Finite Group Databasebeta

← #25124076

Subgroups — #25124076

Order 11008.

1610 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C211yesmaximal, characteristic
2C2×#14582935C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic, complemented
4C22×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
5#19136974C211yesmaximal, characteristic, complemented
6#19135796C212yesmaximal, complemented
7#19135789C212yesmaximal, complemented
8#19135782C212yesmaximal, complemented
9#19135775C212yesmaximal, complemented
10#19134312C211yesmaximal, characteristic, complemented
11C2×C43×#416C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C23×C43⋊C8C2211yescharacteristic
14#14583406—24no—
15#14583406—24no—
16C2×#13063306—21no—
17C2×#13063301C2212yes—
18C2×#13063296C2212yes—
19C2×#13063293—21no—
20C2×C4×C22⋊D43—22no—
21C2×#13063284C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23#14582935—24no—
24C2×#13063258C2212yescomplemented
25C2×#13063256C2212yescomplemented
26#14582895—24no—
27C2×#13063249C2211yescharacteristic, complemented
28C2×#13063249C2211yescharacteristic, complemented
29C2×#13063246C2211yescharacteristic, complemented
30C2×#13063246C2211yescharacteristic, complemented
31C2×(C2×D43)⋊C8—24no—
32C2×(C2×D43)⋊C8C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34#14582760—21no—
35#14582756C2212yes—
36#14582756C2212yes—
37#14582754—21no—
38C4×(C2×D43)⋊C4—22no—
39#14582662C2212yescomplemented
40#14582662C2212yescomplemented
41C22×#41×C43C2211yescharacteristic
42C23×C8×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C43×#416—24no—
45C2×#103×C43C2212yescomplemented
46C2×#102×C43C2212yescomplemented
47C24×D43D411yescharacteristic
48C22×C22⋊D43—22no—
49C23×Dic43D411yescharacteristic
50C22×C4×D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43—22no—
55C22×C4×D43—22no—
56C22×C4×D43D412yes—
57C22×C4×D43C2312yes—
58C22×C43⋊C8—22no—
59C22×C43⋊C8—22no—
60C22×C43⋊C8D414yescomplemented
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063306—28no—
64#13063301—24no—
65#13063301—24no—
66#13063296—24no—
67#13063296—24no—
68#13063293—28no—
69C4×C22⋊D43—216no—
70#13063284—22no—
71#13063284—22no—
72#13063284—22no—
73#13063284D414yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2312yes—
77C2×Dic43⋊C4—22no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—22no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063258—24no—
87#13063256—24no—
88#13063249—22no—
89#13063249—22no—
90#13063246—22no—
91#13063246—22no—
92(C2×D43)⋊C8—24no—
93(C2×D43)⋊C8—24no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C2×#41×C43—22no—
97C2×#41×C43—22no—
98C2×#41×C43—22no—
99C2×#41×C43—22no—
100C2×#41×C43—22no—
101C2×#41×C43D414yes—
102C22×Q8×C43C2311yescharacteristic
103C22×D4×C43—21no—
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C23×C4×C43C2311yescharacteristic
107C22×C8×C43—22no—
108C22×C8×C43—22no—
109C22×C8×C43—22no—
110C22×C8×C43C2312yes—
111#117×C43—22no—
112#117×C43—22no—
113C2×C4⋊C4×C43C2312yes—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43—21no—
116#103×C43—24no—
117#102×C43—24no—
118C24×C43—21no—
119C24×C43C2×D411yescharacteristic
120C23×D43—22no—
121C23×D43—24no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—42no—
125C23×D43C2×D412yes—
126#41×C43—28no—
127#41×C43—28no—
128#41×C43—44no—
129#41×C43—44no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43C2×D412yes—
136C2×D4×C43—21no—
137C2×D4×C43—24no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—42no—
143C2×D4×C43—42no—
144C2×D4×C43C2×D412yes—
145C22×C4×C43—24no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4112yes—
155C22×C4×C43#4112yes—
156C22×C4×C43#4112yes—
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—28no—
159C2×C22⋊D43—44no—
160C2×C22⋊D43—44no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43C2×D412yes—
168C2×C4×D43—24no—
169C2×C4×D43—24no—
170C2×C4×D43—24no—
171C2×C4×D43—22no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—44no—
178C2×C4×D43—44no—
179C2×C4×D43—44no—
180C2×C4×D43—44no—
181C2×C8×C43—22no—
182C2×C8×C43—22no—
183C2×C8×C43—22no—
184C2×C8×C43—44no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43—22no—
187C22⋊C4×C43—42no—
188C42×C43—42no—
189C22⋊Dic43—28no—
190C22⋊Dic43—24no—
191C22⋊Dic43—42no—
192(C2×D43)⋊C4—28no—
193(C2×D43)⋊C4—44no—
194(C2×D43)⋊C4—44no—
195C4⋊Dic43—22no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C2×D414yes—
201Dic43⋊C4—28no—
202C4×Dic43—24no—
203C4×Dic43—42no—
204C2×C43⋊C8—28no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×D412yes—
210C2×C43⋊C8C2×D412yes—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—42no—
217C23×C43—42no—
218C23×C43#12012yes—
219C23×C43#12112yes—
220C23×C43#12312yes—
221C23×C43C22×D411yescharacteristic
222C22×D43—28no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—48no—
230C22×D43—48no—
231C22×D43—44no—
232C22×D43—44no—
233C22×D43#13514yes—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—48no—
241D4×C43—41no—
242D4×C43—41no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—48no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43#12012yes—
251C2×C4×C43#12114yes—
252C2×C4×C43#12114yes—
253C2×C4×C43#12112yes—
254C2×C4×C43#12312yes—
255C2×C4×C43#12314yes—
256C2×C4×C43#12414yes—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C22⋊D43—416no—
264C2×Dic43—24no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—44no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C4×D43—42no—
276C4×D43—42no—
277C4×D43—42no—
278C4×D43—42no—
279C4×D43—48no—
280C8×C43—42no—
281C43⋊C8—22no—
282C43⋊C8—22no—
283#23479—431nomaximal, Sylow
284C22×C43—24no—
285C22×C43—24no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—42no—
289C22×C43—44no—
290C22×C43—82no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43#39414yes—
294C22×C43C2×#12011yescharacteristic
295C22×C43C2×#12111yescharacteristic
296C22×C43C2×#12311yescharacteristic
297C22×C43C2×#13512yes—
298C22×C43#57512yes—
299C2×D43—24no—
300C2×D43—24no—
301C2×D43—24no—
302C2×D43—416no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C4×C43—42no—
308C4×C43—82no—
309C4×C43#39414yes—
310C4×C43C2×#12111yescharacteristic
311C4×C43C2×#12111yescharacteristic
312C4×C43C2×#12311yescharacteristic
313C4×C43C2×#12411yescharacteristic
314Dic43—42no—
315Dic43—44no—
316Dic43—81no—
317Dic43—81no—
318C2×#525—431no—
319C2×#427—431no—
320C2×#416—431no—
321C2×#416D4311yescharacteristic, complemented
322C22×C22⋊C8—431no—
323#2280—431no—
324#2036—432no—
325#2035—432no—
326#2034—432no—
327#2033—432no—
328#1735—431no—
329C2×C43—24no—
330C2×C43—82no—
331C2×C43C2×#39411yescharacteristic
332C2×C43#300212yes—
333C2×C43#305011yescharacteristic
334C2×C43#305411yescharacteristic
335C2×C43#309112yes—
336D43—44no—
337C22×#41C2×D4311yescharacteristic
338C24×C4—431no—
339C23×C8—431no—
340C23×C8C2×D4311yescharacteristic
341#525—864no—
342#525—864no—
343C2×#123—861no—
344C2×C22⋊Q8—432no—
345C2×#121—432no—
346C2×#120—861no—
347C2×C4×D4—862no—
348C2×#117—431no—
349C2×#117—431no—
350C2×#117C2×D4311yescharacteristic
351#427—864no—
352C2×#107—432no—
353C2×#106—432no—
354#416—24no—
355#416—864no—
356C2×#103—431no—
357C2×#103—431no—
358C2×#103C2×D4312yescomplemented
359C2×#102—431no—
360C2×#102—431no—
361C2×#102C2×D4312yescomplemented
362C2×C22⋊C8—432no—
363C2×C22⋊C8—432no—
364C2×C22⋊C8—864no—
365#381—861no—
366#380—432no—
367#380—432no—
368#379—861no—
369C4×C22⋊C4—862no—
370#340—432no—
371#340—432no—
372C43#2347911yescharacteristic, complemented, Sylow
373C25—431no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41C22⋊D4314yes—
380C22×Q8C22×D4311yescharacteristic
381C22×D4—21no—
382C22×D4—862no—
383C22×D4C22×D4311yescharacteristic
384C23×C4—21no—
385C23×C4—431no—
386C23×C4—432no—
387C23×C4—432no—
388C23×C4—862no—
389C23×C4—862no—
390C23×C4—862no—
391C23×C4—862no—
392C23×C4—862no—
393C23×C4—862no—
394C23×C4C22×D4311yescharacteristic
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—22no—
398C22×C8—434no—
399C22×C8—431no—
400C22×C8—431no—
401C22×C8—862no—
402C22×C8—862no—
403C22×C8C22×D4312yes—
404#123—868no—
405C22⋊Q8—864no—
406C22⋊Q8—864no—
407#121—864no—
408#121—864no—
409#120—868no—
410C4×D4—8616no—
411#117—22no—
412#117—22no—
413#117—434no—
414#117—862no—
415#117—862no—
416#117—862no—
417C2×C4⋊C4—432no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—862no—
421C2×C4⋊C4C22×D4312yes—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—862no—
424C2×C22⋊C4—862no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—862no—
427C2×C22⋊C4—862no—
428C2×C22⋊C4—861no—
429C2×C42—21no—
430C2×C42—861no—
431C2×C42—861no—
432#107—864no—
433#106—864no—
434#103—24no—
435#103—862no—
436#103—862no—
437#102—24no—
438#102—862no—
439#102—862no—
440C22⋊C8—864no—
441C22⋊C8—864no—
442#95—862no—
443#95—862no—
444C24—21no—
445C24—432no—
446C24—864no—
447C24—862no—
448C24—862no—
449C24—862no—
450C24—1722no—
451C24D4×D4311yescharacteristic
452#41—28no—
453#41—28no—
454#41—44no—
455#41—44no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8C2×C22⋊D4312yes—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—868no—
471C2×D4—1724no—
472C2×D4—1724no—
473C2×D4C2×C22⋊D4312yes—
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—432no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—864no—
485C22×C4—864no—
486C22×C4—864no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—1724no—
496C22×C4—1724no—
497C22×C4—1724no—
498C22×C4—1724no—
499C22×C4#1062189812yes—
500C22×C4#1062189812yes—
501C22×C4D4×D4312yes—
502C22×C4D4×D4312yes—
503C22×C4D4×D4311yescharacteristic
504C22×C4#1062190012yes—
505C22×C4C2×C22⋊D4312yes—
506C22×C4C23×D4311yescharacteristic
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—44no—
511C2×C8—432no—
512C2×C8—432no—
513C2×C8—868no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—434no—
521C4⋊C4—868no—
522C4⋊C4—862no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C22⋊C4—42no—
528C22⋊C4—868no—
529C22⋊C4—868no—
530C22⋊C4—864no—
531C22⋊C4—1724no—
532C22⋊C4—1724no—
533C22⋊C4—1722no—
534C42—42no—
535C42—864no—
536C42—1722no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—41no—
541C23—41no—
542C23—42no—
543C23—42no—
544C23—434no—
545C23—868no—
546C23—862no—
547C23—862no—
548C23—862no—
549C23—862no—
550C23—862no—
551C23—862no—
552C23—1728no—
553C23—1728no—
554C23—1724no—
555C23—1724no—
556C23#1306329312yes—
557C23#1306329812yes—
558C23#1306330712yes—
559C23C2×D4×D4311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564D4—22no—
565D4—22no—
566D4—48no—
567D4—41no—
568D4—41no—
569D4—17216no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—48no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—864no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1724no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1728no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4#1306329312yes—
594C2×C4#1306329714yes—
595C2×C4#1306329812yes—
596C2×C4#1306329814yes—
597C2×C4#1306330712yes—
598C2×C4#1306330814yes—
599C2×C4#1306331114yes—
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4C22×C22⋊D4311yescharacteristic
603C2×C4C2×#1062190011yescharacteristic
604C2×C4C2×#1062189811yescharacteristic
605C2×C4C2×#1062189811yescharacteristic
606C8—42no—
607C8—862no—
608C8—862no—
609C22—22no—
610C22—24no—
611C22—24no—
612C22—22no—
613C22—42no—
614C22—44no—
615C22—81no—
616C22—82no—
617C22—81no—
618C22—864no—
619C22—864no—
620C22—864no—
621C22—17216no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22—1722no—
626C22#1458281414yes—
627C22C2×#1306329311yescharacteristic
628C22C2×#1306329811yescharacteristic
629C22C2×#1306330711yescharacteristic
630C22#135×D4312yes—
631C22#1458369612yes—
632C4—42no—
633C4—82no—
634C4—3441no—
635C4—3441no—
636C4—1722no—
637C4—1724no—
638C4#1458281414yes—
639C4C2×#1306329711yescharacteristic
640C4C2×#1306329811yescharacteristic
641C4C2×#1306330811yescharacteristic
642C4C2×#1306331111yescharacteristic
643C2—24no—
644C2—82no—
645C2—1724no—
646C2C2×#1458281411yescharacteristic
647C2#1914380912yes—
648C2#1914417511yescharacteristic
649C2#1914420311yescharacteristic
650C2#1914450612yes—
subgroupG/H
centerC22×C4D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#416C2
socleC23×C43C22×D4
prime radicalC2×#14583406C2
hypercenterC2×#416D43
hypocenterC43#23479
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#14582935C2semidirect
3. C2×#14582895C2semidirect
4. C22×(C2×D43)⋊C8C2semidirect
5. #19136974C2semidirect
6. #19135796C2semidirect
7. #19135789C2semidirect
8. #19135782C2semidirect
9. #19135775C2semidirect
10. #19134312C2semidirect
11. C2×C43×#416C2semidirect
24. C2×#13063258C22semidirect
25. C2×#13063256C22semidirect
27. C2×#13063249C22semidirect
28. C2×#13063249C22semidirect
29. C2×#13063246C22semidirect
30. C2×#13063246C22semidirect
39. #14582662C22semidirect
40. #14582662C22semidirect
45. C2×#103×C43C22semidirect
46. C2×#102×C43C22semidirect
60. C22×C43⋊C8D4semidirect
321. C2×#416D43semidirect
358. C2×#103C2×D43semidirect
361. C2×#102C2×D43semidirect
372. C43#23479semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#145829352
C2×#145828952
C22×(C2×D43)⋊C82
#191369742
#191357962
#191357892
#191357822
#191357752
#191343122
C2×C43×#4162
#2347943