Finite Group Databasebeta

← #25967707

Subgroups — #25967707

Order 11008.

2254 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148256C212yesmaximal, complemented
2#19145502C212yesmaximal, complemented
3#19145457C212yesmaximal, complemented
4#19145448C214yesmaximal, complemented
5#19145438C212yesmaximal, complemented
6#19145410C214yesmaximal, complemented
7#19145391C212yesmaximal, complemented
8#19144582C212yesmaximal, complemented
9#19144556C212yesmaximal, complemented
10#19144216C212yesmaximal, complemented
11C2×#14583152C211yesmaximal, characteristic, complemented
12#19143895C212yesmaximal, complemented
13#19143866C212yesmaximal, complemented
14#19143039C211yesmaximal, characteristic, complemented
15C43×#3054C211yesmaximal, characteristic, complemented
16C2×#13063371C2212yescomplemented
17C22×#10621898C2211yescharacteristic
18C2×#13063350C2212yescomplemented
19C22×D344C2211yescharacteristic, complemented
20C22×#10621877C2211yescharacteristic, complemented
21#14583570—22no—
22#14583558—22no—
23#14583545—22no—
24#14583541—24no—
25D4×D172—22no—
26#14583531—24no—
27#14583479C2214yescomplemented
28#14583477C2212yes—
29#14583468C2212yes—
30#14583465C2214yescomplemented
31#14583412C2214yescomplemented
32C2×#13063299C2212yescomplemented
33#121×D43C2214yescomplemented
34#14583379C2212yescomplemented
35#14583238C2214yescomplemented
36#14583228C2214yescomplemented
37#14583226C2214yescomplemented
38#14583225C2214yescomplemented
39#14583222C2214yescomplemented
40#14583219C2214yescomplemented
41#14583216C2214yescomplemented
42#14583214C2214yescomplemented
43#14583152C2212yescomplemented
44#14583152C2212yescomplemented
45#14583152C2212yescomplemented
46#14583152C2212yescomplemented
47#14583150C2214yescomplemented
48#14583147C2214yescomplemented
49#14583133C2214yescomplemented
50#14583130C2214yescomplemented
51#14583060C2214yescomplemented
52#14583048C2214yescomplemented
53#14583047C2214yescomplemented
54#14583047C2214yescomplemented
55#14583043C2214yescomplemented
56#14583034C2214yescomplemented
57#14583034C2214yescomplemented
58#14583031C2214yescomplemented
59#14582942C2212yescomplemented
60C2×#13063257C2211yescharacteristic, complemented
61#14582903C2212yescomplemented
62#14582900C2212yescomplemented
63C2×#13063247C2212yescomplemented
64#14582867C2212yescomplemented
65#14582867C2212yescomplemented
66#14582865C2212yescomplemented
67#14582865C2212yescomplemented
68#14582862C2212yescomplemented
69#14582862C2212yescomplemented
70C2×#135×C43C2211yescharacteristic, complemented
71C22×M16×C43C2211yescharacteristic, complemented
72C43×#525C2212yescomplemented
73C43×#470C2211yescharacteristic, complemented
74C43×#470C2211yescharacteristic, complemented
75C43×#469C2211yescharacteristic, complemented
76C43×#469C2211yescharacteristic, complemented
77C43×#468C2212yescomplemented
78C43×#468C2212yescomplemented
79C43×#427C2211yescharacteristic, complemented
80C43×#416C2212yescomplemented
81#13063371—44no—
82#13063371—44no—
83C2×#10621902C2314yes—
84C2×#10621898—22no—
85C2×#10621898—42no—
86C2×#10621898—42no—
87C2×#10621898D412yes—
88C2×#10621898D412yes—
89C2×#10621898C2312yes—
90C2×#10621898C2312yes—
91C22×Dic86D411yescharacteristic
92C22×D172—22no—
93C22×D172D411yescharacteristic
94C22×D172C2312yes—
95C22×C22⋊D43—22no—
96C22×C22⋊D43D412yes—
97C2×D4×D43—24no—
98C2×D4×D43—24no—
99C2×D4×D43C2314yes—
100C22×C4×D43C2312yes—
101#13063350—44no—
102C2×#10621884C2314yes—
103C2×D344—42no—
104C2×D344C2312yes—
105C2×D344C2312yes—
106C2×#10621882C2314yes—
107C2×#10621877—42no—
108C2×#10621877C2312yes—
109C2×#10621877C2312yes—
110C22×C43⋊C8C2312yes—
111#13063322—22no—
112#13063321—24no—
113#13063313—22no—
114#13063311—24no—
115#13063310—24no—
116#13063304—22no—
117#13063303—24no—
118#13063301C2314yes—
119#13063300—24no—
120#13063300C2314yes—
121#13063300C2314yes—
122#13063299—22no—
123#13063299—22no—
124#13063299—22no—
125#13063299C2314yes—
126#13063299C2314yes—
127#13063298—24no—
128#13063298—24no—
129#13063298—24no—
130#13063297—24no—
131#13063297—24no—
132#13063296C2314yes—
133#13063295—24no—
134#13063295—24no—
135#13063295—24no—
136#13063293—24no—
137C4×Dic86—22no—
138C4×D172—22no—
139#13063287—24no—
140(C22⋊D43)⋊C4—24no—
141(C22⋊D43)⋊C4—24no—
142#13063283C2314yes—
143C2×C4⋊Dic43C2312yes—
144C4⋊C4×D43C2314yes—
145C2×(C2×D43)⋊C4—22no—
146C22⋊C4×D43—24no—
147#13063258C2314yes—
148#13063257C2312yes—
149#13063257C2312yes—
150#13063256C2314yes—
151#13063249C2314yes—
152#13063247C2314yes—
153#13063247C2314yes—
154#13063246C2314yes—
155#13063245C2314yes—
156#13063245C2314yes—
157(C2×D43)⋊C8C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160(C2×D43)⋊C8C2314yes—
161C2×#41×C43C2312yes—
162C23×C4×C43C2311yescharacteristic
163#135×C43—42no—
164C2×Q16×C43C2311yescharacteristic
165C2×SD16×C43C2312yes—
166C2×D8×C43C2311yescharacteristic
167C2×M16×C43—42no—
168C2×M16×C43C2311yescharacteristic
169C2×M16×C43C2311yescharacteristic
170C2×M16×C43C2311yescharacteristic
171C2×M16×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174#123×C43—22no—
175C22⋊Q8×C43C2312yes—
176C22⋊Q8×C43C2312yes—
177#121×C43C2312yes—
178#121×C43C2312yes—
179#120×C43—22no—
180C4×D4×C43—22no—
181C4×D4×C43—22no—
182#117×C43C2312yes—
183#107×C43C2312yes—
184#106×C43C2311yescharacteristic
185#106×C43C2311yescharacteristic
186#103×C43C2312yes—
187#103×C43C2312yes—
188#102×C43C2312yes—
189#102×C43C2312yes—
190C24×C43C2×D411yescharacteristic
191C23×D43—22no—
192C23×D43—24no—
193C23×D43C2×D412yes—
194#41×C43—24no—
195#41×C43—24no—
196C2×Q8×C43C2412yes—
197C2×D4×C43—22no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43C2412yes—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—44no—
215C2×C22⋊D43—84no—
216C2×C22⋊D43C2×D414yes—
217C2×C22⋊D43C2×D414yes—
218C22×Dic43—22no—
219C22×Dic43C2×D412yes—
220#10621902—44no—
221#10621902—44no—
222D4×D43—44no—
223D4×D43—44no—
224D4×D43—416no—
225D4×D43—88no—
226#10621898—24no—
227#10621898—24no—
228#10621898—44no—
229#10621898—48no—
230#10621898—42no—
231#10621898—42no—
232#10621898—44no—
233C2×D172—22no—
234C2×D172—24no—
235C2×D172—24no—
236C2×D172—24no—
237C2×D172—24no—
238C2×D172—24no—
239C2×D172—42no—
240C2×D172—48no—
241C2×D172C2×D412yes—
242C2×D172C2×D412yes—
243C2×D172C2414yes—
244C2×C4×D43—24no—
245C2×C4×D43—24no—
246C2×C4×D43—42no—
247C2×C4×D43—42no—
248C2×C4×D43C2×D414yes—
249C2×C4×D43C2414yes—
250C2×Dic86—42no—
251C2×Dic86C2×D412yes—
252C2×Dic86C2×D412yes—
253Q16×C43—41no—
254SD16×C43—42no—
255D8×C43—41no—
256M16×C43—41no—
257M16×C43—41no—
258M16×C43—41no—
259M16×C43—41no—
260C2×C8×C43—22no—
261C2×C8×C43—22no—
262C2×C8×C43C2411yescharacteristic
263C2×C8×C43C2411yescharacteristic
264C2×C8×C43C2411yescharacteristic
265C2×C8×C43C2411yescharacteristic
266C4⋊C4×C43—22no—
267C4⋊C4×C43—22no—
268C4⋊C4×C43C2412yes—
269C4⋊C4×C43C2412yes—
270C22⋊C4×C43—22no—
271C22⋊C4×C43—22no—
272C22⋊C4×C43—22no—
273C22⋊C4×C43—22no—
274C22⋊C4×C43—22no—
275C42×C43—22no—
276C22⋊Dic43—24no—
277#10621884—44no—
278#10621882—44no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285C4⋊Dic43—22no—
286C4⋊Dic43C2414yes—
287Dic43⋊C4—24no—
288Dic43⋊C4—24no—
289C4×Dic43—24no—
290#10621877—24no—
291#10621877—42no—
292C2×C43⋊C8—42no—
293C2×C43⋊C8C2414yes—
294D344—42no—
295D344—42no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—42no—
299C23×C43C22×D411yescharacteristic
300C23×C43C22×D411yescharacteristic
301C23×C43C22×D411yescharacteristic
302C22×D43—24no—
303C22×D43—42no—
304C22×D43—44no—
305C22×D43—48no—
306C22×D43—44no—
307C22×D43—84no—
308C22×D43—84no—
309C22×D43—82no—
310C22×D43—82no—
311C22×D43C22×D414yes—
312Q8×C43—22no—
313Q8×C43—22no—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—44no—
317D4×C43—44no—
318D4×C43—82no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—44no—
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43H(5,𝔽2)12yes—
335C2×C4×C43C2511yescharacteristic
336C22⋊D43—28no—
337C22⋊D43—44no—
338C22⋊D43—48no—
339C22⋊D43—48no—
340C22⋊D43—84no—
341C22⋊D43—84no—
342C2×Dic43—24no—
343C2×Dic43—42no—
344C2×Dic43—82no—
345C2×Dic43C22×D414yes—
346D172—24no—
347D172—24no—
348D172—24no—
349D172—42no—
350D172—48no—
351D172—44no—
352D172—84no—
353D172—84no—
354C4×D43—24no—
355C4×D43—24no—
356C4×D43—44no—
357C4×D43—48no—
358C4×D43—84no—
359Dic86—24no—
360Dic86—42no—
361C8×C43—21no—
362C8×C43—21no—
363C8×C43—21no—
364C8×C43—21no—
365C43⋊C8—24no—
366#60771—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—82no—
376C22×C43#53412yes—
377C22×C43C23×D411yescharacteristic
378C2×D43—24no—
379C2×D43—24no—
380C2×D43—24no—
381C2×D43—44no—
382C2×D43—44no—
383C2×D43—44no—
384C2×D43—84no—
385C2×D43—168no—
386C2×D43—164no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43#53412yes—
393C4×C43C2×H(5,𝔽2)11yescharacteristic
394C4×C43C2×H(5,𝔽2)11yescharacteristic
395Dic43—24no—
396Dic43—44no—
397#3488—432no—
398#3204—432no—
399#3199—432no—
400#3198—434no—
401#3197—432no—
402#3194—434no—
403#3192—432no—
404#3099—432no—
405#3096—432no—
406#3055—432no—
407#3054D4311yescharacteristic, complemented
408C2×#469—431no—
409#3012—432no—
410#3008—432no—
411#2879—431no—
412C2×C43—22no—
413C2×C43—41no—
414C2×C43—41no—
415C2×C43—82no—
416C2×C43C2×#53411yescharacteristic
417C2×C43#358512yes—
418D43—44no—
419D43—84no—
420C2×H(5,𝔽2)—432no—
421C22×#41—431no—
422C2×AGL(1,ℤ/8)—432no—
423C2×#135C2×D4311yescharacteristic, complemented
424C22×D8—431no—
425C22×M16—431no—
426C22×M16C2×D4311yescharacteristic, complemented
427#550—862no—
428#548—862no—
429#546—862no—
430#546—864no—
431D42—862no—
432D42—864no—
433#537—432no—
434#537—434no—
435#535—434no—
436#535—432no—
437#525—434no—
438#525C2×D4312yescomplemented
439C2×#121—432no—
440C2×#121—434no—
441#520—432no—
442#485—434no—
443#483—434no—
444#482—434no—
445#482—434no—
446#482—434no—
447#481—434no—
448#481—434no—
449#480—434no—
450#470C2×D4311yescharacteristic, complemented
451#470C2×D4311yescharacteristic, complemented
452#469—432no—
453#469—432no—
454#469—432no—
455#469—432no—
456#469—434no—
457#469C2×D4311yescharacteristic, complemented
458#469C2×D4311yescharacteristic, complemented
459#468—434no—
460#468C2×D4312yescomplemented
461#468C2×D4312yescomplemented
462#466—434no—
463#465—434no—
464#452—434no—
465#450—434no—
466#449—434no—
467#449—434no—
468#449—434no—
469#447—434no—
470#447—434no—
471#447—434no—
472#428—432no—
473#427C2×D4311yescharacteristic, complemented
474C2×#106—431no—
475#418—432no—
476#417—432no—
477#416C2×D4312yescomplemented
478C2×#102—432no—
479#408—432no—
480#408—432no—
481#408—432no—
482#408—432no—
483#407—432no—
484#407—432no—
485C43#6077111yescharacteristic, complemented, Sylow
486H(5,𝔽2)—1724no—
487H(5,𝔽2)—1724no—
488C2×#41—432no—
489C2×#41—432no—
490C2×#41—432no—
491C2×#41—432no—
492C2×#41—434no—
493C2×#41—862no—
494C2×#41—1722no—
495C2×#41—1722no—
496C2×#41C22×D4312yes—
497C22×Q8—431no—
498C22×D4—432no—
499C22×D4—434no—
500C22×D4—431no—
501C22×D4—432no—
502C22×D4—862no—
503C22×D4—864no—
504C22×D4—864no—
505C22×D4—862no—
506C23×C4—432no—
507C23×C4C22×D4311yescharacteristic
508AGL(1,ℤ/8)—1724no—
509#135—42no—
510C2×Q16C22×D4311yescharacteristic
511C2×SD16—434no—
512C2×SD16C22×D4312yes—
513C2×D8—434no—
514C2×D8—432no—
515C2×D8—432no—
516C2×D8—1722no—
517C2×D8C22×D4311yescharacteristic
518C2×M16—42no—
519C2×M16—432no—
520C2×M16—432no—
521C2×M16—1722no—
522C2×M16C22×D4311yescharacteristic
523C2×M16C22×D4311yescharacteristic
524C2×M16C22×D4311yescharacteristic
525C2×M16C22×D4311yescharacteristic
526C22×C8—432no—
527C22×C8C22×D4311yescharacteristic
528C22×C8C22×D4311yescharacteristic
529#127—862no—
530#127—864no—
531#124—862no—
532#124—864no—
533#123—22no—
534#123—864no—
535C22⋊Q8—434no—
536C22⋊Q8—864no—
537C22⋊Q8—862no—
538C22⋊Q8C22×D4312yes—
539C22⋊Q8C22×D4312yes—
540#121—434no—
541#121—434no—
542#121—434no—
543#121—434no—
544#121—434no—
545#121—864no—
546#121—864no—
547#121—864no—
548#121—864no—
549#121—862no—
550#121—864no—
551#121—864no—
552#121—862no—
553#121—862no—
554#121C22×D4312yes—
555#121C22×D4312yes—
556#120—22no—
557#120—864no—
558#120—864no—
559#120—864no—
560#120—864no—
561C4×Q8—862no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—862no—
565C4×D4—864no—
566C4×D4—864no—
567C4×D4—864no—
568#117—434no—
569#117C22×D4312yes—
570C2×C4⋊C4—432no—
571C2×C4⋊C4—434no—
572C2×C22⋊C4—864no—
573C2×C22⋊C4—862no—
574#107—434no—
575#107C22×D4312yes—
576#106—432no—
577#106—432no—
578#106—434no—
579#106C22×D4311yescharacteristic
580#106C22×D4311yescharacteristic
581#103—434no—
582#103C22×D4312yes—
583#103C22×D4312yes—
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588#102—434no—
589#102C22×D4312yes—
590#102C22×D4312yes—
591C22⋊C8—434no—
592C22⋊C8—434no—
593C22⋊C8—434no—
594C22⋊C8—434no—
595C24—432no—
596C24—864no—
597C24—862no—
598C24D4×D4311yescharacteristic
599#41—24no—
600#41—24no—
601#41—864no—
602#41—864no—
603#41—1722no—
604#41—1722no—
605#41—1724no—
606#41—1724no—
607#41—1728no—
608#41—1724no—
609#41—1724no—
610C2×Q8—432no—
611C2×Q8—432no—
612C2×Q8—1722no—
613C2×Q8C23×D4312yes—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—434no—
618C2×D4—434no—
619C2×D4—432no—
620C2×D4—432no—
621C2×D4—434no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—864no—
628C2×D4—864no—
629C2×D4—862no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—3448no—
633C2×D4—3444no—
634C2×D4—1722no—
635C2×D4—1728no—
636C2×D4—1724no—
637C2×D4—1724no—
638C2×D4—17216no—
639C2×D4—1724no—
640C2×D4C23×D4312yes—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—432no—
645C22×C4—434no—
646C22×C4—434no—
647C22×C4—864no—
648C22×C4—864no—
649C22×C4—862no—
650C22×C4—1722no—
651C22×C4—1722no—
652C22×C4D4×D4311yescharacteristic
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656C22×C4C23×D4311yescharacteristic
657C22×C4C23×D4311yescharacteristic
658Q16—41no—
659SD16—42no—
660SD16—1724no—
661D8—41no—
662D8—1722no—
663D8—1722no—
664D8—1724no—
665M16—41no—
666M16—41no—
667M16—41no—
668M16—41no—
669M16—864no—
670M16—1722no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—434no—
674C2×C8—1722no—
675C2×C8C23×D4311yescharacteristic
676C2×C8C23×D4311yescharacteristic
677C2×C8C23×D4311yescharacteristic
678C2×C8C23×D4311yescharacteristic
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—434no—
682C4⋊C4—864no—
683C4⋊C4—864no—
684C4⋊C4—862no—
685C4⋊C4C23×D4312yes—
686C4⋊C4C23×D4312yes—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C22⋊C4—864no—
695C22⋊C4—864no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C42—22no—
700C42—864no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—434no—
705C23—864no—
706C23—3442no—
707C23—3442no—
708C23—3444no—
709C23—3444no—
710C23—1722no—
711C23—1724no—
712C23—1728no—
713C23—1724no—
714C23C2×D4×D4311yescharacteristic
715C23C2×D4×D4311yescharacteristic
716C23C2×D4×D4311yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—864no—
720Q8—1722no—
721D4—22no—
722D4—22no—
723D4—44no—
724D4—44no—
725D4—82no—
726D4—868no—
727D4—864no—
728D4—864no—
729D4—864no—
730D4—3444no—
731D4—3444no—
732D4—3444no—
733D4—3444no—
734D4—1722no—
735D4—1728no—
736D4—1724no—
737D4—1728no—
738D4—1728no—
739D4—1724no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—44no—
751C2×C4—434no—
752C2×C4—864no—
753C2×C4—864no—
754C2×C4—864no—
755C2×C4—3444no—
756C2×C4—3442no—
757C2×C4—1724no—
758C2×C4—1728no—
759C2×C4—1722no—
760C2×C4C2×D4×D4311yescharacteristic
761C2×C4C2×D4×D4311yescharacteristic
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4#1306337012yes—
764C2×C4#1306337112yes—
765C2×C4C24×D4311yescharacteristic
766C8—21no—
767C8—21no—
768C8—21no—
769C8—21no—
770C8—864no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—21no—
775C22—21no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—82no—
780C22—864no—
781C22—864no—
782C22—864no—
783C22—3444no—
784C22—1724no—
785C22—1724no—
786C22—1724no—
787C22—6884no—
788C22—6888no—
789C22#1458345712yes—
790C22C22×D4×D4311yescharacteristic
791C4—21no—
792C4—21no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—864no—
797C4—1724no—
798C4#1458345712yes—
799C4C2×#1306337011yescharacteristic
800C4C2×#1306337111yescharacteristic
801C2—22no—
802C2—41no—
803C2—41no—
804C2—82no—
805C2—3444no—
806C2—1724no—
807C2C2×#1458345711yescharacteristic
808C2#1914937212yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3054C2
socleC22×C43C23×D4
hypercenter#3054D43
hypocenterC43#60771
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3054

Complements

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

NH ≅ G/Ntype
1. #19148256C2semidirect
2. #19145502C2semidirect
3. #19145457C2semidirect
4. #19145448C2semidirect
5. #19145438C2semidirect
6. #19145410C2semidirect
7. #19145391C2semidirect
8. #19144582C2semidirect
9. #19144556C2semidirect
10. #19144216C2semidirect
11. C2×#14583152C2semidirect
12. #19143895C2semidirect
13. #19143866C2semidirect
14. #19143039C2semidirect
15. C43×#3054C2semidirect
16. C2×#13063371C22semidirect
18. C2×#13063350C22semidirect
19. C22×D344C22semidirect
20. C22×#10621877C22semidirect
27. #14583479C22semidirect
30. #14583465C22semidirect
31. #14583412C22semidirect
32. C2×#13063299C22semidirect
33. #121×D43C22semidirect
34. #14583379C22semidirect
35. #14583238C22semidirect
36. #14583228C22semidirect
37. #14583226C22semidirect
38. #14583225C22semidirect
39. #14583222C22semidirect
40. #14583219C22semidirect
41. #14583216C22semidirect
42. #14583214C22semidirect
43. #14583152C22semidirect
44. #14583152C22semidirect
45. #14583152C22semidirect
46. #14583152C22semidirect
47. #14583150C22semidirect
48. #14583147C22semidirect
49. #14583133C22semidirect
50. #14583130C22semidirect
51. #14583060C22semidirect
52. #14583048C22semidirect
53. #14583047C22semidirect
54. #14583047C22semidirect
55. #14583043C22semidirect
56. #14583034C22semidirect
57. #14583034C22semidirect
58. #14583031C22semidirect
59. #14582942C22semidirect
60. C2×#13063257C22semidirect
61. #14582903C22semidirect
62. #14582900C22semidirect
63. C2×#13063247C22semidirect
64. #14582867C22semidirect
65. #14582867C22semidirect
66. #14582865C22semidirect
67. #14582865C22semidirect
68. #14582862C22semidirect
69. #14582862C22semidirect
70. C2×#135×C43C22semidirect
71. C22×M16×C43C22semidirect
72. C43×#525C22semidirect
73. C43×#470C22semidirect
74. C43×#470C22semidirect
75. C43×#469C22semidirect
76. C43×#469C22semidirect
77. C43×#468C22semidirect
78. C43×#468C22semidirect
79. C43×#427C22semidirect
80. C43×#416C22semidirect
407. #3054D43semidirect
423. C2×#135C2×D43semidirect
426. C22×M16C2×D43semidirect
438. #525C2×D43semidirect
450. #470C2×D43semidirect
451. #470C2×D43semidirect
457. #469C2×D43semidirect
458. #469C2×D43semidirect
460. #468C2×D43semidirect
461. #468C2×D43semidirect
473. #427C2×D43semidirect
477. #416C2×D43semidirect
485. C43#60771semidirect

Maximal subgroups

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

subgroupindex
#191482562
#191455022
#191454572
#191454482
#191454382
#191454102
#191453912
#191445822
#191445562
#191442162
C2×#145831522
#191438952
#191438662
#191430392
C43×#30542
#6077143