Finite Group Databasebeta

← #25087453

Subgroups — #25087453

Order 11008.

570 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#19147280C211yesmaximal, characteristic, complemented
2#19147010C211yesmaximal, characteristic
3#19147002C211yesmaximal, characteristic
4#19134226C211yesmaximal, characteristic, complemented
5#19134101C211yesmaximal, characteristic, complemented
6#19134020C211yesmaximal, characteristic, complemented
7#19133975C211yesmaximal, characteristic, complemented
8#19133957C211yesmaximal, characteristic, complemented
9#19133865C211yesmaximal, characteristic, complemented
10#19133863C211yesmaximal, characteristic, complemented
11#19133821C211yesmaximal, characteristic
12#19133753C211yesmaximal, characteristic, complemented
13#19133429C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3398C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583614C2211yescharacteristic
18#14583297C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583256—21no—
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583238—21no—
25#14583237—21no—
26#14583223—21no—
27#14583222—21no—
28#14583203—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583176C2211yescharacteristic
33#14583176C2211yescharacteristic
34#14583130—21no—
35#14583125—21no—
36#14583121—21no—
37#14583109C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39C4×#10621885—21no—
40C4×#10621884C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582935—21no—
44#14582934—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#557C2211yescharacteristic
57C43×#556C2211yescharacteristic
58C43×#497—21no—
59C43×#494C2211yescharacteristic
60C43×#464—21no—
61C43×#462—21no—
62C43×#462C2211yescharacteristic
63C43×#461C2211yescharacteristic
64C43×#446C2211yescharacteristic
65C43×#441—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621884D411yescharacteristic
69C22×C43⋊C8—21no—
70C2×C8×D43—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063320—41no—
74#13063313—21no—
75#13063311—41no—
76#13063301—21no—
77#13063299—21no—
78#13063296—21no—
79C4×Dic86—21no—
80C4×D172C2311yescharacteristic
81#13063284—21no—
82#13063283—21no—
83#13063283—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063257—21no—
90#13063257—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—41no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063249D411yescharacteristic
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—41no—
106#13063246—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#126×C43—41no—
124#125×C43—21no—
125#125×C43—41no—
126#124×C43—21no—
127C22⋊Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#117×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
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—
150C2×C22⋊D43—41no—
151C2×D172C2×D411yescharacteristic
152C2×C4×D43—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155Q16×C43—42no—
156Q16×C43—81no—
157Q16×C43—81no—
158SD16×C43—22no—
159SD16×C43—81no—
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×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43—41no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185#10621885—42no—
186#10621884—41no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—41no—
197C4×Dic43—41no—
198C4×Dic43—41no—
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—42no—
207C23×C43—21no—
208C22×D43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217D4×C43—21no—
218D4×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—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C22⋊D43—161no—
232C2×Dic43—21no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235D172—21no—
236D172—21no—
237C4×D43—41no—
238C4×D43—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—81no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43#13512yes—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251#19856—431nomaximal, Sylow
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43D4211yescharacteristic
256C2×D43—41no—
257C2×D43—41no—
258C2×D43—41no—
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#57711yescharacteristic
270C4×C43#57811yescharacteristic
271Dic43—41no—
272Dic43—81no—
273Dic43—81no—
274#3398D4311yescharacteristic, complemented
275#3364—431no—
276#3340—431no—
277#3340—431no—
278#1716—431no—
279#1692—431no—
280#1679—431no—
281#1672—431no—
282#1669—431no—
283#1652—431no—
284#1652—431no—
285#1646—431no—
286#1636—431no—
287#1582—431no—
288SD16⋊C8—431no—
289C2×C43—81no—
290C2×C43#326911yescharacteristic
291C2×C43#328411yescharacteristic
292C2×C43#328911yescharacteristic
293D43—81no—
294#557C2×D4311yescharacteristic
295#556—431no—
296#556C2×D4311yescharacteristic
297#555—431no—
298#498—431no—
299#498—431no—
300#498—431no—
301#497—21no—
302#494C2×D4311yescharacteristic
303#488—861no—
304#487—431no—
305#487—431no—
306#485—861no—
307#485—861no—
308#482—861no—
309#482—861no—
310#479—861no—
311#477—431no—
312#477—431no—
313#474—431no—
314#474—431no—
315#474—431no—
316#465—861no—
317#465—861no—
318#464—21no—
319#464—861no—
320#462—21no—
321#462—431no—
322#462C2×D4311yescharacteristic
323#461C2×D4311yescharacteristic
324#446C2×D4311yescharacteristic
325C8×Q8—431no—
326#441—21no—
327C4×Q16—861no—
328C4×SD16—431no—
329C4×SD16C2×D4311yescharacteristic
330C8×D4—431no—
331C8×D4—431no—
332#427—861no—
333#427—861no—
334#335—431no—
335#334—431no—
336#333—431no—
337#332—431no—
338#332—431no—
339#332—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342D4⋊C8—431no—
343D4⋊C8—431no—
344#322—431no—
345C43#1985611yescharacteristic, complemented, Sylow
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—861no—
350C2×SD16—21no—
351C2×SD16—431no—
352C2×SD16C22⋊D4311yescharacteristic
353C22×C8—861no—
354C22×C8—861no—
355C4⋊Q8—21no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#126—41no—
361#126—1721no—
362#125—21no—
363#125—41no—
364#124—21no—
365#124—861no—
366#124—1721no—
367C22⋊Q8—21no—
368C22⋊Q8—861no—
369#121—861no—
370#121—861no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—861no—
375C4×Q8C22×D4311yescharacteristic
376C4×Q8C22×D4311yescharacteristic
377C4×D4—431no—
378C4×D4C22×D4311yescharacteristic
379#117—21no—
380#117—861no—
381#117—861no—
382#117—861no—
383#107—861no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—861no—
388#106—431no—
389#106—861no—
390#106—861no—
391#106—861no—
392#106—861no—
393#106—1721no—
394#106C22⋊D4311yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401#103—21no—
402#103—21no—
403#103—431no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—1721no—
410#103C22⋊D4311yescharacteristic
411#102—431no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102C22⋊D4311yescharacteristic
416C22⋊C8—861no—
417C22⋊C8—861no—
418#97—21no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8D4×D4311yescharacteristic
428C2×Q8C2×C22⋊D4311yescharacteristic
429C2×D4—431no—
430C2×D4—1721no—
431C2×D4C2×C22⋊D4311yescharacteristic
432C22×C4—21no—
433C22×C4—861no—
434Q16—42no—
435Q16—81no—
436Q16—81no—
437Q16—1722no—
438SD16—22no—
439SD16—81no—
440SD16—1721no—
441C2×C8—21no—
442C2×C8—431no—
443C2×C8—431no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—1722no—
449C2×C8—1722no—
450C2×C8C2×C22⋊D4311yescharacteristic
451C2×C8C2×C22⋊D4311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—431no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—1721no—
468C4⋊C4D4×D4311yescharacteristic
469C4⋊C4C2×C22⋊D4311yescharacteristic
470C4⋊C4C2×C22⋊D4311yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—861no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C22⋊C4—1721no—
478C22⋊C4—1721no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—41no—
483C42—1721no—
484C42—1721no—
485C42C23×D4311yescharacteristic
486C23—21no—
487C23—861no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—3441no—
497Q8—1721no—
498Q8—1721no—
499D4—21no—
500D4—21no—
501D4—861no—
502D4—861no—
503D4—6881no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—861no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C22×C22⋊D4311yescharacteristic
520C2×C4#1306337011yescharacteristic
521C8—21no—
522C8—41no—
523C8—861no—
524C8—861no—
525C8—1721no—
526C8—1721no—
527C8—1721no—
528C8—1721no—
529C8#1306334512yes—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—1721no—
534C22—1721no—
535C22—1721no—
536C22D4×C22⋊D4311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—81no—
544C4—81no—
545C4—3441no—
546C4—3441no—
547C4—1721no—
548C4C2×#1306334511yescharacteristic
549C4#1458369811yescharacteristic
550C4#1458371011yescharacteristic
551C4#1458371511yescharacteristic
552C2—81no—
553C2—3441no—
554C2#1914614411yescharacteristic
555C2#1914632511yescharacteristic
556C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3398C2
socleC22×C43D42
prime radical#14583614C22
hypercenter#3398D43
hypocenterC43#19856
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3398

Complements

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

NH ≅ G/Ntype
1. #19147280C2semidirect
4. #19134226C2semidirect
5. #19134101C2semidirect
6. #19134020C2semidirect
7. #19133975C2semidirect
8. #19133957C2semidirect
9. #19133865C2semidirect
10. #19133863C2semidirect
12. #19133753C2semidirect
13. #19133429C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
15. C43×#3398C2semidirect
274. #3398D43semidirect
345. C43#19856semidirect

Maximal subgroups

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

subgroupindex
#191472802
#191470102
#191470022
#191342262
#191341012
#191340202
#191339752
#191339572
#191338652
#191338632
#191338212
#191337532
#191334292
SD16⋊(C43⋊C8)2
C43×#33982
#1985643