Finite Group Databasebeta

← #25080338

Subgroups — #25080338

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145926C211yesmaximal, characteristic
2#19145776C211yesmaximal, characteristic
3#19145336C211yesmaximal, characteristic, complemented
4#19143593C211yesmaximal, characteristic
5#19134176C211yesmaximal, characteristic, complemented
6#19134152C211yesmaximal, characteristic, complemented
7#19134093C211yesmaximal, characteristic, complemented
8#19134083C211yesmaximal, characteristic, complemented
9#19134045C211yesmaximal, characteristic, complemented
10#19134021C211yesmaximal, characteristic, complemented
11#19133976C211yesmaximal, characteristic, complemented
12#19133964C211yesmaximal, characteristic, complemented
13#19133348C211yesmaximal, characteristic, complemented
14#19133250C211yesmaximal, characteristic, complemented
15C43×#1544C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583301—21no—
19#14583295C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583254—21no—
22#14583251C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583241—21no—
25#14583224—21no—
26#14583206—21no—
27#14583195C2211yescharacteristic
28#14583190C2211yescharacteristic
29#14583185C2211yescharacteristic
30#14583181C2211yescharacteristic
31#14583180C2211yescharacteristic
32#14583176C2211yescharacteristic
33#14583155—21no—
34#14583155—21no—
35#14583138—21no—
36#14583130—21no—
37#14583121—21no—
38#14583106C2211yescharacteristic
39#14583101C2211yescharacteristic
40#14583026C2211yescharacteristic
41#14583023C2211yescharacteristic
42#14583004—21no—
43#14583004—21no—
44#14582976C2211yescharacteristic
45#14582974—21no—
46#14582973—21no—
47#14582964C2211yescharacteristic
48#14582958—21no—
49C2×C4⋊(C43⋊C8)C2211yescharacteristic
50#14582853—21no—
51C4×#10621877C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582646C2211yescharacteristic
59#14582646C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621884—21no—
71C2×#10621877D411yescharacteristic
72C2×#10621877D411yescharacteristic
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063319—21no—
79#13063317—21no—
80#13063317D411yescharacteristic
81#13063313D411yescharacteristic
82#13063308—21no—
83#13063304—21no—
84#13063304—21no—
85#13063304D411yescharacteristic
86#13063299D411yescharacteristic
87C4×Dic86—21no—
88C4×Dic86—21no—
89C4×Dic86C2311yescharacteristic
90C4×D172C2311yescharacteristic
91C4×C22⋊D43—21no—
92#13063284—21no—
93#13063282—21no—
94#13063259—21no—
95#13063259—21no—
96#13063258—21no—
97#13063257—21no—
98#13063257—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063249—21no—
110#13063249—21no—
111#13063249—21no—
112#13063249—21no—
113#13063248—21no—
114#13063248—21no—
115#13063248—21no—
116#13063247—21no—
117#13063247—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236D411yescharacteristic
122#13063236D411yescharacteristic
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C4⋊Q8×C43C2311yescharacteristic
128C4⋊Q8×C43C2311yescharacteristic
129#125×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4111yescharacteristic
149C2×C22⋊D43—21no—
150C2×D172C2×D411yescharacteristic
151C2×C4×D43—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C2×D411yescharacteristic
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—41no—
164C4⋊C4×C43—41no—
165C22⋊C4×C43—41no—
166C42×C43—41no—
167C42×C43C2×D411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43#4111yescharacteristic
170C42×C43C2411yescharacteristic
171C22⋊Dic43—21no—
172C22⋊Dic43—41no—
173#10621885—42no—
174#10621885—42no—
175#10621885—81no—
176#10621884—81no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C2×D411yescharacteristic
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—41no—
195#10621877—22no—
196#10621877—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204#10621872—42no—
205C8×D43—42no—
206C23×C43#12111yescharacteristic
207C22×D43—21no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—81no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231D172—21no—
232D172—21no—
233C4×D43—41no—
234C4×D43—41no—
235Dic86—21no—
236Dic86—21no—
237Dic86—41no—
238Dic86—41no—
239Dic86—81no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8#13512yes—
250#19251—431nomaximal, Sylow
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43C2×#12111yescharacteristic
255C2×D43—41no—
256C2×D43—41no—
257C2×D43—41no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43C2×#13511yescharacteristic
265C4×C43#57511yescharacteristic
266C4×C43#57711yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—41no—
269Dic43—41no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273#3248—431no—
274#3233—431no—
275#3185—431no—
276#2969—431no—
277#1704—431no—
278#1700—431no—
279#1691—431no—
280#1689—431no—
281#1683—431no—
282#1679—431no—
283#1672—431no—
284#1670—431no—
285#1565—431no—
286#1544D4311yescharacteristic, complemented
287#1542—431no—
288C2×C43—41no—
289C2×C43#303511yescharacteristic
290C2×C43#306311yescharacteristic
291C2×C43#306911yescharacteristic
292D43—81no—
293#533—431no—
294#533C2×D4311yescharacteristic
295#529—431no—
296#499—861no—
297#498—431no—
298#494—431no—
299#488—861no—
300#487—431no—
301#487—431no—
302#485—861no—
303#482—861no—
304#479—861no—
305#477—431no—
306#476—431no—
307#475—431no—
308#475—431no—
309#474—431no—
310#474—431no—
311#470—861no—
312#470—861no—
313#467—861no—
314#465—861no—
315#464—861no—
316#462—431no—
317#461—431no—
318#446—431no—
319C8×Q8—431no—
320#441—861no—
321#441—861no—
322#436—431no—
323#436—861no—
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#431C2×D4311yescharacteristic
328#431C2×D4311yescharacteristic
329C2×C4⋊C8—431no—
330#405—861no—
331C4×M16—431no—
332#335—431no—
333#335—431no—
334#334—431no—
335#334—431no—
336#333—431no—
337#333—431no—
338#332—431no—
339#332—431no—
340#332C2×D4311yescharacteristic
341#332C2×D4311yescharacteristic
342#332C2×D4311yescharacteristic
343#332C2×D4311yescharacteristic
344C43#1925111yescharacteristic, complemented, Sylow
345C2×Q16—861no—
346C2×Q16—861no—
347C2×Q16—861no—
348C2×SD16—861no—
349C2×M16—431no—
350C2×M16—431no—
351C2×M16—861no—
352C22×C8—861no—
353C22×C8—861no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—861no—
359#125—21no—
360#125—431no—
361#125—861no—
362#124—431no—
363#123—861no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—431no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369#121—431no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—431no—
373C4×Q8—861no—
374C4×Q8—861no—
375C4×D4—431no—
376C4×D4—861no—
377#117—21no—
378#117—861no—
379#117—861no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
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#102—861no—
408#102—861no—
409#102—861no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414#97—431no—
415#97—431no—
416#97—861no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—861no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—431no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×D4—431no—
428C2×D4—861no—
429C22×C4—861no—
430C22×C4#1062189811yescharacteristic
431C22×C4D4×D4311yescharacteristic
432C22×C4D4×D4311yescharacteristic
433Q16—3441no—
434Q16—1722no—
435Q16—1722no—
436SD16—3441no—
437M16—862no—
438M16—1722no—
439M16—1721no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—431no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—3441no—
451C2×C8—1722no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—431no—
459C4⋊C4—431no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C22⋊C4—41no—
471C22⋊C4—861no—
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—1721no—
477C42—41no—
478C42—861no—
479C42—1721no—
480C42#1062189811yescharacteristic
481C42D4×D4311yescharacteristic
482C42D4×D4311yescharacteristic
483C42C23×D4311yescharacteristic
484C23—861no—
485C23#1306329811yescharacteristic
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—861no—
491Q8—861no—
492Q8—3441no—
493Q8—1721no—
494Q8—1721no—
495D4—861no—
496D4—861no—
497D4—3441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4#1306329811yescharacteristic
513C2×C4#1306329811yescharacteristic
514C2×C4#1306329811yescharacteristic
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C2×D4×D4311yescharacteristic
517C2×C4C2×#1062189811yescharacteristic
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—432no—
523C8—861no—
524C8—861no—
525C8—861no—
526C8—1721no—
527C8—1721no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—1721no—
532C22—1721no—
533C22—1721no—
534C22C2×#1306329811yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—81no—
540C4—81no—
541C4—3441no—
542C4—3441no—
543C4—1721no—
544C4—1721no—
545C4—1721no—
546C4#135×D4311yescharacteristic
547C4#1458369611yescharacteristic
548C4#1458370611yescharacteristic
549C4#1458371311yescharacteristic
550C2—41no—
551C2—3441no—
552C2#1914404811yescharacteristic
553C2#1914428911yescharacteristic
554C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1544C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#1544D43
hypocenterC43#19251
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
3. #19145336C2semidirect
5. #19134176C2semidirect
6. #19134152C2semidirect
7. #19134093C2semidirect
8. #19134083C2semidirect
9. #19134045C2semidirect
10. #19134021C2semidirect
11. #19133976C2semidirect
12. #19133964C2semidirect
13. #19133348C2semidirect
14. #19133250C2semidirect
15. C43×#1544C2semidirect
286. #1544D43semidirect
344. C43#19251semidirect

Maximal subgroups

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

subgroupindex
#191459262
#191457762
#191453362
#191435932
#191341762
#191341522
#191340932
#191340832
#191340452
#191340212
#191339762
#191339642
#191333482
#191332502
C43×#15442
#1925143