Finite Group Databasebeta

← #25086440

Subgroups — #25086440

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147298C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic, complemented
3#19146402C211yesmaximal, characteristic, complemented
4#19134232C211yesmaximal, characteristic, complemented
5#19134165C211yesmaximal, characteristic, complemented
6#19134004C211yesmaximal, characteristic, complemented
7#19134002C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133807C211yesmaximal, characteristic, complemented
10#19133746C211yesmaximal, characteristic, complemented
11#19133660C211yesmaximal, characteristic, complemented
12#19133648C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15C43×#3284C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583275C2211yescharacteristic
19#14583263—21no—
20#14583251C2211yescharacteristic, complemented
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583245C2211yescharacteristic, complemented
24#14583219—21no—
25#14583212—21no—
26#14583199—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583176C2211yescharacteristic
30#14583133—21no—
31#14583131—21no—
32#14583099C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583091—21no—
35#14583091C2211yescharacteristic
36#14583048—21no—
37#14583032—21no—
38#14583030C2211yescharacteristic, complemented
39#14583009—21no—
40C4×#10621882C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43C2×#13063245—21no—
44#102×D43—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C2×#135×C43—21no—
57C43×#550C2211yescharacteristic, complemented
58C43×#547C2211yescharacteristic
59C43×#492C2211yescharacteristic, complemented
60C43×#465—21no—
61C43×#462C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C43×#452—21no—
64C43×#449—21no—
65C4×SD16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic, complemented
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621884—21no—
70C2×#10621882—21no—
71C2×#10621882—21no—
72C2×#10621882—41no—
73C2×#10621882D411yescharacteristic
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063317—21no—
79#13063303—41no—
80#13063301—21no—
81#13063300—21no—
82#13063299—21no—
83#13063295—41no—
84C4×D172—21no—
85C4×D172C2311yescharacteristic
86C4⋊C4×D43—21no—
87#13063258—21no—
88#13063258D411yescharacteristic
89#13063256—21no—
90#13063256—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063248—41no—
96#13063247—21no—
97#13063247—21no—
98#13063246—21no—
99#13063246—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246D411yescharacteristic
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117#135×C43—44no—
118C2×Q16×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43D411yescharacteristic
122C2×D8×C43—21no—
123C22×C8×C43—21no—
124C4⋊Q8×C43C2311yescharacteristic
125#127×C43—21no—
126#127×C43C2311yescharacteristic
127#123×C43—41no—
128C22⋊Q8×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—41no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—21no—
137#106×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146#41×C43—42no—
147#41×C43—42no—
148#41×C43—81no—
149#41×C43—81no—
150C2×Q8×C43—21no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43C2×D411yescharacteristic
159C2×D4×C43C2×D411yescharacteristic
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164C2×C22⋊D43—41no—
165D4×D43—42no—
166D4×D43—81no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—41no—
171C2×D172—42no—
172C2×D172—81no—
173C2×D172C2×D411yescharacteristic
174C2×C4×D43—21no—
175C2×C4×D43—41no—
176C2×Dic86—21no—
177Q16×C43—42no—
178SD16×C43—22no—
179SD16×C43—42no—
180SD16×C43—81no—
181D8×C43—42no—
182C2×C8×C43—21no—
183C2×C8×C43—42no—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
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—41no—
196C22⋊C4×C43—41no—
197C42×C43—21no—
198C42×C43C2411yescharacteristic
199#10621884—81no—
200#10621882—22no—
201#10621882—42no—
202#10621882—81no—
203#10621882—82no—
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43C2×D411yescharacteristic
210Dic43⋊C4—41no—
211Dic43⋊C4—41no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—81no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219C8×D43—81no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—41no—
223C22×D43—21no—
224C22×D43—41no—
225C22×D43—82no—
226C22×D43—82no—
227C22×D43—161no—
228Q8×C43—21no—
229Q8×C43—21no—
230Q8×C43—41no—
231Q8×C43—41no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—81no—
240D4×C43—82no—
241D4×C43—82no—
242D4×C43—161no—
243D4×C43AGL(1,ℤ/8)12yes—
244C2×C4×C43—21no—
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—82no—
254C2×C4×C43—82no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C22⋊D43—82no—
259C2×Dic43—21no—
260C2×Dic43—41no—
261D172—21no—
262D172—41no—
263D172—41no—
264D172—41no—
265D172—41no—
266D172—81no—
267D172—82no—
268D172#13512yescomplemented
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—161no—
272Dic86—81no—
273C8×C43—21no—
274C8×C43—21no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#19788—431nomaximal, Sylow
283C22×C43—22no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43D4211yescharacteristic
293C2×D43—22no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—81no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—164no—
300C4×C43—21no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43C2×#13511yescharacteristic
307C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C43#57611yescharacteristic
309C4×C43#57711yescharacteristic
310Dic43—41no—
311Dic43—81no—
312#3366—431no—
313#3295—431no—
314#3294—431no—
315#3284D4311yescharacteristic, complemented
316#1717—431no—
317#1702—431no—
318#1677—431no—
319#1677—431no—
320#1665—431no—
321#1644—431no—
322#1635—431no—
323#1621—431no—
324#1619—431no—
325#1582—431no—
326#1580—431no—
327C2×C43—42no—
328C2×C43—81no—
329C2×C43—161no—
330C2×C43#326411yescharacteristic
331C2×C43#328211yescharacteristic
332C2×C43#328811yescharacteristic
333D43—42no—
334D43—161no—
335C2×#135—21no—
336#554—431no—
337#550C2×D4311yescharacteristic, complemented
338#547C2×D4311yescharacteristic
339D42—431no—
340#493—431no—
341#492C2×D4311yescharacteristic, complemented
342#490—861no—
343#487—431no—
344#486—431no—
345#486—431no—
346#486—431no—
347#481—861no—
348#480—861no—
349#478—861no—
350#476—431no—
351#476—431no—
352#474—431no—
353#466—861no—
354#465—21no—
355#465—861no—
356#462C2×D4311yescharacteristic, complemented
357#460—431no—
358#459—431no—
359#459—431no—
360#459—861no—
361#459C2×D4311yescharacteristic
362#452—21no—
363#450—861no—
364#449—21no—
365#447—861no—
366#446—431no—
367#442—861no—
368C4×SD16C2×D4311yescharacteristic
369C4×D8—431no—
370C8×D4—431no—
371C8×D4—431no—
372C8×D4C2×D4311yescharacteristic, complemented
373C2×#102—861no—
374C2×#102—861no—
375#334—431no—
376#334—431no—
377#333—431no—
378#332—431no—
379#331—431no—
380#331—431no—
381Q8⋊C8—431no—
382D4⋊C8—431no—
383D4⋊C8—431no—
384D4⋊C8—431no—
385#322—431no—
386C43#1978811yescharacteristic, complemented, Sylow
387C2×#41—21no—
388C2×#41—21no—
389C22×D4—861no—
390C22×D4—861no—
391#135—44no—
392C2×Q16—21no—
393C2×SD16—21no—
394C2×SD16—21no—
395C2×SD16—861no—
396C2×SD16C22⋊D4311yescharacteristic
397C2×D8—21no—
398C2×D8—431no—
399C2×D8—861no—
400C2×D8—861no—
401C2×D8—1721no—
402C22×C8—21no—
403C22×C8—861no—
404C22×C8—861no—
405C4⋊Q8—431no—
406C4⋊Q8C22×D4311yescharacteristic
407#127—21no—
408#127—431no—
409#127C22×D4311yescharacteristic
410#125—861no—
411#123—41no—
412C22⋊Q8—21no—
413C22⋊Q8—861no—
414C22⋊Q8—1721no—
415#121—21no—
416#121—21no—
417#121—41no—
418#121—861no—
419#121—861no—
420#120—1721no—
421C4×Q8C22×D4311yescharacteristic
422C4×D4—21no—
423C4×D4—431no—
424C4×D4—861no—
425C4×D4C22×D4311yescharacteristic
426C4×D4C22×D4311yescharacteristic
427C2×C4⋊C4—21no—
428C2×C4⋊C4—861no—
429#107—431no—
430#107—861no—
431#106—861no—
432#106—861no—
433#106C22⋊D4311yescharacteristic
434C4⋊C8—431no—
435C4⋊C8—431no—
436C4⋊C8—431no—
437C4⋊C8—861no—
438C4⋊C8C22×D4311yescharacteristic
439#103—21no—
440#103—1721no—
441#103C22⋊D4311yescharacteristic
442#102—21no—
443#102—431no—
444#102—431no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102C22⋊D4311yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461#97—861no—
462C4×C8—431no—
463C4×C8—431no—
464C4×C8C22×D4311yescharacteristic
465C24—1721no—
466#41—42no—
467#41—42no—
468#41—81no—
469#41—81no—
470C2×Q8—21no—
471C2×Q8—861no—
472C2×Q8C2×C22⋊D4311yescharacteristic
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—431no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—3441no—
484C2×D4—3441no—
485C2×D4—1721no—
486C2×D4—1722no—
487C2×D4—1721no—
488C2×D4—1722no—
489C2×D4D4×D4311yescharacteristic
490C2×D4C2×C22⋊D4311yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—861no—
496C22×C4—1721no—
497Q16—42no—
498SD16—22no—
499SD16—42no—
500SD16—81no—
501SD16—3441no—
502D8—42no—
503D8—862no—
504D8—3441no—
505D8—3442no—
506D8—1722no—
507C2×C8—21no—
508C2×C8—42no—
509C2×C8—431no—
510C2×C8—431no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—3441no—
516C2×C8—3441no—
517C2×C8C2×C22⋊D4311yescharacteristic
518C2×C8C2×C22⋊D4311yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—41no—
523C4⋊C4—431no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—1721no—
527C4⋊C4—1721no—
528C4⋊C4D4×D4311yescharacteristic
529C4⋊C4C2×C22⋊D4311yescharacteristic
530C4⋊C4C2×C22⋊D4311yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—861no—
536C22⋊C4—1721no—
537C22⋊C4—1721no—
538C42—21no—
539C42C23×D4311yescharacteristic
540C23—21no—
541C23—21no—
542C23—41no—
543C23—861no—
544C23—3442no—
545C23—3442no—
546C23—1721no—
547C23—6881no—
548Q8—21no—
549Q8—21no—
550Q8—41no—
551Q8—41no—
552Q8—3441no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—81no—
561D4—82no—
562D4—82no—
563D4—161no—
564D4—432no—
565D4—861no—
566D4—3441no—
567D4—3442no—
568D4—3442no—
569D4—1721no—
570D4—1721no—
571D4—1721no—
572D4—1721no—
573D4#1306335112yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—82no—
584C2×C4—82no—
585C2×C4—861no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—6881no—
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4C22×C22⋊D4311yescharacteristic
592C2×C4#1306337011yescharacteristic
593C8—21no—
594C8—21no—
595C8—41no—
596C8—861no—
597C8—861no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C22—22no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—862no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—1721no—
616C22—1721no—
617C22—6884no—
618C22D4×C22⋊D4311yescharacteristic
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—3441no—
626C4—1721no—
627C4#135×D4311yescharacteristic
628C4C2×#1306335111yescharacteristic
629C4#1458370211yescharacteristic
630C4#1458370611yescharacteristic
631C2—42no—
632C2—81no—
633C2—161no—
634C2—1722no—
635C2—6881no—
636C2#1914607111yescharacteristic
637C2#1914629611yescharacteristic
638C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3284C2
socleC22×C43D42
hypercenter#3284D43
hypocenterC43#19788
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3284

Complements

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

NH ≅ G/Ntype
1. #19147298C2semidirect
2. #19146421C2semidirect
3. #19146402C2semidirect
4. #19134232C2semidirect
5. #19134165C2semidirect
6. #19134004C2semidirect
7. #19134002C2semidirect
8. #19133933C2semidirect
9. #19133807C2semidirect
10. #19133746C2semidirect
11. #19133660C2semidirect
12. #19133648C2semidirect
13. #19133432C2semidirect
14. #19133417C2semidirect
15. C43×#3284C2semidirect
20. #14583251C22semidirect
23. #14583245C22semidirect
28. #14583189C22semidirect
38. #14583030C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
57. C43×#550C22semidirect
59. C43×#492C22semidirect
61. C43×#462C22semidirect
66. C8×D4×C43C22semidirect
268. D172#135semidirect
315. #3284D43semidirect
337. #550C2×D43semidirect
341. #492C2×D43semidirect
356. #462C2×D43semidirect
372. C8×D4C2×D43semidirect
386. C43#19788semidirect

Maximal subgroups

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

subgroupindex
#191472982
#191464212
#191464022
#191342322
#191341652
#191340042
#191340022
#191339332
#191338072
#191337462
#191336602
#191336482
#191334322
#191334172
C43×#32842
#1978843