Finite Group Databasebeta

← #25087535

Subgroups — #25087535

Order 11008.

596 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147221C211yesmaximal, characteristic, complemented
2#19146946C211yesmaximal, characteristic, complemented
3#19146525C211yesmaximal, characteristic
4#19134271C211yesmaximal, characteristic, complemented
5#19134096C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19133992C211yesmaximal, characteristic, complemented
8#19133991C211yesmaximal, characteristic, complemented
9#19133802C211yesmaximal, characteristic, complemented
10#19133744C211yesmaximal, characteristic, complemented
11#19133739C211yesmaximal, characteristic, complemented
12#19133729C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15C43×#3380C211yesmaximal, characteristic, complemented
16#14583614C2211yescharacteristic
17#14583553C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583242—21no—
24#14583237—21no—
25#14583227—21no—
26#14583217—21no—
27#14583212—21no—
28#14583194C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583186C2211yescharacteristic
31#14583186C2211yescharacteristic
32#14583184C2211yescharacteristic
33#14583147—21no—
34#14583130—21no—
35#14583127—21no—
36#14583104C2211yescharacteristic
37#14583041—21no—
38C4×#10621884C2211yescharacteristic
39#14582977C2211yescharacteristic
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42#14582939—21no—
43C2×#13063256—21no—
44#14582892—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#554C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#499—21no—
60C43×#478—21no—
61C43×#478—21no—
62C43×#476C2211yescharacteristic
63C43×#476C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×D8×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621885—41no—
69C2×#10621883—21no—
70C2×#10621884D411yescharacteristic
71C2×#10621877—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063311—41no—
77#13063309—41no—
78#13063305—21no—
79#13063299—21no—
80#13063299—21no—
81#13063296—21no—
82C4×D172C2311yescharacteristic
83#13063284—21no—
84#13063283—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—41no—
104#13063249D411yescharacteristic
105#13063248—21no—
106#13063246—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×D8×C43D411yescharacteristic
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#125×C43—21no—
119#125×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—41no—
123C22⋊Q8×C43—41no—
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128C4×D4×C43C2311yescharacteristic
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131#107×C43—21no—
132#107×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—41no—
152C22×C4×C43—41no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155C22×Dic43—41no—
156#10621900—42no—
157#10621900—81no—
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162D8×C43—22no—
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×C43—21no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C42×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185#10621885—82no—
186#10621884—22no—
187#10621883—81no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197C4×Dic43—41no—
198#10621877—42no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C8×D43—81no—
207C23×C43—21no—
208C23×C43—21no—
209C22×D43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—81no—
213Q8×C43—81no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43#13712yes—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—161no—
229C2×C4×C43—161no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C22⋊D43—82no—
234C22⋊D43—161no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—82no—
239D172—21no—
240D172—21no—
241C4×D43—41no—
242C4×D43—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—81no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8#13512yes—
255#19861—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43D4211yescharacteristic
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—41no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43C2×#13511yescharacteristic
274C4×C43C2×#13711yescharacteristic
275C4×C43#57711yescharacteristic
276C4×C43#57811yescharacteristic
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280#3380D4311yescharacteristic, complemented
281#3357—431no—
282#3335—431no—
283#3303—431no—
284#1723—431no—
285#1691—431no—
286#1684—431no—
287#1675—431no—
288#1675—431no—
289#1643—431no—
290#1635—431no—
291#1634—431no—
292#1632—431no—
293#1581—431no—
294SD16⋊C8—431no—
295C2×C43—42no—
296C2×C43—81no—
297C2×C43#326611yescharacteristic
298C2×C43#328311yescharacteristic
299C2×C43#328811yescharacteristic
300D43—81no—
301#555—431no—
302#554C2×D4311yescharacteristic
303#554C2×D4311yescharacteristic
304#547—431no—
305#500—431no—
306#500C2×D4311yescharacteristic
307#499—21no—
308#498—431no—
309#494—431no—
310#487—431no—
311#487—431no—
312#485—861no—
313#485—861no—
314#483—861no—
315#481—861no—
316#480—861no—
317#478—21no—
318#478—21no—
319#477—431no—
320#476—431no—
321#476—431no—
322#476—431no—
323#476C2×D4311yescharacteristic
324#476C2×D4311yescharacteristic
325#475—431no—
326#468—861no—
327#465—861no—
328#465—861no—
329#461—431no—
330#449—861no—
331C8×Q8C2×D4311yescharacteristic
332C4×SD16—431no—
333C4×D8—21no—
334C4×D8C2×D4311yescharacteristic
335#436—431no—
336C8×D4—431no—
337C8×D4—431no—
338#428—861no—
339C2×#106—861no—
340#416—861no—
341#335—431no—
342#335—431no—
343#333—431no—
344#333—431no—
345#333—431no—
346#332—431no—
347Q8⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350D4⋊C8—431no—
351#322—431no—
352C43#1986111yescharacteristic, complemented, Sylow
353C2×#41—861no—
354C2×Q16—1721no—
355C2×SD16—431no—
356C2×SD16—861no—
357C2×D8C22⋊D4311yescharacteristic
358C2×M16—861no—
359C22×C8—861no—
360C22×C8—861no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363C4⋊Q8C22×D4311yescharacteristic
364C4⋊Q8C22×D4311yescharacteristic
365#125—21no—
366#125—21no—
367#124—1721no—
368#123—1721no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372C22⋊Q8—41no—
373C22⋊Q8—861no—
374#121—861no—
375#121—861no—
376#121—861no—
377C4×Q8C22×D4311yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—431no—
381C4×D4C22×D4311yescharacteristic
382C4×D4C22×D4311yescharacteristic
383#117—861no—
384#117—861no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—861no—
388#107—21no—
389#107—21no—
390#107—861no—
391#107—861no—
392#107—861no—
393#107C22⋊D4311yescharacteristic
394#106—21no—
395#106—21no—
396#106—431no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402#106—861no—
403C4⋊C8—21no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8C22×D4311yescharacteristic
408#103—431no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—1721no—
415#102—21no—
416#102—21no—
417#102—431no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102C22⋊D4311yescharacteristic
422#102C22⋊D4311yescharacteristic
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C4×C8—21no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8C22×D4311yescharacteristic
430#41—3441no—
431#41—1722no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8D4×D4311yescharacteristic
437C2×D4—431no—
438C2×D4—1721no—
439C2×D4—1721no—
440C2×D4C2×C22⋊D4311yescharacteristic
441C2×D4C2×C22⋊D4311yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—861no—
447C22×C4—1721no—
448Q16—3442no—
449SD16—862no—
450SD16—3441no—
451D8—22no—
452M16—1722no—
453C2×C8—21no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—3441no—
461C2×C8—1722no—
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—431no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4D4×D4311yescharacteristic
480C4⋊C4C2×C22⋊D4311yescharacteristic
481C4⋊C4C2×C22⋊D4311yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—861no—
487C22⋊C4—1721no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C42—21no—
491C42—1721no—
492C42C23×D4311yescharacteristic
493C23—21no—
494C23—21no—
495C23—861no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—81no—
500Q8—3441no—
501Q8—1721no—
502Q8—1721no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—861no—
507D4—861no—
508D4—3442no—
509D4—6881no—
510D4#1306335612yes—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—161no—
522C2×C4—161no—
523C2×C4—861no—
524C2×C4—3442no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4C2×D4×D4311yescharacteristic
530C2×C4C22×C22⋊D4311yescharacteristic
531C2×C4#1306337011yescharacteristic
532C8—21no—
533C8—21no—
534C8—41no—
535C8—432no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—1721no—
548C22—1721no—
549C22—1721no—
550C22D4×C22⋊D4311yescharacteristic
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—3441no—
559C4—3441no—
560C4—1721no—
561C4#135×D4311yescharacteristic
562C4C2×#1306335611yescharacteristic
563C4#1458370711yescharacteristic
564C4#1458371311yescharacteristic
565C2—42no—
566C2—81no—
567C2—3441no—
568C2#1914610611yescharacteristic
569C2#1914631111yescharacteristic
570C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3380C2
socleC22×C43D42
prime radical#19146525C2
hypercenter#3380D43
hypocenterC43#19861
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #19147221C2semidirect
2. #19146946C2semidirect
4. #19134271C2semidirect
5. #19134096C2semidirect
6. #19134053C2semidirect
7. #19133992C2semidirect
8. #19133991C2semidirect
9. #19133802C2semidirect
10. #19133744C2semidirect
11. #19133739C2semidirect
12. #19133729C2semidirect
13. #19133425C2semidirect
14. #19133405C2semidirect
15. C43×#3380C2semidirect
280. #3380D43semidirect
352. C43#19861semidirect

Maximal subgroups

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

subgroupindex
#191472212
#191469462
#191465252
#191342712
#191340962
#191340532
#191339922
#191339912
#191338022
#191337442
#191337392
#191337292
#191334252
#191334052
C43×#33802
#1986143