Finite Group Databasebeta

← #25086200

Subgroups — #25086200

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146894C211yesmaximal, characteristic, complemented
2#19146410C211yesmaximal, characteristic, complemented
3#19146402C211yesmaximal, characteristic, complemented
4#19134258C211yesmaximal, characteristic, complemented
5#19134158C211yesmaximal, characteristic, complemented
6#19134032C211yesmaximal, characteristic, complemented
7#19134020C211yesmaximal, characteristic, complemented
8#19133957C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133877C211yesmaximal, characteristic, complemented
11#19133772C211yesmaximal, characteristic, complemented
12#19133684C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15C43×#3283C211yesmaximal, characteristic, complemented
16#14583554C2211yescharacteristic
17D4×D172C2211yescharacteristic
18#14583295C2211yescharacteristic, complemented
19#14583251C2211yescharacteristic, complemented
20#14583247C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583234—21no—
24#14583214—21no—
25#14583212—21no—
26#14583179C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583176C2211yescharacteristic
29#14583143—21no—
30#14583134—21no—
31#14583133—21no—
32#14583104C2211yescharacteristic, complemented
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583042—21no—
36#14583032—21no—
37#14583031—21no—
38C4×#10621882C2211yescharacteristic
39#14582977C2211yescharacteristic, complemented
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582898—21no—
43C2×#13063245—21no—
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
56C2×#135×C43—21no—
57C43×#547C2211yescharacteristic
58C43×#547C2211yescharacteristic, complemented
59C43×#494C2211yescharacteristic, complemented
60C43×#467—21no—
61C43×#461C2211yescharacteristic
62C43×#461C2211yescharacteristic, complemented
63C43×#452—21no—
64C43×#452—21no—
65C4×D8×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic, complemented
67C2×#10621898—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70C2×#10621883—21no—
71C2×#10621882—21no—
72C2×#10621882—21no—
73C2×#10621882D411yescharacteristic
74C2×#10621877—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063307—41no—
80#13063304—21no—
81#13063300—21no—
82#13063299—21no—
83#13063296—21no—
84#13063295—41no—
85C4×D172C2311yescharacteristic
86C4⋊C4×D43—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063256—41no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063248—21no—
96#13063248—21no—
97#13063248—21no—
98#13063247—21no—
99#13063247—21no—
100#13063246—21no—
101#13063246D411yescharacteristic
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—41no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×#41×C43—21no—
116C2×#41×C43—21no—
117#135×C43—44no—
118C2×Q16×C43—21no—
119C2×Q16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×D8×C43D411yescharacteristic
123C22×C8×C43—21no—
124C4⋊Q8×C43C2311yescharacteristic
125C4⋊Q8×C43C2311yescharacteristic
126#123×C43—41no—
127#123×C43—41no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137#107×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#102×C43D411yescharacteristic
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×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—41no—
164D4×D43—42no—
165D4×D43—81no—
166#10621898—42no—
167#10621898—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×C4×D43—41no—
177C2×Dic86—21no—
178Q16×C43—42no—
179Q16×C43—81no—
180SD16×C43—42no—
181SD16×C43—42no—
182D8×C43—22no—
183C2×C8×C43—21no—
184C2×C8×C43—42no—
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C22⋊C4×C43—21no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—21no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C42×C43C2411yescharacteristic
202C22⋊Dic43—41no—
203#10621883—81no—
204#10621882—22no—
205#10621882—81no—
206#10621882—81no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—41no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43C2×D411yescharacteristic
212Dic43⋊C4—41no—
213#10621877—81no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—81no—
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C8×D43—81no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C22×D43—21no—
226C22×D43—41no—
227C22×D43—82no—
228C22×D43—82no—
229C22×D43—161no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—82no—
240D4×C43—82no—
241D4×C43AGL(1,ℤ/8)12yes—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
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—
259C22⋊D43—82no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262D172—21no—
263D172—41no—
264D172—41no—
265D172—41no—
266D172—41no—
267D172—81no—
268D172—82no—
269D172#13512yescomplemented
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—82no—
273Dic86—41no—
274Dic86—41no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—41no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#19772—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43D4211yescharacteristic
295C2×D43—22no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—164no—
302C4×C43—21no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43C2×#13511yescharacteristic
309C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
310C4×C43#57611yescharacteristic
311C4×C43#57611yescharacteristic
312Dic43—41no—
313Dic43—81no—
314#3330—431no—
315#3294—431no—
316#3294—431no—
317#3283D4311yescharacteristic, complemented
318#1720—431no—
319#1701—431no—
320#1681—431no—
321#1679—431no—
322#1669—431no—
323#1654—431no—
324#1654—431no—
325#1639—431no—
326#1625—431no—
327#1581—431no—
328#1580—431no—
329C2×C43—42no—
330C2×C43—81no—
331C2×C43—81no—
332C2×C43#326411yescharacteristic
333C2×C43#328011yescharacteristic
334C2×C43#328911yescharacteristic
335D43—42no—
336D43—161no—
337C2×#135—21no—
338#547—431no—
339#547C2×D4311yescharacteristic
340#547C2×D4311yescharacteristic, complemented
341D42—431no—
342#498—431no—
343#494C2×D4311yescharacteristic, complemented
344#487—431no—
345#486—431no—
346#486—431no—
347#486—431no—
348#484—861no—
349#480—861no—
350#480—861no—
351#474—431no—
352#474—431no—
353#474—431no—
354#468—861no—
355#467—21no—
356#466—861no—
357#466—861no—
358#461—431no—
359#461C2×D4311yescharacteristic
360#461C2×D4311yescharacteristic, complemented
361#459—431no—
362#459—431no—
363#452—21no—
364#452—21no—
365#449—861no—
366#447—861no—
367#447—861no—
368C4×D8—431no—
369C4×D8C2×D4311yescharacteristic
370#436—431no—
371C8×D4—431no—
372C8×D4—431no—
373C8×D4C2×D4311yescharacteristic, complemented
374#417—861no—
375C2×#102—861no—
376C2×#102—861no—
377#335—431no—
378#334—431no—
379#332—431no—
380#332—431no—
381#332—431no—
382#331—431no—
383D4⋊C8—431no—
384D4⋊C8—431no—
385D4⋊C8—431no—
386D4⋊C8—431no—
387#322—431no—
388C43#1977211yescharacteristic, complemented, Sylow
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—861no—
392C22×D4—861no—
393C22×D4—861no—
394#135—44no—
395C2×Q16—21no—
396C2×Q16—21no—
397C2×SD16—21no—
398C2×SD16—21no—
399C2×SD16—861no—
400C2×D8—431no—
401C2×D8—861no—
402C2×D8—861no—
403C2×D8C22⋊D4311yescharacteristic
404C2×M16—861no—
405C22×C8—21no—
406C22×C8—861no—
407C22×C8—861no—
408C4⋊Q8—431no—
409C4⋊Q8C22×D4311yescharacteristic
410C4⋊Q8C22×D4311yescharacteristic
411#127—431no—
412#123—41no—
413#123—41no—
414#123—1721no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—861no—
418#121—21no—
419#121—21no—
420#121—861no—
421#121—861no—
422#121—861no—
423#120—1721no—
424C4×D4—431no—
425C4×D4C22×D4311yescharacteristic
426C4×D4C22×D4311yescharacteristic
427C4×D4C22×D4311yescharacteristic
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—861no—
431#107—431no—
432#107—861no—
433#107—861no—
434#107—861no—
435#107C22⋊D4311yescharacteristic
436#106—1721no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8C22×D4311yescharacteristic
441#103—21no—
442#103—21no—
443#103—861no—
444#103—861no—
445#103—861no—
446#102—431no—
447#102—431no—
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#102—1721no—
458#102C22⋊D4311yescharacteristic
459#102C22⋊D4311yescharacteristic
460C22⋊C8—21no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463C22⋊C8—861no—
464C4×C8—431no—
465C4×C8—431no—
466C4×C8C22×D4311yescharacteristic
467C24—1721no—
468#41—42no—
469#41—42no—
470#41—81no—
471#41—81no—
472#41—3441no—
473#41—1722no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—861no—
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—1721no—
489C2×D4—1722no—
490C2×D4D4×D4311yescharacteristic
491C2×D4C2×C22⋊D4311yescharacteristic
492C2×D4C2×C22⋊D4311yescharacteristic
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—861no—
499C22×C4—1721no—
500Q16—42no—
501Q16—81no—
502SD16—42no—
503SD16—42no—
504SD16—3441no—
505D8—22no—
506D8—862no—
507D8—3441no—
508D8—3441no—
509M16—3441no—
510C2×C8—21no—
511C2×C8—42no—
512C2×C8—431no—
513C2×C8—431no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—3441no—
519C2×C8—3441no—
520C2×C8C2×C22⋊D4311yescharacteristic
521C2×C8C2×C22⋊D4311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—431no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—1721no—
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—861no—
541C22⋊C4—1721no—
542C22⋊C4—1721no—
543C42C23×D4311yescharacteristic
544C23—21no—
545C23—21no—
546C23—21no—
547C23—861no—
548C23—3442no—
549C23—3442no—
550C23—1721no—
551C23—6881no—
552Q8—41no—
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—1721no—
557Q8—1721no—
558D4—21no—
559D4—21no—
560D4—21no—
561D4—21no—
562D4—21no—
563D4—82no—
564D4—82no—
565D4—432no—
566D4—861no—
567D4—3441no—
568D4—3442no—
569D4—3442no—
570D4—3442no—
571D4—1721no—
572D4—1721no—
573D4—1721no—
574D4—1721no—
575D4#1306335112yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4—861no—
590C2×C4—3442no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4C22×C22⋊D4311yescharacteristic
596C2×C4#1306337011yescharacteristic
597C8—21no—
598C8—21no—
599C8—41no—
600C8—861no—
601C8—861no—
602C8—1721no—
603C8—1721no—
604C8—1721no—
605C8—1721no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—862no—
616C22—3441no—
617C22—3441no—
618C22—3441no—
619C22—1721no—
620C22—1721no—
621C22—6884no—
622C22D4×C22⋊D4311yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—3441no—
630C4—1721no—
631C4#135×D4311yescharacteristic
632C4C2×#1306335111yescharacteristic
633C4#1458370111yescharacteristic
634C4#1458370211yescharacteristic
635C2—42no—
636C2—81no—
637C2—81no—
638C2—1722no—
639C2—6881no—
640C2#1914607111yescharacteristic
641C2#1914627411yescharacteristic
642C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3283C2
socleC22×C43D42
hypercenter#3283D43
hypocenterC43#19772
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #19146894C2semidirect
2. #19146410C2semidirect
3. #19146402C2semidirect
4. #19134258C2semidirect
5. #19134158C2semidirect
6. #19134032C2semidirect
7. #19134020C2semidirect
8. #19133957C2semidirect
9. #19133879C2semidirect
10. #19133877C2semidirect
11. #19133772C2semidirect
12. #19133684C2semidirect
13. #19133425C2semidirect
14. #19133417C2semidirect
15. C43×#3283C2semidirect
18. #14583295C22semidirect
19. #14583251C22semidirect
32. #14583104C22semidirect
39. #14582977C22semidirect
45. #14582652C22semidirect
46. #14582649C22semidirect
47. #14582645C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
58. C43×#547C22semidirect
59. C43×#494C22semidirect
62. C43×#461C22semidirect
66. C8×D4×C43C22semidirect
269. D172#135semidirect
317. #3283D43semidirect
340. #547C2×D43semidirect
343. #494C2×D43semidirect
360. #461C2×D43semidirect
373. C8×D4C2×D43semidirect
388. C43#19772semidirect

Maximal subgroups

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

subgroupindex
#191468942
#191464102
#191464022
#191342582
#191341582
#191340322
#191340202
#191339572
#191338792
#191338772
#191337722
#191336842
#191334252
#191334172
C43×#32832
#1977243