Finite Group Databasebeta

← #25166574

Subgroups — #25166574

Order 11008.

776 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144547C211yesmaximal, characteristic, complemented
2#19144420C211yesmaximal, characteristic, complemented
3#19143430C211yesmaximal, characteristic, complemented
4#19135955C211yesmaximal, characteristic, complemented
5#19135937C211yesmaximal, characteristic, complemented
6#19135885C211yesmaximal, characteristic, complemented
7#19135608C211yesmaximal, characteristic
8#19135399C211yesmaximal, characteristic, complemented
9#19135301C211yesmaximal, characteristic, complemented
10#19135257C211yesmaximal, characteristic, complemented
11#19135254C211yesmaximal, characteristic, complemented
12#19134990C211yesmaximal, characteristic, complemented
13#19134819C211yesmaximal, characteristic, complemented
14#19134475C211yesmaximal, characteristic, complemented
15C43×#3136C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583373C2211yescharacteristic
20#14583220—21no—
21#14583220—21no—
22#14583215—21no—
23#14583210—21no—
24#14583196—21no—
25#14583196—21no—
26#14583186—21no—
27#14583176—21no—
28#14583008—21no—
29#14583002—21no—
30#14582984—21no—
31#14582979—21no—
32C2×#13063260C2211yescharacteristic
33#14582942C2211yescharacteristic
34#14582942C2211yescharacteristic
35#14582939C2211yescharacteristic
36#14582935C2211yescharacteristic
37#14582926C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39#14582904C2211yescharacteristic
40#14582903C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063242C2211yescharacteristic
45C2×#13063241C2211yescharacteristic
46#14582866C2211yescharacteristic
47#14582854C2211yescharacteristic
48C2×C8×Dic43C2211yescharacteristic
49#14582768C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582658C2211yescharacteristic
56C43×#544C2211yescharacteristic
57C43×#535C2211yescharacteristic
58C43×#490—21no—
59C43×#489—21no—
60C43×#488—21no—
61C43×#486—21no—
62C43×#418C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C2×#102×C43C2211yescharacteristic
66C43×#405C2211yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C22⋊D43—41no—
69#13063350—22no—
70#13063350—22no—
71C2×#10621884—21no—
72C2×#10621882—21no—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063321—22no—
78#13063321—22no—
79Q8×Dic43—21no—
80C4×D172—21no—
81C4×D172—21no—
82D4×Dic43—21no—
83D4×Dic43—41no—
84#13063287—21no—
85#13063287—21no—
86#13063284—21no—
87#13063284C2311yescharacteristic
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—41no—
91C22⋊C4×D43—41no—
92C2×C4×Dic43C2311yescharacteristic
93#13063260—22no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258D411yescharacteristic, complemented
98#13063258D411yescharacteristic, complemented
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256D411yescharacteristic, complemented
103#13063256D411yescharacteristic, complemented
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)—21no—
106#13063252—22no—
107#13063247—21no—
108#13063247—21no—
109#13063246—21no—
110#13063246—21no—
111#13063246—21no—
112#13063246—21no—
113#13063245—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117#13063242—22no—
118#13063241—22no—
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121#13063235—21no—
122C8×Dic43—21no—
123C8×Dic43—22no—
124C2×#41×C43C2311yescharacteristic
125C22×D4×C43C2311yescharacteristic
126C2×M16×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C4⋊Q8×C43—21no—
129C4⋊Q8×C43—21no—
130#127×C43—21no—
131#125×C43—21no—
132#125×C43—21no—
133#124×C43—21no—
134C22⋊Q8×C43—41no—
135#121×C43—21no—
136#121×C43—21no—
137#120×C43—41no—
138#117×C43C2311yescharacteristic
139#117×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141#103×C43—21no—
142#103×C43D411yescharacteristic, complemented
143#103×C43D411yescharacteristic, complemented
144#102×C43—21no—
145#102×C43—21no—
146#102×C43—21no—
147#102×C43—21no—
148#102×C43—21no—
149#102×C43D411yescharacteristic, complemented
150#102×C43D411yescharacteristic, complemented
151#97×C43—21no—
152C4×C8×C43—21no—
153C24×C43—21no—
154C23×D43—21no—
155#41×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159C2×Q8×C43—41no—
160C2×Q8×C43C2×D411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—41no—
169C2×D4×C43—41no—
170C2×D4×C43C2×D411yescharacteristic
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2411yescharacteristic
174C2×C22⋊D43—44no—
175C2×C22⋊D43—82no—
176C2×C22⋊D43—82no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—41no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172#4112yes—
186C2×C4×D43—41no—
187C2×C4×D43—41no—
188M16×C43—21no—
189M16×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—41no—
198C4⋊C4×C43—41no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43C2×D411yescharacteristic
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C42×C43—21no—
209C42×C43—21no—
210C22⋊Dic43—21no—
211C22⋊Dic43—41no—
212#10621884—24no—
213#10621882—24no—
214(C2×D43)⋊C4—41no—
215(C2×D43)⋊C4—41no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—41no—
219C4⋊Dic43C2×D411yescharacteristic
220C4⋊Dic43C2×D411yescharacteristic
221Dic43⋊C4—82no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—41no—
225C4×Dic43#4112yes—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877#4112yes—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8C2×D411yescharacteristic
238C2×C43⋊C8C2×D411yescharacteristic
239C23×C43—21no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—81no—
244C23×C43—81no—
245C23×C43H(5,𝔽2)11yescharacteristic
246C22×D43—22no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—81no—
250C22×D43—81no—
251Q8×C43—21no—
252Q8×C43—21no—
253Q8×C43—161no—
254D4×C43—21no—
255D4×C43—21no—
256D4×C43—41no—
257D4×C43—41no—
258D4×C43—41no—
259D4×C43—41no—
260D4×C43—41no—
261D4×C43—41no—
262D4×C43—161no—
263D4×C43—161no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—81no—
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×C4×C432−1+411yescharacteristic
279C22⋊D43—88no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—41no—
286C2×Dic43—81no—
287C2×Dic43—161no—
288D172—22no—
289D172—22no—
290D172—41no—
291D172—41no—
292C4×D43—161no—
293C4×D43—161no—
294C8×C43—21no—
295C8×C43—21no—
296C8×C43—41no—
297C43⋊C8—22no—
298C43⋊C8—21no—
299C43⋊C8—21no—
300C43⋊C8—41no—
301C43⋊C8—41no—
302#26850—431nomaximal, Sylow
303C22×C43—21no—
304C22×C43—21no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—82no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—161no—
313C22×C43#54211yescharacteristic
314C22×C43D4211yescharacteristic
315C22×C43#55111yescharacteristic
316C2×D43—42no—
317C2×D43—81no—
318C2×D43—81no—
319C2×D43—82no—
320C2×D43—161no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43—41no—
325C4×C43—41no—
326C4×C43—81no—
327C4×C43#52511yescharacteristic
328C4×C43#53211yescharacteristic
329C4×C43#54711yescharacteristic
330C4×C43#54811yescharacteristic
331Dic43—24no—
332Dic43—41no—
333Dic43—41no—
334Dic43—81no—
335#3136D4311yescharacteristic, complemented
336#3096—431no—
337#3081—431no—
338#2946—431no—
339#2063—431no—
340#2060—431no—
341#2051—431no—
342#2002—431no—
343#1957—431no—
344#1937—431no—
345#1931—431no—
346#1931—431no—
347#1887—431no—
348#1859—431no—
349#1772—431no—
350C2×C43—21no—
351C2×C43—21no—
352C2×C43—81no—
353C2×C43—161no—
354C2×C43#246111yescharacteristic
355C2×C43#329111yescharacteristic
356C2×C43#329211yescharacteristic
357D43—82no—
358C2×AGL(1,ℤ/8)—431no—
359#544C2×D4311yescharacteristic
360#535C2×D4311yescharacteristic
361C2×#127—431no—
362#520—431no—
363#518—431no—
364#490—21no—
365#489—21no—
366#488—21no—
367#486—21no—
368#482—861no—
369#482—861no—
370#481—861no—
371#480—861no—
372#478—861no—
373#478—861no—
374#476—861no—
375#474—861no—
376#442—861no—
377#440—861no—
378C4×SD16—861no—
379C4×D8—861no—
380C2×#108—431no—
381#428—431no—
382#428—431no—
383#428—431no—
384#427—431no—
385#424—431no—
386C2×#104—431no—
387#418—431no—
388#418—431no—
389#418C2×D4311yescharacteristic
390#417C2×D4311yescharacteristic
391#416C2×D4311yescharacteristic
392C2×#102—431no—
393C2×#102—431no—
394C2×#102—431no—
395C2×#102C2×D4311yescharacteristic
396C2×#100—431no—
397C2×#100—431no—
398#408—431no—
399#405—431no—
400#405C2×D4311yescharacteristic
401C2×C4×C8—431no—
402#384—431no—
403#343—431no—
404#343—431no—
405#341—431no—
406#339—431no—
407#339—431no—
408#339—431no—
409C43#2685011yescharacteristic, complemented, Sylow
410C2×#41C22×D4311yescharacteristic
411C22×D4—431no—
412C22×D4—1721no—
413C22×D4C22×D4311yescharacteristic
414AGL(1,ℤ/8)—862no—
415AGL(1,ℤ/8)—862no—
416C2×SD16—861no—
417C2×D8—861no—
418C2×M16—431no—
419C2×M16—431no—
420C2×M16—431no—
421C2×M16C22×D4311yescharacteristic
422C22×C8—431no—
423C22×C8C22×D4311yescharacteristic
424C4⋊Q8—21no—
425C4⋊Q8—21no—
426#127—21no—
427#127—862no—
428#127—862no—
429#125—21no—
430#125—21no—
431#124—21no—
432C22⋊Q8—41no—
433#121—21no—
434#121—21no—
435#120—41no—
436C4×Q8—861no—
437C4×D4—861no—
438C4×D4—861no—
439C4×D4—861no—
440C4×D4—861no—
441C4×D4—861no—
442C4×D4—1721no—
443#117—431no—
444#117—861no—
445#117C22×D4311yescharacteristic
446#117C22×D4311yescharacteristic
447C2×C4⋊C4—431no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—1721no—
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C22⋊C4—1721no—
452C2×C42—431no—
453#108—862no—
454#107—431no—
455#107—431no—
456#107—861no—
457#107—861no—
458#107—861no—
459#106—431no—
460#106—431no—
461#106—861no—
462#106—861no—
463#106—861no—
464C4⋊C8—861no—
465C4⋊C8—861no—
466#104—862no—
467#103—21no—
468#103C22⋊D4311yescharacteristic, complemented
469#103C22⋊D4311yescharacteristic, complemented
470#102—21no—
471#102—21no—
472#102—21no—
473#102—21no—
474#102—21no—
475#102—861no—
476#102—861no—
477#102—861no—
478#102—861no—
479#102—861no—
480#102—861no—
481#102—861no—
482#102—861no—
483#102—861no—
484#102—861no—
485#102C22⋊D4311yescharacteristic, complemented
486#102C22⋊D4311yescharacteristic, complemented
487#100—862no—
488#100—862no—
489C22⋊C8—861no—
490C22⋊C8—861no—
491#97—21no—
492#97—861no—
493C4×C8—21no—
494C4×C8—862no—
495C4×C8—861no—
496C24—21no—
497C24—861no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41—21no—
502C2×Q8—41no—
503C2×Q8C2×C22⋊D4311yescharacteristic
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—432no—
514C2×D4—861no—
515C2×D4—861no—
516C2×D4—861no—
517C2×D4—861no—
518C2×D4—861no—
519C2×D4—3442no—
520C2×D4—3442no—
521C2×D4—1724no—
522C2×D4C2×C22⋊D4311yescharacteristic
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—1721no—
528C22×C4—1721no—
529C22×C4—1721no—
530C22×C4C23×D4311yescharacteristic
531SD16—864no—
532D8—864no—
533M16—21no—
534M16—21no—
535M16—432no—
536M16—861no—
537M16—861no—
538M16—861no—
539M16—861no—
540M16—861no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—431no—
545C2×C8—431no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8C2×C22⋊D4311yescharacteristic
552C2×C8C2×C22⋊D4311yescharacteristic
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—431no—
559C4⋊C4—431no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—3442no—
563C4⋊C4—1721no—
564C4⋊C4D4×D4311yescharacteristic
565C4⋊C4D4×D4311yescharacteristic
566C4⋊C4C2×C22⋊D4311yescharacteristic
567C4⋊C4C2×C22⋊D4311yescharacteristic
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—861no—
573C22⋊C4—1721no—
574C22⋊C4—1721no—
575C22⋊C4—1721no—
576C42—21no—
577C42—21no—
578C42—432no—
579C42—861no—
580C42—861no—
581C42—1721no—
582C23—21no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—81no—
587C23—81no—
588C23—862no—
589C23—3441no—
590C23—3441no—
591C23—1721no—
592C23—1721no—
593C23#1306337011yescharacteristic
594Q8—21no—
595Q8—21no—
596Q8—161no—
597D4—21no—
598D4—21no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—161no—
606D4—161no—
607D4—862no—
608D4—862no—
609D4—3448no—
610D4—1721no—
611D4—1721no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—81no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—3441no—
627C2×C4—1721no—
628C2×C4—6881no—
629C2×C4—6881no—
630C2×C4—6881no—
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4C22×C22⋊D4311yescharacteristic
633C2×C4#41×D4311yescharacteristic
634C2×C4#41×D4311yescharacteristic
635C2×C4#41×D4311yescharacteristic
636C2×C4#1306337211yescharacteristic
637C8—21no—
638C8—21no—
639C8—41no—
640C8—862no—
641C8—861no—
642C8—861no—
643C8—1721no—
644C8—1721no—
645C22—21no—
646C22—21no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—82no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—161no—
655C22—3442no—
656C22—3441no—
657C22—3441no—
658C22—1722no—
659C22—6881no—
660C22#1458351311yescharacteristic
661C22D4×C22⋊D4311yescharacteristic
662C22#1458357911yescharacteristic
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—81no—
669C4—864no—
670C4—3441no—
671C4—1721no—
672C4—1721no—
673C4#1458340611yescharacteristic
674C4#1458344811yescharacteristic
675C4#1458354811yescharacteristic
676C4#1458355711yescharacteristic
677C2—21no—
678C2—21no—
679C2—81no—
680C2—161no—
681C2—3442no—
682C2#1913855811yescharacteristic
683C2#1914638611yescharacteristic
684C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3136C2
socleC22×C43D42
prime radical#19135608C2
hypercenter#3136D43
hypocenterC43#26850
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3136

Complements

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

NH ≅ G/Ntype
1. #19144547C2semidirect
2. #19144420C2semidirect
3. #19143430C2semidirect
4. #19135955C2semidirect
5. #19135937C2semidirect
6. #19135885C2semidirect
8. #19135399C2semidirect
9. #19135301C2semidirect
10. #19135257C2semidirect
11. #19135254C2semidirect
12. #19134990C2semidirect
13. #19134819C2semidirect
14. #19134475C2semidirect
15. C43×#3136C2semidirect
97. #13063258D4semidirect
98. #13063258D4semidirect
102. #13063256D4semidirect
103. #13063256D4semidirect
142. #103×C43D4semidirect
143. #103×C43D4semidirect
149. #102×C43D4semidirect
150. #102×C43D4semidirect
335. #3136D43semidirect
409. C43#26850semidirect
468. #103C22⋊D43semidirect
469. #103C22⋊D43semidirect
485. #102C22⋊D43semidirect
486. #102C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191445472
#191444202
#191434302
#191359552
#191359372
#191358852
#191356082
#191353992
#191353012
#191352572
#191352542
#191349902
#191348192
#191344752
C43×#31362
#2685043