Finite Group Databasebeta

← #25099143

Subgroups — #25099143

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143182C211yesmaximal, characteristic, complemented
2#19143109C211yesmaximal, characteristic
3C2×#14582892C211yesmaximal, characteristic
4C2×#14582880C211yesmaximal, characteristic
5#405×D43C211yesmaximal, characteristic, complemented
6#19135260C211yesmaximal, characteristic, complemented
7#19135259C211yesmaximal, characteristic, complemented
8#19135254C211yesmaximal, characteristic, complemented
9#19135251C211yesmaximal, characteristic, complemented
10#19135250C211yesmaximal, characteristic, complemented
11#19135249C211yesmaximal, characteristic, complemented
12#19135248C211yesmaximal, characteristic, complemented
13#19134332C211yesmaximal, characteristic, complemented
14#341×D43C211yesmaximal, characteristic, complemented
15C43×#1931C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22#117×D43C2211yescharacteristic
23#14582942C2211yescharacteristic
24#14582941C2211yescharacteristic
25#14582940—21no—
26#14582939C2211yescharacteristic
27#14582938—21no—
28#14582936—21no—
29#14582934—21no—
30#14582909C2211yescharacteristic
31#14582907C2211yescharacteristic
32#14582904C2211yescharacteristic
33#14582897—21no—
34#14582897—21no—
35#14582892—21no—
36#14582892—21no—
37#14582892—21no—
38#14582892—21no—
39#14582892—21no—
40#14582892—21no—
41C2×#13063250C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44#14582880C418yescomplemented
45C2×#13063243C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47C2×#13063242C2211yescharacteristic
48#14582857C2211yescharacteristic
49#14582856—21no—
50#14582855C2211yescharacteristic
51#14582854C2211yescharacteristic
52#14582853—21no—
53#97×D43—21no—
54C4×C8×D43—21no—
55#14582668C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582664C2211yescharacteristic
59#14582663C2211yescharacteristic
60#14582663C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C43×#418C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C2×#100×C43C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#341C2211yescharacteristic
68C2×#10621900—21no—
69C2×#10621900—21no—
70C2×#10621900—21no—
71C2×#10621900—21no—
72C2×#10621900—22no—
73C2×#10621900—22no—
74C2×#10621900—22no—
75C2×#10621900C2×C414yes—
76C22×Dic86C2311yescharacteristic
77C22×C22⋊D43—21no—
78C23×Dic43—21no—
79C22×C4×D43C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621872—21no—
84C2×#10621872—21no—
85C2×#10621872—21no—
86M16×D43—22no—
87M16×D43—22no—
88M16×D43—22no—
89M16×D43—22no—
90M16×D43C2×C414yes—
91M16×D43C2×C414yes—
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—21no—
94C2×C8×D43—21no—
95C2×C8×D43—22no—
96C2×C8×D43—22no—
97C2×C8×D43—21no—
98C2×C8×D43D411yescharacteristic
99C2×C8×D43D411yescharacteristic
100C2×C8×D43D411yescharacteristic
101C2×C8×D43D411yescharacteristic
102#13063284C2311yescharacteristic
103#13063283—21no—
104#13063283—21no—
105#13063283—21no—
106#13063283—21no—
107#13063283D411yescharacteristic
108#13063283D411yescharacteristic
109#13063282—21no—
110#13063281—21no—
111C2×C4⋊Dic43C2311yescharacteristic
112C4⋊C4×D43D411yescharacteristic
113C4⋊C4×D43D411yescharacteristic
114C2×(C2×D43)⋊C4—21no—
115C22⋊C4×D43—21no—
116C2×C4×Dic43—21no—
117C42×D43—21no—
118#13063259—21no—
119#13063258—21no—
120#13063258—21no—
121#13063257—21no—
122#13063256—21no—
123#13063256—21no—
124#13063250—21no—
125#13063250—21no—
126#13063250—21no—
127#13063250—21no—
128#13063248—21no—
129#13063248—21no—
130#13063248—21no—
131#13063248—21no—
132#13063246—21no—
133#13063246—21no—
134#13063246—21no—
135#13063246—21no—
136#13063243C2×C414yescomplemented
137#13063243C2×C414yescomplemented
138#13063242C2×C414yescomplemented
139#13063236—21no—
140#13063235—21no—
141#13063235—21no—
142C4×C43⋊C8—21no—
143C8×Dic43—21no—
144C8×Dic43—21no—
145C22×D4×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150#117×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152#107×C43—21no—
153#106×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156#102×C43—21no—
157#102×C43—21no—
158#100×C43C2×C414yescomplemented
159#97×C43—21no—
160C4×C8×C43—21no—
161C24×C43—21no—
162C23×D43#4111yescharacteristic
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43C22×C412yes—
169C22×C4×C43—21no—
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—24no—
172C2×C22⋊D43—41no—
173C2×C22⋊D43—41no—
174C2×C22⋊D43—42no—
175C22×Dic43—24no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—41no—
179C22×Dic43—41no—
180C22×Dic43—42no—
181C22×Dic43#4111yescharacteristic
182#10621900—24no—
183#10621900—24no—
184#10621900—24no—
185#10621900—24no—
186#10621900—42no—
187#10621900—42no—
188#10621900—42no—
189#10621900—42no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43C22×C412yes—
193C2×C4×D43C2×D411yescharacteristic
194C2×C4×D43C2×D411yescharacteristic
195C2×C4×D43C2×D411yescharacteristic
196C2×C4×D43C2×D411yescharacteristic
197C2×C4×D43#4112yes—
198C2×C4×D43#4112yes—
199C2×C4×D43#4112yes—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86C22×C412yes—
206M16×C43—21no—
207M16×C43—21no—
208M16×C43—21no—
209M16×C43—21no—
210M16×C43C22×C412yes—
211M16×C43C22×C412yes—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43C2×D411yescharacteristic
218C2×C8×C43C2×D411yescharacteristic
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43C2×D411yescharacteristic
222C4⋊C4×C43C2×D411yescharacteristic
223C22⋊C4×C43—21no—
224C42×C43—21no—
225C22⋊Dic43—21no—
226(C2×D43)⋊C4—21no—
227(C2×D43)⋊C4—21no—
228(C2×D43)⋊C4—41no—
229(C2×D43)⋊C4—41no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43C2×D411yescharacteristic
233C4⋊Dic43C2×D411yescharacteristic
234Dic43⋊C4—21no—
235Dic43⋊C4—21no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—41no—
240C4×Dic43—41no—
241#10621877—21no—
242#10621877—21no—
243#10621877—21no—
244#10621877—21no—
245#10621877C22×C412yes—
246#10621877C22×C412yes—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8C2×D411yescharacteristic
253C2×C43⋊C8C2×D411yescharacteristic
254#10621872—24no—
255#10621872—24no—
256#10621872—42no—
257C8×D43—24no—
258C8×D43—24no—
259C8×D43—22no—
260C8×D43—22no—
261C8×D43—22no—
262C8×D43—22no—
263C8×D43—42no—
264C23×C43—22no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—81no—
268C23×C43—81no—
269C23×C43C2×#4111yescharacteristic
270C22×D43—41no—
271C22×D43—41no—
272C22×D43#11712yes—
273C22×D43#12111yescharacteristic
274C22×D43#12111yescharacteristic
275C22×D43#12612yes—
276D4×C43—22no—
277D4×C43—22no—
278D4×C43—41no—
279D4×C43—41no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—41no—
283C2×C4×C43—81no—
284C2×C4×C43C23×C411yescharacteristic
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C22⋊D43—44no—
291C22⋊D43—44no—
292C2×Dic43—22no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—44no—
298C2×Dic43—44no—
299C2×Dic43—41no—
300C2×Dic43—81no—
301C2×Dic43#11712yes—
302C2×Dic43#12111yescharacteristic
303C2×Dic43#12111yescharacteristic
304C2×Dic43#12612yes—
305C4×D43—42no—
306C4×D43—42no—
307C4×D43C4×D412yes—
308C4×D43C4×D412yes—
309C4×D43C4×D412yes—
310C4×D43C4×D412yes—
311C4×D43#12312yes—
312C4×D43#12312yes—
313C4×D43#12412yes—
314C4×D43#12412yes—
315Dic86—22no—
316Dic86—22no—
317Dic86—41no—
318Dic86—41no—
319C8×C43—22no—
320C8×C43—22no—
321C8×C43—21no—
322C8×C43—21no—
323C8×C43—41no—
324C43⋊C8—22no—
325C43⋊C8—22no—
326C43⋊C8—21no—
327C43⋊C8—21no—
328C43⋊C8—41no—
329#21075—431nomaximal, Sylow
330C22×C43—21no—
331C22×C43—21no—
332C22×C43—42no—
333C22×C43—82no—
334C22×C43—82no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43C2×#11711yescharacteristic
338C22×C43C2×#12111yescharacteristic
339C22×C43C2×#12611yescharacteristic
340C2×D43—21no—
341C2×D43—21no—
342C2×D43—21no—
343C2×D43—21no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43#38812yes—
347C2×D43#38812yes—
348C4×C43—41no—
349C4×C43—41no—
350C4×C43—81no—
351C4×C43C2×C4×D411yescharacteristic
352C4×C43C2×C4×D411yescharacteristic
353C4×C43C2×#12311yescharacteristic
354C4×C43C2×#12411yescharacteristic
355Dic43—42no—
356Dic43—41no—
357Dic43—41no—
358Dic43—81no—
359Dic43#38812yes—
360Dic43#38812yes—
361#2911—431no—
362#2896—431no—
363C2×#416—431no—
364C2×#413—431no—
365C2×#405—431no—
366#1931—431no—
367#1931—431no—
368#1931—431no—
369#1931D4311yescharacteristic, complemented
370#1930—431no—
371#1930—431no—
372#1930—431no—
373#1930—431no—
374#1742—431no—
375C2×#341—431no—
376C2×C43—21no—
377C2×C43—21no—
378C2×C43—82no—
379C2×C43C2×#38811yescharacteristic
380C2×C43#306711yescharacteristic
381C2×C43#306711yescharacteristic
382D43—22no—
383D43—22no—
384C22×#41—431no—
385C22×M16—431no—
386C22×M16—431no—
387C22×M16—431no—
388C23×C8—431no—
389C2×#117—431no—
390C2×#117—431no—
391#428—431no—
392#428—431no—
393#428—431no—
394#428—861no—
395#428—861no—
396#428C2×D4311yescharacteristic
397#427—861no—
398#427—861no—
399#419—431no—
400#419—431no—
401#418—431no—
402#418C2×D4311yescharacteristic
403#417—861no—
404#417—861no—
405#416—861no—
406#416—861no—
407#416—861no—
408#416—861no—
409#416—861no—
410#416—861no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#102—431no—
414C2×#102C2×D4311yescharacteristic
415#413—438no—
416C2×#101—431no—
417C2×#101—431no—
418C2×#100—431no—
419C2×#100C2×D4311yescharacteristic
420#405—431no—
421#405—431no—
422#405—431no—
423#405—861no—
424#405—861no—
425#405C2×D4311yescharacteristic
426C2×#97—861no—
427C2×C4×C8—861no—
428#343—431no—
429#343—431no—
430#343—431no—
431#343C2×D4311yescharacteristic
432#341—431no—
433#341—431no—
434#341—431no—
435#341C2×D4311yescharacteristic
436C43#2107511yescharacteristic, complemented, Sylow
437C2×#41—434no—
438C2×#41—862no—
439C2×#41—861no—
440C2×#41—861no—
441C2×#41—861no—
442C2×#41—861no—
443C2×#41—862no—
444C2×#41—862no—
445C22×Q8—431no—
446C22×D4—861no—
447C22×D4C22×D4311yescharacteristic
448C23×C4—431no—
449C23×C4—861no—
450C2×M16—431no—
451C2×M16—431no—
452C2×M16—434no—
453C2×M16—434no—
454C2×M16—431no—
455C2×M16—861no—
456C2×M16—861no—
457C2×M16—861no—
458C2×M16—862no—
459C2×M16—862no—
460C2×M16—862no—
461C2×M16—862no—
462C2×M16C22×D4311yescharacteristic
463C2×M16C22×D4311yescharacteristic
464C2×M16C22×D4311yescharacteristic
465C22×C8—431no—
466C22×C8—431no—
467C22×C8—431no—
468C22×C8—431no—
469C22×C8—431no—
470C22×C8—862no—
471C22×C8—862no—
472C22×C8—861no—
473C22×C8—861no—
474C22×C8—861no—
475C22×C8C22×D4311yescharacteristic
476#117—431no—
477#117—431no—
478#117—431no—
479#117—861no—
480#117—861no—
481#117—861no—
482#117—861no—
483#117—861no—
484#117—861no—
485#117C22×D4311yescharacteristic
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C42—861no—
493C2×C42—861no—
494#107—21no—
495#107—861no—
496#107—861no—
497#107—861no—
498#106—21no—
499#106—861no—
500#106—861no—
501#106—861no—
502#103—861no—
503#103—861no—
504#103—861no—
505#103—861no—
506#103—861no—
507#103—861no—
508#103—861no—
509#103—861no—
510#102—21no—
511#102—21no—
512#102—21no—
513#102—21no—
514#102—861no—
515#102—861no—
516#102—861no—
517#102—861no—
518#101—434no—
519#101—434no—
520#100—434no—
521#100C4×D4314yescomplemented
522#97—21no—
523#97—861no—
524#97—861no—
525#97—861no—
526C4×C8—21no—
527C4×C8—861no—
528C4×C8—861no—
529C4×C8—861no—
530C24—21no—
531C24—431no—
532#41—864no—
533#41—864no—
534#41—864no—
535#41—864no—
536#41—1722no—
537#41—1722no—
538#41—1722no—
539#41—1722no—
540C2×Q8—432no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—864no—
552C2×D4—1721no—
553C2×D4—1721no—
554C2×D4—1722no—
555C2×D4C2×C4×D4312yes—
556C22×C4—21no—
557C22×C4—431no—
558C22×C4—432no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—864no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—1721no—
572C22×C4—1721no—
573C22×C4—1722no—
574C22×C4C23×D4311yescharacteristic
575M16—21no—
576M16—21no—
577M16—21no—
578M16—21no—
579M16—432no—
580M16—432no—
581M16—864no—
582M16—864no—
583M16—861no—
584M16—861no—
585M16—861no—
586M16—861no—
587M16—1722no—
588M16C2×C4×D4312yes—
589M16C2×C4×D4312yes—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—431no—
596C2×C8—431no—
597C2×C8—862no—
598C2×C8—862no—
599C2×C8—862no—
600C2×C8—862no—
601C2×C8—864no—
602C2×C8—864no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—1722no—
609C2×C8D4×D4311yescharacteristic
610C2×C8D4×D4311yescharacteristic
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—431no—
614C4⋊C4—431no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4D4×D4311yescharacteristic
620C4⋊C4D4×D4311yescharacteristic
621C22⋊C4—21no—
622C22⋊C4—861no—
623C22⋊C4—861no—
624C22⋊C4—861no—
625C22⋊C4—1721no—
626C22⋊C4—1721no—
627C42—21no—
628C42—861no—
629C42—861no—
630C42—861no—
631C42—1721no—
632C42—1721no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—81no—
637C23—81no—
638C23—431no—
639C23—431no—
640C23—432no—
641C23—432no—
642C23—1721no—
643C23—1721no—
644C23#41×D4311yescharacteristic
645Q8—862no—
646Q8—862no—
647Q8—1721no—
648Q8—1721no—
649D4—22no—
650D4—22no—
651D4—41no—
652D4—41no—
653D4—1724no—
654D4—1724no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—81no—
659C2×C4—432no—
660C2×C4—431no—
661C2×C4—431no—
662C2×C4—432no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—432no—
667C2×C4—432no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—862no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—3441no—
675C2×C4—1722no—
676C2×C4—1722no—
677C2×C4—1724no—
678C2×C4—1724no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4C22×C4×D4311yescharacteristic
683C2×C4C2×D4×D4311yescharacteristic
684C2×C4C2×D4×D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C8—22no—
689C8—22no—
690C8—21no—
691C8—21no—
692C8—41no—
693C8—862no—
694C8—862no—
695C8—861no—
696C8—861no—
697C8—1721no—
698C22—21no—
699C22—21no—
700C22—42no—
701C22—82no—
702C22—82no—
703C22—81no—
704C22—81no—
705C22—432no—
706C22—432no—
707C22—861no—
708C22—861no—
709C22—861no—
710C22—861no—
711C22—1722no—
712C22—1722no—
713C22#117×D4311yescharacteristic
714C22#121×D4311yescharacteristic
715C22#126×D4311yescharacteristic
716C4—41no—
717C4—41no—
718C4—81no—
719C4—432no—
720C4—432no—
721C4—3441no—
722C4—1721no—
723C4—1721no—
724C4—1722no—
725C4C4×D4×D4311yescharacteristic
726C4C4×D4×D4311yescharacteristic
727C4#123×D4311yescharacteristic
728C4#124×D4311yescharacteristic
729C2—21no—
730C2—21no—
731C2—82no—
732C2—862no—
733C2—862no—
734C2#388×D4311yescharacteristic
735C2#1914431011yescharacteristic
736C2#1914431311yescharacteristic
subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1931C2
socleC22×C43C2×#121
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1931D43
hypocenterC43#21075
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1931

Complements

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

NH ≅ G/Ntype
1. #19143182C2semidirect
5. #405×D43C2semidirect
6. #19135260C2semidirect
7. #19135259C2semidirect
8. #19135254C2semidirect
9. #19135251C2semidirect
10. #19135250C2semidirect
11. #19135249C2semidirect
12. #19135248C2semidirect
13. #19134332C2semidirect
14. #341×D43C2semidirect
15. C43×#1931C2semidirect
44. #14582880C4semidirect
136. #13063243C2×C4semidirect
137. #13063243C2×C4semidirect
138. #13063242C2×C4semidirect
158. #100×C43C2×C4semidirect
369. #1931D43semidirect
436. C43#21075semidirect
521. #100C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191431822
#191431092
C2×#145828922
C2×#145828802
#405×D432
#191352602
#191352592
#191352542
#191352512
#191352502
#191352492
#191352482
#191343322
#341×D432
C43×#19312
#2107543