Finite Group Databasebeta

← #25088055

Subgroups — #25088055

Order 11008.

724 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147013C211yesmaximal, characteristic, complemented
2#19146839C211yesmaximal, characteristic, complemented
3D4×#10621882C211yesmaximal, characteristic, complemented
4#19134186C211yesmaximal, characteristic, complemented
5#19134128C211yesmaximal, characteristic, complemented
6#19134125C211yesmaximal, characteristic, complemented
7#19133992C211yesmaximal, characteristic, complemented
8#19133948C211yesmaximal, characteristic, complemented
9#19133711C211yesmaximal, characteristic, complemented
10#19133710C211yesmaximal, characteristic, complemented
11#19133678C211yesmaximal, characteristic, complemented
12#19133677C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3325C211yesmaximal, characteristic, complemented
16C22×#10621882—21no—
17#14583614C2211yescharacteristic, complemented
18D4×D172C2211yescharacteristic
19#14583302C2211yescharacteristic, complemented
20#14583275C2211yescharacteristic
21#14583273C2211yescharacteristic, complemented
22#14583271C2211yescharacteristic, complemented
23#14583246C2211yescharacteristic, complemented
24#14583226—21no—
25#14583223—21no—
26#14583220—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583186C2211yescharacteristic, complemented
30#14583151—21no—
31#14583133—21no—
32#14583133—21no—
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic, complemented
35#14583091C2211yescharacteristic
36#14583033—21no—
37#14583032—21no—
38#14583031—21no—
39C4×#10621882C2211yescharacteristic
40#14582978C2211yescharacteristic, complemented
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43#14582935—21no—
44#14582902—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic, complemented
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#555C2211yescharacteristic, complemented
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic, complemented
59C43×#482—21no—
60C43×#476C2211yescharacteristic
61C43×#469—21no—
62C43×#459C2211yescharacteristic, complemented
63C43×#447—21no—
64C4×D8×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic, complemented
66C43×#418—21no—
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621883—41no—
70C2×#10621884—41no—
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621882—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—44no—
77C2×#10621882D411yescharacteristic
78C2×#10621872—21no—
79C22×C43⋊C8—21no—
80C22×C43⋊C8—21no—
81#13063325C2311yescharacteristic
82#13063322C2311yescharacteristic
83#13063311—41no—
84#13063300—21no—
85#13063299—21no—
86#13063299—21no—
87#13063296—21no—
88#13063295—41no—
89C4×D172C2311yescharacteristic
90#13063284—21no—
91#13063283—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258D411yescharacteristic
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063247—21no—
102#13063247—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246D411yescharacteristic
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×D8×C43—21no—
119C2×D8×C43D411yescharacteristic
120C2×M16×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#124×C43—41no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#120×C43—41no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43—21no—
134#107×C43D411yescharacteristic
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—42no—
155C2×D4×C43—42no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C2×D4×C43C2×D411yescharacteristic
159C2×D4×C43C2×D411yescharacteristic
160C2×D4×C43C2×D411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C2×C22⋊D43—41no—
165C2×C22⋊D43—41no—
166D4×D43—42no—
167D4×D43—81no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—41no—
172C2×D172—42no—
173C2×D172—81no—
174C2×D172C2×D411yescharacteristic
175C2×C4×D43—21no—
176C2×Dic86—21no—
177D8×C43—22no—
178D8×C43—81no—
179M16×C43—81no—
180C2×C8×C43—21no—
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—41no—
192C22⋊C4×C43—41no—
193C22⋊C4×C43—41no—
194C42×C43—41no—
195C42×C43C2411yescharacteristic
196C22⋊Dic43—41no—
197#10621884—82no—
198#10621883—82no—
199#10621882—22no—
200#10621882—42no—
201#10621882—42no—
202#10621882—42no—
203#10621882—81no—
204#10621882—81no—
205(C2×D43)⋊C4—21no—
206(C2×D43)⋊C4—41no—
207(C2×D43)⋊C4—41no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43C2×D411yescharacteristic
211C4×Dic43—41no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—42no—
217C2×C43⋊C8—42no—
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220#10621872—81no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—82no—
226C23×C43—82no—
227C23×C43—161no—
228C22×D43—21no—
229C22×D43—41no—
230C22×D43—82no—
231C22×D43—82no—
232C22×D43—161no—
233Q8×C43—81no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—81no—
244D4×C43—82no—
245D4×C43—82no—
246D4×C43—161no—
247D4×C43#13512yes—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C22⋊D43—82no—
262C22⋊D43—161no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265D172—21no—
266D172—21no—
267D172—41no—
268D172—41no—
269D172—41no—
270D172—41no—
271D172—81no—
272D172—82no—
273C4×D43—41no—
274C4×D43—41no—
275Dic86—81no—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—41no—
279C43⋊C8—22no—
280C43⋊C8—21no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284C43⋊C8AGL(1,ℤ/8)12yes—
285#19898—431nomaximal, Sylow
286C22×C43—22no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—164no—
299C22×C43D4211yescharacteristic
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—164no—
307C4×C43—21no—
308C4×C43—41no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—81no—
312C4×C43C2×#13511yescharacteristic
313C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
314C4×C43#57611yescharacteristic
315C4×C43#57711yescharacteristic
316Dic43—41no—
317Dic43—81no—
318#3341—431no—
319#3325—431no—
320#3325D4311yescharacteristic, complemented
321D4×D8—431no—
322#1706—431no—
323#1697—431no—
324#1697—431no—
325#1675—431no—
326#1667—431no—
327#1629—431no—
328#1629—431no—
329#1624—431no—
330#1624—431no—
331#1589—431no—
332C8×D8—431no—
333C2×C43—42no—
334C2×C43—81no—
335C2×C43—81no—
336C2×C43—161no—
337C2×C43#327211yescharacteristic
338C2×C43#328011yescharacteristic
339C2×C43#329211yescharacteristic
340D43—81no—
341D43—161no—
342C22×D8—861no—
343#555—431no—
344#555C2×D4311yescharacteristic, complemented
345D42—431no—
346D42C2×D4311yescharacteristic
347#500—431no—
348#493—431no—
349#492—431no—
350#492—431no—
351#486—431no—
352#486C2×D4311yescharacteristic, complemented
353#482—21no—
354#482—861no—
355#482—861no—
356#482—861no—
357#476—431no—
358#476—431no—
359#476—431no—
360#476C2×D4311yescharacteristic
361#469—21no—
362#469—861no—
363#466—861no—
364#466—861no—
365#459—431no—
366#459—431no—
367#459—431no—
368#459C2×D4311yescharacteristic, complemented
369#447—21no—
370#447—861no—
371#447—861no—
372#447—861no—
373C4×D8—431no—
374C4×D8C2×D4311yescharacteristic
375#436—431no—
376#436C2×D4311yescharacteristic, complemented
377C8×D4—431no—
378C8×D4—431no—
379#427—861no—
380#418—21no—
381#418—861no—
382#335—431no—
383#335—431no—
384#333—431no—
385#333—431no—
386#331—431no—
387#331—431no—
388D4⋊C8—431no—
389D4⋊C8—431no—
390D4⋊C8—431no—
391D4⋊C8—431no—
392C82—431no—
393C43#1989811yescharacteristic, complemented, Sylow
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—861no—
397C22×D4—861no—
398C2×SD16—1721no—
399C2×SD16—1721no—
400C2×D8—21no—
401C2×D8—431no—
402C2×D8—861no—
403C2×D8—861no—
404C2×D8—861no—
405C2×D8—861no—
406C2×D8—861no—
407C2×D8—1724no—
408C2×D8C22⋊D4311yescharacteristic
409C2×M16—21no—
410C2×M16—861no—
411C22×C8—861no—
412C22×C8—861no—
413C4⋊Q8—431no—
414C4⋊Q8C22×D4311yescharacteristic
415#127—431no—
416#127C22×D4311yescharacteristic
417#124—41no—
418#124—1721no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121—21no—
423#121—861no—
424#121—861no—
425#121—861no—
426#121—861no—
427#120—41no—
428#120—1721no—
429C4×D4—431no—
430C4×D4C22×D4311yescharacteristic
431C4×D4C22×D4311yescharacteristic
432C4×D4C22×D4311yescharacteristic
433#117—21no—
434#117—21no—
435#117—861no—
436#117—861no—
437#107—431no—
438#107—861no—
439#107—861no—
440#107C22⋊D4311yescharacteristic
441#106—21no—
442#106—861no—
443#106—861no—
444#106—861no—
445C4⋊C8—431no—
446C4⋊C8—431no—
447C4⋊C8—431no—
448C4⋊C8C22×D4311yescharacteristic
449#102—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—431no—
454#102—431no—
455#102—861no—
456#102—861no—
457#102—861no—
458#102—861no—
459#102—861no—
460#102—861no—
461#102—861no—
462#102—861no—
463#102C22⋊D4311yescharacteristic
464#102C22⋊D4311yescharacteristic
465C22⋊C8—21no—
466C22⋊C8—861no—
467C22⋊C8—861no—
468C22⋊C8—861no—
469C4×C8—431no—
470C4×C8—431no—
471C4×C8C22×D4311yescharacteristic
472C24—41no—
473C24—1721no—
474C2×Q8—21no—
475C2×Q8—861no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—41no—
484C2×D4—81no—
485C2×D4—81no—
486C2×D4—431no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—3441no—
491C2×D4—3441no—
492C2×D4—1721no—
493C2×D4—1722no—
494C2×D4—1721no—
495C2×D4—1722no—
496C2×D4—1721no—
497C2×D4D4×D4311yescharacteristic
498C2×D4C2×C22⋊D4311yescharacteristic
499C2×D4C2×C22⋊D4311yescharacteristic
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—861no—
504SD16—3442no—
505SD16—3442no—
506D8—22no—
507D8—81no—
508D8—862no—
509D8—3441no—
510D8—3441no—
511D8—1722no—
512D8—1722no—
513D8—1722no—
514M16—81no—
515M16—3441no—
516C2×C8—21no—
517C2×C8—431no—
518C2×C8—431no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—1722no—
524C2×C8—1722no—
525C2×C8C2×C22⋊D4311yescharacteristic
526C2×C8C2×C22⋊D4311yescharacteristic
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—431no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4D4×D4311yescharacteristic
533C4⋊C4C2×C22⋊D4311yescharacteristic
534C4⋊C4C2×C22⋊D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—861no—
542C22⋊C4—1721no—
543C22⋊C4—1721no—
544C22⋊C4—1721no—
545C42—41no—
546C42—1721no—
547C42C23×D4311yescharacteristic
548C23—21no—
549C23—21no—
550C23—21no—
551C23—41no—
552C23—82no—
553C23—82no—
554C23—161no—
555C23—861no—
556C23—3442no—
557C23—3442no—
558C23—1721no—
559C23—6881no—
560Q8—81no—
561Q8—3441no—
562D4—21no—
563D4—21no—
564D4—21no—
565D4—21no—
566D4—21no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—81no—
572D4—82no—
573D4—82no—
574D4—161no—
575D4—861no—
576D4—861no—
577D4—3441no—
578D4—3442no—
579D4—3442no—
580D4—1721no—
581D4—1721no—
582D4—1721no—
583D4—1721no—
584D4—6881no—
585D4#1306334512yes—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—861no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C22×C22⋊D4311yescharacteristic
602C2×C4#1306337011yescharacteristic
603C8—21no—
604C8—21no—
605C8—41no—
606C8—432no—
607C8—862no—
608C8—861no—
609C8—1721no—
610C8—1721no—
611C8—1721no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—164no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—1721no—
629C22—1721no—
630C22—1721no—
631C22—6884no—
632C22D4×C22⋊D4311yescharacteristic
633C4—21no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—3441no—
639C4—1721no—
640C4C2×#1306334511yescharacteristic
641C4AGL(1,ℤ/8)×D4311yescharacteristic
642C4#1458370211yescharacteristic
643C4#1458370911yescharacteristic
644C2—42no—
645C2—81no—
646C2—81no—
647C2—161no—
648C2—3441no—
649C2—6881no—
650C2#1914618911yescharacteristic
651C2#1914627611yescharacteristic
652C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3325C2
socleC22×C43D42
hypercenter#3325D43
hypocenterC43#19898
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #19147013C2semidirect
2. #19146839C2semidirect
3. D4×#10621882C2semidirect
4. #19134186C2semidirect
5. #19134128C2semidirect
6. #19134125C2semidirect
7. #19133992C2semidirect
8. #19133948C2semidirect
9. #19133711C2semidirect
10. #19133710C2semidirect
11. #19133678C2semidirect
12. #19133677C2semidirect
13. #19133478C2semidirect
14. D8×C43⋊C8C2semidirect
15. C43×#3325C2semidirect
17. #14583614C22semidirect
19. #14583302C22semidirect
21. #14583273C22semidirect
22. #14583271C22semidirect
23. #14583246C22semidirect
28. #14583189C22semidirect
29. #14583186C22semidirect
34. #14583094C22semidirect
40. #14582978C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582643C22semidirect
50. #14582642C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
56. C43×#555C22semidirect
58. C43×#486C22semidirect
62. C43×#459C22semidirect
65. C43×#436C22semidirect
320. #3325D43semidirect
344. #555C2×D43semidirect
352. #486C2×D43semidirect
368. #459C2×D43semidirect
376. #436C2×D43semidirect
393. C43#19898semidirect

Maximal subgroups

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

subgroupindex
#191470132
#191468392
D4×#106218822
#191341862
#191341282
#191341252
#191339922
#191339482
#191337112
#191337102
#191336782
#191336772
#191334782
D8×C43⋊C82
C43×#33252
#1989843