Finite Group Databasebeta

← #25152796

Subgroups — #25152796

Order 11008.

1422 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063312C211yesmaximal, characteristic
2C2×#14583252C212yesmaximal, complemented
3#19142903C211yesmaximal, characteristic, complemented
4#19135835C212yesmaximal, complemented
5#19135834C212yesmaximal, complemented
6#19135405C212yesmaximal, complemented
7#19134531C211yesmaximal, characteristic, complemented
8#19134529C211yesmaximal, characteristic, complemented
9#19134526C211yesmaximal, characteristic
10C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
11C43×#1786C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C2×#13063316C2211yescharacteristic, complemented
14C2×#13063312—28no—
15C2×#13063312—21no—
16C2×#13063312—21no—
17C2×#13063312C2212yes—
18C2×#13063312C2212yes—
19C22×C22⋊Dic43—21no—
20C22×C22⋊Dic43—21no—
21C22×C4×Dic43C2211yescharacteristic
22#14583252—28no—
23C2×#13063250C2212yescomplemented
24C2×#13063250C2212yescomplemented
25C2×#13063248C2212yescomplemented
26C2×#13063248C2212yescomplemented
27C2×#13063246C2212yes—
28C2×#13063246C2212yes—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C8×Dic43C2212yescomplemented
31#14582798C2211yescharacteristic, complemented
32#14582795C2211yescharacteristic, complemented
33#14582786—21no—
34#14582782—21no—
35#14582774—21no—
36#14582771—21no—
37#14582764C2211yescharacteristic, complemented
38#14582759C2211yescharacteristic
39#14582653C2212yescomplemented
40C23×D4×C43C2211yescharacteristic
41C2×#102×C43C2212yes—
42C2×#102×C43C2212yes—
43C2×C22⋊C8×C43C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C22×Dic86—21no—
46C22×Dic86—24no—
47C22×Dic86—22no—
48C22×Dic86—22no—
49C22×Dic86—42no—
50C22×Dic86C2312yes—
51C23×Dic43—21no—
52C23×Dic43D411yescharacteristic
53C23×Dic43D411yescharacteristic
54C22×C43⋊C8C2312yes—
55#13063316—24no—
56#13063312—28no—
57#13063312—28no—
58#13063312—24no—
59#13063312—24no—
60#13063312—24no—
61#13063312D418yes—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43C2311yescharacteristic
65C2×C4⋊Dic43C2311yescharacteristic
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×C22⋊Dic43—28no—
69C2×C22⋊Dic43—28no—
70C2×C22⋊Dic43—22no—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—22no—
73C2×C22⋊Dic43—22no—
74C2×C22⋊Dic43—21no—
75C2×C4×Dic43—24no—
76C2×C4×Dic43D411yescharacteristic
77C2×C4×Dic43D411yescharacteristic
78C2×C4×Dic43C2311yescharacteristic
79C2×C4×Dic43C2311yescharacteristic
80#13063250—24no—
81#13063250—42no—
82#13063248—24no—
83#13063248—42no—
84#13063246—24no—
85#13063246—42no—
86C22⋊(C43⋊C8)—22no—
87C8×Dic43—24no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C25×C43—21no—
94C22×D4×C43—24no—
95C22×D4×C43—21no—
96C22×D4×C43—22no—
97C22×D4×C43—22no—
98C22×D4×C43—42no—
99C22×D4×C43C2312yes—
100C23×C4×C43C2311yescharacteristic
101C22×C8×C43C2312yes—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C22⋊C4×C43—21no—
105#102×C43—24no—
106#102×C43—42no—
107C22⋊C8×C43—22no—
108#95×C43—21no—
109C24×C43—24no—
110C24×C43—22no—
111C24×C43—42no—
112C24×C43—42no—
113C24×C43—42no—
114C24×C43—42no—
115C24×C43—42no—
116C24×C43—42no—
117C24×C43C2×D411yescharacteristic
118C2×D4×C43—24no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—48no—
125C2×D4×C43—48no—
126C2×D4×C43—42no—
127C2×D4×C43—42no—
128C2×D4×C43C2×D414yes—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43#4112yes—
135C22×C4×C43#4112yes—
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—24no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—41no—
146C22×Dic43—41no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×Dic86—22no—
154C2×Dic86—22no—
155C2×Dic86—22no—
156C2×Dic86—22no—
157C2×Dic86—24no—
158C2×Dic86—22no—
159C2×Dic86—48no—
160C2×Dic86—48no—
161C2×Dic86—42no—
162C2×Dic86—42no—
163C2×Dic86C2×D414yes—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C22⋊C4×C43—42no—
170C22⋊Dic43—28no—
171C22⋊Dic43—28no—
172C22⋊Dic43—28no—
173C22⋊Dic43—28no—
174C22⋊Dic43—42no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43—42no—
178C4⋊Dic43—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181C4×Dic43—22no—
182C4×Dic43—22no—
183C4×Dic43—22no—
184C4×Dic43C2×D414yes—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C23×C43—21no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—24no—
193C23×C43—48no—
194C23×C43—48no—
195C23×C43—48no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—84no—
203C23×C43—84no—
204C23×C43—84no—
205C23×C43—84no—
206C23×C43#12412yes—
207C23×C43#13512yes—
208C23×C43#13512yes—
209C23×C43C22×D411yescharacteristic
210D4×C43—24no—
211D4×C43—24no—
212D4×C43—48no—
213D4×C43—42no—
214D4×C43—42no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43#12412yes—
226C2×C4×C43C22×D412yes—
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43H(5,𝔽2)12yes—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—24no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—44no—
242C2×Dic43—44no—
243C2×Dic43—48no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43#12012yes—
253C2×Dic43#12012yes—
254Dic86—24no—
255Dic86—24no—
256Dic86—48no—
257Dic86—42no—
258Dic86—42no—
259C8×C43—42no—
260C43⋊C8—42no—
261#25859—431nomaximal, Sylow
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—44no—
269C22×C43—44no—
270C22×C43—44no—
271C22×C43—816no—
272C22×C43—82no—
273C22×C43—82no—
274C22×C43—82no—
275C22×C43—82no—
276C22×C43#48814yescomplemented
277C22×C43C2×#12011yescharacteristic
278C22×C43C2×#12411yescharacteristic
279C22×C43#53511yescharacteristic
280C22×C43C2×#13511yescharacteristic
281C22×C43C2×#13511yescharacteristic
282C22×C43#57511yescharacteristic
283C22×C43#57511yescharacteristic
284C4×C43—22no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43#54612yes—
288C4×C43#54612yes—
289Dic43—22no—
290Dic43—22no—
291Dic43—44no—
292Dic43—41no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296C22×#124—431no—
297C2×#488—432no—
298#2851—431no—
299#2042—432no—
300#2042—432no—
301#1958—432no—
302#1787—431no—
303#1787—431no—
304#1786—431no—
305#1786D4311yescharacteristic
306C4×C22⋊C8—431no—
307C2×C43—24no—
308C2×C43—84no—
309C2×C43#243511yescharacteristic
310C2×C43#300211yescharacteristic
311C2×C43#300211yescharacteristic
312C2×C43C2×#48811yescharacteristic
313C2×C43#314011yescharacteristic
314C2×C43#321111yescharacteristic
315C2×C43#321111yescharacteristic
316C23×Q8—431no—
317C23×D4C2×D4311yescharacteristic
318C2×#125—431no—
319C2×#124—432no—
320C2×#124—432no—
321C2×#124—861no—
322C2×#124—861no—
323C2×#124—868no—
324C22×C22⋊C4—861no—
325C22×C22⋊C4—861no—
326C22×C42—431no—
327#488—868no—
328C2×#103—432no—
329C2×#103—432no—
330C2×#103—432no—
331C2×#103—432no—
332C2×#102—432no—
333C2×#102—432no—
334C2×#102C2×D4312yes—
335C2×#102C2×D4312yes—
336C2×C22⋊C8—431no—
337C2×C22⋊C8C2×D4311yescharacteristic
338C2×C4×C8—432no—
339#389—431no—
340#389—431no—
341#387—861no—
342#387—861no—
343#385—861no—
344#385—861no—
345#382—431no—
346#380—431no—
347#380C2×D4311yescharacteristic
348#336—432no—
349C43#2585911yescharacteristic, complemented, Sylow
350C25—21no—
351C22×Q8—432no—
352C22×Q8—864no—
353C22×Q8—861no—
354C22×Q8—862no—
355C22×Q8—862no—
356C22×Q8—1722no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—21no—
360C22×D4—22no—
361C22×D4—42no—
362C22×D4C22×D4312yes—
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—861no—
366C23×C4C22×D4311yescharacteristic
367C22×C8—432no—
368C22×C8C22×D4312yes—
369#125—864no—
370#124—438no—
371#124—864no—
372#124—864no—
373#124—868no—
374#124—868no—
375#124—864no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4—862no—
387C2×C22⋊C4—862no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4—868no—
390C2×C22⋊C4—868no—
391C2×C22⋊C4—861no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—864no—
397#103—864no—
398#103—864no—
399#103—1722no—
400#103—1722no—
401#102—24no—
402#102—42no—
403#102—864no—
404#102—1722no—
405C22⋊C8—22no—
406C22⋊C8—862no—
407C4×C8—864no—
408#95—21no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414C24—24no—
415C24—22no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24D4×D4311yescharacteristic
423C2×Q8—434no—
424C2×Q8—864no—
425C2×Q8—862no—
426C2×Q8—862no—
427C2×Q8—862no—
428C2×Q8—862no—
429C2×Q8—862no—
430C2×Q8—1728no—
431C2×Q8—1728no—
432C2×Q8—1722no—
433C2×Q8—1722no—
434C2×D4—24no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4D4×D4314yes—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—864no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4#1062189812yes—
466C22×C4D4×D4311yescharacteristic
467C22×C4#1062190012yes—
468C22×C4C23×D4311yescharacteristic
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—862no—
473C2×C8—862no—
474C2×C8—862no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—1722no—
480C4⋊C4—1722no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C22⋊C4—42no—
484C22⋊C4—868no—
485C22⋊C4—868no—
486C22⋊C4—868no—
487C22⋊C4—868no—
488C22⋊C4—1722no—
489C42—434no—
490C42—862no—
491C42—862no—
492C42—862no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—24no—
498C23—48no—
499C23—48no—
500C23—48no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—84no—
508C23—84no—
509C23—84no—
510C23—84no—
511C23#1306331112yes—
512C23#1306334412yes—
513C23#1306334612yes—
514C23C2×D4×D4311yescharacteristic
515Q8—864no—
516Q8—864no—
517Q8—1728no—
518Q8—1722no—
519Q8—1722no—
520D4—24no—
521D4—24no—
522D4—48no—
523D4—42no—
524D4—42no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—864no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—1724no—
549C2×C4—1724no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1728no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4#1306331112yes—
560C2×C4C2×D4×D4312yes—
561C2×C4C2×#1062190011yescharacteristic
562C2×C4C2×#1062189811yescharacteristic
563C2×C4#1306337012yes—
564C8—42no—
565C8—1722no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—816no—
576C22—82no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22#1458325214yescomplemented
581C22#120×D4311yescharacteristic
582C22C2×#1306331111yescharacteristic
583C22#1458346411yescharacteristic
584C22C2×#1306334411yescharacteristic
585C22C2×#1306334611yescharacteristic
586C22#1458369511yescharacteristic
587C22#1458369511yescharacteristic
588C4—22no—
589C4—81no—
590C4—81no—
591C4—862no—
592C4—862no—
593C4—3441no—
594C4—3441no—
595C4—1721no—
596C4—1721no—
597C4—1724no—
598C4#1458353612yes—
599C4#1458353912yes—
600C2—24no—
601C2—84no—
602C2#1913824411yescharacteristic
603C2#1914380811yescharacteristic
604C2#1914381411yescharacteristic
605C2C2×#1458325211yescharacteristic
606C2#1914497911yescharacteristic
607C2#1914555711yescharacteristic
608C2#1914556311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenter#1786D43
hypocenterC43#25859
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#14583252C2semidirect
3. #19142903C2semidirect
4. #19135835C2semidirect
5. #19135834C2semidirect
6. #19135405C2semidirect
7. #19134531C2semidirect
8. #19134529C2semidirect
10. C22⋊C8×Dic43C2semidirect
13. C2×#13063316C22semidirect
23. C2×#13063250C22semidirect
24. C2×#13063250C22semidirect
25. C2×#13063248C22semidirect
26. C2×#13063248C22semidirect
30. C2×C8×Dic43C22semidirect
31. #14582798C22semidirect
32. #14582795C22semidirect
37. #14582764C22semidirect
39. #14582653C22semidirect
276. C22×C43#488semidirect
349. C43#25859semidirect
580. C22#14583252semidirect

Maximal subgroups

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

subgroupindex
C22×#130633122
C2×#145832522
#191429032
#191358352
#191358342
#191354052
#191345312
#191345292
#191345262
C22⋊C8×Dic432
C43×#17862
#2585943