Finite Group Databasebeta

← #25087610

Subgroups — #25087610

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#19147581C211yesmaximal, characteristic
2#19147210C211yesmaximal, characteristic, complemented
3#19147021C211yesmaximal, characteristic, complemented
4#19134274C211yesmaximal, characteristic, complemented
5#19134106C211yesmaximal, characteristic, complemented
6#19134050C211yesmaximal, characteristic, complemented
7#19133972C211yesmaximal, characteristic, complemented
8#19133965C211yesmaximal, characteristic, complemented
9#19133851C211yesmaximal, characteristic, complemented
10#19133849C211yesmaximal, characteristic, complemented
11#19133802C211yesmaximal, characteristic, complemented
12#19133765C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic
14#19133412C211yesmaximal, characteristic, complemented
15C43×#3360C211yesmaximal, characteristic
16#14583619C2211yescharacteristic
17#14583619C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583282—21no—
22#14583279C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583240—21no—
25#14583237—21no—
26#14583237—21no—
27#14583229—21no—
28#14583191C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583184C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583155—21no—
33#14583138—21no—
34#14583120—21no—
35#14583120—21no—
36#14583104C2211yescharacteristic
37#14583104C2211yescharacteristic
38C8×Dic86C2211yescharacteristic
39#14582993—21no—
40C4×#10621885C2211yescharacteristic
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582939—21no—
44#14582935—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#556C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#488—21no—
59C43×#487C2211yescharacteristic
60C43×#479—21no—
61C43×#476C2211yescharacteristic
62C43×#463—21no—
63C43×#461C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C2×Dic172—21no—
68C2×Dic172—21no—
69C2×#10621885D411yescharacteristic
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063318—41no—
77#13063318—41no—
78#13063312—21no—
79#13063312—21no—
80#13063304—21no—
81#13063304—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290—21no—
85#13063284—21no—
86#13063284—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—41no—
91#13063258D411yescharacteristic
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—41no—
104#13063249D411yescharacteristic
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248—21no—
109#13063248D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×SD16×C43—21no—
116C2×D8×C43D411yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#126×C43—41no—
120#125×C43—21no—
121#124×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131C2×C4⋊C4×C43—21no—
132#107×C43D411yescharacteristic
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×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—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C2×D411yescharacteristic
155SD16×C43—42no—
156D8×C43—41no—
157C2×C8×C43—21no—
158C2×C8×C43C2×D411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—41no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43—41no—
168C4⋊C4×C43C2×D411yescharacteristic
169C4⋊C4×C43C2×D411yescharacteristic
170C4⋊C4×C43C2×D411yescharacteristic
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C42×C43—21no—
177C42×C43—41no—
178C42×C43C2411yescharacteristic
179C22⋊Dic43—41no—
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182C22⋊Dic43—41no—
183#10621885—22no—
184#10621883—81no—
185#10621883—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—41no—
196C4×Dic43—41no—
197#10621877—42no—
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
205Dic172—42no—
206Dic172—81no—
207C23×C43—21no—
208C23×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—81no—
214D4×C43—21no—
215D4×C43—21no—
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—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×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43H(5,𝔽2)11yescharacteristic
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236Dic86—21no—
237Dic86—21no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C43⋊C8—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8#13512yes—
251#19866—431nomaximal, Sylow
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43D4211yescharacteristic
259C4×C43—21no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43C2×#13511yescharacteristic
267C4×C43#57511yescharacteristic
268C4×C43#57711yescharacteristic
269C4×C43#57811yescharacteristic
270Dic43—41no—
271Dic43—41no—
272Dic43—81no—
273Dic43—81no—
274#3393—431no—
275#3360D4311yescharacteristic
276#3356—431no—
277#3342—431no—
278#1723—431no—
279#1693—431no—
280#1684—431no—
281#1671—431no—
282#1670—431no—
283#1650—431no—
284#1650—431no—
285#1643—431no—
286#1638—431no—
287#1581—431no—
288#1579—431no—
289C2×C43—81no—
290C2×C43—81no—
291C2×C43#327111yescharacteristic
292C2×C43#328311yescharacteristic
293C2×C43#328911yescharacteristic
294#556—431no—
295#556—431no—
296#556C2×D4311yescharacteristic
297#554C2×D4311yescharacteristic
298#500—431no—
299#500—431no—
300#498—431no—
301#495—861no—
302#494—431no—
303#488—21no—
304#487—431no—
305#487C2×D4311yescharacteristic
306#485—861no—
307#485—861no—
308#485—861no—
309#483—861no—
310#479—21no—
311#477—431no—
312#476C2×D4311yescharacteristic
313#475—431no—
314#475—431no—
315#475—431no—
316#470—861no—
317#467—861no—
318#464—861no—
319#464—861no—
320#463—21no—
321#461—431no—
322#461—431no—
323#461C2×D4311yescharacteristic
324C8×Q8—431no—
325C8×Q8C2×D4311yescharacteristic
326C4×Q16—431no—
327C4×Q16—861no—
328C4×SD16—21no—
329C4×D8C2×D4311yescharacteristic
330#436—431no—
331C8×D4—431no—
332#428—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#1986611yescharacteristic, complemented, Sylow
346C2×Q16—431no—
347C2×Q16—861no—
348C2×Q16—861no—
349C2×SD16—21no—
350C2×SD16—861no—
351C2×SD16—861no—
352C2×D8C22⋊D4311yescharacteristic
353C2×M16—861no—
354C22×C8—861no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8C22×D4311yescharacteristic
358C4⋊Q8C22×D4311yescharacteristic
359#126—41no—
360#126—1721no—
361#126—1721no—
362#125—21no—
363#124—21no—
364#124—861no—
365#124—861no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—41no—
369C22⋊Q8—861no—
370C22⋊Q8—861no—
371C4×Q8—21no—
372C4×Q8—431no—
373C4×Q8—861no—
374C4×Q8—861no—
375C4×Q8C22×D4311yescharacteristic
376C4×D4—21no—
377C4×D4C22×D4311yescharacteristic
378C4×D4C22×D4311yescharacteristic
379#117—21no—
380#117—861no—
381#117—861no—
382C2×C4⋊C4—21no—
383#107—431no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—1721no—
388#107C22⋊D4311yescharacteristic
389#106—21no—
390#106—861no—
391#106—861no—
392#106—861no—
393#106—861no—
394#106—861no—
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—21no—
404#103—431no—
405#103—431no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—1721no—
413#102—21no—
414#102C22⋊D4311yescharacteristic
415#102C22⋊D4311yescharacteristic
416C22⋊C8—861no—
417C22⋊C8—861no—
418C4×C8—21no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—431no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8D4×D4311yescharacteristic
429C2×D4C2×C22⋊D4311yescharacteristic
430C2×D4C2×C22⋊D4311yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434Q16—862no—
435Q16—3441no—
436Q16—1722no—
437SD16—42no—
438SD16—3441no—
439SD16—3441no—
440D8—41no—
441M16—1722no—
442C2×C8—21no—
443C2×C8—431no—
444C2×C8—431no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
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—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—431no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4D4×D4311yescharacteristic
469C4⋊C4C2×C22⋊D4311yescharacteristic
470C4⋊C4C2×C22⋊D4311yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—1721no—
477C22⋊C4—1721no—
478C22⋊C4—1721no—
479C22⋊C4—1721no—
480C42—21no—
481C42—41no—
482C42—861no—
483C42—1721no—
484C42—1721no—
485C42C23×D4311yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—861no—
494Q8—861no—
495Q8—1721no—
496Q8—1721no—
497Q8—1721no—
498Q8—1721no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—161no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C22×C22⋊D4311yescharacteristic
520C2×C4#1306337011yescharacteristic
521C8—21no—
522C8—21no—
523C8—41no—
524C8—432no—
525C8—861no—
526C8—1721no—
527C8—1721no—
528C8—1721no—
529C8—1721no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22D4×C22⋊D4311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—3441no—
545C4—3441no—
546C4—1721no—
547C4—1721no—
548C4#135×D4311yescharacteristic
549C4#1458369711yescharacteristic
550C4#1458370711yescharacteristic
551C4#1458371311yescharacteristic
552C2—81no—
553C2—81no—
554C2#1914618111yescharacteristic
555C2#1914631111yescharacteristic
556C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3360C2
socleC22×C43D42
prime radicalC2×D8×C43D4
hypercenter#3360D43
hypocenterC43#19866
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3360

Complements

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

NH ≅ G/Ntype
2. #19147210C2semidirect
3. #19147021C2semidirect
4. #19134274C2semidirect
5. #19134106C2semidirect
6. #19134050C2semidirect
7. #19133972C2semidirect
8. #19133965C2semidirect
9. #19133851C2semidirect
10. #19133849C2semidirect
11. #19133802C2semidirect
12. #19133765C2semidirect
14. #19133412C2semidirect
345. C43#19866semidirect

Maximal subgroups

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

subgroupindex
#191475812
#191472102
#191470212
#191342742
#191341062
#191340502
#191339722
#191339652
#191338512
#191338492
#191338022
#191337652
#191334252
#191334122
C43×#33602
#1986643