Finite Group Databasebeta

← #25082075

Subgroups — #25082075

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145735C211yesmaximal, characteristic, complemented
2#19144376C211yesmaximal, characteristic
3#19144077C211yesmaximal, characteristic
4#19143702C211yesmaximal, characteristic
5#19134024C211yesmaximal, characteristic, complemented
6#19134022C211yesmaximal, characteristic, complemented
7#19134016C211yesmaximal, characteristic, complemented
8#19133978C211yesmaximal, characteristic, complemented
9#19133976C211yesmaximal, characteristic, complemented
10#19133970C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133284C211yesmaximal, characteristic, complemented
14#332×D43C211yesmaximal, characteristic, complemented
15C43×#1679C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17#14583454C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×#10621900C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583228—21no—
24#14583228—21no—
25#14583205—21no—
26#14583197—21no—
27#14583195C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583182—21no—
30#14583182—21no—
31#14583181C2211yescharacteristic
32#14583110C2211yescharacteristic
33#14583108—21no—
34#14583106C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583102—21no—
37C8×Dic86C2211yescharacteristic
38#14583023C2211yescharacteristic
39D4×C43⋊C8C2211yescharacteristic
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582950C2211yescharacteristic
43#14582949—21no—
44#14582936—21no—
45#14582921C2211yescharacteristic
46C2×Dic43⋊C8—21no—
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582906—21no—
50#14582892—21no—
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×Q8×D43—21no—
69#13063354—44no—
70C2×Dic172—21no—
71C2×#10621885—21no—
72C2×#10621883—21no—
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063324—21no—
81#13063323—21no—
82#13063316—21no—
83#13063305—21no—
84#13063301—21no—
85Q8×Dic43—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290D411yescharacteristic
89D4×Dic43D411yescharacteristic
90C4×C22⋊D43—21no—
91(C22⋊D43)⋊C4—21no—
92#13063283—21no—
93#13063283D411yescharacteristic
94#13063281—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C2×C4×Dic43—21no—
98C42×D43C2311yescharacteristic
99#13063259—21no—
100#13063257—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256—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—
114Dic43⋊C8D411yescharacteristic
115Dic43⋊C8D411yescharacteristic
116#13063250—21no—
117#13063250—21no—
118#13063249—21no—
119#13063249—21no—
120#13063249—21no—
121#13063248—21no—
122#13063248—21no—
123#13063246—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8D411yescharacteristic
126(C2×D43)⋊C8D411yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
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—
154#10621900—22no—
155#10621900SD1614yes—
156C2×C4×D43—41no—
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163C2×Dic86C2×D411yescharacteristic
164SD16×C43—42no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
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×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179#10621885—42no—
180#10621883—42no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—41no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—41no—
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207Dic172—42no—
208#10621872—42no—
209C8×D43—42no—
210C8×D43—81no—
211C23×C43—21no—
212C22×D43#12111yescharacteristic
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217D4×C43—21no—
218D4×C43C2×SD1612yes—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C22⋊D43—24no—
228C2×Dic43—21no—
229C2×Dic43—24no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—81no—
234C2×Dic43#12111yescharacteristic
235C2×Dic43#12111yescharacteristic
236C2×Dic43#12111yescharacteristic
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—41no—
240C4×D43—82no—
241C4×D43C2×SD1612yes—
242C4×D43#13512yes—
243Dic86—21no—
244Dic86—41no—
245Dic86—41no—
246Dic86—82no—
247Dic86—81no—
248Dic86C2×SD1612yes—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#19415—431nomaximal, Sylow
260C22×C43—22no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43C2×#12111yescharacteristic
264C2×D43—21no—
265C2×D43—21no—
266C2×D43#46512yes—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43C22×SD1611yescharacteristic
272C4×C43C2×#13511yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—21no—
276Dic43—22no—
277Dic43—21no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281Dic43#46512yes—
282#3229—431no—
283#3076—431no—
284#3039—431no—
285#2988—431no—
286#1680—431no—
287#1680—431no—
288#1679—431no—
289#1679D4311yescharacteristic, complemented
290#1672—431no—
291#1672—431no—
292#1671—431no—
293#1671—431no—
294#1570—431no—
295#1550—431no—
296C2×#332—431no—
297C2×C43—42no—
298C2×C43#304611yescharacteristic
299C2×C43C2×#46511yescharacteristic
300C2×C43#306911yescharacteristic
301D43—22no—
302C2×#137—861no—
303#533—431no—
304C2×C4⋊Q8—431no—
305C4×#41—431no—
306#498—431no—
307#498—431no—
308#487—431no—
309#487C2×D4311yescharacteristic
310#483—861no—
311#483—861no—
312#479—861no—
313#478—861no—
314#477—431no—
315#476—431no—
316#475—431no—
317#475—861no—
318#475—861no—
319#474C2×D4311yescharacteristic
320#462—431no—
321#462—431no—
322#462—861no—
323#461—431no—
324#461—861no—
325#461C2×D4311yescharacteristic
326C8×Q8—431no—
327C8×Q8—431no—
328C8×D4—431no—
329C8×D4—861no—
330C8×D4—861no—
331C8×D4C2×D4311yescharacteristic
332#431—431no—
333#431—861no—
334#427—861no—
335#423—431no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8—431no—
338C2×C4⋊C8—861no—
339#419—861no—
340#416—861no—
341#334—431no—
342#334—431no—
343#334—431no—
344#334C2×D4311yescharacteristic
345#333—431no—
346#333—431no—
347#332—431no—
348#332—431no—
349#332—431no—
350#332—431no—
351#332C2×D4311yescharacteristic
352#332C2×D4311yescharacteristic
353C43#1941511yescharacteristic, complemented, Sylow
354C2×#41—431no—
355C22×Q8—861no—
356#137—1724no—
357C2×Q16—861no—
358C2×Q16—861no—
359C2×SD16—21no—
360C2×SD16—861no—
361C2×M16—861no—
362C22×C8—21no—
363C22×C8—861no—
364C22×C8—861no—
365C22×C8—861no—
366C4⋊Q8—431no—
367C4⋊Q8—431no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370C4⋊Q8—861no—
371C4⋊Q8C22×D4311yescharacteristic
372C4⋊Q8C22×D4311yescharacteristic
373#125—861no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376C4×Q8—431no—
377C4×Q8—431no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×D4—431no—
381C4×D4—861no—
382C4×D4—861no—
383C4×D4C22×D4311yescharacteristic
384#117—431no—
385#117—861no—
386#117—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C42—431no—
390C2×C42—861no—
391#107—21no—
392#107—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397#106—861no—
398#106—861no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—861no—
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#102—21no—
423#102—861no—
424C22⋊C8—21no—
425C22⋊C8—431no—
426C22⋊C8—431no—
427C22⋊C8—861no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432#41—434no—
433#41—862no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—431no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—1721no—
440C2×Q8—1722no—
441C2×Q8—1722no—
442C2×D4—861no—
443C2×D4D4×D4311yescharacteristic
444C22×C4—21no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—1721no—
451Q16—1722no—
452Q16—1722no—
453SD16—42no—
454SD16—1722no—
455M16—1722no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—3441no—
466C2×C8—3441no—
467C2×C8—1722no—
468C2×C8D4×D4311yescharacteristic
469C2×C8D4×D4311yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—431no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C4⋊C4D4×D4311yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—1721no—
490C42—431no—
491C42—431no—
492C42—431no—
493C42—861no—
494C42—861no—
495C42—861no—
496C42—1721no—
497C42C23×D4311yescharacteristic
498C23—21no—
499C23—431no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—432no—
505Q8—861no—
506Q8—3441no—
507Q8—3442no—
508Q8—1721no—
509Q8—1721no—
510D4—21no—
511D4—864no—
512D4SD16×D4312yes—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—431no—
519C2×C4—432no—
520C2×C4—432no—
521C2×C4—431no—
522C2×C4—431no—
523C2×C4—864no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—3442no—
529C2×C4—3441no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4#41×D4311yescharacteristic
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—432no—
550C22—861no—
551C22—861no—
552C22#121×D4311yescharacteristic
553C4—21no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—432no—
558C4—861no—
559C4—861no—
560C4—862no—
561C4—3441no—
562C4—3441no—
563C4—1721no—
564C4C2×SD16×D4311yescharacteristic
565C4#135×D4311yescharacteristic
566C4#1458370911yescharacteristic
567C4#1458371311yescharacteristic
568C2—42no—
569C2—862no—
570C2#1914414611yescharacteristic
571C2#465×D4311yescharacteristic
572C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1679C2
socleC22×C43C2×#121
prime radicalC2×#10621900D4
hypercenter#1679D43
hypocenterC43#19415
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. #19145735C2semidirect
5. #19134024C2semidirect
6. #19134022C2semidirect
7. #19134016C2semidirect
8. #19133978C2semidirect
9. #19133976C2semidirect
10. #19133970C2semidirect
11. #19133968C2semidirect
12. #19133364C2semidirect
13. #19133284C2semidirect
14. #332×D43C2semidirect
15. C43×#1679C2semidirect
289. #1679D43semidirect
353. C43#19415semidirect

Maximal subgroups

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

subgroupindex
#191457352
#191443762
#191440772
#191437022
#191340242
#191340222
#191340162
#191339782
#191339762
#191339702
#191339682
#191333642
#191332842
#332×D432
C43×#16792
#1941543