Finite Group Databasebeta

← #25075156

Subgroups — #25075156

Order 11008.

988 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145551C211yesmaximal, characteristic, complemented
2#19144757C211yesmaximal, characteristic, complemented
3#19144383C211yesmaximal, characteristic, complemented
4#19133809C211yesmaximal, characteristic, complemented
5#19133802C211yesmaximal, characteristic, complemented
6#19133781C211yesmaximal, characteristic, complemented
7#19133774C211yesmaximal, characteristic, complemented
8#19133729C211yesmaximal, characteristic, complemented
9#19133729C211yesmaximal, characteristic, complemented
10#19133716C211yesmaximal, characteristic, complemented
11#19133711C211yesmaximal, characteristic, complemented
12#19133290C211yesmaximal, characteristic, complemented
13#19133029C211yesmaximal, characteristic, complemented
14#19132982C211yesmaximal, characteristic, complemented
15C43×#3481C211yesmaximal, characteristic
16#14583456C2211yescharacteristic, complemented
17#14583278C2211yescharacteristic, complemented
18#14583271C2211yescharacteristic
19#14583249C2211yescharacteristic, complemented
20#14583245C2211yescharacteristic
21#14583240—21no—
22#14583206—21no—
23#14583199—21no—
24#14583194C2211yescharacteristic, complemented
25#14583194C2211yescharacteristic, complemented
26#14583189C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583184C2211yescharacteristic, complemented
29#14583179C2211yescharacteristic
30#14583118—22no—
31#14583109C2211yescharacteristic, complemented
32#14583104C2211yescharacteristic
33#14583061—21no—
34#14583061—22no—
35#14583004—21no—
36#14582999—21no—
37#14582956C2211yescharacteristic, complemented
38#14582952C2211yescharacteristic, complemented
39#14582935—21no—
40C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
41#14582895—21no—
42#14582648C2211yescharacteristic, complemented
43#14582648C2211yescharacteristic, complemented
44#14582643C2211yescharacteristic
45#14582643C2211yescharacteristic
46Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
47Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
48Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
49Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
50D4⋊(C43⋊C8)C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54C43×#559C2211yescharacteristic
55C43×#554C2211yescharacteristic
56C43×#554C2211yescharacteristic
57C43×#553—21no—
58C43×#553—21no—
59C43×#551—22no—
60C43×#546—21no—
61C43×#546—21no—
62D42×C43C2211yescharacteristic
63C43×#532C2211yescharacteristic
64C43×#529—21no—
65C43×#529—21no—
66C43×#525—22no—
67C4×#41×C43C2211yescharacteristic
68C4×#41×C43C2211yescharacteristic
69C2×C4×D4×C43—21no—
70C2×C4×D4×C43—21no—
71C2×#10621885—21no—
72C2×#10621885—22no—
73C2×#10621883—21no—
74C2×#10621883—22no—
75C22×C43⋊C8—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83#13063284—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96#13063249—22no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063248—21no—
101#13063248—21no—
102#13063246—22no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106C22⋊(C43⋊C8)—21no—
107C22⋊(C43⋊C8)—21no—
108#13063236—21no—
109C4×C43⋊C8C2311yescharacteristic
110C4×C43⋊C8C2311yescharacteristic
111C2×#41×C43D411yescharacteristic
112C2×#41×C43D411yescharacteristic
113C2×#41×C43D412yes—
114C22×D4×C43—21no—
115C22×D4×C43—21no—
116C23×C4×C43—22no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#126×C43—22no—
120#126×C43—22no—
121#125×C43—21no—
122#125×C43—21no—
123#124×C43—21no—
124#124×C43—21no—
125#124×C43D412yes—
126#123×C43—22no—
127#123×C43—22no—
128#123×C43—22no—
129#123×C43—22no—
130C22⋊Q8×C43—22no—
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134#121×C43—22no—
135#121×C43—22no—
136#121×C43—21no—
137#121×C43—21no—
138#121×C43—21no—
139#121×C43—21no—
140#120×C43—22no—
141#120×C43—22no—
142C4×Q8×C43D411yescharacteristic
143C4×Q8×C43D411yescharacteristic
144C4×Q8×C43C2311yescharacteristic
145C4×Q8×C43C2311yescharacteristic
146C4×D4×C43—22no—
147C4×D4×C43—22no—
148C4×D4×C43—22no—
149C4×D4×C43—22no—
150C4×D4×C43—21no—
151C4×D4×C43—21no—
152C4×D4×C43—21no—
153C4×D4×C43—21no—
154C4×D4×C43—21no—
155C4×D4×C43—21no—
156C4×D4×C43—21no—
157C4×D4×C43—21no—
158C4×D4×C43—21no—
159C4×D4×C43—21no—
160C4×D4×C43D411yescharacteristic
161C4×D4×C43D411yescharacteristic
162C4×D4×C43C2311yescharacteristic
163C4×D4×C43C2311yescharacteristic
164#117×C43—22no—
165#117×C43—21no—
166#117×C43—21no—
167#117×C43D411yescharacteristic
168#117×C43D411yescharacteristic
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C22⋊C4×C43—22no—
172C2×C22⋊C4×C43—22no—
173C2×C42×C43—21no—
174C2×C42×C43—21no—
175C2×C42×C43C2311yescharacteristic
176C24×C43—22no—
177#41×C43—22no—
178#41×C43—22no—
179#41×C43—41no—
180#41×C43—41no—
181#41×C43—82no—
182C2×Q8×C43C2×D411yescharacteristic
183C2×Q8×C43C2×D411yescharacteristic
184C2×Q8×C43C2×D412yes—
185C2×D4×C43—22no—
186C2×D4×C43—22no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—22no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43—42no—
195C2×D4×C43—42no—
196C2×D4×C43C2×D411yescharacteristic
197C2×D4×C43C2×D411yescharacteristic
198C2×D4×C43C2×D412yes—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—22no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—84no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C2×Dic86—21no—
214C2×Dic86—21no—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43C2×D411yescharacteristic
226C4⋊C4×C43C2×D411yescharacteristic
227C4⋊C4×C43C2×D411yescharacteristic
228C4⋊C4×C43C2×D411yescharacteristic
229C22⋊C4×C43—22no—
230C22⋊C4×C43—22no—
231C22⋊C4×C43—22no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—22no—
238C22⋊C4×C43—22no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C22⋊C4×C43—21no—
242C22⋊C4×C43—21no—
243C42×C43—21no—
244C42×C43—21no—
245C42×C43—21no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—21no—
249C42×C43C2×D411yescharacteristic
250C42×C43C2×D411yescharacteristic
251C42×C43C2×D411yescharacteristic
252C42×C43C2411yescharacteristic
253C22⋊Dic43—41no—
254#10621885—42no—
255#10621885—82no—
256#10621883—42no—
257#10621883—82no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262Dic43⋊C4—41no—
263Dic43⋊C4—41no—
264C4×Dic43—41no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—42no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—22no—
275C23×C43—44no—
276C23×C43—44no—
277C23×C43—82no—
278C23×C43#12011yescharacteristic
279Q8×C43—21no—
280Q8×C43—21no—
281Q8×C43—21no—
282Q8×C43—21no—
283Q8×C43—42no—
284D4×C43—21no—
285D4×C43—21no—
286D4×C43—42no—
287D4×C43—42no—
288D4×C43—42no—
289D4×C43—44no—
290D4×C43—44no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43—82no—
296D4×C43#13512yes—
297D4×C43#13712yes—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—22no—
309C2×C4×C43—41no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—44no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—82no—
320C2×C4×C43—82no—
321C2×C4×C43—82no—
322C2×C4×C43#12011yescharacteristic
323C2×C4×C43#12011yescharacteristic
324C2×C4×C43#12011yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C2×Dic43—41no—
329C2×Dic43—41no—
330Dic86—42no—
331Dic86—41no—
332Dic86—41no—
333C43⋊C8—41no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338C43⋊C8—41no—
339#18755—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—21no—
342C22×C43—22no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—88no—
353C22×C43C2×#12011yescharacteristic
354C4×C43—21no—
355C4×C43—21no—
356C4×C43—21no—
357C4×C43—21no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43—41no—
363C4×C43—41no—
364C4×C43—42no—
365C4×C43C2×#13511yescharacteristic
366C4×C43C2×#13711yescharacteristic
367C4×C43#57511yescharacteristic
368C4×C43#57511yescharacteristic
369Dic43—81no—
370Dic43—81no—
371#3481D4311yescharacteristic
372#3210—431no—
373#3116—431no—
374#3076—431no—
375#1644—431no—
376#1643—431no—
377#1640—431no—
378#1639—431no—
379#1632—431no—
380#1632—431no—
381#1630—431no—
382#1629—431no—
383#1551—431no—
384#1488—431no—
385#1477—431no—
386C2×C43—41no—
387C2×C43—42no—
388C2×C43—42no—
389C2×C43—82no—
390C2×C43#300211yescharacteristic
391C2×C43#300711yescharacteristic
392C2×C43#301911yescharacteristic
393#559C2×D4311yescharacteristic
394#554C2×D4311yescharacteristic
395#554C2×D4311yescharacteristic
396#553—21no—
397#553—21no—
398#551—22no—
399#546—21no—
400#546—21no—
401D42C2×D4311yescharacteristic
402#533—431no—
403#532C2×D4311yescharacteristic
404#529—21no—
405#529—21no—
406#525—22no—
407C4×#41C2×D4311yescharacteristic
408C4×#41C2×D4311yescharacteristic
409C2×C4×D4—21no—
410C2×C4×D4—21no—
411#494—431no—
412#492—431no—
413#487—431no—
414#486—431no—
415#485—861no—
416#479—861no—
417#478—861no—
418#477—431no—
419#477—431no—
420#476—431no—
421#476—431no—
422#475—431no—
423#474—431no—
424#464—862no—
425#462—431no—
426#461—431no—
427#452—861no—
428#452—862no—
429#441—861no—
430#440—861no—
431#432—431no—
432#431—431no—
433#427—861no—
434C2×C4⋊C8—431no—
435#416—861no—
436#333—431no—
437#333—431no—
438#331—431no—
439#331—431no—
440Q8⋊C8—431no—
441Q8⋊C8—431no—
442Q8⋊C8—431no—
443Q8⋊C8—431no—
444D4⋊C8—431no—
445D4⋊C8—431no—
446D4⋊C8—431no—
447D4⋊C8—431no—
448C43#1875511yescharacteristic, complemented, Sylow
449C2×#41C22⋊D4311yescharacteristic
450C2×#41C22⋊D4311yescharacteristic
451C2×#41C22⋊D4312yes—
452C22×D4—21no—
453C22×D4—21no—
454C23×C4—22no—
455C2×Q16—862no—
456C2×Q16—861no—
457C2×SD16—862no—
458C2×SD16—861no—
459C22×C8—861no—
460C4⋊Q8—431no—
461C4⋊Q8—431no—
462C4⋊Q8C22×D4311yescharacteristic
463#127C22×D4311yescharacteristic
464#126—22no—
465#126—22no—
466#125—21no—
467#125—21no—
468#125—861no—
469#124—21no—
470#124—21no—
471#124C22⋊D4312yes—
472#123—22no—
473#123—22no—
474#123—22no—
475#123—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—861no—
481C22⋊Q8—861no—
482#121—22no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—21no—
488#120—22no—
489#120—22no—
490C4×Q8—861no—
491C4×Q8—861no—
492C4×Q8C22⋊D4311yescharacteristic
493C4×Q8C22⋊D4311yescharacteristic
494C4×Q8C22×D4311yescharacteristic
495C4×Q8C22×D4311yescharacteristic
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4C22⋊D4311yescharacteristic
511C4×D4C22⋊D4311yescharacteristic
512C4×D4C22×D4311yescharacteristic
513C4×D4C22×D4311yescharacteristic
514#117—22no—
515#117—21no—
516#117—21no—
517#117—861no—
518#117C22⋊D4311yescharacteristic
519#117C22⋊D4311yescharacteristic
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42C22×D4311yescharacteristic
527#107—861no—
528#107—861no—
529#107—861no—
530#106—861no—
531#106—861no—
532#106—861no—
533C4⋊C8—431no—
534C4⋊C8—431no—
535C4⋊C8—431no—
536C4⋊C8—431no—
537C4⋊C8—861no—
538C4⋊C8—861no—
539#103—861no—
540#103—861no—
541#103—861no—
542#103—862no—
543#103—861no—
544#103—861no—
545#102—861no—
546#102—861no—
547#102—861no—
548#102—862no—
549C22⋊C8—861no—
550C22⋊C8—861no—
551#97—861no—
552C4×C8—431no—
553C4×C8—431no—
554C24—22no—
555#41—22no—
556#41—22no—
557#41—41no—
558#41—41no—
559#41—82no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×Q8C2×C22⋊D4311yescharacteristic
563C2×Q8C2×C22⋊D4311yescharacteristic
564C2×Q8C2×C22⋊D4312yes—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4C2×C22⋊D4311yescharacteristic
577C2×D4C2×C22⋊D4311yescharacteristic
578C2×D4C2×C22⋊D4312yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—84no—
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C2×C22⋊D4311yescharacteristic
592C22×C4C2×C22⋊D4311yescharacteristic
593Q16—3442no—
594Q16—1722no—
595SD16—3442no—
596SD16—1722no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—1722no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—1721no—
619C4⋊C4—1721no—
620C4⋊C4C2×C22⋊D4311yescharacteristic
621C4⋊C4C2×C22⋊D4311yescharacteristic
622C4⋊C4C2×C22⋊D4311yescharacteristic
623C4⋊C4C2×C22⋊D4311yescharacteristic
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—1721no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—1721no—
646C42C2×C22⋊D4311yescharacteristic
647C42C2×C22⋊D4311yescharacteristic
648C42C2×C22⋊D4311yescharacteristic
649C42C23×D4311yescharacteristic
650C23—21no—
651C23—21no—
652C23—22no—
653C23—44no—
654C23—44no—
655C23—82no—
656C23#1306329411yescharacteristic
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—42no—
662Q8—1722no—
663Q8—1721no—
664Q8—1721no—
665D4—21no—
666D4—21no—
667D4—42no—
668D4—42no—
669D4—42no—
670D4—44no—
671D4—44no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—82no—
677D4#1306334512yes—
678D4#1306335512yes—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4#1306329411yescharacteristic
706C2×C4#1306329411yescharacteristic
707C2×C4#1306329411yescharacteristic
708C2×C4C22×C22⋊D4311yescharacteristic
709C2×C4C22×C22⋊D4311yescharacteristic
710C2×C4C22×C22⋊D4311yescharacteristic
711C8—1721no—
712C8—1721no—
713C8—1721no—
714C8—1721no—
715C8—1721no—
716C8—1721no—
717C22—21no—
718C22—21no—
719C22—22no—
720C22—21no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—88no—
730C22C2×#1306329411yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—3441no—
743C4—3441no—
744C4C2×#1306334511yescharacteristic
745C4C2×#1306335511yescharacteristic
746C4#1458369711yescharacteristic
747C4#1458369711yescharacteristic
748C2—41no—
749C2—42no—
750C2—42no—
751C2—82no—
752C2#1914381311yescharacteristic
753C2#1914385511yescharacteristic
754C2#1914395211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3481C2
socleC22×C43C2×#120
hypercenter#3481D43
hypocenterC43#18755
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #19145551C2semidirect
2. #19144757C2semidirect
3. #19144383C2semidirect
4. #19133809C2semidirect
5. #19133802C2semidirect
6. #19133781C2semidirect
7. #19133774C2semidirect
8. #19133729C2semidirect
9. #19133729C2semidirect
10. #19133716C2semidirect
11. #19133711C2semidirect
12. #19133290C2semidirect
13. #19133029C2semidirect
14. #19132982C2semidirect
16. #14583456C22semidirect
17. #14583278C22semidirect
19. #14583249C22semidirect
24. #14583194C22semidirect
25. #14583194C22semidirect
28. #14583184C22semidirect
31. #14583109C22semidirect
37. #14582956C22semidirect
38. #14582952C22semidirect
40. C2×C4⋊(C43⋊C8)C22semidirect
42. #14582648C22semidirect
43. #14582648C22semidirect
46. Q8⋊(C43⋊C8)C22semidirect
47. Q8⋊(C43⋊C8)C22semidirect
48. Q8⋊(C43⋊C8)C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
448. C43#18755semidirect

Maximal subgroups

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

subgroupindex
#191455512
#191447572
#191443832
#191338092
#191338022
#191337812
#191337742
#191337292
#191337162
#191337112
#191332902
#191330292
#191329822
C43×#34812
#1875543