Finite Group Databasebeta

← #25086675

Subgroups — #25086675

Order 11008.

720 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621883C211yesmaximal, characteristic, complemented
2#19147264C211yesmaximal, characteristic, complemented
3#19146211C211yesmaximal, characteristic
4#19134222C211yesmaximal, characteristic, complemented
5#19134092C211yesmaximal, characteristic, complemented
6#19134004C211yesmaximal, characteristic, complemented
7#19133953C211yesmaximal, characteristic, complemented
8#19133940C211yesmaximal, characteristic, complemented
9#19133793C211yesmaximal, characteristic, complemented
10#19133711C211yesmaximal, characteristic, complemented
11#19133698C211yesmaximal, characteristic, complemented
12#19133672C211yesmaximal, characteristic, complemented
13#19133439C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic, complemented
16C2×#13063351—21no—
17Q8×Dic86C2211yescharacteristic, complemented
18#14583570C2211yescharacteristic
19#14583295—21no—
20#14583295C2211yescharacteristic, complemented
21#14583275C2211yescharacteristic
22#14583271C2211yescharacteristic
23#14583247C2211yescharacteristic, complemented
24#14583246C2211yescharacteristic, complemented
25#14583244—21no—
26#14583189—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583188—21no—
30#14583181—21no—
31#14583181C2211yescharacteristic, complemented
32#14583150—21no—
33#14583099C2211yescharacteristic, complemented
34#14583097—21no—
35#14583096C2211yescharacteristic
36#14583094C2211yescharacteristic
37#14583042—21no—
38#14583033—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C8×Dic86C2211yescharacteristic, complemented
41C4×#10621883—21no—
42C4×#10621883C2211yescharacteristic
43#14582984—21no—
44#14582977C2211yescharacteristic
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582642C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C22×SD16×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#465—21no—
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C43×#448—21no—
65C4×SD16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C2×#10621898—21no—
68#13063351—44no—
69C2×#10621883—21no—
70C2×#10621883—41no—
71C2×#10621883D411yescharacteristic
72C2×#10621884—21no—
73C2×#10621882—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621877—21no—
77#13063325—21no—
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063324—41no—
81#13063322C2311yescharacteristic
82#13063321—21no—
83#13063299—21no—
84#13063298—41no—
85Q8×Dic43—21no—
86C4×Dic86—21no—
87C4×Dic86C2311yescharacteristic
88#13063287—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100#13063248—21no—
101#13063248D411yescharacteristic
102#13063247—21no—
103#13063247—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245—21no—
110#13063245—41no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C8×Dic43—21no—
116C22×Q8×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43—44no—
124C2×SD16×C43D411yescharacteristic
125C22×C8×C43—21no—
126C4⋊Q8×C43—21no—
127C4⋊Q8×C43C2311yescharacteristic
128#127×C43C2311yescharacteristic
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—41no—
131#121×C43—21no—
132#121×C43—21no—
133#120×C43—41no—
134C4×Q8×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138#106×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#102×C43—21no—
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
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—42no—
158C2×D4×C43—42no—
159C2×D4×C43—81no—
160C2×D4×C43—81no—
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—41no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—41no—
168#10621898—42no—
169#10621898—81no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×C4×D43—41no—
174C2×Dic86—21no—
175C2×Dic86—41no—
176C2×Dic86C2×D411yescharacteristic
177SD16×C43—22no—
178SD16×C43—42no—
179SD16×C43—42no—
180SD16×C43—42no—
181SD16×C43—81no—
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—42no—
200#10621883—42no—
201#10621883—82no—
202#10621883SD1614yescomplemented
203#10621882—42no—
204#10621882—42no—
205#10621882—81no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—41no—
210C4⋊Dic43C2×D411yescharacteristic
211Dic43⋊C4—21no—
212Dic43⋊C4—41no—
213C4×Dic43—21no—
214C4×Dic43—41no—
215#10621877—42no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—82no—
226C23×C43—82no—
227C23×C43—161no—
228C22×D43—41no—
229Q8×C43—21no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—82no—
233Q8×C43AGL(1,ℤ/8)12yescomplemented
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—81no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43C2×SD1612yes—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—82no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C22⋊D43—82no—
259C22⋊D43—161no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263D172—41no—
264D172—41no—
265D172—41no—
266D172—41no—
267D172—81no—
268C4×D43—82no—
269Dic86—21no—
270Dic86—81no—
271Dic86—161no—
272Dic86C2×SD1612yescomplemented
273C8×C43—21no—
274C8×C43—21no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8C2×SD1612yescomplemented
282#19804—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—81no—
295C2×D43—81no—
296C2×D43—81no—
297C4×C43—22no—
298C4×C43—21no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—81no—
303C4×C43C22×SD1611yescharacteristic
304C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C43#57711yescharacteristic
306C4×C43#57711yescharacteristic
307Dic43—22no—
308Dic43—41no—
309Dic43—81no—
310Q8×SD16—431no—
311#3362—431no—
312D4×SD16D4311yescharacteristic, complemented
313#3274—431no—
314#1715—431no—
315#1691—431no—
316#1677—431no—
317#1668—431no—
318#1666—431no—
319#1642—431no—
320#1629—431no—
321#1627—431no—
322#1623—431no—
323#1583—431no—
324SD16⋊C8—431no—
325C2×C43—42no—
326C2×C43—81no—
327C2×C43—161no—
328C2×C43#326511yescharacteristic
329C2×C43D4×SD1611yescharacteristic
330C2×C43#328811yescharacteristic
331D43—161no—
332C2×AGL(1,ℤ/8)—861no—
333C22×SD16—21no—
334Q82—431no—
335#550—431no—
336D4×Q8C2×D4311yescharacteristic
337D42C2×D4311yescharacteristic
338#498—431no—
339#498—861no—
340#493—431no—
341#492—431no—
342#492C2×D4311yescharacteristic
343#486—431no—
344#486—431no—
345#486—861no—
346#476—431no—
347#476—431no—
348#476—861no—
349#476—861no—
350#475—431no—
351#475—861no—
352#469—861no—
353#465—21no—
354#461C2×D4311yescharacteristic
355#460—431no—
356#460—431no—
357#460—861no—
358#460C2×D4311yescharacteristic
359#459—431no—
360#450—21no—
361#449—861no—
362#448—21no—
363#447—861no—
364C8×Q8—431no—
365C8×Q8—431no—
366C4×SD16—431no—
367C4×SD16—861no—
368C4×SD16—861no—
369C4×SD16C2×D4311yescharacteristic
370#436—431no—
371C8×D4C2×D4311yescharacteristic
372#335—431no—
373#334—431no—
374#333—431no—
375#332—431no—
376#331—431no—
377#331—431no—
378Q8⋊C8—431no—
379Q8⋊C8—431no—
380D4⋊C8—431no—
381D4⋊C8—431no—
382#322—431no—
383C43#1980411yescharacteristic, complemented, Sylow
384C2×#41—861no—
385C22×Q8—21no—
386C22×D4—21no—
387C22×D4—21no—
388AGL(1,ℤ/8)—1724no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16—21no—
392C2×SD16—21no—
393C2×SD16—44no—
394C2×SD16—431no—
395C2×SD16—861no—
396C2×SD16—861no—
397C2×SD16—1721no—
398C2×SD16C22⋊D4311yescharacteristic
399C2×D8—861no—
400C2×D8—861no—
401C2×D8—861no—
402C2×M16—861no—
403C22×C8—21no—
404C4⋊Q8—21no—
405C4⋊Q8—431no—
406C4⋊Q8—861no—
407C4⋊Q8—861no—
408C4⋊Q8—1721no—
409C4⋊Q8C22×D4311yescharacteristic
410#127—431no—
411#127—861no—
412#127C22×D4311yescharacteristic
413C22⋊Q8—21no—
414C22⋊Q8—41no—
415#121—21no—
416#121—21no—
417#121—861no—
418#121—1721no—
419#120—41no—
420C4×Q8—431no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×Q8C22×D4311yescharacteristic
424C4×D4—21no—
425C4×D4—861no—
426C4×D4C22×D4311yescharacteristic
427C4×D4C22×D4311yescharacteristic
428#106—431no—
429#106—861no—
430#106—861no—
431#106—861no—
432#106—861no—
433#106—861no—
434#106C22⋊D4311yescharacteristic
435C4⋊C8—431no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—861no—
439C4⋊C8—861no—
440C4⋊C8C22×D4311yescharacteristic
441#103—21no—
442#103—431no—
443#103—861no—
444#103C22⋊D4311yescharacteristic
445#102—21no—
446#102—431no—
447#102—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—1721no—
455#102C22⋊D4311yescharacteristic
456C22⋊C8—21no—
457C22⋊C8—861no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8—861no—
461C4×C8—861no—
462C4×C8C22×D4311yescharacteristic
463C24—41no—
464#41—3441no—
465#41—1722no—
466C2×Q8—21no—
467C2×Q8—41no—
468C2×Q8—42no—
469C2×Q8—81no—
470C2×Q8—431no—
471C2×Q8—861no—
472C2×Q8—1721no—
473C2×Q8C2×C22⋊D4311yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—1721no—
487C2×D4—1721no—
488C2×D4D4×D4311yescharacteristic
489C2×D4C2×C22⋊D4311yescharacteristic
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—41no—
493C22×C4—1721no—
494SD16—22no—
495SD16—42no—
496SD16—42no—
497SD16—42no—
498SD16—81no—
499SD16—434no—
500SD16—3442no—
501SD16—1722no—
502SD16—1722no—
503D8—3441no—
504D8—1722no—
505D8—1722no—
506M16—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×C8C2×C22⋊D4311yescharacteristic
516C2×C8C2×C22⋊D4311yescharacteristic
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—41no—
521C4⋊C4—431no—
522C4⋊C4—861no—
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—1721no—
535C42—21no—
536C42—861no—
537C42—1721no—
538C42C23×D4311yescharacteristic
539C23—21no—
540C23—21no—
541C23—41no—
542C23—82no—
543C23—82no—
544C23—161no—
545C23—1721no—
546Q8—21no—
547Q8—41no—
548Q8—41no—
549Q8—82no—
550Q8—432no—
551Q8—861no—
552Q8—3441no—
553Q8—6881no—
554Q8#1306335112yescomplemented
555D4—21no—
556D4—21no—
557D4—21no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—81no—
563D4—82no—
564D4—82no—
565D4—3441no—
566D4—3442no—
567D4—1721no—
568D4—1721no—
569D4—1721no—
570D4—1721no—
571D4—6881no—
572D4SD16×D4312yes—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—82no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—3442no—
586C2×C4—1721no—
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C22×C22⋊D4311yescharacteristic
589C2×C4#1306337011yescharacteristic
590C8—21no—
591C8—21no—
592C8—41no—
593C8—432no—
594C8—861no—
595C8—1721no—
596C8—1721no—
597C8—1721no—
598C8—1721no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—164no—
609C22—3441no—
610C22—3441no—
611C22—3441no—
612C22D4×C22⋊D4311yescharacteristic
613C4—22no—
614C4—21no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—81no—
619C4—862no—
620C4—3441no—
621C4—1721no—
622C4C2×SD16×D4311yescharacteristic
623C4C2×#1306335111yescharacteristic
624C4#1458370511yescharacteristic
625C4#1458371011yescharacteristic
626C2—42no—
627C2—81no—
628C2—161no—
629C2—6881no—
630C2#1914608611yescharacteristic
631C2SD16×C22⋊D4311yescharacteristic
632C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radical#19146211C2
hypercenterD4×SD16D43
hypocenterC43#19804
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×#10621883C2semidirect
2. #19147264C2semidirect
4. #19134222C2semidirect
5. #19134092C2semidirect
6. #19134004C2semidirect
7. #19133953C2semidirect
8. #19133940C2semidirect
9. #19133793C2semidirect
10. #19133711C2semidirect
11. #19133698C2semidirect
12. #19133672C2semidirect
13. #19133439C2semidirect
14. #19133407C2semidirect
15. D4×SD16×C43C2semidirect
17. Q8×Dic86C22semidirect
20. #14583295C22semidirect
23. #14583247C22semidirect
24. #14583246C22semidirect
31. #14583181C22semidirect
33. #14583099C22semidirect
39. Q8×C43⋊C8C22semidirect
40. C8×Dic86C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
50. #14582642C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. #14582629C22semidirect
55. #14582621C22semidirect
202. #10621883SD16semidirect
233. Q8×C43AGL(1,ℤ/8)semidirect
272. Dic86C2×SD16semidirect
281. C43⋊C8C2×SD16semidirect
312. D4×SD16D43semidirect
383. C43#19804semidirect
554. Q8#13063351semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218832
#191472642
#191462112
#191342222
#191340922
#191340042
#191339532
#191339402
#191337932
#191337112
#191336982
#191336722
#191334392
#191334072
D4×SD16×C432
#1980443