Finite Group Databasebeta

← #25080430

Subgroups — #25080430

Order 11008.

656 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#19145156C211yesmaximal, characteristic
2#19144401C211yesmaximal, characteristic, complemented
3#19144068C211yesmaximal, characteristic
4C8×Q8×D43C211yesmaximal, characteristic, complemented
5#19134028C211yesmaximal, characteristic, complemented
6#19134027C211yesmaximal, characteristic, complemented
7#19134014C211yesmaximal, characteristic, complemented
8#19134013C211yesmaximal, characteristic, complemented
9#19133974C211yesmaximal, characteristic, complemented
10#19133944C211yesmaximal, characteristic, complemented
11#19133943C211yesmaximal, characteristic, complemented
12#19133349C211yesmaximal, characteristic, complemented
13#19133282C211yesmaximal, characteristic, complemented
14#19133271C211yesmaximal, characteristic
15C43×#1672C211yesmaximal, characteristic, complemented
16C2×#13063357—21no—
17#14583454C2211yescharacteristic
18#14583450C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583251C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583205—21no—
24#14583204—21no—
25#14583191C2211yescharacteristic
26#14583185C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583129—21no—
29#14583129—21no—
30#14583124—21no—
31#14583123—21no—
32#14583106C2211yescharacteristic
33#14583100C2211yescharacteristic
34#14583099C2211yescharacteristic
35Q8×C43⋊C8C2211yescharacteristic
36C8×Dic86—21no—
37C8×Dic86C2211yescharacteristic
38#14583023—21no—
39#14583023C2211yescharacteristic
40#14582986—21no—
41#14582986—21no—
42#14582940—21no—
43#14582921C2211yescharacteristic
44#14582921C2211yescharacteristic
45C4⋊C8×D43—21no—
46C4⋊C8×D43C2211yescharacteristic
47#14582906—21no—
48#14582899—21no—
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621902—21no—
68C2×Q8×D43D411yescharacteristic
69#13063357—44no—
70C2×#10621885—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621884—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C2×C8×D43—21no—
78C2×C8×D43D411yescharacteristic
79C2×C8×D43D411yescharacteristic
80#13063325C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063316—21no—
83#13063314—21no—
84#13063305—21no—
85#13063301—21no—
86#13063300—21no—
87#13063300—21no—
88Q8×Dic43—21no—
89Q8×Dic43D411yescharacteristic
90C4×Dic86—21no—
91C4×Dic86C2311yescharacteristic
92#13063290—21no—
93#13063290—21no—
94#13063290D411yescharacteristic
95#13063287—21no—
96#13063287—21no—
97#13063283—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43D411yescharacteristic
100C42×D43—21no—
101C42×D43C2311yescharacteristic
102#13063258—21no—
103#13063257—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063248—21no—
119#13063248—21no—
120#13063247—21no—
121#13063245—21no—
122#13063245—21no—
123#13063245—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
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—42no—
149#10621902—42no—
150Q8×D43—22no—
151Q8×D43SD1614yescomplemented
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—41no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—41no—
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165Q16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C2×D411yescharacteristic
177C42×C43—21no—
178C42×C43C2411yescharacteristic
179#10621885—42no—
180#10621884—42no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—41no—
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621873—42no—
206#10621873—42no—
207#10621873—42no—
208#10621872—42no—
209#10621872—42no—
210C8×D43—22no—
211C8×D43—41no—
212C8×D43—42no—
213C22×D43—41no—
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—21no—
229C2×Dic43—41no—
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C2×Dic43#12111yescharacteristic
233D172—41no—
234D172—41no—
235D172—41no—
236D172—41no—
237D172—81no—
238D172—82no—
239C4×D43—24no—
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—41no—
243C4×D43—42no—
244C4×D43—82no—
245C4×D43C2×SD1612yes—
246C4×D43#13512yes—
247Dic86—21no—
248Dic86—24no—
249Dic86—41no—
250Dic86—41no—
251Dic86C2×SD1612yes—
252C8×C43—21no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43#13712yescomplemented
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#19260—431nomaximal, Sylow
263C22×C43C2×#12111yescharacteristic
264C2×D43—21no—
265C2×D43—21no—
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
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×C43#57511yescharacteristic
279Dic43—21no—
280Dic43—22no—
281Dic43—21no—
282Dic43—41no—
283Dic43—81no—
284Dic43#46512yes—
285#3167—431no—
286#3078—431no—
287#3037—431no—
288C2×C8×Q8—431no—
289#1680—431no—
290#1680—431no—
291#1678—431no—
292#1678—431no—
293#1672—431no—
294#1672D4311yescharacteristic, complemented
295#1666—431no—
296#1666—431no—
297#1566—431no—
298#1550—431no—
299#1547—431no—
300C2×C43#303711yescharacteristic
301C2×C43C2×#46511yescharacteristic
302C2×C43#306711yescharacteristic
303D43—22no—
304D43—161no—
305C2×#137—861no—
306#533—431no—
307#532—431no—
308C2×C4×Q8—431no—
309#498C2×D4311yescharacteristic
310#492—431no—
311#487—431no—
312#486—431no—
313#479—861no—
314#479—861no—
315#477—431no—
316#477C2×D4311yescharacteristic
317#475—431no—
318#475—431no—
319#465—861no—
320#465—861no—
321#464—861no—
322#464—861no—
323#462—431no—
324#462C2×D4311yescharacteristic
325#460—431no—
326#460—431no—
327C8×Q8—431no—
328C8×Q8—431no—
329C8×Q8—431no—
330C8×Q8—861no—
331C8×Q8—861no—
332C8×Q8C2×D4311yescharacteristic
333C4×SD16—861no—
334C4×SD16—861no—
335#428—861no—
336#423—431no—
337#423—431no—
338C2×C4⋊C8—431no—
339C2×C4⋊C8—861no—
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#333C2×D4311yescharacteristic
350#332—431no—
351#332—431no—
352#332—431no—
353#332C2×D4311yescharacteristic
354#331—431no—
355#331—431no—
356C43#1926011yescharacteristic, complemented, Sylow
357C2×#41—861no—
358C22×Q8—431no—
359#137—1724no—
360C2×Q16—21no—
361C2×Q16—861no—
362C2×SD16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×M16—861no—
367C2×M16—861no—
368C22×C8—431no—
369C22×C8—431no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8C22×D4311yescharacteristic
373C4⋊Q8C22×D4311yescharacteristic
374#127—431no—
375#125—861no—
376#124—861no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379#121—861no—
380#121—861no—
381C4×Q8—431no—
382C4×Q8—431no—
383C4×Q8—431no—
384C4×Q8—861no—
385C4×Q8—861no—
386C4×Q8—861no—
387C4×Q8—861no—
388C4×Q8C22×D4311yescharacteristic
389C4×D4—861no—
390C4×D4—861no—
391#117—861no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—861no—
394C2×C42—431no—
395C2×C42—861no—
396#107—21no—
397#107—861no—
398#106—21no—
399#106—21no—
400#106—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415#103—21no—
416#103—21no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427C4×C8—21no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—861no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435#41—1722no—
436#41—1722no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—434no—
440C2×Q8—431no—
441C2×Q8—861no—
442C2×Q8—862no—
443C2×Q8—861no—
444C2×Q8D4×D4311yescharacteristic
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—1721no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—1721no—
455Q16—42no—
456Q16—1722no—
457SD16—1722no—
458SD16—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—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—1721no—
473C2×C8—1722no—
474C2×C8D4×D4311yescharacteristic
475C2×C8D4×D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—431no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4D4×D4311yescharacteristic
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—21no—
495C42—431no—
496C42—431no—
497C42—431no—
498C42—861no—
499C42—861no—
500C42—861no—
501C42—1721no—
502C42C23×D4311yescharacteristic
503C23—431no—
504C23—1721no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—81no—
509Q8—432no—
510Q8—864no—
511Q8—861no—
512Q8—1721no—
513Q8—1721no—
514Q8SD16×D4312yes—
515D4—3441no—
516D4—3442no—
517D4—1721no—
518D4—1721no—
519D4—1721no—
520D4—1721no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—431no—
526C2×C4—432no—
527C2×C4—432no—
528C2×C4—431no—
529C2×C4—431no—
530C2×C4—864no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—3442no—
536C2×C4—1721no—
537C2×C4—1722no—
538C2×C4—1721no—
539C2×C4C2×D4×D4311yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4#41×D4311yescharacteristic
542C8—21no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—861no—
547C8—861no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C8#1306335712yescomplemented
552C22—432no—
553C22—861no—
554C22—861no—
555C22—3441no—
556C22—3441no—
557C22—3441no—
558C22#121×D4311yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—432no—
565C4—861no—
566C4—861no—
567C4—862no—
568C4—3441no—
569C4—1721no—
570C4C2×SD16×D4311yescharacteristic
571C4#135×D4311yescharacteristic
572C4C2×#1306335711yescharacteristic
573C4#1458369811yescharacteristic
574C2—862no—
575C2—6881no—
576C2#1914406811yescharacteristic
577C2#465×D4311yescharacteristic
578C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radical#14583450C22
hypercenter#1672D43
hypocenterC43#19260
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
2. #19144401C2semidirect
4. C8×Q8×D43C2semidirect
5. #19134028C2semidirect
6. #19134027C2semidirect
7. #19134014C2semidirect
8. #19134013C2semidirect
9. #19133974C2semidirect
10. #19133944C2semidirect
11. #19133943C2semidirect
12. #19133349C2semidirect
13. #19133282C2semidirect
15. C43×#1672C2semidirect
151. Q8×D43SD16semidirect
256. C8×C43#137semidirect
294. #1672D43semidirect
356. C43#19260semidirect
551. C8#13063357semidirect

Maximal subgroups

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

subgroupindex
#191451562
#191444012
#191440682
C8×Q8×D432
#191340282
#191340272
#191340142
#191340132
#191339742
#191339442
#191339432
#191333492
#191332822
#191332712
C43×#16722
#1926043