Finite Group Databasebeta

← #25084214

Subgroups — #25084214

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145934C211yesmaximal, characteristic
2#19145742C211yesmaximal, characteristic, complemented
3#19145621C211yesmaximal, characteristic
4#19143756C211yesmaximal, characteristic
5#19134148C211yesmaximal, characteristic, complemented
6#19134112C211yesmaximal, characteristic, complemented
7#19134108C211yesmaximal, characteristic, complemented
8#19134022C211yesmaximal, characteristic, complemented
9#19134016C211yesmaximal, characteristic, complemented
10#19133990C211yesmaximal, characteristic, complemented
11#19133982C211yesmaximal, characteristic, complemented
12#19133379C211yesmaximal, characteristic, complemented
13#19133294C211yesmaximal, characteristic, complemented
14#332×D43C211yesmaximal, characteristic, complemented
15C43×#1699C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18#14583431C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583290—21no—
22#14583266—21no—
23#14583249C2211yescharacteristic
24#14583233—21no—
25#14583233—21no—
26#14583205—21no—
27#14583192—21no—
28#14583192—21no—
29#14583181C2211yescharacteristic
30#14583141—21no—
31#14583127—21no—
32#14583120—21no—
33#14583110C2211yescharacteristic
34#14583110C2211yescharacteristic
35#14583106C2211yescharacteristic
36#14583104C2211yescharacteristic
37#14583104C2211yescharacteristic
38#14583056—21no—
39#14583036—21no—
40#14583026C2211yescharacteristic
41C8×Dic86C2211yescharacteristic
42#14582968—21no—
43D4×C43⋊C8C2211yescharacteristic
44(C22⋊D43)⋊C8—21no—
45#14582957—21no—
46#14582955C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582927—21no—
49C4⋊C8×D43C2211yescharacteristic
50C4⋊C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582650C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Dic172—21no—
69C2×Dic172—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063324—21no—
79#13063324—21no—
80#13063323—21no—
81#13063318—21no—
82#13063316—21no—
83#13063316D411yescharacteristic
84#13063312D411yescharacteristic
85#13063307—21no—
86#13063305—21no—
87#13063305D411yescharacteristic
88#13063301—21no—
89#13063296D411yescharacteristic
90Q8×Dic43—21no—
91C4×Dic86C2311yescharacteristic
92#13063290—21no—
93C4×C22⋊D43—21no—
94#13063284—21no—
95#13063283—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C42×D43C2311yescharacteristic
99#13063259—21no—
100#13063259—21no—
101#13063258—21no—
102#13063258—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063249—21no—
118#13063248—21no—
119#13063248—21no—
120#13063248—21no—
121C22⋊(C43⋊C8)—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125#13063235—21no—
126#13063235—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×M16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149Q8×D43—81no—
150Q8×D43—81no—
151C2×C4×D43—41no—
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43#4111yescharacteristic
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—41no—
158C2×Dic86C2×D411yescharacteristic
159SD16×C43—81no—
160M16×C43—81no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×D411yescharacteristic
171C22⋊C4×C43—21no—
172C42×C43C2411yescharacteristic
173C22⋊Dic43—21no—
174C22⋊Dic43—21no—
175C22⋊Dic43—21no—
176#10621885—81no—
177#10621883—81no—
178#10621883—81no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—41no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
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—41no—
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205Dic172—81no—
206Dic172—81no—
207C8×D43—81no—
208C8×D43—81no—
209C23×C43—21no—
210C22×D43#12111yescharacteristic
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215D4×C43—21no—
216D4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—42no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C2×Dic43#12111yescharacteristic
233C4×D43—22no—
234C4×D43—21no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—82no—
239Dic86—21no—
240Dic86—21no—
241Dic86—41no—
242Dic86—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—82no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256#19590—431nomaximal, Sylow
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43C2×#12111yescharacteristic
261C2×D43—21no—
262C2×D43—21no—
263C2×D43#47312yes—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43#57611yescharacteristic
269C4×C43#57711yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272Dic43—21no—
273Dic43—21no—
274Dic43—21no—
275Dic43—41no—
276Dic43—41no—
277Dic43—81no—
278Dic43—81no—
279#3248—431no—
280#3230—431no—
281#3218—431no—
282#2994—431no—
283#1700—431no—
284#1699D4311yescharacteristic, complemented
285#1694—431no—
286#1693—431no—
287#1680—431no—
288#1679—431no—
289#1674—431no—
290#1673—431no—
291#1573—431no—
292#1552—431no—
293C2×#332—431no—
294C2×C43—81no—
295C2×C43#304611yescharacteristic
296C2×C43#306211yescharacteristic
297C2×C43C2×#47311yescharacteristic
298D43—22no—
299#533—431no—
300C2×C4⋊Q8—431no—
301#529—431no—
302#500—431no—
303#500—431no—
304#497—861no—
305#491—861no—
306#487—431no—
307#487C2×D4311yescharacteristic
308#484—861no—
309#484—861no—
310#479—861no—
311#477—861no—
312#477—861no—
313#475—431no—
314#474C2×D4311yescharacteristic
315#467—861no—
316#465—861no—
317#464—861no—
318#462—431no—
319#462—431no—
320#462—431no—
321#461—431no—
322#461—431no—
323#461C2×D4311yescharacteristic
324#451—861no—
325#448—861no—
326#446—431no—
327C8×Q8—431no—
328#436C2×D4311yescharacteristic
329#435—861no—
330C8×D4—431no—
331C8×D4—861no—
332#433—861no—
333#432—431no—
334#431—431no—
335#424—861no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8—431no—
338#335—431no—
339#335C2×D4311yescharacteristic
340#334—431no—
341#334—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348#332C2×D4311yescharacteristic
349#332C2×D4311yescharacteristic
350C43#1959011yescharacteristic, complemented, Sylow
351C22×Q8—861no—
352C2×Q16—861no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×SD16—21no—
356C2×SD16—861no—
357C2×SD16—861no—
358C2×M16—21no—
359C22×C8—861no—
360C22×C8—861no—
361C22×C8—861no—
362C4⋊Q8—431no—
363C4⋊Q8—431no—
364C4⋊Q8—861no—
365C4⋊Q8—861no—
366C4⋊Q8—861no—
367C4⋊Q8C22×D4311yescharacteristic
368C4⋊Q8C22×D4311yescharacteristic
369#126—861no—
370#125—431no—
371#125—861no—
372#124—431no—
373#123—861no—
374C22⋊Q8—431no—
375C22⋊Q8—861no—
376C22⋊Q8—861no—
377#121—431no—
378C4×Q8—431no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×D4—861no—
382C4×D4C22×D4311yescharacteristic
383#117—861no—
384#117—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C42—431no—
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#102—21no—
418C22⋊C8—21no—
419C22⋊C8—431no—
420C22⋊C8—431no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423#97—861no—
424#97—861no—
425C4×C8—431no—
426C4×C8—861no—
427C4×C8C22×D4311yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—431no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—3441no—
434C2×Q8—3441no—
435C2×Q8—1721no—
436C2×D4—861no—
437C2×D4D4×D4311yescharacteristic
438C22×C4—21no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—1721no—
443Q16—3441no—
444Q16—3441no—
445Q16—3441no—
446SD16—81no—
447SD16—3441no—
448SD16—3441no—
449M16—81no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—3441no—
459C2×C8—3441no—
460C2×C8—3441no—
461C2×C8D4×D4311yescharacteristic
462C2×C8D4×D4311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—431no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4D4×D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—1721no—
487C42—431no—
488C42—431no—
489C42—431no—
490C42—861no—
491C42—1721no—
492C42C23×D4311yescharacteristic
493C23—21no—
494C23—431no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—861no—
500Q8—861no—
501Q8—3442no—
502Q8—1721no—
503Q8—1721no—
504Q8—1721no—
505Q8—1721no—
506D4—21no—
507D4—21no—
508D4—1722no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—431no—
515C2×C4—431no—
516C2×C4—431no—
517C2×C4—862no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—3442no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4#41×D4311yescharacteristic
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—861no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—432no—
544C22—861no—
545C22—861no—
546C22#121×D4311yescharacteristic
547C4—21no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—861no—
552C4—861no—
553C4—861no—
554C4—3441no—
555C4—3441no—
556C4—1721no—
557C4—1721no—
558C4#1458370311yescharacteristic
559C4#1458370811yescharacteristic
560C4#1458370911yescharacteristic
561C4#1458371311yescharacteristic
562C2—81no—
563C2—862no—
564C2#1914414611yescharacteristic
565C2#1914427011yescharacteristic
566C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1699C2
socleC22×C43C2×#121
prime radical#13063296D4
hypercenter#1699D43
hypocenterC43#19590
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1699

Complements

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

NH ≅ G/Ntype
2. #19145742C2semidirect
5. #19134148C2semidirect
6. #19134112C2semidirect
7. #19134108C2semidirect
8. #19134022C2semidirect
9. #19134016C2semidirect
10. #19133990C2semidirect
11. #19133982C2semidirect
12. #19133379C2semidirect
13. #19133294C2semidirect
14. #332×D43C2semidirect
15. C43×#1699C2semidirect
284. #1699D43semidirect
350. C43#19590semidirect

Maximal subgroups

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

subgroupindex
#191459342
#191457422
#191456212
#191437562
#191341482
#191341122
#191341082
#191340222
#191340162
#191339902
#191339822
#191333792
#191332942
#332×D432
C43×#16992
#1959043