Finite Group Databasebeta

← #25965127

Subgroups — #25965127

Order 11008.

2138 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583505C211yesmaximal, characteristic, complemented
2#19147794C211yesmaximal, characteristic, complemented
3#19144888C214yesmaximal, complemented
4#19144840C214yesmaximal, complemented
5#19144801C214yesmaximal, complemented
6#19144799C214yesmaximal, complemented
7#19144537C212yesmaximal, complemented
8#19144413C211yesmaximal, characteristic, complemented
9#19144076C211yesmaximal, characteristic, complemented
10#19144075C211yesmaximal, characteristic, complemented
11#19143848C212yesmaximal, complemented
12#19143408C212yesmaximal, complemented
13#19143402C212yesmaximal, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3080C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063353C2212yes—
18C2×#13063350C2212yes—
19#14583505—21no—
20#14583505—21no—
21#14583505—21no—
22#14583505—21no—
23#14583505C2214yes—
24#14583505C2214yescomplemented
25C2×#13063322C2211yescharacteristic, complemented
26C2×#13063310—22no—
27C2×#13063300—22no—
28C2×#13063300C2212yes—
29#14583381C2212yescomplemented
30#14583378—22no—
31#14583378C2212yescomplemented
32#14583375C2212yescomplemented
33#14583371—22no—
34#14583371C2212yescomplemented
35#41×Dic43C2211yescharacteristic
36C4×#10621898—21no—
37C4×#10621898C2211yescharacteristic
38#14583367—21no—
39#14583367C2211yescharacteristic
40C2×#13063287C2212yescomplemented
41C2×#13063282—21no—
42C2×#13063282C2211yescharacteristic
43#117×D43—21no—
44#117×D43C2211yescharacteristic
45#14583226C2214yescomplemented
46#14583225C2214yescomplemented
47#14583219C2214yescomplemented
48#14583214C2214yescomplemented
49#14583203C2214yescomplemented
50#14583196C2214yescomplemented
51#14583100C2214yescomplemented
52#14583099C2214yescomplemented
53#14583095C2214yescomplemented
54#14583094C2214yescomplemented
55#14583047C2214yescomplemented
56#14583045C2214yescomplemented
57#14583039C2214yescomplemented
58#14583034C2214yescomplemented
59#14583010C2214yescomplemented
60#14583008C2214yescomplemented
61#14583002C2214yescomplemented
62#14582998C2214yescomplemented
63#14582986C2214yescomplemented
64#14582984C2214yescomplemented
65#14582981C2214yescomplemented
66#14582979C2214yescomplemented
67#14582959C2214yescomplemented
68#14582959C2214yescomplemented
69#14582939C2212yescomplemented
70#14582923C2211yescharacteristic, complemented
71#14582905C2212yescomplemented
72#14582903C2212yescomplemented
73#14582898C2212yes—
74#14582862C2212yes—
75M16×Dic43C2212yescomplemented
76C2×#125×C43C2211yescharacteristic, complemented
77C4×#41×C43C2211yescharacteristic
78C43×#479C2214yescomplemented
79C43×#478C2214yescomplemented
80C43×#428C2212yescomplemented
81C43×#423C2211yescharacteristic, complemented
82C43×#417C2212yes—
83C2×#10621902C2311yescharacteristic
84C2×#10621898—21no—
85C2×#10621898C2311yescharacteristic
86C2×#10621900—21no—
87C2×#10621900C2311yescharacteristic
88#41×D43—24no—
89#41×D43—24no—
90C2×Q8×D43C2311yescharacteristic
91C22×D172—22no—
92C22×D172—22no—
93C22×D172C2312yes—
94C2×D4×D43—21no—
95C2×D4×D43C2311yescharacteristic
96C22×C4×D43—21no—
97C22×C4×D43—22no—
98C22×C4×D43C2311yescharacteristic
99#13063353—28no—
100#13063350—28no—
101C2×#10621873C2314yes—
102C2×#10621884C2314yes—
103C2×D344C2314yes—
104C2×#10621882C2314yes—
105C2×#10621877C2312yes—
106#13063322—21no—
107#13063322—21no—
108#13063322C2314yes—
109#13063310—24no—
110#13063310—24no—
111#13063310—24no—
112#13063310—24no—
113#13063300—22no—
114#13063300—22no—
115#13063300—24no—
116#13063300—24no—
117#13063300—24no—
118#13063300—24no—
119#13063300C2314yes—
120#13063300C2314yes—
121Q8×Dic43C2312yes—
122C4×Dic86—22no—
123C4×Dic86C2312yes—
124#13063290—22no—
125#13063290C2312yes—
126C4×D172—22no—
127C4×D172C2312yes—
128D4×Dic43—22no—
129D4×Dic43C2312yes—
130#13063287—22no—
131#13063287—22no—
132#13063287—22no—
133#13063287C2314yes—
134#13063287C2314yes—
135#13063287C2312yes—
136C4×C22⋊D43—22no—
137C4×C22⋊D43—22no—
138C4×C22⋊D43—22no—
139(C22⋊D43)⋊C4—22no—
140(C22⋊D43)⋊C4—22no—
141(C22⋊D43)⋊C4—22no—
142#13063284—21no—
143#13063284C2311yescharacteristic
144#13063283—22no—
145#13063283C2312yes—
146#13063282—21no—
147#13063282—21no—
148#13063282—22no—
149#13063282—22no—
150#13063282—21no—
151#13063282D411yescharacteristic
152#13063282D411yescharacteristic
153#13063282D411yescharacteristic
154#13063282D411yescharacteristic
155#13063282C2312yes—
156#13063282C2312yes—
157#13063281—21no—
158#13063281—22no—
159C2×Dic43⋊C4—22no—
160C2×Dic43⋊C4D412yes—
161C4⋊C4×D43—22no—
162C4⋊C4×D43C2312yes—
163C2×(C2×D43)⋊C4—22no—
164C2×(C2×D43)⋊C4—22no—
165C2×(C2×D43)⋊C4—22no—
166C2×(C2×D43)⋊C4D412yes—
167C22⋊C4×D43—21no—
168C22⋊C4×D43—22no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43C2311yescharacteristic
171C42×D43—21no—
172C42×D43—21no—
173C42×D43—21no—
174#13063258C2314yes—
175#13063256C2314yes—
176C4⋊(C43⋊C8)C2314yes—
177#13063248C2314yes—
178#13063247C2314yes—
179#13063247C2314yes—
180#13063245C2314yes—
181#13063245C2314yes—
182#13063245C2314yes—
183(C2×D43)⋊C8C2314yes—
184(C2×D43)⋊C8C2314yes—
185#13063235C2314yes—
186C8×Dic43C2314yes—
187C2×#41×C43C2311yescharacteristic
188C2×M16×C43C2312yes—
189#125×C43—21no—
190#125×C43—21no—
191#125×C43C2314yes—
192C4×Q8×C43C2312yes—
193C4×D4×C43—22no—
194C4×D4×C43C2312yes—
195#117×C43—21no—
196#117×C43C2311yescharacteristic
197C2×C4⋊C4×C43—22no—
198C2×C4⋊C4×C43C2312yes—
199C2×C42×C43—21no—
200C2×C42×C43C2311yescharacteristic
201#107×C43C2314yes—
202#106×C43C2314yes—
203C4⋊C8×C43C2314yes—
204#103×C43C2314yes—
205#102×C43C2314yes—
206C23×D43—21no—
207C23×D43—22no—
208C23×D43C2×D411yescharacteristic
209#41×C43—22no—
210#41×C43#4114yes—
211C2×Q8×C43C2411yescharacteristic
212C2×D4×C43—21no—
213C2×D4×C43C2411yescharacteristic
214C22×C4×C43—21no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43C2×D412yes—
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C22×Dic43—21no—
223C22×Dic43—22no—
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D412yes—
226#10621902—22no—
227#10621902—22no—
228Q8×D43—22no—
229Q8×D43—22no—
230#10621900—28no—
231#10621900—22no—
232#10621900—22no—
233D4×D43—28no—
234D4×D43—22no—
235D4×D43—22no—
236#10621898—28no—
237#10621898—22no—
238#10621898#4114yes—
239C2×D172—22no—
240C2×D172—24no—
241C2×D172—24no—
242C2×D172—21no—
243C2×D172—24no—
244C2×D172—24no—
245C2×D172—24no—
246C2×D172—24no—
247C2×D172—84no—
248C2×D172—84no—
249C2×D172C2414yes—
250C2×D172C2411yescharacteristic
251C2×C4×D43—28no—
252C2×C4×D43—21no—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—21no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—24no—
259C2×C4×D43—24no—
260C2×C4×D43—21no—
261C2×C4×D43—22no—
262C2×C4×D43—84no—
263C2×C4×D43C2×D411yescharacteristic
264C2×C4×D43C2×D411yescharacteristic
265C2×C4×D43C2411yescharacteristic
266C2×C4×D43C2411yescharacteristic
267C2×Dic86—21no—
268C2×Dic86C2411yescharacteristic
269M16×C43—24no—
270C2×C8×C43C2414yes—
271C4⋊C4×C43—24no—
272C4⋊C4×C43—24no—
273C4⋊C4×C43—22no—
274C4⋊C4×C43—22no—
275C4⋊C4×C43C2414yes—
276C4⋊C4×C43C2412yes—
277C22⋊C4×C43—22no—
278C22⋊C4×C43—21no—
279C42×C43—21no—
280C42×C43—22no—
281C42×C43C2×D411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C42×C43C2412yes—
284C22⋊Dic43—22no—
285C22⋊Dic43—21no—
286#10621884—28no—
287#10621882—28no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293(C2×D43)⋊C4—24no—
294(C2×D43)⋊C4—22no—
295(C2×D43)⋊C4C2×D412yes—
296(C2×D43)⋊C4C2×D412yes—
297(C2×D43)⋊C4C2×D412yes—
298(C2×D43)⋊C4C2×D412yes—
299C4⋊Dic43—22no—
300C4⋊Dic43C2412yes—
301Dic43⋊C4—22no—
302Dic43⋊C4—22no—
303Dic43⋊C4—22no—
304Dic43⋊C4C2×D412yes—
305Dic43⋊C4C2×D412yes—
306Dic43⋊C4C2×D412yes—
307Dic43⋊C4C2×D412yes—
308C4×Dic43—21no—
309C4×Dic43—22no—
310C4×Dic43—22no—
311C4×Dic43—22no—
312C4×Dic43—22no—
313C4×Dic43C2×D411yescharacteristic
314C4×Dic43C2×D411yescharacteristic
315C4×Dic43C2412yes—
316#10621877—24no—
317C2×C43⋊C8C2414yes—
318D344—28no—
319#10621873—28no—
320C23×C43—21no—
321C23×C43C22×D411yescharacteristic
322C22×D43—21no—
323C22×D43—24no—
324C22×D43—22no—
325C22×D43—24no—
326C22×D43—42no—
327C22×D43—44no—
328C22×D43—44no—
329C22×D43—44no—
330C22×D43—82no—
331C22×D43C22×D411yescharacteristic
332C22×D43C22×D411yescharacteristic
333Q8×C43—21no—
334Q8×C43C2×#4112yes—
335D4×C43—24no—
336D4×C43—21no—
337D4×C43C2×#4112yes—
338C2×C4×C43—21no—
339C2×C4×C43—24no—
340C2×C4×C43—22no—
341C2×C4×C43—24no—
342C2×C4×C43—42no—
343C2×C4×C43—44no—
344C2×C4×C43—82no—
345C2×C4×C43C22×D412yes—
346C2×C4×C43C22×D412yes—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4112yes—
349C2×C4×C43C2×#4112yes—
350C2×C4×C43C2511yescharacteristic
351C22⋊D43—24no—
352C22⋊D43—24no—
353C22⋊D43—24no—
354C2×Dic43—24no—
355C2×Dic43—22no—
356C2×Dic43—21no—
357C2×Dic43—22no—
358C2×Dic43—42no—
359C2×Dic43—82no—
360C2×Dic43C22×D411yescharacteristic
361C2×Dic43C22×D412yes—
362C2×Dic43C22×D412yes—
363C2×Dic43C22×D411yescharacteristic
364D172—24no—
365D172—21no—
366D172—24no—
367D172—24no—
368D172—44no—
369D172—84no—
370D172—84no—
371D172—84no—
372D172—84no—
373D172C2×#4112yes—
374C4×D43—24no—
375C4×D43—24no—
376C4×D43—22no—
377C4×D43—24no—
378C4×D43—22no—
379C4×D43—21no—
380C4×D43—21no—
381C4×D43—21no—
382C4×D43—21no—
383C4×D43—82no—
384C4×D43—84no—
385C4×D43—84no—
386C4×D43—82no—
387C4×D43—82no—
388Dic86—24no—
389Dic86—21no—
390Dic86C2×#4112yes—
391C8×C43—24no—
392C43⋊C8—24no—
393#60568—431nomaximal, Sylow
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—42no—
397C22×C43#52512yes—
398C22×C43C23×D411yescharacteristic
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—21no—
402C2×D43—22no—
403C2×D43—21no—
404C2×D43—42no—
405C2×D43—44no—
406C2×D43—44no—
407C2×D43—44no—
408C2×D43—82no—
409C2×D43—84no—
410C2×D43—88no—
411C4×C43—22no—
412C4×C43—22no—
413C4×C43—22no—
414C4×C43—44no—
415C4×C43—42no—
416C4×C43#52512yes—
417C4×C43C22×#4111yescharacteristic
418C4×C43C22×#4111yescharacteristic
419Dic43—22no—
420Dic43—22no—
421Dic43—21no—
422Dic43—22no—
423Dic43—21no—
424Dic43—42no—
425C2×#540—431no—
426#3428—431no—
427#3126—434no—
428#3122—434no—
429#3119—434no—
430#3119—434no—
431#3094—432no—
432#3080—431no—
433#3080D4311yescharacteristic, complemented
434#3038—431no—
435#3038—431no—
436#3006—432no—
437C4×AGL(1,ℤ/8)—432no—
438C4×AGL(1,ℤ/8)—432no—
439#2921—431no—
440C2×C43—22no—
441C2×C43—42no—
442C2×C43C2×#52511yescharacteristic
443C2×C43#358512yes—
444D43—41no—
445D43—41no—
446D43—42no—
447D43—84no—
448C22×#41—431no—
449C2×AGL(1,ℤ/8)—432no—
450C2×AGL(1,ℤ/8)—432no—
451#540—434no—
452#540—434no—
453#540—861no—
454#540—861no—
455#540—861no—
456#540—861no—
457C2×#127—431no—
458C2×#125C2×D4311yescharacteristic, complemented
459C2×#123—862no—
460C2×#121—432no—
461C2×#121—862no—
462#520—432no—
463#520—432no—
464#520—862no—
465#519—432no—
466#518—432no—
467#518—862no—
468C4×#41—431no—
469C4×#41—431no—
470C4×#41—431no—
471C4×#41—861no—
472C4×#41—861no—
473C4×#41C2×D4311yescharacteristic
474C2×C4×D4—432no—
475C2×#117—431no—
476C2×#117—431no—
477C2×#117—861no—
478C2×#117—861no—
479#482—434no—
480#482—434no—
481#481—434no—
482#480—434no—
483#479—434no—
484#479C2×D4314yescomplemented
485#478—434no—
486#478C2×D4314yescomplemented
487#460—434no—
488#460—434no—
489#459—434no—
490#459—434no—
491#449—434no—
492#449—434no—
493#448—434no—
494#447—434no—
495#442—434no—
496#442—434no—
497#440—434no—
498#440—434no—
499C4×SD16—434no—
500C4×SD16—434no—
501C4×D8—434no—
502C4×D8—434no—
503#433—434no—
504#433—434no—
505#428—432no—
506#428C2×D4312yescomplemented
507#423—431no—
508#423C2×D4311yescharacteristic, complemented
509#418—432no—
510#418—432no—
511#417—432no—
512#417C2×D4312yes—
513#407—432no—
514C4×M16—432no—
515C43#6056811yescharacteristic, complemented, Sylow
516C2×#41—431no—
517C2×#41—431no—
518C2×#41—431no—
519C2×#41—861no—
520C2×#41—861no—
521C2×#41—864no—
522C2×#41—864no—
523C2×#41C22×D4311yescharacteristic
524C22×Q8—431no—
525C22×D4—431no—
526C22×D4—432no—
527C22×D4—862no—
528C22×D4—861no—
529C22×D4—862no—
530C23×C4—431no—
531C23×C4—861no—
532C23×C4—862no—
533AGL(1,ℤ/8)—868no—
534AGL(1,ℤ/8)—868no—
535C2×SD16—434no—
536C2×SD16—434no—
537C2×D8—434no—
538C2×D8—434no—
539C2×M16—432no—
540C2×M16C22×D4312yes—
541#127—434no—
542#127—861no—
543#127—861no—
544#125—21no—
545#125—21no—
546#125C22×D4314yes—
547#123—864no—
548#123—864no—
549#123—864no—
550#123—864no—
551#121—434no—
552#121—434no—
553#121—864no—
554#121—864no—
555#121—864no—
556#121—864no—
557#121—862no—
558#121—862no—
559C4×Q8—432no—
560C4×Q8—432no—
561C4×Q8—432no—
562C4×Q8—862no—
563C4×Q8—862no—
564C4×Q8C22×D4312yes—
565C4×D4—22no—
566C4×D4—432no—
567C4×D4—434no—
568C4×D4—434no—
569C4×D4—432no—
570C4×D4—432no—
571C4×D4—862no—
572C4×D4—862no—
573C4×D4—862no—
574C4×D4—862no—
575C4×D4—862no—
576C4×D4—862no—
577C4×D4—862no—
578C4×D4—862no—
579C4×D4—862no—
580C4×D4—862no—
581C4×D4—862no—
582C4×D4C22×D4312yes—
583#117—21no—
584#117—431no—
585#117—431no—
586#117—431no—
587#117—431no—
588#117—432no—
589#117—432no—
590#117—431no—
591#117—432no—
592#117—861no—
593#117—862no—
594#117—862no—
595#117—861no—
596#117—861no—
597#117—862no—
598#117—861no—
599#117—862no—
600#117—861no—
601#117C22×D4311yescharacteristic
602C2×C4⋊C4—22no—
603C2×C4⋊C4—432no—
604C2×C4⋊C4—432no—
605C2×C4⋊C4—862no—
606C2×C4⋊C4—862no—
607C2×C4⋊C4C22×D4312yes—
608C2×C22⋊C4—432no—
609C2×C22⋊C4—862no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—862no—
612C2×C22⋊C4—862no—
613C2×C22⋊C4—862no—
614C2×C42—21no—
615C2×C42—431no—
616C2×C42—861no—
617C2×C42—861no—
618C2×C42—861no—
619C2×C42—861no—
620C2×C42C22×D4311yescharacteristic
621#107—434no—
622#107C22×D4314yes—
623#106—434no—
624#106C22×D4314yes—
625C4⋊C8—434no—
626C4⋊C8C22×D4314yes—
627#103—434no—
628#103C22×D4314yes—
629#102—434no—
630#102—434no—
631#102—434no—
632#102—434no—
633#102—434no—
634#102C22×D4314yes—
635C22⋊C8—434no—
636C22⋊C8—434no—
637#97—434no—
638C4×C8—434no—
639C24—431no—
640C24—861no—
641C24—862no—
642#41—22no—
643#41—434no—
644#41—868no—
645#41—862no—
646#41—868no—
647#41—862no—
648#41—862no—
649#41—862no—
650#41—862no—
651#41#1062190214yes—
652C2×Q8—431no—
653C2×Q8—861no—
654C2×Q8—862no—
655C2×Q8—862no—
656C2×Q8C23×D4311yescharacteristic
657C2×D4—21no—
658C2×D4—431no—
659C2×D4—434no—
660C2×D4—861no—
661C2×D4—864no—
662C2×D4—864no—
663C2×D4—861no—
664C2×D4—862no—
665C2×D4—868no—
666C2×D4—861no—
667C2×D4—861no—
668C2×D4—862no—
669C2×D4—864no—
670C2×D4—864no—
671C2×D4—862no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—3444no—
675C2×D4—3444no—
676C2×D4C23×D4311yescharacteristic
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—431no—
681C22×C4—432no—
682C22×C4—431no—
683C22×C4—431no—
684C22×C4—431no—
685C22×C4—431no—
686C22×C4—861no—
687C22×C4—862no—
688C22×C4—864no—
689C22×C4—864no—
690C22×C4—861no—
691C22×C4—868no—
692C22×C4—862no—
693C22×C4—861no—
694C22×C4—862no—
695C22×C4—861no—
696C22×C4—862no—
697C22×C4—862no—
698C22×C4—862no—
699C22×C4—3444no—
700C22×C4D4×D4312yes—
701C22×C4C23×D4311yescharacteristic
702SD16—868no—
703SD16—868no—
704D8—868no—
705D8—868no—
706M16—24no—
707M16—864no—
708C2×C8—434no—
709C2×C8C23×D4314yes—
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—432no—
715C4⋊C4—432no—
716C4⋊C4—432no—
717C4⋊C4—432no—
718C4⋊C4—432no—
719C4⋊C4—862no—
720C4⋊C4—862no—
721C4⋊C4—862no—
722C4⋊C4—862no—
723C4⋊C4C23×D4312yes—
724C4⋊C4C23×D4314yes—
725C22⋊C4—21no—
726C22⋊C4—22no—
727C22⋊C4—432no—
728C22⋊C4—432no—
729C22⋊C4—432no—
730C22⋊C4—432no—
731C22⋊C4—862no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—862no—
737C22⋊C4—862no—
738C22⋊C4—861no—
739C22⋊C4—862no—
740C42—21no—
741C42—22no—
742C42—431no—
743C42—431no—
744C42—432no—
745C42—862no—
746C42—862no—
747C42—862no—
748C42—861no—
749C42—862no—
750C42D4×D4311yescharacteristic
751C42D4×D4311yescharacteristic
752C42C23×D4312yes—
753C23—21no—
754C23—431no—
755C23—431no—
756C23—864no—
757C23—862no—
758C23—861no—
759C23—864no—
760C23—3442no—
761C23—1722no—
762C23—1724no—
763C23—1724no—
764C23—1724no—
765C23C2×D4×D4311yescharacteristic
766Q8—21no—
767Q8—432no—
768Q8—864no—
769Q8—861no—
770Q8C2×#1062190212yes—
771D4—24no—
772D4—21no—
773D4—432no—
774D4—864no—
775D4—864no—
776D4—864no—
777D4—864no—
778D4—864no—
779D4—861no—
780D4—864no—
781D4—3444no—
782D4—3444no—
783D4—3444no—
784D4—3444no—
785D4—1724no—
786D4C2×#1062190212yes—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—82no—
794C2×C4—432no—
795C2×C4—432no—
796C2×C4—431no—
797C2×C4—431no—
798C2×C4—864no—
799C2×C4—864no—
800C2×C4—864no—
801C2×C4—862no—
802C2×C4—861no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—864no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—861no—
809C2×C4—861no—
810C2×C4—862no—
811C2×C4—3442no—
812C2×C4—3444no—
813C2×C4—3444no—
814C2×C4—3442no—
815C2×C4—3442no—
816C2×C4—3442no—
817C2×C4—1722no—
818C2×C4C2×D4×D4312yes—
819C2×C4C2×D4×D4312yes—
820C2×C4C2×D4×D4311yescharacteristic
821C2×C4#41×D4312yes—
822C2×C4C2×#1062190212yes—
823C2×C4C24×D4311yescharacteristic
824C8—24no—
825C8—864no—
826C22—22no—
827C22—22no—
828C22—42no—
829C22—862no—
830C22—862no—
831C22—861no—
832C22—862no—
833C22—861no—
834C22—3448no—
835C22—3442no—
836C22—3444no—
837C22—1724no—
838C22—1724no—
839C22—1724no—
840C22—1722no—
841C22#1458341212yes—
842C22C22×D4×D4311yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—44no—
847C4—42no—
848C4—862no—
849C4—862no—
850C4—861no—
851C4—861no—
852C4—862no—
853C4—1722no—
854C4#1458341212yes—
855C4C2×#41×D4311yescharacteristic
856C4C22×#1062190211yescharacteristic
857C2—22no—
858C2—42no—
859C2—3444no—
860C2—1721no—
861C2—1721no—
862C2—1722no—
863C2C2×#1458341211yescharacteristic
864C2#1914937212yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3080C2
socleC22×C43C23×D4
hypercenter#3080D43
hypocenterC43#60568
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. C2×#14583505C2semidirect
2. #19147794C2semidirect
3. #19144888C2semidirect
4. #19144840C2semidirect
5. #19144801C2semidirect
6. #19144799C2semidirect
7. #19144537C2semidirect
8. #19144413C2semidirect
9. #19144076C2semidirect
10. #19144075C2semidirect
11. #19143848C2semidirect
12. #19143408C2semidirect
13. #19143402C2semidirect
14. #19143232C2semidirect
15. C43×#3080C2semidirect
24. #14583505C22semidirect
25. C2×#13063322C22semidirect
29. #14583381C22semidirect
31. #14583378C22semidirect
32. #14583375C22semidirect
34. #14583371C22semidirect
40. C2×#13063287C22semidirect
45. #14583226C22semidirect
46. #14583225C22semidirect
47. #14583219C22semidirect
48. #14583214C22semidirect
49. #14583203C22semidirect
50. #14583196C22semidirect
51. #14583100C22semidirect
52. #14583099C22semidirect
53. #14583095C22semidirect
54. #14583094C22semidirect
55. #14583047C22semidirect
56. #14583045C22semidirect
57. #14583039C22semidirect
58. #14583034C22semidirect
59. #14583010C22semidirect
60. #14583008C22semidirect
61. #14583002C22semidirect
62. #14582998C22semidirect
63. #14582986C22semidirect
64. #14582984C22semidirect
65. #14582981C22semidirect
66. #14582979C22semidirect
67. #14582959C22semidirect
68. #14582959C22semidirect
69. #14582939C22semidirect
70. #14582923C22semidirect
71. #14582905C22semidirect
72. #14582903C22semidirect
75. M16×Dic43C22semidirect
76. C2×#125×C43C22semidirect
78. C43×#479C22semidirect
79. C43×#478C22semidirect
80. C43×#428C22semidirect
81. C43×#423C22semidirect
433. #3080D43semidirect
458. C2×#125C2×D43semidirect
484. #479C2×D43semidirect
486. #478C2×D43semidirect
506. #428C2×D43semidirect
508. #423C2×D43semidirect
515. C43#60568semidirect

Maximal subgroups

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

subgroupindex
C2×#145835052
#191477942
#191448882
#191448402
#191448012
#191447992
#191445372
#191444132
#191440762
#191440752
#191438482
#191434082
#191434022
#191432322
C43×#30802
#6056843