Finite Group Databasebeta

← #25154154

Subgroups — #25154154

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144461C211yesmaximal, characteristic, complemented
2#19144450C211yesmaximal, characteristic, complemented
3#19143121C211yesmaximal, characteristic
4#19143121C211yesmaximal, characteristic
5#19136116C211yesmaximal, characteristic, complemented
6#19135951C211yesmaximal, characteristic, complemented
7#19135951C211yesmaximal, characteristic, complemented
8#19135751C211yesmaximal, characteristic, complemented
9#19134868C211yesmaximal, characteristic, complemented
10#19134868C211yesmaximal, characteristic, complemented
11#19134830C211yesmaximal, characteristic, complemented
12#19134830C211yesmaximal, characteristic, complemented
13#19134657C211yesmaximal, characteristic, complemented
14#19134652C211yesmaximal, characteristic, complemented
15C43×#1792C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583530C2211yescharacteristic, complemented
19#14583382C2211yescharacteristic
20#14583382C2211yescharacteristic
21#14583208—21no—
22#14583204—21no—
23#14583201—21no—
24#14583197—21no—
25#14583192—21no—
26#14583187—21no—
27#14583182—21no—
28#14583177—21no—
29C2×#13063260C2211yescharacteristic, complemented
30C2×#13063260C2211yescharacteristic, complemented
31#14582941C2211yescharacteristic, complemented
32#14582941C2211yescharacteristic, complemented
33C2×#13063258C2211yescharacteristic, complemented
34C2×#13063256C2211yescharacteristic, complemented
35#14582927C2211yescharacteristic, complemented
36#14582927C2211yescharacteristic, complemented
37#14582904—21no—
38#14582904—21no—
39#14582904C2211yescharacteristic
40#14582904C2211yescharacteristic
41#14582900—21no—
42#14582900—21no—
43#14582900C2211yescharacteristic
44#14582900C2211yescharacteristic
45#14582895—21no—
46#14582895—21no—
47#14582895C2211yescharacteristic
48#14582895C2211yescharacteristic
49C2×#13063246—21no—
50C2×#13063246—21no—
51C2×#13063246C2211yescharacteristic
52C2×#13063246C2211yescharacteristic
53#14582765C2211yescharacteristic, complemented
54#14582668C2211yescharacteristic, complemented
55#14582667C2211yescharacteristic, complemented
56#14582667C2211yescharacteristic, complemented
57#14582659C2211yescharacteristic, complemented
58#14582659C2211yescharacteristic, complemented
59#14582654C2211yescharacteristic, complemented
60C2×H(5,𝔽2)×C43C2211yescharacteristic
61C2×#104×C43C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C43×#417C2211yescharacteristic
65C2×#100×C43C2211yescharacteristic
66C43×#390C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69#13063332—41no—
70#13063332—41no—
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063324—21no—
80#13063324—21no—
81#13063316—21no—
82#13063316—21no—
83#13063304—41no—
84Q8×Dic43—21no—
85Q8×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43—41no—
89D4×Dic43—41no—
90#13063284—21no—
91#13063284—21no—
92#13063284C2311yescharacteristic
93#13063284C2311yescharacteristic
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98#13063260—41no—
99#13063260—41no—
100#13063259—21no—
101#13063259—21no—
102#13063258—21no—
103#13063258—21no—
104#13063257—21no—
105#13063257—21no—
106#13063256—21no—
107#13063256—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112#13063249—21no—
113#13063249—21no—
114#13063249D411yescharacteristic
115#13063249D411yescharacteristic
116#13063249D411yescharacteristic
117#13063249D411yescharacteristic
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063246—21no—
122#13063246—21no—
123#13063246—21no—
124#13063246—21no—
125#13063246—21no—
126#13063246—21no—
127#13063246—21no—
128#13063246D411yescharacteristic
129#13063246D411yescharacteristic
130#13063246D411yescharacteristic
131#13063246D411yescharacteristic
132C43⋊#95—41no—
133H(5,𝔽2)×C43—22no—
134H(5,𝔽2)×C43—22no—
135H(5,𝔽2)×C43—41no—
136H(5,𝔽2)×C43Q814yescomplemented
137C2×#41×C43—21no—
138C2×#41×C43—21no—
139C2×#41×C43C2311yescharacteristic
140C2×#41×C43C2311yescharacteristic
141C22×D4×C43—21no—
142C22×D4×C43—21no—
143C22×D4×C43—41no—
144C22×D4×C43C2311yescharacteristic
145C2×M16×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—41no—
149C2×C42×C43C2311yescharacteristic
150#104×C43—22no—
151#104×C43—22no—
152#103×C43—21no—
153#103×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156#100×C43—41no—
157C24×C43—21no—
158C24×C43—41no—
159#41×C43—21no—
160#41×C43—21no—
161#41×C43—21no—
162#41×C43—21no—
163#41×C43—24no—
164#41×C43—24no—
165#41×C43—42no—
166#41×C43—42no—
167#41×C43C2×Q812yes—
168#41×C43C2×Q812yes—
169#41×C43#4112yes—
170#41×C43#4112yes—
171C2×Q8×C43C2×D411yescharacteristic
172C2×Q8×C43C2×D411yescharacteristic
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—24no—
177C2×D4×C43—24no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—41no—
183C2×D4×C43—41no—
184C2×D4×C43—44no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43—44no—
188C2×D4×C43C2×D411yescharacteristic
189C2×D4×C43C2×D411yescharacteristic
190C2×D4×C43C2×Q812yes—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—41no—
196C22×C4×C43C2411yescharacteristic
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—41no—
200C22×Dic43—41no—
201C2×Dic86—41no—
202M16×C43—21no—
203M16×C43—21no—
204M16×C43—21no—
205M16×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C22⋊C4×C43—82no—
211C42×C43—21no—
212C42×C43—21no—
213C22⋊Dic43—21no—
214C22⋊Dic43—21no—
215C22⋊Dic43—41no—
216C22⋊Dic43—41no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—41no—
222C4⋊Dic43—41no—
223C4⋊Dic43—41no—
224C4⋊Dic43C2×D411yescharacteristic
225C4⋊Dic43C2×D411yescharacteristic
226C4⋊Dic43C2×D411yescharacteristic
227C4⋊Dic43C2×D411yescharacteristic
228Dic43⋊C4—41no—
229Dic43⋊C4—41no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—41no—
233C4×Dic43—41no—
234#10621877—21no—
235#10621877—21no—
236#10621877—21no—
237#10621877—21no—
238#10621877—42no—
239#10621877—42no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—42no—
247C2×C43⋊C8—42no—
248C2×C43⋊C8C2×D411yescharacteristic
249C2×C43⋊C8C2×D411yescharacteristic
250C2×C43⋊C8C2×D411yescharacteristic
251C2×C43⋊C8C2×D411yescharacteristic
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—22no—
255C23×C43—44no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—81no—
259C23×C43—81no—
260C23×C43—161no—
261C23×C43—161no—
262C23×C43H(5,𝔽2)11yescharacteristic
263Q8×C43—21no—
264Q8×C43—21no—
265Q8×C43C22⋊Q812yes—
266Q8×C43C22⋊Q812yes—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—21no—
274D4×C43—21no—
275D4×C43—44no—
276D4×C43—44no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43C22⋊Q812yes—
280D4×C43C22⋊Q812yes—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—44no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—81no—
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×Q811yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—81no—
306C2×Dic43—81no—
307C2×Dic43—161no—
308C2×Dic43—161no—
309Dic86—161no—
310C8×C43—41no—
311C8×C43—41no—
312C43⋊C8—21no—
313C43⋊C8—21no—
314C43⋊C8—21no—
315C43⋊C8—21no—
316C43⋊C8—41no—
317C43⋊C8—41no—
318#25984—431nomaximal, Sylow
319C22×C43—21no—
320C22×C43—21no—
321C22×C43—22no—
322C22×C43—22no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—42no—
328C22×C43—82no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43—161no—
332C22×C43—164no—
333C22×C43#54311yescharacteristic
334C22×C43D4211yescharacteristic
335C22×C43#55111yescharacteristic
336C4×C43—22no—
337C4×C43—22no—
338C4×C43—81no—
339C4×C43—81no—
340C4×C43C2×C22⋊Q811yescharacteristic
341C4×C43C2×C22⋊Q811yescharacteristic
342C4×C43#54611yescharacteristic
343C4×C43#54611yescharacteristic
344Dic43—41no—
345Dic43—41no—
346Dic43—41no—
347Dic43—41no—
348Dic43—81no—
349Dic43—81no—
350#3084—431no—
351#3083—431no—
352#2897—431no—
353#2897—431no—
354#2092—431no—
355#2063—431no—
356#2063—431no—
357#2027—431no—
358#1866—431no—
359#1866—431no—
360#1860—431no—
361#1860—431no—
362#1816—431no—
363#1815—431no—
364#1792D4311yescharacteristic
365C2×C43—21no—
366C2×C43—21no—
367C2×C43—42no—
368C2×C43—42no—
369C2×C43—82no—
370C2×C43#243711yescharacteristic
371C2×C43#328811yescharacteristic
372C2×C43#329011yescharacteristic
373C2×H(5,𝔽2)C2×D4311yescharacteristic
374C2×#131—431no—
375C2×#131—431no—
376#544—431no—
377#520—431no—
378#520—431no—
379#479—861no—
380#479—861no—
381#478—861no—
382#478—861no—
383#477—861no—
384#476—861no—
385#475—861no—
386#474—861no—
387C2×#108—431no—
388C2×#108—431no—
389#428—431no—
390#428—431no—
391C2×#107—431no—
392C2×#106—431no—
393#424—431no—
394#424—431no—
395C2×#104C2×D4311yescharacteristic
396C2×#104C2×D4311yescharacteristic
397#418—431no—
398#418—431no—
399#418—861no—
400#418—861no—
401#417—431no—
402#417—431no—
403#417—861no—
404#417—861no—
405#417C2×D4311yescharacteristic
406#417C2×D4311yescharacteristic
407#416—431no—
408#416—431no—
409#416—861no—
410#416—861no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—861no—
414C2×#102—861no—
415C2×#100C2×D4311yescharacteristic
416#390C2×D4311yescharacteristic
417#382—431no—
418#343—431no—
419#343—431no—
420#343—431no—
421#339—431no—
422#339—431no—
423#336—431no—
424C43#2598411yescharacteristic, complemented, Sylow
425H(5,𝔽2)—22no—
426H(5,𝔽2)—22no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)Dic8614yescomplemented
429C2×#41—21no—
430C2×#41—21no—
431C2×#41C22×D4311yescharacteristic
432C2×#41C22×D4311yescharacteristic
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—41no—
436C22×D4C22×D4311yescharacteristic
437#131—862no—
438#131—862no—
439#131—1721no—
440#131—1721no—
441C2×M16—431no—
442C2×M16—431no—
443C2×M16—861no—
444C2×M16—861no—
445C2×M16C22×D4311yescharacteristic
446C2×M16C22×D4311yescharacteristic
447C22×C8—431no—
448C22×C8—431no—
449C22×C8—861no—
450C22×C8—861no—
451C4⋊Q8—861no—
452C4⋊Q8—861no—
453#125—861no—
454#125—861no—
455C22⋊Q8—1721no—
456C4×Q8—861no—
457C4×Q8—861no—
458C4×D4—861no—
459C4×D4—861no—
460C4×D4—1721no—
461C4×D4—1721no—
462#117—431no—
463#117—431no—
464#117—861no—
465#117—861no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C22⋊C4—41no—
472C2×C42C22×D4311yescharacteristic
473#108—1721no—
474#108—1721no—
475#107—861no—
476#107—861no—
477#107—861no—
478#107—861no—
479#106—861no—
480#106—861no—
481#106—861no—
482#106—861no—
483C4⋊C8—861no—
484C4⋊C8—861no—
485C4⋊C8—861no—
486C4⋊C8—861no—
487#104—22no—
488#104—22no—
489#103—21no—
490#103—21no—
491#103—431no—
492#103—431no—
493#103—431no—
494#103—431no—
495#103—861no—
496#103—861no—
497#102—21no—
498#102—21no—
499#102—431no—
500#102—431no—
501#102—431no—
502#102—431no—
503#102—861no—
504#102—861no—
505#102—861no—
506#102—861no—
507#102—861no—
508#102—861no—
509#102—861no—
510#102—861no—
511#102—861no—
512#102—861no—
513#100—41no—
514#95—1721no—
515C24—21no—
516C24—41no—
517#41—21no—
518#41—21no—
519#41—21no—
520#41—21no—
521#41—24no—
522#41—24no—
523#41—42no—
524#41—42no—
525#41C2×Dic8612yes—
526#41C2×Dic8612yes—
527#41#1062190012yes—
528#41#1062190012yes—
529C2×Q8—1721no—
530C2×Q8D4×D4311yescharacteristic
531C2×Q8D4×D4311yescharacteristic
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4C2×Dic8612yes—
548C2×D4D4×D4311yescharacteristic
549C2×D4D4×D4311yescharacteristic
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—41no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—1721no—
558C22×C4—1721no—
559C22×C4C23×D4311yescharacteristic
560M16—21no—
561M16—21no—
562M16—21no—
563M16—21no—
564M16—861no—
565M16—861no—
566M16—861no—
567M16—861no—
568M16—1722no—
569M16—1722no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—431no—
573C2×C8—431no—
574C2×C8—431no—
575C2×C8—431no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—1722no—
583C2×C8—1722no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—431no—
587C4⋊C4—431no—
588C4⋊C4—431no—
589C4⋊C4—431no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—1721no—
595C4⋊C4—1721no—
596C4⋊C4—1721no—
597C4⋊C4—1721no—
598C4⋊C4—1721no—
599C22⋊C4—82no—
600C22⋊C4—861no—
601C22⋊C4—861no—
602C22⋊C4—1721no—
603C22⋊C4—1721no—
604C42—21no—
605C42—21no—
606C42—861no—
607C42—861no—
608C42—1721no—
609C42—1721no—
610C23—21no—
611C23—21no—
612C23—22no—
613C23—44no—
614C23—41no—
615C23—41no—
616C23—81no—
617C23—81no—
618C23—161no—
619C23—161no—
620C23#1306337011yescharacteristic
621Q8—21no—
622Q8—21no—
623Q8—6881no—
624Q8#1306330212yes—
625Q8#1306330212yes—
626D4—22no—
627D4—22no—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—22no—
632D4—21no—
633D4—21no—
634D4—44no—
635D4—44no—
636D4—41no—
637D4—41no—
638D4#1306330212yes—
639D4#1306330212yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—44no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—81no—
652C2×C4—861no—
653C2×C4—861no—
654C2×C4—861no—
655C2×C4—861no—
656C2×C4—3441no—
657C2×C4—3441no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—6881no—
661C2×C4—6881no—
662C2×C4C2×D4×D4311yescharacteristic
663C2×C4C2×D4×D4311yescharacteristic
664C2×C4C22×Dic8611yescharacteristic
665C2×C4C2×#1062190011yescharacteristic
666C2×C4C2×#1062190011yescharacteristic
667C2×C4#1306337011yescharacteristic
668C8—41no—
669C8—41no—
670C8—861no—
671C8—861no—
672C8—861no—
673C8—861no—
674C8—1721no—
675C8—1721no—
676C22—21no—
677C22—21no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22—82no—
686C22—81no—
687C22—81no—
688C22—161no—
689C22—164no—
690C22#1458352511yescharacteristic
691C22#1458353111yescharacteristic
692C22#1458358011yescharacteristic
693C4—22no—
694C4—22no—
695C4—81no—
696C4—81no—
697C4—3441no—
698C4—3441no—
699C4—1721no—
700C4—1721no—
701C4—1721no—
702C4—1721no—
703C4C2×#1306330211yescharacteristic
704C4C2×#1306330211yescharacteristic
705C4#1458353611yescharacteristic
706C4#1458353611yescharacteristic
707C2—21no—
708C2—21no—
709C2—42no—
710C2—42no—
711C2—82no—
712C2#1913826111yescharacteristic
713C2#1914635611yescharacteristic
714C2#1914637911yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1792C2
socleC22×C43D42
prime radicalC2×H(5,𝔽2)×C43C22
hypercenter#1792D43
hypocenterC43#25984
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1792

Complements

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

NH ≅ G/Ntype
1. #19144461C2semidirect
2. #19144450C2semidirect
5. #19136116C2semidirect
6. #19135951C2semidirect
7. #19135951C2semidirect
8. #19135751C2semidirect
9. #19134868C2semidirect
10. #19134868C2semidirect
11. #19134830C2semidirect
12. #19134830C2semidirect
13. #19134657C2semidirect
14. #19134652C2semidirect
18. #14583530C22semidirect
29. C2×#13063260C22semidirect
30. C2×#13063260C22semidirect
31. #14582941C22semidirect
32. #14582941C22semidirect
33. C2×#13063258C22semidirect
34. C2×#13063256C22semidirect
35. #14582927C22semidirect
36. #14582927C22semidirect
53. #14582765C22semidirect
54. #14582668C22semidirect
55. #14582667C22semidirect
56. #14582667C22semidirect
57. #14582659C22semidirect
58. #14582659C22semidirect
59. #14582654C22semidirect
136. H(5,𝔽2)×C43Q8semidirect
424. C43#25984semidirect
428. H(5,𝔽2)Dic86semidirect

Maximal subgroups

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

subgroupindex
#191444612
#191444502
#191431212
#191361162
#191359512
#191357512
#191348682
#191348302
#191346572
#191346522
C43×#17922
#2598443