Finite Group Databasebeta

← #25081733

Subgroups — #25081733

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145957C211yesmaximal, characteristic
2#19144991C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic, complemented
4#19134179C211yesmaximal, characteristic, complemented
5#19134172C211yesmaximal, characteristic, complemented
6#19134137C211yesmaximal, characteristic, complemented
7#19134130C211yesmaximal, characteristic, complemented
8#19134055C211yesmaximal, characteristic, complemented
9#19134048C211yesmaximal, characteristic, complemented
10#19134013C211yesmaximal, characteristic, complemented
11#19134006C211yesmaximal, characteristic, complemented
12#19133363C211yesmaximal, characteristic, complemented
13#19133301C211yesmaximal, characteristic, complemented
14#19133276C211yesmaximal, characteristic, complemented
15C43×#3238C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583261—21no—
18#14583261—21no—
19#14583251C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583196—21no—
24#14583184C2211yescharacteristic
25#14583179C2211yescharacteristic
26#14583150—21no—
27#14583147—21no—
28#14583111—21no—
29#14583099C2211yescharacteristic
30#14583094C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14582977—21no—
34#14582977C2211yescharacteristic
35#14582971—21no—
36D4×C43⋊C8C2211yescharacteristic
37#14582960—21no—
38#14582952C2211yescharacteristic
39#14582923C2211yescharacteristic
40#14582898—21no—
41#14582898—21no—
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582648C2211yescharacteristic
51#14582648C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#501—21no—
59C43×#489—21no—
60C43×#483—21no—
61C43×#480—21no—
62C43×#477C2211yescharacteristic
63C43×#477C2211yescharacteristic
64C43×#476C2211yescharacteristic
65C43×#476C2211yescharacteristic
66C43×#432C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621882—21no—
70C2×#10621877—21no—
71C2×#10621877—21no—
72C2×#10621877D411yescharacteristic
73C2×#10621877D411yescharacteristic
74C22×C43⋊C8—21no—
75#13063325C2311yescharacteristic
76#13063322C2311yescharacteristic
77#13063313—21no—
78#13063299—21no—
79#13063299—21no—
80C4×D172—21no—
81C4×D172—21no—
82#13063258—21no—
83#13063256—21no—
84C4⋊(C43⋊C8)—21no—
85C4⋊(C43⋊C8)—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)C2311yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91#13063249—21no—
92#13063248—21no—
93#13063248—21no—
94#13063248—21no—
95#13063248—21no—
96#13063246—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236D411yescharacteristic
108#13063236D411yescharacteristic
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C22×Q8×C43—21no—
114C4⋊Q8×C43—21no—
115C4⋊Q8×C43—21no—
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
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×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—82no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—41no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—41no—
157#10621898—42no—
158#10621898—42no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C42×C43—21no—
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43#4111yescharacteristic
187C42×C43C2411yescharacteristic
188#10621884—81no—
189#10621882—81no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194#10621877—41no—
195#10621877—41no—
196#10621877—42no—
197#10621877—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—42no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43#12111yescharacteristic
209C22×D43—41no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—81no—
213Q8×C43—81no—
214Q8×C43—82no—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—81no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—82no—
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—82no—
238C2×Dic43—41no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—81no—
244C4×D43—82no—
245Dic86—41no—
246Dic86—41no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19382—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43C2×#12111yescharacteristic
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43#57511yescharacteristic
278C4×C43#57511yescharacteristic
279C4×C43#57711yescharacteristic
280C4×C43#57811yescharacteristic
281Dic43—81no—
282#3251—431no—
283#3238D4311yescharacteristic, complemented
284#3141—431no—
285#2969—431no—
286#1704—431no—
287#1703—431no—
288#1698—431no—
289#1697—431no—
290#1684—431no—
291#1683—431no—
292#1678—431no—
293#1677—431no—
294#1569—431no—
295#1553—431no—
296#1548—431no—
297C2×C43—41no—
298C2×C43—81no—
299C2×C43#304011yescharacteristic
300C2×C43#306311yescharacteristic
301C2×C43#306811yescharacteristic
302D43—161no—
303#532—431no—
304C2×C4⋊Q8C2×D4311yescharacteristic
305#529C2×D4311yescharacteristic
306#501—21no—
307#489—21no—
308#489—861no—
309#489—861no—
310#487—431no—
311#487—431no—
312#486—431no—
313#486—431no—
314#483—21no—
315#480—21no—
316#478—861no—
317#477C2×D4311yescharacteristic
318#477C2×D4311yescharacteristic
319#476C2×D4311yescharacteristic
320#476C2×D4311yescharacteristic
321#475—431no—
322#474—431no—
323#469—861no—
324#468—861no—
325#463—861no—
326#460—431no—
327#459—431no—
328#446—431no—
329C8×Q8—431no—
330#436—431no—
331#436—861no—
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#432C2×D4311yescharacteristic
336#431—431no—
337#423—431no—
338#417—861no—
339#417—861no—
340#405—861no—
341C4×M16—431no—
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#331—431no—
353#331—431no—
354C43#1938211yescharacteristic, complemented, Sylow
355C2×#41—861no—
356C22×Q8—21no—
357C2×SD16—861no—
358C2×D8—861no—
359C2×M16—431no—
360C2×M16—431no—
361C2×M16—861no—
362C2×M16—861no—
363C22×C8—861no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—431no—
368C4⋊Q8C22×D4311yescharacteristic
369C4⋊Q8C22×D4311yescharacteristic
370#127—431no—
371#126—21no—
372#125C22⋊D4311yescharacteristic
373#124—861no—
374#124C22⋊D4311yescharacteristic
375#123—21no—
376C22⋊Q8C22⋊D4311yescharacteristic
377#121—861no—
378#121—861no—
379#121C22⋊D4311yescharacteristic
380C4×Q8C22×D4311yescharacteristic
381C4×D4—21no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4C22×D4311yescharacteristic
385#117—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C42C22×D4311yescharacteristic
389#107—21no—
390#107—21no—
391#107—861no—
392#106—21no—
393#106—21no—
394#106—861no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404#103—21no—
405#103—21no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—21no—
412#102—21no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—21no—
425#97—431no—
426#97—431no—
427#97—861no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—861no—
431C4×C8—861no—
432#41—1722no—
433#41—1722no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—82no—
438C2×Q8—861no—
439C2×Q8C2×C22⋊D4311yescharacteristic
440C2×D4—21no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—1721no—
445C2×D4C2×C22⋊D4311yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—1721no—
449C22×C4D4×D4311yescharacteristic
450C22×C4#1062190011yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452SD16—3441no—
453D8—3441no—
454M16—3441no—
455M16—1721no—
456M16—1721no—
457M16—1722no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4C2×C22⋊D4311yescharacteristic
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C42—21no—
491C42D4×D4311yescharacteristic
492C42#1062190011yescharacteristic
493C42C2×C22⋊D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—21no—
496C23—1721no—
497C23#1306329711yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—81no—
501Q8—81no—
502Q8—82no—
503Q8—1721no—
504Q8—1721no—
505D4—21no—
506D4—21no—
507D4—81no—
508D4—3441no—
509D4—3442no—
510D4—1721no—
511D4—1721no—
512D4—1721no—
513D4—1721no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—82no—
527C2×C4—3442no—
528C2×C4—1721no—
529C2×C4#1306329711yescharacteristic
530C2×C4#1306329711yescharacteristic
531C2×C4#1306329711yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C22×C22⋊D4311yescharacteristic
534C2×C4C2×#1062190011yescharacteristic
535C8—41no—
536C8—41no—
537C8—861no—
538C8—861no—
539C8—861no—
540C8—861no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22C2×#1306329711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—3441no—
565C4#1458369811yescharacteristic
566C4#1458369811yescharacteristic
567C4#1458370711yescharacteristic
568C4#1458371411yescharacteristic
569C2—41no—
570C2—81no—
571C2—6881no—
572C2#1914409111yescharacteristic
573C2#1914428211yescharacteristic
574C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3238C2
socleC22×C43C2×#121
prime radical#19145957C2
hypercenter#3238D43
hypocenterC43#19382
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
2. #19144991C2semidirect
3. #19143600C2semidirect
4. #19134179C2semidirect
5. #19134172C2semidirect
6. #19134137C2semidirect
7. #19134130C2semidirect
8. #19134055C2semidirect
9. #19134048C2semidirect
10. #19134013C2semidirect
11. #19134006C2semidirect
12. #19133363C2semidirect
13. #19133301C2semidirect
14. #19133276C2semidirect
15. C43×#3238C2semidirect
283. #3238D43semidirect
354. C43#19382semidirect

Maximal subgroups

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

subgroupindex
#191459572
#191449912
#191436002
#191341792
#191341722
#191341372
#191341302
#191340552
#191340482
#191340132
#191340062
#191333632
#191333012
#191332762
C43×#32382
#1938243