Finite Group Databasebeta

← #25101910

Subgroups — #25101910

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3C2×#14582745C211yesmaximal, characteristic, complemented
4#19135574C212yesmaximal, complemented
5#19135425C212yesmaximal, complemented
6#19135039C211yesmaximal, characteristic, complemented
7#19135038C211yesmaximal, characteristic, complemented
8#19135036C211yesmaximal, characteristic, complemented
9#19134407C212yesmaximal, complemented
10#19134404C212yesmaximal, complemented
11C43×#1896C211yesmaximal, characteristic, complemented
12#14583452C2211yescharacteristic
13#14583451C412yescomplemented
14#14583445C2211yescharacteristic
15#14583444C412yescomplemented
16#14583435C412yescomplemented
17#14583430C412yescomplemented
18#14583429—22no—
19#14583426—22no—
20#14583410C2211yescharacteristic
21#14583405—22no—
22#41×Dic43C2211yescharacteristic
23#14583367C2211yescharacteristic
24C4×#10621900—22no—
25C22×C4×Dic43C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27#14582953—22no—
28#14582949—22no—
29#14582922C2212yes—
30C2×#13063253C2212yes—
31C2×#13063252C2212yes—
32C2×#13063251C2212yes—
33#14582863C2211yescharacteristic
34M16×Dic43C2212yes—
35#14582745—22no—
36#14582745C2212yes—
37#14582745C2212yes—
38C2×C43⋊#95—22no—
39#14582660C2212yes—
40#14582659C2212yes—
41#14582658C2212yes—
42C43×#525C2211yescharacteristic
43C22×C42×C43C2211yescharacteristic
44C2×#104×C43C2212yes—
45C43×#407C2211yescharacteristic
46C43×#339C2212yes—
47C2×#10621898C2311yescharacteristic
48C2×#10621900—22no—
49C23×Dic43—21no—
50C23×Dic43D412yes—
51C2×#10621877C2312yes—
52#13063324C2×C412yescomplemented
53#13063323C2×C411yescharacteristic, complemented
54#13063321C2×C411yescharacteristic, complemented
55#13063320—22no—
56#13063318—22no—
57#13063316C2×C412yescomplemented
58#13063315—22no—
59#13063314C2×C411yescharacteristic, complemented
60#13063312C2×C411yescharacteristic, complemented
61#13063311—22no—
62#13063309—22no—
63#13063308—21no—
64#13063306—22no—
65#13063304C2×C412yes—
66#13063302—22no—
67#13063302—22no—
68#13063299C2×C412yes—
69#13063297—22no—
70#13063297—22no—
71#13063294—21no—
72Q8×Dic43C2×C412yescomplemented
73C4×Dic86—22no—
74#13063290—22no—
75#13063290C2×C412yescomplemented
76D4×Dic43—22no—
77D4×Dic43—22no—
78D4×Dic43C2×C412yescomplemented
79#13063287C2×C412yescomplemented
80C4×C22⋊D43—22no—
81C4×C22⋊D43—22no—
82(C22⋊D43)⋊C4—22no—
83(C22⋊D43)⋊C4—22no—
84(C22⋊D43)⋊C4—22no—
85#13063284—21no—
86#13063284C2311yescharacteristic
87#13063283—22no—
88#13063282—21no—
89#13063281—22no—
90#13063281—22no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—24no—
94C2×C4×Dic43C2×C412yes—
95C2×C4×Dic43C2×C412yes—
96C2×C4×Dic43D412yes—
97C2×C4×Dic43D412yes—
98C2×C4×Dic43D412yes—
99C2×C4×Dic43C2312yes—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102C42×D43—21no—
103Dic43⋊C8—24no—
104#13063253—24no—
105#13063252—24no—
106#13063251—24no—
107C22⋊(C43⋊C8)—22no—
108#13063235—22no—
109C8×Dic43—22no—
110C43⋊#95—24no—
111C43⋊#95—24no—
112C2×#41×C43C2311yescharacteristic
113C23×C4×C43—21no—
114C23×C4×C43C2311yescharacteristic
115C2×M16×C43C2312yes—
116#123×C43—21no—
117C22⋊Q8×C43C2×C412yes—
118#121×C43C2×C412yes—
119#120×C43—21no—
120C4×D4×C43—22no—
121#117×C43C2311yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43—24no—
124C2×C42×C43C2312yes—
125#104×C43—24no—
126C22⋊C8×C43—22no—
127C24×C43C2×D411yescharacteristic
128#41×C43—22no—
129#41×C43—22no—
130C2×Q8×C43C22×C411yescharacteristic
131C2×D4×C43—22no—
132C2×D4×C43—21no—
133C2×D4×C43C22×C411yescharacteristic
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—24no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43—44no—
140C22×C4×C43C22×C412yes—
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C2×C22⋊D43—22no—
145C2×C22⋊D43—22no—
146C2×C22⋊D43—21no—
147C22×Dic43—24no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—44no—
151C22×Dic43—44no—
152C22×Dic43C22⋊C412yes—
153C22×Dic43C22⋊C412yes—
154C22×Dic43C22⋊C412yes—
155C22×Dic43C22⋊C412yes—
156C22×Dic43C2×D412yes—
157C22×Dic43C2×D412yes—
158#10621900—48no—
159#10621898—22no—
160#10621898—22no—
161C2×D172C22×C411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—22no—
164C2×Dic86—22no—
165C2×Dic86C22×C411yescharacteristic
166M16×C43—22no—
167M16×C43—22no—
168C2×C8×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43C22×C412yes—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—21no—
174C42×C43—24no—
175C42×C43—21no—
176C42×C43—22no—
177C42×C43#4114yescomplemented
178C22⋊Dic43—22no—
179C22⋊Dic43—22no—
180C22⋊Dic43—22no—
181C22⋊Dic43—21no—
182(C2×D43)⋊C4—22no—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43C22×C412yes—
188Dic43⋊C4—22no—
189Dic43⋊C4—22no—
190Dic43⋊C4—22no—
191Dic43⋊C4—22no—
192Dic43⋊C4—22no—
193C4×Dic43—24no—
194C4×Dic43—21no—
195C4×Dic43—22no—
196C4×Dic43—22no—
197C4×Dic43—22no—
198C4×Dic43C22⋊C412yes—
199C4×Dic43C22⋊C412yes—
200C4×Dic43C22⋊C412yes—
201C4×Dic43C22⋊C412yes—
202C4×Dic43C22×C412yes—
203C4×Dic43C22×C411yescharacteristic
204C4×Dic43C22×C411yescharacteristic
205C4×Dic43C2×D411yescharacteristic
206C4×Dic43C2×D411yescharacteristic
207C4×Dic43C2×D412yes—
208C4×Dic43#4114yescomplemented
209#10621877—22no—
210#10621877—22no—
211C2×C43⋊C8—22no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—24no—
215C23×C43—21no—
216C23×C43C2×C22⋊C412yes—
217C23×C43C22×D411yescharacteristic
218C22×D43—21no—
219Q8×C43—22no—
220D4×C43—22no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—44no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—48no—
232C2×C4×C43—44no—
233C2×C4×C43—42no—
234C2×C4×C43C2×C22⋊C412yes—
235C2×C4×C43C23×C411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4112yes—
238C2×C4×C43C2×#4112yes—
239C22⋊D43—44no—
240C22⋊D43—41no—
241C22⋊D43—41no—
242C22⋊D43—44no—
243C2×Dic43—24no—
244C2×Dic43—24no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—24no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—44no—
253C2×Dic43—48no—
254C2×Dic43—44no—
255C2×Dic43C2×C22⋊C412yes—
256C2×Dic43C2×C22⋊C412yes—
257C2×Dic43C2×C22⋊C412yes—
258C2×Dic43C2×C22⋊C412yes—
259D172—22no—
260C4×D43—44no—
261C4×D43—42no—
262Dic86—22no—
263Dic86—44no—
264C8×C43—42no—
265C43⋊C8—42no—
266#21417—431nomaximal, Sylow
267C22×C43—24no—
268C22×C43—24no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—42no—
273C22×C43—41no—
274C22×C43#42114yes—
275C22×C43C22×C22⋊C411yescharacteristic
276C22×C43#52511yescharacteristic
277C22×C43#52511yescharacteristic
278C2×D43—42no—
279C2×D43—41no—
280C4×C43—22no—
281C4×C43—44no—
282C4×C43—42no—
283C4×C43—41no—
284C4×C43C4×#4112yes—
285C4×C43#53212yes—
286Dic43—22no—
287Dic43—22no—
288Dic43—22no—
289Dic43—22no—
290Dic43—44no—
291Dic43—42no—
292Dic43—41no—
293#3444—431no—
294#2920—431no—
295C2×#376—431no—
296#1995—432no—
297#1963—432no—
298#1896—431no—
299#1896—431no—
300#1896—431no—
301#1896D4311yescharacteristic, complemented
302#1759—432no—
303#1759—432no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43—24no—
307C2×C43—81no—
308C2×C43#229711yescharacteristic
309C2×C43C2×#42112yes—
310D43—81no—
311#533—431no—
312#533—432no—
313#532—432no—
314#532—431no—
315#529—432no—
316#529—432no—
317#529—862no—
318#529—862no—
319#525—431no—
320#525—862no—
321#525C2×D4311yescharacteristic
322C4×#41—431no—
323C4×#41—431no—
324C4×#41—862no—
325C22×C42—431no—
326C22×C42—431no—
327C22×C42C2×D4311yescharacteristic
328#432—862no—
329#431—862no—
330#423—432no—
331C2×#104—432no—
332C2×#104—432no—
333C2×#104—432no—
334C2×#104C2×D4312yes—
335#407—431no—
336#407C2×D4311yescharacteristic
337C4×M16—432no—
338#376—432no—
339#376—432no—
340#376—862no—
341C2×#95—862no—
342#339—432no—
343#339—432no—
344#339—432no—
345#339C2×D4312yes—
346C43#2141711yescharacteristic, complemented, Sylow
347C2×#41—431no—
348C2×#41—862no—
349C2×#41C22×D4311yescharacteristic
350C23×C4—21no—
351C23×C4—432no—
352C23×C4—861no—
353C23×C4C22×D4311yescharacteristic
354C2×M16—432no—
355C2×M16C22×D4312yes—
356C4⋊Q8—432no—
357C4⋊Q8—431no—
358#127—431no—
359#126—862no—
360#126—862no—
361#125—432no—
362#125—862no—
363#124—431no—
364#124—431no—
365#124—862no—
366#123—21no—
367#123—862no—
368#123—862no—
369#123—861no—
370C22⋊Q8—432no—
371C22⋊Q8—862no—
372C22⋊Q8—862no—
373C22⋊Q8C4×D4312yes—
374#121—432no—
375#121—862no—
376#121—862no—
377#121C4×D4312yes—
378#120—21no—
379#120—861no—
380C4×Q8—432no—
381C4×Q8—432no—
382C4×Q8—862no—
383C4×Q8—862no—
384C4×D4—22no—
385C4×D4—432no—
386C4×D4—432no—
387C4×D4—862no—
388C4×D4—862no—
389C4×D4—862no—
390C4×D4—862no—
391C4×D4—862no—
392C4×D4—862no—
393C4×D4—862no—
394#117—431no—
395#117—861no—
396#117—862no—
397#117—862no—
398#117—861no—
399#117—862no—
400#117C22×D4311yescharacteristic
401C2×C42—21no—
402C2×C42—24no—
403C2×C42—432no—
404C2×C42—432no—
405C2×C42—432no—
406C2×C42—432no—
407C2×C42—432no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—432no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—864no—
414C2×C42—861no—
415C2×C42C22×D4312yes—
416C4⋊C8—864no—
417#104—24no—
418#104—864no—
419#104—864no—
420#104—864no—
421C22⋊C8—22no—
422C22⋊C8—862no—
423#97—862no—
424C4×C8—862no—
425#95—864no—
426#95—864no—
427C24D4×D4311yescharacteristic
428#41—22no—
429#41—22no—
430#41—862no—
431#41—862no—
432#41—1728no—
433C2×Q8—431no—
434C2×Q8—862no—
435C2×Q8C2×C4×D4311yescharacteristic
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—431no—
439C2×D4—862no—
440C2×D4—862no—
441C2×D4—861no—
442C2×D4C2×C4×D4311yescharacteristic
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—44no—
449C22×C4—432no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—432no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—864no—
458C22×C4—862no—
459C22×C4—861no—
460C22×C4—1724no—
461C22×C4—1724no—
462C22×C4C2×C4×D4312yes—
463C22×C4D4×D4311yescharacteristic
464C22×C4D4×D4312yes—
465C22×C4C23×D4311yescharacteristic
466M16—22no—
467M16—22no—
468M16—862no—
469M16—862no—
470C2×C8—22no—
471C2×C8—862no—
472C4⋊C4—22no—
473C4⋊C4—432no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4C2×C4×D4312yes—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—22no—
485C22⋊C4—862no—
486C22⋊C4—862no—
487C22⋊C4—862no—
488C22⋊C4—862no—
489C22⋊C4—862no—
490C22⋊C4—861no—
491C22⋊C4—862no—
492C42—24no—
493C42—21no—
494C42—22no—
495C42—432no—
496C42—432no—
497C42—432no—
498C42—432no—
499C42—432no—
500C42—431no—
501C42—431no—
502C42—431no—
503C42—431no—
504C42—432no—
505C42—434no—
506C42—862no—
507C42—862no—
508C42—864no—
509C42—861no—
510C42—862no—
511C42#1062190014yescomplemented
512C23—21no—
513C23—21no—
514C23—24no—
515C23—21no—
516C23—861no—
517C23C22⋊C4×D4312yes—
518C23C2×D4×D4311yescharacteristic
519Q8—22no—
520Q8—862no—
521Q8—1724no—
522D4—22no—
523D4—41no—
524D4—41no—
525D4—44no—
526D4—862no—
527D4—1724no—
528D4—1721no—
529D4—1721no—
530D4—1724no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—48no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—432no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—864no—
546C2×C4—864no—
547C2×C4—862no—
548C2×C4—861no—
549C2×C4—864no—
550C2×C4—1724no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1724no—
556C2×C4—1728no—
557C2×C4—1724no—
558C2×C4—1722no—
559C2×C4C22⋊C4×D4312yes—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4#41×D4312yes—
563C2×C4C2×#1062190012yes—
564C8—42no—
565C8—1722no—
566C22—24no—
567C22—24no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—42no—
573C22—1721no—
574C22—1722no—
575C22#1458291414yes—
576C22C2×C22⋊C4×D4311yescharacteristic
577C22#1458340511yescharacteristic
578C22#1458340711yescharacteristic
579C4—22no—
580C4—44no—
581C4—41no—
582C4—42no—
583C4—862no—
584C4—862no—
585C4—862no—
586C4—862no—
587C4—1724no—
588C4—1721no—
589C4—1722no—
590C4C4×#1062190012yes—
591C4#1458344412yes—
592C2—21no—
593C2—21no—
594C2—24no—
595C2—81no—
596C2—3441no—
597C2#1913708011yescharacteristic
598C2C2×#1458291412yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1896C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1896D43
hypocenterC43#21417
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. C2×#14582745C2semidirect
4. #19135574C2semidirect
5. #19135425C2semidirect
6. #19135039C2semidirect
7. #19135038C2semidirect
8. #19135036C2semidirect
9. #19134407C2semidirect
10. #19134404C2semidirect
11. C43×#1896C2semidirect
13. #14583451C4semidirect
15. #14583444C4semidirect
16. #14583435C4semidirect
17. #14583430C4semidirect
52. #13063324C2×C4semidirect
53. #13063323C2×C4semidirect
54. #13063321C2×C4semidirect
57. #13063316C2×C4semidirect
59. #13063314C2×C4semidirect
60. #13063312C2×C4semidirect
72. Q8×Dic43C2×C4semidirect
75. #13063290C2×C4semidirect
78. D4×Dic43C2×C4semidirect
79. #13063287C2×C4semidirect
177. C42×C43#41semidirect
208. C4×Dic43#41semidirect
301. #1896D43semidirect
346. C43#21417semidirect
511. C42#10621900semidirect

Maximal subgroups

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

subgroupindex
#191478872
#191432242
C2×#145827452
#191355742
#191354252
#191350392
#191350382
#191350362
#191344072
#191344042
C43×#18962
#2141743