Finite Group Databasebeta

← #25084173

Subgroups — #25084173

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145926C211yesmaximal, characteristic
2#19145816C211yesmaximal, characteristic
3#19143757C211yesmaximal, characteristic
4#19134174C211yesmaximal, characteristic, complemented
5#19134167C211yesmaximal, characteristic, complemented
6#19134098C211yesmaximal, characteristic, complemented
7#19134091C211yesmaximal, characteristic, complemented
8#19134050C211yesmaximal, characteristic, complemented
9#19134043C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#19133380C211yesmaximal, characteristic, complemented
13#19133295C211yesmaximal, characteristic, complemented
14C2×#14582648C211yesmaximal, characteristic, complemented
15C43×#3229C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583305—21no—
18#14583261—21no—
19#14583229—21no—
20#14583212—21no—
21#14583206—21no—
22#14583191C2211yescharacteristic
23#14583191C2211yescharacteristic
24#14583186C2211yescharacteristic
25#14583186C2211yescharacteristic
26#14583181C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583138—21no—
29#14583130—21no—
30#14583121—21no—
31#14583106C2211yescharacteristic
32#14583101C2211yescharacteristic
33#14583029C2211yescharacteristic
34C8×Dic86C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582967—21no—
37C8×D172C2211yescharacteristic
38(C22⋊D43)⋊C8—21no—
39#14582959—21no—
40#14582956C2211yescharacteristic
41#14582924—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582648C2211yescharacteristic
51#14582648C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582645C2211yescharacteristic
55#14582645C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C2×C4⋊Q8×C43C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#498C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#483—21no—
63C43×#483—21no—
64C43×#475—21no—
65C43×#475—21no—
66C43×#431C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621884—21no—
69C2×#10621872—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73#13063319—21no—
74#13063317D411yescharacteristic
75#13063313D411yescharacteristic
76#13063308—21no—
77#13063304D411yescharacteristic
78#13063299D411yescharacteristic
79C4×Dic86C2311yescharacteristic
80C4×D172C2311yescharacteristic
81C4×C22⋊D43—21no—
82#13063282—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87#13063256—21no—
88#13063256—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107C22⋊(C43⋊C8)—21no—
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110#13063236—21no—
111#13063235—21no—
112C8×Dic43—21no—
113C22×Q8×C43—21no—
114C4⋊Q8×C43—21no—
115C4⋊Q8×C43—21no—
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126#117×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130#106×C43—21no—
131#106×C43—21no—
132#106×C43—21no—
133#106×C43—21no—
134C4⋊C8×C43D411yescharacteristic
135C4⋊C8×C43D411yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140C22⋊C8×C43D411yescharacteristic
141C22⋊C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—82no—
150C22×C4×C43—41no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C2×C22⋊D43—21no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×Dic86C2×D411yescharacteristic
158C2×C8×C43C2×D411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C42×C43—41no—
176C42×C43C2×D411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C42×C43#4111yescharacteristic
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181#10621885—81no—
182#10621884—81no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187C4⋊Dic43C2×D411yescharacteristic
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8—81no—
202#10621872—81no—
203C8×D43—81no—
204C23×C43#12111yescharacteristic
205C22×D43—21no—
206Q8×C43—41no—
207Q8×C43—41no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—81no—
211Q8×C43—81no—
212Q8×C43—82no—
213C2×C4×C43—22no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—82no—
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C22⋊D43—42no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233D172—21no—
234D172—21no—
235C4×D43—41no—
236C4×D43—41no—
237Dic86—21no—
238Dic86—21no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#19588—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43#47112yes—
253C22×C43C2×#12111yescharacteristic
254C2×D43—41no—
255C2×D43—41no—
256C2×D43—41no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43#57711yescharacteristic
266C4×C43#57711yescharacteristic
267C4×C43#57811yescharacteristic
268C4×C43#57811yescharacteristic
269Dic43—41no—
270Dic43—41no—
271Dic43—41no—
272#3248—431no—
273#3238—431no—
274#3229D4311yescharacteristic, complemented
275#2994—431no—
276#1704—431no—
277#1703—431no—
278#1692—431no—
279#1691—431no—
280#1684—431no—
281#1683—431no—
282#1672—431no—
283#1671—431no—
284#1573—431no—
285#1552—431no—
286C2×#333—431no—
287C2×C43—22no—
288C2×C43#304611yescharacteristic
289C2×C43#306311yescharacteristic
290C2×C43C2×#47111yescharacteristic
291D43—81no—
292#533C2×D4311yescharacteristic
293C2×C4⋊Q8C2×D4311yescharacteristic
294#529—431no—
295#501—861no—
296#498C2×D4311yescharacteristic
297#498C2×D4311yescharacteristic
298#489—861no—
299#487C2×D4311yescharacteristic
300#487C2×D4311yescharacteristic
301#483—21no—
302#483—21no—
303#483—861no—
304#480—861no—
305#479—861no—
306#477—431no—
307#477—431no—
308#476—431no—
309#476—431no—
310#475—21no—
311#475—21no—
312#475—431no—
313#474—431no—
314#467—861no—
315#465—861no—
316#464—861no—
317#462—431no—
318#461—431no—
319#446—431no—
320C8×Q8—431no—
321#436—431no—
322#435—861no—
323C8×D4—431no—
324C8×D4—861no—
325#433—861no—
326#432—431no—
327#431C2×D4311yescharacteristic
328#424—861no—
329C2×C4⋊C8—431no—
330C2×C4⋊C8—431no—
331#335—431no—
332#335—431no—
333#334—431no—
334#334—431no—
335#333—431no—
336#333—431no—
337#333—431no—
338#333—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343C43#1958811yescharacteristic, complemented, Sylow
344C22×Q8—21no—
345C2×Q16—861no—
346C2×SD16—861no—
347C2×M16—861no—
348C22×C8—861no—
349C22×C8—861no—
350C22×C8—861no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C22×D4311yescharacteristic
355C4⋊Q8C22×D4311yescharacteristic
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—861no—
359#125—21no—
360#125—431no—
361#124—431no—
362#123—861no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—431no—
366#121—431no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—431no—
370C4×D4—431no—
371C4×D4—861no—
372#117—21no—
373#117—861no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C42C22×D4311yescharacteristic
377#107—861no—
378#107—861no—
379#107—861no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8C22⋊D4311yescharacteristic
398C4⋊C8C22⋊D4311yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#102—861no—
409#102—861no—
410#102—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414C22⋊C8C22⋊D4311yescharacteristic
415C22⋊C8C22⋊D4311yescharacteristic
416#97—861no—
417#97—861no—
418C4×C8—861no—
419C4×C8C22×D4311yescharacteristic
420C4×C8C22×D4311yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—82no—
427C2×Q8—431no—
428C2×D4—431no—
429C2×D4—861no—
430C22×C4—41no—
431C22×C4—861no—
432C22×C4D4×D4311yescharacteristic
433C22×C4#1062190011yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435Q16—3441no—
436SD16—3441no—
437M16—3441no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—3441no—
445C2×C8—3441no—
446C2×C8—3441no—
447C2×C8C2×C22⋊D4311yescharacteristic
448C2×C8C2×C22⋊D4311yescharacteristic
449C2×C8C2×C22⋊D4311yescharacteristic
450C2×C8C2×C22⋊D4311yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—431no—
464C4⋊C4—431no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C22⋊C4—41no—
470C22⋊C4—861no—
471C22⋊C4—861no—
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C42—41no—
476C42—861no—
477C42D4×D4311yescharacteristic
478C42#1062190011yescharacteristic
479C42C2×C22⋊D4311yescharacteristic
480C42C23×D4311yescharacteristic
481C23—861no—
482C23#1306329611yescharacteristic
483Q8—41no—
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—81no—
488Q8—81no—
489Q8—82no—
490Q8—861no—
491Q8—861no—
492D4—861no—
493D4—861no—
494D4—1722no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4#1306329611yescharacteristic
511C2×C4#1306329611yescharacteristic
512C2×C4#1306329611yescharacteristic
513C2×C4C2×D4×D4311yescharacteristic
514C2×C4C22×C22⋊D4311yescharacteristic
515C2×C4C2×#1062190011yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—1721no—
521C8—1721no—
522C8—1721no—
523C8—1721no—
524C8—1721no—
525C8—1721no—
526C22—21no—
527C22—21no—
528C22—1721no—
529C22—1721no—
530C22—1721no—
531C22#1458315912yes—
532C22C2×#1306329611yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4—1721no—
542C4—1721no—
543C4—1721no—
544C4#1458370711yescharacteristic
545C4#1458370811yescharacteristic
546C4#1458371411yescharacteristic
547C4#1458371511yescharacteristic
548C2—22no—
549C2—3441no—
550C2#1914414111yescharacteristic
551C2#1914428011yescharacteristic
552C2C2×#1458315911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3229C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#3229D43
hypocenterC43#19588
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
4. #19134174C2semidirect
5. #19134167C2semidirect
6. #19134098C2semidirect
7. #19134091C2semidirect
8. #19134050C2semidirect
9. #19134043C2semidirect
10. #19133974C2semidirect
11. #19133967C2semidirect
12. #19133380C2semidirect
13. #19133295C2semidirect
14. C2×#14582648C2semidirect
15. C43×#3229C2semidirect
274. #3229D43semidirect
343. C43#19588semidirect

Maximal subgroups

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

subgroupindex
#191459262
#191458162
#191437572
#191341742
#191341672
#191340982
#191340912
#191340502
#191340432
#191339742
#191339672
#191333802
#191332952
C2×#145826482
C43×#32292
#1958843