Finite Group Databasebeta

← #25117453

Subgroups — #25117453

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×#14583067C211yesmaximal, characteristic
2#19143430C211yesmaximal, characteristic, complemented
3#19143423C211yesmaximal, characteristic, complemented
4#19143121C211yesmaximal, characteristic, complemented
5#19135399C211yesmaximal, characteristic, complemented
6#19135260C211yesmaximal, characteristic, complemented
7#19135254C211yesmaximal, characteristic, complemented
8#19135103C211yesmaximal, characteristic, complemented
9#19135101C211yesmaximal, characteristic, complemented
10#19134990C211yesmaximal, characteristic, complemented
11#19134821C211yesmaximal, characteristic, complemented
12#19134819C211yesmaximal, characteristic, complemented
13#19134435C211yesmaximal, characteristic, complemented
14#19134430C211yesmaximal, characteristic, complemented
15C43×#2897C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C2×#13063350C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×#13063321C2211yescharacteristic
20#14583382C2211yescharacteristic
21#14583373C2211yescharacteristic, complemented
22#14583067C418yescomplemented
23#14583009—21no—
24#14583008—21no—
25#14583002—21no—
26#14582997—21no—
27C4×#10621884—21no—
28#14582984—21no—
29C4×#10621882—21no—
30#14582979—21no—
31#14582942C2211yescharacteristic, complemented
32#14582939C2211yescharacteristic, complemented
33C2×#13063252C2211yescharacteristic
34C2×#13063252C2211yescharacteristic
35#14582904—21no—
36#14582904C2211yescharacteristic
37#14582900—21no—
38#14582900C2211yescharacteristic
39#14582895—21no—
40#14582895C2211yescharacteristic
41C2×#13063247C2211yescharacteristic, complemented
42C2×#13063246—21no—
43C2×#13063246C2211yescharacteristic
44C2×#13063245C2211yescharacteristic, complemented
45C2×#13063242C2211yescharacteristic
46C2×#13063241C2211yescharacteristic, complemented
47#14582855C2211yescharacteristic, complemented
48#14582854C2211yescharacteristic, complemented
49C2×C8×Dic43C2211yescharacteristic, complemented
50#14582768C2211yescharacteristic, complemented
51#14582668C2211yescharacteristic, complemented
52#14582667C2211yescharacteristic, complemented
53#14582664C2211yescharacteristic, complemented
54#14582663C2211yescharacteristic, complemented
55#14582660C2211yescharacteristic, complemented
56#14582658C2211yescharacteristic, complemented
57C2×H(5,𝔽2)×C43C2211yescharacteristic
58C2×#131×C43C2211yescharacteristic
59C43×#520C2211yescharacteristic
60C43×#418—21no—
61C43×#418C2211yescharacteristic
62C43×#417—21no—
63C43×#417C2211yescharacteristic
64C43×#416—21no—
65C43×#416C2211yescharacteristic
66C2×#102×C43—21no—
67C2×#102×C43C2211yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C22⋊D43—41no—
70#13063350—22no—
71#13063350—22no—
72#13063350C2×C414yescomplemented
73#13063350C2×C414yescomplemented
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621882—21no—
77C2×#10621882—21no—
78#13063332—22no—
79#13063332—41no—
80C2×#10621877—21no—
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C22×C43⋊C8—21no—
85C22×C43⋊C8C2311yescharacteristic
86#13063321—41no—
87#13063321C2×C414yescomplemented
88Q8×Dic43—21no—
89C4×D172—21no—
90C4×D172—21no—
91D4×Dic43—21no—
92D4×Dic43—41no—
93#13063287—21no—
94#13063287—21no—
95#13063284—21no—
96#13063284C2311yescharacteristic
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—41no—
100C22⋊C4×D43—41no—
101C2×C4×Dic43C2311yescharacteristic
102#13063258—21no—
103#13063258—21no—
104#13063256—21no—
105#13063256—21no—
106#13063252C2×C414yescomplemented
107#13063252C2×C414yescomplemented
108#13063249—21no—
109#13063249D411yescharacteristic, complemented
110#13063249D411yescharacteristic, complemented
111#13063247—21no—
112#13063247—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246D411yescharacteristic, complemented
119#13063246D411yescharacteristic, complemented
120#13063245—21no—
121#13063245—21no—
122#13063242C2×C414yescomplemented
123#13063241—41no—
124#13063236—21no—
125#13063235—21no—
126C4×C43⋊C8—21no—
127C8×Dic43—21no—
128C8×Dic43—41no—
129H(5,𝔽2)×C43—22no—
130H(5,𝔽2)×C43—22no—
131H(5,𝔽2)×C43—41no—
132H(5,𝔽2)×C43C2×C414yescomplemented
133C2×#41×C43—21no—
134C2×#41×C43—21no—
135C2×#41×C43C2311yescharacteristic
136C2×#41×C43C2311yescharacteristic
137C22×D4×C43—21no—
138C22×D4×C43—21no—
139C22×D4×C43—41no—
140C22×D4×C43C2311yescharacteristic
141#131×C43—22no—
142#131×C43—41no—
143C2×M16×C43—21no—
144C2×M16×C43C2311yescharacteristic
145C22×C8×C43—21no—
146C22×C8×C43C2311yescharacteristic
147C4×Q8×C43—21no—
148C4×D4×C43—21no—
149C4×D4×C43—41no—
150#117×C43—21no—
151#117×C43C2311yescharacteristic
152C2×C4⋊C4×C43—21no—
153C2×C4⋊C4×C43C2311yescharacteristic
154#103×C43—21no—
155#103×C43D411yescharacteristic, complemented
156#103×C43D411yescharacteristic, complemented
157#102×C43—21no—
158#102×C43—21no—
159#102×C43—21no—
160#102×C43—21no—
161#102×C43—21no—
162#102×C43D411yescharacteristic, complemented
163#102×C43D411yescharacteristic, complemented
164C24×C43—21no—
165C24×C43—41no—
166C23×D43—21no—
167#41×C43—21no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—24no—
172#41×C43—24no—
173#41×C43—42no—
174#41×C43—42no—
175#41×C43C22×C412yes—
176#41×C43C22×C412yes—
177#41×C43#4112yes—
178#41×C43#4112yes—
179C2×Q8×C43C2×D411yescharacteristic
180C2×Q8×C43C2×D411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—24no—
185C2×D4×C43—24no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—41no—
191C2×D4×C43—41no—
192C2×D4×C43—44no—
193C2×D4×C43—42no—
194C2×D4×C43—42no—
195C2×D4×C43—44no—
196C2×D4×C43C22×C412yes—
197C2×D4×C43C2×D411yescharacteristic
198C2×D4×C43C2×D411yescharacteristic
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—41no—
203C22×C4×C43—41no—
204C22×C4×C43C2411yescharacteristic
205C2×C22⋊D43—44no—
206C2×C22⋊D43—82no—
207C2×C22⋊D43—82no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—41no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172C22×C412yes—
217C2×C4×D43—41no—
218C2×C4×D43—41no—
219M16×C43—21no—
220M16×C43—21no—
221M16×C43—42no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—42no—
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
233C22⋊C4×C43—21no—
234C22⋊C4×C43—41no—
235C42×C43—21no—
236C42×C43—41no—
237C22⋊Dic43—21no—
238C22⋊Dic43—41no—
239#10621884—24no—
240#10621884—24no—
241#10621882—24no—
242#10621882—24no—
243(C2×D43)⋊C4—41no—
244(C2×D43)⋊C4—41no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—41no—
248C4⋊Dic43C2×D411yescharacteristic
249C4⋊Dic43C2×D411yescharacteristic
250Dic43⋊C4—82no—
251C4×Dic43—21no—
252C4×Dic43—21no—
253C4×Dic43—41no—
254C4×Dic43C22×C412yes—
255#10621877—21no—
256#10621877—21no—
257#10621877—21no—
258#10621877—21no—
259#10621877—42no—
260#10621877C22×C412yes—
261#10621877C22×C412yes—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—42no—
268C2×C43⋊C8C2×D411yescharacteristic
269C2×C43⋊C8C2×D411yescharacteristic
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—22no—
273C23×C43—44no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—81no—
277C23×C43—81no—
278C23×C43—161no—
279C23×C43—161no—
280C23×C43H(5,𝔽2)11yescharacteristic
281C22×D43—22no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—81no—
285C22×D43—81no—
286Q8×C43—21no—
287Q8×C43—21no—
288Q8×C43C4×D412yes—
289Q8×C43C4×D412yes—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—21no—
297D4×C43—21no—
298D4×C43—44no—
299D4×C43—44no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43C4×D412yes—
303D4×C43C4×D412yes—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—44no—
313C2×C4×C43—41no—
314C2×C4×C43—81no—
315C2×C4×C43—161no—
316C2×C4×C43C23×C411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C22⋊D43—88no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—41no—
329C2×Dic43—81no—
330C2×Dic43—161no—
331D172—22no—
332D172—22no—
333D172—41no—
334D172—41no—
335C4×D43—161no—
336C4×D43—161no—
337C8×C43—21no—
338C8×C43—21no—
339C8×C43—41no—
340C43⋊C8—22no—
341C43⋊C8—22no—
342C43⋊C8—21no—
343C43⋊C8—21no—
344C43⋊C8—41no—
345#22897—431nomaximal, Sylow
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—82no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—161no—
359C22×C43—164no—
360C22×C43#51811yescharacteristic
361C22×C43D4211yescharacteristic
362C22×C43#55111yescharacteristic
363C2×D43—42no—
364C2×D43—81no—
365C2×D43—81no—
366C2×D43—82no—
367C2×D43—161no—
368C4×C43—22no—
369C4×C43—22no—
370C4×C43—41no—
371C4×C43—41no—
372C4×C43—81no—
373C4×C43C2×C4×D411yescharacteristic
374C4×C43C2×C4×D411yescharacteristic
375C4×C43#54611yescharacteristic
376C4×C43#54611yescharacteristic
377Dic43—24no—
378Dic43—41no—
379Dic43—41no—
380Dic43—81no—
381C2×#453—431no—
382#2946—431no—
383#2946—431no—
384#2897—431no—
385#2897D4311yescharacteristic, complemented
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—42no—
400C2×C43—82no—
401C2×C43#235811yescharacteristic
402C2×C43#329111yescharacteristic
403C2×C43#329211yescharacteristic
404D43—82no—
405C2×H(5,𝔽2)C2×D4311yescharacteristic
406C2×AGL(1,ℤ/8)—431no—
407C2×AGL(1,ℤ/8)—431no—
408C2×#131—431no—
409C2×#131C2×D4311yescharacteristic
410C2×#127—431no—
411#520—431no—
412#520C2×D4311yescharacteristic
413#518—431no—
414#453—438no—
415#442—861no—
416#442—861no—
417#440—861no—
418#440—861no—
419C4×SD16—861no—
420C4×SD16—861no—
421C4×D8—861no—
422C4×D8—861no—
423#428—431no—
424#428—431no—
425C2×#104—431no—
426C2×#104—431no—
427#418—21no—
428#418—431no—
429#418—861no—
430#418C2×D4311yescharacteristic
431#417—21no—
432#417—431no—
433#417—861no—
434#417C2×D4311yescharacteristic
435#416—21no—
436#416—431no—
437#416—861no—
438#416C2×D4311yescharacteristic
439C2×#102—21no—
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×#102—861no—
444C2×#102C2×D4311yescharacteristic
445C2×#100—431no—
446C2×#100—431no—
447#405—431no—
448#405—431no—
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)—22no—
459H(5,𝔽2)—22no—
460H(5,𝔽2)—41no—
461H(5,𝔽2)C4×D4314yescomplemented
462C2×#41—21no—
463C2×#41—21no—
464C2×#41C22×D4311yescharacteristic
465C2×#41C22×D4311yescharacteristic
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—41no—
469C22×D4—431no—
470C22×D4—1721no—
471C22×D4C22×D4311yescharacteristic
472AGL(1,ℤ/8)—434no—
473AGL(1,ℤ/8)—434no—
474AGL(1,ℤ/8)—862no—
475AGL(1,ℤ/8)—862no—
476C2×SD16—861no—
477C2×SD16—861no—
478C2×D8—861no—
479C2×D8—861no—
480#131—22no—
481#131—41no—
482#131—862no—
483#131—1721no—
484C2×M16—21no—
485C2×M16—431no—
486C2×M16—431no—
487C2×M16—431no—
488C2×M16—861no—
489C2×M16C22×D4311yescharacteristic
490C22×C8—21no—
491C22×C8—431no—
492C22×C8—861no—
493C22×C8C22×D4311yescharacteristic
494#127—434no—
495#127—1721no—
496C4×Q8—21no—
497C4×Q8—861no—
498C4×D4—21no—
499C4×D4—41no—
500C4×D4—861no—
501C4×D4—861no—
502C4×D4—861no—
503C4×D4—861no—
504C4×D4—861no—
505C4×D4—1721no—
506#117—21no—
507#117—431no—
508#117—861no—
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—1721no—
516C2×C42—431no—
517#107—861no—
518#107—861no—
519#106—861no—
520#106—861no—
521#104—434no—
522#104—434no—
523#103—21no—
524#103—431no—
525#103—431no—
526#103—861no—
527#103C22⋊D4311yescharacteristic, complemented
528#103C22⋊D4311yescharacteristic, complemented
529#102—21no—
530#102—21no—
531#102—21no—
532#102—21no—
533#102—21no—
534#102—431no—
535#102—431no—
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—861no—
550#97—861no—
551C4×C8—861no—
552C4×C8—861no—
553C4×C8—1721no—
554C24—21no—
555C24—41no—
556C24—861no—
557#41—21no—
558#41—21no—
559#41—21no—
560#41—21no—
561#41—24no—
562#41—24no—
563#41—42no—
564#41—42no—
565#41C2×C4×D4312yes—
566#41C2×C4×D4312yes—
567#41#1062189812yes—
568#41#1062190012yes—
569C2×Q8D4×D4311yescharacteristic
570C2×Q8C2×C22⋊D4311yescharacteristic
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—432no—
587C2×D4—861no—
588C2×D4—861no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—3442no—
593C2×D4—3442no—
594C2×D4—1724no—
595C2×D4C2×C4×D4312yes—
596C2×D4D4×D4311yescharacteristic
597C2×D4C2×C22⋊D4311yescharacteristic
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—1721no—
606C22×C4—1721no—
607C22×C4—1721no—
608C22×C4C23×D4311yescharacteristic
609SD16—864no—
610SD16—864no—
611D8—864no—
612D8—864no—
613M16—21no—
614M16—21no—
615M16—42no—
616M16—432no—
617M16—432no—
618M16—861no—
619M16—861no—
620M16—861no—
621M16—861no—
622M16—1722no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—42no—
627C2×C8—431no—
628C2×C8—431no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—1722no—
635C2×C8C2×C22⋊D4311yescharacteristic
636C2×C8C2×C22⋊D4311yescharacteristic
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—41no—
640C4⋊C4—431no—
641C4⋊C4—431no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—3442no—
645C4⋊C4—1721no—
646C4⋊C4C2×C22⋊D4311yescharacteristic
647C4⋊C4C2×C22⋊D4311yescharacteristic
648C22⋊C4—21no—
649C22⋊C4—41no—
650C22⋊C4—861no—
651C22⋊C4—1721no—
652C22⋊C4—1721no—
653C22⋊C4—1721no—
654C42—21no—
655C42—41no—
656C42—432no—
657C42—861no—
658C42—861no—
659C42—1721no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—44no—
664C23—41no—
665C23—41no—
666C23—81no—
667C23—81no—
668C23—161no—
669C23—161no—
670C23—862no—
671C23—3441no—
672C23—3441no—
673C23—1721no—
674C23—1721no—
675C23#1306337011yescharacteristic
676Q8—21no—
677Q8—21no—
678Q8(C22⋊D43)⋊C412yes—
679Q8C4×C22⋊D4312yes—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—44no—
689D4—44no—
690D4—41no—
691D4—41no—
692D4—862no—
693D4—862no—
694D4—3448no—
695D4—1721no—
696D4—1721no—
697D4(C22⋊D43)⋊C412yes—
698D4C4×C22⋊D4312yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—44no—
708C2×C4—41no—
709C2×C4—81no—
710C2×C4—161no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—3441no—
717C2×C4—1721no—
718C2×C4—6881no—
719C2×C4—6881no—
720C2×C4—6881no—
721C2×C4C22×C4×D4311yescharacteristic
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4C22×C22⋊D4311yescharacteristic
724C2×C4C2×#1062190011yescharacteristic
725C2×C4C2×#1062189811yescharacteristic
726C2×C4#1306337011yescharacteristic
727C8—21no—
728C8—21no—
729C8—41no—
730C8—862no—
731C8—862no—
732C8—861no—
733C8—861no—
734C8—1721no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—82no—
745C22—81no—
746C22—81no—
747C22—161no—
748C22—164no—
749C22—3442no—
750C22—3441no—
751C22—3441no—
752C22—1722no—
753C22—6881no—
754C22#1458337211yescharacteristic
755C22D4×C22⋊D4311yescharacteristic
756C22#1458357511yescharacteristic
757C4—22no—
758C4—22no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—864no—
763C4—3441no—
764C4—1721no—
765C4—1721no—
766C4C2×(C22⋊D43)⋊C411yescharacteristic
767C4C2×C4×C22⋊D4311yescharacteristic
768C4#1458353911yescharacteristic
769C4#1458354311yescharacteristic
770C2—21no—
771C2—21no—
772C2—42no—
773C2—42no—
774C2—82no—
775C2—3442no—
776C2#1913757411yescharacteristic
777C2#1914638611yescharacteristic
778C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2897C2
socleC22×C43D42
prime radicalC2×#14583067C2
cosocleC22×C4×C43C24
hypercenter#2897D43
hypocenterC43#22897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. #19143430C2semidirect
3. #19143423C2semidirect
4. #19143121C2semidirect
5. #19135399C2semidirect
6. #19135260C2semidirect
7. #19135254C2semidirect
8. #19135103C2semidirect
9. #19135101C2semidirect
10. #19134990C2semidirect
11. #19134821C2semidirect
12. #19134819C2semidirect
13. #19134435C2semidirect
14. #19134430C2semidirect
15. C43×#2897C2semidirect
21. #14583373C22semidirect
22. #14583067C4semidirect
31. #14582942C22semidirect
32. #14582939C22semidirect
41. C2×#13063247C22semidirect
44. C2×#13063245C22semidirect
46. C2×#13063241C22semidirect
47. #14582855C22semidirect
48. #14582854C22semidirect
49. C2×C8×Dic43C22semidirect
50. #14582768C22semidirect
51. #14582668C22semidirect
52. #14582667C22semidirect
53. #14582664C22semidirect
54. #14582663C22semidirect
55. #14582660C22semidirect
56. #14582658C22semidirect
72. #13063350C2×C4semidirect
73. #13063350C2×C4semidirect
87. #13063321C2×C4semidirect
106. #13063252C2×C4semidirect
107. #13063252C2×C4semidirect
109. #13063249D4semidirect
110. #13063249D4semidirect
118. #13063246D4semidirect
119. #13063246D4semidirect
122. #13063242C2×C4semidirect
132. H(5,𝔽2)×C43C2×C4semidirect
155. #103×C43D4semidirect
156. #103×C43D4semidirect
162. #102×C43D4semidirect
163. #102×C43D4semidirect
385. #2897D43semidirect
457. C43#22897semidirect
461. H(5,𝔽2)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×#145830672
#191434302
#191434232
#191431212
#191353992
#191352602
#191352542
#191351032
#191351012
#191349902
#191348212
#191348192
#191344352
#191344302
C43×#28972
#2289743