no—
41C43×#551—22no—
42D4×Q8×C43C2211yescharacteristic
43C43×#548—21no—
44C43×#547C2211yescharacteristic
45C43×#547C2211yescharacteristic
46C43×#546—21no—
47C43×#542—21no—
48C43×#539—22no—
49C43×#533C2211yescharacteristic
50C43×#529C2211yescharacteristic
51C43×#525—21no—
52C2×C22⋊Q8×C43—21no—
53C43×#520—21no—
54C2×C4×D4×C43C2211yescharacteristic
55C22×Dic86—21no—
56C2×#10621885—22no—
57C2×#10621883—22no—
58C2×#10621877—21no—
59C22×C43⋊C8—21no—
60#13063325—21no—
61#13063325—21no—
62#13063325—21no—
63#13063325C2312yes—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66#13063258—24no—
67#13063258—22no—
68#13063258—22no—
69#13063256—24no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)C2312yes—
72C4⋊(C43⋊C8)C2312yes—
73#13063248—22no—
74#13063248—22no—
75#13063246—22no—
76#13063246—22no—
77C22⋊(C43⋊C8)—21no—
78#13063236—21no—
79#13063236—21no—
80C4×C43⋊C8C2312yes—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C22×Q8×C43—21no—
84C22×D4×C43D411yescharacteristic
85C23×C4×C43—21no—
86C4⋊Q8×C43—21no—
87C4⋊Q8×C43C2311yescharacteristic
88C4⋊Q8×C43C2311yescharacteristic
89#126×C43—22no—
90#126×C43—22no—
91#126×C43—21no—
92#125×C43—22no—
93#125×C43D412yes—
94#125×C43D411yescharacteristic
95#124×C43—22no—
96#124×C43—21no—
97#124×C43D411yescharacteristic
98#123×C43—22no—
99#123×C43—22no—
100#123×C43—21no—
101#123×C43—22no—
102#123×C43—22no—
103C22⋊Q8×C43—22no—
104C22⋊Q8×C43—22no—
105C22⋊Q8×C43—22no—
106C22⋊Q8×C43—21no—
107C22⋊Q8×C43—21no—
108C22⋊Q8×C43—21no—
109C22⋊Q8×C43—21no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—22no—
112C22⋊Q8×C43—21no—
113C22⋊Q8×C43D411yescharacteristic
114#121×C43—22no—
115#121×C43—21no—
116#121×C43—21no—
117#121×C43D411yescharacteristic
118#120×C43—22no—
119C4×Q8×C43—21no—
120C4×Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43C2311yescharacteristic
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C4×D4×C43—22no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43D411yescharacteristic
131C4×D4×C43D411yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#117×C43—22no—
136#117×C43—21no—
137#117×C43—21no—
138#117×C43D412yes—
139C2×C4⋊C4×C43—22no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43D411yescharacteristic
143C2×C22⋊C4×C43—22no—
144C2×C22⋊C4×C43—21no—
145C2×C42×C43C2311yescharacteristic
146C24×C43—21no—
147#41×C43—42no—
148#41×C43—42no—
149#41×C43—82no—
150C2×Q8×C43—22no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—82no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—22no—
160C2×D4×C43—41no—
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—82no—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×Dic43—41no—
178C2×Dic86—22no—
179C2×Dic86—41no—
180C2×Dic86—82no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—22no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D412yes—
199C4⋊C4×C43C2×D412yes—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C22⋊C4×C43—21no—
210C22⋊C4×C43—21no—
211C22⋊C4×C43—21no—
212C22⋊C4×C43—21no—
213C22⋊C4×C43—21no—
214C22⋊C4×C43—22no—
215C42×C43—22no—
216C42×C43—22no—
217C42×C43—21no—
218C42×C43C2×D411yescharacteristic
219C42×C43C2×D411yescharacteristic
220C42×C43C2×D411yescharacteristic
221C42×C43C2411yescharacteristic
222#10621885—82no—
223#10621883—82no—
224C4⋊Dic43—22no—
225C4⋊Dic43—22no—
226C4⋊Dic43—41no—
227C4⋊Dic43—41no—
228#10621877—24no—
229C2×C43⋊C8—22no—
230C2×C43⋊C8—22no—
231C2×C43⋊C8—22no—
232C2×C43⋊C8—42no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—42no—
237C23×C43—42no—
238C23×C43—81no—
239C23×C43#12011yescharacteristic
240Q8×C43—22no—
241Q8×C43—41no—
242Q8×C43—41no—
243Q8×C43—42no—
244Q8×C43—82no—
245D4×C43—21no—
246D4×C43—21no—
247D4×C43—21no—
248D4×C43—22no—
249D4×C43—42no—
250D4×C43—44no—
251D4×C43—42no—
252D4×C43—82no—
253D4×C43#13712yes—
254C2×C4×C43—22no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—22no—
258C2×C4×C43—21no—
259C2×C4×C43—22no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—22no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—44no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43—81no—
271C2×C4×C43—81no—
272C2×C4×C43—81no—
273C2×C4×C43—82no—
274C2×C4×C43—82no—
275C2×C4×C43#12011yescharacteristic
276C2×C4×C43#12011yescharacteristic
277C2×C4×C43#12011yescharacteristic
278C2×C4×C43C22×D411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C22×D411yescharacteristic
281C2×Dic43—42no—
282C2×Dic43—82no—
283Dic86—42no—
284Dic86—42no—
285Dic86—82no—
286C43⋊C8—24no—
287C43⋊C8—42no—
288C43⋊C8—42no—
289#18587—431nomaximal, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—22no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43—41no—
298C22×C43—41no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—84no—
302C22×C43#45612yes—
303C22×C43C2×#12011yescharacteristic
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—41no—
309C4×C43—42no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—42no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43C2×#13711yescharacteristic
316C4×C43#57511yescharacteristic
317C4×C43#57612yes—
318Dic43—82no—
319#3520D4311yescharacteristic
320#3218—431no—
321#3165—431no—
322C2×#474—431no—
323#1654—432no—
324#1652—432no—
325#1649—432no—
326#1647—432no—
327#1552—431no—
328#1490—431no—
329#1483—431no—
330C2×C43—22no—
331C2×C43—42no—
332C2×C43—81no—
333C2×C43—81no—
334C2×C43#300711yescharacteristic
335C2×C43#300811yescharacteristic
336C2×C43C2×#45611yescharacteristic
337#556C2×D4311yescharacteristic
338#554—21no—
339#552—21no—
340#551—22no—
341D4×Q8C2×D4311yescharacteristic
342#548—21no—
343#547C2×D4311yescharacteristic
344#547C2×D4311yescharacteristic
345#546—21no—
346#542—21no—
347#539—22no—
348#533C2×D4311yescharacteristic
349C2×C4⋊Q8—431no—
350#529C2×D4311yescharacteristic
351#525—21no—
352C2×C22⋊Q8—21no—
353#520—21no—
354C2×C4×D4C2×D4311yescharacteristic
355#501—862no—
356#500—432no—
357#498—432no—
358#497—861no—
359#491—861no—
360#474—432no—
361#474—432no—
362#474—861no—
363#474—861no—
364#462—432no—
365#461—432no—
366#451—861no—
367#448—861no—
368#432—431no—
369#428—862no—
370C2×#107—861no—
371C2×C4⋊C8—431no—
372C2×#102—861no—
373C4×M16—431no—
374#332—432no—
375#332—432no—
376Q8⋊C8—432no—
377D4⋊C8—432no—
378D4⋊C8—432no—
379D4⋊C8—432no—
380C43#1858711yescharacteristic, complemented, Sylow
381C2×#41—21no—
382C2×#41—21no—
383C22×Q8—21no—
384C22×Q8—861no—
385C22×D4C22⋊D4311yescharacteristic
386C23×C4—21no—
387C2×Q16—862no—
388C2×SD16—862no—
389C2×M16—861no—
390C22×C8—861no—
391C4⋊Q8—21no—
392C4⋊Q8—432no—
393C4⋊Q8—861no—
394C4⋊Q8—861no—
395C4⋊Q8—861no—
396C4⋊Q8C22×D4311yescharacteristic
397C4⋊Q8C22×D4311yescharacteristic
398#126—22no—
399#126—22no—
400#126—21no—
401#125—22no—
402#125C22⋊D4311yescharacteristic
403#125C22⋊D4312yes—
404#124—22no—
405#124—21no—
406#124C22⋊D4311yescharacteristic
407#123—22no—
408#123—22no—
409#123—21no—
410#123—22no—
411#123—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8—21no—
422C22⋊Q8C22⋊D4311yescharacteristic
423#121—22no—
424#121—21no—
425#121—21no—
426#121C22⋊D4311yescharacteristic
427#120—22no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8C22×D4311yescharacteristic
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4C22⋊D4311yescharacteristic
440C4×D4C22⋊D4311yescharacteristic
441C4×D4C22×D4311yescharacteristic
442C4×D4C22×D4311yescharacteristic
443C4×D4C22×D4311yescharacteristic
444#117—22no—
445#117—21no—
446#117—21no—
447#117C22⋊D4312yes—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4C22⋊D4311yescharacteristic
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C42C22×D4311yescharacteristic
457#107—862no—
458#107—862no—
459#107—864no—
460#106—864no—
461C4⋊C8—432no—
462C4⋊C8—432no—
463C4⋊C8—861no—
464#103—862no—
465#103—862no—
466#102—862no—
467#102—862no—
468C22⋊C8—861no—
469#97—861no—
470#97—861no—
471C4×C8—432no—
472C24—21no—
473#41—42no—
474#41—42no—
475#41—82no—
476C2×Q8—22no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—82no—
480C2×Q8—862no—
481C2×Q8—3442no—
482C2×Q8—1721no—
483C2×Q8C2×C22⋊D4311yescharacteristic
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—41no—
490C2×D4C2×C22⋊D4311yescharacteristic
491C2×D4C2×C22⋊D4311yescharacteristic
492C2×D4C2×C22⋊D4311yescharacteristic
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—82no—
503C22×C4—1721no—
504C22×C4C2×C22⋊D4311yescharacteristic
505C22×C4C2×C22⋊D4311yescharacteristic
506C22×C4C2×C22⋊D4311yescharacteristic
507Q16—3442no—
508SD16—3442no—
509M16—864no—
510C2×C8—862no—
511C2×C8—862no—
512C2×C8—862no—
513C2×C8—1722no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—1721no—
530C4⋊C4—1721no—
531C4⋊C4C2×C22⋊D4311yescharacteristic
532C4⋊C4C2×C22⋊D4311yescharacteristic
533C4⋊C4C2×C22⋊D4312yes—
534C4⋊C4C2×C22⋊D4311yescharacteristic
535C4⋊C4C2×C22⋊D4311yescharacteristic
536C4⋊C4C2×C22⋊D4312yes—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C42—22no—
553C42—22no—
554C42—21no—
555C42C2×C22⋊D4311yescharacteristic
556C42C2×C22⋊D4311yescharacteristic
557C42C2×C22⋊D4311yescharacteristic
558C42C23×D4311yescharacteristic
559C23—21no—
560C23—21no—
561C23—21no—
562C23—42no—
563C23—42no—
564C23—81no—
565C23#1306329411yescharacteristic
566Q8—22no—
567Q8—41no—
568Q8—41no—
569Q8—42no—
570Q8—82no—
571Q8—3442no—
572Q8—1722no—
573Q8—1722no—
574D4—21no—
575D4—21no—
576D4—21no—
577D4—22no—
578D4—42no—
579D4—44no—
580D4—42no—
581D4—82no—
582D4#1306335512yes—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—44no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—81no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—3442no—
605C2×C4—1722no—
606C2×C4#1306329411yescharacteristic
607C2×C4#1306329411yescharacteristic
608C2×C4#1306329411yescharacteristic
609C2×C4C22×C22⋊D4311yescharacteristic
610C2×C4C22×C22⋊D4311yescharacteristic
611C2×C4C22×C22⋊D4311yescharacteristic
612C8—864no—
613C8—1722no—
614C8—1722no—
615C22—21no—
616C22—21no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—84no—
627C22#1458308212yes—
628C22C2×#1306329411yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—3442no—
641C4C2×#1306335511yescharacteristic
642C4#1458369711yescharacteristic
643C4#1458370212yes—
644C2—22no—
645C2—42no—
646C2—81no—
647C2—81no—
648C2#1914385511yescharacteristic
649C2#1914386311yescharacteristic
650C2C2×#1458308211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3520C2
socleC22×C43C2×#120
hypercenter#3520D43
hypocenterC43#18587
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #19145619C2semidirect
2. #19145142C2semidirect
3. C2×#14583179C2semidirect
4. #19133879C2semidirect
5. #19133865C2semidirect
6. #19133844C2semidirect
7. #19133830C2semidirect
8. #19133295C2semidirect
9. #19133038C2semidirect
10. #19133008C2semidirect
14. #14583302C22semidirect
15. #14583295C22semidirect
22. #14583109C22semidirect
23. #14583104C22semidirect
32. #14582645C22semidirect
33. #14582645C22semidirect
34. Q8⋊(C43⋊C8)C22semidirect
37. D4⋊(C43⋊C8)C22semidirect
380. C43#18587semidirect

Maximal subgroups

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

subgroupindex
#191456192
#191451422
C2×#145831792
#191338792
#191338652
#191338442
#191338302
#191332952
#191330382
#191330082
C43×#35202
#1858743