Finite Group Databasebeta

← #25068617

Subgroups — #25068617

Order 11008.

604 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145151C211yesmaximal, characteristic
2#19143693C211yesmaximal, characteristic, complemented
3#19143658C211yesmaximal, characteristic
4#19133495C211yesmaximal, characteristic, complemented
5#19133494C211yesmaximal, characteristic, complemented
6#19133440C211yesmaximal, characteristic, complemented
7#19133439C211yesmaximal, characteristic, complemented
8#19133430C211yesmaximal, characteristic, complemented
9#19133410C211yesmaximal, characteristic, complemented
10#19133407C211yesmaximal, characteristic, complemented
11#19133340C211yesmaximal, characteristic, complemented
12#19133014C211yesmaximal, characteristic, complemented
13#19133010C211yesmaximal, characteristic
14#19132883C211yesmaximal, characteristic, complemented
15C43×#1582C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17#14583446C2211yescharacteristic
18#14583296C411yescharacteristic
19#14583270C411yescharacteristic
20#14583248C411yescharacteristic
21#14583244C411yescharacteristic
22#14583131C411yescharacteristic
23#14583129C411yescharacteristic
24#14583127C411yescharacteristic
25#14583125C411yescharacteristic
26#14583027—21no—
27#14583026C2211yescharacteristic
28Q8×C43⋊C8C2211yescharacteristic
29C8×Dic86C2211yescharacteristic
30#14583023—21no—
31C4×#10621873C2211yescharacteristic
32C4×#10621884C2211yescharacteristic
33C4×#10621883C2211yescharacteristic
34#14582978C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582974—21no—
37#14582964C2211yescharacteristic
38C8×C22⋊D43—21no—
39#14582961—21no—
40#14582959—21no—
41#14582951C2211yescharacteristic
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582865—21no—
45#14582864—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582621C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621873C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71C2×#10621877—21no—
72C2×#10621872—21no—
73C2×#10621872—21no—
74C2×C8×D43—21no—
75C2×C8×D43C2×C411yescharacteristic
76C2×C8×D43C2×C411yescharacteristic
77#13063324C2×C411yescharacteristic
78#13063324C2×C411yescharacteristic
79#13063323C2×C411yescharacteristic
80#13063321C2×C411yescharacteristic
81#13063315—21no—
82#13063311—21no—
83#13063305C2×C411yescharacteristic
84#13063303—21no—
85#13063301C2×C411yescharacteristic
86#13063300C2×C411yescharacteristic
87#13063298—21no—
88#13063296C2×C411yescharacteristic
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91C4×D172C2311yescharacteristic
92C4×C22⋊D43—21no—
93#13063282—21no—
94C42×D43C2311yescharacteristic
95#13063257C2×C411yescharacteristic
96#13063256C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8D411yescharacteristic
104Dic43⋊C8D411yescharacteristic
105#13063250C2×C411yescharacteristic
106#13063249C2×C411yescharacteristic
107#13063248C2×C411yescharacteristic
108#13063247C2×C411yescharacteristic
109#13063246C2×C411yescharacteristic
110#13063245C2×C411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8D411yescharacteristic
117(C2×D43)⋊C8D411yescharacteristic
118#13063235—21no—
119#13063235—21no—
120C4×C43⋊C8—21no—
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43C2×C411yescharacteristic
128C8×Dic43C2×C411yescharacteristic
129C2×SD16×C43C2×C411yescharacteristic
130C22×C8×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C2×C22⋊D43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150#10621898—81no—
151#10621898—81no—
152C2×D172—21no—
153C2×D172C22×C411yescharacteristic
154C2×C4×D43—21no—
155C2×C4×D43C22×C411yescharacteristic
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43#4111yescharacteristic
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86C22×C411yescharacteristic
161SD16×C43—41no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—81no—
166C2×C8×C43C22×C411yescharacteristic
167C2×C8×C43C22×C411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C4⋊C4×C43—21no—
171C4⋊C4×C43C22×C411yescharacteristic
172C4⋊C4×C43C22×C411yescharacteristic
173C22⋊C4×C43—21no—
174C42×C43—21no—
175C42×C43C2411yescharacteristic
176C22⋊Dic43—21no—
177#10621884—22no—
178#10621883—22no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C411yescharacteristic
185C4⋊Dic43C22×C411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192C4×Dic43—21no—
193C4×Dic43C22×C411yescharacteristic
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43#4111yescharacteristic
196#10621877—81no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204#10621873—41no—
205#10621872—42no—
206#10621872—81no—
207C8×D43—22no—
208C8×D43—41no—
209C8×D43—81no—
210C23×C43—21no—
211C22×D43—21no—
212C22×D43C4×D411yescharacteristic
213Q8×C43—21no—
214Q8×C43—21no—
215D4×C43—21no—
216D4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C23×C411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—42no—
226C22⋊D43—81no—
227C22⋊D43—81no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43C4×D411yescharacteristic
232C2×Dic43C4×D411yescharacteristic
233C2×Dic43C4×D411yescharacteristic
234D172—21no—
235D172—21no—
236D172—81no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—22no—
242C4×D43—41no—
243C4×D43—41no—
244Dic86—21no—
245Dic86—21no—
246Dic86—42no—
247Dic86—81no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8#13112yes—
262#18089—431nomaximal, Sylow
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43C2×C4×D411yescharacteristic
267C2×D43—21no—
268C2×D43—21no—
269C2×D43—21no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—41no—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43C2×#13111yescharacteristic
278C4×C43#56811yescharacteristic
279C4×C43#57711yescharacteristic
280C4×C43#57711yescharacteristic
281Dic43—21no—
282Dic43—21no—
283Dic43—41no—
284Dic43—41no—
285Dic43—41no—
286Dic43#44412yes—
287#3167—431no—
288#2986—431no—
289#2979—431no—
290#1592—431no—
291#1592—431no—
292#1583—431no—
293#1583—431no—
294#1582—431no—
295#1582D4311yescharacteristic, complemented
296SD16⋊C8—431no—
297SD16⋊C8—431no—
298#1564—431no—
299#1485—431no—
300#1484—431no—
301#1451—431no—
302C2×C43—81no—
303C2×C43#293511yescharacteristic
304C2×C43#294911yescharacteristic
305C2×C43C2×#44411yescharacteristic
306D43—41no—
307D43—81no—
308#533—431no—
309#532—431no—
310#498—431no—
311#492—431no—
312#487—431no—
313#486—431no—
314#465—431no—
315#465—431no—
316#465—431no—
317#465—431no—
318#446—431no—
319#446—861no—
320#446C2×D4311yescharacteristic
321C8×Q8—431no—
322C8×Q8—431no—
323C8×Q8—861no—
324C4×SD16—431no—
325C4×SD16—431no—
326C4×SD16—431no—
327C4×SD16C2×D4311yescharacteristic
328#436—431no—
329#436—431no—
330#436—861no—
331C8×D4—431no—
332C8×D4—861no—
333C8×D4C2×D4311yescharacteristic
334#433—861no—
335#433—861no—
336#431—431no—
337#431—431no—
338#431—431no—
339#408—861no—
340#408—861no—
341C4×M16—431no—
342C2×C4×C8—431no—
343#335—431no—
344#335—431no—
345#334—431no—
346#334C2×D4311yescharacteristic
347Q8⋊C8—431no—
348Q8⋊C8—431no—
349Q8⋊C8—431no—
350Q8⋊C8C2×D4311yescharacteristic
351D4⋊C8—431no—
352D4⋊C8—431no—
353D4⋊C8—431no—
354D4⋊C8C2×D4311yescharacteristic
355#322—431no—
356#322—431no—
357#322—431no—
358#322C2×D4311yescharacteristic
359C43#1808911yescharacteristic, complemented, Sylow
360C2×#41—861no—
361C2×SD16—431no—
362C2×SD16—431no—
363C2×SD16—431no—
364C2×SD16C4×D4311yescharacteristic
365C2×M16—861no—
366C2×M16—861no—
367C2×M16—861no—
368C22×C8—21no—
369C22×C8—431no—
370C22×C8—431no—
371C22×C8—861no—
372C4⋊Q8—431no—
373C4⋊Q8—431no—
374C4⋊Q8—431no—
375#127—431no—
376#125—861no—
377#124—861no—
378C22⋊Q8—431no—
379C22⋊Q8—431no—
380C22⋊Q8—861no—
381#121—431no—
382#121—431no—
383#121—861no—
384C4×Q8—431no—
385C4×Q8—861no—
386C4×Q8C22×D4311yescharacteristic
387C4×D4—431no—
388C4×D4—861no—
389C4×D4C22×D4311yescharacteristic
390#117—861no—
391C2×C42—431no—
392#106—431no—
393#106—431no—
394#106—431no—
395#106C4×D4311yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—431no—
407#103—431no—
408#103—431no—
409#103C4×D4311yescharacteristic
410#102—431no—
411#102—431no—
412#102—431no—
413#102C4×D4311yescharacteristic
414C22⋊C8—21no—
415C22⋊C8—431no—
416C22⋊C8—431no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—21no—
423#97—861no—
424#97—861no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436C4×C8C22×D4311yescharacteristic
437#41—3441no—
438#41—3441no—
439C2×Q8—431no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8C2×C4×D4311yescharacteristic
443C2×D4—431no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4C2×C4×D4311yescharacteristic
449C22×C4—21no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—861no—
454SD16—41no—
455SD16—862no—
456SD16—862no—
457SD16—1721no—
458M16—3441no—
459M16—3441no—
460M16—1722no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—81no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—862no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—3441no—
474C2×C8—1721no—
475C2×C8C2×C4×D4311yescharacteristic
476C2×C8C2×C4×D4311yescharacteristic
477C2×C8D4×D4311yescharacteristic
478C2×C8D4×D4311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—431no—
481C4⋊C4—431no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4C2×C4×D4311yescharacteristic
490C4⋊C4C2×C4×D4311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C42—21no—
498C42—431no—
499C42—431no—
500C42—431no—
501C42—861no—
502C42C23×D4311yescharacteristic
503C23—21no—
504C23—431no—
505C23—861no—
506Q8—21no—
507Q8—21no—
508Q8—861no—
509Q8—861no—
510Q8—3441no—
511Q8—1722no—
512D4—21no—
513D4—21no—
514D4—861no—
515D4—861no—
516D4—3441no—
517D4—3441no—
518D4—3441no—
519D4—1722no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—431no—
526C2×C4—431no—
527C2×C4—431no—
528C2×C4—862no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4C22×C4×D4311yescharacteristic
539C2×C4C2×D4×D4311yescharacteristic
540C2×C4#41×D4311yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—432no—
549C8—861no—
550C8—861no—
551C8—861no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—861no—
559C22—861no—
560C22—861no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22C4×D4×D4311yescharacteristic
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—432no—
570C4—861no—
571C4—861no—
572C4—1721no—
573C4—1721no—
574C4—1721no—
575C4#131×D4311yescharacteristic
576C4#1458366511yescharacteristic
577C4#1458370511yescharacteristic
578C4#1458370611yescharacteristic
579C2—81no—
580C2—3441no—
581C2—1721no—
582C2#1914333611yescharacteristic
583C2#1914344911yescharacteristic
584C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1582C2
socleC22×C43C2×C4×D4
prime radical#14583446C22
cosocleC42×C43C24
hypercenter#1582D43
hypocenterC43#18089
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #19143693C2semidirect
4. #19133495C2semidirect
5. #19133494C2semidirect
6. #19133440C2semidirect
7. #19133439C2semidirect
8. #19133430C2semidirect
9. #19133410C2semidirect
10. #19133407C2semidirect
11. #19133340C2semidirect
12. #19133014C2semidirect
14. #19132883C2semidirect
15. C43×#1582C2semidirect
295. #1582D43semidirect
359. C43#18089semidirect

Maximal subgroups

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

subgroupindex
#191451512
#191436932
#191436582
#191334952
#191334942
#191334402
#191334392
#191334302
#191334102
#191334072
#191333402
#191330142
#191330102
#191328832
C43×#15822
#1808943