Finite Group Databasebeta

← #25138117

Subgroups — #25138117

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144418C211yesmaximal, characteristic
2C2×#14583206C211yesmaximal, characteristic, complemented
3C4×#13063356C211yesmaximal, characteristic
4#19143263C211yesmaximal, characteristic
5#19136044C211yesmaximal, characteristic
6#19136039C211yesmaximal, characteristic
7#19135894C211yesmaximal, characteristic
8#19135894C211yesmaximal, characteristic
9#19135587C211yesmaximal, characteristic, complemented
10#19135379C211yesmaximal, characteristic, complemented
11#19135374C211yesmaximal, characteristic, complemented
12#19135368C211yesmaximal, characteristic, complemented
13#19135252C211yesmaximal, characteristic, complemented
14#19135252C211yesmaximal, characteristic, complemented
15C43×#1801C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583207—21no—
20#14583207—21no—
21#14583206—21no—
22#14583206—21no—
23#14583206—21no—
24#14583206—21no—
25#14583200—21no—
26#14583200—21no—
27#14583004—21no—
28#14582997—21no—
29C4×#10621885—21no—
30C4×#10621884—21no—
31#14582959—21no—
32#14582959—21no—
33#14582955—21no—
34#14582951—21no—
35C2×#13063260C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582939C2211yescharacteristic
40C2×#13063258C2211yescharacteristic
41C2×#13063256C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43#14582908C2211yescharacteristic
44#14582901C2211yescharacteristic
45#14582901C2211yescharacteristic
46#14582898C2211yescharacteristic
47C2×#13063249C2211yescharacteristic
48C2×#13063249C2211yescharacteristic
49#14582867C2211yescharacteristic
50#14582867C2211yescharacteristic
51#14582857C2211yescharacteristic
52#14582857C2211yescharacteristic
53C4×#10621877C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582663C2211yescharacteristic
59#14582663C2211yescharacteristic
60C2×C4×Q8×C43C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C43×#423C2211yescharacteristic
63C2×#101×C43C2211yescharacteristic
64C2×#101×C43C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063356—22no—
69#13063356—22no—
70C2×#10621885—21no—
71C2×#10621884—21no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063317—21no—
77#13063317—21no—
78#13063317—21no—
79#13063317—21no—
80C4×Dic86D411yescharacteristic
81C4×Dic86D411yescharacteristic
82C4×D172D411yescharacteristic
83C4×D172D411yescharacteristic
84C4×C22⋊D43—21no—
85C4×C22⋊D43—21no—
86#13063284C2311yescharacteristic
87#13063282—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C42×D43—21no—
93#13063260—22no—
94#13063260—22no—
95#13063259—21no—
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)D411yescharacteristic
106C4⋊(C43⋊C8)D411yescharacteristic
107C4⋊(C43⋊C8)D411yescharacteristic
108C4⋊(C43⋊C8)D411yescharacteristic
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063249—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063247—21no—
119#13063247—21no—
120#13063245—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125#13063236—21no—
126#13063235—21no—
127#13063235—21no—
128C4×C43⋊C8—21no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C22×Q8×C43C2311yescharacteristic
132C2×M16×C43C2311yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C4×Q8×C43—21no—
137C4×Q8×C43—21no—
138C4×Q8×C43—21no—
139C4×Q8×C43—21no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C42×C43—21no—
143C2×C42×C43C2311yescharacteristic
144C4⋊C8×C43—21no—
145C4⋊C8×C43—21no—
146C4⋊C8×C43—21no—
147C4⋊C8×C43—21no—
148#101×C43—22no—
149#101×C43—22no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43#4112yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164#10621898—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898—21no—
168C2×D172C2×D411yescharacteristic
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×Dic86C2×D411yescharacteristic
173M16×C43—21no—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43—41no—
189C42×C43—41no—
190C42×C43—41no—
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C22⋊Dic43—21no—
196#10621885—24no—
197#10621884—24no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43C2×D411yescharacteristic
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210Dic43⋊C4—41no—
211Dic43⋊C4—41no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218#10621877#4112yes—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8C2×D411yescharacteristic
226C2×C43⋊C8C2×D411yescharacteristic
227C2×C43⋊C8C2×D411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229C23×C43C2×#4111yescharacteristic
230C22×D43—21no—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—41no—
234Q8×C43—41no—
235C2×C4×C43—22no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—81no—
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C22⋊D43—41no—
253C22⋊D43—41no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—81no—
260C2×Dic43—81no—
261D172—21no—
262D172—21no—
263C4×D43—42no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—81no—
267Dic86—21no—
268Dic86—21no—
269C8×C43—41no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C43⋊C8—22no—
274C43⋊C8—21no—
275C43⋊C8—21no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—41no—
279#24725—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43C2×#12111yescharacteristic
283C22×C43#55211yescharacteristic
284C22×C43#55611yescharacteristic
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—42no—
293C4×C43—81no—
294C4×C43#52511yescharacteristic
295C4×C43#53611yescharacteristic
296C4×C43#54711yescharacteristic
297C4×C43#54811yescharacteristic
298Dic43—41no—
299Dic43—41no—
300Dic43—41no—
301Dic43—81no—
302Dic43—81no—
303#3080—431no—
304C2×#479—431no—
305C4×#137—431no—
306#2925—431no—
307#2079—431no—
308#2078—431no—
309#2052—431no—
310#2052—431no—
311#1998—431no—
312#1952—431no—
313#1951—431no—
314#1950—431no—
315#1930—431no—
316#1930—431no—
317#1801D4311yescharacteristic, complemented
318C2×C43—21no—
319C2×C43—21no—
320C2×C43#241511yescharacteristic
321C2×C43#306711yescharacteristic
322C2×C43#306911yescharacteristic
323D43—81no—
324C2×#137—431no—
325C2×#125—431no—
326C4×#41—431no—
327C2×C4×Q8C2×D4311yescharacteristic
328#479—861no—
329#479—861no—
330#479—861no—
331#479—861no—
332#479—861no—
333#479—861no—
334#478—861no—
335#478—861no—
336#441—861no—
337#440—861no—
338C4×Q16—861no—
339C4×SD16—861no—
340#433—861no—
341#433—861no—
342#432—861no—
343#431—861no—
344C2×#108—431no—
345C2×#108—431no—
346#428—431no—
347#428—431no—
348#428—431no—
349C2×#107—431no—
350C2×#106—431no—
351#423C2×D4311yescharacteristic
352#423C2×D4311yescharacteristic
353C2×C4⋊C8—431no—
354#419—431no—
355#417—431no—
356#417—431no—
357#417—431no—
358C2×#103—431no—
359C2×#103—431no—
360C2×#101C2×D4311yescharacteristic
361C2×#101C2×D4311yescharacteristic
362#408—431no—
363#408—431no—
364#405—431no—
365#405—431no—
366C4×M16—431no—
367#343—431no—
368#343—431no—
369#343—431no—
370#343—431no—
371#343C2×D4311yescharacteristic
372#343C2×D4311yescharacteristic
373#341—431no—
374#341—431no—
375C43#2472511yescharacteristic, complemented, Sylow
376C2×#41—431no—
377C22×Q8C22×D4311yescharacteristic
378#137—862no—
379#137—862no—
380C2×Q16—861no—
381C2×SD16—861no—
382C2×M16—431no—
383C2×M16—431no—
384C2×M16C22×D4311yescharacteristic
385C2×M16C22×D4311yescharacteristic
386C2×M16C22×D4311yescharacteristic
387C2×M16C22×D4311yescharacteristic
388C22×C8—431no—
389C22×C8—431no—
390#125—861no—
391#125—861no—
392#125—861no—
393#125—861no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—431no—
399C4×Q8—431no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404#117—431no—
405#117—861no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C42—21no—
413C2×C42—861no—
414C2×C42C22×D4311yescharacteristic
415#108—862no—
416#108—862no—
417#107—861no—
418#107—861no—
419#107—861no—
420#107—861no—
421#107—861no—
422#106—861no—
423#106—861no—
424#106—861no—
425#106—861no—
426#106—861no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—431no—
435#103—861no—
436#103—861no—
437#103—861no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#103—861no—
443#103—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#101—22no—
448#101—22no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453#97—861no—
454#97—861no—
455#97—861no—
456C4×C8—861no—
457C4×C8—861no—
458C4×C8—861no—
459#41—861no—
460#41—861no—
461#41—861no—
462#41—861no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—431no—
469C2×Q8#1062190012yes—
470C2×D4—431no—
471C2×D4—861no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4#1062189811yescharacteristic
480C22×C4#1062189811yescharacteristic
481C22×C4C23×D4311yescharacteristic
482Q16—864no—
483SD16—864no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—432no—
493M16—861no—
494M16—861no—
495M16—861no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—431no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—431no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—431no—
515C4⋊C4—431no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C22⋊C4—861no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C42—41no—
530C42—41no—
531C42—861no—
532C42—861no—
533C42—861no—
534C42D4×D4311yescharacteristic
535C42D4×D4311yescharacteristic
536C42D4×D4311yescharacteristic
537C42D4×D4311yescharacteristic
538C23—861no—
539C23C2×#1062189811yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—41no—
543Q8—41no—
544Q8—861no—
545Q8—861no—
546D4—861no—
547D4—861no—
548D4—1721no—
549D4—1721no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—81no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—3441no—
561C2×C4—3441no—
562C2×C4—3441no—
563C2×C4—1722no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4#1306329811yescharacteristic
569C2×C4#1306329811yescharacteristic
570C2×C4#1306329811yescharacteristic
571C2×C4#1306329811yescharacteristic
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062190011yescharacteristic
576C2×C4#1306337211yescharacteristic
577C2×C4#1306337311yescharacteristic
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—862no—
583C8—861no—
584C8—861no—
585C8—861no—
586C8—861no—
587C8—1721no—
588C22—21no—
589C22—21no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22C2×#1306329811yescharacteristic
594C22#1458358411yescharacteristic
595C22#1458361711yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—81no—
602C4—3441no—
603C4—3441no—
604C4—1721no—
605C4—1721no—
606C4—1721no—
607C4#1458340911yescharacteristic
608C4#1458347211yescharacteristic
609C4#1458355111yescharacteristic
610C4#1458355511yescharacteristic
611C2—21no—
612C2—21no—
613C2—3441no—
614C2#1913802611yescharacteristic
615C2#1914431411yescharacteristic
616C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1801C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
hypercenter#1801D43
hypocenterC43#24725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. C2×#14583206C2semidirect
9. #19135587C2semidirect
10. #19135379C2semidirect
11. #19135374C2semidirect
12. #19135368C2semidirect
13. #19135252C2semidirect
14. #19135252C2semidirect
15. C43×#1801C2semidirect
317. #1801D43semidirect
375. C43#24725semidirect

Maximal subgroups

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

subgroupindex
#191444182
C2×#145832062
C4×#130633562
#191432632
#191360442
#191360392
#191358942
#191355872
#191353792
#191353742
#191353682
#191352522
C43×#18012
#2472543