Finite Group Databasebeta

← #25138073

Subgroups — #25138073

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144408C211yesmaximal, characteristic
2C2×#14583192C211yesmaximal, characteristic, complemented
3#19143410C211yesmaximal, characteristic
4#19143259C211yesmaximal, characteristic
5#19136039C211yesmaximal, characteristic
6#19136037C211yesmaximal, characteristic
7#19135895C211yesmaximal, characteristic
8#19135894C211yesmaximal, characteristic
9#19135582C211yesmaximal, characteristic, complemented
10#19135380C211yesmaximal, characteristic, complemented
11#19135377C211yesmaximal, characteristic, complemented
12#19135369C211yesmaximal, characteristic, complemented
13#19135253C211yesmaximal, characteristic, complemented
14#19134589C211yesmaximal, characteristic, complemented
15C43×#1930C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18#14583367C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20#14583193—21no—
21#14583192—21no—
22#14583192—21no—
23#14583192—21no—
24#14583192—21no—
25#14583188—21no—
26#14583183—21no—
27#14583178—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×#13063258C2211yescharacteristic
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
68C22×Dic86—21no—
69#13063356—22no—
70#13063356—22no—
71C2×#10621885—21no—
72C2×#10621884—21no—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063324—21no—
78#13063324—21no—
79#13063324—21no—
80#13063324—21no—
81Q8×Dic43—21no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84Q8×Dic43—21no—
85#13063290D411yescharacteristic
86#13063290D411yescharacteristic
87#13063287D411yescharacteristic
88#13063287D411yescharacteristic
89(C22⋊D43)⋊C4—21no—
90(C22⋊D43)⋊C4—21no—
91#13063282—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#13063258—21no—
106#13063258—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×Dic86—41no—
173C2×Dic86—41no—
174C2×Dic86—82no—
175C2×Dic86C2×D411yescharacteristic
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C22⋊C4×C43—21no—
194C42×C43—21no—
195#10621885—24no—
196#10621884—24no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—41no—
204C4⋊Dic43—41no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—41no—
208Dic43⋊C4—41no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—41no—
212C4×Dic43—41no—
213C4×Dic43C2×D411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877#4112yes—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C23×C43C2×#4111yescharacteristic
231C22×D43—21no—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43—41no—
235Q8×C43—41no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—81no—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C22⋊D43—41no—
250C22⋊D43—41no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—81no—
257C2×Dic43—81no—
258C2×Dic43#12111yescharacteristic
259C2×Dic43#12111yescharacteristic
260C2×Dic43#12111yescharacteristic
261C2×Dic43#12111yescharacteristic
262D172—21no—
263D172—21no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—42no—
267C4×D43—81no—
268Dic86—21no—
269Dic86—21no—
270Dic86—82no—
271Dic86—82no—
272C8×C43—21no—
273C8×C43—21no—
274C8×C43—41no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—22no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#24722—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43C2×#12111yescharacteristic
286C22×C43#55211yescharacteristic
287C22×C43#55611yescharacteristic
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C4×C43—42no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43#52511yescharacteristic
296C4×C43#53611yescharacteristic
297C4×C43#54711yescharacteristic
298C4×C43#54811yescharacteristic
299Dic43—21no—
300Dic43—21no—
301Dic43—21no—
302Dic43—41no—
303Dic43—81no—
304Dic43—81no—
305Dic43#47312yes—
306#3079—431no—
307C2×#477—431no—
308C4×#137—431no—
309#2925—431no—
310#2078—431no—
311#2078—431no—
312#2052—431no—
313#2052—431no—
314#1997—431no—
315#1952—431no—
316#1952—431no—
317#1950—431no—
318#1930—431no—
319#1930D4311yescharacteristic, complemented
320#1801—431no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43#241511yescharacteristic
324C2×C43C2×#47311yescharacteristic
325C2×C43#306811yescharacteristic
326D43—81no—
327C2×#137—431no—
328C2×C4⋊Q8—431no—
329C4×#41—431no—
330C2×C4×Q8—431no—
331#477—861no—
332#477—861no—
333#477—861no—
334#477—861no—
335#477—861no—
336#476—861no—
337#475—861no—
338#474—861no—
339#441—861no—
340#440—861no—
341C4×Q16—861no—
342C4×SD16—861no—
343#433—861no—
344#433—861no—
345#432—861no—
346#431—861no—
347C2×#108—431no—
348C2×#108—431no—
349#428—431no—
350#428—431no—
351#428C2×D4311yescharacteristic
352C2×#107—431no—
353C2×#107—431no—
354#423—431no—
355#423—431no—
356C2×C4⋊C8—431no—
357#419C2×D4311yescharacteristic
358#417—431no—
359#417—431no—
360#417—431no—
361C2×#103—431no—
362C2×#103C2×D4311yescharacteristic
363C2×#101—431no—
364C2×#101C2×D4311yescharacteristic
365#408—431no—
366#408—431no—
367#405—431no—
368#405C2×D4311yescharacteristic
369C4×M16—431no—
370#343—431no—
371#343—431no—
372#343—431no—
373#343—431no—
374#343—431no—
375#343C2×D4311yescharacteristic
376#341—431no—
377#341C2×D4311yescharacteristic
378C43#2472211yescharacteristic, complemented, Sylow
379C2×#41—431no—
380C22×Q8—861no—
381C22×Q8C22×D4311yescharacteristic
382#137—862no—
383#137—862no—
384C2×Q16—861no—
385C2×SD16—861no—
386C2×M16—431no—
387C2×M16—431no—
388C2×M16—431no—
389C2×M16C22×D4311yescharacteristic
390C2×M16C22×D4311yescharacteristic
391C2×M16C22×D4311yescharacteristic
392C22×C8—431no—
393C22×C8C22×D4311yescharacteristic
394C4⋊Q8—861no—
395C4⋊Q8—861no—
396C4⋊Q8—861no—
397C4⋊Q8—861no—
398C4×Q8—431no—
399C4×Q8—431no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×D4—431no—
405C4×D4—431no—
406C4×D4—861no—
407C4×D4—861no—
408#117—861no—
409#117C22×D4311yescharacteristic
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418#108—862no—
419#108—862no—
420#107—21no—
421#107—861no—
422#107—861no—
423#107—861no—
424#107—861no—
425#107—861no—
426#107—861no—
427#106—21no—
428#106—861no—
429#106—861no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437C4⋊C8—861no—
438#103—21no—
439#103—21no—
440#103—21no—
441#103—21no—
442#103—861no—
443#103—861no—
444#103—861no—
445#103—861no—
446#103—861no—
447#102—861no—
448#102—861no—
449#102—861no—
450#101—22no—
451#101—862no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456#97—21no—
457#97—861no—
458#97—861no—
459C4×C8—21no—
460C4×C8—861no—
461C4×C8—861no—
462#41—861no—
463#41—861no—
464#41—861no—
465#41—861no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—431no—
472C2×Q8—3442no—
473C2×Q8—1721no—
474C2×Q8—1721no—
475C2×Q8#1062189812yes—
476C2×D4—431no—
477C2×D4—861no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4C23×D4311yescharacteristic
488Q16—864no—
489SD16—864no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—21no—
496M16—432no—
497M16—861no—
498M16—861no—
499M16—861no—
500M16—861no—
501M16—861no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8D4×D4311yescharacteristic
515C2×C8D4×D4311yescharacteristic
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C4⋊C4—1721no—
528C4⋊C4D4×D4311yescharacteristic
529C4⋊C4D4×D4311yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—861no—
532C22⋊C4—861no—
533C42—21no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—861no—
539C42—861no—
540C42—1721no—
541C42—1721no—
542C23—861no—
543C23#41×D4311yescharacteristic
544Q8—22no—
545Q8—22no—
546Q8—41no—
547Q8—41no—
548Q8—861no—
549Q8—861no—
550Q8—3442no—
551Q8—3442no—
552D4—861no—
553D4—861no—
554D4—1721no—
555D4—1721no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—431no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—431no—
567C2×C4—862no—
568C2×C4—861no—
569C2×C4—3441no—
570C2×C4—3441no—
571C2×C4—3441no—
572C2×C4—1722no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C2×D4×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C2×C4C2×#1062189811yescharacteristic
582C2×C4#1306337211yescharacteristic
583C2×C4#1306337211yescharacteristic
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—862no—
590C8—861no—
591C8—861no—
592C8—1721no—
593C8—1721no—
594C22—21no—
595C22—21no—
596C22—1721no—
597C22—1721no—
598C22—1721no—
599C22#121×D4311yescharacteristic
600C22#1458358211yescharacteristic
601C22#1458361611yescharacteristic
602C4—41no—
603C4—41no—
604C4—42no—
605C4—81no—
606C4—432no—
607C4—861no—
608C4—861no—
609C4—861no—
610C4—3441no—
611C4—3441no—
612C4—1721no—
613C4#1458340811yescharacteristic
614C4#1458346911yescharacteristic
615C4#1458354711yescharacteristic
616C4#1458355811yescharacteristic
617C2—21no—
618C2—21no—
619C2—3441no—
620C2#1913802111yescharacteristic
621C2#473×D4311yescharacteristic
622C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1930C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
hypercenter#1930D43
hypocenterC43#24722
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×#14583192C2semidirect
9. #19135582C2semidirect
10. #19135380C2semidirect
11. #19135377C2semidirect
12. #19135369C2semidirect
13. #19135253C2semidirect
14. #19134589C2semidirect
15. C43×#1930C2semidirect
319. #1930D43semidirect
378. C43#24722semidirect

Maximal subgroups

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

subgroupindex
#191444082
C2×#145831922
#191434102
#191432592
#191360392
#191360372
#191358952
#191358942
#191355822
#191353802
#191353772
#191353692
#191352532
#191345892
C43×#19302
#2472243