Finite Group Databasebeta

← #25082006

Subgroups — #25082006

Order 11008.

758 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#19145509C211yesmaximal, characteristic, complemented
2#19144070C211yesmaximal, characteristic, complemented
3#19144043C211yesmaximal, characteristic, complemented
4#19143702C211yesmaximal, characteristic, complemented
5#19134040C211yesmaximal, characteristic, complemented
6#19134038C211yesmaximal, characteristic, complemented
7#19134032C211yesmaximal, characteristic, complemented
8#19134030C211yesmaximal, characteristic, complemented
9#19133954C211yesmaximal, characteristic, complemented
10#19133952C211yesmaximal, characteristic, complemented
11#19133948C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133269C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic, complemented
15C43×#1667C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C2×#13063344—21no—
18#14583447C2211yescharacteristic
19#127×D43C2211yescharacteristic
20C4×#10621900C2211yescharacteristic
21#14583275C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583120—21no—
25#14583112—21no—
26#14583110C2211yescharacteristic, complemented
27#14583104C2211yescharacteristic, complemented
28#14583100C2211yescharacteristic
29#14583098—21no—
30#14583096C2211yescharacteristic
31#14583096C2211yescharacteristic, complemented
32#14583094C2211yescharacteristic
33#14583092—21no—
34#14583092—21no—
35#14583092—21no—
36#14583031—21no—
37#14583031—21no—
38C8×Dic86C2211yescharacteristic, complemented
39#14583023C2211yescharacteristic, complemented
40D4×C43⋊C8C2211yescharacteristic, complemented
41C8×C22⋊D43—21no—
42(C22⋊D43)⋊C8—21no—
43#14582950C2211yescharacteristic
44#14582949—21no—
45#14582921C2211yescharacteristic
46C2×Dic43⋊C8—21no—
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582902—21no—
50#14582892—21no—
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582644C2211yescharacteristic, complemented
56#14582643C2211yescharacteristic
57#14582643C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#493C2211yescharacteristic
61C43×#459C2211yescharacteristic
62C43×#459C2211yescharacteristic, complemented
63C8×D4×C43C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×#10621900D411yescharacteristic
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43—21no—
72#13063349—44no—
73#13063344—44no—
74C2×Dic172—21no—
75C2×#10621873—21no—
76C2×#10621883—21no—
77C2×#10621883—21no—
78C2×#10621883—21no—
79C2×#10621882—21no—
80C2×#10621882—21no—
81C2×#10621882—21no—
82C2×#10621872—21no—
83C22×C43⋊C8—21no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86#13063325C2311yescharacteristic
87#13063322C2311yescharacteristic
88#13063321—21no—
89#13063321—21no—
90#13063321—21no—
91#13063312—21no—
92#13063296—21no—
93#13063296—21no—
94C4×Dic86C2311yescharacteristic
95#13063290D411yescharacteristic
96D4×Dic43—21no—
97D4×Dic43—21no—
98D4×Dic43D411yescharacteristic
99C4×C22⋊D43—21no—
100(C22⋊D43)⋊C4—21no—
101#13063283D411yescharacteristic
102#13063281—21no—
103C2×C4×Dic43—21no—
104C42×D43C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8D411yescharacteristic
114Dic43⋊C8D411yescharacteristic
115#13063250—21no—
116#13063248—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063246—21no—
121#13063246—21no—
122#13063246—21no—
123#13063246—21no—
124#13063245—21no—
125C22⋊(C43⋊C8)—21no—
126(C2×D43)⋊C8D411yescharacteristic
127(C2×D43)⋊C8D411yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43—21no—
130C8×Dic43—21no—
131C2×D8×C43—21no—
132C2×D8×C43—21no—
133C2×D8×C43—21no—
134C2×D8×C43—21no—
135C22×C8×C43—21no—
136#127×C43C2311yescharacteristic
137#127×C43C2311yescharacteristic
138C4×D4×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142#102×C43—21no—
143#102×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C2×C22⋊D43—21no—
156C2×C22⋊D43—41no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—41no—
163#10621900—22no—
164#10621900—42no—
165#10621900—42no—
166#10621900D814yescomplemented
167D4×D43—42no—
168D4×D43—42no—
169D4×D43—81no—
170D4×D43—81no—
171D4×D43—82no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×C4×D43#4111yescharacteristic
178C2×Dic86—21no—
179C2×Dic86C2×D411yescharacteristic
180D8×C43—42no—
181D8×C43—42no—
182D8×C43—81no—
183D8×C43—81no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—81no—
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C22⋊C4×C43—21no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—21no—
194C22⋊Dic43—41no—
195C22⋊Dic43—41no—
196#10621883—42no—
197#10621883—42no—
198#10621883—42no—
199#10621882—42no—
200#10621882—81no—
201#10621882—81no—
202(C2×D43)⋊C4—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43C2×D411yescharacteristic
212C4×Dic43C2×D411yescharacteristic
213C4×Dic43#4111yescharacteristic
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—81no—
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220Dic172—42no—
221#10621873—42no—
222#10621872—42no—
223C8×D43—42no—
224C8×D43—81no—
225C23×C43—21no—
226C23×C43—41no—
227C23×C43—41no—
228C22×D43—41no—
229C22×D43—82no—
230C22×D43—82no—
231C22×D43—82no—
232C22×D43#12111yescharacteristic
233D4×C43—21no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—81no—
243D4×C43—81no—
244D4×C43C2×D812yes—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C22⋊D43—24no—
252C22⋊D43—82no—
253C22⋊D43—82no—
254C22⋊D43—82no—
255C22⋊D43—82no—
256C2×Dic43—21no—
257C2×Dic43—24no—
258C2×Dic43—21no—
259C2×Dic43—41no—
260C2×Dic43—81no—
261C2×Dic43—82no—
262C2×Dic43#12111yescharacteristic
263C2×Dic43#12111yescharacteristic
264C2×Dic43#12111yescharacteristic
265D172—41no—
266D172—41no—
267D172—41no—
268D172—41no—
269D172—81no—
270C4×D43—21no—
271C4×D43—21no—
272C4×D43—41no—
273C4×D43C2×D812yes—
274C4×D43#13512yes—
275Dic86—21no—
276Dic86—41no—
277Dic86—41no—
278Dic86C2×D812yes—
279C8×C43—21no—
280C8×C43—21no—
281C8×C43—41no—
282C8×C43—41no—
283C8×C43—41no—
284C43⋊C8—21no—
285C43⋊C8—21no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#19410—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43C2×#12111yescharacteristic
300C2×D43—21no—
301C2×D43—21no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—164no—
306C2×D43#46612yes—
307C4×C43—21no—
308C4×C43—41no—
309C4×C43C22×D811yescharacteristic
310C4×C43C2×#13511yescharacteristic
311C4×C43#57611yescharacteristic
312C4×C43#57711yescharacteristic
313Dic43—21no—
314Dic43—22no—
315Dic43—21no—
316Dic43—41no—
317Dic43—81no—
318Dic43#46612yes—
319#3205—431no—
320#3038—431no—
321#3035—431no—
322#2988—431no—
323#1682—431no—
324#1682—431no—
325#1681—431no—
326#1681—431no—
327#1668—431no—
328#1668—431no—
329#1667—431no—
330#1667D4311yescharacteristic, complemented
331#1571—431no—
332#1547—431no—
333C2×#331—431no—
334C2×C43—42no—
335C2×C43—161no—
336C2×C43—161no—
337C2×C43#304511yescharacteristic
338C2×C43C2×#46611yescharacteristic
339C2×C43#306811yescharacteristic
340D43—22no—
341D43—161no—
342C2×AGL(1,ℤ/8)—861no—
343C2×#135—861no—
344#532—431no—
345C2×#127—431no—
346C4×#41—431no—
347#493—431no—
348#493C2×D4311yescharacteristic
349#486—431no—
350#486—431no—
351#464—861no—
352#463—861no—
353#462—431no—
354#461—431no—
355#460—431no—
356#460—431no—
357#460—431no—
358#460—861no—
359#459—431no—
360#459—861no—
361#459—861no—
362#459—861no—
363#459C2×D4311yescharacteristic
364#459C2×D4311yescharacteristic, complemented
365#447—861no—
366#447—861no—
367C8×Q8—431no—
368C8×Q8—431no—
369C8×D4—431no—
370C8×D4—861no—
371C8×D4—861no—
372C8×D4C2×D4311yescharacteristic, complemented
373#431—431no—
374#431—861no—
375#423—431no—
376C2×C4⋊C8—431no—
377C2×C4⋊C8—431no—
378C2×C4⋊C8—861no—
379#418—861no—
380#416—861no—
381#335—431no—
382#335—431no—
383#335—431no—
384#335C2×D4311yescharacteristic, complemented
385#332—431no—
386#332—431no—
387#331—431no—
388#331—431no—
389#331—431no—
390#331—431no—
391#331C2×D4311yescharacteristic
392#331C2×D4311yescharacteristic, complemented
393C43#1941011yescharacteristic, complemented, Sylow
394C2×#41—431no—
395C2×#41—861no—
396C22×D4—861no—
397C22×D4—861no—
398C22×D4—861no—
399AGL(1,ℤ/8)—1724no—
400#135—1724no—
401C2×Q16—861no—
402C2×SD16—861no—
403C2×SD16—861no—
404C2×SD16—861no—
405C2×SD16—861no—
406C2×D8—21no—
407C2×D8—21no—
408C2×D8—21no—
409C2×D8—21no—
410C2×D8—861no—
411C2×D8—861no—
412C2×D8—861no—
413C2×M16—861no—
414C22×C8—21no—
415C22×C8—861no—
416C22×C8—861no—
417C22×C8—861no—
418C4⋊Q8—431no—
419#127—431no—
420#127—861no—
421#127—861no—
422#127—861no—
423#127C22×D4311yescharacteristic
424#127C22×D4311yescharacteristic
425#124—861no—
426#121—861no—
427#121—861no—
428C4×Q8—431no—
429C4×Q8—431no—
430C4×D4—431no—
431C4×D4—861no—
432C4×D4—861no—
433C4×D4—861no—
434C4×D4—861no—
435C4×D4C22×D4311yescharacteristic
436#117—431no—
437#117—861no—
438C2×C42—431no—
439C2×C42—861no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—431no—
443C4⋊C8—431no—
444C4⋊C8—431no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C4⋊C8—861no—
449C4⋊C8—861no—
450C4⋊C8C22×D4311yescharacteristic
451C4⋊C8C22×D4311yescharacteristic
452C4⋊C8C22×D4311yescharacteristic
453#103—861no—
454#103—861no—
455#102—21no—
456#102—21no—
457#102—861no—
458#102—861no—
459#102—861no—
460#102—861no—
461#102—861no—
462#102—861no—
463#102—861no—
464#102—861no—
465C22⋊C8—21no—
466C22⋊C8—431no—
467C22⋊C8—431no—
468C22⋊C8—861no—
469C4×C8—431no—
470C4×C8—861no—
471C4×C8—861no—
472C4×C8C22×D4311yescharacteristic
473C24—1721no—
474#41—434no—
475#41—862no—
476#41—1722no—
477#41—1722no—
478C2×Q8—431no—
479C2×Q8—861no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—3441no—
491C2×D4—3441no—
492C2×D4—3442no—
493C2×D4—1722no—
494C2×D4—1722no—
495C2×D4—1721no—
496C2×D4—1721no—
497C2×D4—1721no—
498C2×D4—1721no—
499C2×D4D4×D4311yescharacteristic
500C22×C4—21no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—861no—
505C22×C4—861no—
506C22×C4—1721no—
507Q16—1722no—
508SD16—1722no—
509SD16—1722no—
510SD16—1722no—
511SD16—1722no—
512D8—42no—
513D8—42no—
514D8—81no—
515D8—81no—
516D8—3441no—
517D8—3441no—
518D8—1722no—
519M16—1722no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—81no—
524C2×C8—431no—
525C2×C8—431no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—3441no—
530C2×C8—3441no—
531C2×C8—1722no—
532C2×C8D4×D4311yescharacteristic
533C2×C8D4×D4311yescharacteristic
534C4⋊C4—431no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4D4×D4311yescharacteristic
540C22⋊C4—21no—
541C22⋊C4—861no—
542C22⋊C4—861no—
543C22⋊C4—1721no—
544C22⋊C4—1721no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—861no—
549C42—861no—
550C42—861no—
551C42C23×D4311yescharacteristic
552C23—21no—
553C23—41no—
554C23—41no—
555C23—431no—
556C23—3442no—
557C23—3442no—
558C23—3442no—
559C23—1721no—
560Q8—432no—
561Q8—861no—
562Q8—1721no—
563Q8—1721no—
564D4—21no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—81no—
574D4—81no—
575D4—864no—
576D4—3441no—
577D4—3442no—
578D4—3442no—
579D4—3442no—
580D4—3442no—
581D4—1721no—
582D4—1721no—
583D4—1721no—
584D4—1721no—
585D4D8×D4312yes—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—431no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—431no—
593C2×C4—431no—
594C2×C4—864no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—3442no—
600C2×C4—3441no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4C2×D4×D4311yescharacteristic
604C2×C4C2×D4×D4311yescharacteristic
605C2×C4#41×D4311yescharacteristic
606C8—21no—
607C8—21no—
608C8—41no—
609C8—41no—
610C8—41no—
611C8—861no—
612C8—861no—
613C8—1721no—
614C8—1721no—
615C8—1721no—
616C22—22no—
617C22—41no—
618C22—41no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—432no—
626C22—861no—
627C22—861no—
628C22—3441no—
629C22—3441no—
630C22—3441no—
631C22—6884no—
632C22#121×D4311yescharacteristic
633C4—21no—
634C4—41no—
635C4—432no—
636C4—861no—
637C4—861no—
638C4—862no—
639C4—3441no—
640C4—1721no—
641C4C2×D8×D4311yescharacteristic
642C4#135×D4311yescharacteristic
643C4#1458370011yescharacteristic
644C4#1458370911yescharacteristic
645C2—42no—
646C2—161no—
647C2—161no—
648C2—862no—
649C2—6881no—
650C2#1914412911yescharacteristic
651C2#466×D4311yescharacteristic
652C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1667C2
socleC22×C43C2×#121
hypercenter#1667D43
hypocenterC43#19410
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #19145509C2semidirect
2. #19144070C2semidirect
3. #19144043C2semidirect
4. #19143702C2semidirect
5. #19134040C2semidirect
6. #19134038C2semidirect
7. #19134032C2semidirect
8. #19134030C2semidirect
9. #19133954C2semidirect
10. #19133952C2semidirect
11. #19133948C2semidirect
12. #19133368C2semidirect
13. #19133269C2semidirect
14. #331×D43C2semidirect
15. C43×#1667C2semidirect
26. #14583110C22semidirect
27. #14583104C22semidirect
31. #14583096C22semidirect
38. C8×Dic86C22semidirect
39. #14583023C22semidirect
40. D4×C43⋊C8C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582646C22semidirect
55. #14582644C22semidirect
57. #14582643C22semidirect
62. C43×#459C22semidirect
63. C8×D4×C43C22semidirect
64. C43×#335C22semidirect
66. C43×#331C22semidirect
166. #10621900D8semidirect
330. #1667D43semidirect
364. #459C2×D43semidirect
372. C8×D4C2×D43semidirect
384. #335C2×D43semidirect
392. #331C2×D43semidirect
393. C43#19410semidirect

Maximal subgroups

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

subgroupindex
#191455092
#191440702
#191440432
#191437022
#191340402
#191340382
#191340322
#191340302
#191339542
#191339522
#191339482
#191333682
#191332692
#331×D432
C43×#16672
#1941043