Finite Group Databasebeta

← #25086208

Subgroups — #25086208

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147240C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic, complemented
3D4×#10621882C211yesmaximal, characteristic
4#19134231C211yesmaximal, characteristic, complemented
5#19134128C211yesmaximal, characteristic, complemented
6#19134044C211yesmaximal, characteristic, complemented
7#19134029C211yesmaximal, characteristic, complemented
8#19133953C211yesmaximal, characteristic, complemented
9#19133773C211yesmaximal, characteristic, complemented
10#19133711C211yesmaximal, characteristic, complemented
11#19133705C211yesmaximal, characteristic, complemented
12#19133666C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3324C211yesmaximal, characteristic, complemented
16C22×#10621882—21no—
17#14583609C2211yescharacteristic, complemented
18D4×D172C2211yescharacteristic
19#14583275C2211yescharacteristic
20#14583271C2211yescharacteristic, complemented
21#14583253—21no—
22#14583249C2211yescharacteristic, complemented
23#14583247C2211yescharacteristic, complemented
24#14583246C2211yescharacteristic, complemented
25#14583219—21no—
26#14583206—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583133—21no—
30#14583131—21no—
31#14583111—21no—
32#14583101C2211yescharacteristic, complemented
33#14583099C2211yescharacteristic, complemented
34#14583094C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583048—21no—
37#14583033—21no—
38#14583032—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C4×#10621884—21no—
41C4×#10621882C2211yescharacteristic
42C8×D172C2211yescharacteristic, complemented
43D4×C43⋊C8C2211yescharacteristic
44#102×D43—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, complemented
56C43×#556C2211yescharacteristic, complemented
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic, complemented
59C43×#482—21no—
60C43×#474C2211yescharacteristic
61C43×#468—21no—
62C43×#460C2211yescharacteristic, complemented
63C43×#450—21no—
64C4×SD16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic, complemented
66C43×#418—21no—
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621883—41no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621882—21no—
73C2×#10621882—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—44no—
77C2×#10621882D411yescharacteristic
78C22×C43⋊C8—21no—
79C2×C8×D43—21no—
80#13063325C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063317—21no—
83#13063303—41no—
84#13063301—21no—
85#13063300—21no—
86#13063299—21no—
87#13063295—41no—
88C4×D172—21no—
89C4×D172C2311yescharacteristic
90C4⋊C4×D43—21no—
91#13063258D411yescharacteristic
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
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—41no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C2×M16×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#126×C43—41no—
124#124×C43—21no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#120×C43—41no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#117×C43—21no—
134#107×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C24×C43—41no—
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
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
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C2×C22⋊D43—41no—
163D4×D43—42no—
164D4×D43—81no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—41no—
169C2×D172—42no—
170C2×D172—81no—
171C2×D172C2×D411yescharacteristic
172C2×C4×D43—21no—
173C2×C4×D43—41no—
174C2×Dic86—21no—
175SD16×C43—22no—
176SD16×C43—81no—
177M16×C43—81no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—41no—
191C22⋊C4×C43—41no—
192C22⋊C4×C43—41no—
193C42×C43—21no—
194C42×C43—41no—
195C42×C43C2411yescharacteristic
196#10621884—42no—
197#10621884—81no—
198#10621883—82no—
199#10621882—22no—
200#10621882—42no—
201#10621882—42no—
202#10621882—42no—
203#10621882—81no—
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—42no—
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219C8×D43—81no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—41no—
223C23×C43—82no—
224C23×C43—82no—
225C23×C43—161no—
226C22×D43—21no—
227C22×D43—41no—
228C22×D43—82no—
229C22×D43—82no—
230C22×D43—161no—
231Q8×C43—21no—
232Q8×C43—21no—
233Q8×C43—41no—
234Q8×C43—41no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—81no—
243D4×C43—82no—
244D4×C43—82no—
245D4×C43#13512yes—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
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—
268D172AGL(1,ℤ/8)12yes—
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#19773—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×C43—164no—
293C22×C43D4211yescharacteristic
294C2×D43—22no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—164no—
301C4×C43—21no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43C2×#13511yescharacteristic
308C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
309C4×C43#57611yescharacteristic
310C4×C43#57711yescharacteristic
311Dic43—41no—
312Dic43—81no—
313#3360—431no—
314#3324D4311yescharacteristic, complemented
315#3295—431no—
316D4×D8—431no—
317#1717—431no—
318#1697—431no—
319#1683—431no—
320#1681—431no—
321#1668—431no—
322#1639—431no—
323#1629—431no—
324#1628—431no—
325#1622—431no—
326#1581—431no—
327SD16⋊C8—431no—
328C2×C43—42no—
329C2×C43—81no—
330C2×C43—161no—
331C2×C43#326511yescharacteristic
332C2×C43#328011yescharacteristic
333C2×C43#328811yescharacteristic
334D43—42no—
335D43—161no—
336C22×D8—861no—
337#556C2×D4311yescharacteristic, complemented
338#554—431no—
339D42—431no—
340D42C2×D4311yescharacteristic
341#493—431no—
342#492—431no—
343#488—861no—
344#487—431no—
345#486—431no—
346#486—431no—
347#486C2×D4311yescharacteristic, complemented
348#482—21no—
349#481—861no—
350#479—861no—
351#476—431no—
352#476—431no—
353#474C2×D4311yescharacteristic
354#468—21no—
355#466—861no—
356#465—861no—
357#463—861no—
358#461—431no—
359#460—431no—
360#460C2×D4311yescharacteristic, complemented
361#459—431no—
362#459—431no—
363#450—21no—
364#450—861no—
365#447—861no—
366#447—861no—
367C8×Q8—431no—
368C4×SD16—861no—
369C4×SD16C2×D4311yescharacteristic
370C4×D8—431no—
371#436C2×D4311yescharacteristic, complemented
372C8×D4—431no—
373C8×D4—431no—
374#418—21no—
375C2×#102—861no—
376#335—431no—
377#335—431no—
378#333—431no—
379#332—431no—
380#331—431no—
381#331—431no—
382Q8⋊C8—431no—
383D4⋊C8—431no—
384D4⋊C8—431no—
385D4⋊C8—431no—
386#322—431no—
387C43#1977311yescharacteristic, complemented, Sylow
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—861no—
391C22×D4—861no—
392C2×SD16—21no—
393C2×SD16—861no—
394C2×SD16—861no—
395C2×SD16—1721no—
396C2×SD16C22⋊D4311yescharacteristic
397C2×D8—431no—
398C2×D8—861no—
399C2×D8—861no—
400C2×D8—861no—
401C2×D8—861no—
402C2×D8—1724no—
403C2×M16—21no—
404C22×C8—861no—
405C22×C8—861no—
406C4⋊Q8—431no—
407C4⋊Q8C22×D4311yescharacteristic
408#127—431no—
409#127C22×D4311yescharacteristic
410#126—41no—
411#125—861no—
412#124—21no—
413C22⋊Q8—21no—
414C22⋊Q8—861no—
415C22⋊Q8—1721no—
416#121—21no—
417#121—21no—
418#121—861no—
419#121—861no—
420#120—41no—
421#120—1721no—
422C4×Q8—21no—
423C4×Q8C22×D4311yescharacteristic
424C4×D4—431no—
425C4×D4—861no—
426C4×D4C22×D4311yescharacteristic
427C4×D4C22×D4311yescharacteristic
428#117—21no—
429C2×C4⋊C4—861no—
430#107—21no—
431#107—431no—
432#106—861no—
433#106—861no—
434#106C22⋊D4311yescharacteristic
435C4⋊C8—431no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—861no—
439C4⋊C8C22×D4311yescharacteristic
440#103—861no—
441#103—861no—
442#103—861no—
443#103C22⋊D4311yescharacteristic
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—431no—
449#102—431no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102—1721no—
458#102C22⋊D4311yescharacteristic
459C22⋊C8—21no—
460C22⋊C8—861no—
461C22⋊C8—861no—
462C4×C8—431no—
463C4×C8—431no—
464C4×C8—861no—
465C4×C8C22×D4311yescharacteristic
466C24—41no—
467C24—1721no—
468C2×Q8—21no—
469C2×Q8—861no—
470C2×Q8C2×C22⋊D4311yescharacteristic
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—81no—
479C2×D4—81no—
480C2×D4—431no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—3441no—
485C2×D4—3441no—
486C2×D4—1721no—
487C2×D4—1722no—
488C2×D4—1721no—
489C2×D4—1722no—
490C2×D4D4×D4311yescharacteristic
491C2×D4C2×C22⋊D4311yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—861no—
495C22×C4—1721no—
496SD16—22no—
497SD16—81no—
498SD16—3442no—
499SD16—3441no—
500SD16—1722no—
501D8—862no—
502D8—3441no—
503D8—1722no—
504D8—1722no—
505D8—1722no—
506M16—81no—
507C2×C8—21no—
508C2×C8—431no—
509C2×C8—431no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—3441no—
515C2×C8—1722no—
516C2×C8C2×C22⋊D4311yescharacteristic
517C2×C8C2×C22⋊D4311yescharacteristic
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—41no—
522C4⋊C4—431no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4D4×D4311yescharacteristic
528C4⋊C4C2×C22⋊D4311yescharacteristic
529C4⋊C4C2×C22⋊D4311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—861no—
536C22⋊C4—1721no—
537C22⋊C4—1721no—
538C42—21no—
539C42—41no—
540C42C23×D4311yescharacteristic
541C23—21no—
542C23—21no—
543C23—41no—
544C23—82no—
545C23—82no—
546C23—161no—
547C23—861no—
548C23—3442no—
549C23—3442no—
550C23—1721no—
551C23—6881no—
552Q8—21no—
553Q8—21no—
554Q8—41no—
555Q8—41no—
556Q8—3441no—
557D4—21no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—81no—
565D4—82no—
566D4—82no—
567D4—432no—
568D4—861no—
569D4—3441no—
570D4—3442no—
571D4—3442no—
572D4—1721no—
573D4—1721no—
574D4—1721no—
575D4—1721no—
576D4#1306334512yes—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—861no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—6881no—
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4C22×C22⋊D4311yescharacteristic
593C2×C4#1306337011yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—861no—
598C8—861no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C22—22no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—164no—
613C22—862no—
614C22—3441no—
615C22—3441no—
616C22—3441no—
617C22—1721no—
618C22—1721no—
619C22—6884no—
620C22D4×C22⋊D4311yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—81no—
627C4—3441no—
628C4—1721no—
629C4C2×#1306334511yescharacteristic
630C4AGL(1,ℤ/8)×D4311yescharacteristic
631C4#1458370211yescharacteristic
632C4#1458370911yescharacteristic
633C2—42no—
634C2—81no—
635C2—161no—
636C2—1722no—
637C2—6881no—
638C2#1914608411yescharacteristic
639C2#1914627611yescharacteristic
640C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3324C2
socleC22×C43D42
prime radicalD4×#10621882C2
hypercenter#3324D43
hypocenterC43#19773
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3324

Complements

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

NH ≅ G/Ntype
1. #19147240C2semidirect
2. #19146421C2semidirect
4. #19134231C2semidirect
5. #19134128C2semidirect
6. #19134044C2semidirect
7. #19134029C2semidirect
8. #19133953C2semidirect
9. #19133773C2semidirect
10. #19133711C2semidirect
11. #19133705C2semidirect
12. #19133666C2semidirect
13. #19133422C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3324C2semidirect
17. #14583609C22semidirect
20. #14583271C22semidirect
22. #14583249C22semidirect
23. #14583247C22semidirect
24. #14583246C22semidirect
28. #14583189C22semidirect
32. #14583101C22semidirect
33. #14583099C22semidirect
39. Q8×C43⋊C8C22semidirect
42. C8×D172C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582643C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582620C22semidirect
56. C43×#556C22semidirect
58. C43×#486C22semidirect
62. C43×#460C22semidirect
65. C43×#436C22semidirect
314. #3324D43semidirect
337. #556C2×D43semidirect
347. #486C2×D43semidirect
360. #460C2×D43semidirect
371. #436C2×D43semidirect
387. C43#19773semidirect

Maximal subgroups

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

subgroupindex
#191472402
#191464212
D4×#106218822
#191342312
#191341282
#191340442
#191340292
#191339532
#191337732
#191337112
#191337052
#191336662
#191334222
SD16⋊(C43⋊C8)2
C43×#33242
#1977343