Finite Group Databasebeta

← #25086095

Subgroups — #25086095

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147501C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic
3D4×#10621884C211yesmaximal, characteristic
4#19134220C211yesmaximal, characteristic, complemented
5#19134069C211yesmaximal, characteristic, complemented
6#19134011C211yesmaximal, characteristic, complemented
7#19133992C211yesmaximal, characteristic, complemented
8#19133967C211yesmaximal, characteristic, complemented
9#19133801C211yesmaximal, characteristic, complemented
10#19133760C211yesmaximal, characteristic, complemented
11#19133710C211yesmaximal, characteristic
12#19133673C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15Q8×SD16×C43C211yesmaximal, characteristic, complemented
16C22×#10621884—21no—
17#14583609C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583305—21no—
20#14583302C2211yescharacteristic, complemented
21#14583273C2211yescharacteristic
22#14583273C2211yescharacteristic
23#14583251C2211yescharacteristic, complemented
24#14583246C2211yescharacteristic
25#14583219—21no—
26#14583206—21no—
27#14583194C2211yescharacteristic, complemented
28#14583189C2211yescharacteristic
29#14583186C2211yescharacteristic
30#14583176—21no—
31#14583131—21no—
32#14583130—21no—
33#14583101C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583099C2211yescharacteristic
36#14583049—21no—
37#14583048—21no—
38#14583038—21no—
39#14583030C2211yescharacteristic, complemented
40#14582997—21no—
41C4×#10621884C2211yescharacteristic
42C8×D172C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44#102×D43—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56Q82×C43C2211yescharacteristic, complemented
57D4×Q8×C43C2211yescharacteristic
58C43×#498—21no—
59C43×#498C2211yescharacteristic, complemented
60C43×#476—21no—
61C43×#476C2211yescharacteristic
62C43×#475—21no—
63C43×#475C2211yescharacteristic, complemented
64C8×Q8×C43C2211yescharacteristic, complemented
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621884—41no—
75C2×#10621884—44no—
76C2×#10621884D411yescharacteristic
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063317—21no—
82#13063303—41no—
83#13063301—21no—
84#13063300—21no—
85#13063299—21no—
86#13063295—41no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C4⋊C4×D43—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063249—21no—
101#13063249—21no—
102#13063249D411yescharacteristic
103#13063248—41no—
104#13063247—21no—
105#13063247—21no—
106#13063246—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×Q8×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43—41no—
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#106×C43—21no—
133#106×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136#106×C43D411yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—41no—
150C2×Q8×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C2×C22⋊D43—41no—
158D4×D43—42no—
159D4×D43—81no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—41no—
164C2×D172—42no—
165C2×D172—81no—
166C2×D172C2×D411yescharacteristic
167C2×C4×D43—21no—
168C2×C4×D43—41no—
169C2×Dic86—21no—
170SD16×C43—22no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—41no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—41no—
191C42×C43C2411yescharacteristic
192#10621884—42no—
193#10621884—42no—
194#10621884—42no—
195#10621884—81no—
196#10621884—81no—
197#10621884—82no—
198#10621884SD1614yescomplemented
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—41no—
201(C2×D43)⋊C4—41no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43C2×D411yescharacteristic
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—42no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C8×D43—81no—
215C23×C43—21no—
216C22×D43—21no—
217C22×D43—41no—
218C22×D43—82no—
219C22×D43—82no—
220C22×D43—161no—
221Q8×C43—21no—
222Q8×C43—21no—
223Q8×C43—21no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—82no—
227Q8×C43—81no—
228Q8×C43—161no—
229Q8×C43C2×SD1612yes—
230D4×C43—21no—
231D4×C43#13712yes—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—82no—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C22⋊D43—82no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248D172—21no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—81no—
254D172—82no—
255D172C2×SD1612yes—
256C4×D43—41no—
257C4×D43—41no—
258C4×D43—161no—
259Dic86—81no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8C2×SD1612yes—
269#19765—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43D4211yescharacteristic
274C2×D43—22no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—164no—
281C4×C43—22no—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C22×SD1611yescharacteristic
290C4×C43C2×#13711yescharacteristic
291C4×C43#57711yescharacteristic
292C4×C43#57711yescharacteristic
293Dic43—41no—
294Dic43—81no—
295#3385—431no—
296Q8×SD16D4311yescharacteristic, complemented
297#3295—431no—
298D4×SD16—431no—
299#1714—431no—
300#1686—431no—
301#1678—431no—
302#1675—431no—
303#1671—431no—
304#1643—431no—
305#1637—431no—
306#1629—431no—
307#1623—431no—
308#1582—431no—
309SD16⋊C8—431no—
310C2×C43—42no—
311C2×C43#326611yescharacteristic
312C2×C43D4×SD1611yescharacteristic
313C2×C43#328811yescharacteristic
314D43—42no—
315D43—161no—
316C22×SD16—861no—
317Q82C2×D4311yescharacteristic, complemented
318#554—431no—
319D4×Q8C2×D4311yescharacteristic
320D42—431no—
321#501—861no—
322#500—431no—
323#498—21no—
324#498C2×D4311yescharacteristic, complemented
325#492—431no—
326#492—431no—
327#487—431no—
328#486—431no—
329#481—861no—
330#479—861no—
331#477—431no—
332#476—21no—
333#476—431no—
334#476—431no—
335#476C2×D4311yescharacteristic
336#475—21no—
337#475C2×D4311yescharacteristic, complemented
338#474—861no—
339#465—861no—
340#465—861no—
341#461—431no—
342#460—431no—
343#460—431no—
344#450—861no—
345#450—861no—
346#448—861no—
347#446—431no—
348C8×Q8C2×D4311yescharacteristic, complemented
349#440—861no—
350C4×SD16—21no—
351C4×SD16—431no—
352C4×SD16C2×D4311yescharacteristic
353C8×D4—431no—
354C8×D4—431no—
355C2×#102—861no—
356#335—431no—
357#334—431no—
358#333—431no—
359#333—431no—
360#332—431no—
361#331—431no—
362Q8⋊C8—431no—
363Q8⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366#322—431no—
367C43#1976511yescharacteristic, complemented, Sylow
368C22×Q8—21no—
369C22×D4—861no—
370C22×D4—861no—
371C2×SD16—431no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×SD16—1721no—
378C2×SD16—1724no—
379C2×SD16C22⋊D4311yescharacteristic
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8—21no—
383C4⋊Q8—21no—
384C4⋊Q8—21no—
385C4⋊Q8—41no—
386C4⋊Q8—431no—
387C4⋊Q8C22×D4311yescharacteristic
388C4⋊Q8C22×D4311yescharacteristic
389#127—431no—
390#125—861no—
391C22⋊Q8—21no—
392C22⋊Q8—41no—
393C22⋊Q8—861no—
394C22⋊Q8—1721no—
395#121—861no—
396#121—861no—
397#120—1721no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8C22×D4311yescharacteristic
401C4×Q8C22×D4311yescharacteristic
402C4×D4—21no—
403C4×D4—431no—
404C4×D4—861no—
405C4×D4C22×D4311yescharacteristic
406C2×C4⋊C4—861no—
407#107—861no—
408#107—861no—
409#107—861no—
410#106—21no—
411#106—21no—
412#106—21no—
413#106—21no—
414#106—431no—
415#106—861no—
416#106—861no—
417#106C22⋊D4311yescharacteristic
418C4⋊C8—21no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—861no—
423C4⋊C8C22×D4311yescharacteristic
424#103—21no—
425#103—431no—
426#103—861no—
427#103—861no—
428#103—1721no—
429#103C22⋊D4311yescharacteristic
430#102—21no—
431#102—431no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102C22⋊D4311yescharacteristic
439C22⋊C8—861no—
440C22⋊C8—861no—
441#97—861no—
442C4×C8—21no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8C22×D4311yescharacteristic
446C24—1721no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—42no—
452C2×Q8—81no—
453C2×Q8—861no—
454C2×Q8D4×D4311yescharacteristic
455C2×Q8C2×C22⋊D4311yescharacteristic
456C2×D4—431no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—3441no—
461C2×D4—3441no—
462C2×D4—1721no—
463C2×D4—1722no—
464C2×D4—1721no—
465C2×D4—1722no—
466C2×D4C2×C22⋊D4311yescharacteristic
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—861no—
470C22×C4—1721no—
471SD16—22no—
472SD16—434no—
473SD16—3441no—
474SD16—3442no—
475SD16—3441no—
476SD16—1722no—
477SD16—1722no—
478SD16—1722no—
479C2×C8—21no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—3441no—
487C2×C8—1722no—
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—431no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4D4×D4311yescharacteristic
505C4⋊C4C2×C22⋊D4311yescharacteristic
506C4⋊C4C2×C22⋊D4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—861no—
510C22⋊C4—1721no—
511C22⋊C4—1721no—
512C42—21no—
513C42—21no—
514C42—41no—
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—861no—
518C23—3442no—
519C23—3442no—
520C23—1721no—
521C23—6881no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—41no—
526Q8—41no—
527Q8—82no—
528Q8—81no—
529Q8—161no—
530Q8—3441no—
531Q8SD16×D4312yes—
532D4—21no—
533D4—432no—
534D4—861no—
535D4—3441no—
536D4—3442no—
537D4—3442no—
538D4—1721no—
539D4—1721no—
540D4—1721no—
541D4—1721no—
542D4#1306335612yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—861no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—6881no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C22×C22⋊D4311yescharacteristic
560C2×C4#1306337011yescharacteristic
561C8—21no—
562C8—21no—
563C8—41no—
564C8—432no—
565C8—861no—
566C8—1721no—
567C8—1721no—
568C8—1721no—
569C8—1721no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—862no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—1721no—
578C22—1721no—
579C22—6884no—
580C22D4×C22⋊D4311yescharacteristic
581C4—22no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—3441no—
590C4—1721no—
591C4C2×SD16×D4311yescharacteristic
592C4C2×#1306335611yescharacteristic
593C4#1458370511yescharacteristic
594C4#1458370711yescharacteristic
595C2—42no—
596C2—1722no—
597C2—6881no—
598C2#1914610611yescharacteristic
599C2SD16×C22⋊D4311yescharacteristic
600C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×SD16×C43C2
socleC22×C43D42
prime radicalD4×D172C22
hypercenterQ8×SD16D43
hypocenterC43#19765
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8×SD16

Complements

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

NH ≅ G/Ntype
1. #19147501C2semidirect
4. #19134220C2semidirect
5. #19134069C2semidirect
6. #19134011C2semidirect
7. #19133992C2semidirect
8. #19133967C2semidirect
9. #19133801C2semidirect
10. #19133760C2semidirect
12. #19133673C2semidirect
13. #19133432C2semidirect
14. #19133405C2semidirect
15. Q8×SD16×C43C2semidirect
20. #14583302C22semidirect
23. #14583251C22semidirect
27. #14583194C22semidirect
39. #14583030C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
56. Q82×C43C22semidirect
59. C43×#498C22semidirect
63. C43×#475C22semidirect
64. C8×Q8×C43C22semidirect
198. #10621884SD16semidirect
296. Q8×SD16D43semidirect
317. Q82C2×D43semidirect
324. #498C2×D43semidirect
337. #475C2×D43semidirect
348. C8×Q8C2×D43semidirect
367. C43#19765semidirect

Maximal subgroups

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

subgroupindex
#191475012
#191464212
D4×#106218842
#191342202
#191340692
#191340112
#191339922
#191339672
#191338012
#191337602
#191337102
#191336732
#191334322
#191334052
Q8×SD16×C432
#1976543