Finite Group Databasebeta

← #25079351

Subgroups — #25079351

Order 11008.

598 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#19145180C211yesmaximal, characteristic, complemented
2#19144668C211yesmaximal, characteristic
3#19144663C211yesmaximal, characteristic
4#19143558C211yesmaximal, characteristic
5#19134150C211yesmaximal, characteristic, complemented
6#19134146C211yesmaximal, characteristic, complemented
7#19134142C211yesmaximal, characteristic, complemented
8#19134112C211yesmaximal, characteristic, complemented
9#19134106C211yesmaximal, characteristic, complemented
10#19134088C211yesmaximal, characteristic, complemented
11#19134082C211yesmaximal, characteristic, complemented
12#19133342C211yesmaximal, characteristic, complemented
13#19133258C211yesmaximal, characteristic, complemented
14#19133258C211yesmaximal, characteristic, complemented
15C43×#1699C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583242—21no—
23#14583238—21no—
24#14583185C2211yescharacteristic
25#14583181C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583139—21no—
28#14583139—21no—
29#14583110C2211yescharacteristic
30#14583106C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583062—21no—
33#14583058—21no—
34#14583029C2211yescharacteristic
35#14583026C2211yescharacteristic
36#14582993—21no—
37#14582991—21no—
38#14582991—21no—
39#14582991—21no—
40#14582990—21no—
41SD16×Dic43—21no—
42#14582977C2211yescharacteristic
43#14582973—21no—
44#14582968—21no—
45#14582951C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582949—21no—
49M16×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
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×#10621900D411yescharacteristic
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621883—21no—
73C2×#10621877—21no—
74C2×C8×D43D411yescharacteristic
75C2×C8×D43D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063316—21no—
79#13063316—21no—
80#13063305—21no—
81#13063305—21no—
82#13063301—21no—
83#13063301—21no—
84Q8×Dic43—21no—
85Q8×Dic43—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290—21no—
89#13063290D411yescharacteristic
90D4×Dic43D411yescharacteristic
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93#13063283—21no—
94#13063283—21no—
95#13063283D411yescharacteristic
96#13063281—21no—
97C2×C4×Dic43—21no—
98C42×D43C2311yescharacteristic
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063257—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063249—21no—
114#13063248—21no—
115#13063248—21no—
116#13063246—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
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—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621900—41no—
152#10621900—41no—
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43#4111yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C2×D411yescharacteristic
159SD16×C43—42no—
160M16×C43—42no—
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—
174#10621885—42no—
175#10621885—42no—
176#10621885—42no—
177#10621883—42no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—41no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—41no—
186C4⋊Dic43—41no—
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—41no—
196C4×Dic43—41no—
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200#10621877—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206Dic172—42no—
207C8×D43—22no—
208C8×D43—41no—
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—42no—
229C2×Dic43—42no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43#12111yescharacteristic
233C2×Dic43#12111yescharacteristic
234C2×Dic43#12111yescharacteristic
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—22no—
240Dic86—21no—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—41no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8#13512yes—
256#19161—431nomaximal, Sylow
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43C2×#12111yescharacteristic
261C2×D43—21no—
262C2×D43—21no—
263C2×D43—21no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43C2×#13511yescharacteristic
269C4×C43#57511yescharacteristic
270C4×C43#57511yescharacteristic
271C4×C43#57511yescharacteristic
272Dic43—21no—
273Dic43—21no—
274Dic43—41no—
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278Dic43#47312yes—
279#3170—431no—
280#3107—431no—
281#3107—431no—
282#2965—431no—
283#1700—431no—
284#1700—431no—
285#1699—431no—
286#1699D4311yescharacteristic, complemented
287#1694—431no—
288#1693—431no—
289#1690—431no—
290#1689—431no—
291#1564—431no—
292#1544—431no—
293#1544—431no—
294C2×C43—81no—
295C2×C43#303511yescharacteristic
296C2×C43#305411yescharacteristic
297C2×C43C2×#47311yescharacteristic
298D43—41no—
299#533—431no—
300#533—431no—
301C4×#41—431no—
302#500—431no—
303#494—431no—
304#487—431no—
305#487C2×D4311yescharacteristic
306#485—861no—
307#485—861no—
308#475—431no—
309#475—431no—
310#474—431no—
311#474C2×D4311yescharacteristic
312#467—861no—
313#467—861no—
314#462—431no—
315#462—431no—
316#461—431no—
317#461C2×D4311yescharacteristic
318#452—861no—
319#452—861no—
320#446—431no—
321#446—431no—
322C4×Q16—861no—
323C4×Q16—861no—
324C4×Q16—861no—
325C4×Q16—861no—
326C4×SD16—861no—
327C4×SD16—861no—
328#436—431no—
329#436C2×D4311yescharacteristic
330#435—861no—
331#435—861no—
332#431—431no—
333#431—431no—
334#431—431no—
335#431—861no—
336C4×M16—861no—
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#1916111yescharacteristic, complemented, Sylow
351C2×#41—431no—
352C2×Q16—861no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×Q16—861no—
356C2×SD16—21no—
357C2×SD16—861no—
358C2×M16—21no—
359C2×M16—861no—
360C22×C8—431no—
361C22×C8—431no—
362C4⋊Q8—431no—
363C4⋊Q8—431no—
364C4⋊Q8C22×D4311yescharacteristic
365C4⋊Q8C22×D4311yescharacteristic
366#125—861no—
367#125—861no—
368C22⋊Q8—861no—
369C22⋊Q8—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372C4×Q8—431no—
373C4×Q8—431no—
374C4×Q8—861no—
375C4×Q8—861no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×D4—431no—
379C4×D4—861no—
380C4×D4—861no—
381C4×D4C22×D4311yescharacteristic
382#117—431no—
383#117—861no—
384#117—861no—
385#117—861no—
386C2×C42—431no—
387C2×C42—861no—
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—21no—
413#102—861no—
414C22⋊C8—21no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419#97—861no—
420#97—861no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—861no—
425C4×C8—861no—
426C4×C8—861no—
427C4×C8C22×D4311yescharacteristic
428#41—1721no—
429#41—1721no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—431no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×D4—861no—
436C2×D4D4×D4311yescharacteristic
437C22×C4—21no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—861no—
442C22×C4—861no—
443Q16—1722no—
444Q16—1722no—
445Q16—1722no—
446Q16—1722no—
447SD16—42no—
448SD16—1722no—
449M16—42no—
450M16—1722no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—862no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—1721no—
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—1721no—
475C4⋊C4—1721no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4D4×D4311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—1721no—
483C22⋊C4—1721no—
484C42—431no—
485C42—431no—
486C42—431no—
487C42—861no—
488C42—861no—
489C42—861no—
490C42—1721no—
491C42—1721no—
492C42C23×D4311yescharacteristic
493C23—21no—
494C23—431no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—861no—
500Q8—861no—
501Q8—1721no—
502Q8—1721no—
503Q8—1721no—
504Q8—1721no—
505D4—21no—
506D4—21no—
507D4—1722no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—431no—
514C2×C4—431no—
515C2×C4—431no—
516C2×C4—862no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—1722no—
524C2×C4—1722no—
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—432no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—861no—
544C22—861no—
545C22—861no—
546C22#121×D4311yescharacteristic
547C4—21no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—432no—
552C4—861no—
553C4—861no—
554C4—3441no—
555C4—3441no—
556C4—1721no—
557C4—1721no—
558C4#135×D4311yescharacteristic
559C4#1458369511yescharacteristic
560C4#1458369511yescharacteristic
561C4#1458369811yescharacteristic
562C2—81no—
563C2—1721no—
564C2#1914404711yescharacteristic
565C2#1914419911yescharacteristic
566C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1699C2
socleC22×C43C2×#121
prime radicalC2×#10621900D4
hypercenter#1699D43
hypocenterC43#19161
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1699

Complements

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

NH ≅ G/Ntype
1. #19145180C2semidirect
5. #19134150C2semidirect
6. #19134146C2semidirect
7. #19134142C2semidirect
8. #19134112C2semidirect
9. #19134106C2semidirect
10. #19134088C2semidirect
11. #19134082C2semidirect
12. #19133342C2semidirect
13. #19133258C2semidirect
14. #19133258C2semidirect
15. C43×#1699C2semidirect
286. #1699D43semidirect
350. C43#19161semidirect

Maximal subgroups

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

subgroupindex
#191451802
#191446682
#191446632
#191435582
#191341502
#191341462
#191341422
#191341122
#191341062
#191340882
#191340822
#191333422
#191332582
C43×#16992
#1916143