Finite Group Databasebeta

← #25087189

Subgroups — #25087189

Order 11008.

574 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147482C211yesmaximal, characteristic, complemented
2#19147374C211yesmaximal, characteristic
3#19146471C211yesmaximal, characteristic
4#19134242C211yesmaximal, characteristic, complemented
5#19134146C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134051C211yesmaximal, characteristic, complemented
8#19133982C211yesmaximal, characteristic
9#19133871C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic
11#19133800C211yesmaximal, characteristic
12#19133753C211yesmaximal, characteristic, complemented
13#19133445C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic
15C43×#3359C211yesmaximal, characteristic
16#14583627C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583298—21no—
20#14583295C2211yescharacteristic
21#14583266—21no—
22#14583251C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583232—21no—
26#14583209—21no—
27#14583206—21no—
28#14583203—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583184C2211yescharacteristic
32#14583181C2211yescharacteristic
33#14583138—21no—
34#14583106C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583102—21no—
37#14583055—21no—
38#14583029C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14582996—21no—
41C4×#10621885—21no—
42C4×#10621885C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063249—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#557C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#487—21no—
59C43×#487C2211yescharacteristic
60C43×#475—21no—
61C43×#475C2211yescharacteristic
62C43×#461—21no—
63C43×#461C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885D411yescharacteristic
69C2×#10621883—21no—
70C22×C43⋊C8—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063323—21no—
74#13063317—21no—
75#13063316—21no—
76#13063315—41no—
77#13063304—21no—
78#13063302—41no—
79C4×Dic86—21no—
80C4×Dic86C2311yescharacteristic
81#13063290—21no—
82D4×Dic43—21no—
83C2×C4⋊Dic43—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258D411yescharacteristic
89#13063256—21no—
90#13063256—21no—
91#13063256—41no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063250—21no—
98#13063250—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249D411yescharacteristic
106#13063248—21no—
107#13063248—21no—
108#13063248—41no—
109#13063248D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111#13063235—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123#125×C43—41no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#106×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
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—42no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154C22×Dic43—41no—
155C2×Dic86—21no—
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×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—41no—
181C42×C43C2411yescharacteristic
182C22⋊Dic43—41no—
183#10621885—22no—
184#10621885—81no—
185#10621883—42no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C23×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—82no—
215Q8×C43#13712yes—
216D4×C43—21no—
217D4×C43#13512yes—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—82no—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—161no—
236Dic86—21no—
237Dic86—21no—
238Dic86—41no—
239Dic86—41no—
240Dic86—81no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250#19838—431nomaximal, Sylow
251C22×C43—22no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43D4211yescharacteristic
255C4×C43—22no—
256C4×C43—21no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43C2×#13511yescharacteristic
264C4×C43C2×#13711yescharacteristic
265C4×C43#57711yescharacteristic
266C4×C43#57811yescharacteristic
267Dic43—41no—
268Dic43—41no—
269Dic43—81no—
270Dic43—81no—
271#3383—431no—
272#3372—431no—
273#3359D4311yescharacteristic
274#3299—431no—
275#1718—431no—
276#1700—431no—
277#1684—431no—
278#1684—431no—
279#1673—431no—
280#1653—431no—
281#1651—431no—
282#1643—431no—
283#1636—431no—
284#1584—431no—
285SD16⋊C8—431no—
286C2×C43—42no—
287C2×C43#326611yescharacteristic
288C2×C43#328511yescharacteristic
289C2×C43#328911yescharacteristic
290#557—431no—
291#557C2×D4311yescharacteristic
292#554—431no—
293D4×Q8C2×D4311yescharacteristic
294#500—431no—
295#499—861no—
296#498—431no—
297#491—861no—
298#487—21no—
299#487—431no—
300#487—431no—
301#487—431no—
302#487C2×D4311yescharacteristic
303#484—861no—
304#479—861no—
305#479—861no—
306#479—861no—
307#477—431no—
308#477—431no—
309#475—21no—
310#475—431no—
311#475—431no—
312#475C2×D4311yescharacteristic
313#467—861no—
314#462—431no—
315#461—21no—
316#461—431no—
317#461—861no—
318#461C2×D4311yescharacteristic
319#451—861no—
320#446—431no—
321C8×Q8—431no—
322C8×Q8C2×D4311yescharacteristic
323#440—861no—
324C4×Q16—431no—
325C4×Q16—861no—
326C4×SD16—21no—
327C4×SD16C2×D4311yescharacteristic
328C8×D4—431no—
329C2×#103—861no—
330#335—431no—
331#335—431no—
332#333—431no—
333#332—431no—
334#332—431no—
335#332—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339D4⋊C8—431no—
340#322—431no—
341C43#1983811yescharacteristic, complemented, Sylow
342C22×Q8—21no—
343C2×Q16—431no—
344C2×Q16—861no—
345C2×SD16—21no—
346C2×SD16—861no—
347C2×SD16C22⋊D4311yescharacteristic
348C22×C8—861no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—431no—
352C4⋊Q8—431no—
353C4⋊Q8—861no—
354C4⋊Q8C22×D4311yescharacteristic
355C4⋊Q8C22×D4311yescharacteristic
356#125—21no—
357#125—41no—
358#125—861no—
359#125—861no—
360#125—1721no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363C22⋊Q8—861no—
364C22⋊Q8—1721no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8C22×D4311yescharacteristic
371C4×Q8C22×D4311yescharacteristic
372C4×D4—21no—
373C4×D4—861no—
374C4×D4C22×D4311yescharacteristic
375C2×C4⋊C4—861no—
376#107—431no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#106—21no—
382#106—861no—
383#106—861no—
384#106—1721no—
385#106C22⋊D4311yescharacteristic
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8C22×D4311yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—431no—
398#103—431no—
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#103—1721no—
410#103C22⋊D4311yescharacteristic
411#102C22⋊D4311yescharacteristic
412C22⋊C8—861no—
413#97—861no—
414C4×C8—21no—
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—861no—
418C4×C8C22×D4311yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—41no—
422C2×Q8—42no—
423C2×Q8—81no—
424C2×Q8—431no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8D4×D4311yescharacteristic
428C2×Q8C2×C22⋊D4311yescharacteristic
429C2×D4C2×C22⋊D4311yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—1721no—
433Q16—862no—
434Q16—3441no—
435SD16—22no—
436SD16—42no—
437SD16—1722no—
438C2×C8—21no—
439C2×C8—431no—
440C2×C8—431no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—3441no—
446C2×C8C2×C22⋊D4311yescharacteristic
447C2×C8C2×C22⋊D4311yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—431no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4D4×D4311yescharacteristic
470C4⋊C4C2×C22⋊D4311yescharacteristic
471C4⋊C4C2×C22⋊D4311yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—1721no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—861no—
479C42—1721no—
480C42C23×D4311yescharacteristic
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—82no—
490Q8—861no—
491Q8—861no—
492Q8—3441no—
493Q8—1721no—
494Q8—1721no—
495Q8#1306335412yes—
496D4—21no—
497D4#1306334512yes—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—82no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—6881no—
513C2×C4C2×D4×D4311yescharacteristic
514C2×C4C22×C22⋊D4311yescharacteristic
515C2×C4#1306337011yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—861no—
520C8—861no—
521C8—1721no—
522C8—1721no—
523C8—1721no—
524C8—1721no—
525C22—22no—
526C22—41no—
527C22—41no—
528C22D4×C22⋊D4311yescharacteristic
529C4—22no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—81no—
536C4—81no—
537C4—3441no—
538C4—3441no—
539C4—1721no—
540C4—1721no—
541C4C2×#1306334511yescharacteristic
542C4C2×#1306335411yescharacteristic
543C4#1458370511yescharacteristic
544C4#1458371411yescharacteristic
545C2—42no—
546C2#1914610511yescharacteristic
547C2#1914633211yescharacteristic
548C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3359C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenter#3359D43
hypocenterC43#19838
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3359

Complements

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

NH ≅ G/Ntype
1. #19147482C2semidirect
4. #19134242C2semidirect
5. #19134146C2semidirect
6. #19134053C2semidirect
7. #19134051C2semidirect
9. #19133871C2semidirect
12. #19133753C2semidirect
13. #19133445C2semidirect
341. C43#19838semidirect

Maximal subgroups

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

subgroupindex
#191474822
#191473742
#191464712
#191342422
#191341462
#191340532
#191340512
#191339822
#191338712
#191338582
#191338002
#191337532
#191334452
SD16⋊(C43⋊C8)2
C43×#33592
#1983843