Finite Group Databasebeta

← #25124082

Subgroups — #25124082

Order 11008.

1610 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
1C2×#14583411C211yesmaximal, characteristic
2C2×#14582896C211yesmaximal, characteristic, complemented
3C2×#14582893C211yesmaximal, characteristic, complemented
4C22×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
5#19136974C211yesmaximal, characteristic, complemented
6#19135800C212yesmaximal, complemented
7#19135793C212yesmaximal, complemented
8#19135786C212yesmaximal, complemented
9#19135779C212yesmaximal, complemented
10#19134311C211yesmaximal, characteristic, complemented
11C2×C43×#427C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C23×C43⋊C8C2211yescharacteristic
15#14583411—24no—
16#14583411—24no—
17C2×#13063309—21no—
18C2×#13063305C2212yes—
19C2×#13063300C2212yes—
20C2×#13063295—21no—
21C2×C4×D172—22no—
22C2×#13063284C2211yescharacteristic
23#14582896—24no—
24#14582893—24no—
25C2×#13063250C2211yescharacteristic, complemented
26C2×#13063250C2211yescharacteristic, complemented
27C2×#13063248C2212yescomplemented
28C2×#13063247C2211yescharacteristic, complemented
29C2×#13063247C2211yescharacteristic, complemented
30C2×#13063245C2212yescomplemented
31C2×(C2×D43)⋊C8—24no—
32C2×(C2×D43)⋊C8C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34#14582760—21no—
35#14582756C2212yes—
36#14582756C2212yes—
37#14582754—21no—
38C4×(C2×D43)⋊C4—22no—
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C23×C8×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C43×#427—24no—
45C2×#107×C43C2212yescomplemented
46C2×#106×C43C2212yescomplemented
47C24×D43D411yescharacteristic
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898—22no—
53C2×#10621898D414yes—
54C22×Dic86C2311yescharacteristic
55C22×D172—22no—
56C22×D172C2311yescharacteristic
57C22×C22⋊D43—21no—
58C23×Dic43D411yescharacteristic
59C22×C4×D43—21no—
60C22×C4×D43—22no—
61C22×C4×D43—22no—
62C22×C4×D43—22no—
63C22×C4×D43—22no—
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43D412yes—
67C22×C4×D43C2312yes—
68C22×C43⋊C8—22no—
69C22×C43⋊C8—22no—
70C22×C43⋊C8—22no—
71C22×C43⋊C8C2312yes—
72#13063309—28no—
73#13063305—24no—
74#13063305—24no—
75#13063300—24no—
76#13063300—24no—
77#13063295—28no—
78C4×D172—216no—
79#13063284—22no—
80#13063284—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—22no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—22no—
89C2×C4×Dic43—21no—
90#13063250—22no—
91#13063250—22no—
92#13063248—24no—
93#13063247—22no—
94#13063247—22no—
95#13063245—24no—
96(C2×D43)⋊C8—24no—
97(C2×D43)⋊C8—24no—
98C43⋊#95—22no—
99C43⋊#95—22no—
100C23×C4×C43C2311yescharacteristic
101C22×C8×C43—22no—
102C22×C8×C43—22no—
103C22×C8×C43D414yescomplemented
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106#117×C43—22no—
107#117×C43—22no—
108#117×C43—22no—
109#117×C43D414yes—
110C2×C4⋊C4×C43C2312yes—
111C2×C4⋊C4×C43C2312yes—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116#107×C43—24no—
117#106×C43—24no—
118C24×C43C2×D411yescharacteristic
119C23×D43—22no—
120C23×D43—24no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—21no—
124C23×D43—42no—
125C23×D43C2×D412yes—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43#4112yes—
133C22×C4×C43#4112yes—
134C22×C4×C43#4112yes—
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—24no—
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D412yes—
146#10621898—28no—
147#10621898—28no—
148#10621898—44no—
149#10621898—44no—
150C2×D172—28no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—44no—
157C2×D172—44no—
158C2×D172C2×D412yes—
159C2×C4×D43—24no—
160C2×C4×D43—24no—
161C2×C4×D43—24no—
162C2×C4×D43—24no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—44no—
170C2×C4×D43—44no—
171C2×C4×D43—42no—
172C2×C4×D43—44no—
173C2×C4×D43—42no—
174C2×C4×D43—44no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86C2×D412yes—
181C2×C8×C43—28no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43C2×D412yes—
187C2×C8×C43C2×D412yes—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43C2×D414yes—
192C22⋊C4×C43—24no—
193C22⋊C4×C43—42no—
194C42×C43—24no—
195C42×C43—42no—
196C22⋊Dic43—42no—
197(C2×D43)⋊C4—28no—
198(C2×D43)⋊C4—28no—
199(C2×D43)⋊C4—44no—
200(C2×D43)⋊C4—44no—
201C4⋊Dic43—28no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4×Dic43—42no—
207C2×C43⋊C8—22no—
208C2×C43⋊C8—22no—
209C2×C43⋊C8—22no—
210C2×C43⋊C8—44no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43#12012yes—
214C23×C43#12112yes—
215C23×C43#12312yes—
216C23×C43C22×D411yescharacteristic
217C22×D43—28no—
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—48no—
226C22×D43—48no—
227C22×D43—44no—
228C22×D43—44no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—42no—
232C22×D43—42no—
233C22×D43#13514yes—
234C2×C4×C43—24no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43#12012yes—
241C2×C4×C43#12114yes—
242C2×C4×C43#12114yes—
243C2×C4×C43#12112yes—
244C2×C4×C43#12314yes—
245C2×C4×C43#12312yes—
246C2×C4×C43#12414yes—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C22⋊D43—48no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—44no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265D172—22no—
266D172—22no—
267D172—416no—
268D172—41no—
269D172—41no—
270C4×D43—42no—
271C4×D43—42no—
272C4×D43—42no—
273C4×D43—42no—
274C4×D43—48no—
275C4×D43—48no—
276Dic86—22no—
277Dic86—22no—
278Dic86—41no—
279Dic86—41no—
280C8×C43—22no—
281C8×C43—22no—
282C43⋊C8—42no—
283#23479—431nomaximal, Sylow
284C22×C43—24no—
285C22×C43—24no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43#39414yes—
289C22×C43C2×#12011yescharacteristic
290C22×C43C2×#12111yescharacteristic
291C22×C43C2×#12311yescharacteristic
292C22×C43C2×#13512yes—
293C22×C43#57512yes—
294C2×D43—24no—
295C2×D43—24no—
296C2×D43—24no—
297C2×D43—416no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—44no—
304C2×D43—82no—
305C2×D43—81no—
306C2×D43—81no—
307C4×C43—44no—
308C4×C43—82no—
309C4×C43#39414yes—
310C4×C43C2×#12111yescharacteristic
311C4×C43C2×#12111yescharacteristic
312C4×C43C2×#12311yescharacteristic
313C4×C43C2×#12411yescharacteristic
314Dic43—42no—
315Dic43—42no—
316Dic43—81no—
317Dic43—81no—
318C2×#525—431no—
319C2×#427D4311yescharacteristic, complemented
320C2×#416—431no—
321C2×#416—431no—
322C22×C22⋊C8—431no—
323#2280—431no—
324#2036—432no—
325#2035—432no—
326#2034—432no—
327#2033—432no—
328#1735—431no—
329C2×C43—24no—
330C2×C43C2×#39411yescharacteristic
331C2×C43#300212yes—
332C2×C43#305011yescharacteristic
333C2×C43#305411yescharacteristic
334C2×C43#309112yes—
335D43—44no—
336D43—82no—
337C22×#41—431no—
338C24×C4—431no—
339C23×C8—431no—
340C23×C8C2×D4311yescharacteristic
341#525—864no—
342#525—864no—
343C2×#123—861no—
344C2×C22⋊Q8—432no—
345C2×#121—432no—
346C2×#120—861no—
347C2×C4×D4—862no—
348C2×#117—431no—
349C2×#117C2×D4311yescharacteristic
350C2×#117C2×D4311yescharacteristic
351#427—24no—
352C2×#107C2×D4312yescomplemented
353C2×#106C2×D4312yescomplemented
354#416—864no—
355#416—864no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103—432no—
359C2×#102—431no—
360C2×#102—431no—
361C2×#102—432no—
362C2×C22⋊C8—432no—
363C2×C22⋊C8—432no—
364C2×C22⋊C8—864no—
365#381—861no—
366#380—432no—
367#380—432no—
368#379—861no—
369C4×C22⋊C4—862no—
370#340—432no—
371#340—432no—
372C43#2347911yescharacteristic, complemented, Sylow
373C25—431no—
374C2×#41—434no—
375C2×#41—862no—
376C2×#41—862no—
377C2×#41—862no—
378C2×#41—862no—
379C2×#41—862no—
380C22×Q8—431no—
381C22×D4—431no—
382C22×D4—862no—
383C22×D4—861no—
384C23×C4—431no—
385C23×C4—432no—
386C23×C4—432no—
387C23×C4—862no—
388C23×C4—862no—
389C23×C4—862no—
390C23×C4—861no—
391C23×C4—862no—
392C23×C4—862no—
393C23×C4—862no—
394C23×C4C22×D4311yescharacteristic
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—432no—
398C22×C8—862no—
399C22×C8—862no—
400C22×C8—862no—
401C22×C8D17214yescomplemented
402C22×C8C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
404#123—868no—
405C22⋊Q8—864no—
406C22⋊Q8—864no—
407#121—864no—
408#121—864no—
409#120—868no—
410C4×D4—8616no—
411#117—22no—
412#117—22no—
413#117—22no—
414#117—862no—
415#117—862no—
416#117C22⋊D4314yes—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—862no—
420C2×C4⋊C4C22×D4312yes—
421C2×C4⋊C4C22×D4312yes—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—862no—
425C2×C22⋊C4—862no—
426C2×C22⋊C4—862no—
427C2×C22⋊C4—862no—
428C2×C22⋊C4—861no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—861no—
432#107—24no—
433#106—24no—
434#103—864no—
435#103—862no—
436#103—862no—
437#102—864no—
438#102—862no—
439#102—862no—
440C22⋊C8—864no—
441C22⋊C8—864no—
442#95—862no—
443#95—862no—
444C24—432no—
445C24—864no—
446C24—862no—
447C24—862no—
448C24—862no—
449C24—861no—
450C24—1722no—
451C24D4×D4311yescharacteristic
452#41—868no—
453#41—868no—
454#41—1724no—
455#41—1724no—
456C2×Q8—432no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8—861no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×D4—432no—
463C2×D4—868no—
464C2×D4—864no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—1724no—
471C2×D4—1724no—
472C2×D4—1722no—
473C2×D4—1722no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—432no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—861no—
481C22×C4—864no—
482C22×C4—864no—
483C22×C4—864no—
484C22×C4—864no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—1724no—
494C22×C4—1724no—
495C22×C4—1722no—
496C22×C4—1724no—
497C22×C4—1722no—
498C22×C4—1724no—
499C22×C4C2×D17212yes—
500C22×C4#1062189812yes—
501C22×C4D4×D4312yes—
502C22×C4D4×D4311yescharacteristic
503C22×C4#1062190212yes—
504C22×C4#1062190212yes—
505C22×C4C2×C22⋊D4312yes—
506C22×C4C23×D4311yescharacteristic
507C2×C8—28no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—862no—
513C2×C8—862no—
514C2×C8—862no—
515C2×C8—1724no—
516C2×C8C2×D17212yes—
517C2×C8C2×D17212yes—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—868no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4C2×C22⋊D4314yes—
527C22⋊C4—24no—
528C22⋊C4—42no—
529C22⋊C4—868no—
530C22⋊C4—868no—
531C22⋊C4—1724no—
532C22⋊C4—1724no—
533C22⋊C4—1722no—
534C42—24no—
535C42—42no—
536C42—1722no—
537C23—22no—
538C23—22no—
539C23—434no—
540C23—868no—
541C23—862no—
542C23—862no—
543C23—862no—
544C23—862no—
545C23—862no—
546C23—862no—
547C23—862no—
548C23—1728no—
549C23—1728no—
550C23—1724no—
551C23—1721no—
552C23—1721no—
553C23—1722no—
554C23—1722no—
555C23—1724no—
556C23#1306329312yes—
557C23#1306330012yes—
558C23#1306331012yes—
559C23C2×D4×D4311yescharacteristic
560Q8—862no—
561Q8—862no—
562Q8—1721no—
563Q8—1721no—
564D4—862no—
565D4—862no—
566D4—17216no—
567D4—1728no—
568D4—1721no—
569D4—1721no—
570C2×C4—24no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1724no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1728no—
588C2×C4—1728no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4#1306329312yes—
594C2×C4#1306329914yes—
595C2×C4#1306330012yes—
596C2×C4#1306330014yes—
597C2×C4#1306331012yes—
598C2×C4#1306331014yes—
599C2×C4#1306331414yes—
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C22×C22⋊D4311yescharacteristic
602C2×C4C22×D17211yescharacteristic
603C2×C4C2×#1062189811yescharacteristic
604C2×C4C2×#1062190211yescharacteristic
605C2×C4C2×#1062190211yescharacteristic
606C8—22no—
607C8—22no—
608C8—1722no—
609C22—22no—
610C22—24no—
611C22—24no—
612C22—22no—
613C22—864no—
614C22—864no—
615C22—864no—
616C22—3441no—
617C22—3442no—
618C22—3441no—
619C22—17216no—
620C22—1722no—
621C22—1724no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22—1722no—
626C22#1458281614yes—
627C22C2×#1306329311yescharacteristic
628C22C2×#1306330011yescharacteristic
629C22C2×#1306331011yescharacteristic
630C22#135×D4312yes—
631C22#1458369612yes—
632C4—44no—
633C4—82no—
634C4—3441no—
635C4—3441no—
636C4—1722no—
637C4—1722no—
638C4#1458281614yes—
639C4C2×#1306329911yescharacteristic
640C4C2×#1306330011yescharacteristic
641C4C2×#1306331011yescharacteristic
642C4C2×#1306331411yescharacteristic
643C2—24no—
644C2—3442no—
645C2—1724no—
646C2C2×#1458281611yescharacteristic
647C2#1914380912yes—
648C2#1914417711yescharacteristic
649C2#1914420511yescharacteristic
650C2#1914451212yes—
subgroupG/H
centerC22×C4D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#427C2
socleC23×C43C22×D4
prime radicalC2×#14583411C2
hypercenterC2×#427D43
hypocenterC43#23479
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#14582896C2semidirect
3. C2×#14582893C2semidirect
4. C22×(C2×D43)⋊C8C2semidirect
5. #19136974C2semidirect
6. #19135800C2semidirect
7. #19135793C2semidirect
8. #19135786C2semidirect
9. #19135779C2semidirect
10. #19134311C2semidirect
11. C2×C43×#427C2semidirect
25. C2×#13063250C22semidirect
26. C2×#13063250C22semidirect
27. C2×#13063248C22semidirect
28. C2×#13063247C22semidirect
29. C2×#13063247C22semidirect
30. C2×#13063245C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
45. C2×#107×C43C22semidirect
46. C2×#106×C43C22semidirect
103. C22×C8×C43D4semidirect
319. C2×#427D43semidirect
352. C2×#107C2×D43semidirect
353. C2×#106C2×D43semidirect
372. C43#23479semidirect
401. C22×C8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145834112
C2×#145828962
C2×#145828932
C22×(C2×D43)⋊C82
#191369742
#191358002
#191357932
#191357862
#191357792
#191343112
C2×C43×#4272
#2347943