Finite Group Databasebeta

← #25160048

Subgroups — #25160048

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144459C211yesmaximal, characteristic
2#19144440C211yesmaximal, characteristic, complemented
3#19143440C211yesmaximal, characteristic
4#19143187C211yesmaximal, characteristic
5#19136137C211yesmaximal, characteristic, complemented
6#19136107C211yesmaximal, characteristic, complemented
7#19135961C211yesmaximal, characteristic, complemented
8#19135939C211yesmaximal, characteristic, complemented
9#19135375C211yesmaximal, characteristic, complemented
10#19135109C211yesmaximal, characteristic
11#19134965C211yesmaximal, characteristic
12#19134873C211yesmaximal, characteristic
13#19134822C211yesmaximal, characteristic
14#19134811C211yesmaximal, characteristic, complemented
15C43×#1922C211yesmaximal, characteristic, complemented
16C2×#13063358C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18#14583527C2211yescharacteristic
19#14583379C2211yescharacteristic
20#14583379C2211yescharacteristic
21#14583376C2211yescharacteristic
22#14583209—21no—
23#14583207—21no—
24#14583205—21no—
25#14583200—21no—
26#14583193—21no—
27#14583190—21no—
28#14583185—21no—
29#14583183—21no—
30#14583007—21no—
31#14583001—21no—
32C4×Dic172—21no—
33C4×#10621873—21no—
34C2×#13063261C2211yescharacteristic
35#14582942C2211yescharacteristic
36#14582942C2211yescharacteristic
37#14582942C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582941C2211yescharacteristic
40#14582940—21no—
41#14582940—21no—
42#14582934—21no—
43C2×#13063257C2211yescharacteristic
44C2×#13063257C2211yescharacteristic
45#106×D43—21no—
46#14582925C2211yescharacteristic
47C2×#13063253C2211yescharacteristic
48#14582907C2211yescharacteristic
49#14582901C2211yescharacteristic
50#14582896C2211yescharacteristic
51C2×#13063250C2211yescharacteristic
52C2×#13063250C2211yescharacteristic
53C2×#13063243C2211yescharacteristic
54#14582805C2211yescharacteristic
55#14582769C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582659C2211yescharacteristic
60C43×#427C2211yescharacteristic
61C43×#424C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#341C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C22×Dic86C2311yescharacteristic
69#13063358—22no—
70#13063358Q814yescomplemented
71C2×Dic172—21no—
72C2×#10621873—21no—
73#13063331—22no—
74#13063331—22no—
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621872—21no—
78C2×C8×D43—21no—
79#13063325—21no—
80#13063324—21no—
81#13063317—21no—
82#13063316—21no—
83#13063302—41no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88#13063290—21no—
89#13063290—21no—
90C4×D172—21no—
91C4×D172—21no—
92(C22⋊D43)⋊C4—41no—
93(C22⋊D43)⋊C4—41no—
94#13063284C2311yescharacteristic
95#13063283—21no—
96#13063283—21no—
97#13063281—41no—
98C2×C4⋊Dic43—41no—
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C4⋊C4×D43—21no—
103C4⋊C4×D43—21no—
104#13063261—22no—
105#13063259—21no—
106#13063259—21no—
107#13063258—21no—
108#13063258—21no—
109#13063258—21no—
110#13063257—21no—
111#13063257—21no—
112#13063257—21no—
113#13063257—21no—
114#13063257—21no—
115#13063257—21no—
116#13063256—21no—
117#13063256—21no—
118#13063256—21no—
119Dic43⋊C8—21no—
120Dic43⋊C8—21no—
121#13063253—22no—
122#13063250—21no—
123#13063250—21no—
124#13063250—21no—
125#13063250—21no—
126#13063250—21no—
127#13063250D411yescharacteristic
128#13063250D411yescharacteristic
129#13063248—21no—
130#13063248—21no—
131#13063247—21no—
132#13063247D411yescharacteristic
133#13063247D411yescharacteristic
134#13063243—22no—
135C43⋊#95—41no—
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140#117×C43C2311yescharacteristic
141#117×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143#107×C43D411yescharacteristic
144#107×C43D411yescharacteristic
145#106×C43D411yescharacteristic
146#106×C43D411yescharacteristic
147C4⋊C8×C43—21no—
148C4⋊C8×C43—21no—
149#97×C43—21no—
150C4×C8×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158#10621898—21no—
159#10621898—21no—
160#10621898C2×Q812yes—
161#10621898#4112yes—
162C2×D172C2×D411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—41no—
165C2×C4×D43—41no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—41no—
172C2×Dic86C2×D411yescharacteristic
173C2×Dic86C2×Q812yes—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43C2×Q812yes—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C22⋊Dic43—21no—
199(C2×D43)⋊C4—41no—
200(C2×D43)⋊C4—41no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—41no—
208C4⋊Dic43—82no—
209C4⋊Dic43C2×D411yescharacteristic
210C4⋊Dic43C2×D411yescharacteristic
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215Dic43⋊C4—41no—
216Dic43⋊C4—41no—
217C4×Dic43—21no—
218C4×Dic43—41no—
219C4×Dic43—41no—
220C4×Dic43—41no—
221C4×Dic43—41no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877#4112yes—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228Dic172—24no—
229#10621873—24no—
230#10621872—24no—
231C8×D43—24no—
232C23×C43H(5,𝔽2)11yescharacteristic
233C22×D43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×Q811yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C22⋊D43—22no—
248C22⋊D43—22no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—81no—
259C2×Dic43—81no—
260C2×Dic43—81no—
261D172—21no—
262D172C22⋊Q812yes—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—161no—
266C4×D43—161no—
267Dic86—21no—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272Dic86—161no—
273Dic86C22⋊Q812yes—
274C8×C43—22no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—21no—
279C8×C43—41no—
280C43⋊C8—22no—
281C43⋊C8—41no—
282#26401—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43#53911yescharacteristic
286C22×C43D4211yescharacteristic
287C22×C43#55411yescharacteristic
288C2×D43—22no—
289C2×D43—41no—
290C2×D43—41no—
291C4×C43—42no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43C2×C22⋊Q811yescharacteristic
297C4×C43#52511yescharacteristic
298C4×C43#54711yescharacteristic
299C4×C43D4×Q811yescharacteristic
300Dic43—22no—
301Dic43—42no—
302Dic43—41no—
303Dic43—41no—
304Dic43—81no—
305Dic43—81no—
306Dic43—81no—
307#3084—431no—
308#3082—431no—
309#2947—431no—
310#2912—431no—
311#2096—431no—
312#2090—431no—
313#2064—431no—
314#2060—431no—
315#1951—431no—
316#1922D4311yescharacteristic, complemented
317#1908—431no—
318#1882—431no—
319#1866—431no—
320#1859—431no—
321#1857—431no—
322C2×C43—21no—
323C2×C43—21no—
324C2×C43#244911yescharacteristic
325C2×C43#328911yescharacteristic
326C2×C43#329111yescharacteristic
327D43—42no—
328C2×#137—431no—
329C2×#131—431no—
330#544—431no—
331#520—431no—
332#520—431no—
333#519—431no—
334#479—861no—
335#479—861no—
336#479—861no—
337#478—861no—
338#477—861no—
339#476—861no—
340#475—861no—
341#475—861no—
342#441—861no—
343#440—861no—
344C4×Q16—861no—
345C4×SD16—861no—
346C2×#108—431no—
347#428—431no—
348#428—431no—
349#428—431no—
350#428—431no—
351#428—431no—
352#428—861no—
353#428—861no—
354#427—861no—
355#427C2×D4311yescharacteristic
356C2×#106—431no—
357C2×#106—431no—
358C2×#106—861no—
359#424—431no—
360#424C2×D4311yescharacteristic
361C2×#104—431no—
362#419—431no—
363#417—431no—
364#416—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#101—431no—
368#405C2×D4311yescharacteristic
369#391—431no—
370#384—431no—
371#343—431no—
372#343—431no—
373#343—431no—
374#341C2×D4311yescharacteristic
375#339—431no—
376#339C2×D4311yescharacteristic
377#339C2×D4311yescharacteristic
378#336C2×D4311yescharacteristic
379C43#2640111yescharacteristic, complemented, Sylow
380C2×#41—431no—
381C22×Q8—431no—
382#137—434no—
383#137—862no—
384C2×Q16—861no—
385C2×SD16—861no—
386#131—862no—
387#131—862no—
388C2×M16—431no—
389C2×M16—431no—
390C2×M16—861no—
391C2×M16C22×D4311yescharacteristic
392C2×M16C22×D4311yescharacteristic
393C22×C8—861no—
394C22×C8C22×D4311yescharacteristic
395C22×C8C22×D4311yescharacteristic
396C4⋊Q8—861no—
397C4⋊Q8—861no—
398#125—861no—
399#125—861no—
400C22⋊Q8—1721no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×Q8—861no—
405C4×Q8—861no—
406C4×Q8—861no—
407C4×D4—861no—
408C4×D4—861no—
409C4×D4—1721no—
410C4×D4—1721no—
411#117—431no—
412#117—861no—
413#117—861no—
414#117—1721no—
415#117C22×D4311yescharacteristic
416#117C22×D4311yescharacteristic
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—1721no—
423C2×C42C22×D4311yescharacteristic
424#108—862no—
425#107—861no—
426#107—861no—
427#107—861no—
428#107—861no—
429#107—861no—
430#107D17211yescharacteristic
431#107D17211yescharacteristic
432#106—861no—
433#106—861no—
434#106—861no—
435#106—861no—
436#106—861no—
437#106—861no—
438#106—861no—
439#106—861no—
440#106—861no—
441#106D17211yescharacteristic
442#106D17211yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447#104—862no—
448#103—431no—
449#103—431no—
450#103—861no—
451#103—861no—
452#103—861no—
453#103—861no—
454#103—861no—
455#103—861no—
456#103—861no—
457#102—431no—
458#102—431no—
459#102—861no—
460#101—862no—
461#97—21no—
462C4×C8—21no—
463#95—1721no—
464#41—432no—
465#41—432no—
466#41—861no—
467#41—861no—
468C2×Q8—431no—
469C2×Q8—432no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—1721no—
476C2×D4—431no—
477C2×D4—861no—
478C22×C4—21no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—1721no—
485C22×C4—1721no—
486C22×C4C23×D4311yescharacteristic
487Q16—864no—
488SD16—864no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—432no—
493M16—864no—
494M16—861no—
495M16—861no—
496M16—861no—
497M16Q8×D4312yes—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—864no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8C2×D17211yescharacteristic
508C2×C8C2×D17211yescharacteristic
509C2×C8D4×D4311yescharacteristic
510C2×C8D4×D4311yescharacteristic
511C4⋊C4—431no—
512C4⋊C4—431no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—3442no—
520C4⋊C4—1721no—
521C4⋊C4—1721no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4C2×D17211yescharacteristic
528C4⋊C4C2×D17211yescharacteristic
529C4⋊C4C2×D17211yescharacteristic
530C4⋊C4C2×D17211yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—861no—
534C22⋊C4—1721no—
535C22⋊C4—1721no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—861no—
541C42—1721no—
542C42—1721no—
543C42—1721no—
544C42—1721no—
545C23—861no—
546C23#1306337111yescharacteristic
547Q8—432no—
548Q8—861no—
549Q8—862no—
550Q8—862no—
551Q8—1721no—
552Q8—1721no—
553Q8—6881no—
554D4—432no—
555D4—862no—
556D4—862no—
557D4—861no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—861no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—3441no—
572C2×C4—3441no—
573C2×C4—3441no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—6881no—
580C2×C4—6881no—
581C2×C4C2×D4×D4311yescharacteristic
582C2×C4C22×D17211yescharacteristic
583C2×C4C2×Q8×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4#41×D4311yescharacteristic
586C2×C4#1306337211yescharacteristic
587C8—22no—
588C8—21no—
589C8—21no—
590C8—21no—
591C8—21no—
592C8—41no—
593C8—862no—
594C8—1721no—
595C22—21no—
596C22—21no—
597C22—862no—
598C22—1721no—
599C22—1721no—
600C22#1458349011yescharacteristic
601C22D4×D17211yescharacteristic
602C22#1458360511yescharacteristic
603C4—42no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—862no—
609C4—3441no—
610C4—3441no—
611C4—3441no—
612C4—1722no—
613C4—1721no—
614C4—1721no—
615C4C22⋊Q8×D4311yescharacteristic
616C4#1458341111yescharacteristic
617C4#1458354711yescharacteristic
618C4Q8×D17211yescharacteristic
619C2—21no—
620C2—21no—
621C2—1722no—
622C2#1913840911yescharacteristic
623C2#1914637111yescharacteristic
624C2#1914638911yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1922C2
socleC22×C43D42
prime radicalC2×#10621898C23
hypercenter#1922D43
hypocenterC43#26401
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1922

Complements

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

NH ≅ G/Ntype
2. #19144440C2semidirect
5. #19136137C2semidirect
6. #19136107C2semidirect
7. #19135961C2semidirect
8. #19135939C2semidirect
9. #19135375C2semidirect
14. #19134811C2semidirect
15. C43×#1922C2semidirect
70. #13063358Q8semidirect
316. #1922D43semidirect
379. C43#26401semidirect

Maximal subgroups

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

subgroupindex
#191444592
#191444402
#191434402
#191431872
#191361372
#191361072
#191359612
#191359392
#191353752
#191351092
#191349652
#191348732
#191348222
#191348112
C43×#19222
#2640143