Finite Group Databasebeta

← #25154139

Subgroups — #25154139

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#19144453C211yesmaximal, characteristic, complemented
2#19143118C211yesmaximal, characteristic
3#19143117C211yesmaximal, characteristic
4#19136125C211yesmaximal, characteristic, complemented
5#19135954C211yesmaximal, characteristic, complemented
6#19135952C211yesmaximal, characteristic, complemented
7#19135748C211yesmaximal, characteristic, complemented
8#19134872C211yesmaximal, characteristic, complemented
9#19134869C211yesmaximal, characteristic, complemented
10#19134821C211yesmaximal, characteristic, complemented
11#19134818C211yesmaximal, characteristic, complemented
12#19134655C211yesmaximal, characteristic, complemented
13#19134652C211yesmaximal, characteristic, complemented
14#19134547C211yesmaximal, characteristic
15C43×#3084C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19#14583379C2211yescharacteristic
20#14583203—21no—
21#14583196—21no—
22#14583186—21no—
23#14583181—21no—
24C2×#13063261C2211yescharacteristic, complemented
25C2×#13063260C2211yescharacteristic, complemented
26#14582942C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28#14582926C2211yescharacteristic, complemented
29C2×#13063252C2211yescharacteristic
30C2×#13063251C2211yescharacteristic
31#14582903—21no—
32#14582903C2211yescharacteristic
33#14582903C2211yescharacteristic
34#14582902—21no—
35#14582900C2211yescharacteristic
36#14582899—21no—
37#14582898—21no—
38#14582898C2211yescharacteristic
39#14582898C2211yescharacteristic
40#14582894—21no—
41#14582893—21no—
42#14582893C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44C2×#13063245—21no—
45C2×#13063245C2211yescharacteristic
46#102×D43—21no—
47C2×#13063241C2211yescharacteristic
48#14582800C2211yescharacteristic
49#14582768C2211yescharacteristic, complemented
50#14582668C2211yescharacteristic, complemented
51#14582668C2211yescharacteristic, complemented
52#14582667C2211yescharacteristic, complemented
53#14582658C2211yescharacteristic, complemented
54#14582658C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56C43×#544C2211yescharacteristic, complemented
57C43×#520C2211yescharacteristic
58C43×#479—21no—
59C43×#478—21no—
60C43×#476—21no—
61C43×#475—21no—
62C43×#428C2211yescharacteristic, complemented
63C2×#106×C43C2211yescharacteristic, complemented
64C43×#424C2211yescharacteristic, complemented
65C43×#417C2211yescharacteristic
66C43×#416C2211yescharacteristic
67#13063371—22no—
68#13063371—22no—
69#13063371—41no—
70#13063371Q814yescomplemented
71C2×#10621902—21no—
72C2×#10621898—21no—
73C2×#10621898C2311yescharacteristic
74C22×D172—21no—
75C22×D172C2311yescharacteristic
76C2×D4×D43—21no—
77C2×D4×D43—41no—
78#13063332—22no—
79#13063332—41no—
80#13063331—22no—
81#13063331—41no—
82C2×#10621877—21no—
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621872—21no—
87C22×C43⋊C8—21no—
88C22×C43⋊C8C2311yescharacteristic
89C2×C8×D43—21no—
90C4×Dic86—21no—
91C4×D172—21no—
92(C22⋊D43)⋊C4—41no—
93#13063283—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—41no—
96C4⋊C4×D43—21no—
97C2×(C2×D43)⋊C4—41no—
98C2×C4×Dic43C2311yescharacteristic
99#13063261—41no—
100#13063260—41no—
101#13063258—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)—21no—
107#13063252—22no—
108#13063251—22no—
109#13063249—21no—
110#13063248—21no—
111#13063248—21no—
112#13063248D411yescharacteristic
113#13063248D411yescharacteristic
114#13063247—21no—
115#13063247—21no—
116#13063246—21no—
117#13063245—21no—
118#13063245—21no—
119#13063245—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123#13063245—21no—
124#13063245—21no—
125#13063245D411yescharacteristic
126#13063245D411yescharacteristic
127#13063241—41no—
128C2×#41×C43C2311yescharacteristic
129C2×M16×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C4⋊Q8×C43—21no—
132C4⋊Q8×C43—21no—
133#125×C43—21no—
134#125×C43—21no—
135C22⋊Q8×C43—41no—
136C4×Q8×C43—21no—
137C4×D4×C43—21no—
138C4×D4×C43—41no—
139#117×C43—21no—
140#117×C43C2311yescharacteristic
141#117×C43C2311yescharacteristic
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145#107×C43—21no—
146#106×C43—21no—
147#106×C43—21no—
148#106×C43—21no—
149C4⋊C8×C43—21no—
150C4⋊C8×C43—21no—
151#103×C43—21no—
152#103×C43D411yescharacteristic
153#103×C43D411yescharacteristic
154#102×C43—21no—
155#102×C43D411yescharacteristic
156#102×C43D411yescharacteristic
157C23×D43—21no—
158C23×D43—41no—
159#41×C43—21no—
160#41×C43—21no—
161#41×C43C2×Q812yes—
162#41×C43#4112yes—
163C2×Q8×C43—41no—
164C2×Q8×C43C2×D411yescharacteristic
165C2×D4×C43—21no—
166C2×D4×C43C2×D411yescharacteristic
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—41no—
171C22×C4×C43C2411yescharacteristic
172C2×C22⋊D43—21no—
173C2×C22⋊D43—41no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176#10621902—24no—
177#10621902—42no—
178D4×D43—24no—
179D4×D43—44no—
180D4×D43—42no—
181D4×D43—44no—
182#10621898—21no—
183#10621898—21no—
184#10621898—24no—
185#10621898—42no—
186#10621898C2×Q812yes—
187#10621898#4112yes—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—24no—
194C2×D172—41no—
195C2×D172—42no—
196C2×D172C2×D411yescharacteristic
197C2×D172C2×Q812yes—
198C2×C4×D43—21no—
199C2×C4×D43—41no—
200C2×C4×D43—41no—
201C2×Dic86C2×D411yescharacteristic
202M16×C43—21no—
203M16×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43C2×D411yescharacteristic
208C2×C8×C43C2×D411yescharacteristic
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—41no—
214C4⋊C4×C43—41no—
215C4⋊C4×C43—41no—
216C4⋊C4×C43—41no—
217C4⋊C4×C43C2×D411yescharacteristic
218C4⋊C4×C43C2×D411yescharacteristic
219C4⋊C4×C43C2×D411yescharacteristic
220C4⋊C4×C43C2×D411yescharacteristic
221C22⋊C4×C43—21no—
222C22⋊C4×C43—21no—
223C22⋊C4×C43—41no—
224C42×C43—21no—
225C42×C43—21no—
226C42×C43—41no—
227(C2×D43)⋊C4—41no—
228(C2×D43)⋊C4—82no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231Dic43⋊C4—41no—
232Dic43⋊C4—82no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—41no—
236#10621877—21no—
237#10621877—21no—
238#10621877—21no—
239#10621877—21no—
240#10621877—21no—
241#10621877—21no—
242#10621877—42no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—42no—
249C2×C43⋊C8C2×D411yescharacteristic
250C2×C43⋊C8C2×D411yescharacteristic
251#10621872—42no—
252C8×D43—42no—
253C23×C43—21no—
254C23×C43H(5,𝔽2)11yescharacteristic
255C22×D43—21no—
256C22×D43—22no—
257C22×D43—44no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—81no—
261C22×D43—81no—
262C22×D43—161no—
263C22×D43—161no—
264Q8×C43—21no—
265Q8×C43—161no—
266Q8×C43C22⋊Q812yes—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—21no—
270D4×C43C22⋊Q812yes—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—81no—
281C2×C4×C43—81no—
282C2×C4×C43—161no—
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C22×Q811yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43H(5,𝔽2)11yescharacteristic
289C22⋊D43—22no—
290C22⋊D43—22no—
291C22⋊D43—44no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—81no—
298D172—22no—
299D172—22no—
300D172—21no—
301D172—44no—
302D172—41no—
303D172—41no—
304D172C22⋊Q812yes—
305C4×D43—22no—
306C4×D43—22no—
307C4×D43—44no—
308C4×D43—161no—
309Dic86—21no—
310Dic86C22⋊Q812yes—
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#25983—431nomaximal, Sylow
320C22×C43—21no—
321C22×C43—21no—
322C22×C43—22no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43#54311yescharacteristic
326C22×C43D4211yescharacteristic
327C22×C43#55111yescharacteristic
328C2×D43—22no—
329C2×D43—41no—
330C2×D43—41no—
331C2×D43—42no—
332C2×D43—81no—
333C2×D43—81no—
334C2×D43—82no—
335C2×D43—164no—
336C2×D43—161no—
337C4×C43—22no—
338C4×C43—41no—
339C4×C43—41no—
340C4×C43—41no—
341C4×C43—41no—
342C4×C43—81no—
343C4×C43—81no—
344C4×C43C2×C22⋊Q811yescharacteristic
345C4×C43C2×C22⋊Q811yescharacteristic
346C4×C43#54611yescharacteristic
347C4×C43#54611yescharacteristic
348Dic43—22no—
349Dic43—42no—
350Dic43—81no—
351#3084—431no—
352#3084D4311yescharacteristic, complemented
353#2897—431no—
354#2897—431no—
355#2094—431no—
356#2063—431no—
357#2063—431no—
358#2027—431no—
359#1866—431no—
360#1866—431no—
361#1859—431no—
362#1859—431no—
363#1815—431no—
364#1815—431no—
365#1792—431no—
366C2×C43—21no—
367C2×C43—21no—
368C2×C43—42no—
369C2×C43#243711yescharacteristic
370C2×C43#328811yescharacteristic
371C2×C43#329111yescharacteristic
372D43—42no—
373D43—82no—
374C2×H(5,𝔽2)—431no—
375C2×#131—431no—
376C2×#131—431no—
377#544C2×D4311yescharacteristic, complemented
378#520—431no—
379#520C2×D4311yescharacteristic
380#479—21no—
381#479—861no—
382#478—21no—
383#478—861no—
384#476—21no—
385#476—861no—
386#475—21no—
387#475—861no—
388C2×#108—431no—
389C2×#108—431no—
390#428—431no—
391#428C2×D4311yescharacteristic, complemented
392C2×#106—431no—
393C2×#106C2×D4311yescharacteristic, complemented
394#424—431no—
395#424C2×D4311yescharacteristic, complemented
396C2×#104—431no—
397C2×#104—431no—
398#418—431no—
399#418—431no—
400#418—861no—
401#418—861no—
402#417—431no—
403#417—431no—
404#417—431no—
405#417—861no—
406#417—861no—
407#417C2×D4311yescharacteristic
408#416—431no—
409#416—861no—
410#416—861no—
411#416C2×D4311yescharacteristic
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—861no—
415C2×#102—861no—
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#2598311yescharacteristic, complemented, Sylow
426H(5,𝔽2)—434no—
427H(5,𝔽2)—862no—
428H(5,𝔽2)—862no—
429H(5,𝔽2)—1721no—
430C2×#41—431no—
431C2×#41—861no—
432C2×#41—861no—
433C2×#41C22×D4311yescharacteristic
434C22×D4—431no—
435C22×D4—861no—
436C22×D4—861no—
437C22×D4—1721no—
438#131—862no—
439#131—862no—
440#131—1721no—
441#131—1721no—
442C2×M16—431no—
443C2×M16—431no—
444C2×M16—431no—
445C2×M16—861no—
446C2×M16—861no—
447C2×M16C22×D4311yescharacteristic
448C22×C8—431no—
449C22×C8—861no—
450C22×C8—861no—
451C22×C8C22×D4311yescharacteristic
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454#125—21no—
455#125—21no—
456C22⋊Q8—41no—
457C4×Q8—21no—
458C4×Q8—861no—
459C4×D4—21no—
460C4×D4—41no—
461C4×D4—861no—
462C4×D4—1721no—
463#117—21no—
464#117—861no—
465#117C22×D4311yescharacteristic
466#117C22×D4311yescharacteristic
467C2×C4⋊C4—21no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—1721no—
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C4⋊C4C22×D4311yescharacteristic
473C2×C22⋊C4—1721no—
474C2×C42—431no—
475#108—1721no—
476#108—1721no—
477#107—21no—
478#107—861no—
479#106—21no—
480#106—21no—
481#106—21no—
482#106—861no—
483#106—861no—
484#106—861no—
485C4⋊C8—21no—
486C4⋊C8—21no—
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—431no—
501#102—431no—
502#102—861no—
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#102C22⋊D4311yescharacteristic
514#102C22⋊D4311yescharacteristic
515#100—1721no—
516C24—861no—
517C24—1721no—
518#41—21no—
519#41—21no—
520#41—432no—
521#41—432no—
522#41—864no—
523#41—861no—
524#41—861no—
525#41—864no—
526#41—1722no—
527#41—1722no—
528#41Q8×D4312yes—
529#41#1062190212yes—
530C2×Q8—41no—
531C2×Q8—431no—
532C2×Q8C2×C22⋊D4311yescharacteristic
533C2×D4—21no—
534C2×D4—431no—
535C2×D4—432no—
536C2×D4—864no—
537C2×D4—861no—
538C2×D4—864no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—1722no—
545C2×D4—1721no—
546C2×D4—1722no—
547C2×D4—1721no—
548C2×D4—1724no—
549C2×D4—1724no—
550C2×D4C2×C22⋊D4311yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—41no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—1721no—
559C22×C4—1721no—
560C22×C4C23×D4311yescharacteristic
561M16—21no—
562M16—21no—
563M16—861no—
564M16—861no—
565M16—861no—
566M16—861no—
567M16—861no—
568M16—861no—
569M16—1722no—
570M16—1722no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—431no—
575C2×C8—431no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—1722no—
582C2×C8—1722no—
583C2×C8C2×C22⋊D4311yescharacteristic
584C2×C8C2×C22⋊D4311yescharacteristic
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—3442no—
596C4⋊C4—1721no—
597C4⋊C4D4×D4311yescharacteristic
598C4⋊C4D4×D4311yescharacteristic
599C4⋊C4C2×C22⋊D4311yescharacteristic
600C4⋊C4C2×C22⋊D4311yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—41no—
604C22⋊C4—3442no—
605C22⋊C4—1721no—
606C42—21no—
607C42—21no—
608C42—41no—
609C42—861no—
610C42—861no—
611C42—1721no—
612C23—21no—
613C23—861no—
614C23—862no—
615C23—3441no—
616C23—3441no—
617C23—1724no—
618C23—1721no—
619C23—1721no—
620C23—6881no—
621C23—6881no—
622C23#1306337011yescharacteristic
623Q8—21no—
624Q8—161no—
625Q8—432no—
626Q8—861no—
627Q8#1306330112yes—
628D4—22no—
629D4—22no—
630D4—21no—
631D4—432no—
632D4—862no—
633D4—862no—
634D4—862no—
635D4—862no—
636D4—861no—
637D4—1724no—
638D4—1724no—
639D4—1721no—
640D4—1721no—
641D4#1306330112yes—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—161no—
654C2×C4—861no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—3441no—
659C2×C4—1724no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—6881no—
664C2×C4C2×D4×D4311yescharacteristic
665C2×C4C22×C22⋊D4311yescharacteristic
666C2×C4C2×Q8×D4311yescharacteristic
667C2×C4#41×D4311yescharacteristic
668C2×C4C2×#1062190211yescharacteristic
669C2×C4#1306337111yescharacteristic
670C8—21no—
671C8—21no—
672C8—41no—
673C8—861no—
674C8—861no—
675C8—1721no—
676C8—1721no—
677C8—1721no—
678C22—21no—
679C22—21no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—862no—
684C22—3442no—
685C22—3441no—
686C22—3441no—
687C22—1722no—
688C22—1721no—
689C22—1721no—
690C22—6881no—
691C22—6884no—
692C22#1458352411yescharacteristic
693C22D4×C22⋊D4311yescharacteristic
694C22#1458357611yescharacteristic
695C4—22no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—81no—
701C4—81no—
702C4—862no—
703C4—3441no—
704C4—1722no—
705C4C22⋊Q8×D4311yescharacteristic
706C4C2×#1306330111yescharacteristic
707C4#1458353711yescharacteristic
708C4#1458354011yescharacteristic
709C2—21no—
710C2—21no—
711C2—42no—
712C2—3442no—
713C2—1722no—
714C2#1913825811yescharacteristic
715C2#1914635711yescharacteristic
716C2#1914638611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3084C2
socleC22×C43D42
prime radicalC2×#13063371C22
hypercenter#3084D43
hypocenterC43#25983
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3084

Complements

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

NH ≅ G/Ntype
1. #19144453C2semidirect
4. #19136125C2semidirect
5. #19135954C2semidirect
6. #19135952C2semidirect
7. #19135748C2semidirect
8. #19134872C2semidirect
9. #19134869C2semidirect
10. #19134821C2semidirect
11. #19134818C2semidirect
12. #19134655C2semidirect
13. #19134652C2semidirect
15. C43×#3084C2semidirect
24. C2×#13063261C22semidirect
25. C2×#13063260C22semidirect
26. #14582942C22semidirect
27. C2×#13063256C22semidirect
28. #14582926C22semidirect
49. #14582768C22semidirect
50. #14582668C22semidirect
51. #14582668C22semidirect
52. #14582667C22semidirect
53. #14582658C22semidirect
54. #14582658C22semidirect
55. #14582653C22semidirect
56. C43×#544C22semidirect
62. C43×#428C22semidirect
63. C2×#106×C43C22semidirect
64. C43×#424C22semidirect
70. #13063371Q8semidirect
352. #3084D43semidirect
377. #544C2×D43semidirect
391. #428C2×D43semidirect
393. C2×#106C2×D43semidirect
395. #424C2×D43semidirect
425. C43#25983semidirect

Maximal subgroups

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

subgroupindex
#191444532
#191431182
#191431172
#191361252
#191359542
#191359522
#191357482
#191348722
#191348692
#191348212
#191348182
#191346552
#191346522
#191345472
C43×#30842
#2598343