Finite Group Databasebeta

← #25079352

Subgroups — #25079352

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#19145177C211yesmaximal, characteristic, complemented
2#19144667C211yesmaximal, characteristic
3#19144660C211yesmaximal, characteristic
4#19143556C211yesmaximal, characteristic
5#19134152C211yesmaximal, characteristic, complemented
6#19134148C211yesmaximal, characteristic, complemented
7#19134145C211yesmaximal, characteristic, complemented
8#19134141C211yesmaximal, characteristic, complemented
9#19134112C211yesmaximal, characteristic, complemented
10#19134107C211yesmaximal, characteristic, complemented
11#19134088C211yesmaximal, characteristic, complemented
12#19134083C211yesmaximal, characteristic, complemented
13#19133341C211yesmaximal, characteristic, complemented
14#19133259C211yesmaximal, characteristic, complemented
15C43×#1544C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583278C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583241—21no—
23#14583237—21no—
24#14583185C2211yescharacteristic
25#14583181C2211yescharacteristic
26#14583180C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583138—21no—
29#14583138—21no—
30#14583110C2211yescharacteristic
31#14583106C2211yescharacteristic
32#14583105C2211yescharacteristic
33#14583101C2211yescharacteristic
34#14583063—21no—
35#14583059—21no—
36#14583026C2211yescharacteristic
37#14583026C2211yescharacteristic
38C4×Dic172—21no—
39C4×#10621885—21no—
40C4×#10621885—21no—
41C4×#10621885—21no—
42C4×#10621873—21no—
43C4×#10621884—21no—
44#14582976C2211yescharacteristic
45#14582976C2211yescharacteristic
46#14582967—21no—
47#14582967—21no—
48#14582952C2211yescharacteristic
49#14582950—21no—
50C4×#10621872—21no—
51C2×C4×C43⋊C8C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621873—21no—
73C2×#10621884—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8D411yescharacteristic
77C22×C43⋊C8D411yescharacteristic
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063317—21no—
81#13063304—21no—
82#13063304—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86D411yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×D172D411yescharacteristic
88C4×D172C2311yescharacteristic
89C4×C22⋊D43—21no—
90C4×C22⋊D43—21no—
91#13063284—21no—
92#13063284D411yescharacteristic
93#13063282—21no—
94C42×D43—21no—
95#13063259—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063250—21no—
107#13063250—21no—
108#13063249—21no—
109#13063249—21no—
110#13063249—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063248—21no—
115#13063247—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120#13063235—21no—
121#13063235—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8D411yescharacteristic
124C4×C43⋊C8D411yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4⋊Q8×C43C2311yescharacteristic
128C4⋊Q8×C43C2311yescharacteristic
129#125×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4111yescharacteristic
149C2×C22⋊D43—21no—
150#10621898—41no—
151#10621898—41no—
152C2×D172C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C2×D411yescharacteristic
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—41no—
168C4⋊C4×C43—41no—
169C22⋊C4×C43—41no—
170C42×C43—41no—
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43#4111yescharacteristic
174C42×C43C2411yescharacteristic
175C22⋊Dic43—21no—
176C22⋊Dic43—41no—
177#10621885—42no—
178#10621885—42no—
179#10621885—42no—
180#10621884—42no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C2×D411yescharacteristic
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—41no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205Dic172—42no—
206#10621873—42no—
207#10621872—42no—
208#10621872—42no—
209C23×C43#12111yescharacteristic
210C22×D43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—42no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234D172—21no—
235D172—21no—
236C4×D43—42no—
237C4×D43—41no—
238C4×D43—41no—
239C4×D43—42no—
240Dic86—21no—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8#13512yes—
256#19161—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43C2×#12111yescharacteristic
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43#47312yes—
270C4×C43C2×#13511yescharacteristic
271C4×C43#57511yescharacteristic
272C4×C43#57511yescharacteristic
273C4×C43#57511yescharacteristic
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277Dic43—81no—
278Dic43—81no—
279#3170—431no—
280#3107—431no—
281#3107—431no—
282#2965—431no—
283#1700—431no—
284#1700—431no—
285#1699—431no—
286#1699—431no—
287#1694—431no—
288#1693—431no—
289#1690—431no—
290#1689—431no—
291#1564—431no—
292#1544—431no—
293#1544D4311yescharacteristic, complemented
294C2×C43—41no—
295C2×C43#303511yescharacteristic
296C2×C43#305411yescharacteristic
297C2×C43C2×#47311yescharacteristic
298D43—81no—
299#533—431no—
300#533C2×D4311yescharacteristic
301C4×#41—431no—
302#500—431no—
303#494—431no—
304#487—431no—
305#487—431no—
306#485—861no—
307#485—861no—
308#475—431no—
309#475—431no—
310#474—431no—
311#474—431no—
312#467—861no—
313#467—861no—
314#462—431no—
315#462—431no—
316#461—431no—
317#461—431no—
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#436—431no—
330#435—861no—
331#435—861no—
332#431—431no—
333#431—861no—
334#431C2×D4311yescharacteristic
335#431C2×D4311yescharacteristic
336C4×M16—861no—
337C2×C4×C8—431no—
338#335—431no—
339#335—431no—
340#334—431no—
341#334—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332C2×D4311yescharacteristic
347#332C2×D4311yescharacteristic
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—861no—
357C2×SD16—861no—
358C2×M16—861no—
359C2×M16—861no—
360C22×C8—431no—
361C22×C8—431no—
362C4⋊Q8—431no—
363C4⋊Q8—431no—
364C4⋊Q8C22×D4311yescharacteristic
365C4⋊Q8C22×D4311yescharacteristic
366#125—21no—
367#125—861no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×D4—431no—
379C4×D4—431no—
380C4×D4—861no—
381C4×D4—861no—
382#117—21no—
383#117—431no—
384#117—861no—
385#117—861no—
386C2×C42—861no—
387C2×C42C22×D4311yescharacteristic
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—861no—
413#102—861no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419#97—861no—
420#97—861no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—861no—
428#41—1721no—
429#41—1721no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—431no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×D4—431no—
436C2×D4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4#1062189811yescharacteristic
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443Q16—1722no—
444Q16—1722no—
445Q16—1722no—
446Q16—1722no—
447SD16—1722no—
448SD16—1722no—
449M16—1722no—
450M16—1722no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—862no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—1721no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—431no—
470C4⋊C4—431no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C22⋊C4—41no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—1721no—
484C42—41no—
485C42—861no—
486C42—861no—
487C42—861no—
488C42—1721no—
489C42#1062189811yescharacteristic
490C42D4×D4311yescharacteristic
491C42D4×D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—861no—
494C23#1306329811yescharacteristic
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—861no—
500Q8—861no—
501Q8—1721no—
502Q8—1721no—
503Q8—1721no—
504Q8—1721no—
505D4—861no—
506D4—861no—
507D4—1722no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—1722no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1722no—
523C2×C4—1721no—
524C2×C4#1306329811yescharacteristic
525C2×C4#1306329811yescharacteristic
526C2×C4#1306329811yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C2×#1062189811yescharacteristic
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—432no—
535C8—861no—
536C8—861no—
537C8—861no—
538C8—1721no—
539C8—1721no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—1721no—
544C22—1721no—
545C22—1721no—
546C22C2×#1306329811yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—81no—
551C4—81no—
552C4—3441no—
553C4—3441no—
554C4—1721no—
555C4—1721no—
556C4—1721no—
557C4#1458317312yes—
558C4#135×D4311yescharacteristic
559C4#1458369611yescharacteristic
560C4#1458369611yescharacteristic
561C4#1458369611yescharacteristic
562C2—41no—
563C2—3441no—
564C2#1914404811yescharacteristic
565C2#1914420311yescharacteristic
566C2C2×#1458317311yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1544C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#1544D43
hypocenterC43#19161
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
1. #19145177C2semidirect
5. #19134152C2semidirect
6. #19134148C2semidirect
7. #19134145C2semidirect
8. #19134141C2semidirect
9. #19134112C2semidirect
10. #19134107C2semidirect
11. #19134088C2semidirect
12. #19134083C2semidirect
13. #19133341C2semidirect
14. #19133259C2semidirect
15. C43×#1544C2semidirect
293. #1544D43semidirect
350. C43#19161semidirect

Maximal subgroups

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

subgroupindex
#191451772
#191446672
#191446602
#191435562
#191341522
#191341482
#191341452
#191341412
#191341122
#191341072
#191340882
#191340832
#191333412
#191332592
C43×#15442
#1916143