Finite Group Databasebeta

← #25138110

Subgroups — #25138110

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#19144416C211yesmaximal, characteristic
2C2×#14583208C211yesmaximal, characteristic, complemented
3#19143410C211yesmaximal, characteristic
4#19143259C211yesmaximal, characteristic
5#19136044C211yesmaximal, characteristic
6#19136037C211yesmaximal, characteristic
7#19135895C211yesmaximal, characteristic
8#19135894C211yesmaximal, characteristic
9#19135586C211yesmaximal, characteristic, complemented
10#19135380C211yesmaximal, characteristic, complemented
11#19135372C211yesmaximal, characteristic, complemented
12#19135369C211yesmaximal, characteristic, complemented
13#19135253C211yesmaximal, characteristic, complemented
14#19134589C211yesmaximal, characteristic, complemented
15C43×#1930C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18#14583367C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20#14583209—21no—
21#14583208—21no—
22#14583208—21no—
23#14583208—21no—
24#14583208—21no—
25#14583205—21no—
26#14583202—21no—
27#14583198—21no—
28#14583003—21no—
29#14583002—21no—
30#14582991—21no—
31#14582984—21no—
32#14582961—21no—
33#14582958—21no—
34#14582954—21no—
35#14582950—21no—
36C2×#13063261C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38#14582942C2211yescharacteristic
39#14582942C2211yescharacteristic
40C2×#13063259C2211yescharacteristic
41C2×#13063256C2211yescharacteristic
42#14582922C2211yescharacteristic
43#14582922C2211yescharacteristic
44C2×Dic43⋊C8C2211yescharacteristic
45#14582901C2211yescharacteristic
46#14582901C2211yescharacteristic
47#14582898C2211yescharacteristic
48C2×#13063249C2211yescharacteristic
49C2×#13063244C2211yescharacteristic
50#14582867C2211yescharacteristic
51#14582865C2211yescharacteristic
52#14582855C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582663C2211yescharacteristic
60C43×#428C2211yescharacteristic
61C43×#419C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×#101×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063356—22no—
69#13063356—22no—
70C2×#10621885—21no—
71C2×#10621884—21no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063316—21no—
77#13063316—21no—
78#13063316—21no—
79#13063316—21no—
80Q8×Dic43—21no—
81Q8×Dic43—21no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84#13063290D411yescharacteristic
85#13063290D411yescharacteristic
86#13063287D411yescharacteristic
87#13063287D411yescharacteristic
88(C22⋊D43)⋊C4—21no—
89(C22⋊D43)⋊C4—21no—
90#13063282—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C42×D43—21no—
99#13063261—22no—
100#13063260—22no—
101#13063259—21no—
102#13063259—21no—
103#13063258—21no—
104#13063258—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#13063249—21no—
120#13063249—21no—
121#13063248—21no—
122#13063247—21no—
123#13063247—21no—
124#13063245—21no—
125#13063244—22no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129(C2×D43)⋊C8—21no—
130#13063236—21no—
131#13063235—21no—
132C4×C43⋊C8—21no—
133C8×Dic43—21no—
134C22×Q8×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139#117×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141#107×C43—21no—
142#106×C43—21no—
143#103×C43—21no—
144#103×C43—21no—
145#103×C43—21no—
146#103×C43—21no—
147#101×C43—22no—
148#97×C43—21no—
149C4×C8×C43—21no—
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×C43C2411yescharacteristic
159C2×C22⋊D43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43#4111yescharacteristic
163C22×Dic43#4111yescharacteristic
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—
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×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C42×C43—21no—
192#10621885—24no—
193#10621884—24no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—41no—
201C4⋊Dic43—41no—
202C4⋊Dic43—41no—
203C4⋊Dic43—41no—
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
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×C43C2×#4111yescharacteristic
230C22×D43—21no—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—41no—
234Q8×C43—41no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—81no—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C22⋊D43—41no—
249C22⋊D43—41no—
250C2×Dic43—21no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—81no—
256C2×Dic43—81no—
257C2×Dic43#12111yescharacteristic
258C2×Dic43#12111yescharacteristic
259C2×Dic43#12111yescharacteristic
260C2×Dic43#12111yescharacteristic
261D172—21no—
262D172—21no—
263C4×D43—42no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—81no—
267Dic86—21no—
268Dic86—21no—
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×C43C2×#12111yescharacteristic
283C22×C43#55211yescharacteristic
284C22×C43#55611yescharacteristic
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43#52511yescharacteristic
293C4×C43#53611yescharacteristic
294C4×C43#54711yescharacteristic
295C4×C43#54811yescharacteristic
296Dic43—21no—
297Dic43—21no—
298Dic43—21no—
299Dic43—21no—
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#1930D4311yescharacteristic, complemented
317#1801—431no—
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×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#428C2×D4311yescharacteristic
349C2×#107—431no—
350C2×#106—431no—
351#423—431no—
352#423—431no—
353C2×C4⋊C8—431no—
354#419C2×D4311yescharacteristic
355#417—431no—
356#417—431no—
357#417—431no—
358C2×#103—431no—
359C2×#103C2×D4311yescharacteristic
360C2×#101—431no—
361C2×#101C2×D4311yescharacteristic
362#408—431no—
363#408—431no—
364#405—431no—
365#405C2×D4311yescharacteristic
366C4×M16—431no—
367#343—431no—
368#343—431no—
369#343—431no—
370#343—431no—
371#343—431no—
372#343C2×D4311yescharacteristic
373#341—431no—
374#341C2×D4311yescharacteristic
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×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—861no—
405#117C22×D4311yescharacteristic
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C42—431no—
413C2×C42—861no—
414C2×C42—861no—
415#108—862no—
416#108—862no—
417#107—21no—
418#107—861no—
419#107—861no—
420#107—861no—
421#107—861no—
422#106—21no—
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—21no—
438#103—21no—
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—862no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453#97—21no—
454#97—861no—
455#97—861no—
456C4×C8—21no—
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#1062189812yes—
470C2×D4—431no—
471C2×D4—861no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—861no—
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—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—1721no—
519C4⋊C4—1721no—
520C4⋊C4—1721no—
521C4⋊C4—1721no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4D4×D4311yescharacteristic
525C4⋊C4D4×D4311yescharacteristic
526C22⋊C4—21no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C42—21no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—861no—
535C42—861no—
536C42—1721no—
537C42—1721no—
538C23—861no—
539C23#41×D4311yescharacteristic
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—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—81no—
557C2×C4—431no—
558C2×C4—431no—
559C2×C4—431no—
560C2×C4—431no—
561C2×C4—861no—
562C2×C4—3441no—
563C2×C4—3441no—
564C2×C4—3441no—
565C2×C4—1722no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
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—1721no—
591C22—1721no—
592C22—1721no—
593C22#121×D4311yescharacteristic
594C22#1458358211yescharacteristic
595C22#1458361611yescharacteristic
596C4—41no—
597C4—41no—
598C4—42no—
599C4—81no—
600C4—861no—
601C4—861no—
602C4—861no—
603C4—861no—
604C4—3441no—
605C4—3441no—
606C4—1721no—
607C4#1458340811yescharacteristic
608C4#1458346911yescharacteristic
609C4#1458354711yescharacteristic
610C4#1458355811yescharacteristic
611C2—21no—
612C2—21no—
613C2—3441no—
614C2#1913802111yescharacteristic
615C2#1914431711yescharacteristic
616C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1930C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
hypercenter#1930D43
hypocenterC43#24725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1930

Complements

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

NH ≅ G/Ntype
2. C2×#14583208C2semidirect
9. #19135586C2semidirect
10. #19135380C2semidirect
11. #19135372C2semidirect
12. #19135369C2semidirect
13. #19135253C2semidirect
14. #19134589C2semidirect
15. C43×#1930C2semidirect
316. #1930D43semidirect
375. C43#24725semidirect

Maximal subgroups

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

subgroupindex
#191444162
C2×#145832082
#191434102
#191432592
#191360442
#191360372
#191358952
#191358942
#191355862
#191353802
#191353722
#191353692
#191352532
#191345892
C43×#19302
#2472543