Finite Group Databasebeta

← #25138094

Subgroups — #25138094

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144413C211yesmaximal, characteristic, complemented
2C4×#13063351C211yesmaximal, characteristic
3#19143260C211yesmaximal, characteristic, complemented
4#19136041C211yesmaximal, characteristic, complemented
5#19136036C211yesmaximal, characteristic, complemented
6#19135888C211yesmaximal, characteristic
7#19135888C211yesmaximal, characteristic
8#19135589C211yesmaximal, characteristic, complemented
9#19135378C211yesmaximal, characteristic, complemented
10#19135373C211yesmaximal, characteristic, complemented
11#19135371C211yesmaximal, characteristic, complemented
12#19135254C211yesmaximal, characteristic, complemented
13#19135254C211yesmaximal, characteristic, complemented
14#19134587C211yesmaximal, characteristic, complemented
15C2×C43×#478C211yesmaximal, characteristic, complemented
16C2×#13063351C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583203—21no—
19#14583203—21no—
20#14583196—21no—
21#14583196—21no—
22#14583009—21no—
23#14582999—21no—
24C4×#10621883—21no—
25C4×#10621882—21no—
26#14582959—21no—
27#14582959—21no—
28#14582955—21no—
29#14582951—21no—
30C2×#13063261C2211yescharacteristic
31C2×#13063261C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582939C2211yescharacteristic
34#14582939C2211yescharacteristic
35#14582923C2211yescharacteristic
36#14582923C2211yescharacteristic
37#14582904C2211yescharacteristic
38#14582898C2211yescharacteristic
39#14582898C2211yescharacteristic
40#14582898C2211yescharacteristic
41C2×#13063242C2211yescharacteristic
42C2×#13063242C2211yescharacteristic
43#14582865C2211yescharacteristic
44#14582865C2211yescharacteristic
45#14582854C2211yescharacteristic
46#14582854C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582668C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C2×#125×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#478—21no—
59C43×#478—21no—
60C43×#478—21no—
61C43×#478—21no—
62C2×#107×C43C2211yescharacteristic
63C2×#106×C43C2211yescharacteristic
64C2×C4⋊C8×C43C2211yescharacteristic
65C2×#102×C43C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063351—22no—
69#13063351—22no—
70C2×#10621883—21no—
71C2×#10621882—21no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C4×Dic86D411yescharacteristic
79C4×Dic86D411yescharacteristic
80C4×D172D411yescharacteristic
81C4×D172D411yescharacteristic
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84#13063284C2311yescharacteristic
85#13063282—21no—
86C42×D43—21no—
87#13063261—22no—
88#13063261—22no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063246—21no—
103#13063246—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063242—22no—
108#13063242—22no—
109(C2×D43)⋊C8—21no—
110(C2×D43)⋊C8—21no—
111(C2×D43)⋊C8—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114#13063235—21no—
115#13063235—21no—
116C4×C43⋊C8—21no—
117C8×Dic43—21no—
118C8×Dic43—21no—
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43—21no—
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123#125×C43—21no—
124#125×C43—21no—
125#125×C43—21no—
126#125×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138#107×C43—21no—
139#107×C43—21no—
140#106×C43—21no—
141#106×C43—21no—
142C4⋊C8×C43D411yescharacteristic
143C4⋊C8×C43D411yescharacteristic
144C4⋊C8×C43D411yescharacteristic
145C4⋊C8×C43D411yescharacteristic
146#102×C43—21no—
147#102×C43—21no—
148#102×C43—21no—
149#102×C43—21no—
150C24×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43#4112yes—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×C4×C43—82no—
163C22×C4×C43#4111yescharacteristic
164C22×C4×C43#4111yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—21no—
167#10621898—21no—
168#10621898—21no—
169#10621898—21no—
170#10621898—21no—
171C2×D172C2×D411yescharacteristic
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×Dic86C2×D411yescharacteristic
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43—41no—
194C22⋊C4×C43—41no—
195C22⋊C4×C43—41no—
196C42×C43C2×D411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C22⋊Dic43—21no—
201#10621883—24no—
202#10621882—24no—
203(C2×D43)⋊C4—21no—
204(C2×D43)⋊C4—21no—
205C4⋊Dic43C2×D411yescharacteristic
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—21no—
208Dic43⋊C4—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—21no—
223#10621877#4112yes—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C23×C43—22no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—81no—
234C23×C43—81no—
235C23×C43C2×#4111yescharacteristic
236C22×D43—21no—
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—41no—
240D4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—82no—
247C2×C4×C43—82no—
248C2×C4×C43—81no—
249C2×C4×C43—81no—
250C2×C4×C43—81no—
251C2×C4×C43#12111yescharacteristic
252C2×C4×C43#12111yescharacteristic
253C2×C4×C43#12111yescharacteristic
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C22⋊D43—41no—
262C22⋊D43—41no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266D172—21no—
267D172—21no—
268C4×D43—42no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—81no—
272Dic86—21no—
273Dic86—21no—
274C8×C43—21no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—21no—
278C43⋊C8—22no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#24724—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—42no—
288C22×C43—82no—
289C22×C43—82no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43C2×#12111yescharacteristic
293C22×C43#55211yescharacteristic
294C22×C43#55611yescharacteristic
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43#52511yescharacteristic
306C4×C43#53611yescharacteristic
307C4×C43#54711yescharacteristic
308C4×C43#54811yescharacteristic
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312#3080—431no—
313C2×#478D4311yescharacteristic, complemented
314C4×AGL(1,ℤ/8)—431no—
315#2925—431no—
316#2079—431no—
317#2078—431no—
318#2051—431no—
319#2051—431no—
320#1998—431no—
321#1952—431no—
322#1951—431no—
323#1950—431no—
324#1931—431no—
325#1931—431no—
326#1800—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—82no—
330C2×C43#241511yescharacteristic
331C2×C43#306711yescharacteristic
332C2×C43#306811yescharacteristic
333D43—81no—
334C2×AGL(1,ℤ/8)—431no—
335C2×#125C2×D4311yescharacteristic
336C4×#41—431no—
337C2×C4×D4C2×D4311yescharacteristic
338#479—861no—
339#479—861no—
340#478—21no—
341#478—21no—
342#478—21no—
343#478—21no—
344#478—861no—
345#478—861no—
346#442—861no—
347#440—861no—
348C4×SD16—861no—
349C4×D8—861no—
350#433—861no—
351#433—861no—
352#432—861no—
353#431—861no—
354C2×#108—431no—
355C2×#108—431no—
356#428—431no—
357#428—431no—
358#428—431no—
359C2×#107C2×D4311yescharacteristic
360C2×#106C2×D4311yescharacteristic
361#423—431no—
362#423—431no—
363C2×C4⋊C8C2×D4311yescharacteristic
364#418—431no—
365#417—431no—
366#417—431no—
367#417—431no—
368C2×#102C2×D4311yescharacteristic
369C2×#102C2×D4311yescharacteristic
370C2×#100—431no—
371C2×#100—431no—
372#408—431no—
373#408—431no—
374#405—431no—
375#405—431no—
376C4×M16—431no—
377#343—431no—
378#343—431no—
379#343—431no—
380#343—431no—
381#343—431no—
382#343—431no—
383#341—431no—
384#341—431no—
385C43#2472411yescharacteristic, complemented, Sylow
386C2×#41—431no—
387C22×D4C22×D4311yescharacteristic
388C23×C4—21no—
389AGL(1,ℤ/8)—862no—
390AGL(1,ℤ/8)—862no—
391C2×SD16—861no—
392C2×D8—861no—
393C2×M16—431no—
394C2×M16—431no—
395C2×M16—431no—
396C2×M16—431no—
397C2×M16—431no—
398C2×M16—431no—
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401#125—21no—
402#125—21no—
403#125—21no—
404#125—21no—
405C4×Q8—431no—
406C4×Q8—431no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—861no—
414C4×D4—861no—
415#117—431no—
416#117—861no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C42—861no—
424C2×C42C22×D4311yescharacteristic
425#108—862no—
426#108—862no—
427#107—21no—
428#107—21no—
429#107—861no—
430#107—861no—
431#107—861no—
432#106—21no—
433#106—21no—
434#106—861no—
435#106—861no—
436#106—861no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439C4⋊C8—861no—
440C4⋊C8—861no—
441C4⋊C8C22⋊D4311yescharacteristic
442C4⋊C8C22⋊D4311yescharacteristic
443C4⋊C8C22⋊D4311yescharacteristic
444C4⋊C8C22⋊D4311yescharacteristic
445#103—861no—
446#103—861no—
447#103—861no—
448#102—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#100—862no—
458#100—862no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463#97—861no—
464#97—861no—
465#97—861no—
466C4×C8—861no—
467C4×C8—861no—
468C4×C8—861no—
469C24—21no—
470#41—861no—
471#41—861no—
472#41—861no—
473#41—861no—
474C2×Q8—431no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—431no—
481C2×D4—861no—
482C2×D4#1062190212yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—82no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4#1062190011yescharacteristic
493C22×C4#1062190011yescharacteristic
494C22×C4C23×D4311yescharacteristic
495SD16—864no—
496D8—864no—
497M16—432no—
498M16—861no—
499M16—861no—
500M16—861no—
501M16—861no—
502M16—861no—
503M16—861no—
504M16—861no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16—861no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8C2×C22⋊D4311yescharacteristic
520C2×C8C2×C22⋊D4311yescharacteristic
521C2×C8C2×C22⋊D4311yescharacteristic
522C2×C8C2×C22⋊D4311yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—431no—
534C4⋊C4—431no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C42—861no—
543C42—861no—
544C42—861no—
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42C2×C22⋊D4311yescharacteristic
548C42C2×C22⋊D4311yescharacteristic
549C23—22no—
550C23—41no—
551C23—41no—
552C23—81no—
553C23—81no—
554C23—861no—
555C23C2×#1062190011yescharacteristic
556Q8—861no—
557Q8—861no—
558D4—22no—
559D4—22no—
560D4—41no—
561D4—41no—
562D4—861no—
563D4—861no—
564D4—1721no—
565D4—1721no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—81no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—3441no—
580C2×C4—1722no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4#1306329611yescharacteristic
584C2×C4#1306329611yescharacteristic
585C2×C4#1306329611yescharacteristic
586C2×C4#1306329611yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C22×C22⋊D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4C2×#1062190211yescharacteristic
591C2×C4#1306337211yescharacteristic
592C2×C4#1306337311yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—862no—
598C8—1721no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C22—21no—
604C22—21no—
605C22—42no—
606C22—82no—
607C22—82no—
608C22—81no—
609C22—81no—
610C22—1721no—
611C22—1721no—
612C22—1721no—
613C22C2×#1306329611yescharacteristic
614C22#1458359111yescharacteristic
615C22#1458362011yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—1721no—
624C4—1721no—
625C4—1721no—
626C4#1458341211yescharacteristic
627C4#1458347211yescharacteristic
628C4#1458354811yescharacteristic
629C4#1458356011yescharacteristic
630C2—21no—
631C2—21no—
632C2—82no—
633C2—3441no—
634C2#1913802011yescharacteristic
635C2#1914431111yescharacteristic
636C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#478C2
socleC22×C43C2×#121
prime radicalC2×#13063351C22
hypercenterC2×#478D43
hypocenterC43#24724
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. #19144413C2semidirect
3. #19143260C2semidirect
4. #19136041C2semidirect
5. #19136036C2semidirect
8. #19135589C2semidirect
9. #19135378C2semidirect
10. #19135373C2semidirect
11. #19135371C2semidirect
12. #19135254C2semidirect
13. #19135254C2semidirect
14. #19134587C2semidirect
15. C2×C43×#478C2semidirect
313. C2×#478D43semidirect
385. C43#24724semidirect

Maximal subgroups

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

subgroupindex
#191444132
C4×#130633512
#191432602
#191360412
#191360362
#191358882
#191355892
#191353782
#191353732
#191353712
#191352542
#191345872
C2×C43×#4782
#2472443