Finite Group Databasebeta

← #25084179

Subgroups — #25084179

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#19145932C211yesmaximal, characteristic
2#19145813C211yesmaximal, characteristic
3#19145741C211yesmaximal, characteristic, complemented
4#19134177C211yesmaximal, characteristic, complemented
5#19134170C211yesmaximal, characteristic, complemented
6#19134101C211yesmaximal, characteristic, complemented
7#19134094C211yesmaximal, characteristic, complemented
8#19134053C211yesmaximal, characteristic, complemented
9#19134046C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133970C211yesmaximal, characteristic, complemented
12#19133380C211yesmaximal, characteristic, complemented
13#19133293C211yesmaximal, characteristic, complemented
14C2×#14582647C211yesmaximal, characteristic, complemented
15C43×#2994C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583309—21no—
19#14583297C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583258—21no—
22#14583250C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583230—21no—
25#14583230—21no—
26#14583227—21no—
27#14583210—21no—
28#14583203—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583185—21no—
34#14583185—21no—
35#14583184C2211yescharacteristic
36#14583179C2211yescharacteristic
37#14583138—21no—
38#14583126—21no—
39#14583118—21no—
40#14583109C2211yescharacteristic
41#14583104C2211yescharacteristic
42#14582956C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436C2211yescharacteristic
60C43×#435—21no—
61C8×D4×C43—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#424—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C22×C43⋊C8—21no—
71#13063325—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83#13063284—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063257—21no—
90#13063257—21no—
91#13063257—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063250—21no—
102#13063250—21no—
103#13063250—21no—
104#13063250—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063248—21no—
109#13063248—21no—
110#13063246—21no—
111#13063246—21no—
112#13063246—21no—
113C22⋊(C43⋊C8)—21no—
114#13063236—21no—
115C2×M16×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118#126×C43—21no—
119#125×C43D411yescharacteristic
120#124×C43D411yescharacteristic
121#123×C43—21no—
122C22⋊Q8×C43D411yescharacteristic
123#121×C43D411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C22×Dic43—41no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—41no—
157C2×Dic86—82no—
158M16×C43—81no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—81no—
162C2×C8×C43—81no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43#4111yescharacteristic
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184#10621885—81no—
185#10621883—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43—41no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204C23×C43—21no—
205C23×C43#12111yescharacteristic
206Q8×C43—21no—
207Q8×C43—21no—
208D4×C43—21no—
209D4×C43—21no—
210D4×C43—42no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—82no—
232Dic86—41no—
233Dic86—41no—
234Dic86—41no—
235Dic86—41no—
236Dic86—82no—
237Dic86—81no—
238Dic86—81no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—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—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43#47112yes—
256C22×C43C2×#12111yescharacteristic
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43#57711yescharacteristic
265C4×C43#57711yescharacteristic
266C4×C43#57811yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—81no—
269Dic43—81no—
270Dic43—81no—
271Dic43—81no—
272#3248—431no—
273#3238—431no—
274#3229—431no—
275#2994D4311yescharacteristic
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—81no—
289C2×C43#304611yescharacteristic
290C2×C43#306311yescharacteristic
291C2×C43C2×#47111yescharacteristic
292#533—431no—
293C2×C4⋊Q8—431no—
294#529C2×D4311yescharacteristic
295#501—861no—
296#498—431no—
297#498—431no—
298#489—861no—
299#487—431no—
300#487—431no—
301#483—861no—
302#483—861no—
303#483—861no—
304#480—861no—
305#479—861no—
306#477—431no—
307#477—431no—
308#476—431no—
309#476—431no—
310#475—431no—
311#475—861no—
312#475—861no—
313#474—431no—
314#467—861no—
315#465—861no—
316#464—861no—
317#462—431no—
318#461—431no—
319#446C2×D4311yescharacteristic
320C8×Q8C2×D4311yescharacteristic
321#436C2×D4311yescharacteristic
322#435—21no—
323C8×D4—21no—
324C8×D4C2×D4311yescharacteristic
325#433—21no—
326#432—431no—
327#431C2×D4311yescharacteristic
328#424—21no—
329C2×C4⋊C8—431no—
330C2×C4⋊C8C2×D4311yescharacteristic
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—861no—
345C2×Q16—861no—
346C2×SD16—861no—
347C2×M16—21no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—861no—
351C4⋊Q8—431no—
352C4⋊Q8—431no—
353C4⋊Q8—431no—
354C4⋊Q8—431no—
355C4⋊Q8—861no—
356C4⋊Q8—861no—
357C4⋊Q8—861no—
358#126—21no—
359#125—861no—
360#125D17211yescharacteristic
361#124D17211yescharacteristic
362#123—21no—
363C22⋊Q8—861no—
364C22⋊Q8—861no—
365C22⋊Q8D17211yescharacteristic
366#121D17211yescharacteristic
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8C22×D4311yescharacteristic
370C4×D4—21no—
371C4×D4C22×D4311yescharacteristic
372#117—21no—
373#117—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C42C22×D4311yescharacteristic
377#107—861no—
378#107—861no—
379#107—861no—
380#106—861no—
381#106—861no—
382#106—861no—
383#106—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—861no—
395C4⋊C8C22⋊D4311yescharacteristic
396C4⋊C8C22⋊D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
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—21no—
412C22⋊C8—21no—
413C22⋊C8—861no—
414C22⋊C8C22⋊D4311yescharacteristic
415C22⋊C8C22⋊D4311yescharacteristic
416#97—21no—
417#97—861no—
418C4×C8—21no—
419C4×C8C22×D4311yescharacteristic
420C4×C8C22×D4311yescharacteristic
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—3442no—
426C2×Q8—1721no—
427C2×Q8C2×D17211yescharacteristic
428C2×D4—21no—
429C2×D4C2×D17211yescharacteristic
430C22×C4—21no—
431C22×C4—1721no—
432C22×C4C2×D17211yescharacteristic
433C22×C4#1062189811yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435Q16—3441no—
436SD16—3441no—
437M16—81no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—81no—
441C2×C8—81no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
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—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4C2×D17211yescharacteristic
468C4⋊C4C2×D17211yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—1721no—
475C42—21no—
476C42—1721no—
477C42C2×D17211yescharacteristic
478C42#1062189811yescharacteristic
479C42C2×C22⋊D4311yescharacteristic
480C42C23×D4311yescharacteristic
481C23—21no—
482C23#1306329911yescharacteristic
483Q8—21no—
484Q8—21no—
485Q8—3441no—
486Q8—3441no—
487Q8—3442no—
488Q8—1721no—
489Q8—1721no—
490Q8—1721no—
491Q8—1721no—
492D4—21no—
493D4—21no—
494D4—42no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—3442no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4#1306329911yescharacteristic
511C2×C4#1306329911yescharacteristic
512C2×C4#1306329911yescharacteristic
513C2×C4C22×C22⋊D4311yescharacteristic
514C2×C4C22×D17211yescharacteristic
515C2×C4C2×#1062189811yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—1721no—
523C8—1721no—
524C8—1721no—
525C8—1721no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22#1458316212yes—
532C22C2×#1306329911yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—3441no—
541C4—3441no—
542C4—3441no—
543C4—3441no—
544C4#1458371011yescharacteristic
545C4#1458371111yescharacteristic
546C4#1458371411yescharacteristic
547C4#1458371611yescharacteristic
548C2—22no—
549C2—81no—
550C2#1914414511yescharacteristic
551C2#1914428611yescharacteristic
552C2C2×#1458316211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2994C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#2994D43
hypocenterC43#19588
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2994

Complements

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

NH ≅ G/Ntype
3. #19145741C2semidirect
4. #19134177C2semidirect
5. #19134170C2semidirect
6. #19134101C2semidirect
7. #19134094C2semidirect
8. #19134053C2semidirect
9. #19134046C2semidirect
10. #19133977C2semidirect
11. #19133970C2semidirect
12. #19133380C2semidirect
13. #19133293C2semidirect
14. C2×#14582647C2semidirect
343. C43#19588semidirect

Maximal subgroups

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

subgroupindex
#191459322
#191458132
#191457412
#191341772
#191341702
#191341012
#191340942
#191340532
#191340462
#191339772
#191339702
#191333802
#191332932
C2×#145826472
C43×#29942
#1958843