Finite Group Databasebeta

← #25066343

Subgroups — #25066343

Order 11008.

682 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143560C211yesmaximal, characteristic, complemented
2#19143558C211yesmaximal, characteristic, complemented
3C4×#13063346C211yesmaximal, characteristic
4#19133490C211yesmaximal, characteristic, complemented
5#19133489C211yesmaximal, characteristic, complemented
6#19133487C211yesmaximal, characteristic, complemented
7#19133486C211yesmaximal, characteristic, complemented
8#19133484C211yesmaximal, characteristic, complemented
9#19133478C211yesmaximal, characteristic, complemented
10#19133477C211yesmaximal, characteristic, complemented
11#19133340C211yesmaximal, characteristic, complemented
12#19132976C211yesmaximal, characteristic, complemented
13#19132974C211yesmaximal, characteristic, complemented
14C82×D43C211yesmaximal, characteristic, complemented
15C43×#1590C211yesmaximal, characteristic, complemented
16C2×#13063346C411yescharacteristic
17C4×#10621902C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583030C2211yescharacteristic
20#14583029C2211yescharacteristic
21#14583026C2211yescharacteristic
22C4×#10621885C2211yescharacteristic
23#14582991C411yescharacteristic
24C4×#10621873C2211yescharacteristic
25SD16×Dic43C411yescharacteristic
26#14582986C411yescharacteristic
27C4×#10621882C2211yescharacteristic
28#14582979C411yescharacteristic
29#14582978C2211yescharacteristic
30#14582977C2211yescharacteristic
31#14582976C2211yescharacteristic
32#14582973—21no—
33#14582972—21no—
34#14582969—21no—
35#14582968—21no—
36#14582951—21no—
37#14582951C2211yescharacteristic
38#14582951C2211yescharacteristic
39#14582949—21no—
40#14582934C411yescharacteristic
41#14582894C411yescharacteristic
42#14582892C411yescharacteristic
43#14582851—21no—
44M16×Dic43—21no—
45C4×C8×D43C2211yescharacteristic
46C4×C8×D43C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57C8×C43⋊C8C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621902C2×C411yescharacteristic
68C2×#10621900C2×C411yescharacteristic
69#13063346—24no—
70C2×#10621885C2×C411yescharacteristic
71C2×#10621873C2×C411yescharacteristic
72C2×#10621882C2×C411yescharacteristic
73C2×#10621877—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C2×C8×D43—21no—
77C2×C8×D43C2×C411yescharacteristic
78C2×C8×D43C2×C411yescharacteristic
79C2×C8×D43D411yescharacteristic
80C2×C8×D43D411yescharacteristic
81Q8×Dic43C2×C411yescharacteristic
82C4×Dic86C2311yescharacteristic
83#13063290C2×C411yescharacteristic
84C4×D172—21no—
85C4×D172C2311yescharacteristic
86D4×Dic43C2×C411yescharacteristic
87#13063287—21no—
88#13063287C2×C411yescharacteristic
89C4×C22⋊D43—21no—
90(C22⋊D43)⋊C4—21no—
91#13063283—21no—
92#13063283C2×C411yescharacteristic
93#13063283C2×C411yescharacteristic
94#13063281—21no—
95C2×C4×Dic43—21no—
96C42×D43—21no—
97C42×D43C2311yescharacteristic
98#13063258C2×C411yescharacteristic
99#13063258C2×C411yescharacteristic
100#13063257C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106#13063250C2×C411yescharacteristic
107#13063249C2×C411yescharacteristic
108#13063248C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111#13063245C2×C411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117#13063236—21no—
118#13063235—21no—
119#13063235—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—21no—
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43C2×C411yescharacteristic
127C8×Dic43C2×C411yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43C2×C411yescharacteristic
131C2×M16×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43C2×C411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621902—22no—
152#10621902—22no—
153#10621900—22no—
154#10621900—22no—
155C2×D172—21no—
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43C22×C411yescharacteristic
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43#4111yescharacteristic
163C2×Dic86C22×C411yescharacteristic
164SD16×C43—22no—
165M16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43C22×C411yescharacteristic
175C4⋊C4×C43C22×C411yescharacteristic
176C22⋊C4×C43—21no—
177C42×C43—21no—
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180#10621885—22no—
181#10621882—22no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C22×C411yescharacteristic
188C4⋊Dic43C22×C411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199#10621877—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621873—22no—
208#10621872—42no—
209#10621872—42no—
210C8×D43—24no—
211C8×D43—22no—
212C8×D43—22no—
213C8×D43—22no—
214C8×D43M1614yescomplemented
215C23×C43—21no—
216C22×D43—21no—
217C22×D43C4×D411yescharacteristic
218Q8×C43—21no—
219Q8×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—42no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43C4×D411yescharacteristic
237C2×Dic43C4×D411yescharacteristic
238C2×Dic43C4×D411yescharacteristic
239D172—21no—
240D172—21no—
241D172—42no—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—22no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—42no—
248C4×D43—42no—
249C4×D43C2×M1612yes—
250C4×D43#13112yes—
251Dic86—21no—
252Dic86—21no—
253C8×C43—22no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43C2×M1612yes—
259C8×C43#13512yescomplemented
260C43⋊C8—22no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8C2×M1612yes—
266C43⋊C8#13512yescomplemented
267#17886—431nomaximal, Sylow
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43C2×C4×D411yescharacteristic
272C2×D43—21no—
273C2×D43—21no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43#43612yes—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43C22×M1611yescharacteristic
283C4×C43C2×#13111yescharacteristic
284C4×C43C2×#13511yescharacteristic
285C4×C43C2×#13511yescharacteristic
286Dic43—21no—
287Dic43—41no—
288Dic43—41no—
289Dic43—41no—
290Dic43#43612yes—
291Dic43#44312yes—
292#2965—431no—
293#2965—431no—
294C4×#135—431no—
295#1591—431no—
296#1591—431no—
297#1590—431no—
298#1590—431no—
299#1590—431no—
300#1590D4311yescharacteristic, complemented
301#1589—431no—
302#1589—431no—
303#1564—431no—
304#1476—431no—
305#1476—431no—
306C2×C82—431no—
307C2×C43—81no—
308C2×C43C2×#43611yescharacteristic
309C2×C43C4×#13511yescharacteristic
310C2×C43C2×#44311yescharacteristic
311D43—22no—
312D43—81no—
313C2×#135—431no—
314C4×#41—431no—
315C4×#41—431no—
316#446—431no—
317#446—431no—
318#446—431no—
319#446C2×D4311yescharacteristic
320C4×Q16—431no—
321C4×Q16—431no—
322C4×SD16—431no—
323C4×SD16—431no—
324C4×SD16—431no—
325C4×SD16C2×D4311yescharacteristic
326C4×D8—431no—
327C4×D8—431no—
328#436—431no—
329#436—431no—
330#436—431no—
331#436C2×D4311yescharacteristic
332#435—861no—
333#435—861no—
334#435—861no—
335#435—861no—
336#431—431no—
337#431—431no—
338#431—861no—
339#431—861no—
340#427—431no—
341#416—431no—
342#416—431no—
343C4×M16—861no—
344C4×M16—861no—
345C2×C4×C8—431no—
346C2×C4×C8—431no—
347C2×C4×C8—431no—
348#335—431no—
349#335—431no—
350#334—431no—
351#334C2×D4311yescharacteristic
352Q8⋊C8—431no—
353Q8⋊C8—431no—
354Q8⋊C8—431no—
355Q8⋊C8C2×D4311yescharacteristic
356D4⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8C2×D4311yescharacteristic
360C82—431no—
361C82—431no—
362C82—431no—
363C82C2×D4311yescharacteristic
364C43#1788611yescharacteristic, complemented, Sylow
365C2×#41—431no—
366C2×#41—431no—
367#135—864no—
368C2×Q16—431no—
369C2×SD16—431no—
370C2×SD16C4×D4311yescharacteristic
371C2×D8—431no—
372C2×M16—21no—
373C2×M16—861no—
374C2×M16—861no—
375C2×M16—861no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8—861no—
381C4×Q8—431no—
382C4×Q8—431no—
383C4×Q8—431no—
384C4×Q8C22×D4311yescharacteristic
385C4×D4—431no—
386C4×D4—431no—
387C4×D4—431no—
388C4×D4—861no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4C22×D4311yescharacteristic
393#117—431no—
394#117—431no—
395#117—861no—
396#117—861no—
397C2×C42—431no—
398C2×C42—861no—
399C2×C42—861no—
400#107—431no—
401#107—431no—
402#106—431no—
403#106C4×D4311yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412#103—431no—
413#103—431no—
414#103—431no—
415#103C4×D4311yescharacteristic
416#102—431no—
417#102—431no—
418#102—431no—
419#102C4×D4311yescharacteristic
420C22⋊C8—21no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—21no—
427#97—861no—
428#97—861no—
429#97—861no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—431no—
437C4×C8—861no—
438C4×C8—861no—
439C4×C8—861no—
440C4×C8C22×D4311yescharacteristic
441C4×C8C22×D4311yescharacteristic
442C4×C8C22×D4311yescharacteristic
443#41—862no—
444#41—862no—
445#41—862no—
446#41—862no—
447C2×Q8—431no—
448C2×Q8C2×C4×D4311yescharacteristic
449C2×D4—431no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4C2×C4×D4311yescharacteristic
453C22×C4—21no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462Q16—862no—
463SD16—22no—
464SD16—862no—
465D8—862no—
466M16—42no—
467M16—1722no—
468M16—1722no—
469M16—1722no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—434no—
476C2×C8—431no—
477C2×C8—431no—
478C2×C8—862no—
479C2×C8—862no—
480C2×C8—864no—
481C2×C8—861no—
482C2×C8—862no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8C2×C4×D4311yescharacteristic
486C2×C8C2×C4×D4311yescharacteristic
487C2×C8D4×D4311yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—431no—
491C4⋊C4—431no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4C2×C4×D4311yescharacteristic
496C4⋊C4C2×C4×D4311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C22⋊C4—861no—
503C42—21no—
504C42—431no—
505C42—431no—
506C42—431no—
507C42—861no—
508C42—861no—
509C42—861no—
510C42—861no—
511C42—861no—
512C42C23×D4311yescharacteristic
513C23—21no—
514C23—431no—
515C23—861no—
516Q8—21no—
517Q8—21no—
518Q8—861no—
519Q8—861no—
520D4—21no—
521D4—21no—
522D4—861no—
523D4—861no—
524D4—1722no—
525D4—1722no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—431no—
532C2×C4—431no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—431no—
536C2×C4—862no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4C22×C4×D4311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4#41×D4311yescharacteristic
551C8—22no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—432no—
557C8—432no—
558C8—862no—
559C8—861no—
560C8—861no—
561C8—1721no—
562C8—1721no—
563C8M16×D4312yes—
564C8#1306334612yescomplemented
565C22—41no—
566C22—41no—
567C22—41no—
568C22—432no—
569C22—861no—
570C22—861no—
571C22—1721no—
572C22—1721no—
573C22—1721no—
574C22C4×D4×D4311yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—432no—
580C4—432no—
581C4—861no—
582C4—1721no—
583C4—1721no—
584C4—1721no—
585C4C2×M16×D4311yescharacteristic
586C4#131×D4311yescharacteristic
587C4#135×D4311yescharacteristic
588C4C2×#1306334611yescharacteristic
589C2—81no—
590C2—862no—
591C2—3441no—
592C2#436×D4311yescharacteristic
593C2C4×#1306334611yescharacteristic
594C2#443×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1590C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063346C4
cosocleC42×C43C24
hypercenter#1590D43
hypocenterC43#17886
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
1. #19143560C2semidirect
2. #19143558C2semidirect
4. #19133490C2semidirect
5. #19133489C2semidirect
6. #19133487C2semidirect
7. #19133486C2semidirect
8. #19133484C2semidirect
9. #19133478C2semidirect
10. #19133477C2semidirect
11. #19133340C2semidirect
12. #19132976C2semidirect
13. #19132974C2semidirect
14. C82×D43C2semidirect
15. C43×#1590C2semidirect
214. C8×D43M16semidirect
259. C8×C43#135semidirect
266. C43⋊C8#135semidirect
300. #1590D43semidirect
364. C43#17886semidirect
564. C8#13063346semidirect

Maximal subgroups

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

subgroupindex
#191435602
#191435582
C4×#130633462
#191334902
#191334892
#191334872
#191334862
#191334842
#191334782
#191334772
#191333402
#191329762
#191329742
C82×D432
C43×#15902
#1788643