Finite Group Databasebeta

← #25066388

Subgroups — #25066388

Order 11008.

648 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#19143558C211yesmaximal, characteristic
2#446×D43C211yesmaximal, characteristic, complemented
3C4×#13063354C211yesmaximal, characteristic
4#19133503C211yesmaximal, characteristic, complemented
5#19133501C211yesmaximal, characteristic, complemented
6#19133498C211yesmaximal, characteristic, complemented
7#19133494C211yesmaximal, characteristic, complemented
8#19133493C211yesmaximal, characteristic, complemented
9#19133490C211yesmaximal, characteristic, complemented
10#19133483C211yesmaximal, characteristic, complemented
11#19133344C211yesmaximal, characteristic, complemented
12#19132988C211yesmaximal, characteristic, complemented
13#19132979C211yesmaximal, characteristic
14C8×#10621872C211yesmaximal, characteristic, complemented
15C43×#1590C211yesmaximal, characteristic, complemented
16C2×#13063354C411yescharacteristic
17C4×#10621900C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583030C2211yescharacteristic
20#14583029C2211yescharacteristic
21#14583029C2211yescharacteristic
22#14583028—21no—
23#14583027—21no—
24#14583026C2211yescharacteristic
25#14583026C2211yescharacteristic
26#14583005C411yescharacteristic
27#14583003C411yescharacteristic
28#14583000C411yescharacteristic
29#14582996C411yescharacteristic
30C4×Dic172C2211yescharacteristic
31C4×#10621885C2211yescharacteristic
32C4×#10621883C2211yescharacteristic
33#14582977C2211yescharacteristic
34#14582973—21no—
35#14582968—21no—
36#14582951C2211yescharacteristic
37#14582950C2211yescharacteristic
38#14582949—21no—
39#14582938C411yescharacteristic
40C4⋊C8×D43—21no—
41C4⋊C8×D43C2211yescharacteristic
42#14582906C411yescharacteristic
43#14582897C411yescharacteristic
44M16×Dic43—21no—
45C4×#10621872C2211yescharacteristic
46#97×D43—21no—
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582629C2211yescharacteristic
55#14582629C2211yescharacteristic
56D4⋊(C43⋊C8)C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621900C2×C411yescharacteristic
68C2×Q8×D43C2×C411yescharacteristic
69#13063354—24no—
70C2×Dic172C2×C411yescharacteristic
71C2×#10621885C2×C411yescharacteristic
72C2×#10621883C2×C411yescharacteristic
73C2×#10621877—21no—
74C2×#10621872C2×C411yescharacteristic
75C2×#10621872C2×C411yescharacteristic
76C2×C8×D43—21no—
77C2×C8×D43D411yescharacteristic
78C2×C8×D43D411yescharacteristic
79Q8×Dic43C2×C411yescharacteristic
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290C2×C411yescharacteristic
85#13063290C2×C411yescharacteristic
86D4×Dic43C2×C411yescharacteristic
87C4×C22⋊D43—21no—
88(C22⋊D43)⋊C4—21no—
89#13063283C2×C411yescharacteristic
90#13063281—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43C2×C411yescharacteristic
93C2×C4×Dic43—21no—
94C42×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259C2×C411yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108#13063250C2×C411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063249C2×C411yescharacteristic
111#13063248C2×C411yescharacteristic
112#13063248C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117#13063236—21no—
118#13063235—21no—
119#13063235—21no—
120#13063235—21no—
121#13063235—21no—
122#13063235C2×C411yescharacteristic
123#13063235C2×C411yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43C2×C411yescharacteristic
131C2×M16×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43C2×C411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151Q8×D43—22no—
152Q8×D43—22no—
153#10621900—22no—
154#10621900—22no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43C22×C411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86C22×C411yescharacteristic
162C2×Dic86C22×C411yescharacteristic
163SD16×C43—22no—
164M16×C43—42no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C22⋊C4×C43—21no—
176C42×C43—21no—
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179#10621885—22no—
180#10621883—22no—
181(C2×D43)⋊C4—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43C22×C411yescharacteristic
184C4⋊Dic43C22×C411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199#10621877—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207Dic172—22no—
208#10621872—22no—
209#10621872M1614yescomplemented
210C8×D43—22no—
211C8×D43—41no—
212C8×D43—42no—
213C23×C43—21no—
214C22×D43C4×D411yescharacteristic
215Q8×C43—21no—
216Q8×C43—21no—
217D4×C43—21no—
218D4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C23×C411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C22⋊D43—42no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43C4×D411yescharacteristic
235C2×Dic43C4×D411yescharacteristic
236C2×Dic43C4×D411yescharacteristic
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—41no—
240C4×D43—42no—
241C4×D43—42no—
242C4×D43C2×M1612yes—
243C4×D43#13112yes—
244Dic86—21no—
245Dic86—21no—
246Dic86—21no—
247Dic86—21no—
248Dic86—42no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43C2×M1612yes—
255C8×C43#13712yescomplemented
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8C2×M1612yes—
263#17892—431nomaximal, Sylow
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43C2×C4×D411yescharacteristic
268C2×D43—21no—
269C2×D43—21no—
270C2×D43#43612yes—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43C22×M1611yescharacteristic
276C4×C43C2×#13111yescharacteristic
277C4×C43C2×#13711yescharacteristic
278C4×C43#57511yescharacteristic
279Dic43—21no—
280Dic43—21no—
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284Dic43—41no—
285Dic43#43612yes—
286#2965—431no—
287C2×#446—431no—
288C4×#137—431no—
289#1593—431no—
290#1593—431no—
291#1592—431no—
292#1592—431no—
293#1591—431no—
294#1591—431no—
295#1590—431no—
296#1590D4311yescharacteristic, complemented
297#1565—431no—
298#1479—431no—
299#1477—431no—
300C8×M16—431no—
301C2×C43—81no—
302C2×C43C2×#43611yescharacteristic
303C2×C43C4×#13711yescharacteristic
304C2×C43#295511yescharacteristic
305D43—22no—
306C2×#137—431no—
307C4×#41—431no—
308C2×C4×Q8—431no—
309#446—431no—
310#446—431no—
311#446—431no—
312#446—431no—
313#446—431no—
314#446—861no—
315#446—861no—
316#446C2×D4311yescharacteristic
317#441—431no—
318#441—431no—
319#440—431no—
320#440—431no—
321C4×Q16—431no—
322C4×Q16—431no—
323C4×SD16—431no—
324C4×SD16C2×D4311yescharacteristic
325#436—431no—
326#436C2×D4311yescharacteristic
327#435—861no—
328#435—861no—
329#431—431no—
330#431—431no—
331#431—861no—
332#428—431no—
333C2×C4⋊C8—431no—
334C2×C4⋊C8—861no—
335#419—431no—
336#417—431no—
337C4×M16—431no—
338C4×M16—861no—
339C2×#97—861no—
340C2×C4×C8—431no—
341#335—431no—
342#335—431no—
343#334—431no—
344#334C2×D4311yescharacteristic
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348Q8⋊C8—431no—
349Q8⋊C8—431no—
350Q8⋊C8C2×D4311yescharacteristic
351D4⋊C8—431no—
352D4⋊C8C2×D4311yescharacteristic
353#322—431no—
354#322—431no—
355C82—431no—
356C82C2×D4311yescharacteristic
357C43#1789211yescharacteristic, complemented, Sylow
358C2×#41—431no—
359C22×Q8—431no—
360#137—864no—
361C2×Q16—431no—
362C2×Q16—431no—
363C2×SD16—431no—
364C2×SD16C4×D4311yescharacteristic
365C2×M16—21no—
366C2×M16—431no—
367C2×M16—431no—
368C2×M16—861no—
369C22×C8—431no—
370C22×C8—431no—
371C22×C8—861no—
372C4×Q8—431no—
373C4×Q8—431no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—431no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8C22×D4311yescharacteristic
380C4×D4—431no—
381C4×D4—861no—
382C4×D4—861no—
383C4×D4C22×D4311yescharacteristic
384#117—431no—
385#117—861no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C42—431no—
389C2×C42—861no—
390C2×C42—861no—
391#107—431no—
392#107—431no—
393#106—431no—
394#106C4×D4311yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—431no—
408#103—431no—
409#103—431no—
410#103—431no—
411#103—431no—
412#103C4×D4311yescharacteristic
413#102—431no—
414#102C4×D4311yescharacteristic
415C22⋊C8—21no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419#97—21no—
420#97—431no—
421#97—431no—
422#97—861no—
423#97—861no—
424#97—861no—
425#97—861no—
426#97—861no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436#41—862no—
437#41—862no—
438C2×Q8—431no—
439C2×Q8—431no—
440C2×Q8—861no—
441C2×Q8—862no—
442C2×Q8—862no—
443C2×Q8C2×C4×D4311yescharacteristic
444C2×D4—861no—
445C2×D4C2×C4×D4311yescharacteristic
446C22×C4—21no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454Q16—862no—
455Q16—862no—
456SD16—22no—
457SD16—862no—
458M16—42no—
459M16—434no—
460M16—862no—
461M16—1722no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
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—1721no—
474C2×C8—1722no—
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⋊C4C2×C4×D4311yescharacteristic
489C4⋊C4C2×C4×D4311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C42—21no—
494C42—431no—
495C42—431no—
496C42—431no—
497C42—861no—
498C42—861no—
499C42—861no—
500C42—861no—
501C42—861no—
502C42—861no—
503C42C23×D4311yescharacteristic
504C23—21no—
505C23—431no—
506Q8—21no—
507Q8—21no—
508Q8—861no—
509Q8—861no—
510Q8—861no—
511Q8—861no—
512Q8—1722no—
513D4—21no—
514D4—21no—
515D4—1722no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—431no—
522C2×C4—432no—
523C2×C4—432no—
524C2×C4—431no—
525C2×C4—431no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—1721no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4C22×C4×D4311yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4#41×D4311yescharacteristic
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—432no—
546C8—861no—
547C8—861no—
548C8—861no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8M16×D4312yes—
553C8#1306335412yescomplemented
554C22—41no—
555C22—41no—
556C22—41no—
557C22—432no—
558C22—861no—
559C22—861no—
560C22C4×D4×D4311yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—432no—
566C4—861no—
567C4—861no—
568C4—1721no—
569C4—1721no—
570C4—1721no—
571C4—1721no—
572C4C2×M16×D4311yescharacteristic
573C4#131×D4311yescharacteristic
574C4C2×#1306335411yescharacteristic
575C4#1458369611yescharacteristic
576C2—81no—
577C2—862no—
578C2#436×D4311yescharacteristic
579C2C4×#1306335411yescharacteristic
580C2#1914349311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1590C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621900C2×C4
cosocleC42×C43C24
hypercenter#1590D43
hypocenterC43#17892
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #446×D43C2semidirect
4. #19133503C2semidirect
5. #19133501C2semidirect
6. #19133498C2semidirect
7. #19133494C2semidirect
8. #19133493C2semidirect
9. #19133490C2semidirect
10. #19133483C2semidirect
11. #19133344C2semidirect
12. #19132988C2semidirect
14. C8×#10621872C2semidirect
15. C43×#1590C2semidirect
209. #10621872M16semidirect
255. C8×C43#137semidirect
296. #1590D43semidirect
357. C43#17892semidirect
553. C8#13063354semidirect

Maximal subgroups

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

subgroupindex
#191435582
#446×D432
C4×#130633542
#191335032
#191335012
#191334982
#191334942
#191334932
#191334902
#191334832
#191333442
#191329882
#191329792
C8×#106218722
C43×#15902
#1789243