Finite Group Databasebeta

← #25157065

Subgroups — #25157065

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144547C211yesmaximal, characteristic, complemented
2#19143479C211yesmaximal, characteristic, complemented
3#19143188C211yesmaximal, characteristic, complemented
4#19136126C211yesmaximal, characteristic, complemented
5#19136105C211yesmaximal, characteristic, complemented
6#19136043C211yesmaximal, characteristic, complemented
7#19135802C211yesmaximal, characteristic, complemented
8#19135254C211yesmaximal, characteristic, complemented
9#19135191C211yesmaximal, characteristic, complemented
10#19135105C211yesmaximal, characteristic, complemented
11#19134973C211yesmaximal, characteristic, complemented
12#19134924C211yesmaximal, characteristic, complemented
13#19134821C211yesmaximal, characteristic, complemented
14#19134819C211yesmaximal, characteristic, complemented
15C43×#3045C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583382C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583220—21no—
20#14583220—21no—
21#14583215—21no—
22#14583210—21no—
23#14583011—21no—
24#14583006—21no—
25SD16×Dic43—21no—
26SD16×Dic43—21no—
27#14582942—21no—
28#14582942C2211yescharacteristic
29#14582942C2211yescharacteristic
30#14582939—21no—
31#14582939C2211yescharacteristic
32#14582935—21no—
33#14582935C2211yescharacteristic
34C2×#13063257C2211yescharacteristic
35C2×#13063256—21no—
36C2×#13063256C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39#14582904C2211yescharacteristic
40#14582900C2211yescharacteristic
41#14582900C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063242C2211yescharacteristic
44#14582866C2211yescharacteristic
45#14582854C2211yescharacteristic
46#14582802C2211yescharacteristic
47#14582768C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582664C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
57C2×#135×C43C2211yescharacteristic
58C43×#535C2211yescharacteristic
59C43×#520C2211yescharacteristic
60C43×#464—21no—
61C43×#463—21no—
62C43×#460—21no—
63C43×#459—21no—
64C43×#424C2211yescharacteristic
65C43×#417C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C22×C43⋊C8—21no—
74C22×C43⋊C8C2311yescharacteristic
75Q8×Dic43—21no—
76Q8×Dic43—21no—
77D4×Dic43—21no—
78D4×Dic43—21no—
79D4×Dic43—41no—
80D4×Dic43—41no—
81#13063284—21no—
82#13063284—21no—
83#13063284C2311yescharacteristic
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—41no—
89C2×C22⋊Dic43—41no—
90C2×C4×Dic43C2311yescharacteristic
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258D411yescharacteristic
95#13063258D411yescharacteristic
96#13063257—21no—
97#13063257—21no—
98#13063256—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256D411yescharacteristic
104#13063256D411yescharacteristic
105#13063252—22no—
106#13063252—22no—
107#13063249—21no—
108#13063249—21no—
109#13063246—21no—
110#13063246—21no—
111#13063246—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063242—22no—
116C22⋊(C43⋊C8)—21no—
117C22⋊(C43⋊C8)—21no—
118#13063235—21no—
119C8×Dic43—21no—
120C2×#41×C43C2311yescharacteristic
121C2×#41×C43C2311yescharacteristic
122C22×D4×C43C2311yescharacteristic
123AGL(1,ℤ/8)×C43—22no—
124AGL(1,ℤ/8)×C43—22no—
125#135×C43—22no—
126#135×C43—22no—
127C2×Q16×C43D411yescharacteristic
128C2×SD16×C43—21no—
129C2×SD16×C43D411yescharacteristic
130C2×SD16×C43D411yescharacteristic
131C2×D8×C43—21no—
132C2×D8×C43D411yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135#127×C43—21no—
136#124×C43—21no—
137#121×C43—21no—
138#121×C43—21no—
139#120×C43—41no—
140C4×Q8×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43—41no—
143#117×C43—21no—
144#117×C43C2311yescharacteristic
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C4⋊C8×C43—21no—
148C4⋊C8×C43—21no—
149#103×C43—21no—
150#102×C43—21no—
151#102×C43—21no—
152#102×C43—21no—
153C24×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43—21no—
160#41×C43#4112yes—
161#41×C43#4112yes—
162C2×Q8×C43C2×D411yescharacteristic
163C2×Q8×C43C2×D411yescharacteristic
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—41no—
173C2×D4×C43—41no—
174C2×D4×C43C2×D411yescharacteristic
175C2×D4×C43C2×D411yescharacteristic
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—41no—
180C22×C4×C43C2411yescharacteristic
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—41no—
185C22×Dic43—41no—
186Q16×C43—22no—
187SD16×C43—22no—
188SD16×C43—22no—
189SD16×C43—42no—
190D8×C43—22no—
191D8×C43—42no—
192M16×C43—21no—
193M16×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C2×D411yescharacteristic
198C2×C8×C43C2×D411yescharacteristic
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C22⋊C4×C43—21no—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C42×C43—21no—
209C42×C43—41no—
210C22⋊Dic43—21no—
211C22⋊Dic43—41no—
212C22⋊Dic43—41no—
213C22⋊Dic43—82no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—41no—
219C4⋊Dic43—41no—
220C4⋊Dic43C2×D411yescharacteristic
221C4⋊Dic43C2×D411yescharacteristic
222Dic43⋊C4—82no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—41no—
227C4×Dic43—41no—
228#10621877—24no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877#4112yes—
235C2×C43⋊C8—24no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8C2×D411yescharacteristic
242C2×C43⋊C8C2×D411yescharacteristic
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—81no—
249C23×C43—81no—
250C23×C43H(5,𝔽2)11yescharacteristic
251Q8×C43—21no—
252Q8×C43—21no—
253Q8×C43—21no—
254Q8×C43#12312yes—
255D4×C43—22no—
256D4×C43—22no—
257D4×C43—21no—
258D4×C43—21no—
259D4×C43—21no—
260D4×C43—41no—
261D4×C43—41no—
262D4×C43—41no—
263D4×C43—41no—
264D4×C43—41no—
265D4×C43—41no—
266D4×C43—161no—
267D4×C43—161no—
268D4×C43#12312yes—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—81no—
279C2×C4×C43—161no—
280C2×C4×C43C22×D411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C432−1+411yescharacteristic
286C2×Dic43—22no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—81no—
294C2×Dic43—81no—
295C2×Dic43—161no—
296C2×Dic43—161no—
297C8×C43—21no—
298C8×C43—21no—
299C8×C43—41no—
300C43⋊C8—21no—
301C43⋊C8—22no—
302C43⋊C8—21no—
303C43⋊C8—41no—
304C43⋊C8—41no—
305#26191—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—22no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—82no—
315C22×C43—81no—
316C22×C43—81no—
317C22×C43—81no—
318C22×C43—161no—
319C22×C43#53911yescharacteristic
320C22×C43D4211yescharacteristic
321C22×C43#55311yescharacteristic
322C4×C43—22no—
323C4×C43—41no—
324C4×C43—41no—
325C4×C43—41no—
326C4×C43—81no—
327C4×C43C2×#12311yescharacteristic
328C4×C43#52511yescharacteristic
329C4×C43#54711yescharacteristic
330C4×C43#54811yescharacteristic
331Dic43—42no—
332Dic43—41no—
333Dic43—41no—
334Dic43—81no—
335Dic43—81no—
336#3096—431no—
337#3045D4311yescharacteristic
338#2952—431no—
339#2912—431no—
340#2094—431no—
341#2090—431no—
342#2079—431no—
343#2037—431no—
344#1931—431no—
345#1922—431no—
346#1907—431no—
347#1883—431no—
348#1876—431no—
349#1859—431no—
350#1859—431no—
351C2×C43—21no—
352C2×C43—21no—
353C2×C43—42no—
354C2×C43—81no—
355C2×C43—161no—
356C2×C43#244311yescharacteristic
357C2×C43#328811yescharacteristic
358C2×C43#329111yescharacteristic
359C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
360C2×#135C2×D4311yescharacteristic
361C2×#131—431no—
362#535C2×D4311yescharacteristic
363#520—431no—
364#520—431no—
365#520C2×D4311yescharacteristic
366#482—861no—
367#482—861no—
368#481—861no—
369#480—861no—
370#464—21no—
371#463—21no—
372#460—21no—
373#459—21no—
374#442—861no—
375#441—861no—
376C4×SD16—861no—
377C4×SD16—861no—
378#428—431no—
379#428—431no—
380#428—431no—
381#428—861no—
382#428—861no—
383#427—431no—
384#427—861no—
385C2×#106—431no—
386C2×#106—431no—
387C2×#106—861no—
388#424C2×D4311yescharacteristic
389C2×#104—431no—
390C2×#104—431no—
391#418—431no—
392#417—431no—
393#417—431no—
394#417C2×D4311yescharacteristic
395C2×#102—431no—
396C2×#102C2×D4311yescharacteristic
397C2×#100—431no—
398#408—431no—
399#405—431no—
400#390—431no—
401#384—431no—
402#343—431no—
403#343—431no—
404#343—431no—
405#341—431no—
406#341—431no—
407#339—431no—
408#339—431no—
409#336—431no—
410C43#2619111yescharacteristic, complemented, Sylow
411C2×#41C22×D4311yescharacteristic
412C2×#41C22×D4311yescharacteristic
413C22×D4C22×D4311yescharacteristic
414AGL(1,ℤ/8)—22no—
415AGL(1,ℤ/8)—22no—
416#135—22no—
417#135—22no—
418C2×Q16C22⋊D4311yescharacteristic
419C2×SD16—21no—
420C2×SD16C22⋊D4311yescharacteristic
421C2×SD16C22⋊D4311yescharacteristic
422C2×D8—21no—
423C2×D8C22⋊D4311yescharacteristic
424#131—862no—
425#131—862no—
426C2×M16—431no—
427C2×M16—431no—
428C2×M16—431no—
429C2×M16—861no—
430C2×M16C22×D4311yescharacteristic
431C22×C8—431no—
432C22×C8—861no—
433C22×C8C22×D4311yescharacteristic
434#127—21no—
435#124—21no—
436#121—21no—
437#121—21no—
438#120—41no—
439C4×Q8—21no—
440C4×Q8—861no—
441C4×Q8—861no—
442C4×D4—21no—
443C4×D4—41no—
444C4×D4—861no—
445C4×D4—861no—
446C4×D4—1721no—
447C4×D4—1721no—
448#117—21no—
449#117—431no—
450#117—861no—
451#117—861no—
452#117C22×D4311yescharacteristic
453C2×C4⋊C4—21no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—1721no—
459C2×C4⋊C4C22×D4311yescharacteristic
460C2×C22⋊C4—1721no—
461C2×C42—431no—
462#107—431no—
463#107—431no—
464#107—861no—
465#107—861no—
466#107—861no—
467#106—431no—
468#106—431no—
469#106—861no—
470#106—861no—
471#106—861no—
472#106—861no—
473#106—861no—
474#106—861no—
475#106—861no—
476C4⋊C8—21no—
477C4⋊C8—21no—
478#104—862no—
479#104—862no—
480#103—21no—
481#103—861no—
482#103—861no—
483#102—21no—
484#102—21no—
485#102—21no—
486#102—861no—
487#102—861no—
488#102—861no—
489#102—861no—
490#102—861no—
491#102—861no—
492#100—862no—
493C22⋊C8—861no—
494C22⋊C8—861no—
495#97—861no—
496C4×C8—861no—
497C24—21no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41—21no—
502#41—21no—
503#41—21no—
504#41#1062190012yes—
505#41#1062190012yes—
506C2×Q8C2×C22⋊D4311yescharacteristic
507C2×Q8C2×C22⋊D4311yescharacteristic
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4C2×C22⋊D4311yescharacteristic
519C2×D4C2×C22⋊D4311yescharacteristic
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—41no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—1721no—
528C22×C4—1721no—
529C22×C4C23×D4311yescharacteristic
530Q16—22no—
531SD16—22no—
532SD16—22no—
533SD16—42no—
534D8—22no—
535D8—42no—
536M16—21no—
537M16—21no—
538M16—432no—
539M16—864no—
540M16—861no—
541M16—861no—
542M16—861no—
543M16—861no—
544M16—861no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—431no—
549C2×C8—431no—
550C2×C8—864no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—861no—
556C2×C8C2×C22⋊D4311yescharacteristic
557C2×C8C2×C22⋊D4311yescharacteristic
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—41no—
561C4⋊C4—431no—
562C4⋊C4—431no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4—3442no—
568C4⋊C4—1721no—
569C4⋊C4—1721no—
570C4⋊C4D4×D4311yescharacteristic
571C4⋊C4D4×D4311yescharacteristic
572C22⋊C4—21no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—861no—
577C22⋊C4—3442no—
578C22⋊C4—1721no—
579C22⋊C4—1721no—
580C42—21no—
581C42—41no—
582C42—861no—
583C42—861no—
584C42—861no—
585C42—1721no—
586C42—1721no—
587C23—21no—
588C23—21no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—81no—
593C23—81no—
594C23#1306337011yescharacteristic
595Q8—21no—
596Q8—21no—
597Q8—21no—
598Q8#1306330612yes—
599D4—22no—
600D4—22no—
601D4—21no—
602D4—21no—
603D4—21no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—161no—
611D4—161no—
612D4#1306330612yes—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—81no—
623C2×C4—161no—
624C2×C4—862no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—3441no—
628C2×C4—3441no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—6881no—
634C2×C4—6881no—
635C2×C4C2×D4×D4311yescharacteristic
636C2×C4C22×C22⋊D4311yescharacteristic
637C2×C4#41×D4311yescharacteristic
638C2×C4C2×#1062190011yescharacteristic
639C2×C4C2×#1062190011yescharacteristic
640C2×C4#1306337211yescharacteristic
641C8—21no—
642C8—21no—
643C8—41no—
644C8—861no—
645C8—861no—
646C8—862no—
647C8—1721no—
648C8—1721no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—82no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—161no—
662C22#1458349411yescharacteristic
663C22D4×C22⋊D4311yescharacteristic
664C22#1458359211yescharacteristic
665C4—22no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—81no—
670C4—3441no—
671C4—3441no—
672C4—1722no—
673C4—1721no—
674C4—1721no—
675C4C2×#1306330611yescharacteristic
676C4#1458340911yescharacteristic
677C4#1458354811yescharacteristic
678C4#1458355511yescharacteristic
679C2—21no—
680C2—21no—
681C2—42no—
682C2—81no—
683C2—161no—
684C2#1913832611yescharacteristic
685C2#1914635911yescharacteristic
686C2#1914638611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3045C2
socleC22×C43D42
hypercenter#3045D43
hypocenterC43#26191
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3045

Complements

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

NH ≅ G/Ntype
1. #19144547C2semidirect
2. #19143479C2semidirect
3. #19143188C2semidirect
4. #19136126C2semidirect
5. #19136105C2semidirect
6. #19136043C2semidirect
7. #19135802C2semidirect
8. #19135254C2semidirect
9. #19135191C2semidirect
10. #19135105C2semidirect
11. #19134973C2semidirect
12. #19134924C2semidirect
13. #19134821C2semidirect
14. #19134819C2semidirect
410. C43#26191semidirect

Maximal subgroups

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

subgroupindex
#191445472
#191434792
#191431882
#191361262
#191361052
#191360432
#191358022
#191352542
#191351912
#191351052
#191349732
#191349242
#191348212
#191348192
C43×#30452
#2619143