Finite Group Databasebeta

← #25085990

Subgroups — #25085990

Order 11008.

736 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146410C211yesmaximal, characteristic, complemented
2#19146313C211yesmaximal, characteristic, complemented
3#19146195C211yesmaximal, characteristic, complemented
4#19134265C211yesmaximal, characteristic, complemented
5#19134082C211yesmaximal, characteristic, complemented
6#19134032C211yesmaximal, characteristic, complemented
7#19133981C211yesmaximal, characteristic, complemented
8#19133938C211yesmaximal, characteristic, complemented
9#19133830C211yesmaximal, characteristic, complemented
10#19133829C211yesmaximal, characteristic, complemented
11#19133773C211yesmaximal, characteristic, complemented
12#19133684C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15C43×#3334C211yesmaximal, characteristic, complemented
16C2×#13063350—21no—
17C2×#13063345—21no—
18#14583554C2211yescharacteristic
19D4×D172C2211yescharacteristic
20#14583302C2211yescharacteristic, complemented
21#14583278C2211yescharacteristic, complemented
22#14583273C2211yescharacteristic
23#14583247C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583214—21no—
26#14583179C2211yescharacteristic
27#14583147—21no—
28#14583138—21no—
29#14583134—21no—
30#14583104C2211yescharacteristic, complemented
31#14583101C2211yescharacteristic
32#14583101C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583061—21no—
36#14583059—21no—
37#14583049—21no—
38#14583044—21no—
39#14583031—21no—
40C4×#10621882C2211yescharacteristic
41#14582977C2211yescharacteristic
42C8×D172C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic, complemented
44#102×D43—21no—
45#14582652C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582645C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C43×#547C2211yescharacteristic
57C43×#547C2211yescharacteristic, complemented
58C43×#500C2211yescharacteristic, complemented
59C43×#480—21no—
60C43×#480—21no—
61C43×#474C2211yescharacteristic
62C43×#474C2211yescharacteristic, complemented
63C43×#466—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic, complemented
66C2×#107×C43—21no—
67C2×#10621898—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70#13063350—44no—
71#13063345—44no—
72C2×#10621885—21no—
73C2×#10621885—21no—
74C2×#10621883—21no—
75C2×#10621884—21no—
76C2×#10621884—21no—
77C2×#10621884—21no—
78C2×#10621884—21no—
79C2×#10621882—21no—
80C2×#10621882—21no—
81C2×#10621882D411yescharacteristic
82C2×#10621877—21no—
83C22×C43⋊C8—21no—
84C2×C8×D43—21no—
85#13063325C2311yescharacteristic
86#13063322C2311yescharacteristic
87#13063307—41no—
88#13063304—21no—
89#13063300—21no—
90#13063299—21no—
91#13063296—21no—
92#13063295—41no—
93C4×D172C2311yescharacteristic
94C4⋊C4×D43—21no—
95#13063258—21no—
96#13063258—41no—
97#13063258D411yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063249—21no—
103#13063248—21no—
104#13063247—21no—
105#13063247—21no—
106#13063246—21no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245—21no—
110#13063245—41no—
111#13063245D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114(C2×D43)⋊C8—21no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C2×#41×C43—21no—
118C2×#41×C43—21no—
119C2×D8×C43D411yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#123×C43—41no—
124#123×C43—41no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136#107×C43—21no—
137#107×C43—21no—
138#107×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147#41×C43—42no—
148#41×C43—42no—
149#41×C43—81no—
150#41×C43—81no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163C2×C22⋊D43—41no—
164C2×C22⋊D43—41no—
165D4×D43—42no—
166D4×D43—81no—
167#10621898—42no—
168#10621898—81no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—41no—
173C2×D172—42no—
174C2×D172—81no—
175C2×D172C2×D411yescharacteristic
176C2×C4×D43—21no—
177C2×C4×D43—41no—
178C2×Dic86—21no—
179D8×C43—41no—
180C2×C8×C43—21no—
181C2×C8×C43—42no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C42×C43C2411yescharacteristic
199C22⋊Dic43—41no—
200#10621885—42no—
201#10621885—81no—
202#10621884—42no—
203#10621884—42no—
204#10621884—42no—
205#10621884—81no—
206#10621883—42no—
207#10621882—42no—
208#10621882—81no—
209#10621882D814yescomplemented
210(C2×D43)⋊C4—21no—
211(C2×D43)⋊C4—41no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43C2×D411yescharacteristic
215Dic43⋊C4—41no—
216#10621877—42no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—42no—
222C2×C43⋊C8C2×D411yescharacteristic
223C2×C43⋊C8C2×D411yescharacteristic
224C8×D43—81no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C22×D43—21no—
229C22×D43—41no—
230C22×D43—82no—
231C22×D43—82no—
232C22×D43—161no—
233Q8×C43—41no—
234Q8×C43—41no—
235Q8×C43—41no—
236Q8×C43—41no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—21no—
240D4×C43—21no—
241D4×C43—21no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43C2×D812yes—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—82no—
257C2×C4×C43—82no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C22⋊D43—82no—
262C22⋊D43—82no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265D172—21no—
266D172—41no—
267D172—41no—
268D172—41no—
269D172—41no—
270D172—81no—
271D172—82no—
272D172C2×D812yes—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—82no—
276Dic86—41no—
277Dic86—41no—
278C8×C43—21no—
279C8×C43—21no—
280C8×C43—41no—
281C43⋊C8—21no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286C43⋊C8C2×D812yes—
287#19758—431nomaximal, Sylow
288C22×C43—22no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43D4211yescharacteristic
298C2×D43—22no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—164no—
305C4×C43—21no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43C22×D811yescharacteristic
312C4×C43#57511yescharacteristic
313C4×C43#57611yescharacteristic
314C4×C43#57711yescharacteristic
315Dic43—41no—
316Dic43—81no—
317#3334D4311yescharacteristic, complemented
318#3294—431no—
319#3283—431no—
320#3272—431no—
321#1722—431no—
322#1689—431no—
323#1681—431no—
324#1673—431no—
325#1665—431no—
326#1647—431no—
327#1647—431no—
328#1639—431no—
329#1625—431no—
330#1581—431no—
331#1580—431no—
332C2×C43—42no—
333C2×C43—81no—
334C2×C43—81no—
335C2×C43#326711yescharacteristic
336C2×C43D4×D811yescharacteristic
337C2×C43#328911yescharacteristic
338D43—42no—
339D43—161no—
340C2×AGL(1,ℤ/8)—861no—
341C2×#135—861no—
342#547—431no—
343#547C2×D4311yescharacteristic
344#547C2×D4311yescharacteristic, complemented
345D42—431no—
346#500—431no—
347#500C2×D4311yescharacteristic, complemented
348#494—431no—
349#492—431no—
350#486—431no—
351#486—431no—
352#480—21no—
353#480—21no—
354#480—861no—
355#474—431no—
356#474C2×D4311yescharacteristic
357#474C2×D4311yescharacteristic, complemented
358#468—861no—
359#467—861no—
360#466—21no—
361#466—861no—
362#461—431no—
363#461—431no—
364#461—431no—
365#459—431no—
366#459—431no—
367#452—861no—
368#452—861no—
369#450—861no—
370#449—861no—
371#447—861no—
372C4×D8—431no—
373C4×D8C2×D4311yescharacteristic
374#436—431no—
375C8×D4—431no—
376C8×D4—431no—
377C8×D4C2×D4311yescharacteristic, complemented
378C2×#107—21no—
379C2×#102—861no—
380#335—431no—
381#334—431no—
382#332—431no—
383#332—431no—
384#332—431no—
385#331—431no—
386D4⋊C8—431no—
387D4⋊C8—431no—
388D4⋊C8—431no—
389D4⋊C8—431no—
390#322—431no—
391C43#1975811yescharacteristic, complemented, Sylow
392C2×#41—21no—
393C2×#41—21no—
394C2×#41—861no—
395C22×D4—861no—
396C22×D4—861no—
397AGL(1,ℤ/8)—1724no—
398#135—1724no—
399C2×Q16—861no—
400C2×Q16—861no—
401C2×SD16—861no—
402C2×SD16—861no—
403C2×SD16—861no—
404C2×SD16—861no—
405C2×SD16—861no—
406C2×D8—431no—
407C2×D8—861no—
408C2×D8—861no—
409C2×D8C22⋊D4311yescharacteristic
410C2×M16—861no—
411C22×C8—21no—
412C22×C8—861no—
413C22×C8—861no—
414C4⋊Q8—431no—
415C4⋊Q8C22×D4311yescharacteristic
416C4⋊Q8C22×D4311yescharacteristic
417#127—431no—
418#123—41no—
419#123—41no—
420#123—1721no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—861no—
424#121—21no—
425#121—21no—
426#121—861no—
427#121—861no—
428#121—861no—
429#120—1721no—
430C4×D4—431no—
431C4×D4C22×D4311yescharacteristic
432C4×D4C22×D4311yescharacteristic
433C4×D4C22×D4311yescharacteristic
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—861no—
437#107—21no—
438#107—21no—
439#107—21no—
440#107—21no—
441#107—431no—
442#107—861no—
443#107—1721no—
444#107C22⋊D4311yescharacteristic
445C4⋊C8—431no—
446C4⋊C8—431no—
447C4⋊C8—431no—
448C4⋊C8C22×D4311yescharacteristic
449#103—861no—
450#103—861no—
451#103—861no—
452#102—21no—
453#102—21no—
454#102—431no—
455#102—431no—
456#102—861no—
457#102—861no—
458#102—861no—
459#102—861no—
460#102—861no—
461#102—1721no—
462#102C22⋊D4311yescharacteristic
463#102C22⋊D4311yescharacteristic
464C22⋊C8—21no—
465C22⋊C8—861no—
466C22⋊C8—861no—
467C22⋊C8—861no—
468C4×C8—431no—
469C4×C8—431no—
470C4×C8C22×D4311yescharacteristic
471C24—1721no—
472#41—42no—
473#41—42no—
474#41—81no—
475#41—81no—
476#41—3441no—
477#41—1722no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—861no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—431no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—3441no—
488C2×D4—3441no—
489C2×D4—1721no—
490C2×D4—1722no—
491C2×D4—1721no—
492C2×D4—1722no—
493C2×D4—1721no—
494C2×D4D4×D4311yescharacteristic
495C2×D4C2×C22⋊D4311yescharacteristic
496C2×D4C2×C22⋊D4311yescharacteristic
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—861no—
503C22×C4—1721no—
504Q16—3441no—
505Q16—1722no—
506SD16—3441no—
507SD16—1722no—
508SD16—1722no—
509SD16—1722no—
510SD16—1722no—
511D8—41no—
512D8—434no—
513D8—3441no—
514D8—1722no—
515M16—1722no—
516C2×C8—21no—
517C2×C8—42no—
518C2×C8—431no—
519C2×C8—431no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—3441no—
525C2×C8—1722no—
526C2×C8C2×C22⋊D4311yescharacteristic
527C2×C8C2×C22⋊D4311yescharacteristic
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—431no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—1721no—
538C4⋊C4D4×D4311yescharacteristic
539C4⋊C4C2×C22⋊D4311yescharacteristic
540C4⋊C4C2×C22⋊D4311yescharacteristic
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—861no—
547C22⋊C4—1721no—
548C22⋊C4—1721no—
549C42C23×D4311yescharacteristic
550C23—21no—
551C23—21no—
552C23—21no—
553C23—861no—
554C23—3442no—
555C23—3442no—
556C23—1721no—
557C23—6881no—
558Q8—41no—
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—1721no—
563Q8—1721no—
564D4—21no—
565D4—21no—
566D4—21no—
567D4—21no—
568D4—21no—
569D4—82no—
570D4—82no—
571D4—432no—
572D4—861no—
573D4—3441no—
574D4—3442no—
575D4—3442no—
576D4—3442no—
577D4—1721no—
578D4—1721no—
579D4—1721no—
580D4—1721no—
581D4D8×D4312yes—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—861no—
596C2×C4—3442no—
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—861no—
608C8—1721no—
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—862no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—1721no—
626C22—1721no—
627C22—6884no—
628C22D4×C22⋊D4311yescharacteristic
629C4—21no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—3441no—
636C4—1721no—
637C4C2×D8×D4311yescharacteristic
638C4#1458369711yescharacteristic
639C4#1458370011yescharacteristic
640C4#1458370711yescharacteristic
641C2—42no—
642C2—81no—
643C2—81no—
644C2—1722no—
645C2—6881no—
646C2#1914612111yescharacteristic
647C2D8×C22⋊D4311yescharacteristic
648C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3334C2
socleC22×C43D42
hypercenter#3334D43
hypocenterC43#19758
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #19146410C2semidirect
2. #19146313C2semidirect
3. #19146195C2semidirect
4. #19134265C2semidirect
5. #19134082C2semidirect
6. #19134032C2semidirect
7. #19133981C2semidirect
8. #19133938C2semidirect
9. #19133830C2semidirect
10. #19133829C2semidirect
11. #19133773C2semidirect
12. #19133684C2semidirect
13. #19133425C2semidirect
14. #19133417C2semidirect
15. C43×#3334C2semidirect
20. #14583302C22semidirect
21. #14583278C22semidirect
30. #14583104C22semidirect
43. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582645C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
57. C43×#547C22semidirect
58. C43×#500C22semidirect
62. C43×#474C22semidirect
65. C8×D4×C43C22semidirect
209. #10621882D8semidirect
317. #3334D43semidirect
344. #547C2×D43semidirect
347. #500C2×D43semidirect
357. #474C2×D43semidirect
377. C8×D4C2×D43semidirect
391. C43#19758semidirect

Maximal subgroups

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

subgroupindex
#191464102
#191463132
#191461952
#191342652
#191340822
#191340322
#191339812
#191339382
#191338302
#191338292
#191337732
#191336842
#191334252
#191334172
C43×#33342
#1975843