Finite Group Databasebeta

← #25148749

Subgroups — #25148749

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#19145144C211yesmaximal, characteristic, complemented
2#19144392C211yesmaximal, characteristic
3#19143538C211yesmaximal, characteristic, complemented
4#19136106C211yesmaximal, characteristic, complemented
5#19136101C211yesmaximal, characteristic, complemented
6#19135953C211yesmaximal, characteristic
7#19135953C211yesmaximal, characteristic
8#19135589C211yesmaximal, characteristic, complemented
9#19135378C211yesmaximal, characteristic, complemented
10#19135373C211yesmaximal, characteristic, complemented
11#19135371C211yesmaximal, characteristic, complemented
12#19135254C211yesmaximal, characteristic
13#19135254C211yesmaximal, characteristic
14C4×#13063242C211yesmaximal, characteristic
15C2×C43×#478C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583309—21no—
18#14583309—21no—
19#14583298—21no—
20#14583298—21no—
21#14583199—21no—
22#14583199—21no—
23#14583189—21no—
24#14583179—21no—
25#14583028—21no—
26#14583028—21no—
27#14583026—21no—
28#14583023—21no—
29C2×#13063261C2211yescharacteristic
30C2×#13063261C2211yescharacteristic
31#14582939C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582939C2211yescharacteristic
34#14582939C2211yescharacteristic
35#14582939C2211yescharacteristic
36#14582939C2211yescharacteristic
37#14582925C2211yescharacteristic
38#14582925C2211yescharacteristic
39#14582923C2211yescharacteristic
40#14582904C2211yescharacteristic
41#14582904C2211yescharacteristic
42C2×#13063242C2211yescharacteristic
43C2×#13063242C2211yescharacteristic
44#14582854C2211yescharacteristic
45#14582854C2211yescharacteristic
46C4×#10621877C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582668C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#478—21no—
59C43×#478—21no—
60C43×#478—21no—
61C43×#478—21no—
62C2×#107×C43C2211yescharacteristic
63C2×#106×C43C2211yescharacteristic
64C2×C4⋊C8×C43C2211yescharacteristic
65C2×#102×C43C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73#13063325D411yescharacteristic
74#13063325D411yescharacteristic
75#13063317D411yescharacteristic
76#13063317D411yescharacteristic
77#13063304—21no—
78#13063304—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81#13063284C2311yescharacteristic
82#13063284C2311yescharacteristic
83#13063261—22no—
84#13063261—22no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063242—22no—
108#13063242Q814yescomplemented
109#13063236—21no—
110#13063236—21no—
111#13063235—21no—
112#13063235—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8—21no—
115C8×Dic43—21no—
116C8×Dic43—21no—
117C22×D4×C43C2311yescharacteristic
118C23×C4×C43—21no—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121#125×C43—21no—
122#125×C43—21no—
123#125×C43—21no—
124#125×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#107×C43—21no—
137#107×C43—21no—
138#106×C43—21no—
139#106×C43—21no—
140C4⋊C8×C43D411yescharacteristic
141C4⋊C8×C43D411yescharacteristic
142C4⋊C8×C43D411yescharacteristic
143C4⋊C8×C43D411yescharacteristic
144#102×C43—21no—
145#102×C43—21no—
146#102×C43—21no—
147#102×C43—21no—
148C24×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43C2×Q812yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×C4×C43—82no—
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
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×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C22⋊Dic43—21no—
191C22⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×D411yescharacteristic
195C4⋊Dic43C2×D411yescharacteristic
196C4⋊Dic43C2×D411yescharacteristic
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204#10621877—21no—
205#10621877—21no—
206#10621877—21no—
207#10621877—21no—
208#10621877—21no—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877C2×Q812yes—
214#10621877C2×Q812yes—
215#10621877#4112yes—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C23×C43—22no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—81no—
226C23×C43—81no—
227C23×C43C2×#4111yescharacteristic
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—41no—
231D4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—82no—
238C2×C4×C43—82no—
239C2×C4×C43—81no—
240C2×C4×C43—81no—
241C2×C4×C43—81no—
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×Q811yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256Dic86—42no—
257Dic86—81no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C43⋊C8—22no—
263C43⋊C8—22no—
264C43⋊C8—22no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#25493—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—42no—
272C22×C43—82no—
273C22×C43—82no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43C2×#12111yescharacteristic
277C22×C43#53311yescharacteristic
278C22×C43#54111yescharacteristic
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43#54711yescharacteristic
287C4×C43#54811yescharacteristic
288C4×C43D4×Q811yescharacteristic
289C4×C43D4×Q811yescharacteristic
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294#3166—431no—
295#3077—431no—
296C2×#478D4311yescharacteristic
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—82no—
312C2×C43#242911yescharacteristic
313C2×C43#306711yescharacteristic
314C2×C43#306811yescharacteristic
315#533—431no—
316C2×#125C2×D4311yescharacteristic
317C2×C4×D4C2×D4311yescharacteristic
318#501—861no—
319#501—861no—
320#499—861no—
321#499—861no—
322#478—21no—
323#478—21no—
324#478—21no—
325#478—21no—
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#428—431no—
339#428—431no—
340#428—431no—
341#428—431no—
342C2×#107C2×D4311yescharacteristic
343C2×#106C2×D4311yescharacteristic
344#424—431no—
345#424—431no—
346#423—431no—
347C2×C4⋊C8C2×D4311yescharacteristic
348#418—431no—
349#418—431no—
350C2×#102C2×D4311yescharacteristic
351C2×#102C2×D4311yescharacteristic
352C2×#100—431no—
353C2×#100—431no—
354#405—431no—
355#405—431no—
356C4×M16—431no—
357C4×M16—431no—
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×D4C22×D4311yescharacteristic
368C23×C4—21no—
369C2×M16—431no—
370C2×M16—431no—
371C2×M16—431no—
372C2×M16—431no—
373C2×M16—431no—
374C2×M16—431no—
375C22×C8C22×D4311yescharacteristic
376C22×C8C22×D4311yescharacteristic
377C4⋊Q8—431no—
378C4⋊Q8—431no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125—431no—
384#125—431no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387C4×Q8—861no—
388C4×Q8—861no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393#117—431no—
394#117—431no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C22×D4311yescharacteristic
402#108—862no—
403#108—862no—
404#107—21no—
405#107—21no—
406#107—861no—
407#107—861no—
408#107—861no—
409#107—861no—
410#107—861no—
411#107—861no—
412#106—21no—
413#106—21no—
414#106—861no—
415#106—861no—
416#106—861no—
417#106—861no—
418#106—861no—
419#106—861no—
420C4⋊C8—861no—
421C4⋊C8—861no—
422C4⋊C8—861no—
423C4⋊C8—861no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8C22⋊D4311yescharacteristic
427C4⋊C8C22⋊D4311yescharacteristic
428C4⋊C8C22⋊D4311yescharacteristic
429C4⋊C8C22⋊D4311yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#100—434no—
439#100—862no—
440#97—861no—
441#97—861no—
442#97—861no—
443#97—861no—
444C4×C8—861no—
445C4×C8—861no—
446C4×C8—861no—
447C4×C8—861no—
448C24—21no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4Q8×D4312yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—82no—
463C22×C4#1062190011yescharacteristic
464C22×C4#1062190011yescharacteristic
465C22×C4C23×D4311yescharacteristic
466M16—432no—
467M16—432no—
468M16—432no—
469M16—861no—
470M16—861no—
471M16—861no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16—861no—
476M16—861no—
477M16—861no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C2×C8C2×C22⋊D4311yescharacteristic
491C2×C8C2×C22⋊D4311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—431no—
503C4⋊C4—431no—
504C4⋊C4—431no—
505C4⋊C4—431no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C42—861no—
517C42—861no—
518C42D4×D4311yescharacteristic
519C42D4×D4311yescharacteristic
520C42C2×C22⋊D4311yescharacteristic
521C42C2×C22⋊D4311yescharacteristic
522C23—22no—
523C23—41no—
524C23—41no—
525C23—81no—
526C23—81no—
527C23C2×#1062190011yescharacteristic
528Q8—3441no—
529Q8—1722no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4#1306329611yescharacteristic
549C2×C4#1306329611yescharacteristic
550C2×C4#1306329611yescharacteristic
551C2×C4#1306329611yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C22×C22⋊D4311yescharacteristic
554C2×C4C2×Q8×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C2×C4#1306337211yescharacteristic
557C2×C4#1306337311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—862no—
563C8—862no—
564C8—862no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C22—21no—
569C22—21no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—81no—
574C22—81no—
575C22C2×#1306329611yescharacteristic
576C22#1458345111yescharacteristic
577C22#1458350911yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4—1721no—
589C4#1458354811yescharacteristic
590C4#1458355911yescharacteristic
591C4#1458356211yescharacteristic
592C4Q8×C22⋊D4311yescharacteristic
593C2—21no—
594C2—21no—
595C2—82no—
596C2#1913819011yescharacteristic
597C2#1914431111yescharacteristic
598C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#478C2
socleC22×C43C2×#121
prime radicalC22×D4×C43C23
hypercenterC2×#478D43
hypocenterC43#25493
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. #19145144C2semidirect
3. #19143538C2semidirect
4. #19136106C2semidirect
5. #19136101C2semidirect
8. #19135589C2semidirect
9. #19135378C2semidirect
10. #19135373C2semidirect
11. #19135371C2semidirect
108. #13063242Q8semidirect
366. C43#25493semidirect

Maximal subgroups

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

subgroupindex
#191451442
#191443922
#191435382
#191361062
#191361012
#191359532
#191355892
#191353782
#191353732
#191353712
#191352542
C4×#130632422
C2×C43×#4782
#2549343