Finite Group Databasebeta

← #25154128

Subgroups — #25154128

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144446C211yesmaximal, characteristic, complemented
2#19144444C211yesmaximal, characteristic, complemented
3#19143121C211yesmaximal, characteristic
4#19136121C211yesmaximal, characteristic, complemented
5#19135955C211yesmaximal, characteristic, complemented
6#19135953C211yesmaximal, characteristic, complemented
7#19135749C211yesmaximal, characteristic, complemented
8#19134872C211yesmaximal, characteristic, complemented
9#19134870C211yesmaximal, characteristic, complemented
10#19134821C211yesmaximal, characteristic, complemented
11#19134819C211yesmaximal, characteristic, complemented
12#19134659C211yesmaximal, characteristic, complemented
13#19134657C211yesmaximal, characteristic, complemented
14#19134549C211yesmaximal, characteristic
15C43×#2897C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583527C2211yescharacteristic, complemented
18#14583382C2211yescharacteristic
19#14583208—21no—
20#14583206—21no—
21#14583199—21no—
22#14583197—21no—
23#14583194—21no—
24#14583192—21no—
25#14583179—21no—
26#14583177—21no—
27C2×#13063261C2211yescharacteristic, complemented
28C2×#13063260C2211yescharacteristic, complemented
29#14582942C2211yescharacteristic, complemented
30#14582939C2211yescharacteristic, complemented
31C2×#13063259C2211yescharacteristic, complemented
32C2×#13063258C2211yescharacteristic, complemented
33#14582926C2211yescharacteristic, complemented
34#14582925C2211yescharacteristic, complemented
35C2×#13063252C2211yescharacteristic
36C2×#13063252C2211yescharacteristic
37#14582904—21no—
38#14582904C2211yescharacteristic
39#14582900—21no—
40#14582900C2211yescharacteristic
41#14582900C2211yescharacteristic
42#14582900C2211yescharacteristic
43#14582895—21no—
44#14582895C2211yescharacteristic
45C2×#13063246—21no—
46C2×#13063246C2211yescharacteristic
47C2×#13063242C2211yescharacteristic
48#14582802C2211yescharacteristic
49#14582768C2211yescharacteristic, complemented
50#14582668C2211yescharacteristic, complemented
51#14582667C2211yescharacteristic, complemented
52#14582667C2211yescharacteristic, complemented
53#14582660C2211yescharacteristic, complemented
54#14582658C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56C2×H(5,𝔽2)×C43C2211yescharacteristic
57C2×#131×C43C2211yescharacteristic
58C43×#520C2211yescharacteristic
59C43×#418—21no—
60C43×#418C2211yescharacteristic
61C43×#417—21no—
62C43×#417C2211yescharacteristic
63C43×#416—21no—
64C43×#416C2211yescharacteristic
65C2×#102×C43—21no—
66C2×#102×C43C2211yescharacteristic
67#13063332—22no—
68#13063332—41no—
69C2×#10621877—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C22×C43⋊C8—21no—
74C22×C43⋊C8C2311yescharacteristic
75#13063325—21no—
76#13063324—21no—
77#13063317—21no—
78#13063316—21no—
79#13063302—41no—
80Q8×Dic43—21no—
81D4×Dic43—21no—
82D4×Dic43—41no—
83#13063284—21no—
84#13063284C2311yescharacteristic
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—41no—
89C2×C22⋊Dic43—41no—
90C2×C4×Dic43C2311yescharacteristic
91#13063261—41no—
92#13063260—41no—
93#13063259—21no—
94#13063259—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063256—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063252—22no—
106#13063252—22no—
107#13063249—21no—
108#13063249—21no—
109#13063249—21no—
110#13063249D411yescharacteristic
111#13063249D411yescharacteristic
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246D411yescharacteristic
120#13063246D411yescharacteristic
121#13063242—41no—
122H(5,𝔽2)×C43—22no—
123H(5,𝔽2)×C43—22no—
124H(5,𝔽2)×C43—41no—
125H(5,𝔽2)×C43Q814yescomplemented
126C2×#41×C43—21no—
127C2×#41×C43—21no—
128C2×#41×C43C2311yescharacteristic
129C2×#41×C43C2311yescharacteristic
130C22×D4×C43—21no—
131C22×D4×C43—21no—
132C22×D4×C43—41no—
133C22×D4×C43C2311yescharacteristic
134#131×C43—22no—
135#131×C43—41no—
136C2×M16×C43—21no—
137C2×M16×C43C2311yescharacteristic
138C22×C8×C43—21no—
139C22×C8×C43C2311yescharacteristic
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
147#103×C43—21no—
148#103×C43D411yescharacteristic
149#103×C43D411yescharacteristic
150#102×C43—21no—
151#102×C43—21no—
152#102×C43—21no—
153#102×C43—21no—
154#102×C43—21no—
155#102×C43D411yescharacteristic
156#102×C43D411yescharacteristic
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—41no—
195C22×C4×C43—41no—
196C22×C4×C43C2411yescharacteristic
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—41no—
201C2×Dic86—41no—
202M16×C43—21no—
203M16×C43—21no—
204M16×C43—42no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—42no—
209C2×C8×C43C2×D411yescharacteristic
210C2×C8×C43C2×D411yescharacteristic
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—41no—
214C4⋊C4×C43C2×D411yescharacteristic
215C4⋊C4×C43C2×D411yescharacteristic
216C22⋊C4×C43—21no—
217C22⋊C4×C43—41no—
218C42×C43—21no—
219C42×C43—41no—
220C22⋊Dic43—21no—
221C22⋊Dic43—41no—
222C22⋊Dic43—82no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—41no—
228C4⋊Dic43—41no—
229C4⋊Dic43C2×D411yescharacteristic
230C4⋊Dic43C2×D411yescharacteristic
231Dic43⋊C4—41no—
232Dic43⋊C4—41no—
233Dic43⋊C4—82no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—41no—
238#10621877—21no—
239#10621877—21no—
240#10621877—21no—
241#10621877—21no—
242#10621877—21no—
243#10621877—21no—
244#10621877—42no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—42no—
251C2×C43⋊C8C2×D411yescharacteristic
252C2×C43⋊C8C2×D411yescharacteristic
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—44no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—81no—
260C23×C43—81no—
261C23×C43—161no—
262C23×C43—161no—
263C23×C43H(5,𝔽2)11yescharacteristic
264Q8×C43—21no—
265Q8×C43—21no—
266Q8×C43C22⋊Q812yes—
267Q8×C43C22⋊Q812yes—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—21no—
275D4×C43—21no—
276D4×C43—44no—
277D4×C43—44no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43C22⋊Q812yes—
281D4×C43C22⋊Q812yes—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—44no—
291C2×C4×C43—41no—
292C2×C4×C43—81no—
293C2×C4×C43—161no—
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×Q811yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×Dic43—22no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—81no—
308C2×Dic43—81no—
309C2×Dic43—161no—
310Dic86—161no—
311C8×C43—21no—
312C8×C43—21no—
313C8×C43—41no—
314C43⋊C8—21no—
315C43⋊C8—21no—
316C43⋊C8—41no—
317C43⋊C8—41no—
318C43⋊C8—41no—
319#25982—431nomaximal, Sylow
320C22×C43—21no—
321C22×C43—21no—
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—42no—
329C22×C43—82no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43—161no—
333C22×C43—164no—
334C22×C43#54311yescharacteristic
335C22×C43D4211yescharacteristic
336C22×C43#55111yescharacteristic
337C4×C43—22no—
338C4×C43—22no—
339C4×C43—41no—
340C4×C43—41no—
341C4×C43—81no—
342C4×C43C2×C22⋊Q811yescharacteristic
343C4×C43C2×C22⋊Q811yescharacteristic
344C4×C43#54611yescharacteristic
345C4×C43#54611yescharacteristic
346Dic43—42no—
347Dic43—41no—
348Dic43—41no—
349Dic43—81no—
350Dic43—81no—
351#3083—431no—
352#3083—431no—
353#2897—431no—
354#2897D4311yescharacteristic
355#2093—431no—
356#2063—431no—
357#2063—431no—
358#2027—431no—
359#1866—431no—
360#1866—431no—
361#1859—431no—
362#1859—431no—
363#1816—431no—
364#1816—431no—
365#1792—431no—
366C2×C43—21no—
367C2×C43—21no—
368C2×C43—42no—
369C2×C43—42no—
370C2×C43—82no—
371C2×C43#243711yescharacteristic
372C2×C43#328911yescharacteristic
373C2×C43#329211yescharacteristic
374C2×H(5,𝔽2)C2×D4311yescharacteristic
375C2×#131—431no—
376C2×#131C2×D4311yescharacteristic
377#544—431no—
378#520—431no—
379#520C2×D4311yescharacteristic
380#479—861no—
381#479—861no—
382#478—861no—
383#478—861no—
384#477—861no—
385#477—861no—
386#474—861no—
387#474—861no—
388C2×#108—431no—
389C2×#108—431no—
390#428—431no—
391#428—431no—
392C2×#107—431no—
393C2×#107—431no—
394#424—431no—
395#424—431no—
396C2×#104—431no—
397C2×#104—431no—
398#418—21no—
399#418—431no—
400#418—861no—
401#418C2×D4311yescharacteristic
402#417—21no—
403#417—431no—
404#417—431no—
405#417—431no—
406#417—861no—
407#417C2×D4311yescharacteristic
408#416—21no—
409#416—431no—
410#416—861no—
411#416C2×D4311yescharacteristic
412C2×#102—21no—
413C2×#102—431no—
414C2×#102—861no—
415C2×#102C2×D4311yescharacteristic
416C2×#100—431no—
417#390—431no—
418#384—431no—
419#343—431no—
420#343—431no—
421#343—431no—
422#339—431no—
423#339—431no—
424#336—431no—
425C43#2598211yescharacteristic, complemented, Sylow
426H(5,𝔽2)—22no—
427H(5,𝔽2)—22no—
428H(5,𝔽2)—41no—
429H(5,𝔽2)Dic8614yescomplemented
430C2×#41—21no—
431C2×#41—21no—
432C2×#41C22×D4311yescharacteristic
433C2×#41C22×D4311yescharacteristic
434C22×D4—21no—
435C22×D4—21no—
436C22×D4—41no—
437C22×D4C22×D4311yescharacteristic
438#131—22no—
439#131—41no—
440#131—862no—
441#131—1721no—
442C2×M16—21no—
443C2×M16—431no—
444C2×M16—431no—
445C2×M16—431no—
446C2×M16—861no—
447C2×M16C22×D4311yescharacteristic
448C22×C8—21no—
449C22×C8—431no—
450C22×C8—861no—
451C22×C8C22×D4311yescharacteristic
452C4⋊Q8—861no—
453C4⋊Q8—861no—
454#125—861no—
455#125—861no—
456C22⋊Q8—1721no—
457C4×Q8—21no—
458C4×Q8—861no—
459C4×D4—21no—
460C4×D4—41no—
461C4×D4—861no—
462C4×D4—1721no—
463#117—21no—
464#117—431no—
465#117—861no—
466#117C22×D4311yescharacteristic
467C2×C4⋊C4—21no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—1721no—
472C2×C4⋊C4C22×D4311yescharacteristic
473C2×C22⋊C4—1721no—
474C2×C42—431no—
475#108—1721no—
476#108—1721no—
477#107—861no—
478#107—861no—
479#107—861no—
480#107—861no—
481#107—861no—
482#107—861no—
483#106—861no—
484#106—861no—
485C4⋊C8—861no—
486C4⋊C8—861no—
487C4⋊C8—861no—
488C4⋊C8—861no—
489#104—862no—
490#104—862no—
491#103—21no—
492#103—431no—
493#103—431no—
494#103—861no—
495#103—861no—
496#103—861no—
497#103C22⋊D4311yescharacteristic
498#103C22⋊D4311yescharacteristic
499#102—21no—
500#102—21no—
501#102—21no—
502#102—21no—
503#102—21no—
504#102—431no—
505#102—431no—
506#102—861no—
507#102—861no—
508#102—861no—
509#102—861no—
510#102—861no—
511#102—861no—
512#102—861no—
513#102C22⋊D4311yescharacteristic
514#102C22⋊D4311yescharacteristic
515#100—1721no—
516C24—21no—
517C24—41no—
518#41—21no—
519#41—21no—
520#41—21no—
521#41—21no—
522#41—24no—
523#41—24no—
524#41—42no—
525#41—42no—
526#41C2×Dic8612yes—
527#41C2×Dic8612yes—
528#41#1062189812yes—
529#41#1062190012yes—
530C2×Q8—1721no—
531C2×Q8D4×D4311yescharacteristic
532C2×Q8C2×C22⋊D4311yescharacteristic
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4C2×Dic8612yes—
549C2×D4D4×D4311yescharacteristic
550C2×D4C2×C22⋊D4311yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—1721no—
560C22×C4C23×D4311yescharacteristic
561M16—21no—
562M16—21no—
563M16—42no—
564M16—861no—
565M16—861no—
566M16—861no—
567M16—861no—
568M16—861no—
569M16—861no—
570M16—1722no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—42no—
575C2×C8—431no—
576C2×C8—431no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—1722no—
583C2×C8C2×C22⋊D4311yescharacteristic
584C2×C8C2×C22⋊D4311yescharacteristic
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—41no—
588C4⋊C4—431no—
589C4⋊C4—431no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—3442no—
595C4⋊C4—1721no—
596C4⋊C4—1721no—
597C4⋊C4—1721no—
598C4⋊C4—1721no—
599C4⋊C4C2×C22⋊D4311yescharacteristic
600C4⋊C4C2×C22⋊D4311yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—41no—
603C22⋊C4—861no—
604C22⋊C4—3442no—
605C22⋊C4—1721no—
606C42—21no—
607C42—41no—
608C42—861no—
609C42—861no—
610C42—861no—
611C42—1721no—
612C23—21no—
613C23—21no—
614C23—22no—
615C23—44no—
616C23—41no—
617C23—41no—
618C23—81no—
619C23—81no—
620C23—161no—
621C23—161no—
622C23#1306337011yescharacteristic
623Q8—21no—
624Q8—21no—
625Q8—6881no—
626Q8#1306330212yes—
627Q8#1306330412yes—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—21no—
635D4—21no—
636D4—44no—
637D4—44no—
638D4—41no—
639D4—41no—
640D4#1306330212yes—
641D4#1306330412yes—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—44no—
651C2×C4—41no—
652C2×C4—81no—
653C2×C4—161no—
654C2×C4—862no—
655C2×C4—861no—
656C2×C4—861no—
657C2×C4—3441no—
658C2×C4—3441no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—6881no—
664C2×C4C2×D4×D4311yescharacteristic
665C2×C4C22×C22⋊D4311yescharacteristic
666C2×C4C22×Dic8611yescharacteristic
667C2×C4C2×#1062190011yescharacteristic
668C2×C4C2×#1062189811yescharacteristic
669C2×C4#1306337011yescharacteristic
670C8—21no—
671C8—21no—
672C8—41no—
673C8—861no—
674C8—861no—
675C8—1721no—
676C8—1721no—
677C8—1721no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—42no—
687C22—82no—
688C22—81no—
689C22—81no—
690C22—161no—
691C22—164no—
692C22#1458352511yescharacteristic
693C22D4×C22⋊D4311yescharacteristic
694C22#1458357511yescharacteristic
695C4—22no—
696C4—22no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—3441no—
701C4—3441no—
702C4—1722no—
703C4—1721no—
704C4—1721no—
705C4C2×#1306330211yescharacteristic
706C4C2×#1306330411yescharacteristic
707C4#1458353911yescharacteristic
708C4#1458354311yescharacteristic
709C2—21no—
710C2—21no—
711C2—42no—
712C2—42no—
713C2—82no—
714C2#1913825611yescharacteristic
715C2#1914636811yescharacteristic
716C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2897C2
socleC22×C43D42
prime radicalC2×H(5,𝔽2)×C43C22
hypercenter#2897D43
hypocenterC43#25982
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2897

Complements

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

NH ≅ G/Ntype
1. #19144446C2semidirect
2. #19144444C2semidirect
4. #19136121C2semidirect
5. #19135955C2semidirect
6. #19135953C2semidirect
7. #19135749C2semidirect
8. #19134872C2semidirect
9. #19134870C2semidirect
10. #19134821C2semidirect
11. #19134819C2semidirect
12. #19134659C2semidirect
13. #19134657C2semidirect
17. #14583527C22semidirect
27. C2×#13063261C22semidirect
28. C2×#13063260C22semidirect
29. #14582942C22semidirect
30. #14582939C22semidirect
31. C2×#13063259C22semidirect
32. C2×#13063258C22semidirect
33. #14582926C22semidirect
34. #14582925C22semidirect
49. #14582768C22semidirect
50. #14582668C22semidirect
51. #14582667C22semidirect
52. #14582667C22semidirect
53. #14582660C22semidirect
54. #14582658C22semidirect
55. #14582653C22semidirect
125. H(5,𝔽2)×C43Q8semidirect
425. C43#25982semidirect
429. H(5,𝔽2)Dic86semidirect

Maximal subgroups

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

subgroupindex
#191444462
#191444442
#191431212
#191361212
#191359552
#191359532
#191357492
#191348722
#191348702
#191348212
#191348192
#191346592
#191346572
#191345492
C43×#28972
#2598243