Finite Group Databasebeta

← #25093890

Subgroups — #25093890

Order 11008.

556 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147622C211yesmaximal, characteristic
2#19147501C211yesmaximal, characteristic
3#19147212C211yesmaximal, characteristic
4#19134190C211yesmaximal, characteristic, complemented
5#19134121C211yesmaximal, characteristic, complemented
6#19134101C211yesmaximal, characteristic, complemented
7#19134091C211yesmaximal, characteristic
8#19134087C211yesmaximal, characteristic, complemented
9#19133816C211yesmaximal, characteristic, complemented
10#19133801C211yesmaximal, characteristic
11#19133766C211yesmaximal, characteristic
12#19133753C211yesmaximal, characteristic, complemented
13#19133492C211yesmaximal, characteristic, complemented
14#19133485C211yesmaximal, characteristic
15C43×#3387C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583609C2211yescharacteristic
18#14583305—21no—
19#14583302C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583291—21no—
22#14583278C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583238—21no—
26#14583228—21no—
27#14583206—21no—
28#14583194C2211yescharacteristic
29#14583194C2211yescharacteristic
30#14583186C2211yescharacteristic
31#14583184C2211yescharacteristic
32#14583176—21no—
33#14583154—21no—
34#14583121—21no—
35#14583109C2211yescharacteristic
36#14583106—21no—
37#14583101C2211yescharacteristic
38#14583030C2211yescharacteristic
39#14583030C2211yescharacteristic
40#14583004—21no—
41#14582997—21no—
42C4×#10621884C2211yescharacteristic
43#14582978C2211yescharacteristic
44#14582940—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#557C2211yescharacteristic
58C43×#501—21no—
59C43×#498C2211yescharacteristic
60C43×#479—21no—
61C43×#477C2211yescharacteristic
62C43×#475—21no—
63C43×#475C2211yescharacteristic
64C43×#446C2211yescharacteristic
65C43×#441—21no—
66C4×Q16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621884—21no—
71C2×#10621884D411yescharacteristic
72C2×#10621872—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063320—41no—
76#13063317—21no—
77#13063313—21no—
78#13063303—41no—
79#13063301—21no—
80#13063301—21no—
81C4×Dic86—21no—
82C4×D172—21no—
83C4×D172C2311yescharacteristic
84#13063283—21no—
85C4⋊C4×D43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063257—21no—
91#13063257—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—41no—
105#13063249D411yescharacteristic
106#13063248—21no—
107#13063248—41no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111#13063236—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43D411yescharacteristic
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—41no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123#125×C43—41no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131#107×C43—21no—
132#107×C43D411yescharacteristic
133#106×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142#97×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×C4×D43—41no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155Q16×C43—22no—
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—81no—
182#10621885—81no—
183#10621884—22no—
184#10621884—81no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4—41no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C2×D411yescharacteristic
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204#10621872—42no—
205C22×D43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215Q8×C43—161no—
216C2×C4×C43—21no—
217C2×C4×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×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43H(5,𝔽2)11yescharacteristic
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230D172—21no—
231D172—21no—
232C4×D43—41no—
233C4×D43—41no—
234C4×D43—161no—
235Dic86—41no—
236Dic86—41no—
237Dic86—81no—
238C8×C43—21no—
239C8×C43—41no—
240C8×C43#13712yes—
241C43⋊C8—21no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8#13712yes—
247#20322—431nomaximal, Sylow
248C22×C43D4211yescharacteristic
249C2×D43—41no—
250C2×D43—41no—
251C2×D43—41no—
252C4×C43—21no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—81no—
260C4×C43—81no—
261C4×C43C2×#13711yescharacteristic
262C4×C43C2×#13711yescharacteristic
263C4×C43#57711yescharacteristic
264C4×C43#57811yescharacteristic
265Dic43—41no—
266Dic43—81no—
267Dic43—81no—
268#3398—431no—
269#3387D4311yescharacteristic, complemented
270#3385—431no—
271#3356—431no—
272#1707—431no—
273#1696—431no—
274#1692—431no—
275#1691—431no—
276#1690—431no—
277#1645—431no—
278#1643—431no—
279#1638—431no—
280#1636—431no—
281#1591—431no—
282#1590—431no—
283C2×C43#327611yescharacteristic
284C2×C43#327811yescharacteristic
285C2×C43#329011yescharacteristic
286D43—81no—
287Q82C2×D4311yescharacteristic
288#557C2×D4311yescharacteristic
289#556—431no—
290#554—431no—
291#501—21no—
292#501—861no—
293#500—431no—
294#498—431no—
295#498C2×D4311yescharacteristic
296#497—861no—
297#494—431no—
298#487—431no—
299#487—431no—
300#485—861no—
301#483—861no—
302#479—21no—
303#479—861no—
304#477—431no—
305#477—431no—
306#477C2×D4311yescharacteristic
307#476—431no—
308#475—21no—
309#475—431no—
310#475C2×D4311yescharacteristic
311#474—861no—
312#470—861no—
313#464—861no—
314#462—431no—
315#462—861no—
316#461—431no—
317#446—431no—
318#446—431no—
319#446C2×D4311yescharacteristic
320#441—21no—
321#441—861no—
322#440—861no—
323C4×Q16C2×D4311yescharacteristic
324C4×SD16—431no—
325#436—431no—
326#428—861no—
327#335—431no—
328#334—431no—
329#333—431no—
330#333—431no—
331#332—431no—
332#332—431no—
333Q8⋊C8—431no—
334Q8⋊C8—431no—
335Q8⋊C8—431no—
336D4⋊C8—431no—
337C82—431no—
338C43#2032211yescharacteristic, complemented, Sylow
339C2×Q16—861no—
340C2×Q16—861no—
341C2×Q16—861no—
342C2×Q16C22⋊D4311yescharacteristic
343C2×SD16—431no—
344C2×SD16—861no—
345C2×M16—861no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—41no—
350C4⋊Q8—431no—
351C4⋊Q8—431no—
352C4⋊Q8C22×D4311yescharacteristic
353C4⋊Q8C22×D4311yescharacteristic
354#126—1721no—
355#125—21no—
356#125—41no—
357#125—861no—
358#124—861no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8—1721no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—861no—
367C4×Q8C22×D4311yescharacteristic
368C4×Q8C22×D4311yescharacteristic
369C4×Q8C22×D4311yescharacteristic
370C4×D4—431no—
371C4×D4—861no—
372#117—861no—
373C2×C4⋊C4—861no—
374#107—21no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107C22⋊D4311yescharacteristic
380#106—21no—
381#106—21no—
382#106—21no—
383#106—431no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388C4⋊C8—21no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395#103—21no—
396#103—21no—
397#103—431no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—1721no—
404#103—1721no—
405#103C22⋊D4311yescharacteristic
406#103C22⋊D4311yescharacteristic
407#102—431no—
408#102—861no—
409C22⋊C8—861no—
410#97—21no—
411#97—861no—
412#97—861no—
413C4×C8—431no—
414C4×C8—431no—
415C4×C8C22×D4311yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—41no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8D4×D4311yescharacteristic
422C2×Q8C2×C22⋊D4311yescharacteristic
423C2×Q8C2×C22⋊D4311yescharacteristic
424C2×D4—431no—
425C22×C4—861no—
426C22×C4—1721no—
427Q16—22no—
428Q16—3441no—
429Q16—3441no—
430Q16—1722no—
431SD16—862no—
432SD16—3441no—
433M16—1722no—
434C2×C8—21no—
435C2×C8—431no—
436C2×C8—431no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8C2×C22⋊D4311yescharacteristic
442C2×C8C2×C22⋊D4311yescharacteristic
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—431no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4—1721no—
463C4⋊C4D4×D4311yescharacteristic
464C4⋊C4C2×C22⋊D4311yescharacteristic
465C4⋊C4C2×C22⋊D4311yescharacteristic
466C22⋊C4—861no—
467C22⋊C4—1721no—
468C22⋊C4—1721no—
469C22⋊C4—1721no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—41no—
474C42—41no—
475C42—1721no—
476C42C23×D4311yescharacteristic
477C23—861no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—41no—
485Q8—41no—
486Q8—81no—
487Q8—161no—
488Q8—3441no—
489Q8—1721no—
490Q8—1721no—
491D4—861no—
492D4—861no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—861no—
502C2×C4—1721no—
503C2×C4—1721no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—6881no—
507C2×C4C2×D4×D4311yescharacteristic
508C2×C4C22×C22⋊D4311yescharacteristic
509C2×C4#1306337011yescharacteristic
510C8—21no—
511C8—41no—
512C8—432no—
513C8—861no—
514C8—1721no—
515C8—1721no—
516C8—1721no—
517C8—1721no—
518C8#1306335612yes—
519C22—1721no—
520C22—1721no—
521C22—1721no—
522C22D4×C22⋊D4311yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—81no—
531C4—81no—
532C4—3441no—
533C4—3441no—
534C4—1721no—
535C4#137×D4311yescharacteristic
536C4C2×#1306335611yescharacteristic
537C4#1458370811yescharacteristic
538C4#1458371411yescharacteristic
539C2—3441no—
540C2#1914624111yescharacteristic
541C2#1914625511yescharacteristic
542C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3387C2
socleC22×C43D42
prime radicalC2×D172C2×D4
hypercenter#3387D43
hypocenterC43#20322
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3387

Complements

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

NH ≅ G/Ntype
4. #19134190C2semidirect
5. #19134121C2semidirect
6. #19134101C2semidirect
8. #19134087C2semidirect
9. #19133816C2semidirect
12. #19133753C2semidirect
13. #19133492C2semidirect
15. C43×#3387C2semidirect
269. #3387D43semidirect
338. C43#20322semidirect

Maximal subgroups

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

subgroupindex
#191476222
#191475012
#191472122
#191341902
#191341212
#191341012
#191340912
#191340872
#191338162
#191338012
#191337662
#191337532
#191334922
#191334852
C43×#33872
#2032243