Finite Group Databasebeta

← #25085974

Subgroups — #25085974

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621882C211yesmaximal, characteristic, complemented
2#19146408C211yesmaximal, characteristic
3#19146242C211yesmaximal, characteristic, complemented
4#19134264C211yesmaximal, characteristic, complemented
5#19134057C211yesmaximal, characteristic, complemented
6#19134037C211yesmaximal, characteristic, complemented
7#19133982C211yesmaximal, characteristic, complemented
8#19133960C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic, complemented
10#19133828C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133696C211yesmaximal, characteristic, complemented
13#19133424C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17Q8×D172C2211yescharacteristic, complemented
18#14583553C2211yescharacteristic
19#14583302—21no—
20#14583302C2211yescharacteristic, complemented
21#14583302C2211yescharacteristic, complemented
22#14583279C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583210—21no—
26#14583179—21no—
27#14583179C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583176—21no—
30#14583176C2211yescharacteristic, complemented
31#14583158—21no—
32#14583133—21no—
33#14583109C2211yescharacteristic, complemented
34#14583104C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583062—21no—
37#14583056—21no—
38#14583033—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C4×#10621882—21no—
41C4×#10621882C2211yescharacteristic
42#14582978C2211yescharacteristic, complemented
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063246—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic, complemented
55#14582620C2211yescharacteristic, 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×#10621900—21no—
68C2×Q8×D43—21no—
69#13063354—44no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621882—21no—
75C2×#10621882D411yescharacteristic
76C2×#10621872—21no—
77C22×C43⋊C8—21no—
78#13063325—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063309—41no—
82#13063305—21no—
83#13063305—21no—
84#13063305—41no—
85#13063299—21no—
86C4×D172—21no—
87C4×D172C2311yescharacteristic
88C2×C4⋊Dic43—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—41no—
95#13063258D411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063248—21no—
101#13063248—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
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—
167C22×Dic43—41no—
168Q8×D43—42no—
169Q8×D43—81no—
170#10621900—42no—
171#10621900—81no—
172C2×D172C2×D411yescharacteristic
173C2×C4×D43—21no—
174C2×C4×D43—41no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—41no—
178SD16×C43—42no—
179SD16×C43—42no—
180SD16×C43—42no—
181SD16×C43—81no—
182SD16×C43D814yescomplemented
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—41no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C42×C43—21no—
199C42×C43C2411yescharacteristic
200#10621885—42no—
201#10621883—42no—
202#10621882—22no—
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⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—41no—
212C4⋊Dic43—41no—
213C4⋊Dic43C2×D411yescharacteristic
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
221Dic172—42no—
222Dic172—81no—
223#10621872—42no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—41no—
227C23×C43—82no—
228C23×C43—82no—
229C23×C43—161no—
230C22×D43—21no—
231Q8×C43—21no—
232Q8×C43—41no—
233Q8×C43—41no—
234Q8×C43—82no—
235Q8×C43C2×D812yes—
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×C43C2×D812yes—
246D4×C43#13712yescomplemented
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—82no—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C22⋊D43—82no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—82no—
265D172—21no—
266D172—21no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—82no—
270Dic86—41no—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274Dic86—82no—
275C8×C43—21no—
276C8×C43—41no—
277C8×C43C2×D812yes—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#19757—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—164no—
295C22×C43D4211yescharacteristic
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C4×C43—22no—
300C4×C43—21no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43C22×D811yescharacteristic
306C4×C43C2×#13711yescharacteristic
307C4×C43#57611yescharacteristic
308C4×C43#57711yescharacteristic
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312Q8×D8—431no—
313#3294—431no—
314D4×SD16D4311yescharacteristic, complemented
315#3276—431no—
316#1722—431no—
317#1685—431no—
318#1682—431no—
319#1673—431no—
320#1669—431no—
321#1649—431no—
322#1647—431no—
323#1639—431no—
324#1627—431no—
325#1581—431no—
326SD16⋊C8—431no—
327C2×C43—42no—
328C2×C43—42no—
329C2×C43—161no—
330C2×C43#326611yescharacteristic
331C2×C43D4×D811yescharacteristic
332C2×C43#328911yescharacteristic
333D43—81no—
334C2×#137—861no—
335C22×SD16—21no—
336D4×Q8—431no—
337D4×Q8C2×D4311yescharacteristic
338#547—431no—
339D42C2×D4311yescharacteristic
340#500—431no—
341#500—431no—
342#500—861no—
343#494—431no—
344#492C2×D4311yescharacteristic
345#486—431no—
346#486—431no—
347#480—861no—
348#474—431no—
349#474—431no—
350#474—431no—
351#474—861no—
352#474—861no—
353#470—861no—
354#466—861no—
355#465—21no—
356#462—431no—
357#461—431no—
358#461C2×D4311yescharacteristic
359#460C2×D4311yescharacteristic
360#459—431no—
361#452—861no—
362#451—861no—
363#450—21no—
364#448—21no—
365#447—861no—
366C8×Q8—431no—
367C4×SD16C2×D4311yescharacteristic
368C4×D8—431no—
369C4×D8—861no—
370#436—431no—
371C8×D4—431no—
372C8×D4C2×D4311yescharacteristic
373C2×#102—861no—
374#335—431no—
375#335—431no—
376#332—431no—
377#332—431no—
378#332—431no—
379#331—431no—
380Q8⋊C8—431no—
381D4⋊C8—431no—
382D4⋊C8—431no—
383D4⋊C8—431no—
384#322—431no—
385C43#1975711yescharacteristic, complemented, Sylow
386C2×#41—861no—
387C22×Q8—21no—
388C22×Q8—861no—
389C22×D4—21no—
390C22×D4—21no—
391#137—1724no—
392C2×Q16—861no—
393C2×Q16—861no—
394C2×Q16—861no—
395C2×SD16—21no—
396C2×SD16—21no—
397C2×SD16—21no—
398C2×SD16—21no—
399C2×SD16—44no—
400C2×SD16—861no—
401C2×SD16C22⋊D4311yescharacteristic
402C2×D8—431no—
403C2×D8—861no—
404C2×M16—861no—
405C22×C8—21no—
406C22×C8—861no—
407C4⋊Q8—21no—
408C4⋊Q8—431no—
409C4⋊Q8—431no—
410C4⋊Q8—861no—
411C4⋊Q8C22×D4311yescharacteristic
412#127C22×D4311yescharacteristic
413#123—1721no—
414C22⋊Q8—21no—
415C22⋊Q8—41no—
416C22⋊Q8—861no—
417C22⋊Q8—861no—
418C22⋊Q8—1721no—
419#121—21no—
420#121—21no—
421#121—861no—
422#120—41no—
423C4×Q8C22×D4311yescharacteristic
424C4×D4—21no—
425C4×D4—431no—
426C4×D4—861no—
427C4×D4C22×D4311yescharacteristic
428C4×D4C22×D4311yescharacteristic
429C2×C4⋊C4—861no—
430#107—431no—
431#107—861no—
432#107—861no—
433#107—861no—
434#107—861no—
435#107—861no—
436#107—1721no—
437#106C22⋊D4311yescharacteristic
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—861no—
442C4⋊C8C22×D4311yescharacteristic
443#103—21no—
444#103—861no—
445#103—861no—
446#103C22⋊D4311yescharacteristic
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—1721no—
457#102C22⋊D4311yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461C4×C8—431no—
462C4×C8—431no—
463C4×C8—861no—
464C4×C8C22×D4311yescharacteristic
465C24—41no—
466#41—3441no—
467#41—1722no—
468C2×Q8—21no—
469C2×Q8—41no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—3441no—
475C2×Q8—1721no—
476C2×Q8—1722no—
477C2×Q8C2×C22⋊D4311yescharacteristic
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4—431no—
488C2×D4—1721no—
489C2×D4D4×D4311yescharacteristic
490C2×D4C2×C22⋊D4311yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—861no—
495C22×C4—1721no—
496C22×C4—1721no—
497Q16—3441no—
498Q16—1722no—
499Q16—1722no—
500SD16—42no—
501SD16—42no—
502SD16—42no—
503SD16—81no—
504SD16—1722no—
505SD16#1062188214yescomplemented
506D8—862no—
507D8—3441no—
508M16—1722no—
509C2×C8—21no—
510C2×C8—42no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—3441no—
518C2×C8C2×C22⋊D4311yescharacteristic
519C2×C8C2×C22⋊D4311yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—41no—
524C4⋊C4—431no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—1721no—
530C4⋊C4—1721no—
531C4⋊C4D4×D4311yescharacteristic
532C4⋊C4C2×C22⋊D4311yescharacteristic
533C4⋊C4C2×C22⋊D4311yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—861no—
539C22⋊C4—1721no—
540C22⋊C4—1721no—
541C42—21no—
542C42C23×D4311yescharacteristic
543C23—21no—
544C23—21no—
545C23—41no—
546C23—82no—
547C23—82no—
548C23—161no—
549C23—861no—
550Q8—21no—
551Q8—41no—
552Q8—41no—
553Q8—82no—
554Q8—3442no—
555Q8—1721no—
556Q8—1721no—
557Q8—1721no—
558Q8—1721no—
559Q8C2×#1062188212yes—
560D4—21no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—861no—
570D4—861no—
571D4—3442no—
572D4C2×#1062188212yes—
573D4#1306335412yescomplemented
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—861no—
585C2×C4—3442no—
586C2×C4—3442no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4C22×C22⋊D4311yescharacteristic
593C2×C4#1306337011yescharacteristic
594C8—21no—
595C8—41no—
596C8—861no—
597C8—861no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8C2×#1062188212yes—
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—164no—
613C22—1721no—
614C22—1721no—
615C22—1721no—
616C22D4×C22⋊D4311yescharacteristic
617C4—22no—
618C4—21no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—81no—
623C4—3441no—
624C4—3441no—
625C4—1721no—
626C4C22×#1062188211yescharacteristic
627C4C2×#1306335411yescharacteristic
628C4#1458370211yescharacteristic
629C4#1458370511yescharacteristic
630C2—42no—
631C2—42no—
632C2—161no—
633C2—3441no—
634C2#1914610511yescharacteristic
635C2D4×#1062188211yescharacteristic
636C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radical#19146408C2
hypercenterD4×SD16D43
hypocenterC43#19757
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×#10621882C2semidirect
3. #19146242C2semidirect
4. #19134264C2semidirect
5. #19134057C2semidirect
6. #19134037C2semidirect
7. #19133982C2semidirect
8. #19133960C2semidirect
9. #19133844C2semidirect
10. #19133828C2semidirect
11. #19133774C2semidirect
12. #19133696C2semidirect
13. #19133424C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. D4×SD16×C43C2semidirect
17. Q8×D172C22semidirect
20. #14583302C22semidirect
21. #14583302C22semidirect
22. #14583279C22semidirect
30. #14583176C22semidirect
33. #14583109C22semidirect
39. Q8×C43⋊C8C22semidirect
42. #14582978C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582646C22semidirect
48. #14582646C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582620C22semidirect
182. SD16×C43D8semidirect
246. D4×C43#137semidirect
314. D4×SD16D43semidirect
385. C43#19757semidirect
505. SD16#10621882semidirect
573. D4#13063354semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218822
#191464082
#191462422
#191342642
#191340572
#191340372
#191339822
#191339602
#191338442
#191338282
#191337742
#191336962
#191334242
SD16⋊(C43⋊C8)2
D4×SD16×C432
#1975743