Finite Group Databasebeta

← #25087335

Subgroups — #25087335

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147335C211yesmaximal, characteristic
2#19147280C211yesmaximal, characteristic
3#19147027C211yesmaximal, characteristic
4#19134244C211yesmaximal, characteristic, complemented
5#19134151C211yesmaximal, characteristic, complemented
6#19134055C211yesmaximal, characteristic, complemented
7#19134043C211yesmaximal, characteristic
8#19133989C211yesmaximal, characteristic, complemented
9#19133872C211yesmaximal, characteristic, complemented
10#19133863C211yesmaximal, characteristic
11#19133816C211yesmaximal, characteristic, complemented
12#19133766C211yesmaximal, characteristic
13#19133446C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic
15C43×#3363C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583622C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583261—21no—
21#14583256—21no—
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583239—21no—
26#14583239—21no—
27#14583203—21no—
28#14583186C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583184C2211yescharacteristic
31#14583181—21no—
32#14583176C2211yescharacteristic
33#14583137—21no—
34#14583121—21no—
35#14583121—21no—
36#14583109C2211yescharacteristic
37#14583109C2211yescharacteristic
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14583004—21no—
41C4×#10621885—21no—
42C4×#10621884C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#14582936—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#557C2211yescharacteristic
58C43×#487—21no—
59C43×#487C2211yescharacteristic
60C43×#477—21no—
61C43×#477C2211yescharacteristic
62C43×#462—21no—
63C43×#462C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×Q16×C43—21no—
66C4×Q16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621884D411yescharacteristic
70C2×C8×D43—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063320—41no—
74#13063320—41no—
75#13063313—21no—
76#13063313—21no—
77#13063301—21no—
78#13063301—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×D172C2311yescharacteristic
82#13063283—21no—
83#13063283—21no—
84#13063259—21no—
85#13063259—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—41no—
91#13063256D411yescharacteristic
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249—21no—
98#13063249—21no—
99#13063249—41no—
100#13063249D411yescharacteristic
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111#13063236—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43—21no—
116C2×Q16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—41no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#125×C43—21no—
124#125×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#107×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#103×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×D172C2×D411yescharacteristic
151C2×C4×D43—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154Q16×C43—41no—
155Q16×C43—42no—
156C2×C8×C43—21no—
157C2×C8×C43C2×D411yescharacteristic
158C2×C8×C43C2×D411yescharacteristic
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43—41no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—41no—
178C42×C43—41no—
179C42×C43C2411yescharacteristic
180#10621885—42no—
181#10621885—42no—
182#10621884—22no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—41no—
196C4×Dic43—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C8×D43—42no—
204C22×D43—21no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213Q8×C43—161no—
214Q8×C43#13512yes—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229D172—21no—
230D172—21no—
231C4×D43—41no—
232C4×D43—41no—
233Dic86—41no—
234Dic86—41no—
235Dic86—41no—
236Dic86—41no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C43⋊C8—21no—
241C43⋊C8—21no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246#19848—431nomaximal, Sylow
247C22×C43D4211yescharacteristic
248C2×D43—41no—
249C2×D43—41no—
250C2×D43—41no—
251C4×C43—22no—
252C4×C43—21no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—81no—
259C4×C43—81no—
260C4×C43C2×#13511yescharacteristic
261C4×C43#57511yescharacteristic
262C4×C43#57811yescharacteristic
263C4×C43#57811yescharacteristic
264Dic43—41no—
265Dic43—81no—
266Dic43—81no—
267#3369—431no—
268#3364—431no—
269#3363D4311yescharacteristic, complemented
270#3342—431no—
271#1718—431no—
272#1700—431no—
273#1684—431no—
274#1683—431no—
275#1674—431no—
276#1653—431no—
277#1652—431no—
278#1645—431no—
279#1638—431no—
280#1584—431no—
281SD16⋊C8—431no—
282C2×C43#326911yescharacteristic
283C2×C43#328511yescharacteristic
284C2×C43#328911yescharacteristic
285D43—81no—
286Q82C2×D4311yescharacteristic
287#557C2×D4311yescharacteristic
288#556—431no—
289#556—431no—
290#500—431no—
291#498—431no—
292#489—861no—
293#488—861no—
294#487—21no—
295#487—431no—
296#487—431no—
297#487—431no—
298#487C2×D4311yescharacteristic
299#485—861no—
300#485—861no—
301#479—861no—
302#477—21no—
303#477C2×D4311yescharacteristic
304#476—431no—
305#475—431no—
306#475—431no—
307#475—861no—
308#474—431no—
309#467—861no—
310#464—861no—
311#464—861no—
312#462—21no—
313#462—431no—
314#462—431no—
315#462C2×D4311yescharacteristic
316#446—431no—
317C8×Q8—431no—
318C8×Q8C2×D4311yescharacteristic
319#441—861no—
320C4×Q16—21no—
321C4×Q16—861no—
322C4×Q16C2×D4311yescharacteristic
323C4×SD16—431no—
324C8×D4—431no—
325#427—861no—
326#335—431no—
327#335—431no—
328#333—431no—
329#332—431no—
330#332—431no—
331#332—431no—
332Q8⋊C8—431no—
333Q8⋊C8—431no—
334Q8⋊C8—431no—
335D4⋊C8—431no—
336#322—431no—
337C43#1984811yescharacteristic, complemented, Sylow
338C2×Q16—21no—
339C2×Q16—861no—
340C2×Q16—861no—
341C2×Q16C22⋊D4311yescharacteristic
342C2×SD16—431no—
343C22×C8—861no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—41no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350C4⋊Q8C22×D4311yescharacteristic
351C4⋊Q8C22×D4311yescharacteristic
352#126—1721no—
353#126—1721no—
354#125—21no—
355#125—41no—
356#124—861no—
357#124—861no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8C22×D4311yescharacteristic
367C4×Q8C22×D4311yescharacteristic
368C4×Q8C22×D4311yescharacteristic
369C4×D4—431no—
370#117—861no—
371#117—861no—
372#107—21no—
373#107—861no—
374#107—861no—
375#107—861no—
376#107C22⋊D4311yescharacteristic
377#106—431no—
378#106—861no—
379#106—861no—
380#106—861no—
381#106—1721no—
382C4⋊C8—21no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—861no—
387C4⋊C8—861no—
388C4⋊C8C22×D4311yescharacteristic
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—431no—
394#103—861no—
395#103—861no—
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—1721no—
403#103C22⋊D4311yescharacteristic
404#103C22⋊D4311yescharacteristic
405#102—431no—
406#102—861no—
407#102—861no—
408C22⋊C8—861no—
409#97—861no—
410C4×C8—21no—
411C4×C8—431no—
412C4×C8—431no—
413C4×C8—861no—
414C4×C8C22×D4311yescharacteristic
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—41no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8D4×D4311yescharacteristic
421C2×Q8C2×C22⋊D4311yescharacteristic
422C2×Q8C2×C22⋊D4311yescharacteristic
423C2×D4—431no—
424C22×C4—861no—
425Q16—41no—
426Q16—42no—
427Q16—1722no—
428Q16—1722no—
429SD16—862no—
430C2×C8—21no—
431C2×C8—431no—
432C2×C8—431no—
433C2×C8—861no—
434C2×C8—861no—
435C2×C8—861no—
436C2×C8—861no—
437C2×C8—1722no—
438C2×C8C2×C22⋊D4311yescharacteristic
439C2×C8C2×C22⋊D4311yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—431no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—1721no—
458C4⋊C4—1721no—
459C4⋊C4D4×D4311yescharacteristic
460C4⋊C4C2×C22⋊D4311yescharacteristic
461C4⋊C4C2×C22⋊D4311yescharacteristic
462C22⋊C4—861no—
463C22⋊C4—1721no—
464C22⋊C4—1721no—
465C22⋊C4—1721no—
466C22⋊C4—1721no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—41no—
471C42—41no—
472C42—1721no—
473C42—1721no—
474C42C23×D4311yescharacteristic
475C23—861no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—81no—
484Q8—161no—
485Q8—1721no—
486Q8—1721no—
487Q8—1721no—
488Q8—1721no—
489Q8#1306334812yes—
490D4—861no—
491D4—861no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—861no—
501C2×C4—1721no—
502C2×C4—1721no—
503C2×C4—1721no—
504C2×C4—1721no—
505C2×C4C2×D4×D4311yescharacteristic
506C2×C4C22×C22⋊D4311yescharacteristic
507C2×C4#1306337011yescharacteristic
508C8—21no—
509C8—21no—
510C8—41no—
511C8—861no—
512C8—861no—
513C8—1721no—
514C8—1721no—
515C8—1721no—
516C8—1721no—
517C22—1721no—
518C22—1721no—
519C22—1721no—
520C22D4×C22⋊D4311yescharacteristic
521C4—22no—
522C4—21no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—81no—
529C4—81no—
530C4—3441no—
531C4—3441no—
532C4—1721no—
533C4C2×#1306334811yescharacteristic
534C4#1458369711yescharacteristic
535C4#1458371211yescharacteristic
536C4#1458371411yescharacteristic
537C2—3441no—
538C2#1914615111yescharacteristic
539C2#1914633611yescharacteristic
540C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3363C2
socleC22×C43D42
prime radicalC2×D172C2×D4
hypercenter#3363D43
hypocenterC43#19848
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3363

Complements

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

NH ≅ G/Ntype
4. #19134244C2semidirect
5. #19134151C2semidirect
6. #19134055C2semidirect
8. #19133989C2semidirect
9. #19133872C2semidirect
11. #19133816C2semidirect
13. #19133446C2semidirect
15. C43×#3363C2semidirect
269. #3363D43semidirect
337. C43#19848semidirect

Maximal subgroups

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

subgroupindex
#191473352
#191472802
#191470272
#191342442
#191341512
#191340552
#191340432
#191339892
#191338722
#191338632
#191338162
#191337662
#191334462
#191334052
C43×#33632
#1984843