Finite Group Databasebeta

← #25138108

Subgroups — #25138108

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#19144415C211yesmaximal, characteristic
2C2×#14583205C211yesmaximal, characteristic, complemented
3#19143419C211yesmaximal, characteristic
4#19143257C211yesmaximal, characteristic
5#19136043C211yesmaximal, characteristic
6#19135893C211yesmaximal, characteristic
7#19135892C211yesmaximal, characteristic
8#19135586C211yesmaximal, characteristic, complemented
9#19135378C211yesmaximal, characteristic, complemented
10#19135374C211yesmaximal, characteristic, complemented
11#19135369C211yesmaximal, characteristic, complemented
12#19135251C211yesmaximal, characteristic, complemented
13#19135248C211yesmaximal, characteristic, complemented
14#19134590C211yesmaximal, characteristic, complemented
15C43×#2078C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18#41×Dic43C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20#14583208—21no—
21#14583205—21no—
22#14583205—21no—
23#14583205—21no—
24#14583205—21no—
25#14583204—21no—
26#14583201—21no—
27#14583197—21no—
28#14583003—21no—
29#14582996—21no—
30#14582991—21no—
31#14582990—21no—
32#14582957—21no—
33#14582957—21no—
34#14582953—21no—
35#14582949—21no—
36C2×#13063261C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582939C2211yescharacteristic
40#14582939C2211yescharacteristic
41C2×#13063256C2211yescharacteristic
42#14582922C2211yescharacteristic
43#14582922C2211yescharacteristic
44C2×Dic43⋊C8C2211yescharacteristic
45#14582909C2211yescharacteristic
46#14582900C2211yescharacteristic
47C2×#13063250C2211yescharacteristic
48C2×#13063248C2211yescharacteristic
49C2×#13063243C2211yescharacteristic
50C2×#13063243C2211yescharacteristic
51#14582866C2211yescharacteristic
52#14582857C2211yescharacteristic
53#14582854C2211yescharacteristic
54M16×Dic43C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582668C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582663C2211yescharacteristic
60C2×#107×C43C2211yescharacteristic
61C43×#417C2211yescharacteristic
62C43×#417C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C43×#343C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68#13063355—22no—
69#13063355—22no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063316—21no—
77#13063316—21no—
78#13063316—21no—
79#13063316—21no—
80Q8×Dic43D411yescharacteristic
81Q8×Dic43D411yescharacteristic
82#13063290—21no—
83#13063290—21no—
84#13063290—21no—
85#13063290—21no—
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43D411yescharacteristic
89D4×Dic43D411yescharacteristic
90#13063284—21no—
91#13063284C2311yescharacteristic
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063261—22no—
100#13063260—22no—
101#13063259—21no—
102#13063258—21no—
103#13063258—21no—
104#13063257—21no—
105#13063256—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8D411yescharacteristic
114Dic43⋊C8D411yescharacteristic
115Dic43⋊C8D411yescharacteristic
116Dic43⋊C8D411yescharacteristic
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063250—21no—
121#13063249—21no—
122#13063248—21no—
123#13063248—21no—
124#13063246—21no—
125#13063243—22no—
126#13063243—22no—
127C22⋊(C43⋊C8)—21no—
128C22⋊(C43⋊C8)—21no—
129#13063235—21no—
130#13063235—21no—
131#13063235—21no—
132C8×Dic43—21no—
133C8×Dic43—21no—
134C8×Dic43—21no—
135C2×#41×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142#107×C43—21no—
143#107×C43—21no—
144#103×C43—21no—
145#103×C43—21no—
146#102×C43—21no—
147#102×C43—21no—
148C22⋊C8×C43—21no—
149C22⋊C8×C43—21no—
150#41×C43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43—21no—
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—21no—
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C2411yescharacteristic
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43#4111yescharacteristic
166C22×Dic43#4111yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86#4112yes—
173M16×C43—21no—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C22⋊Dic43—21no—
191C22⋊Dic43—21no—
192C22⋊Dic43—21no—
193#10621885—24no—
194#10621883—24no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—41no—
200C4⋊Dic43—41no—
201C4⋊Dic43C2×D411yescharacteristic
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—41no—
211C4×Dic43—41no—
212C4×Dic43C2×D411yescharacteristic
213C4×Dic43C2×D411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877#4112yes—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C2×D411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229C23×C43—21no—
230C23×C43C2×#4111yescharacteristic
231Q8×C43—21no—
232Q8×C43—21no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—41no—
236D4×C43—41no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—81no—
243C2×C4×C43—81no—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—81no—
260C2×Dic43—81no—
261C2×Dic43#12111yescharacteristic
262C2×Dic43#12111yescharacteristic
263C2×Dic43#12111yescharacteristic
264C2×Dic43#12111yescharacteristic
265Dic86—22no—
266Dic86—22no—
267Dic86—41no—
268Dic86—41no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C43⋊C8—22no—
275C43⋊C8—21no—
276C43⋊C8—21no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#24725—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×#12111yescharacteristic
286C22×C43#55211yescharacteristic
287C22×C43#55611yescharacteristic
288C4×C43—41no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43#52511yescharacteristic
292C4×C43#53611yescharacteristic
293C4×C43#54711yescharacteristic
294C4×C43#54811yescharacteristic
295Dic43—21no—
296Dic43—21no—
297Dic43—21no—
298Dic43—21no—
299Dic43—42no—
300Dic43—41no—
301Dic43—41no—
302Dic43—81no—
303#3080—431no—
304C2×#479—431no—
305C4×#137—431no—
306#2925—431no—
307#2079—431no—
308#2078D4311yescharacteristic
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#1801—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—81no—
321C2×C43#241511yescharacteristic
322C2×C43#306711yescharacteristic
323C2×C43#306911yescharacteristic
324C2×#137—431no—
325C2×#125—431no—
326C4×#41—431no—
327C2×C4×Q8—431no—
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×#107C2×D4311yescharacteristic
350C2×#106—431no—
351#423—431no—
352#423—431no—
353C2×C4⋊C8—431no—
354#419—431no—
355#417—431no—
356#417C2×D4311yescharacteristic
357#417C2×D4311yescharacteristic
358C2×#103—431no—
359C2×#103—431no—
360C2×#101—431no—
361C2×#101—431no—
362#408—431no—
363#408C2×D4311yescharacteristic
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#341C2×D4311yescharacteristic
375C43#2472511yescharacteristic, complemented, Sylow
376C2×#41C22×D4311yescharacteristic
377C22×Q8—431no—
378#137—862no—
379#137—862no—
380C2×Q16—861no—
381C2×SD16—861no—
382C2×M16—431no—
383C2×M16—431no—
384C2×M16—431no—
385C2×M16C22×D4311yescharacteristic
386C2×M16C22×D4311yescharacteristic
387C2×M16C22×D4311yescharacteristic
388C22×C8—431no—
389C22×C8C22×D4311yescharacteristic
390#125—861no—
391#125—861no—
392#125—861no—
393#125—861no—
394C4×Q8—431no—
395C4×Q8—431no—
396C4×Q8—861no—
397C4×Q8—861no—
398C4×Q8—861no—
399C4×Q8—861no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404#117—431no—
405#117—861no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C42—431no—
413C2×C42—861no—
414C2×C42—861no—
415#108—862no—
416#108—862no—
417#107—21no—
418#107—21no—
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—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435#103—21no—
436#103—21no—
437#103—861no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#103—861no—
443#103—861no—
444#102—21no—
445#102—21no—
446#102—861no—
447#101—862no—
448#101—862no—
449C22⋊C8—21no—
450C22⋊C8—21no—
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—21no—
460#41—21no—
461#41—21no—
462#41—21no—
463C2×Q8—432no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8D4×D4311yescharacteristic
470C2×D4—21no—
471C2×D4D4×D4311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4C23×D4311yescharacteristic
482Q16—864no—
483SD16—864no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—432no—
491M16—861no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16—861no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8D4×D4311yescharacteristic
509C2×C8D4×D4311yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—431no—
515C4⋊C4—431no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—1721no—
521C4⋊C4—1721no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C22⋊C4—861no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—861no—
534C42—861no—
535C42—861no—
536C42—1721no—
537C42—1721no—
538C23—21no—
539C23#41×D4311yescharacteristic
540Q8—21no—
541Q8—21no—
542Q8—862no—
543Q8—862no—
544Q8—1721no—
545Q8—1721no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—431no—
558C2×C4—431no—
559C2×C4—431no—
560C2×C4—431no—
561C2×C4—862no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—3441no—
565C2×C4—3441no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1722no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#1306337211yescharacteristic
577C2×C4#1306337211yescharacteristic
578C8—21no—
579C8—21no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—862no—
584C8—861no—
585C8—861no—
586C8—1721no—
587C8—1721no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#121×D4311yescharacteristic
594C22#1458358511yescharacteristic
595C22#1458361611yescharacteristic
596C4—41no—
597C4—81no—
598C4—81no—
599C4—861no—
600C4—861no—
601C4—861no—
602C4—861no—
603C4—3441no—
604C4—1721no—
605C4—1721no—
606C4—1722no—
607C4#1458340711yescharacteristic
608C4#1458347111yescharacteristic
609C4#1458354711yescharacteristic
610C4#1458355711yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2#1913801911yescharacteristic
615C2#1914431311yescharacteristic
616C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2078C2
socleC22×C43C2×#121
prime radicalC2×#41×C43C23
hypercenter#2078D43
hypocenterC43#24725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2078

Complements

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

NH ≅ G/Ntype
2. C2×#14583205C2semidirect
8. #19135586C2semidirect
9. #19135378C2semidirect
10. #19135374C2semidirect
11. #19135369C2semidirect
12. #19135251C2semidirect
13. #19135248C2semidirect
14. #19134590C2semidirect
375. C43#24725semidirect

Maximal subgroups

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

subgroupindex
#191444152
C2×#145832052
#191434192
#191432572
#191360432
#191358932
#191358922
#191355862
#191353782
#191353742
#191353692
#191352512
#191352482
#191345902
C43×#20782
#2472543