Finite Group Databasebeta

← #25148759

Subgroups — #25148759

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144388C211yesmaximal, characteristic
2C2×#14583196C211yesmaximal, characteristic
3#19143544C211yesmaximal, characteristic, complemented
4#19136108C211yesmaximal, characteristic, complemented
5#19136103C211yesmaximal, characteristic, complemented
6#19135952C211yesmaximal, characteristic
7#19135952C211yesmaximal, characteristic
8#19135589C211yesmaximal, characteristic, complemented
9#19135377C211yesmaximal, characteristic, complemented
10#19135372C211yesmaximal, characteristic, complemented
11#19135370C211yesmaximal, characteristic, complemented
12#19135256C211yesmaximal, characteristic
13#19135256C211yesmaximal, characteristic
14C4×#13063241C211yesmaximal, characteristic
15C43×#3166C211yesmaximal, characteristic, complemented
16C2×C4×D172C2211yescharacteristic
17#14583196—21no—
18#14583196—21no—
19#14583196—21no—
20#14583196—21no—
21#14583196—21no—
22#14583196—21no—
23#14583186—21no—
24#14583176—21no—
25#14583030—21no—
26#14583030—21no—
27#14583030—21no—
28Q8×C43⋊C8—21no—
29C2×#13063260C2211yescharacteristic
30C2×#13063260C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582942C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35#14582926C2211yescharacteristic
36#14582926C2211yescharacteristic
37#14582923C2211yescharacteristic
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39#14582903C2211yescharacteristic
40#14582903C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063241C2211yescharacteristic
44C2×#13063241C2211yescharacteristic
45#14582855C2211yescharacteristic
46#14582855C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C2×#125×C43C2211yescharacteristic
58C43×#501—21no—
59C43×#501—21no—
60C43×#499—21no—
61C43×#499—21no—
62C43×#428C2211yescharacteristic
63C43×#428C2211yescharacteristic
64C43×#428C2211yescharacteristic
65C43×#428C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C4×D43—21no—
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C4×D172—21no—
76C4×D172—21no—
77C4×D172—21no—
78C4×D172—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×(C2×D43)⋊C4—21no—
81#13063260—22no—
82#13063260—22no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)D411yescharacteristic
98C4⋊(C43⋊C8)D411yescharacteristic
99C4⋊(C43⋊C8)D411yescharacteristic
100C4⋊(C43⋊C8)D411yescharacteristic
101#13063245—21no—
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063241—22no—
110#13063241Q814yescomplemented
111#13063236—21no—
112#13063236—21no—
113#13063236—21no—
114C4×C43⋊C8—21no—
115C4×C43⋊C8—21no—
116C4×C43⋊C8—21no—
117C2×M16×C43C2311yescharacteristic
118C2×M16×C43C2311yescharacteristic
119C4⋊Q8×C43D411yescharacteristic
120C4⋊Q8×C43D411yescharacteristic
121#125×C43—21no—
122#125×C43—21no—
123#125×C43—21no—
124#125×C43—21no—
125#125×C43D411yescharacteristic
126#125×C43D411yescharacteristic
127C22⋊Q8×C43—21no—
128C22⋊Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131#117×C43C2311yescharacteristic
132#117×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138#107×C43—21no—
139#107×C43—21no—
140#107×C43—21no—
141#107×C43—21no—
142#106×C43—21no—
143#106×C43—21no—
144#106×C43—21no—
145#106×C43—21no—
146#97×C43—21no—
147C4×C8×C43—21no—
148C23×D43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43#4111yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C2×Q812yes—
163C2×C4×D43—41no—
164C2×C4×D43—41no—
165C2×C4×D43—82no—
166M16×C43—21no—
167M16×C43—21no—
168M16×C43C2×Q812yes—
169M16×C43#4112yes—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
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—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C42×C43C2×D411yescharacteristic
197C42×C43C2×D411yescharacteristic
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202#10621877—21no—
203#10621877—21no—
204#10621877—21no—
205#10621877—21no—
206#10621877—21no—
207#10621877—21no—
208#10621877—21no—
209#10621877C2×Q812yes—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222C23×C43C2×#4111yescharacteristic
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—81no—
227C22×D43—81no—
228Q8×C43—42no—
229Q8×C43—81no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—81no—
239C2×C4×C43—81no—
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×Q811yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×Dic43—41no—
251C2×Dic43—81no—
252D172—22no—
253D172—22no—
254D172—41no—
255D172—41no—
256C4×D43—82no—
257C4×D43—82no—
258C8×C43—22no—
259C8×C43—22no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—22no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#25493—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43C2×#12111yescharacteristic
272C22×C43#53311yescharacteristic
273C22×C43#54111yescharacteristic
274C2×D43—42no—
275C2×D43—82no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—82no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43#54711yescharacteristic
290C4×C43#54811yescharacteristic
291C4×C43D4×Q811yescharacteristic
292C4×C43D4×Q811yescharacteristic
293Dic43—81no—
294#3166D4311yescharacteristic, complemented
295#3077—431no—
296C2×#478—431no—
297#2962—431no—
298#2090—431no—
299#2089—431no—
300#2063—431no—
301#2063—431no—
302#1998—431no—
303#1952—431no—
304#1951—431no—
305#1950—431no—
306#1931—431no—
307#1931—431no—
308C4×#100—431no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43#242911yescharacteristic
312C2×C43#306711yescharacteristic
313C2×C43#306811yescharacteristic
314D43—82no—
315#533C2×D4311yescharacteristic
316C2×#125C2×D4311yescharacteristic
317C2×C4×D4—431no—
318#501—21no—
319#501—21no—
320#499—21no—
321#499—21no—
322#478—861no—
323#478—861no—
324#478—861no—
325#478—861no—
326#478—861no—
327#478—861no—
328#476—861no—
329#474—861no—
330#446—861no—
331#446—861no—
332#446—861no—
333C8×Q8—861no—
334C2×#108—431no—
335C2×#108—431no—
336#428—431no—
337#428—431no—
338#428C2×D4311yescharacteristic
339#428C2×D4311yescharacteristic
340#428C2×D4311yescharacteristic
341#428C2×D4311yescharacteristic
342C2×#107—431no—
343C2×#106—431no—
344#424—431no—
345#424—431no—
346#423—431no—
347C2×C4⋊C8—431no—
348#418—431no—
349#418—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#100—431no—
353C2×#100—431no—
354#405—431no—
355#405—431no—
356C4×M16—431no—
357C4×M16C2×D4311yescharacteristic
358#343—431no—
359#343—431no—
360#343—431no—
361#343—431no—
362#343—431no—
363#343—431no—
364#341—431no—
365#341—431no—
366C43#2549311yescharacteristic, complemented, Sylow
367C22×D4—431no—
368C23×C4—861no—
369C2×M16—431no—
370C2×M16—431no—
371C2×M16—431no—
372C2×M16—431no—
373C2×M16C22×D4311yescharacteristic
374C2×M16C22×D4311yescharacteristic
375C22×C8—431no—
376C22×C8—431no—
377C4⋊Q8C22⋊D4311yescharacteristic
378C4⋊Q8C22⋊D4311yescharacteristic
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125C22⋊D4311yescharacteristic
384#125C22⋊D4311yescharacteristic
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4—861no—
393#117C22×D4311yescharacteristic
394#117C22×D4311yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—861no—
401C2×C42C22×D4311yescharacteristic
402#108—862no—
403#108—862no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107—861no—
409#107—861no—
410#107—861no—
411#107—861no—
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416#106—861no—
417#106—861no—
418#106—861no—
419#106—861no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8—861no—
427C4⋊C8—861no—
428C4⋊C8—861no—
429C4⋊C8—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#100—434no—
439#100—862no—
440#97—21no—
441#97—861no—
442#97—861no—
443#97—861no—
444C4×C8—21no—
445C4×C8—861no—
446C4×C8—861no—
447C4×C8—861no—
448C24—861no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×D4—432no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—861no—
460C22×C4—3442no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4#1062190011yescharacteristic
464C22×C4#1062190011yescharacteristic
465C22×C4C23×D4311yescharacteristic
466M16—21no—
467M16—21no—
468M16—432no—
469M16—861no—
470M16—861no—
471M16—861no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16—861no—
476M16Q8×D4312yes—
477M16#1062190212yes—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4C2×C22⋊D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C4⋊C4C2×C22⋊D4311yescharacteristic
511C4⋊C4C2×C22⋊D4311yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—1721no—
515C22⋊C4—1721no—
516C42—21no—
517C42—21no—
518C42D4×D4311yescharacteristic
519C42D4×D4311yescharacteristic
520C42C2×C22⋊D4311yescharacteristic
521C42C2×C22⋊D4311yescharacteristic
522C23—862no—
523C23—3441no—
524C23—3441no—
525C23—1721no—
526C23—1721no—
527C23C2×#1062190011yescharacteristic
528Q8—42no—
529Q8—81no—
530D4—862no—
531D4—862no—
532D4—1721no—
533D4—1721no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—3442no—
545C2×C4—3442no—
546C2×C4—3441no—
547C2×C4—1721no—
548C2×C4#1306329711yescharacteristic
549C2×C4#1306329711yescharacteristic
550C2×C4#1306329711yescharacteristic
551C2×C4#1306329711yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C22×C22⋊D4311yescharacteristic
554C2×C4C2×Q8×D4311yescharacteristic
555C2×C4C2×#1062190211yescharacteristic
556C2×C4#1306337311yescharacteristic
557C2×C4#1306337311yescharacteristic
558C8—22no—
559C8—22no—
560C8—861no—
561C8—861no—
562C8—861no—
563C8—861no—
564C8—862no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C22—21no—
569C22—21no—
570C22—3442no—
571C22—3442no—
572C22—3441no—
573C22—3441no—
574C22—1722no—
575C22C2×#1306329711yescharacteristic
576C22#1458345411yescharacteristic
577C22#1458351011yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—3441no—
589C4#1458355211yescharacteristic
590C4#1458356011yescharacteristic
591C4Q8×C22⋊D4311yescharacteristic
592C4#1458356411yescharacteristic
593C2—21no—
594C2—21no—
595C2—3442no—
596C2#1913819711yescharacteristic
597C2#1914431211yescharacteristic
598C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3166C2
socleC22×C43C2×#121
prime radicalC22×D172C23
hypercenter#3166D43
hypocenterC43#25493
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
3. #19143544C2semidirect
4. #19136108C2semidirect
5. #19136103C2semidirect
8. #19135589C2semidirect
9. #19135377C2semidirect
10. #19135372C2semidirect
11. #19135370C2semidirect
15. C43×#3166C2semidirect
110. #13063241Q8semidirect
294. #3166D43semidirect
366. C43#25493semidirect

Maximal subgroups

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

subgroupindex
#191443882
C2×#145831962
#191435442
#191361082
#191361032
#191359522
#191355892
#191353772
#191353722
#191353702
#191352562
C4×#130632412
C43×#31662
#2549343