Finite Group Databasebeta

← #25080555

Subgroups — #25080555

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#487×D43C211yesmaximal, characteristic, complemented
2#19144403C211yesmaximal, characteristic
3#19144077C211yesmaximal, characteristic
4C8×#10621900C211yesmaximal, characteristic
5#19134028C211yesmaximal, characteristic, complemented
6#19134026C211yesmaximal, characteristic, complemented
7#19134024C211yesmaximal, characteristic, complemented
8#19134022C211yesmaximal, characteristic, complemented
9#19134020C211yesmaximal, characteristic, complemented
10#19134018C211yesmaximal, characteristic, complemented
11#19134016C211yesmaximal, characteristic, complemented
12#19133349C211yesmaximal, characteristic, complemented
13#19133278C211yesmaximal, characteristic, complemented
14#19133265C211yesmaximal, characteristic, complemented
15C43×#1679C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×#10621900C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583248—21no—
24#14583248—21no—
25#14583193—21no—
26#14583187—21no—
27#14583185C2211yescharacteristic
28#14583181C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583110C2211yescharacteristic
31#14583108—21no—
32#14583106C2211yescharacteristic
33#14583104C2211yescharacteristic
34#14583102—21no—
35C8×Dic86C2211yescharacteristic
36#14583023C2211yescharacteristic
37D4×C43⋊C8C2211yescharacteristic
38C8×C22⋊D43—21no—
39(C22⋊D43)⋊C8—21no—
40#14582951C2211yescharacteristic
41#14582949—21no—
42#14582940—21no—
43#14582921C2211yescharacteristic
44#14582921C2211yescharacteristic
45#14582906—21no—
46#14582897—21no—
47#103×D43—21no—
48#103×D43—21no—
49C2×C8×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×Q8×D43—21no—
69C2×Q8×D43—21no—
70#13063354—44no—
71C2×Dic172—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43D411yescharacteristic
78C2×C8×D43D411yescharacteristic
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063324—21no—
82#13063324—21no—
83#13063324—21no—
84#13063324—21no—
85#13063323—21no—
86#13063323—21no—
87C4×Dic86C2311yescharacteristic
88#13063290D411yescharacteristic
89D4×Dic43D411yescharacteristic
90C4×C22⋊D43—21no—
91(C22⋊D43)⋊C4—21no—
92#13063283D411yescharacteristic
93#13063281—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C2×C4×Dic43—21no—
99C42×D43C2311yescharacteristic
100#13063258—21no—
101#13063257—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063249—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063248—21no—
119#13063248—21no—
120#13063248—21no—
121#13063246—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133C4⋊Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×D4×C43C2×D411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152Q8×D43—42no—
153Q8×D43—42no—
154Q8×D43—42no—
155Q8×D43—42no—
156#10621900—22no—
157#10621900SD1614yes—
158C2×C4×D43—41no—
159C2×C4×D43—41no—
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43#4111yescharacteristic
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—41no—
166C2×Dic86—41no—
167C2×Dic86C2×D411yescharacteristic
168SD16×C43—42no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—42no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183#10621885—42no—
184#10621883—42no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43#4111yescharacteristic
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209Dic172—42no—
210#10621872—42no—
211#10621872—42no—
212C8×D43—41no—
213C8×D43—41no—
214C23×C43—21no—
215C22×D43#12111yescharacteristic
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220D4×C43—21no—
221D4×C43C2×SD1612yes—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—24no—
231C2×Dic43—21no—
232C2×Dic43—24no—
233C2×Dic43—21no—
234C2×Dic43—42no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43#12111yescharacteristic
238C2×Dic43#12111yescharacteristic
239C2×Dic43#12111yescharacteristic
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—22no—
243C4×D43—82no—
244C4×D43—82no—
245C4×D43C2×SD1612yes—
246C4×D43#13512yes—
247Dic86—21no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—82no—
253Dic86—82no—
254Dic86C2×SD1612yes—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43—41no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265#19275—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43C2×#12111yescharacteristic
270C2×D43—21no—
271C2×D43—21no—
272C2×D43#46512yes—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43C22×SD1611yescharacteristic
278C4×C43C2×#13511yescharacteristic
279C4×C43#57511yescharacteristic
280C4×C43#57511yescharacteristic
281Dic43—21no—
282Dic43—22no—
283Dic43—41no—
284Dic43—81no—
285Dic43—81no—
286Dic43#46512yes—
287Dic43#47312yes—
288C2×#487—431no—
289#3079—431no—
290#3039—431no—
291C8×#41—431no—
292#1680—431no—
293#1680—431no—
294#1680—431no—
295#1680—431no—
296#1679—431no—
297#1679—431no—
298#1679—431no—
299#1679D4311yescharacteristic, complemented
300#1566—431no—
301#1549—431no—
302#1546—431no—
303C2×C43—42no—
304C2×C43#304011yescharacteristic
305C2×C43C2×#46511yescharacteristic
306C2×C43C2×#47311yescharacteristic
307D43—22no—
308C2×#137—861no—
309C2×C4⋊Q8—431no—
310C2×C4⋊Q8—431no—
311C4×#41—431no—
312#487—431no—
313#487—431no—
314#487—431no—
315#487—861no—
316#487—861no—
317#487C2×D4311yescharacteristic
318#477—861no—
319#476—861no—
320#475—431no—
321#475—431no—
322#474—431no—
323#474C2×D4311yescharacteristic
324#462—431no—
325#462—431no—
326#462—861no—
327#461—431no—
328#461—861no—
329#461C2×D4311yescharacteristic
330C8×Q8—431no—
331C8×Q8—431no—
332C8×D4—431no—
333C8×D4—861no—
334C8×D4—861no—
335C8×D4C2×D4311yescharacteristic
336#431—431no—
337#431—861no—
338#428—861no—
339#423—431no—
340#423—431no—
341#419—861no—
342#417—861no—
343C2×#103—861no—
344C2×#103—861no—
345C2×C4×C8—431no—
346C2×C4×C8—861no—
347#334—431no—
348#334—431no—
349#334—431no—
350#334C2×D4311yescharacteristic
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332C2×D4311yescharacteristic
358#332C2×D4311yescharacteristic
359C43#1927511yescharacteristic, complemented, Sylow
360C2×#41—431no—
361C22×Q8—861no—
362C22×Q8—861no—
363#137—1724no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×SD16—21no—
367C2×SD16—861no—
368C2×M16—861no—
369C2×M16—861no—
370C22×C8—21no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—861no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8—861no—
377C4⋊Q8—861no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8C22×D4311yescharacteristic
383C4⋊Q8C22×D4311yescharacteristic
384C4×Q8—431no—
385C4×Q8—431no—
386C4×D4—431no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4C22×D4311yescharacteristic
390#117—431no—
391#117—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C42—431no—
397C2×C42—861no—
398#107—21no—
399#107—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#103—861no—
426#102—21no—
427#102—861no—
428C22⋊C8—21no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438#41—434no—
439#41—862no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—431no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—1721no—
446C2×Q8—1721no—
447C2×Q8—1722no—
448C2×Q8—1722no—
449C2×Q8—1722no—
450C2×Q8—1722no—
451C2×D4—861no—
452C2×D4D4×D4311yescharacteristic
453C22×C4—21no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—1721no—
460C22×C4—1721no—
461Q16—1722no—
462Q16—1722no—
463SD16—42no—
464SD16—1722no—
465M16—1722no—
466M16—1722no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—42no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—1721no—
477C2×C8—1721no—
478C2×C8—1722no—
479C2×C8D4×D4311yescharacteristic
480C2×C8D4×D4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—431no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C4⋊C4D4×D4311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C42—431no—
501C42—431no—
502C42—431no—
503C42—861no—
504C42—861no—
505C42—861no—
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—431no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—432no—
514Q8—861no—
515Q8—3442no—
516Q8—3442no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520Q8—1721no—
521D4—21no—
522D4—864no—
523D4SD16×D4312yes—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—431no—
530C2×C4—431no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—431no—
534C2×C4—862no—
535C2×C4—864no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—3442no—
541C2×C4—3442no—
542C2×C4—1722no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4C2×D4×D4311yescharacteristic
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—861no—
554C8—861no—
555C8—1721no—
556C8—1721no—
557C8—1721no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—432no—
562C22—861no—
563C22—861no—
564C22#121×D4311yescharacteristic
565C4—21no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—432no—
570C4—432no—
571C4—861no—
572C4—862no—
573C4—3441no—
574C4—3441no—
575C4—1721no—
576C4C2×SD16×D4311yescharacteristic
577C4#135×D4311yescharacteristic
578C4#1458369511yescharacteristic
579C4#1458369611yescharacteristic
580C2—42no—
581C2—862no—
582C2#1914408411yescharacteristic
583C2#465×D4311yescharacteristic
584C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1679C2
socleC22×C43C2×#121
prime radicalC2×#10621900D4
hypercenter#1679D43
hypocenterC43#19275
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1679

Complements

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

NH ≅ G/Ntype
1. #487×D43C2semidirect
5. #19134028C2semidirect
6. #19134026C2semidirect
7. #19134024C2semidirect
8. #19134022C2semidirect
9. #19134020C2semidirect
10. #19134018C2semidirect
11. #19134016C2semidirect
12. #19133349C2semidirect
13. #19133278C2semidirect
14. #19133265C2semidirect
15. C43×#1679C2semidirect
299. #1679D43semidirect
359. C43#19275semidirect

Maximal subgroups

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

subgroupindex
#487×D432
#191444032
#191440772
C8×#106219002
#191340282
#191340262
#191340242
#191340222
#191340202
#191340182
#191340162
#191333492
#191332782
#191332652
C43×#16792
#1927543