Finite Group Databasebeta

← #25155547

Subgroups — #25155547

Order 11008.

678 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#19145126C211yesmaximal, characteristic, complemented
2#19144456C211yesmaximal, characteristic
3#19144445C211yesmaximal, characteristic
4#19143191C211yesmaximal, characteristic
5#19136109C211yesmaximal, characteristic, complemented
6#19136104C211yesmaximal, characteristic, complemented
7#19135943C211yesmaximal, characteristic, complemented
8#19135938C211yesmaximal, characteristic, complemented
9#19135346C211yesmaximal, characteristic, complemented
10#19134831C211yesmaximal, characteristic
11#19134824C211yesmaximal, characteristic
12#19134762C211yesmaximal, characteristic, complemented
13#19134651C211yesmaximal, characteristic
14#19134441C211yesmaximal, characteristic
15C43×#1952C211yesmaximal, characteristic, complemented
16C2×#13063331C2211yescharacteristic
17#14583527C2211yescharacteristic
18#14583527C2211yescharacteristic
19#14583380C2211yescharacteristic
20#14583380C2211yescharacteristic
21#14583308—21no—
22#14583308—21no—
23#14583301—21no—
24#14583297—21no—
25#14583209—21no—
26#14583205—21no—
27#14583202—21no—
28#14583198—21no—
29#14583193—21no—
30#14583188—21no—
31#14583183—21no—
32#14583178—21no—
33#14582941C2211yescharacteristic
34#14582941C2211yescharacteristic
35#14582940—21no—
36#14582940—21no—
37#14582939C2211yescharacteristic
38#14582939C2211yescharacteristic
39#14582937C2211yescharacteristic
40#14582936—21no—
41C2×#13063258C2211yescharacteristic
42#107×D43—21no—
43C2×#13063257C2211yescharacteristic
44C2×#13063256C2211yescharacteristic
45#14582927C2211yescharacteristic
46#14582927C2211yescharacteristic
47C2×#13063251C2211yescharacteristic
48#14582901C2211yescharacteristic
49#14582901C2211yescharacteristic
50#14582893C2211yescharacteristic
51C2×#13063235C2211yescharacteristic
52#14582768C2211yescharacteristic
53#14582764C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582663C2211yescharacteristic
57#14582660C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582658C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C43×#428C2211yescharacteristic
63C2×#107×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063331—22no—
69#13063331Q814yescomplemented
70C2×#10621877C2311yescharacteristic
71C2×#10621872—21no—
72C22×C43⋊C8C2311yescharacteristic
73C2×C8×D43—21no—
74#13063325—21no—
75#13063325—21no—
76#13063324—21no—
77#13063324—21no—
78#13063317—21no—
79#13063317—21no—
80#13063316—21no—
81#13063316—21no—
82#13063302—41no—
83#13063302—41no—
84#13063290—21no—
85#13063290—21no—
86#13063287—21no—
87#13063287—21no—
88C4×C22⋊D43—41no—
89C4×C22⋊D43—41no—
90#13063284C2311yescharacteristic
91#13063284C2311yescharacteristic
92#13063283—21no—
93#13063283—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—41no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C2×C4×Dic43C2311yescharacteristic
100#13063259—21no—
101#13063259—21no—
102#13063259D411yescharacteristic
103#13063259D411yescharacteristic
104#13063258—21no—
105#13063258—21no—
106#13063258—21no—
107#13063258—21no—
108#13063257—21no—
109#13063257—21no—
110#13063257—21no—
111#13063257—21no—
112#13063257D411yescharacteristic
113#13063257D411yescharacteristic
114#13063256—21no—
115#13063256—21no—
116#13063256—21no—
117#13063256—21no—
118Dic43⋊C8—21no—
119Dic43⋊C8—21no—
120Dic43⋊C8—21no—
121Dic43⋊C8—21no—
122#13063251Q814yescomplemented
123#13063250—21no—
124#13063250—21no—
125#13063248D411yescharacteristic
126#13063248D411yescharacteristic
127#13063247—21no—
128#13063247—21no—
129#13063245D411yescharacteristic
130#13063245D411yescharacteristic
131#13063235—22no—
132C43⋊#95—41no—
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137#117×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140#108×C43—22no—
141#107×C43—21no—
142#107×C43—21no—
143#107×C43—21no—
144#107×C43—21no—
145#106×C43—21no—
146#106×C43—21no—
147#97×C43—21no—
148C4×C8×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156#10621898—21no—
157#10621898—21no—
158#10621898C2×Q812yes—
159#10621898C2×Q812yes—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—41no—
163C2×C4×D43—41no—
164C2×Dic86—41no—
165C2×Dic86—41no—
166C2×Dic86C2×D411yescharacteristic
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43—21no—
171M16×C43—21no—
172M16×C43C2×Q812yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×Q812yes—
179C2×C8×C43#4112yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C22⋊Dic43—21no—
189C22⋊Dic43—21no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199C4⋊Dic43C2×D411yescharacteristic
200C4⋊Dic43C2×D411yescharacteristic
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208Dic43⋊C4—82no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—41no—
213C4×Dic43—41no—
214C4×Dic43C2×Q812yes—
215#10621877—21no—
216#10621877C2×Q812yes—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222#10621872—24no—
223C8×D43—24no—
224C23×C43H(5,𝔽2)11yescharacteristic
225C22×D43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—81no—
231C2×C4×C43—81no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×Q811yescharacteristic
235C2×C4×C43C22×Q811yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C22⋊D43—22no—
239C22⋊D43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—81no—
251C2×Dic43—81no—
252D172—21no—
253D172C4⋊Q812yes—
254C4×D43—22no—
255C4×D43—22no—
256C4×D43—161no—
257C4×D43—161no—
258Dic86—21no—
259Dic86—161no—
260Dic86—161no—
261Dic86C4⋊Q812yes—
262C8×C43—22no—
263C8×C43—41no—
264C8×C43—41no—
265C8×C43C22⋊Q812yes—
266C8×C43C22⋊Q812yes—
267C43⋊C8—22no—
268C43⋊C8—21no—
269C43⋊C8—21no—
270#26085—431nomaximal, Sylow
271C22×C43—21no—
272C22×C43—21no—
273C22×C43#54411yescharacteristic
274C22×C43D4211yescharacteristic
275C22×C43#55411yescharacteristic
276C2×D43—22no—
277C2×D43—41no—
278C2×D43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43C2×C22⋊Q811yescharacteristic
284C4×C43C2×C4⋊Q811yescharacteristic
285C4×C43#54711yescharacteristic
286C4×C43D4×Q811yescharacteristic
287Dic43—22no—
288Dic43—42no—
289Dic43—41no—
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43—81no—
294Dic43—81no—
295#3163—431no—
296#3084—431no—
297#3083—431no—
298#2913—431no—
299#2090—431no—
300#2089—431no—
301#2061—431no—
302#2060—431no—
303#1952D4311yescharacteristic, complemented
304#1946—431no—
305#1860—431no—
306#1859—431no—
307#1847—431no—
308#1815—431no—
309#1765—431no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43#244011yescharacteristic
313C2×C43#328811yescharacteristic
314C2×C43#328911yescharacteristic
315D43—42no—
316C2×#131—431no—
317#544—431no—
318#544—431no—
319#520—431no—
320#520—431no—
321#501—861no—
322#501—861no—
323#499—861no—
324#498—861no—
325#479—861no—
326#479—861no—
327#478—861no—
328#478—861no—
329#477—861no—
330#476—861no—
331#475—861no—
332#474—861no—
333C2×#108C2×D4311yescharacteristic
334#428—431no—
335#428—431no—
336#428—431no—
337#428—431no—
338#428—861no—
339#428—861no—
340#428C2×D4311yescharacteristic
341#428C2×D4311yescharacteristic
342#427—431no—
343#427—861no—
344C2×#107—431no—
345C2×#107—861no—
346C2×#107C2×D4311yescharacteristic
347C2×#106—431no—
348C2×#106—431no—
349#424—431no—
350#424—431no—
351C2×#104—431no—
352#417—431no—
353#417—431no—
354#416—431no—
355#405C2×D4311yescharacteristic
356C2×#97—431no—
357#384—431no—
358#382—431no—
359#343—431no—
360#343—431no—
361#343C2×D4311yescharacteristic
362#343C2×D4311yescharacteristic
363#341—431no—
364#339—431no—
365#339—431no—
366#339—431no—
367C43#2608511yescharacteristic, complemented, Sylow
368C2×#41—431no—
369#131—434no—
370#131—862no—
371C2×M16—431no—
372C2×M16—861no—
373C2×M16C22×D4311yescharacteristic
374C2×M16C22×D4311yescharacteristic
375C2×M16C22×D4311yescharacteristic
376C22×C8—431no—
377C22×C8—861no—
378C22×C8C22×D4311yescharacteristic
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383#125—861no—
384#125—861no—
385#125—861no—
386#125—861no—
387C22⋊Q8—1721no—
388C22⋊Q8—1721no—
389C4×Q8—861no—
390C4×Q8—861no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4—1721no—
394C4×D4—1721no—
395#117—431no—
396#117—431no—
397#117—861no—
398#117—861no—
399#117C22×D4311yescharacteristic
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—1721no—
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C42—431no—
408#108—22no—
409#107—21no—
410#107—21no—
411#107—21no—
412#107—21no—
413#107—431no—
414#107—431no—
415#107—861no—
416#107—861no—
417#107—861no—
418#107—861no—
419#107—861no—
420#107—861no—
421#106—21no—
422#106—21no—
423#106—431no—
424#106—431no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106—861no—
429#106—861no—
430#106—861no—
431#106—861no—
432#106—861no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437#104—434no—
438#103—431no—
439#103—431no—
440#103—861no—
441#103—861no—
442#102—431no—
443#102—431no—
444#102—861no—
445#102—861no—
446#97—21no—
447#97—862no—
448C4×C8—21no—
449#95—1721no—
450#41—432no—
451#41—432no—
452#41—861no—
453#41—861no—
454C2×Q8—431no—
455C2×Q8—1721no—
456C2×Q8—1721no—
457C2×D4—431no—
458C2×D4—861no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—1721no—
466C22×C4—1721no—
467C22×C4C23×D4311yescharacteristic
468M16—21no—
469M16—21no—
470M16—21no—
471M16—21no—
472M16—21no—
473M16—432no—
474M16—861no—
475M16—864no—
476M16Q8×D4312yes—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—864no—
486C2×C8#1062189812yes—
487C2×C8D4×D4311yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C2×C8Q8×D4312yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—431no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—3442no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4—1721no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4D4×D4311yescharacteristic
512C4⋊C4D4×D4311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C42—21no—
519C42—432no—
520C42—861no—
521C42—861no—
522C42—861no—
523C42—1721no—
524C42—1721no—
525C23—861no—
526C23#1306337111yescharacteristic
527Q8—432no—
528Q8—861no—
529Q8—6881no—
530Q8—6881no—
531D4—432no—
532D4—862no—
533D4—862no—
534D4—861no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—861no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—3441no—
550C2×C4—3441no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—6881no—
556C2×C4—6881no—
557C2×C4C2×D4×D4311yescharacteristic
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×Q8×D4311yescharacteristic
560C2×C4C2×Q8×D4311yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C2×C4#1306337211yescharacteristic
563C8—22no—
564C8—41no—
565C8—41no—
566C8—861no—
567C8—861no—
568C8—862no—
569C8#1306330312yes—
570C8#1306330312yes—
571C22—21no—
572C22—21no—
573C22—862no—
574C22—1721no—
575C22—1721no—
576C22#1458352911yescharacteristic
577C22#1458353311yescharacteristic
578C22#1458360911yescharacteristic
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—862no—
584C4—3441no—
585C4—3441no—
586C4—1722no—
587C4—1721no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C4C2×#1306330311yescharacteristic
592C4C4⋊Q8×D4311yescharacteristic
593C4#1458355411yescharacteristic
594C4#1458356211yescharacteristic
595C2—21no—
596C2—21no—
597C2—1722no—
598C2#1913829911yescharacteristic
599C2#1914635811yescharacteristic
600C2#1914636911yescharacteristic
subgroupG/H
centerC22#14583533
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1952C2
socleC22×C43D42
prime radicalC2×#10621898C23
hypercenter#1952D43
hypocenterC43#26085
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
1. #19145126C2semidirect
5. #19136109C2semidirect
6. #19136104C2semidirect
7. #19135943C2semidirect
8. #19135938C2semidirect
9. #19135346C2semidirect
12. #19134762C2semidirect
15. C43×#1952C2semidirect
69. #13063331Q8semidirect
122. #13063251Q8semidirect
303. #1952D43semidirect
367. C43#26085semidirect

Maximal subgroups

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

subgroupindex
#191451262
#191444562
#191444452
#191431912
#191361092
#191361042
#191359432
#191359382
#191353462
#191348312
#191348242
#191347622
#191346512
#191344412
C43×#19522
#2608543