Finite Group Databasebeta

← #25965123

Subgroups — #25965123

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×#14583503C211yesmaximal, characteristic, complemented
2#19147794C211yesmaximal, characteristic, complemented
3#19144884C214yesmaximal, complemented
4#19144836C214yesmaximal, complemented
5#19144793C214yesmaximal, complemented
6#19144791C214yesmaximal, complemented
7#19144533C212yesmaximal, complemented
8#19144418C211yesmaximal, characteristic, complemented
9#19144417C211yesmaximal, characteristic, complemented
10#19144071C211yesmaximal, characteristic, complemented
11#19143843C212yesmaximal, complemented
12AGL(1,ℤ/8)×Dic43C212yesmaximal, complemented
13#19143399C212yesmaximal, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3038C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063351C2212yes—
18#14583503—21no—
19#14583503—21no—
20#14583503—21no—
21#14583503—21no—
22#14583503C2214yes—
23#14583503C2214yescomplemented
24C2×#13063317C2211yescharacteristic, complemented
25C2×#13063306—22no—
26C2×#13063297—22no—
27C2×#13063296C2212yes—
28#14583381C2212yescomplemented
29#14583378—22no—
30#14583378C2212yescomplemented
31#14583375C2212yescomplemented
32#14583371—22no—
33#14583371C2212yescomplemented
34#41×Dic43C2211yescharacteristic
35C4×#10621898—21no—
36C4×#10621898C2211yescharacteristic
37#14583367—21no—
38#14583367C2211yescharacteristic
39C2×D4×Dic43C2212yescomplemented
40C2×#13063282—21no—
41C2×#13063282C2211yescharacteristic
42#117×D43—21no—
43#117×D43C2211yescharacteristic
44#14583222C2214yescomplemented
45#14583221C2214yescomplemented
46#14583216C2214yescomplemented
47#14583211C2214yescomplemented
48#14583207C2214yescomplemented
49#14583206C2214yescomplemented
50#14583200C2214yescomplemented
51#14583199C2214yescomplemented
52#14583096C2214yescomplemented
53#14583091C2214yescomplemented
54#14583043C2214yescomplemented
55#14583041C2214yescomplemented
56#14583036C2214yescomplemented
57#14583031C2214yescomplemented
58#14583011C2214yescomplemented
59#14583008C2214yescomplemented
60#14583000C2214yescomplemented
61#14582996C2214yescomplemented
62#14582990C2214yescomplemented
63SD16×Dic43C2214yescomplemented
64D8×Dic43C2214yescomplemented
65#14582979C2214yescomplemented
66#14582959C2214yescomplemented
67#14582959C2214yescomplemented
68#14582942C2212yescomplemented
69#14582941C2212yescomplemented
70#14582923C2211yescharacteristic, complemented
71#14582904C2212yescomplemented
72#14582901C2212yes—
73#14582900C2212yes—
74#14582862C2212yes—
75M16×Dic43C2212yescomplemented
76C2×AGL(1,ℤ/8)×C43C2212yes—
77C2×#127×C43C2211yescharacteristic, complemented
78C4×#41×C43C2211yescharacteristic
79C43×#460C2214yescomplemented
80C43×#459C2214yescomplemented
81C43×#423C2211yescharacteristic, complemented
82C43×#418C2212yescomplemented
83C2×#10621902C2311yescharacteristic
84C2×#10621898—21no—
85C2×#10621898C2311yescharacteristic
86C2×#10621900—21no—
87C2×#10621900C2311yescharacteristic
88#41×D43—24no—
89#41×D43—24no—
90C2×Q8×D43C2311yescharacteristic
91C22×C22⋊D43—22no—
92C2×D4×D43—21no—
93C2×D4×D43C2311yescharacteristic
94C23×Dic43—22no—
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97#13063351—28no—
98C2×#10621883C2314yes—
99C2×#10621882C2314yes—
100C2×#10621877C2312yes—
101#13063317—21no—
102#13063317—21no—
103#13063317C2314yes—
104#13063306—24no—
105#13063306—24no—
106#13063306—24no—
107#13063306—24no—
108#13063297—24no—
109#13063297—24no—
110#13063297—24no—
111#13063297—24no—
112#13063296—22no—
113#13063296—22no—
114#13063296C2314yes—
115#13063296C2314yes—
116Q8×Dic43C2312yes—
117C4×Dic86—22no—
118C4×Dic86C2312yes—
119#13063290—22no—
120#13063290C2312yes—
121C4×D172—22no—
122C4×D172C2312yes—
123D4×Dic43—22no—
124D4×Dic43—22no—
125D4×Dic43—22no—
126D4×Dic43C2314yes—
127D4×Dic43C2314yes—
128D4×Dic43C2312yes—
129#13063287—22no—
130#13063287C2312yes—
131C4×C22⋊D43—22no—
132C4×C22⋊D43—22no—
133C4×C22⋊D43—22no—
134(C22⋊D43)⋊C4—22no—
135(C22⋊D43)⋊C4—22no—
136(C22⋊D43)⋊C4—22no—
137#13063284—21no—
138#13063284C2311yescharacteristic
139#13063283—22no—
140#13063283C2312yes—
141#13063282—21no—
142#13063282—21no—
143#13063282—22no—
144#13063282—22no—
145#13063282—21no—
146#13063282D411yescharacteristic
147#13063282D411yescharacteristic
148#13063282D411yescharacteristic
149#13063282D411yescharacteristic
150#13063282C2312yes—
151#13063282C2312yes—
152#13063281—21no—
153#13063281—22no—
154C2×C4⋊Dic43C2312yes—
155C2×Dic43⋊C4—22no—
156C2×Dic43⋊C4—22no—
157C2×Dic43⋊C4D412yes—
158C4⋊C4×D43—22no—
159C4⋊C4×D43C2312yes—
160C2×C22⋊Dic43—22no—
161C2×C22⋊Dic43—22no—
162C2×(C2×D43)⋊C4—22no—
163C2×(C2×D43)⋊C4D412yes—
164C22⋊C4×D43—21no—
165C22⋊C4×D43—22no—
166C2×C4×Dic43—21no—
167C2×C4×Dic43C2311yescharacteristic
168C42×D43—21no—
169C42×D43—21no—
170C42×D43—21no—
171#13063259C2314yes—
172#13063258C2314yes—
173#13063257C2314yes—
174#13063256C2314yes—
175C4⋊(C43⋊C8)C2314yes—
176#13063250C2314yes—
177#13063249C2314yes—
178#13063247C2314yes—
179#13063246C2314yes—
180#13063246C2314yes—
181#13063246C2314yes—
182(C2×D43)⋊C8C2314yes—
183(C2×D43)⋊C8C2314yes—
184#13063235C2314yes—
185C8×Dic43C2314yes—
186C2×#41×C43C2311yescharacteristic
187C22×D4×C43—22no—
188C22×D4×C43C2312yes—
189AGL(1,ℤ/8)×C43—28no—
190C2×SD16×C43C2314yes—
191C2×D8×C43C2314yes—
192C2×M16×C43C2312yes—
193#127×C43—21no—
194#127×C43—21no—
195#127×C43C2314yes—
196C4×Q8×C43C2312yes—
197C4×D4×C43—22no—
198C4×D4×C43C2312yes—
199#117×C43—21no—
200#117×C43C2311yescharacteristic
201C2×C42×C43—21no—
202C2×C42×C43C2311yescharacteristic
203C4⋊C8×C43C2314yes—
204#102×C43C2314yes—
205#102×C43C2314yes—
206C24×C43—22no—
207C23×D43—21no—
208C23×D43C2×D411yescharacteristic
209#41×C43—22no—
210#41×C43#4114yes—
211C2×Q8×C43C2411yescharacteristic
212C2×D4×C43—22no—
213C2×D4×C43—24no—
214C2×D4×C43—24no—
215C2×D4×C43—21no—
216C2×D4×C43—24no—
217C2×D4×C43—24no—
218C2×D4×C43—84no—
219C2×D4×C43C2414yes—
220C2×D4×C43C2411yescharacteristic
221C22×C4×C43—21no—
222C22×C4×C43—22no—
223C22×C4×C43C2×D412yes—
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—24no—
229C2×C22⋊D43—24no—
230C2×C22⋊D43—84no—
231C22×Dic43—21no—
232C22×Dic43—22no—
233C22×Dic43—24no—
234C22×Dic43—24no—
235C22×Dic43—22no—
236C22×Dic43—84no—
237C22×Dic43C2×D411yescharacteristic
238C22×Dic43C2×D412yes—
239#10621902—22no—
240#10621902—22no—
241Q8×D43—22no—
242Q8×D43—22no—
243#10621900—28no—
244#10621900—22no—
245#10621900—22no—
246D4×D43—28no—
247D4×D43—22no—
248D4×D43—22no—
249#10621898—28no—
250#10621898—22no—
251#10621898#4114yes—
252C2×D172—21no—
253C2×D172C2411yescharacteristic
254C2×C4×D43—28no—
255C2×C4×D43—21no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—21no—
259C2×C4×D43—22no—
260C2×C4×D43—22no—
261C2×C4×D43—21no—
262C2×C4×D43—22no—
263C2×C4×D43C2×D411yescharacteristic
264C2×C4×D43C2×D411yescharacteristic
265C2×C4×D43C2411yescharacteristic
266C2×C4×D43C2411yescharacteristic
267C2×Dic86—21no—
268C2×Dic86C2411yescharacteristic
269SD16×C43—28no—
270D8×C43—28no—
271M16×C43—24no—
272C2×C8×C43C2414yes—
273C4⋊C4×C43—22no—
274C4⋊C4×C43C2412yes—
275C22⋊C4×C43—22no—
276C22⋊C4×C43—21no—
277C42×C43—21no—
278C42×C43—22no—
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2412yes—
282C22⋊Dic43—22no—
283C22⋊Dic43—24no—
284C22⋊Dic43—24no—
285C22⋊Dic43—24no—
286C22⋊Dic43—24no—
287C22⋊Dic43—21no—
288#10621883—28no—
289#10621882—28no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4C2×D412yes—
294(C2×D43)⋊C4C2×D412yes—
295(C2×D43)⋊C4C2×D412yes—
296(C2×D43)⋊C4C2×D412yes—
297C4⋊Dic43—22no—
298C4⋊Dic43—22no—
299C4⋊Dic43C2412yes—
300C4⋊Dic43C2414yes—
301Dic43⋊C4—22no—
302Dic43⋊C4—24no—
303Dic43⋊C4—24no—
304Dic43⋊C4—22no—
305Dic43⋊C4—22no—
306Dic43⋊C4C2×D412yes—
307Dic43⋊C4C2×D412yes—
308Dic43⋊C4C2×D412yes—
309Dic43⋊C4C2×D412yes—
310C4×Dic43—21no—
311C4×Dic43—22no—
312C4×Dic43—22no—
313C4×Dic43—22no—
314C4×Dic43—22no—
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2412yes—
318#10621877—24no—
319C2×C43⋊C8C2414yes—
320C23×C43—21no—
321C23×C43—24no—
322C23×C43—44no—
323C23×C43—44no—
324C23×C43—44no—
325C23×C43C22×D411yescharacteristic
326C22×D43—21no—
327C22×D43—24no—
328C22×D43—22no—
329C22×D43—42no—
330C22×D43—82no—
331C22×D43C22×D411yescharacteristic
332C22×D43C22×D411yescharacteristic
333Q8×C43—21no—
334Q8×C43C2×#4112yes—
335D4×C43—24no—
336D4×C43—21no—
337D4×C43—24no—
338D4×C43—24no—
339D4×C43—44no—
340D4×C43—84no—
341D4×C43—84no—
342D4×C43C2×#4112yes—
343C2×C4×C43—21no—
344C2×C4×C43—24no—
345C2×C4×C43—22no—
346C2×C4×C43—42no—
347C2×C4×C43—82no—
348C2×C4×C43C22×D412yes—
349C2×C4×C43C22×D412yes—
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C2×#4112yes—
352C2×C4×C43C2×#4112yes—
353C2×C4×C43C2511yescharacteristic
354C22⋊D43—24no—
355C22⋊D43—24no—
356C22⋊D43—24no—
357C22⋊D43—84no—
358C22⋊D43—84no—
359C2×Dic43—24no—
360C2×Dic43—22no—
361C2×Dic43—21no—
362C2×Dic43—22no—
363C2×Dic43—24no—
364C2×Dic43—42no—
365C2×Dic43—44no—
366C2×Dic43—82no—
367C2×Dic43—84no—
368C2×Dic43—84no—
369C2×Dic43C22×D411yescharacteristic
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D412yes—
372C2×Dic43C22×D411yescharacteristic
373D172—24no—
374D172—21no—
375D172C2×#4112yes—
376C4×D43—24no—
377C4×D43—24no—
378C4×D43—22no—
379C4×D43—24no—
380C4×D43—22no—
381C4×D43—21no—
382C4×D43—21no—
383C4×D43—21no—
384C4×D43—21no—
385C4×D43—82no—
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—44no—
398C22×C43—44no—
399C22×C43—44no—
400C22×C43—88no—
401C22×C43#52512yes—
402C22×C43C23×D411yescharacteristic
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—21no—
406C2×D43—22no—
407C2×D43—21no—
408C2×D43—42no—
409C2×D43—82no—
410C2×D43—84no—
411C4×C43—22no—
412C4×C43—22no—
413C4×C43—22no—
414C4×C43—42no—
415C4×C43#52512yes—
416C4×C43C22×#4111yescharacteristic
417C4×C43C22×#4111yescharacteristic
418Dic43—22no—
419Dic43—22no—
420Dic43—21no—
421Dic43—22no—
422Dic43—21no—
423Dic43—42no—
424Dic43—44no—
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#3080—431no—
434#3038—431no—
435#3038D4311yescharacteristic, complemented
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×C43—84no—
443C2×C43C2×#52511yescharacteristic
444C2×C43#358512yes—
445D43—41no—
446D43—41no—
447D43—42no—
448C22×#41—431no—
449C2×AGL(1,ℤ/8)—432no—
450C2×AGL(1,ℤ/8)C2×D4312yes—
451#540—434no—
452#540—434no—
453#540—861no—
454#540—861no—
455#540—861no—
456#540—861no—
457C2×#127C2×D4311yescharacteristic, complemented
458C2×#125—431no—
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#479—434no—
485#478—434no—
486#478—434no—
487#460—434no—
488#460C2×D4314yescomplemented
489#459—434no—
490#459C2×D4314yescomplemented
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#428—432no—
507#423—431no—
508#423C2×D4311yescharacteristic, complemented
509#418—432no—
510#418C2×D4312yescomplemented
511#417—432no—
512#417—432no—
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—22no—
526C22×D4—431no—
527C22×D4—861no—
528C22×D4—862no—
529C22×D4C22×D4312yes—
530C23×C4—431no—
531C23×C4—861no—
532C23×C4—862no—
533AGL(1,ℤ/8)—28no—
534AGL(1,ℤ/8)—868no—
535C2×SD16—434no—
536C2×SD16C22×D4314yes—
537C2×D8—434no—
538C2×D8C22×D4314yes—
539C2×M16—432no—
540C2×M16C22×D4312yes—
541#127—21no—
542#127—21no—
543#127C22×D4314yes—
544#125—434no—
545#125—861no—
546#125—861no—
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—434no—
567C4×D4—434no—
568C4×D4—432no—
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—432no—
603C2×C4⋊C4—432no—
604C2×C4⋊C4—432no—
605C2×C4⋊C4—862no—
606C2×C4⋊C4—862no—
607C2×C4⋊C4—862no—
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#107—434no—
623#106—434no—
624#106—434no—
625C4⋊C8—434no—
626C4⋊C8C22×D4314yes—
627#103—434no—
628#103—434no—
629#102—434no—
630#102—434no—
631#102—434no—
632#102—434no—
633#102C22×D4314yes—
634#102C22×D4314yes—
635C22⋊C8—434no—
636C22⋊C8—434no—
637#97—434no—
638C4×C8—434no—
639C24—22no—
640C24—431no—
641C24—861no—
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#1062190014yes—
652C2×Q8—431no—
653C2×Q8—861no—
654C2×Q8—862no—
655C2×Q8—862no—
656C2×Q8C23×D4311yescharacteristic
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—84no—
664C2×D4—431no—
665C2×D4—861no—
666C2×D4—861no—
667C2×D4—862no—
668C2×D4—868no—
669C2×D4—861no—
670C2×D4—861no—
671C2×D4—862no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—3444no—
675C2×D4C23×D4314yes—
676C2×D4C23×D4311yescharacteristic
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—431no—
680C22×C4—432no—
681C22×C4—431no—
682C22×C4—431no—
683C22×C4—431no—
684C22×C4—431no—
685C22×C4—861no—
686C22×C4—862no—
687C22×C4—861no—
688C22×C4—868no—
689C22×C4—862no—
690C22×C4—861no—
691C22×C4—862no—
692C22×C4—864no—
693C22×C4—864no—
694C22×C4—861no—
695C22×C4—862no—
696C22×C4—862no—
697C22×C4—862no—
698C22×C4—862no—
699C22×C4—3444no—
700C22×C4D4×D4312yes—
701C22×C4C23×D4311yescharacteristic
702SD16—28no—
703SD16—868no—
704D8—28no—
705D8—868no—
706M16—24no—
707M16—864no—
708C2×C8—434no—
709C2×C8C23×D4314yes—
710C4⋊C4—22no—
711C4⋊C4—432no—
712C4⋊C4—432no—
713C4⋊C4—432no—
714C4⋊C4—432no—
715C4⋊C4—432no—
716C4⋊C4—434no—
717C4⋊C4—862no—
718C4⋊C4—862no—
719C4⋊C4—862no—
720C4⋊C4—862no—
721C4⋊C4—862no—
722C4⋊C4—864no—
723C4⋊C4—864no—
724C4⋊C4C23×D4312yes—
725C22⋊C4—21no—
726C22⋊C4—22no—
727C22⋊C4—432no—
728C22⋊C4—432no—
729C22⋊C4—432no—
730C22⋊C4—432no—
731C22⋊C4—862no—
732C22⋊C4—862no—
733C22⋊C4—862no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C22⋊C4—864no—
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—24no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—431no—
759C23—431no—
760C23—864no—
761C23—862no—
762C23—861no—
763C23—3442no—
764C23—1722no—
765C23C2×D4×D4311yescharacteristic
766Q8—21no—
767Q8—432no—
768Q8—864no—
769Q8—861no—
770Q8C2×#1062190012yes—
771D4—24no—
772D4—21no—
773D4—24no—
774D4—24no—
775D4—44no—
776D4—84no—
777D4—84no—
778D4—432no—
779D4—864no—
780D4—864no—
781D4—864no—
782D4—864no—
783D4—861no—
784D4—3444no—
785D4—3444no—
786D4C2×#1062190012yes—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—42no—
791C2×C4—82no—
792C2×C4—432no—
793C2×C4—432no—
794C2×C4—431no—
795C2×C4—431no—
796C2×C4—864no—
797C2×C4—864no—
798C2×C4—864no—
799C2×C4—862no—
800C2×C4—861no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—864no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—862no—
809C2×C4—864no—
810C2×C4—3442no—
811C2×C4—3442no—
812C2×C4—3442no—
813C2×C4—3444no—
814C2×C4—3444no—
815C2×C4—3442no—
816C2×C4—1722no—
817C2×C4—1724no—
818C2×C4C2×D4×D4312yes—
819C2×C4C2×D4×D4312yes—
820C2×C4C2×D4×D4311yescharacteristic
821C2×C4#41×D4312yes—
822C2×C4C2×#1062190012yes—
823C2×C4C24×D4311yescharacteristic
824C8—24no—
825C8—864no—
826C22—22no—
827C22—22no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—88no—
833C22—862no—
834C22—862no—
835C22—861no—
836C22—862no—
837C22—861no—
838C22—3442no—
839C22—3444no—
840C22—1722no—
841C22#1458340912yes—
842C22C22×D4×D4311yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—42no—
847C4—862no—
848C4—862no—
849C4—861no—
850C4—861no—
851C4—862no—
852C4—1722no—
853C4—1724no—
854C4#1458340912yes—
855C4C2×#41×D4311yescharacteristic
856C4C22×#1062190011yescharacteristic
857C2—22no—
858C2—42no—
859C2—84no—
860C2—1721no—
861C2—1721no—
862C2—1722no—
863C2C2×#1458340911yescharacteristic
864C2#1914937112yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3038C2
socleC22×C43C23×D4
hypercenter#3038D43
hypocenterC43#60568
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. C2×#14583503C2semidirect
2. #19147794C2semidirect
3. #19144884C2semidirect
4. #19144836C2semidirect
5. #19144793C2semidirect
6. #19144791C2semidirect
7. #19144533C2semidirect
8. #19144418C2semidirect
9. #19144417C2semidirect
10. #19144071C2semidirect
11. #19143843C2semidirect
12. AGL(1,ℤ/8)×Dic43C2semidirect
13. #19143399C2semidirect
14. #19143232C2semidirect
15. C43×#3038C2semidirect
23. #14583503C22semidirect
24. C2×#13063317C22semidirect
28. #14583381C22semidirect
30. #14583378C22semidirect
31. #14583375C22semidirect
33. #14583371C22semidirect
39. C2×D4×Dic43C22semidirect
44. #14583222C22semidirect
45. #14583221C22semidirect
46. #14583216C22semidirect
47. #14583211C22semidirect
48. #14583207C22semidirect
49. #14583206C22semidirect
50. #14583200C22semidirect
51. #14583199C22semidirect
52. #14583096C22semidirect
53. #14583091C22semidirect
54. #14583043C22semidirect
55. #14583041C22semidirect
56. #14583036C22semidirect
57. #14583031C22semidirect
58. #14583011C22semidirect
59. #14583008C22semidirect
60. #14583000C22semidirect
61. #14582996C22semidirect
62. #14582990C22semidirect
63. SD16×Dic43C22semidirect
64. D8×Dic43C22semidirect
65. #14582979C22semidirect
66. #14582959C22semidirect
67. #14582959C22semidirect
68. #14582942C22semidirect
69. #14582941C22semidirect
70. #14582923C22semidirect
71. #14582904C22semidirect
75. M16×Dic43C22semidirect
77. C2×#127×C43C22semidirect
79. C43×#460C22semidirect
80. C43×#459C22semidirect
81. C43×#423C22semidirect
82. C43×#418C22semidirect
435. #3038D43semidirect
457. C2×#127C2×D43semidirect
488. #460C2×D43semidirect
490. #459C2×D43semidirect
508. #423C2×D43semidirect
510. #418C2×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×#145835032
#191477942
#191448842
#191448362
#191447932
#191447912
#191445332
#191444182
#191444172
#191440712
#191438432
AGL(1,ℤ/8)×Dic432
#191433992
#191432322
C43×#30382
#6056843