Finite Group Databasebeta

← #25087065

Subgroups — #25087065

Order 11008.

572 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#19147278C211yesmaximal, characteristic
2#19147273C211yesmaximal, characteristic, complemented
3#19146878C211yesmaximal, characteristic
4#19134239C211yesmaximal, characteristic, complemented
5#19134172C211yesmaximal, characteristic
6#19134025C211yesmaximal, characteristic, complemented
7#19134023C211yesmaximal, characteristic, complemented
8#19133974C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic
10#19133836C211yesmaximal, characteristic, complemented
11#19133816C211yesmaximal, characteristic, complemented
12#19133765C211yesmaximal, characteristic
13#19133439C211yesmaximal, characteristic
14#19133412C211yesmaximal, characteristic, complemented
15Q8×SD16×C43C211yesmaximal, characteristic
16#14583628C2211yescharacteristic
17#14583619C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583252—21no—
20#14583251—21no—
21#14583251C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583237—21no—
26#14583209—21no—
27#14583191—21no—
28#14583191C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583155—21no—
32#14583119—21no—
33#14583109—21no—
34#14583109C2211yescharacteristic
35#14583109C2211yescharacteristic
36#14583106C2211yescharacteristic
37#14583055—21no—
38Q8×C43⋊C8C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40C4×#10621885—21no—
41C4×#10621885C2211yescharacteristic
42#14582991—21no—
43#14582977C2211yescharacteristic
44#14582908—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#498—21no—
59C43×#498C2211yescharacteristic
60C43×#476—21no—
61C43×#476C2211yescharacteristic
62C43×#475—21no—
63C43×#475C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621885D411yescharacteristic
71C2×#10621877—21no—
72#13063325—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063318—41no—
76#13063316—21no—
77#13063316—41no—
78#13063312—21no—
79#13063304—21no—
80Q8×Dic43—21no—
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063284—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—41no—
88#13063258D411yescharacteristic
89#13063256—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95#13063250—21no—
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—41no—
102#13063249D411yescharacteristic
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248D411yescharacteristic
109#13063246—21no—
110C22⋊(C43⋊C8)—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×Q8×C43—21no—
116C2×SD16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—41no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
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
131#106×C43—21no—
132#106×C43—21no—
133#106×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
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—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158SD16×C43—22no—
159C2×C8×C43—21no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—41no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—41no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182#10621885—22no—
183#10621885—42no—
184#10621885—42no—
185#10621885—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43—41no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C4×Dic43—41no—
199#10621877—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C23×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—82no—
212Q8×C43—81no—
213Q8×C43—161no—
214Q8×C43#13512yes—
215Q8×C43#13712yes—
216D4×C43—21no—
217D4×C43—21no—
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—
235Dic86—21no—
236Dic86—21no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
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#19830—431nomaximal, Sylow
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43D4211yescharacteristic
255C4×C43—22no—
256C4×C43—22no—
257C4×C43—21no—
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—
271Q8×SD16D4311yescharacteristic
272#3364—431no—
273#3363—431no—
274#3328—431no—
275#1718—431no—
276#1703—431no—
277#1680—431no—
278#1680—431no—
279#1672—431no—
280#1649—431no—
281#1648—431no—
282#1645—431no—
283#1638—431no—
284#1583—431no—
285#1579—431no—
286C2×C43—81no—
287C2×C43#327011yescharacteristic
288C2×C43#328211yescharacteristic
289C2×C43#328911yescharacteristic
290Q82C2×D4311yescharacteristic
291#557—431no—
292#556—431no—
293D4×Q8C2×D4311yescharacteristic
294#500—431no—
295#498—21no—
296#498C2×D4311yescharacteristic
297#488—861no—
298#487—431no—
299#487—431no—
300#487—431no—
301#487—431no—
302#487—861no—
303#485—861no—
304#479—861no—
305#477—431no—
306#477—861no—
307#476—21no—
308#476C2×D4311yescharacteristic
309#475—21no—
310#475—431no—
311#475C2×D4311yescharacteristic
312#474—431no—
313#470—861no—
314#464—861no—
315#462—431no—
316#462—431no—
317#462—431no—
318#462—861no—
319#451—861no—
320C8×Q8—431no—
321C8×Q8—431no—
322C8×Q8C2×D4311yescharacteristic
323C4×Q16—431no—
324C4×Q16—861no—
325C4×Q16—861no—
326C4×SD16—21no—
327C4×SD16C2×D4311yescharacteristic
328#436—431no—
329#419—861no—
330#334—431no—
331#334—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#1983011yescharacteristic, complemented, Sylow
342C22×Q8—21no—
343C2×Q16—431no—
344C2×Q16—861no—
345C2×Q16—861no—
346C2×Q16—861no—
347C2×SD16C22⋊D4311yescharacteristic
348C2×M16—861no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—41no—
353C4⋊Q8—431no—
354C4⋊Q8—431no—
355C4⋊Q8—861no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—1721no—
359#125—861no—
360#125—1721no—
361#124—861no—
362C22⋊Q8—21no—
363C22⋊Q8—41no—
364C22⋊Q8—861no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8C22×D4311yescharacteristic
372C4×Q8C22×D4311yescharacteristic
373C4×D4—21no—
374C4×D4C22×D4311yescharacteristic
375#117—861no—
376#107—431no—
377#107—861no—
378#107—861no—
379#107—1721no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—861no—
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—431no—
395#103—431no—
396#103—861no—
397#103—861no—
398#103—861no—
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—1721no—
408#103C22⋊D4311yescharacteristic
409#102—21no—
410#102—861no—
411#102C22⋊D4311yescharacteristic
412C22⋊C8—861no—
413C4×C8—21no—
414C4×C8—431no—
415C4×C8—431no—
416C4×C8—861no—
417C4×C8—861no—
418C4×C8C22×D4311yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—42no—
424C2×Q8—81no—
425C2×Q8—431no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8D4×D4311yescharacteristic
429C2×Q8C2×C22⋊D4311yescharacteristic
430C2×D4C2×C22⋊D4311yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433Q16—862no—
434Q16—3441no—
435Q16—1722no—
436Q16—1722no—
437SD16—22no—
438M16—3441no—
439C2×C8—21no—
440C2×C8—431no—
441C2×C8—431no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
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—431no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4D4×D4311yescharacteristic
468C4⋊C4C2×C22⋊D4311yescharacteristic
469C4⋊C4C2×C22⋊D4311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—1721no—
473C22⋊C4—1721no—
474C42—21no—
475C42—21no—
476C42—41no—
477C42—861no—
478C42—1721no—
479C42—1721no—
480C42C23×D4311yescharacteristic
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—41no—
485Q8—41no—
486Q8—82no—
487Q8—81no—
488Q8—161no—
489Q8—861no—
490Q8—861no—
491Q8—1721no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495Q8#1306334612yes—
496Q8#1306335612yes—
497D4—21no—
498D4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—82no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—1721no—
512C2×C4—1721no—
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—41no—
526C22—41no—
527C22—41no—
528C22D4×C22⋊D4311yescharacteristic
529C4—22no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—81no—
536C4—81no—
537C4—3441no—
538C4—3441no—
539C4—1721no—
540C4—1721no—
541C4C2×#1306334611yescharacteristic
542C4C2×#1306335611yescharacteristic
543C4#1458370511yescharacteristic
544C4#1458371411yescharacteristic
545C2—81no—
546C2#1914616611yescharacteristic
547C2#1914630211yescharacteristic
548C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×SD16×C43C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenterQ8×SD16D43
hypocenterC43#19830
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8×SD16

Complements

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

NH ≅ G/Ntype
2. #19147273C2semidirect
4. #19134239C2semidirect
6. #19134025C2semidirect
7. #19134023C2semidirect
8. #19133974C2semidirect
10. #19133836C2semidirect
11. #19133816C2semidirect
14. #19133412C2semidirect
341. C43#19830semidirect

Maximal subgroups

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

subgroupindex
#191472782
#191472732
#191468782
#191342392
#191341722
#191340252
#191340232
#191339742
#191338442
#191338362
#191338162
#191337652
#191334392
#191334122
Q8×SD16×C432
#1983043