Finite Group Databasebeta

← #25081714

Subgroups — #25081714

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145968C211yesmaximal, characteristic
2#19145822C211yesmaximal, characteristic
3#19144976C211yesmaximal, characteristic, complemented
4#19134177C211yesmaximal, characteristic, complemented
5#19134170C211yesmaximal, characteristic, complemented
6#19134149C211yesmaximal, characteristic, complemented
7#19134142C211yesmaximal, characteristic, complemented
8#19134053C211yesmaximal, characteristic, complemented
9#19134046C211yesmaximal, characteristic, complemented
10#19134025C211yesmaximal, characteristic, complemented
11#19134018C211yesmaximal, characteristic, complemented
12#19133362C211yesmaximal, characteristic, complemented
13#19133303C211yesmaximal, characteristic, complemented
14#19133279C211yesmaximal, characteristic, complemented
15C43×#2969C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583309—21no—
19#14583268—21no—
20#14583268—21no—
21#14583258—21no—
22#14583250C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583250C2211yescharacteristic
26#14583232—21no—
27#14583215—21no—
28#14583203—21no—
29#14583194C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583184C2211yescharacteristic
32#14583184C2211yescharacteristic
33#14583179C2211yescharacteristic
34#14583179C2211yescharacteristic
35#14583155—21no—
36#14583143—21no—
37#14583118—21no—
38#14583109C2211yescharacteristic
39#14583104C2211yescharacteristic
40#14582956C2211yescharacteristic
41#14582923C2211yescharacteristic
42#14582909—21no—
43#14582909—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436C2211yescharacteristic
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#405—21no—
66C4×M16×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621877—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#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063250—21no—
100#13063250—21no—
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—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C22×C8×C43—21no—
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43D411yescharacteristic
124#121×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43D411yescharacteristic
139#97×C43D411yescharacteristic
140C4×C8×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—42no—
157C2×Dic86—42no—
158C2×Dic86—41no—
159M16×C43—41no—
160M16×C43—41no—
161M16×C43—42no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—42no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C42×C43—21no—
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43#4111yescharacteristic
184C42×C43C2411yescharacteristic
185C22⋊Dic43—41no—
186#10621885—81no—
187#10621883—81no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—41no—
201#10621877—81no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C23×C43—21no—
207C23×C43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210D4×C43—21no—
211D4×C43—21no—
212D4×C43—81no—
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—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—82no—
234Dic86—41no—
235Dic86—41no—
236Dic86—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—82no—
241Dic86—81no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19381—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43C2×#12111yescharacteristic
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43#57511yescharacteristic
268C4×C43#57511yescharacteristic
269C4×C43#57711yescharacteristic
270C4×C43#57811yescharacteristic
271Dic43—81no—
272Dic43—81no—
273Dic43—81no—
274Dic43—81no—
275#3252—431no—
276#3239—431no—
277#3139—431no—
278#2969D4311yescharacteristic
279#1704—431no—
280#1703—431no—
281#1700—431no—
282#1699—431no—
283#1684—431no—
284#1683—431no—
285#1680—431no—
286#1679—431no—
287#1569—431no—
288#1554—431no—
289#1549—431no—
290C2×C43—41no—
291C2×C43—81no—
292C2×C43#304011yescharacteristic
293C2×C43#306311yescharacteristic
294C2×C43#306911yescharacteristic
295#533—431no—
296C2×C4⋊Q8—431no—
297#529C2×D4311yescharacteristic
298#501—861no—
299#491—861no—
300#491—861no—
301#489—861no—
302#487—431no—
303#487—431no—
304#487—431no—
305#487—431no—
306#484—861no—
307#481—861no—
308#479—861no—
309#477—431no—
310#476—431no—
311#475—431no—
312#475—431no—
313#474—431no—
314#474—431no—
315#470—861no—
316#468—861no—
317#464—861no—
318#462—431no—
319#461—431no—
320#446C2×D4311yescharacteristic
321C8×Q8C2×D4311yescharacteristic
322#436—21no—
323#436C2×D4311yescharacteristic
324#435—21no—
325C8×D4C2×D4311yescharacteristic
326#433—21no—
327#432—431no—
328#431C2×D4311yescharacteristic
329#423—431no—
330#419—861no—
331#419—861no—
332#405—21no—
333C4×M16C2×D4311yescharacteristic
334#335—431no—
335#335—431no—
336#334—431no—
337#334—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346C43#1938111yescharacteristic, complemented, Sylow
347C22×Q8—861no—
348C2×Q16—861no—
349C2×SD16—861no—
350C2×M16—21no—
351C2×M16—861no—
352C2×M16C22⋊D4311yescharacteristic
353C2×M16C22⋊D4311yescharacteristic
354C22×C8—21no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8—431no—
359C4⋊Q8—861no—
360C4⋊Q8—861no—
361C4⋊Q8—861no—
362#126—21no—
363#125—861no—
364#125D17211yescharacteristic
365#124D17211yescharacteristic
366#123—21no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369C22⋊Q8D17211yescharacteristic
370#121D17211yescharacteristic
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8C22×D4311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4311yescharacteristic
376#117—21no—
377#117—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—861no—
397#103—861no—
398#103—861no—
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#103—861no—
409#102—861no—
410#102—861no—
411#102—861no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—861no—
416#97—21no—
417#97—861no—
418#97C22⋊D4311yescharacteristic
419#97C22⋊D4311yescharacteristic
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C22×D4311yescharacteristic
423C4×C8C22×D4311yescharacteristic
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—1722no—
429C2×Q8—1722no—
430C2×Q8—1721no—
431C2×Q8C2×D17211yescharacteristic
432C2×D4—21no—
433C2×D4C2×D17211yescharacteristic
434C22×C4—21no—
435C22×C4—1721no—
436C22×C4C2×D17211yescharacteristic
437C22×C4#1062189811yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439Q16—3441no—
440SD16—3441no—
441M16—41no—
442M16—41no—
443M16—42no—
444M16—3441no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8C2×C22⋊D4311yescharacteristic
453C2×C8C2×C22⋊D4311yescharacteristic
454C2×C8C2×C22⋊D4311yescharacteristic
455C2×C8C2×C22⋊D4311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4C2×D17211yescharacteristic
473C4⋊C4C2×D17211yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—1721no—
480C42—21no—
481C42—1721no—
482C42C2×D17211yescharacteristic
483C42#1062189811yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C42C23×D4311yescharacteristic
486C23—21no—
487C23#1306329911yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—3441no—
491Q8—3442no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495Q8—1721no—
496Q8—1721no—
497Q8—1721no—
498D4—21no—
499D4—21no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—3442no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306329911yescharacteristic
517C2×C4#1306329911yescharacteristic
518C2×C4#1306329911yescharacteristic
519C2×C4C22×C22⋊D4311yescharacteristic
520C2×C4C22×D17211yescharacteristic
521C2×C4C2×#1062189811yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#1306329911yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—3441no—
547C4—3441no—
548C4—3441no—
549C4—3441no—
550C4#1458369711yescharacteristic
551C4#1458369711yescharacteristic
552C4#1458371111yescharacteristic
553C4#1458371611yescharacteristic
554C2—41no—
555C2—81no—
556C2#1914408911yescharacteristic
557C2#1914428611yescharacteristic
558C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2969C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#2969D43
hypocenterC43#19381
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
3. #19144976C2semidirect
4. #19134177C2semidirect
5. #19134170C2semidirect
6. #19134149C2semidirect
7. #19134142C2semidirect
8. #19134053C2semidirect
9. #19134046C2semidirect
10. #19134025C2semidirect
11. #19134018C2semidirect
12. #19133362C2semidirect
13. #19133303C2semidirect
14. #19133279C2semidirect
346. C43#19381semidirect

Maximal subgroups

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

subgroupindex
#191459682
#191458222
#191449762
#191341772
#191341702
#191341492
#191341422
#191340532
#191340462
#191340252
#191340182
#191333622
#191333032
#191332792
C43×#29692
#1938143