Finite Group Databasebeta

← #25138109

Subgroups — #25138109

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144413C211yesmaximal, characteristic
2C4×#13063356C211yesmaximal, characteristic
3#19143260C211yesmaximal, characteristic
4#19136041C211yesmaximal, characteristic
5#19136036C211yesmaximal, characteristic
6#19135895C211yesmaximal, characteristic
7#19135895C211yesmaximal, characteristic
8#19135589C211yesmaximal, characteristic, complemented
9#19135378C211yesmaximal, characteristic, complemented
10#19135373C211yesmaximal, characteristic, complemented
11#19135371C211yesmaximal, characteristic, complemented
12#19135247C211yesmaximal, characteristic, complemented
13#19135247C211yesmaximal, characteristic, complemented
14#19134591C211yesmaximal, characteristic, complemented
15C2×C43×#479C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583203—21no—
19#14583203—21no—
20#14583196—21no—
21#14583196—21no—
22#14583004—21no—
23#14582997—21no—
24C4×#10621885—21no—
25C4×#10621884—21no—
26#14582959—21no—
27#14582959—21no—
28#14582955—21no—
29#14582951—21no—
30C2×#13063261C2211yescharacteristic
31C2×#13063261C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582939C2211yescharacteristic
34#14582939C2211yescharacteristic
35#14582923C2211yescharacteristic
36#14582923C2211yescharacteristic
37#14582908C2211yescharacteristic
38#14582898C2211yescharacteristic
39#14582898C2211yescharacteristic
40#14582898C2211yescharacteristic
41C2×#13063244C2211yescharacteristic
42C2×#13063244C2211yescharacteristic
43#14582865C2211yescharacteristic
44#14582865C2211yescharacteristic
45#14582854C2211yescharacteristic
46#14582854C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582668C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C43×#479—21no—
59C43×#479—21no—
60C43×#479—21no—
61C43×#479—21no—
62C2×#107×C43C2211yescharacteristic
63C2×#106×C43C2211yescharacteristic
64C2×C4⋊C8×C43C2211yescharacteristic
65C2×#103×C43C2211yescharacteristic
66C2×#103×C43C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063356—22no—
69#13063356—22no—
70C2×#10621885—21no—
71C2×#10621884—21no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C4×Dic86D411yescharacteristic
79C4×Dic86D411yescharacteristic
80C4×D172D411yescharacteristic
81C4×D172D411yescharacteristic
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84#13063284C2311yescharacteristic
85#13063282—21no—
86C42×D43—21no—
87#13063261—22no—
88#13063261—22no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063244—22no—
108#13063244—22no—
109(C2×D43)⋊C8—21no—
110(C2×D43)⋊C8—21no—
111(C2×D43)⋊C8—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114#13063235—21no—
115#13063235—21no—
116C4×C43⋊C8—21no—
117C8×Dic43—21no—
118C8×Dic43—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122#125×C43—21no—
123#125×C43—21no—
124#125×C43—21no—
125#125×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43C2311yescharacteristic
138#107×C43—21no—
139#107×C43—21no—
140#106×C43—21no—
141#106×C43—21no—
142C4⋊C8×C43D411yescharacteristic
143C4⋊C8×C43D411yescharacteristic
144C4⋊C8×C43D411yescharacteristic
145C4⋊C8×C43D411yescharacteristic
146#103×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#103×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43#4112yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—21no—
164#10621898—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898—21no—
168C2×D172C2×D411yescharacteristic
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×Dic86C2×D411yescharacteristic
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43—41no—
193C42×C43—41no—
194C42×C43—41no—
195C42×C43C2×D411yescharacteristic
196C42×C43C2×D411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C22⋊Dic43—21no—
200#10621885—24no—
201#10621884—24no—
202(C2×D43)⋊C4—21no—
203(C2×D43)⋊C4—21no—
204C4⋊Dic43C2×D411yescharacteristic
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877#4112yes—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C23×C43C2×#4111yescharacteristic
230C22×D43—21no—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—41no—
234Q8×C43—41no—
235C2×C4×C43—22no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—81no—
244C2×C4×C43—81no—
245C2×C4×C43—81no—
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43#12111yescharacteristic
248C2×C4×C43#12111yescharacteristic
249C2×C4×C43#12111yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C22⋊D43—41no—
257C22⋊D43—41no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261D172—21no—
262D172—21no—
263C4×D43—42no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—81no—
267Dic86—21no—
268Dic86—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—21no—
273C43⋊C8—22no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#24725—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43C2×#12111yescharacteristic
283C22×C43#55211yescharacteristic
284C22×C43#55611yescharacteristic
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—42no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43#52511yescharacteristic
297C4×C43#53611yescharacteristic
298C4×C43#54711yescharacteristic
299C4×C43#54811yescharacteristic
300Dic43—41no—
301Dic43—41no—
302Dic43—41no—
303#3080—431no—
304C2×#479D4311yescharacteristic, complemented
305C4×#137—431no—
306#2925—431no—
307#2079—431no—
308#2078—431no—
309#2052—431no—
310#2052—431no—
311#1998—431no—
312#1952—431no—
313#1951—431no—
314#1950—431no—
315#1930—431no—
316#1930—431no—
317#1801—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43#241511yescharacteristic
321C2×C43#306711yescharacteristic
322C2×C43#306911yescharacteristic
323D43—81no—
324C2×#137—431no—
325C2×#125C2×D4311yescharacteristic
326C4×#41—431no—
327C2×C4×Q8C2×D4311yescharacteristic
328#479—21no—
329#479—21no—
330#479—21no—
331#479—21no—
332#479—861no—
333#479—861no—
334#478—861no—
335#478—861no—
336#441—861no—
337#440—861no—
338C4×Q16—861no—
339C4×SD16—861no—
340#433—861no—
341#433—861no—
342#432—861no—
343#431—861no—
344C2×#108—431no—
345C2×#108—431no—
346#428—431no—
347#428—431no—
348#428—431no—
349C2×#107C2×D4311yescharacteristic
350C2×#106C2×D4311yescharacteristic
351#423—431no—
352#423—431no—
353C2×C4⋊C8C2×D4311yescharacteristic
354#419—431no—
355#417—431no—
356#417—431no—
357#417—431no—
358C2×#103C2×D4311yescharacteristic
359C2×#103C2×D4311yescharacteristic
360C2×#101—431no—
361C2×#101—431no—
362#408—431no—
363#408—431no—
364#405—431no—
365#405—431no—
366C4×M16—431no—
367#343—431no—
368#343—431no—
369#343—431no—
370#343—431no—
371#343—431no—
372#343—431no—
373#341—431no—
374#341—431no—
375C43#2472511yescharacteristic, complemented, Sylow
376C2×#41—431no—
377C22×Q8C22×D4311yescharacteristic
378#137—862no—
379#137—862no—
380C2×Q16—861no—
381C2×SD16—861no—
382C2×M16—431no—
383C2×M16—431no—
384C2×M16—431no—
385C2×M16—431no—
386C2×M16—431no—
387C2×M16—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390#125—21no—
391#125—21no—
392#125—21no—
393#125—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—431no—
399C4×Q8—431no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404#117—431no—
405#117—861no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C42—21no—
413C2×C42—861no—
414C2×C42C22×D4311yescharacteristic
415#108—862no—
416#108—862no—
417#107—21no—
418#107—21no—
419#107—861no—
420#107—861no—
421#107—861no—
422#106—21no—
423#106—21no—
424#106—861no—
425#106—861no—
426#106—861no—
427C4⋊C8—861no—
428C4⋊C8—861no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8C22⋊D4311yescharacteristic
432C4⋊C8C22⋊D4311yescharacteristic
433C4⋊C8C22⋊D4311yescharacteristic
434C4⋊C8C22⋊D4311yescharacteristic
435#103—21no—
436#103—21no—
437#103—21no—
438#103—21no—
439#103—861no—
440#103—861no—
441#103—861no—
442#103—861no—
443#103—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#101—862no—
448#101—862no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453#97—861no—
454#97—861no—
455#97—861no—
456C4×C8—861no—
457C4×C8—861no—
458C4×C8—861no—
459#41—861no—
460#41—861no—
461#41—861no—
462#41—861no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—431no—
469C2×Q8#1062190212yes—
470C2×D4—431no—
471C2×D4—861no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4#1062190011yescharacteristic
480C22×C4#1062190011yescharacteristic
481C22×C4C23×D4311yescharacteristic
482Q16—864no—
483SD16—864no—
484M16—432no—
485M16—861no—
486M16—861no—
487M16—861no—
488M16—861no—
489M16—861no—
490M16—861no—
491M16—861no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16—861no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8C2×C22⋊D4311yescharacteristic
507C2×C8C2×C22⋊D4311yescharacteristic
508C2×C8C2×C22⋊D4311yescharacteristic
509C2×C8C2×C22⋊D4311yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—431no—
523C4⋊C4—431no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C22⋊C4—861no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C42—41no—
530C42—41no—
531C42—861no—
532C42—861no—
533C42—861no—
534C42D4×D4311yescharacteristic
535C42D4×D4311yescharacteristic
536C42C2×C22⋊D4311yescharacteristic
537C42C2×C22⋊D4311yescharacteristic
538C23—861no—
539C23C2×#1062190011yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—41no—
543Q8—41no—
544Q8—861no—
545Q8—861no—
546D4—861no—
547D4—861no—
548D4—1721no—
549D4—1721no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—3441no—
565C2×C4—1722no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4#1306329611yescharacteristic
569C2×C4#1306329611yescharacteristic
570C2×C4#1306329611yescharacteristic
571C2×C4#1306329611yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C22×C22⋊D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062190211yescharacteristic
576C2×C4#1306337211yescharacteristic
577C2×C4#1306337311yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—862no—
583C8—1721no—
584C8—1721no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C22—21no—
589C22—21no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22C2×#1306329611yescharacteristic
594C22#1458359111yescharacteristic
595C22#1458362011yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—1721no—
605C4—1721no—
606C4—1721no—
607C4#1458341211yescharacteristic
608C4#1458347211yescharacteristic
609C4#1458354811yescharacteristic
610C4#1458356011yescharacteristic
611C2—21no—
612C2—21no—
613C2—3441no—
614C2#1913802011yescharacteristic
615C2#1914431111yescharacteristic
616C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#479C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
hypercenterC2×#479D43
hypocenterC43#24725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
8. #19135589C2semidirect
9. #19135378C2semidirect
10. #19135373C2semidirect
11. #19135371C2semidirect
12. #19135247C2semidirect
13. #19135247C2semidirect
14. #19134591C2semidirect
15. C2×C43×#479C2semidirect
304. C2×#479D43semidirect
375. C43#24725semidirect

Maximal subgroups

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

subgroupindex
#191444132
C4×#130633562
#191432602
#191360412
#191360362
#191358952
#191355892
#191353782
#191353732
#191353712
#191352472
#191345912
C2×C43×#4792
#2472543