Finite Group Databasebeta

← #25160040

Subgroups — #25160040

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#19144453C211yesmaximal, characteristic
2#19143438C211yesmaximal, characteristic
3#19143187C211yesmaximal, characteristic
4#19136136C211yesmaximal, characteristic, complemented
5#19136105C211yesmaximal, characteristic, complemented
6#19135962C211yesmaximal, characteristic, complemented
7#19135937C211yesmaximal, characteristic, complemented
8#19135372C211yesmaximal, characteristic, complemented
9#19135196C211yesmaximal, characteristic, complemented
10#19135113C211yesmaximal, characteristic
11#19134961C211yesmaximal, characteristic
12#19134869C211yesmaximal, characteristic
13#19134818C211yesmaximal, characteristic
14#19134810C211yesmaximal, characteristic, complemented
15C43×#3082C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18#14583379C2211yescharacteristic
19#14583379C2211yescharacteristic
20#14583203—21no—
21#14583196—21no—
22#14583186—21no—
23#14583181—21no—
24#14583004—21no—
25#14582997—21no—
26C4×#10621885—21no—
27C4×#10621884—21no—
28C2×#13063260C2211yescharacteristic
29#14582942C2211yescharacteristic
30#14582942C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582942C2211yescharacteristic
33#14582940—21no—
34#14582940—21no—
35#14582934—21no—
36C2×#13063257C2211yescharacteristic
37C2×#13063256C2211yescharacteristic
38#106×D43—21no—
39#14582926C2211yescharacteristic
40C2×#13063251C2211yescharacteristic
41#14582898C2211yescharacteristic
42#14582893C2211yescharacteristic
43C2×#13063249C2211yescharacteristic
44C2×#13063244C2211yescharacteristic
45#14582855C2211yescharacteristic
46#14582806C2211yescharacteristic
47#14582768C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582664C2211yescharacteristic
52#14582658C2211yescharacteristic
53#14582658C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582653C2211yescharacteristic
56C43×#544C2211yescharacteristic
57C43×#519C2211yescharacteristic
58C43×#479—21no—
59C43×#479—21no—
60C43×#477—21no—
61C43×#475—21no—
62C43×#428C2211yescharacteristic
63C43×#427C2211yescharacteristic
64C43×#424C2211yescharacteristic
65C43×#419C2211yescharacteristic
66C2×#103×C43C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063356—22no—
69#13063356Q814yescomplemented
70C2×#10621885—21no—
71C2×#10621884—21no—
72#13063331—22no—
73#13063331—22no—
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621872—21no—
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×D172—21no—
83C4×D172—21no—
84(C22⋊D43)⋊C4—41no—
85(C22⋊D43)⋊C4—41no—
86#13063283—21no—
87#13063283—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—41no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C2×C4×Dic43C2311yescharacteristic
94#13063260—22no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256—21no—
106#13063256—21no—
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109#13063251—22no—
110#13063249—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248D411yescharacteristic
114#13063248D411yescharacteristic
115#13063245—21no—
116#13063245D411yescharacteristic
117#13063245D411yescharacteristic
118#13063244—22no—
119#13063236—21no—
120C4×C43⋊C8—21no—
121C43⋊#95—41no—
122C22×Q8×C43C2311yescharacteristic
123C2×M16×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C4⋊Q8×C43—21no—
126C4⋊Q8×C43—21no—
127#125×C43—21no—
128#125×C43—21no—
129C22⋊Q8×C43—41no—
130C4×Q8×C43—21no—
131C4×Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134#117×C43—41no—
135#117×C43C2311yescharacteristic
136#117×C43C2311yescharacteristic
137#117×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139#107×C43—21no—
140#107×C43D411yescharacteristic
141#107×C43D411yescharacteristic
142#106×C43—21no—
143#106×C43D411yescharacteristic
144#106×C43D411yescharacteristic
145C4⋊C8×C43—21no—
146C4⋊C8×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#103×C43—21no—
150#103×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—41no—
157C2×Q8×C43C2×Q812yes—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898C2×Q812yes—
168#10621898#4112yes—
169C2×D172C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×C4×D43—41no—
172C2×C4×D43—41no—
173C2×Dic86C2×D411yescharacteristic
174M16×C43—21no—
175M16×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—41no—
201C42×C43—41no—
202#10621885—24no—
203#10621884—24no—
204(C2×D43)⋊C4—41no—
205(C2×D43)⋊C4—41no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210Dic43⋊C4—41no—
211Dic43⋊C4—41no—
212Dic43⋊C4—82no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—41no—
216C4×Dic43—41no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877C2×Q812yes—
222#10621877#4112yes—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230#10621872—24no—
231C8×D43—24no—
232C23×C43H(5,𝔽2)11yescharacteristic
233C22×D43—21no—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238Q8×C43—161no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—81no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×Q811yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C22⋊D43—22no—
257C22⋊D43—22no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—81no—
265C2×Dic43—81no—
266D172—21no—
267D172C22⋊Q812yes—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—161no—
271C4×D43—161no—
272Dic86—21no—
273Dic86C22⋊Q812yes—
274C8×C43—21no—
275C8×C43—21no—
276C8×C43—41no—
277C43⋊C8—22no—
278C43⋊C8—22no—
279C43⋊C8—21no—
280C43⋊C8—21no—
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×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43C2×C22⋊Q811yescharacteristic
300C4×C43#52511yescharacteristic
301C4×C43#54711yescharacteristic
302C4×C43D4×Q811yescharacteristic
303Dic43—22no—
304Dic43—42no—
305Dic43—81no—
306Dic43—81no—
307#3084—431no—
308#3082D4311yescharacteristic, complemented
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#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#544C2×D4311yescharacteristic
331#520—431no—
332#520—431no—
333#519C2×D4311yescharacteristic
334#479—21no—
335#479—21no—
336#479—861no—
337#478—861no—
338#477—21no—
339#476—861no—
340#475—21no—
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—861no—
352#428—861no—
353#428C2×D4311yescharacteristic
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#419C2×D4311yescharacteristic
363#417—431no—
364#416—431no—
365C2×#103—431no—
366C2×#103C2×D4311yescharacteristic
367C2×#101—431no—
368#405—431no—
369#391—431no—
370#384—431no—
371#343—431no—
372#343—431no—
373#343—431no—
374#341—431no—
375#339—431no—
376#339—431no—
377#339—431no—
378#336—431no—
379C43#2640111yescharacteristic, complemented, Sylow
380C2×#41—431no—
381C22×Q8C22×D4311yescharacteristic
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—431no—
391C2×M16—861no—
392C2×M16C22×D4311yescharacteristic
393C22×C8—431no—
394C22×C8—861no—
395C22×C8C22×D4311yescharacteristic
396C4⋊Q8—21no—
397C4⋊Q8—21no—
398#125—21no—
399#125—21no—
400C22⋊Q8—41no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—861no—
406C4×Q8—861no—
407C4×D4—861no—
408C4×D4—861no—
409C4×D4—1721no—
410C4×D4—1721no—
411#117—41no—
412#117—861no—
413#117—861no—
414#117C22×D4311yescharacteristic
415#117C22×D4311yescharacteristic
416#117C22×D4311yescharacteristic
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—21no—
426#107—861no—
427#107—861no—
428#107—861no—
429#107—861no—
430#107C22⋊D4311yescharacteristic
431#107C22⋊D4311yescharacteristic
432#106—21no—
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#106C22⋊D4311yescharacteristic
442#106C22⋊D4311yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447#104—862no—
448#103—21no—
449#103—21no—
450#103—21no—
451#103—21no—
452#103—431no—
453#103—431no—
454#103—861no—
455#103—861no—
456#103—861no—
457#102—431no—
458#102—431no—
459#102—861no—
460#101—862no—
461#97—861no—
462C4×C8—861no—
463#95—1721no—
464#41—432no—
465#41—432no—
466#41—861no—
467#41—861no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—41no—
474C2×Q8—431no—
475C2×Q8Q8×D4312yes—
476C2×D4—431no—
477C2×D4—861no—
478C22×C4—21no—
479C22×C4—21no—
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—432no—
492M16—432no—
493M16—864no—
494M16—861no—
495M16—861no—
496M16—861no—
497M16—861no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—864no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8C2×C22⋊D4311yescharacteristic
510C2×C8C2×C22⋊D4311yescharacteristic
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—3442no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4D4×D4311yescharacteristic
526C4⋊C4D4×D4311yescharacteristic
527C4⋊C4C2×C22⋊D4311yescharacteristic
528C4⋊C4C2×C22⋊D4311yescharacteristic
529C4⋊C4C2×C22⋊D4311yescharacteristic
530C4⋊C4C2×C22⋊D4311yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—1721no—
535C22⋊C4—1721no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—41no—
540C42—41no—
541C42—861no—
542C42—861no—
543C42—1721no—
544C42—1721no—
545C23—861no—
546C23#1306337011yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—41no—
550Q8—41no—
551Q8—161no—
552Q8—432no—
553Q8—861no—
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—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—81no—
569C2×C4—861no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
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×C4C22×C22⋊D4311yescharacteristic
583C2×C4C2×Q8×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4#41×D4311yescharacteristic
586C2×C4#1306337311yescharacteristic
587C8—21no—
588C8—21no—
589C8—41no—
590C8—862no—
591C8—862no—
592C8—861no—
593C8—861no—
594C8—1721no—
595C22—21no—
596C22—21no—
597C22—862no—
598C22—1721no—
599C22—1721no—
600C22#1458349511yescharacteristic
601C22D4×C22⋊D4311yescharacteristic
602C22#1458360311yescharacteristic
603C4—42no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—862no—
612C4—3441no—
613C4—3441no—
614C4—1722no—
615C4C22⋊Q8×D4311yescharacteristic
616C4#1458340611yescharacteristic
617C4#1458355111yescharacteristic
618C4Q8×C22⋊D4311yescharacteristic
619C2—21no—
620C2—21no—
621C2—1722no—
622C2#1913840111yescharacteristic
623C2#1914636611yescharacteristic
624C2#1914638611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3082C2
socleC22×C43D42
prime radicalC2×#10621898C23
hypercenter#3082D43
hypocenterC43#26401
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3082

Complements

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

NH ≅ G/Ntype
4. #19136136C2semidirect
5. #19136105C2semidirect
6. #19135962C2semidirect
7. #19135937C2semidirect
8. #19135372C2semidirect
9. #19135196C2semidirect
14. #19134810C2semidirect
15. C43×#3082C2semidirect
69. #13063356Q8semidirect
308. #3082D43semidirect
379. C43#26401semidirect

Maximal subgroups

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

subgroupindex
#191444532
#191434382
#191431872
#191361362
#191361052
#191359622
#191359372
#191353722
#191351962
#191351132
#191349612
#191348692
#191348182
#191348102
C43×#30822
#2640143