Finite Group Databasebeta

← #25087249

Subgroups — #25087249

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#19147374C211yesmaximal, characteristic, complemented
2#19147287C211yesmaximal, characteristic, complemented
3#19146983C211yesmaximal, characteristic, complemented
4#19134245C211yesmaximal, characteristic, complemented
5#19134132C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134030C211yesmaximal, characteristic
8#19133997C211yesmaximal, characteristic, complemented
9#19133802C211yesmaximal, characteristic, complemented
10#19133751C211yesmaximal, characteristic, complemented
11#19133716C211yesmaximal, characteristic, complemented
12#19133665C211yesmaximal, characteristic
13#19133445C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
15C43×#3361C211yesmaximal, characteristic
16#14583627C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583271C2211yescharacteristic
20#14583266—21no—
21#14583253—21no—
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583234—21no—
26#14583232—21no—
27#14583209—21no—
28#14583199—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583191C2211yescharacteristic
32#14583184C2211yescharacteristic
33#14583138—21no—
34#14583118—21no—
35#14583104C2211yescharacteristic
36#14583102—21no—
37#14583096C2211yescharacteristic
38#14583029C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14582996—21no—
41C4×#10621885C2211yescharacteristic
42C4×#10621883—21no—
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063258—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#559C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#488—21no—
59C43×#486C2211yescharacteristic
60C43×#478—21no—
61C43×#477C2211yescharacteristic
62C43×#463—21no—
63C43×#459C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43C2211yescharacteristic
66C4×D8×C43—21no—
67C2×#10621885D411yescharacteristic
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621883—41no—
71C22×C43⋊C8—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063323—21no—
75#13063317—21no—
76#13063316—21no—
77#13063315—41no—
78#13063304—21no—
79#13063302—41no—
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82#13063290—21no—
83D4×Dic43—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#13063250—21no—
98#13063250—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—41no—
103#13063249D411yescharacteristic
104#13063248—21no—
105#13063248—21no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246—21no—
110C22⋊(C43⋊C8)—21no—
111#13063235—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×SD16×C43D411yescharacteristic
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#125×C43—21no—
120#124×C43—21no—
121#124×C43—21no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43C2311yescharacteristic
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
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×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C2×D411yescharacteristic
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—41no—
153C22×C4×C43—41no—
154C22×Dic43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158SD16×C43—22no—
159D8×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—41no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43C2×D411yescharacteristic
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181#10621885—41no—
182#10621883—42no—
183#10621883—42no—
184#10621883—82no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—41no—
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—
206C23×C43—41no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—81no—
212D4×C43—21no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—81no—
218D4×C43#13512yes—
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—161no—
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—
236C2×Dic43—161no—
237Dic86—21no—
238Dic86—21no—
239Dic86—41no—
240Dic86—41no—
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×C43—81no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43D4211yescharacteristic
259C4×C43—21no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—81no—
266C4×C43C2×#13511yescharacteristic
267C4×C43#57511yescharacteristic
268C4×C43#57811yescharacteristic
269C4×C43#57811yescharacteristic
270Dic43—41no—
271Dic43—41no—
272Dic43—81no—
273Dic43—81no—
274#3372—431no—
275#3365—431no—
276#3361D4311yescharacteristic
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—161no—
291C2×C43#326911yescharacteristic
292C2×C43#328511yescharacteristic
293C2×C43#328811yescharacteristic
294#559C2×D4311yescharacteristic
295#557—431no—
296#554—431no—
297#554C2×D4311yescharacteristic
298#500—431no—
299#492—431no—
300#491—861no—
301#488—21no—
302#488—861no—
303#487—431no—
304#487—431no—
305#486—431no—
306#486C2×D4311yescharacteristic
307#484—861no—
308#484—861no—
309#479—861no—
310#478—21no—
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—21no—
320#461—431no—
321#461—861no—
322#460—431no—
323#459C2×D4311yescharacteristic
324#446—431no—
325C8×Q8—431no—
326C8×Q8C2×D4311yescharacteristic
327#440—861no—
328C4×Q16—431no—
329C4×SD16—861no—
330C4×SD16C2×D4311yescharacteristic
331C4×D8—21no—
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—861no—
348C2×SD16—861no—
349C2×SD16—1721no—
350C2×SD16C22⋊D4311yescharacteristic
351C2×D8—21no—
352C22×C8—861no—
353C4⋊Q8—431no—
354C4⋊Q8—431no—
355C4⋊Q8—861no—
356C4⋊Q8C22×D4311yescharacteristic
357#127C22×D4311yescharacteristic
358#125—21no—
359#125—861no—
360#125—861no—
361#125—1721no—
362#124—21no—
363#124—21no—
364#123—41no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C22⋊Q8—861no—
368C22⋊Q8—1721no—
369C4×Q8—431no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×Q8C22×D4311yescharacteristic
373C4×Q8C22×D4311yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
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—431no—
399#103—431no—
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—21no—
411#102—21no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102C22⋊D4311yescharacteristic
416C22⋊C8—861no—
417#97—861no—
418C4×C8—21no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C2×Q8—21no—
424C2×Q8—431no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8D4×D4311yescharacteristic
428C2×Q8C2×C22⋊D4311yescharacteristic
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C2×C22⋊D4311yescharacteristic
433C22×C4—21no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—1721no—
437Q16—1721no—
438SD16—22no—
439SD16—3442no—
440SD16—1722no—
441SD16—1722no—
442D8—42no—
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—41no—
458C4⋊C4—41no—
459C4⋊C4—431no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
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—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—1721no—
479C42—21no—
480C42—21no—
481C42—861no—
482C42—1721no—
483C42C23×D4311yescharacteristic
484C23—21no—
485C23—41no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—81no—
491Q8—861no—
492Q8—861no—
493Q8—3441no—
494Q8—1721no—
495Q8—1721no—
496D4—21no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—81no—
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—161no—
512C2×C4—161no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—1721no—
516C2×C4—1721no—
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—81no—
534C22—81no—
535C22—81no—
536C22D4×C22⋊D4311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—81no—
544C4—3441no—
545C4—3441no—
546C4—1721no—
547C4—1721no—
548C4C2×#1306334511yescharacteristic
549C4#1458369611yescharacteristic
550C4#1458371311yescharacteristic
551C4#1458371411yescharacteristic
552C2—42no—
553C2—161no—
554C2#1914615011yescharacteristic
555C2#1914633211yescharacteristic
556C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3361C2
socleC22×C43D42
prime radicalC43×#459C22
hypercenter#3361D43
hypocenterC43#19842
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3361

Complements

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

NH ≅ G/Ntype
1. #19147374C2semidirect
2. #19147287C2semidirect
3. #19146983C2semidirect
4. #19134245C2semidirect
5. #19134132C2semidirect
6. #19134053C2semidirect
8. #19133997C2semidirect
9. #19133802C2semidirect
10. #19133751C2semidirect
11. #19133716C2semidirect
13. #19133445C2semidirect
14. SD16⋊(C43⋊C8)C2semidirect
345. C43#19842semidirect

Maximal subgroups

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

subgroupindex
#191473742
#191472872
#191469832
#191342452
#191341322
#191340532
#191340302
#191339972
#191338022
#191337512
#191337162
#191336652
#191334452
SD16⋊(C43⋊C8)2
C43×#33612
#1984243