Finite Group Databasebeta

← #25087243

Subgroups — #25087243

Order 11008.

576 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147291C211yesmaximal, characteristic, complemented
2#19147253C211yesmaximal, characteristic
3#19146983C211yesmaximal, characteristic, complemented
4#19134249C211yesmaximal, characteristic, complemented
5#19134135C211yesmaximal, characteristic, complemented
6#19134050C211yesmaximal, characteristic, complemented
7#19134034C211yesmaximal, characteristic
8#19133997C211yesmaximal, characteristic, complemented
9#19133800C211yesmaximal, characteristic, complemented
10#19133753C211yesmaximal, characteristic, complemented
11#19133715C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic
13#19133443C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3372C211yesmaximal, characteristic, complemented
16#14583634C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583273C2211yescharacteristic
20#14583256—21no—
21#14583255—21no—
22#14583251C2211yescharacteristic
23#14583247C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583234—21no—
26#14583232—21no—
27#14583198—21no—
28#14583196—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583191C2211yescharacteristic
32#14583181C2211yescharacteristic
33#14583138—21no—
34#14583121—21no—
35#14583116—21no—
36#14583099C2211yescharacteristic
37#14583094C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40C4×#10621885C2211yescharacteristic
41C4×#10621884—21no—
42#14582979—21no—
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063258—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#557C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#491—21no—
59C43×#487C2211yescharacteristic
60C43×#479—21no—
61C43×#477C2211yescharacteristic
62C43×#461—21no—
63C43×#461C2211yescharacteristic
64C43×#446C2211yescharacteristic
65C43×#440—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621885D411yescharacteristic
68C2×#10621884—21no—
69C2×#10621884—41no—
70C2×#10621882—21no—
71C22×C43⋊C8—21no—
72#13063325C2311yescharacteristic
73#13063322C2311yescharacteristic
74#13063316—21no—
75#13063314—21no—
76#13063313—21no—
77#13063310—41no—
78#13063304—21no—
79#13063302—41no—
80C4×Dic86C2311yescharacteristic
81C4×D172—21no—
82D4×Dic43—21no—
83#13063287—21no—
84C2×C4⋊Dic43—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063256—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249D411yescharacteristic
100#13063248—21no—
101#13063248—21no—
102#13063248—41no—
103#13063248D411yescharacteristic
104#13063247—21no—
105#13063247—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110C22⋊(C43⋊C8)—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×SD16×C43—21no—
116C2×SD16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120#125×C43—21no—
121#125×C43—21no—
122#125×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#106×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—41no—
151C22×Dic43—41no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×C4×D43—41no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158SD16×C43—22no—
159SD16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184#10621885—41no—
185#10621884—42no—
186#10621884—82no—
187#10621882—42no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—41no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
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
205C23×C43—21no—
206C22×D43—41no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—81no—
214D4×C43—21no—
215D4×C43#13512yes—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—161no—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—161no—
233D172—41no—
234D172—41no—
235D172—41no—
236D172—41no—
237D172—81no—
238C4×D43—161no—
239Dic86—21no—
240Dic86—21no—
241Dic86—81no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251#19842—431nomaximal, Sylow
252C22×C43—22no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43D4211yescharacteristic
256C2×D43—81no—
257C2×D43—81no—
258C2×D43—81no—
259C4×C43—21no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43C2×#13511yescharacteristic
268C4×C43#57511yescharacteristic
269C4×C43#57811yescharacteristic
270C4×C43#57811yescharacteristic
271Dic43—41no—
272Dic43—41no—
273Dic43—81no—
274#3372D4311yescharacteristic, complemented
275#3365—431no—
276#3361—431no—
277#3338—431no—
278#1719—431no—
279#1698—431no—
280#1684—431no—
281#1681—431no—
282#1676—431no—
283#1643—431no—
284#1636—431no—
285#1630—431no—
286#1622—431no—
287#1584—431no—
288SD16⋊C8—431no—
289C2×C43—42no—
290C2×C43#326911yescharacteristic
291C2×C43#328511yescharacteristic
292C2×C43#328811yescharacteristic
293D43—161no—
294#559—431no—
295#557C2×D4311yescharacteristic
296#554—431no—
297#554C2×D4311yescharacteristic
298#500—431no—
299#492—431no—
300#491—21no—
301#488—861no—
302#488—861no—
303#487—431no—
304#487C2×D4311yescharacteristic
305#486—431no—
306#486—431no—
307#484—861no—
308#484—861no—
309#479—21no—
310#478—861no—
311#478—861no—
312#477—431no—
313#477—431no—
314#477—431no—
315#477C2×D4311yescharacteristic
316#475—431no—
317#467—861no—
318#464—861no—
319#463—861no—
320#461—21no—
321#461C2×D4311yescharacteristic
322#460—431no—
323#459—431no—
324#446C2×D4311yescharacteristic
325C8×Q8—431no—
326C8×Q8—431no—
327#440—21no—
328C4×Q16—431no—
329C4×SD16—861no—
330C4×SD16C2×D4311yescharacteristic
331C4×D8—861no—
332C8×D4—431no—
333C2×#107—861no—
334#335—431no—
335#335—431no—
336#333—431no—
337#333—431no—
338#332—431no—
339#331—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343D4⋊C8—431no—
344#322—431no—
345C43#1984211yescharacteristic, complemented, Sylow
346C2×Q16—431no—
347C2×SD16—21no—
348C2×SD16—861no—
349C2×SD16—1721no—
350C2×SD16C22⋊D4311yescharacteristic
351C2×D8—861no—
352C22×C8—861no—
353C4⋊Q8—21no—
354C4⋊Q8—431no—
355C4⋊Q8C22×D4311yescharacteristic
356C4⋊Q8C22×D4311yescharacteristic
357#127—431no—
358#125—21no—
359#125—21no—
360#125—41no—
361#125—861no—
362#124—861no—
363#124—861no—
364#123—1721no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C22⋊Q8—861no—
368C22⋊Q8—1721no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—431no—
372C4×Q8C22×D4311yescharacteristic
373C4×Q8C22×D4311yescharacteristic
374C4×D4—21no—
375C4×D4—861no—
376C4×D4—861no—
377C4×D4—861no—
378C4×D4C22×D4311yescharacteristic
379C2×C4⋊C4—21no—
380C2×C4⋊C4—861no—
381#107—21no—
382#107—431no—
383#107—861no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—861no—
388#106—861no—
389#106C22⋊D4311yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8C22×D4311yescharacteristic
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—431no—
402#103—431no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—1721no—
408#103C22⋊D4311yescharacteristic
409#102—861no—
410#102—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102C22⋊D4311yescharacteristic
416C22⋊C8—861no—
417#97—21no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—431no—
426C2×Q8—861no—
427C2×Q8D4×D4311yescharacteristic
428C2×Q8C2×C22⋊D4311yescharacteristic
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4C2×C22⋊D4311yescharacteristic
433C22×C4—21no—
434C22×C4—41no—
435C22×C4—1721no—
436C22×C4—1721no—
437Q16—1721no—
438SD16—22no—
439SD16—42no—
440SD16—3442no—
441SD16—1722no—
442D8—1722no—
443C2×C8—21no—
444C2×C8—431no—
445C2×C8—431no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—1722no—
451C2×C8C2×C22⋊D4311yescharacteristic
452C2×C8C2×C22⋊D4311yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—431no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4D4×D4311yescharacteristic
471C4⋊C4C2×C22⋊D4311yescharacteristic
472C4⋊C4C2×C22⋊D4311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—41no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C22⋊C4—1721no—
478C22⋊C4—1721no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—861no—
483C42C23×D4311yescharacteristic
484C23—21no—
485C23—1721no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—861no—
494Q8—861no—
495Q8—3441no—
496D4—21no—
497D4—3441no—
498D4—1721no—
499D4—1721no—
500D4—1721no—
501D4—1721no—
502D4#1306334512yes—
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—41no—
512C2×C4—161no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—1721no—
516C2×C4—6881no—
517C2×C4—6881no—
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C22×C22⋊D4311yescharacteristic
520C2×C4#1306337011yescharacteristic
521C8—21no—
522C8—21no—
523C8—41no—
524C8—861no—
525C8—861no—
526C8—1721no—
527C8—1721no—
528C8—1721no—
529C8—1721no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—3441no—
534C22—3441no—
535C22—3441no—
536C22D4×C22⋊D4311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—81no—
544C4—81no—
545C4—3441no—
546C4—1721no—
547C4—1721no—
548C4C2×#1306334511yescharacteristic
549C4#1458369811yescharacteristic
550C4#1458371411yescharacteristic
551C4#1458371511yescharacteristic
552C2—42no—
553C2—6881no—
554C2#1914614411yescharacteristic
555C2#1914633211yescharacteristic
556C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3372C2
socleC22×C43D42
prime radical#14583094C22
hypercenter#3372D43
hypocenterC43#19842
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3372

Complements

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

NH ≅ G/Ntype
1. #19147291C2semidirect
3. #19146983C2semidirect
4. #19134249C2semidirect
5. #19134135C2semidirect
6. #19134050C2semidirect
8. #19133997C2semidirect
9. #19133800C2semidirect
10. #19133753C2semidirect
11. #19133715C2semidirect
13. #19133443C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3372C2semidirect
274. #3372D43semidirect
345. C43#19842semidirect

Maximal subgroups

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

subgroupindex
#191472912
#191472532
#191469832
#191342492
#191341352
#191340502
#191340342
#191339972
#191338002
#191337532
#191337152
#191336672
#191334432
SD16⋊(C43⋊C8)2
C43×#33722
#1984243