Finite Group Databasebeta

← #25080514

Subgroups — #25080514

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#498×D43C211yesmaximal, characteristic, complemented
2#19144409C211yesmaximal, characteristic
3#19144079C211yesmaximal, characteristic
4C8×#10621902C211yesmaximal, characteristic
5#19133979C211yesmaximal, characteristic, complemented
6#19133977C211yesmaximal, characteristic, complemented
7#19133975C211yesmaximal, characteristic, complemented
8#19133973C211yesmaximal, characteristic, complemented
9#19133971C211yesmaximal, characteristic, complemented
10#19133969C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#19133349C211yesmaximal, characteristic, complemented
13#19133274C211yesmaximal, characteristic, complemented
14#19133265C211yesmaximal, characteristic, complemented
15C43×#1672C211yesmaximal, characteristic, complemented
16C2×#13063357—21no—
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×#10621902C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583296—21no—
22#14583296—21no—
23#14583295C2211yescharacteristic
24#14583295C2211yescharacteristic
25#14583194C2211yescharacteristic
26#14583190C2211yescharacteristic
27#14583186C2211yescharacteristic
28#14583182—21no—
29#14583178—21no—
30#14583109C2211yescharacteristic
31#14583107—21no—
32#14583105C2211yescharacteristic
33#14583103—21no—
34#14583101C2211yescharacteristic
35Q8×C43⋊C8C2211yescharacteristic
36C8×D172—21no—
37C8×D172C2211yescharacteristic
38#14582964—21no—
39#14582964C2211yescharacteristic
40#14582951—21no—
41#14582951C2211yescharacteristic
42#14582940—21no—
43#106×D43—21no—
44#106×D43—21no—
45#14582921C2211yescharacteristic
46#14582921C2211yescharacteristic
47#14582906—21no—
48#14582899—21no—
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621902D411yescharacteristic
68C2×Q8×D43—21no—
69C2×Q8×D43—21no—
70#13063357—44no—
71C2×#10621885—21no—
72C2×#10621873—21no—
73C2×#10621884—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43D411yescharacteristic
79C2×C8×D43D411yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063324—21no—
85#13063324—21no—
86#13063323—21no—
87#13063323—21no—
88Q8×Dic43D411yescharacteristic
89C4×D172—21no—
90C4×D172C2311yescharacteristic
91#13063287—21no—
92#13063287D411yescharacteristic
93#13063283—21no—
94#13063283D411yescharacteristic
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C42×D43—21no—
100C42×D43C2311yescharacteristic
101#13063258—21no—
102#13063257—21no—
103#13063257—21no—
104#13063257—21no—
105#13063256—21no—
106#13063256—21no—
107#13063256—21no—
108#13063256—21no—
109#13063256—21no—
110C4⋊(C43⋊C8)—21no—
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113C4⋊(C43⋊C8)C2311yescharacteristic
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116#13063250—21no—
117#13063249—21no—
118#13063249—21no—
119#13063248—21no—
120#13063247—21no—
121#13063245—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×Q16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#103×C43—21no—
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148#10621902—22no—
149#10621902SD1614yes—
150Q8×D43—42no—
151Q8×D43—42no—
152Q8×D43—82no—
153C2×D172—21no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
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—
167Q16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C2×D411yescharacteristic
179C42×C43—21no—
180C42×C43C2411yescharacteristic
181#10621885—42no—
182#10621884—42no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206#10621873—42no—
207#10621872—42no—
208#10621872—42no—
209C8×D43—22no—
210C8×D43—22no—
211C8×D43—42no—
212C8×D43—42no—
213C22×D43—21no—
214C22×D43#12111yescharacteristic
215Q8×C43—21no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—81no—
219Q8×C43C2×SD1612yes—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C2×Dic43#12111yescharacteristic
233D172—24no—
234D172—21no—
235D172C2×SD1612yes—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—24no—
239C4×D43—22no—
240C4×D43—41no—
241C4×D43—41no—
242C4×D43—42no—
243C4×D43—82no—
244C4×D43—82no—
245C4×D43C2×SD1612yes—
246C4×D43#13512yes—
247Dic86—41no—
248Dic86—41no—
249Dic86—82no—
250Dic86—82no—
251Dic86—81no—
252C8×C43—21no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43#13712yescomplemented
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8#13712yescomplemented
262#19270—431nomaximal, Sylow
263C22×C43C2×#12111yescharacteristic
264C2×D43—21no—
265C2×D43—21no—
266C2×D43—22no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43#46512yes—
270C4×C43—22no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43C22×SD1611yescharacteristic
276C4×C43C2×#13511yescharacteristic
277C4×C43C2×#13711yescharacteristic
278C4×C43C2×#13711yescharacteristic
279Dic43—21no—
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283Dic43#46512yes—
284Dic43#47112yes—
285C2×#498—431no—
286#3079—431no—
287#3039—431no—
288C8×#41—431no—
289#1672—431no—
290#1672—431no—
291#1672—431no—
292#1672D4311yescharacteristic, complemented
293#1671—431no—
294#1671—431no—
295#1671—431no—
296#1671—431no—
297#1566—431no—
298#1548—431no—
299#1546—431no—
300C2×C43#303911yescharacteristic
301C2×C43C2×#46511yescharacteristic
302C2×C43C2×#47111yescharacteristic
303D43—22no—
304D43—42no—
305C2×#137—861no—
306C2×C4⋊Q8—431no—
307C2×C4⋊Q8—431no—
308C4×#41—431no—
309#498—431no—
310#498—431no—
311#498—431no—
312#498—861no—
313#498—861no—
314#498C2×D4311yescharacteristic
315#477—431no—
316#477C2×D4311yescharacteristic
317#476—431no—
318#476—431no—
319#475—861no—
320#474—861no—
321#462—431no—
322#462—861no—
323#462C2×D4311yescharacteristic
324#461—431no—
325#461—431no—
326#461—861no—
327C8×Q8—431no—
328C8×Q8C2×D4311yescharacteristic
329C8×D4—431no—
330C8×D4—431no—
331C8×D4—861no—
332C8×D4—861no—
333#431—431no—
334#431—861no—
335#428—861no—
336C2×#106—861no—
337C2×#106—861no—
338#423—431no—
339#423—431no—
340#419—861no—
341#417—861no—
342C2×C4×C8—431no—
343C2×C4×C8—861no—
344#334—431no—
345#334—431no—
346#334—431no—
347#334C2×D4311yescharacteristic
348#333—431no—
349#333—431no—
350#333—431no—
351#333C2×D4311yescharacteristic
352#332—431no—
353#332—431no—
354#332—431no—
355#332C2×D4311yescharacteristic
356C43#1927011yescharacteristic, complemented, Sylow
357C2×#41—431no—
358C22×Q8—861no—
359C22×Q8—861no—
360#137—1724no—
361C2×Q16—21no—
362C2×Q16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×M16—861no—
366C2×M16—861no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—861no—
374C4⋊Q8—861no—
375C4⋊Q8—861no—
376C4⋊Q8—861no—
377C4⋊Q8—861no—
378C4⋊Q8—861no—
379C4⋊Q8C22×D4311yescharacteristic
380C4⋊Q8C22×D4311yescharacteristic
381C4×Q8—431no—
382C4×Q8C22×D4311yescharacteristic
383C4×D4—431no—
384C4×D4—431no—
385C4×D4—861no—
386C4×D4—861no—
387#117—431no—
388#117—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C42—431no—
394C2×C42—861no—
395#107—21no—
396#107—861no—
397#106—21no—
398#106—21no—
399#106—861no—
400#106—861no—
401#106—861no—
402#106—861no—
403#106—861no—
404#106—861no—
405#106—861no—
406#106—861no—
407C4⋊C8—21no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417#103—21no—
418#103—21no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#102—861no—
424#102—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C4×C8—21no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435#41—434no—
436#41—862no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—3442no—
442C2×Q8—1721no—
443C2×Q8—1721no—
444C2×Q8—1722no—
445C2×Q8—1722no—
446C2×Q8D4×D4311yescharacteristic
447C2×D4—431no—
448C2×D4—861no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—1721no—
456C22×C4—1721no—
457Q16—42no—
458Q16—1722no—
459SD16—1722no—
460SD16—1722no—
461M16—1722no—
462M16—1722no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—862no—
469C2×C8—862no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—1722no—
474C2×C8—1722no—
475C2×C8D4×D4311yescharacteristic
476C2×C8D4×D4311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—431no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4D4×D4311yescharacteristic
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C42—21no—
497C42—431no—
498C42—431no—
499C42—431no—
500C42—861no—
501C42—861no—
502C42C23×D4311yescharacteristic
503C23—431no—
504C23—861no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—81no—
509Q8—3441no—
510Q8—3442no—
511Q8—3442no—
512Q8—1721no—
513Q8—1721no—
514Q8SD16×D4312yes—
515D4—432no—
516D4—864no—
517D4—861no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—431no—
523C2×C4—431no—
524C2×C4—432no—
525C2×C4—432no—
526C2×C4—431no—
527C2×C4—862no—
528C2×C4—864no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—3442no—
533C2×C4—3442no—
534C2×C4—1722no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4C2×D4×D4311yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4#41×D4311yescharacteristic
542C8—21no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—432no—
547C8—861no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C8#1306335712yescomplemented
552C22—432no—
553C22—861no—
554C22—861no—
555C22—862no—
556C22—1721no—
557C22—1721no—
558C22#121×D4311yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—432no—
565C4—432no—
566C4—861no—
567C4—3441no—
568C4—3441no—
569C4—1721no—
570C4C2×SD16×D4311yescharacteristic
571C4#135×D4311yescharacteristic
572C4#137×D4311yescharacteristic
573C4C2×#1306335711yescharacteristic
574C2—862no—
575C2—1722no—
576C2#1914407911yescharacteristic
577C2#465×D4311yescharacteristic
578C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radicalC2×#10621902D4
hypercenter#1672D43
hypocenterC43#19270
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
1. #498×D43C2semidirect
5. #19133979C2semidirect
6. #19133977C2semidirect
7. #19133975C2semidirect
8. #19133973C2semidirect
9. #19133971C2semidirect
10. #19133969C2semidirect
11. #19133967C2semidirect
12. #19133349C2semidirect
13. #19133274C2semidirect
14. #19133265C2semidirect
15. C43×#1672C2semidirect
256. C8×C43#137semidirect
261. C43⋊C8#137semidirect
292. #1672D43semidirect
356. C43#19270semidirect
551. C8#13063357semidirect

Maximal subgroups

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

subgroupindex
#498×D432
#191444092
#191440792
C8×#106219022
#191339792
#191339772
#191339752
#191339732
#191339712
#191339692
#191339672
#191333492
#191332742
#191332652
C43×#16722
#1927043