Finite Group Databasebeta

← #25110283

Subgroups — #25110283

Order 11008.

614 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145107C211yesmaximal, characteristic
2#19143528C211yesmaximal, characteristic
3#19143527C211yesmaximal, characteristic
4#19135570C211yesmaximal, characteristic
5#19135570C211yesmaximal, characteristic
6#19135197C211yesmaximal, characteristic
7#19135196C211yesmaximal, characteristic
8#19135195C211yesmaximal, characteristic
9#19135194C211yesmaximal, characteristic
10#19135193C211yesmaximal, characteristic
11#19135192C211yesmaximal, characteristic
12#19135191C211yesmaximal, characteristic
13#19134731C211yesmaximal, characteristic
14#19134339C211yesmaximal, characteristic
15C43×#1922C211yesmaximal, characteristic
16#14583452C2211yescharacteristic
17#14583452C2211yescharacteristic
18#14583303C411yescharacteristic, complemented
19#14583303C411yescharacteristic, complemented
20#14583300C411yescharacteristic, complemented
21#14583300C411yescharacteristic, complemented
22#14583299C411yescharacteristic, complemented
23#14583299C411yescharacteristic, complemented
24#14583296C411yescharacteristic, complemented
25#14583296C411yescharacteristic, complemented
26#14583028—21no—
27#14583028—21no—
28#14583027—21no—
29#14583027—21no—
30C8×Dic86—21no—
31C8×Dic86—21no—
32#14583023—21no—
33#14583023—21no—
34#14582937C2211yescharacteristic
35#14582935C2211yescharacteristic
36#14582935C2211yescharacteristic
37#14582927C2211yescharacteristic
38#14582926C2211yescharacteristic
39#14582925C2211yescharacteristic
40#14582922C2211yescharacteristic
41#14582922C2211yescharacteristic
42#14582857C2211yescharacteristic
43#14582855C2211yescharacteristic
44#14582854C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46C2×C8×Dic43C2211yescharacteristic
47C42×Dic43C2211yescharacteristic
48#14582664C2211yescharacteristic
49#14582663C2211yescharacteristic
50#14582663C2211yescharacteristic
51#14582660C2211yescharacteristic
52#14582660C2211yescharacteristic
53#14582659C2211yescharacteristic
54#14582659C2211yescharacteristic
55#14582658C2211yescharacteristic
56#14582658C2211yescharacteristic
57#14582654C2211yescharacteristic
58#14582653C2211yescharacteristic
59#14582653C2211yescharacteristic
60C43×#427C2211yescharacteristic
61C43×#424C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#341C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063324C2×C411yescharacteristic
72#13063324C2×C411yescharacteristic
73#13063324C2×C411yescharacteristic
74#13063324C2×C411yescharacteristic
75#13063316C2×C411yescharacteristic
76#13063316C2×C411yescharacteristic
77#13063316C2×C411yescharacteristic
78#13063316C2×C411yescharacteristic
79#13063302—21no—
80#13063302—21no—
81#13063302—21no—
82#13063302—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87#13063284C2311yescharacteristic
88#13063284C2311yescharacteristic
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063259C2×C411yescharacteristic
94#13063259C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063258C2×C411yescharacteristic
99#13063257C2×C411yescharacteristic
100#13063257C2×C411yescharacteristic
101#13063256C2×C411yescharacteristic
102#13063256C2×C411yescharacteristic
103#13063256C2×C411yescharacteristic
104#13063256C2×C411yescharacteristic
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115#13063236—21no—
116#13063235—21no—
117#13063235—21no—
118C4×C43⋊C8—21no—
119C8×Dic43—21no—
120C8×Dic43—21no—
121C8×Dic43C2×C411yescharacteristic
122C8×Dic43C2×C411yescharacteristic
123C8×Dic43C2×C411yescharacteristic
124C8×Dic43C2×C411yescharacteristic
125C8×Dic43D411yescharacteristic
126C8×Dic43D411yescharacteristic
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×M16×C43C2311yescharacteristic
130C2×M16×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133#117×C43C2311yescharacteristic
134#117×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#107×C43C2×C411yescharacteristic
137#107×C43C2×C411yescharacteristic
138#106×C43C2×C411yescharacteristic
139#106×C43C2×C411yescharacteristic
140C4⋊C8×C43—21no—
141C4⋊C8×C43—21no—
142#97×C43—21no—
143C4×C8×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43#4111yescharacteristic
148C22×Dic43#4111yescharacteristic
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153M16×C43—21no—
154M16×C43—21no—
155M16×C43—21no—
156M16×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43C22×C411yescharacteristic
168C4⋊C4×C43C22×C411yescharacteristic
169C4⋊C4×C43C22×C411yescharacteristic
170C4⋊C4×C43C22×C411yescharacteristic
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C22⋊Dic43—21no—
178C22⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43C22×C411yescharacteristic
184C4⋊Dic43C22×C411yescharacteristic
185C4⋊Dic43C22×C411yescharacteristic
186C4⋊Dic43C22×C411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—24no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—42no—
201C4×Dic43C22×C411yescharacteristic
202C4×Dic43C22×C411yescharacteristic
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43C2×D411yescharacteristic
205#10621877—21no—
206#10621877—21no—
207#10621877—21no—
208#10621877—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C22×C411yescharacteristic
216C2×C43⋊C8C22×C411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218C2×C43⋊C8C2×D411yescharacteristic
219C23×C43C2×#4111yescharacteristic
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×C4×C432−1+411yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43C4×D411yescharacteristic
243C2×Dic43C4×D411yescharacteristic
244C2×Dic43C4×D411yescharacteristic
245C2×Dic43C4×D411yescharacteristic
246Dic86—42no—
247Dic86—42no—
248Dic86—42no—
249Dic86—42no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#22256—431nomaximal, Sylow
263C22×C43—21no—
264C22×C43—21no—
265C22×C43C2×C4×D411yescharacteristic
266C22×C43#54111yescharacteristic
267C22×C43#54111yescharacteristic
268C4×C43—42no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43#51911yescharacteristic
274C4×C43#51911yescharacteristic
275C4×C43#53611yescharacteristic
276C4×C43#53611yescharacteristic
277Dic43—21no—
278Dic43—21no—
279Dic43—42no—
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284Dic43#44312yes—
285Dic43#44412yes—
286#3160—431no—
287#2960—431no—
288#2960—431no—
289#1994—431no—
290#1994—431no—
291#1922—431no—
292#1922—431no—
293#1922—431no—
294#1922—431no—
295#1922—431no—
296#1922—431no—
297#1922—431no—
298#1922D4311yescharacteristic
299#1837—431no—
300#1744—431no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43#232711yescharacteristic
304C2×C43C2×#44311yescharacteristic
305C2×C43C2×#44411yescharacteristic
306#533—431no—
307#533—431no—
308#500—431no—
309#500—431no—
310#499—431no—
311#499—431no—
312#499—431no—
313#499—431no—
314#498—431no—
315#498—431no—
316#446—861no—
317#446—861no—
318#446—861no—
319#446—861no—
320C8×Q8—861no—
321C8×Q8—861no—
322C8×Q8—861no—
323C8×Q8—861no—
324#427—431no—
325#427—431no—
326#427—431no—
327#427C2×D4311yescharacteristic
328#424—431no—
329#424—431no—
330#424—431no—
331#424C2×D4311yescharacteristic
332#423—431no—
333#423—431no—
334#405—431no—
335#405—431no—
336#405—431no—
337#405C2×D4311yescharacteristic
338C2×C4×C8—431no—
339C2×C4×C8—431no—
340C43—431no—
341#341—431no—
342#341—431no—
343#341—431no—
344#341C2×D4311yescharacteristic
345#339—431no—
346#339—431no—
347#339—431no—
348#339—431no—
349#339—431no—
350#339—431no—
351#339C2×D4311yescharacteristic
352#339C2×D4311yescharacteristic
353#336—431no—
354#336—431no—
355#336—431no—
356#336C2×D4311yescharacteristic
357C43#2225611yescharacteristic, complemented, Sylow
358C2×M16—431no—
359C2×M16—431no—
360C2×M16C22×D4311yescharacteristic
361C2×M16C22×D4311yescharacteristic
362C22×C8—431no—
363C22×C8—431no—
364C22×C8C22×D4311yescharacteristic
365C22×C8C22×D4311yescharacteristic
366C4⋊Q8—431no—
367C4⋊Q8—431no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370#125—431no—
371#125—431no—
372#125—431no—
373#125—431no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376C22⋊Q8—861no—
377C22⋊Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8—861no—
382#117—431no—
383#117—431no—
384#117C22×D4311yescharacteristic
385#117C22×D4311yescharacteristic
386C2×C42—431no—
387C2×C42—431no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42C22×D4311yescharacteristic
391#107—431no—
392#107—431no—
393#107—431no—
394#107—431no—
395#107—431no—
396#107—431no—
397#107C4×D4311yescharacteristic
398#107C4×D4311yescharacteristic
399#106—431no—
400#106—431no—
401#106—431no—
402#106—431no—
403#106—431no—
404#106—431no—
405#106C4×D4311yescharacteristic
406#106C4×D4311yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419#97—21no—
420#97—861no—
421#97—861no—
422#97—861no—
423C4×C8—21no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C22×C4—21no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—861no—
443C22×C4C23×D4311yescharacteristic
444M16—21no—
445M16—21no—
446M16—21no—
447M16—21no—
448M16—861no—
449M16—861no—
450M16—861no—
451M16—861no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8C2×C4×D4311yescharacteristic
469C2×C8C2×C4×D4311yescharacteristic
470C2×C8D4×D4311yescharacteristic
471C2×C8D4×D4311yescharacteristic
472C4⋊C4—431no—
473C4⋊C4—431no—
474C4⋊C4—431no—
475C4⋊C4—431no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4C2×C4×D4311yescharacteristic
489C4⋊C4C2×C4×D4311yescharacteristic
490C4⋊C4C2×C4×D4311yescharacteristic
491C4⋊C4C2×C4×D4311yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—431no—
501C42—431no—
502C42—431no—
503C42—431no—
504C42—864no—
505C42—861no—
506C42—861no—
507C42—861no—
508C42—861no—
509C42—1722no—
510C23#41×D4311yescharacteristic
511Q8—1722no—
512Q8—1722no—
513Q8—1722no—
514Q8—1722no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—431no—
523C2×C4—431no—
524C2×C4—431no—
525C2×C4—431no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4C22×C4×D4311yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4#1306337211yescharacteristic
538C2×C4#1306337211yescharacteristic
539C2×C4#1306337211yescharacteristic
540C2×C4#1306337311yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—861no—
548C8—861no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C22—21no—
554C22—21no—
555C22C4×D4×D4311yescharacteristic
556C22#1458350611yescharacteristic
557C22#1458350811yescharacteristic
558C4—42no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—432no—
564C4—432no—
565C4—861no—
566C4—861no—
567C4—1722no—
568C4—1721no—
569C4—1721no—
570C4—1721no—
571C4—1721no—
572C4#1458337511yescharacteristic
573C4#1458337611yescharacteristic
574C4#1458347111yescharacteristic
575C4#1458347211yescharacteristic
576C2—21no—
577C2—21no—
578C2#1913731011yescharacteristic
579C2#443×D4311yescharacteristic
580C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1922C2
socleC22×C43C2×C4×D4
prime radicalC23×C43C2×#41
cosocleC22×C4×C43C24
hypercenter#1922D43
hypocenterC43#22256
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
18. #14583303C4semidirect
19. #14583303C4semidirect
20. #14583300C4semidirect
21. #14583300C4semidirect
22. #14583299C4semidirect
23. #14583299C4semidirect
24. #14583296C4semidirect
25. #14583296C4semidirect
357. C43#22256semidirect

Maximal subgroups

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

subgroupindex
#191451072
#191435282
#191435272
#191355702
#191351972
#191351962
#191351952
#191351942
#191351932
#191351922
#191351912
#191347312
#191343392
C43×#19222
#2225643