Finite Group Databasebeta

← #25117451

Subgroups — #25117451

Order 11008.

1074 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583065C211yesmaximal, characteristic
2#19143427C211yesmaximal, characteristic, complemented
3#19143118C211yesmaximal, characteristic, complemented
4#19143117C211yesmaximal, characteristic, complemented
5#19135399C211yesmaximal, characteristic, complemented
6#19135257C211yesmaximal, characteristic, complemented
7#19135256C211yesmaximal, characteristic, complemented
8#19135106C211yesmaximal, characteristic, complemented
9#19135105C211yesmaximal, characteristic, complemented
10#19134993C211yesmaximal, characteristic, complemented
11#19134821C211yesmaximal, characteristic, complemented
12#19134818C211yesmaximal, characteristic, complemented
13#19134435C211yesmaximal, characteristic, complemented
14#19134434C211yesmaximal, characteristic, complemented
15C43×#2946C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17C2×#13063351C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21#14583379C2211yescharacteristic
22#14583065C418yescomplemented
23#14583009—21no—
24#14582999—21no—
25C4×#10621883—21no—
26C4×#10621882—21no—
27#14582942C2211yescharacteristic, complemented
28C2×#13063252C2211yescharacteristic
29C2×#13063251C2211yescharacteristic
30#14582903—21no—
31#14582903C2211yescharacteristic
32#14582903C2211yescharacteristic
33#14582902—21no—
34#14582900C2211yescharacteristic
35#14582899—21no—
36#14582898—21no—
37#14582898C2211yescharacteristic
38#14582894—21no—
39#14582893—21no—
40#14582893C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063246C2211yescharacteristic, complemented
43C2×#13063245—21no—
44C2×#13063245C2211yescharacteristic
45#102×D43—21no—
46C2×#13063242C2211yescharacteristic, complemented
47C2×#13063241C2211yescharacteristic
48#14582855C2211yescharacteristic, complemented
49C2×C8×Dic43C2211yescharacteristic, complemented
50#14582768C2211yescharacteristic, complemented
51#14582668C2211yescharacteristic, complemented
52#14582667C2211yescharacteristic, complemented
53#14582664C2211yescharacteristic, complemented
54#14582663C2211yescharacteristic, complemented
55#14582658C2211yescharacteristic, complemented
56#14582658C2211yescharacteristic, complemented
57C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
58C43×#520C2211yescharacteristic
59C43×#518C2211yescharacteristic, complemented
60C43×#442—21no—
61C43×#440—21no—
62C4×SD16×C43—21no—
63C4×D8×C43—21no—
64C43×#428C2211yescharacteristic, complemented
65C43×#416C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic, complemented
67C43×#405C2211yescharacteristic, complemented
68#13063371—22no—
69#13063371—22no—
70#13063371—41no—
71#13063371C2×C414yescomplemented
72C2×#10621902—21no—
73C2×#10621898—21no—
74C2×#10621898C2311yescharacteristic
75C22×D172—21no—
76C22×D172C2311yescharacteristic
77C22×C22⋊D43—41no—
78C2×D4×D43—21no—
79C2×D4×D43—41no—
80#13063351—22no—
81#13063351C2×C414yescomplemented
82C2×#10621883—21no—
83C2×#10621882—21no—
84#13063332—22no—
85#13063332—41no—
86#13063331—22no—
87#13063331—41no—
88C2×#10621877—21no—
89C2×#10621877C2311yescharacteristic
90C2×#10621877C2311yescharacteristic
91C2×#10621877C2311yescharacteristic
92C2×#10621872—21no—
93C22×C43⋊C8—21no—
94C22×C43⋊C8C2311yescharacteristic
95C2×C8×D43—21no—
96#13063321—41no—
97#13063321C2×C414yescomplemented
98C4×Dic86—21no—
99C4×D172—21no—
100(C22⋊D43)⋊C4—41no—
101#13063283—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—41no—
104C4⋊C4×D43—21no—
105C2×C4×Dic43C2311yescharacteristic
106#13063258—21no—
107#13063256—21no—
108#13063252C2×C414yescomplemented
109#13063251C2×C414yescomplemented
110#13063249—21no—
111#13063248—21no—
112#13063248D411yescharacteristic, complemented
113#13063248D411yescharacteristic, complemented
114#13063247—21no—
115#13063247—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063245—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123#13063245—21no—
124#13063245—21no—
125#13063245—21no—
126#13063245D411yescharacteristic, complemented
127#13063245D411yescharacteristic, complemented
128#13063242—41no—
129#13063241C2×C414yescomplemented
130#13063236—21no—
131C4×C43⋊C8—21no—
132C8×Dic43—41no—
133C2×#41×C43C2311yescharacteristic
134C22×D4×C43C2311yescharacteristic
135AGL(1,ℤ/8)×C43—22no—
136AGL(1,ℤ/8)×C43C2×C414yescomplemented
137C2×SD16×C43—21no—
138C2×D8×C43—21no—
139C2×M16×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C4×Q8×C43—21no—
142C4×D4×C43—21no—
143C4×D4×C43—21no—
144C4×D4×C43—21no—
145C4×D4×C43—21no—
146C4×D4×C43—21no—
147C4×D4×C43—41no—
148#117×C43—21no—
149#117×C43C2311yescharacteristic
150#117×C43C2311yescharacteristic
151C2×C4⋊C4×C43—21no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—41no—
154#107×C43—21no—
155#106×C43—21no—
156#103×C43D411yescharacteristic, complemented
157#103×C43D411yescharacteristic, complemented
158#102×C43—21no—
159#102×C43—21no—
160#102×C43D411yescharacteristic, complemented
161#102×C43D411yescharacteristic, complemented
162#97×C43—21no—
163C4×C8×C43—21no—
164C24×C43—21no—
165C23×D43—21no—
166C23×D43—41no—
167#41×C43—21no—
168#41×C43—21no—
169#41×C43C22×C412yes—
170#41×C43#4112yes—
171C2×Q8×C43C2×D411yescharacteristic
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43C22×C412yes—
179C2×D4×C43C2×D411yescharacteristic
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—41no—
183C22×C4×C43—41no—
184C22×C4×C43—41no—
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—21no—
187C2×C22⋊D43—44no—
188C2×C22⋊D43—41no—
189C2×C22⋊D43—82no—
190C2×C22⋊D43—82no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193#10621902—24no—
194#10621902—42no—
195D4×D43—24no—
196D4×D43—44no—
197D4×D43—42no—
198D4×D43—44no—
199#10621898—21no—
200#10621898—21no—
201#10621898—24no—
202#10621898—42no—
203#10621898C22×C412yes—
204#10621898#4112yes—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—24no—
211C2×D172—41no—
212C2×D172—42no—
213C2×D172C22×C412yes—
214C2×D172C2×D411yescharacteristic
215C2×C4×D43—21no—
216C2×C4×D43—41no—
217C2×C4×D43—41no—
218C2×Dic86C2×D411yescharacteristic
219SD16×C43—24no—
220D8×C43—24no—
221M16×C43—21no—
222M16×C43C22×C412yes—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43C2×D411yescharacteristic
227C2×C8×C43C2×D411yescharacteristic
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—41no—
231C4⋊C4×C43C2×D411yescharacteristic
232C4⋊C4×C43C2×D411yescharacteristic
233C4⋊C4×C43C2×D411yescharacteristic
234C4⋊C4×C43C2×D411yescharacteristic
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—41no—
238C22⋊C4×C43—41no—
239C22⋊C4×C43—41no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—41no—
243#10621883—24no—
244#10621882—24no—
245(C2×D43)⋊C4—41no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248Dic43⋊C4—41no—
249Dic43⋊C4—82no—
250C4×Dic43—21no—
251C4×Dic43—41no—
252C4×Dic43C22×C412yes—
253#10621877—21no—
254#10621877—21no—
255#10621877—21no—
256#10621877—21no—
257#10621877—21no—
258#10621877—42no—
259#10621877C22×C412yes—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—42no—
266C2×C43⋊C8C2×D411yescharacteristic
267C2×C43⋊C8C2×D411yescharacteristic
268#10621872—42no—
269C8×D43—42no—
270C23×C43—21no—
271C23×C43—22no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—81no—
275C23×C43—81no—
276C23×C43H(5,𝔽2)11yescharacteristic
277C22×D43—21no—
278C22×D43—22no—
279C22×D43—44no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—81no—
283C22×D43—81no—
284C22×D43—161no—
285C22×D43—161no—
286Q8×C43—21no—
287Q8×C43C4×D412yes—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—21no—
293D4×C43—41no—
294D4×C43—41no—
295D4×C43C4×D412yes—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—41no—
304C2×C4×C43—81no—
305C2×C4×C43—161no—
306C2×C4×C43—161no—
307C2×C4×C43—161no—
308C2×C4×C43C23×C411yescharacteristic
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C22⋊D43—22no—
315C22⋊D43—22no—
316C22⋊D43—44no—
317C22⋊D43—88no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—21no—
322C2×Dic43—41no—
323C2×Dic43—81no—
324D172—22no—
325D172—22no—
326D172—21no—
327D172—44no—
328D172—41no—
329D172—41no—
330D172C4×D412yes—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—44no—
334C4×D43—161no—
335Dic86—21no—
336Dic86C4×D412yes—
337C8×C43—22no—
338C8×C43—21no—
339C8×C43—21no—
340C43⋊C8—22no—
341C43⋊C8—21no—
342C43⋊C8—21no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345#22897—431nomaximal, Sylow
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—22no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—82no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—161no—
356C22×C43#51811yescharacteristic
357C22×C43D4211yescharacteristic
358C22×C43#55111yescharacteristic
359C2×D43—22no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—42no—
363C2×D43—81no—
364C2×D43—81no—
365C2×D43—82no—
366C2×D43—164no—
367C2×D43—161no—
368C4×C43—22no—
369C4×C43—41no—
370C4×C43—41no—
371C4×C43—41no—
372C4×C43—41no—
373C4×C43—81no—
374C4×C43C2×C4×D411yescharacteristic
375C4×C43C2×C4×D411yescharacteristic
376C4×C43#54611yescharacteristic
377C4×C43#54611yescharacteristic
378Dic43—24no—
379Dic43—22no—
380Dic43—81no—
381C2×#453—431no—
382#2946—431no—
383#2946D4311yescharacteristic, complemented
384#2897—431no—
385#2897—431no—
386#1957—431no—
387#1931—431no—
388#1931—431no—
389#1907—431no—
390#1907—431no—
391#1887—431no—
392#1859—431no—
393#1859—431no—
394#1764—431no—
395#1764—431no—
396C2×C43—21no—
397C2×C43—21no—
398C2×C43—42no—
399C2×C43—82no—
400C2×C43#235811yescharacteristic
401C2×C43#329111yescharacteristic
402C2×C43#329211yescharacteristic
403D43—42no—
404D43—82no—
405C2×H(5,𝔽2)—431no—
406C2×AGL(1,ℤ/8)—431no—
407C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
408C2×#131—431no—
409C2×#131—431no—
410C2×#127—431no—
411#520—431no—
412#520C2×D4311yescharacteristic
413#518C2×D4311yescharacteristic, complemented
414#453—438no—
415#442—21no—
416#442—861no—
417#440—21no—
418#440—861no—
419C4×SD16—21no—
420C4×SD16—861no—
421C4×D8—21no—
422C4×D8—861no—
423#428—431no—
424#428C2×D4311yescharacteristic, complemented
425C2×#104—431no—
426C2×#104—431no—
427#418—431no—
428#418—431no—
429#418—861no—
430#418—861no—
431#417—431no—
432#417—431no—
433#417—861no—
434#417—861no—
435#416—431no—
436#416—861no—
437#416—861no—
438#416C2×D4311yescharacteristic
439C2×#102—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—861no—
443C2×#102—861no—
444C2×#102C2×D4311yescharacteristic, complemented
445C2×#100—431no—
446C2×#100—431no—
447#405—431no—
448#405C2×D4311yescharacteristic, complemented
449C2×C4×C8—431no—
450#384—431no—
451#343—431no—
452#343—431no—
453#341—431no—
454#341—431no—
455#339—431no—
456#339—431no—
457C43#2289711yescharacteristic, complemented, Sylow
458H(5,𝔽2)—434no—
459H(5,𝔽2)—862no—
460H(5,𝔽2)—862no—
461H(5,𝔽2)—1721no—
462C2×#41—431no—
463C2×#41—861no—
464C2×#41—861no—
465C2×#41C22×D4311yescharacteristic
466C22×D4—431no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4—1721no—
470C22×D4—1721no—
471C22×D4C22×D4311yescharacteristic
472AGL(1,ℤ/8)—22no—
473AGL(1,ℤ/8)—434no—
474AGL(1,ℤ/8)—862no—
475AGL(1,ℤ/8)C4×D4314yescomplemented
476C2×SD16—21no—
477C2×SD16—861no—
478C2×D8—21no—
479C2×D8—861no—
480#131—862no—
481#131—862no—
482#131—1721no—
483#131—1721no—
484C2×M16—431no—
485C2×M16—431no—
486C2×M16—431no—
487C2×M16—861no—
488C2×M16—861no—
489C2×M16C22×D4311yescharacteristic
490C22×C8—431no—
491C22×C8—861no—
492C22×C8—861no—
493C22×C8C22×D4311yescharacteristic
494#127—434no—
495#127—1721no—
496C4×Q8—21no—
497C4×Q8—861no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—41no—
504C4×D4—861no—
505C4×D4—1721no—
506#117—21no—
507#117—861no—
508#117C22×D4311yescharacteristic
509#117C22×D4311yescharacteristic
510C2×C4⋊C4—21no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—1721no—
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—41no—
516C2×C42—431no—
517#107—21no—
518#107—861no—
519#106—21no—
520#106—861no—
521#104—434no—
522#104—434no—
523#103—431no—
524#103—431no—
525#103—861no—
526#103—861no—
527#103C22⋊D4311yescharacteristic, complemented
528#103C22⋊D4311yescharacteristic, complemented
529#102—21no—
530#102—21no—
531#102—431no—
532#102—431no—
533#102—861no—
534#102—861no—
535#102—861no—
536#102—861no—
537#102—861no—
538#102—861no—
539#102—861no—
540#102—861no—
541#102—861no—
542#102—861no—
543#102—861no—
544#102—861no—
545#102C22⋊D4311yescharacteristic, complemented
546#102C22⋊D4311yescharacteristic, complemented
547#100—434no—
548#100—1721no—
549#97—21no—
550#97—861no—
551C4×C8—21no—
552C4×C8—861no—
553C4×C8—1721no—
554C24—21no—
555C24—861no—
556C24—1721no—
557#41—21no—
558#41—21no—
559#41—432no—
560#41—432no—
561#41—864no—
562#41—861no—
563#41—861no—
564#41—864no—
565#41—1722no—
566#41—1722no—
567#41C2×C4×D4312yes—
568#41#1062189812yes—
569C2×Q8—431no—
570C2×Q8C2×C22⋊D4311yescharacteristic
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—432no—
578C2×D4—431no—
579C2×D4—864no—
580C2×D4—861no—
581C2×D4—864no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—3442no—
588C2×D4—3442no—
589C2×D4—1722no—
590C2×D4—1721no—
591C2×D4—1722no—
592C2×D4—1724no—
593C2×D4—1721no—
594C2×D4—1724no—
595C2×D4—1724no—
596C2×D4C2×C4×D4312yes—
597C2×D4C2×C22⋊D4311yescharacteristic
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—1721no—
607C22×C4—1721no—
608C22×C4C23×D4311yescharacteristic
609SD16—24no—
610SD16—864no—
611D8—24no—
612D8—864no—
613M16—21no—
614M16—432no—
615M16—861no—
616M16—861no—
617M16—861no—
618M16—861no—
619M16—861no—
620M16—1722no—
621M16—1722no—
622M16C2×C4×D4312yes—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—431no—
627C2×C8—431no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—1722no—
634C2×C8—1722no—
635C2×C8C2×C22⋊D4311yescharacteristic
636C2×C8C2×C22⋊D4311yescharacteristic
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—41no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—3442no—
643C4⋊C4—1721no—
644C4⋊C4D4×D4311yescharacteristic
645C4⋊C4D4×D4311yescharacteristic
646C4⋊C4C2×C22⋊D4311yescharacteristic
647C4⋊C4C2×C22⋊D4311yescharacteristic
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C22⋊C4—1721no—
654C42—21no—
655C42—21no—
656C42—41no—
657C42—432no—
658C42—861no—
659C42—1721no—
660C23—21no—
661C23—22no—
662C23—41no—
663C23—41no—
664C23—81no—
665C23—81no—
666C23—861no—
667C23—862no—
668C23—3441no—
669C23—3441no—
670C23—1724no—
671C23—1721no—
672C23—1721no—
673C23—6881no—
674C23—6881no—
675C23#1306337011yescharacteristic
676Q8—21no—
677Q8—432no—
678Q8—861no—
679Q8C4×C22⋊D4312yes—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—21no—
685D4—41no—
686D4—41no—
687D4—432no—
688D4—862no—
689D4—862no—
690D4—862no—
691D4—862no—
692D4—861no—
693D4—3448no—
694D4—1724no—
695D4—1724no—
696D4—1721no—
697D4—1721no—
698D4C4×C22⋊D4312yes—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—81no—
708C2×C4—161no—
709C2×C4—161no—
710C2×C4—161no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—861no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—3441no—
718C2×C4—1724no—
719C2×C4—1721no—
720C2×C4—6881no—
721C2×C4C22×C4×D4311yescharacteristic
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4C22×C22⋊D4311yescharacteristic
724C2×C4#41×D4311yescharacteristic
725C2×C4C2×#1062189811yescharacteristic
726C2×C4#1306337111yescharacteristic
727C8—22no—
728C8—21no—
729C8—21no—
730C8—862no—
731C8—861no—
732C8—861no—
733C8—1721no—
734C8—1721no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—82no—
742C22—81no—
743C22—81no—
744C22—161no—
745C22—862no—
746C22—3442no—
747C22—3441no—
748C22—3441no—
749C22—1722no—
750C22—1721no—
751C22—1721no—
752C22—6881no—
753C22—6884no—
754C22#1458337111yescharacteristic
755C22D4×C22⋊D4311yescharacteristic
756C22#1458357811yescharacteristic
757C4—22no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—81no—
763C4—864no—
764C4—862no—
765C4—3441no—
766C4C4×D4×D4311yescharacteristic
767C4C2×C4×C22⋊D4311yescharacteristic
768C4#1458353711yescharacteristic
769C4#1458354511yescharacteristic
770C2—21no—
771C2—21no—
772C2—42no—
773C2—82no—
774C2—3442no—
775C2—1722no—
776C2#1913757211yescharacteristic
777C2#1914638611yescharacteristic
778C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2946C2
socleC22×C43D42
prime radicalC2×#14583065C2
cosocleC22×C4×C43C24
hypercenter#2946D43
hypocenterC43#22897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2946

Complements

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

NH ≅ G/Ntype
2. #19143427C2semidirect
3. #19143118C2semidirect
4. #19143117C2semidirect
5. #19135399C2semidirect
6. #19135257C2semidirect
7. #19135256C2semidirect
8. #19135106C2semidirect
9. #19135105C2semidirect
10. #19134993C2semidirect
11. #19134821C2semidirect
12. #19134818C2semidirect
13. #19134435C2semidirect
14. #19134434C2semidirect
15. C43×#2946C2semidirect
22. #14583065C4semidirect
27. #14582942C22semidirect
42. C2×#13063246C22semidirect
46. C2×#13063242C22semidirect
48. #14582855C22semidirect
49. C2×C8×Dic43C22semidirect
50. #14582768C22semidirect
51. #14582668C22semidirect
52. #14582667C22semidirect
53. #14582664C22semidirect
54. #14582663C22semidirect
55. #14582658C22semidirect
56. #14582658C22semidirect
59. C43×#518C22semidirect
64. C43×#428C22semidirect
66. C2×#102×C43C22semidirect
67. C43×#405C22semidirect
71. #13063371C2×C4semidirect
81. #13063351C2×C4semidirect
97. #13063321C2×C4semidirect
108. #13063252C2×C4semidirect
109. #13063251C2×C4semidirect
112. #13063248D4semidirect
113. #13063248D4semidirect
126. #13063245D4semidirect
127. #13063245D4semidirect
129. #13063241C2×C4semidirect
136. AGL(1,ℤ/8)×C43C2×C4semidirect
156. #103×C43D4semidirect
157. #103×C43D4semidirect
160. #102×C43D4semidirect
161. #102×C43D4semidirect
383. #2946D43semidirect
413. #518C2×D43semidirect
424. #428C2×D43semidirect
444. C2×#102C2×D43semidirect
448. #405C2×D43semidirect
457. C43#22897semidirect
475. AGL(1,ℤ/8)C4×D43semidirect
527. #103C22⋊D43semidirect
528. #103C22⋊D43semidirect
545. #102C22⋊D43semidirect
546. #102C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830652
#191434272
#191431182
#191431172
#191353992
#191352572
#191352562
#191351062
#191351052
#191349932
#191348212
#191348182
#191344352
#191344342
C43×#29462
#2289743