Finite Group Databasebeta

← #25160049

Subgroups — #25160049

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#19144461C211yesmaximal, characteristic
2#19144433C211yesmaximal, characteristic, complemented
3#19143439C211yesmaximal, characteristic
4#19143190C211yesmaximal, characteristic
5#19136136C211yesmaximal, characteristic, complemented
6#19136107C211yesmaximal, characteristic, complemented
7#19135958C211yesmaximal, characteristic, complemented
8#19135941C211yesmaximal, characteristic, complemented
9#19135374C211yesmaximal, characteristic, complemented
10#19135193C211yesmaximal, characteristic, complemented
11#19134966C211yesmaximal, characteristic
12#19134870C211yesmaximal, characteristic
13#19134819C211yesmaximal, characteristic
14#19134812C211yesmaximal, characteristic, complemented
15C43×#1908C211yesmaximal, characteristic
16#14583530C2211yescharacteristic
17#14583382C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583377C2211yescharacteristic
20#14583208—21no—
21#14583208—21no—
22#14583204—21no—
23#14583197—21no—
24#14583192—21no—
25#14583187—21no—
26#14583182—21no—
27#14583182—21no—
28#14583006—21no—
29#14583000—21no—
30Q16×Dic43—21no—
31SD16×Dic43—21no—
32C2×#13063260C2211yescharacteristic
33#14582941—21no—
34#14582941—21no—
35#14582941C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582939C2211yescharacteristic
40#14582937—21no—
41#14582937C2211yescharacteristic
42C2×#13063257—21no—
43C2×#13063257C2211yescharacteristic
44C2×#13063256C2211yescharacteristic
45#14582927C2211yescharacteristic
46#14582925C2211yescharacteristic
47C2×#13063252C2211yescharacteristic
48#14582908C2211yescharacteristic
49#14582895C2211yescharacteristic
50C2×#13063249C2211yescharacteristic
51#14582857C2211yescharacteristic
52#14582806C2211yescharacteristic
53#14582768C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582660C2211yescharacteristic
57#14582660C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#137×C43C2211yescharacteristic
61C2×#131×C43C2211yescharacteristic
62C43×#417C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×#101×C43C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063324—21no—
70#13063324—21no—
71#13063316—21no—
72#13063316—21no—
73#13063304—41no—
74Q8×Dic43—21no—
75Q8×Dic43—21no—
76Q8×Dic43—21no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80D4×Dic43—21no—
81D4×Dic43—21no—
82D4×Dic43—41no—
83D4×Dic43—41no—
84#13063284—21no—
85#13063284—21no—
86#13063284—41no—
87#13063284C2311yescharacteristic
88#13063284C2311yescharacteristic
89#13063284C2311yescharacteristic
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—41no—
95C2×C4×Dic43C2311yescharacteristic
96#13063260—22no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259D411yescharacteristic
102#13063259D411yescharacteristic
103#13063258—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108#13063257—21no—
109#13063257—21no—
110#13063257D411yescharacteristic
111#13063257D411yescharacteristic
112#13063256—21no—
113#13063256—21no—
114#13063256—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118Dic43⋊C8—21no—
119#13063252—22no—
120#13063249—21no—
121#13063249—21no—
122#13063249—21no—
123#13063249—21no—
124#13063249D411yescharacteristic
125#13063249D411yescharacteristic
126#13063246D411yescharacteristic
127#13063246D411yescharacteristic
128#13063235—21no—
129C8×Dic43—21no—
130C43⋊#95—41no—
131C2×#41×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133#137×C43—22no—
134#137×C43Q814yescomplemented
135C2×Q16×C43—21no—
136C2×SD16×C43—21no—
137#131×C43—22no—
138#131×C43—22no—
139C2×M16×C43—21no—
140C2×M16×C43C2311yescharacteristic
141C2×M16×C43C2311yescharacteristic
142C2×M16×C43C2311yescharacteristic
143C22×C8×C43—21no—
144C22×C8×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146#103×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#102×C43—21no—
150#101×C43—22no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43C2×Q812yes—
154#41×C43#4112yes—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C2×D411yescharacteristic
161C2×Q8×C43C2×Q812yes—
162C2×D4×C43—21no—
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43C2411yescharacteristic
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—41no—
172C22×Dic43—41no—
173C2×Dic86—41no—
174Q16×C43—24no—
175SD16×C43—24no—
176M16×C43—24no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43C2×Q812yes—
182M16×C43#4112yes—
183C2×C8×C43—24no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C22⋊Dic43—21no—
194C22⋊Dic43—21no—
195C22⋊Dic43—21no—
196C22⋊Dic43—41no—
197C22⋊Dic43—41no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43—41no—
204C4⋊Dic43—41no—
205C4⋊Dic43—41no—
206C4⋊Dic43—41no—
207C4⋊Dic43C2×D411yescharacteristic
208C4⋊Dic43C2×D411yescharacteristic
209C4⋊Dic43C2×D411yescharacteristic
210C4⋊Dic43C2×D411yescharacteristic
211C4⋊Dic43C2×D411yescharacteristic
212C4⋊Dic43C2×D411yescharacteristic
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215Dic43⋊C4—82no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—41no—
222C4×Dic43—41no—
223C4×Dic43—41no—
224C4×Dic43—41no—
225#10621877—21no—
226#10621877—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8C2×D411yescharacteristic
231C2×C43⋊C8C2×D411yescharacteristic
232C23×C43—21no—
233C23×C43H(5,𝔽2)11yescharacteristic
234Q8×C43—21no—
235Q8×C43—22no—
236Q8×C43—22no—
237Q8×C43—41no—
238Q8×C43—41no—
239Q8×C43C22⋊Q812yes—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—21no—
243D4×C43C22⋊Q812yes—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—81no—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×Q811yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—81no—
270C2×Dic43—81no—
271C2×Dic43—161no—
272C2×Dic43—161no—
273Dic86—161no—
274C8×C43—22no—
275C8×C43—21no—
276C8×C43—22no—
277C8×C43—21no—
278C8×C43—41no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—41no—
282#26401—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43#53911yescharacteristic
289C22×C43D4211yescharacteristic
290C22×C43#55411yescharacteristic
291C4×C43—22no—
292C4×C43—42no—
293C4×C43—81no—
294C4×C43C2×C22⋊Q811yescharacteristic
295C4×C43#52511yescharacteristic
296C4×C43#54711yescharacteristic
297C4×C43D4×Q811yescharacteristic
298Dic43—42no—
299Dic43—41no—
300Dic43—41no—
301Dic43—41no—
302Dic43—41no—
303Dic43—41no—
304Dic43—41no—
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#1922—431no—
317#1908D4311yescharacteristic
318#1882—431no—
319#1866—431no—
320#1859—431no—
321#1857—431no—
322C2×C43—21no—
323C2×C43—21no—
324C2×C43—42no—
325C2×C43#244911yescharacteristic
326C2×C43#328911yescharacteristic
327C2×C43#329111yescharacteristic
328C2×#137C2×D4311yescharacteristic
329C2×#131C2×D4311yescharacteristic
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—431no—
355#427—861no—
356C2×#106—431no—
357C2×#106—431no—
358C2×#106—861no—
359#424—431no—
360#424—431no—
361C2×#104—431no—
362#419—431no—
363#417C2×D4311yescharacteristic
364#416—431no—
365C2×#103—431no—
366C2×#103C2×D4311yescharacteristic
367C2×#101C2×D4311yescharacteristic
368#405—431no—
369#391—431no—
370#384—431no—
371#343—431no—
372#343—431no—
373#343C2×D4311yescharacteristic
374#341C2×D4311yescharacteristic
375#339—431no—
376#339—431no—
377#339—431no—
378#336—431no—
379C43#2640111yescharacteristic, complemented, Sylow
380C2×#41C22×D4311yescharacteristic
381C22×Q8C22×D4311yescharacteristic
382#137—22no—
383#137Dic8614yescomplemented
384C2×Q16—21no—
385C2×SD16—21no—
386#131—22no—
387#131—22no—
388C2×M16—21no—
389C2×M16—431no—
390C2×M16C22×D4311yescharacteristic
391C2×M16C22×D4311yescharacteristic
392C2×M16C22×D4311yescharacteristic
393C22×C8—21no—
394C22×C8—431no—
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—431no—
413#117—431no—
414#117—861no—
415#117—861no—
416#117—1721no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—1721no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C42—431no—
424#108—862no—
425#107—431no—
426#107—431no—
427#107—861no—
428#107—861no—
429#107—861no—
430#107—861no—
431#107—861no—
432#106—431no—
433#106—431no—
434#106—861no—
435#106—861no—
436#106—861no—
437#106—861no—
438#106—861no—
439#106—861no—
440#106—861no—
441#106—861no—
442#106—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447#104—862no—
448#103—21no—
449#103—21no—
450#103—21no—
451#103—431no—
452#103—431no—
453#103—861no—
454#103—861no—
455#103—861no—
456#103—861no—
457#102—21no—
458#102—431no—
459#102—431no—
460#101—22no—
461#97—861no—
462C4×C8—861no—
463#95—1721no—
464#41—21no—
465#41—21no—
466#41C2×Dic8612yes—
467#41#1062190012yes—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—1721no—
474C2×Q8C2×Dic8612yes—
475C2×Q8D4×D4311yescharacteristic
476C2×D4—21no—
477C2×D4D4×D4311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—1721no—
485C22×C4—1721no—
486C22×C4C23×D4311yescharacteristic
487Q16—24no—
488SD16—24no—
489M16—24no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—861no—
495M16—861no—
496M16C2×Dic8612yes—
497M16#1062190012yes—
498C2×C8—24no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—431no—
505C2×C8—431no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8D4×D4311yescharacteristic
510C2×C8D4×D4311yescharacteristic
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—431no—
514C4⋊C4—431no—
515C4⋊C4—431no—
516C4⋊C4—431no—
517C4⋊C4—431no—
518C4⋊C4—431no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—3442no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4—1721no—
528C4⋊C4—1721no—
529C4⋊C4—1721no—
530C4⋊C4—1721no—
531C22⋊C4—861no—
532C22⋊C4—861no—
533C22⋊C4—861no—
534C22⋊C4—1721no—
535C22⋊C4—1721no—
536C42—861no—
537C42—861no—
538C42—861no—
539C42—861no—
540C42—861no—
541C42—1721no—
542C42—1721no—
543C42—1721no—
544C42—1721no—
545C23—21no—
546C23#1306337111yescharacteristic
547Q8—21no—
548Q8—22no—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8—6881no—
553Q8#1306330212yes—
554D4—22no—
555D4—22no—
556D4—21no—
557D4#1306330212yes—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—81no—
566C2×C4—862no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—3441no—
574C2×C4—3441no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—6881no—
580C2×C4—6881no—
581C2×C4C2×D4×D4311yescharacteristic
582C2×C4C2×D4×D4311yescharacteristic
583C2×C4C22×Dic8611yescharacteristic
584C2×C4C2×#1062190011yescharacteristic
585C2×C4C2×#1062190011yescharacteristic
586C2×C4#1306337211yescharacteristic
587C8—22no—
588C8—21no—
589C8—22no—
590C8—21no—
591C8—41no—
592C8—861no—
593C8—861no—
594C8—1721no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22#1458349311yescharacteristic
601C22#1458353311yescharacteristic
602C22#1458360611yescharacteristic
603C4—22no—
604C4—42no—
605C4—81no—
606C4—3441no—
607C4—3441no—
608C4—1722no—
609C4—1721no—
610C4—1721no—
611C4—1721no—
612C4—1721no—
613C4—1721no—
614C4—1721no—
615C4C2×#1306330211yescharacteristic
616C4#1458340511yescharacteristic
617C4#1458354911yescharacteristic
618C4D4×Dic8611yescharacteristic
619C2—21no—
620C2—21no—
621C2—42no—
622C2#1913841011yescharacteristic
623C2#1914636911yescharacteristic
624C2#1914638711yescharacteristic
subgroupG/H
centerC22#14583533
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1908C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#1908D43
hypocenterC43#26401
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1908

Complements

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

NH ≅ G/Ntype
2. #19144433C2semidirect
5. #19136136C2semidirect
6. #19136107C2semidirect
7. #19135958C2semidirect
8. #19135941C2semidirect
9. #19135374C2semidirect
10. #19135193C2semidirect
14. #19134812C2semidirect
134. #137×C43Q8semidirect
379. C43#26401semidirect
383. #137Dic86semidirect

Maximal subgroups

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

subgroupindex
#191444612
#191444332
#191434392
#191431902
#191361362
#191361072
#191359582
#191359412
#191353742
#191351932
#191349662
#191348702
#191348192
#191348122
C43×#19082
#2640143