Finite Group Databasebeta

← #25106613

Subgroups — #25106613

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147983C211yesmaximal, characteristic
2#19143230C211yesmaximal, characteristic, complemented
3#19137077C211yesmaximal, characteristic, complemented
4#19135537C212yesmaximal, complemented
5#19135512C212yesmaximal, complemented
6#19135043C211yesmaximal, characteristic, complemented
7#19135039C211yesmaximal, characteristic, complemented
8#19135036C211yesmaximal, characteristic, complemented
9#19134614C212yesmaximal, complemented
10#19134613C212yesmaximal, complemented
11C43×#1897C211yesmaximal, characteristic, complemented
12#14583522C412yescomplemented
13#14583516C412yescomplemented
14#14583509C412yescomplemented
15#14583502C412yescomplemented
16#14583493—22no—
17#14583484—22no—
18#14583452C2211yescharacteristic
19#14583445C2211yescharacteristic
20#14583431—22no—
21#14583429—22no—
22#14583410C2211yescharacteristic
23#41×Dic43C2211yescharacteristic
24#14583367C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27#14582957—22no—
28#14582957—22no—
29#14582922C2212yes—
30C2×#13063253C2212yes—
31C2×#13063252C2212yes—
32C2×#13063251C2212yes—
33#14582863C2211yescharacteristic
34M16×Dic43C2212yes—
35#14582795—22no—
36#14582771—22no—
37C4×Dic43⋊C4C2212yes—
38C4×Dic43⋊C4C2212yes—
39#14582660C2212yes—
40#14582659C2212yes—
41#14582658C2212yes—
42C43×#525C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C2×#104×C43C2212yes—
45C43×#407C2211yescharacteristic
46C43×#339C2212yes—
47C2×#10621898C2311yescharacteristic
48C23×Dic43—21no—
49C2×#10621877C2312yes—
50#13063324C2×C412yescomplemented
51#13063323C2×C411yescharacteristic, complemented
52#13063321C2×C411yescharacteristic, complemented
53#13063320—22no—
54#13063318—22no—
55#13063318—22no—
56#13063318—22no—
57#13063316—22no—
58#13063316C2×C412yescomplemented
59#13063315—22no—
60#13063314C2×C411yescharacteristic, complemented
61#13063312—22no—
62#13063312C2×C411yescharacteristic, complemented
63#13063311—22no—
64#13063309—22no—
65#13063308—21no—
66#13063307—22no—
67#13063307—22no—
68#13063306—22no—
69#13063305—22no—
70#13063304C2×C412yes—
71#13063302—22no—
72#13063302—22no—
73#13063299C2×C412yes—
74#13063297—22no—
75#13063297—22no—
76#13063296—22no—
77#13063294—21no—
78Q8×Dic43C2×C412yescomplemented
79C4×Dic86—22no—
80#13063290C2×C412yescomplemented
81D4×Dic43—22no—
82D4×Dic43C2×C412yescomplemented
83#13063287C2×C412yescomplemented
84C4×C22⋊D43—22no—
85C4×C22⋊D43—22no—
86(C22⋊D43)⋊C4—22no—
87#13063284—21no—
88#13063284C2×C412yes—
89#13063284C2×C412yes—
90#13063284D412yes—
91#13063284D412yes—
92#13063284C2311yescharacteristic
93#13063282—21no—
94C2×C4⋊Dic43D412yes—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×C22⋊Dic43D412yes—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—42no—
101C2×C4×Dic43C2312yes—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104C42×D43—21no—
105Dic43⋊C8—22no—
106Dic43⋊C8—22no—
107#13063253—42no—
108#13063252—42no—
109#13063251—42no—
110C22⋊(C43⋊C8)—22no—
111#13063235—22no—
112C8×Dic43—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C2×#41×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C2×M16×C43C2312yes—
118#123×C43—21no—
119C22⋊Q8×C43C2×C412yes—
120#121×C43C2×C412yes—
121#120×C43—21no—
122C4×D4×C43—22no—
123#117×C43—42no—
124#117×C43C2311yescharacteristic
125C2×C4⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2312yes—
128#104×C43—42no—
129C22⋊C8×C43—22no—
130C24×C43C2×D411yescharacteristic
131#41×C43—22no—
132#41×C43—22no—
133C2×Q8×C43C22×C411yescharacteristic
134C2×D4×C43—22no—
135C2×D4×C43—21no—
136C2×D4×C43C22×C411yescharacteristic
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—22no—
141C22×C4×C43C22×C412yes—
142C22×C4×C43C2×D412yes—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—22no—
146C2×C22⋊D43—22no—
147C2×C22⋊D43—21no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—42no—
151C22×Dic43—44no—
152C22×Dic43C2×D412yes—
153C22×Dic43C2×D412yes—
154#10621898—22no—
155#10621898—22no—
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—22no—
159C2×Dic86—22no—
160C2×Dic86C22×C411yescharacteristic
161M16×C43—22no—
162M16×C43—22no—
163C2×C8×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—42no—
166C4⋊C4×C43C22×C412yes—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—21no—
170C22⋊C4×C43—42no—
171C42×C43—21no—
172C42×C43—22no—
173C42×C43—22no—
174C22⋊Dic43—22no—
175C22⋊Dic43—22no—
176C22⋊Dic43—22no—
177C22⋊Dic43—21no—
178C22⋊Dic43C22⋊C412yes—
179C22⋊Dic43C22⋊C412yes—
180C22⋊Dic43C22⋊C412yes—
181C22⋊Dic43C22⋊C412yes—
182(C2×D43)⋊C4—22no—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43C22⋊C412yes—
188C4⋊Dic43C22⋊C412yes—
189C4⋊Dic43C22⋊C412yes—
190C4⋊Dic43C22⋊C412yes—
191C4⋊Dic43C22×C412yes—
192Dic43⋊C4—22no—
193Dic43⋊C4—22no—
194Dic43⋊C4—22no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—44no—
198Dic43⋊C4—44no—
199C4×Dic43—21no—
200C4×Dic43—22no—
201C4×Dic43—22no—
202C4×Dic43—22no—
203C4×Dic43—22no—
204C4×Dic43—42no—
205C4×Dic43C22×C412yes—
206C4×Dic43C22×C411yescharacteristic
207C4×Dic43C22×C411yescharacteristic
208C4×Dic43C2×D412yes—
209C4×Dic43C2×D411yescharacteristic
210C4×Dic43C2×D411yescharacteristic
211#10621877—22no—
212#10621877—22no—
213C2×C43⋊C8—22no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—42no—
218C23×C43C2×C22⋊C412yes—
219C23×C43C22×D411yescharacteristic
220C22×D43—21no—
221Q8×C43—22no—
222D4×C43—22no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—82no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43C2×C22⋊C412yes—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43H(5,𝔽2)12yes—
240C2×C4×C432−1+412yes—
241C22⋊D43—41no—
242C22⋊D43—41no—
243C22⋊D43—82no—
244C22⋊D43—82no—
245C2×Dic43—24no—
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—48no—
252C2×Dic43—42no—
253C2×Dic43—82no—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256C2×Dic43C2×C22⋊C412yes—
257C2×Dic43C2×C22⋊C412yes—
258D172—22no—
259C4×D43—42no—
260C4×D43—82no—
261Dic86—22no—
262Dic86—82no—
263C8×C43—42no—
264C43⋊C8—42no—
265#21901—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—41no—
273C22×C43—42no—
274C22×C43C22×C22⋊C411yescharacteristic
275C22×C43#53511yescharacteristic
276C22×C43#53611yescharacteristic
277C2×D43—41no—
278C2×D43—42no—
279C4×C43—22no—
280C4×C43—41no—
281C4×C43—42no—
282C4×C43—82no—
283C4×C43#52012yes—
284C4×C43#53712yes—
285Dic43—22no—
286Dic43—22no—
287Dic43—22no—
288Dic43—22no—
289Dic43—44no—
290Dic43—41no—
291Dic43—42no—
292#3455—431no—
293#2921—431no—
294#2296—431no—
295#1986—432no—
296#1980—432no—
297#1897—431no—
298#1897D4311yescharacteristic, complemented
299#1896—431no—
300#1896—431no—
301#1806—432no—
302#1806—432no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—42no—
306C2×C43—81no—
307C2×C43#231111yescharacteristic
308C2×C43#290112yes—
309D43—81no—
310#542—432no—
311#542—432no—
312#541—432no—
313#540—432no—
314#539—862no—
315#538—862no—
316#533—431no—
317#532—431no—
318#529—862no—
319#529—862no—
320#525—431no—
321#525C2×D4311yescharacteristic
322C4×#41—431no—
323C4×#41—431no—
324C2×#117—431no—
325C2×#117C2×D4311yescharacteristic
326C22×C42—431no—
327#433—862no—
328#433—862no—
329#423—432no—
330C2×#104—432no—
331C2×#104—432no—
332C2×#104—432no—
333C2×#104C2×D4312yes—
334#407—431no—
335#407C2×D4311yescharacteristic
336C4×M16—432no—
337#389—862no—
338#385—862no—
339C4×C4⋊C4—432no—
340C4×C4⋊C4—432no—
341#339—432no—
342#339—432no—
343#339—432no—
344#339C2×D4312yes—
345C43#2190111yescharacteristic, complemented, Sylow
346C2×#41—431no—
347C2×#41C22×D4311yescharacteristic
348C23×C4—861no—
349C23×C4C22×D4311yescharacteristic
350C2×M16—432no—
351C2×M16C22×D4312yes—
352C4⋊Q8—432no—
353C4⋊Q8—431no—
354#127—431no—
355#126—862no—
356#126—862no—
357#126—862no—
358#126—862no—
359#125—432no—
360#125—862no—
361#125—862no—
362#124—431no—
363#124—431no—
364#124—862no—
365#124—862no—
366#123—21no—
367#123—862no—
368#123—862no—
369#123—862no—
370#123—862no—
371#123—861no—
372C22⋊Q8—432no—
373C22⋊Q8—862no—
374C22⋊Q8—862no—
375C22⋊Q8—862no—
376C22⋊Q8C4×D4312yes—
377#121—432no—
378#121—862no—
379#121—862no—
380#121—862no—
381#121C4×D4312yes—
382#120—21no—
383#120—861no—
384C4×Q8—432no—
385C4×Q8—432no—
386C4×Q8—862no—
387C4×D4—22no—
388C4×D4—432no—
389C4×D4—432no—
390C4×D4—862no—
391C4×D4—862no—
392C4×D4—862no—
393C4×D4—862no—
394#117—42no—
395#117—432no—
396#117—432no—
397#117—432no—
398#117—432no—
399#117—431no—
400#117—861no—
401#117—861no—
402#117C22×D4311yescharacteristic
403C2×C4⋊C4—21no—
404C2×C4⋊C4—432no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—862no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—432no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—432no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—1722no—
416C2×C42C22×D4312yes—
417C4⋊C8—862no—
418C4⋊C8—862no—
419#104—42no—
420#104—1722no—
421#104—1722no—
422#104—1722no—
423C22⋊C8—22no—
424C22⋊C8—862no—
425#97—862no—
426C4×C8—862no—
427#95—862no—
428#95—862no—
429C24D4×D4311yescharacteristic
430#41—22no—
431#41—22no—
432#41—862no—
433#41—862no—
434C2×Q8—431no—
435C2×Q8—862no—
436C2×Q8C2×C4×D4311yescharacteristic
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—431no—
440C2×D4—862no—
441C2×D4—862no—
442C2×D4—861no—
443C2×D4C2×C4×D4311yescharacteristic
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—432no—
449C22×C4—432no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—861no—
454C22×C4—1724no—
455C22×C4—1722no—
456C22×C4C2×C4×D4312yes—
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4312yes—
459C22×C4C23×D4311yescharacteristic
460M16—22no—
461M16—22no—
462M16—862no—
463M16—862no—
464C2×C8—22no—
465C2×C8—862no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—432no—
469C4⋊C4—432no—
470C4⋊C4—432no—
471C4⋊C4—432no—
472C4⋊C4—432no—
473C4⋊C4—862no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—1724no—
481C4⋊C4—1724no—
482C4⋊C4C2×C4×D4312yes—
483C22⋊C4—22no—
484C22⋊C4—21no—
485C22⋊C4—22no—
486C22⋊C4—42no—
487C22⋊C4—432no—
488C22⋊C4—432no—
489C22⋊C4—432no—
490C22⋊C4—432no—
491C22⋊C4—862no—
492C22⋊C4—862no—
493C22⋊C4—862no—
494C22⋊C4—862no—
495C22⋊C4—862no—
496C22⋊C4—861no—
497C22⋊C4—862no—
498C42—21no—
499C42—22no—
500C42—22no—
501C42—432no—
502C42—431no—
503C42—431no—
504C42—432no—
505C42—431no—
506C42—431no—
507C42—862no—
508C42—862no—
509C42—861no—
510C42—862no—
511C42—862no—
512C42—1722no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—42no—
517C23—861no—
518C23C22⋊C4×D4312yes—
519C23C2×D4×D4311yescharacteristic
520Q8—22no—
521Q8—862no—
522Q8—3442no—
523D4—22no—
524D4—41no—
525D4—41no—
526D4—82no—
527D4—862no—
528D4—3442no—
529D4—3442no—
530D4—1721no—
531D4—1721no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—432no—
546C2×C4—864no—
547C2×C4—862no—
548C2×C4—861no—
549C2×C4—3442no—
550C2×C4—3442no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1728no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4C22⋊C4×D4312yes—
558C2×C4C22×C4×D4311yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4#1306337012yes—
561C2×C4#1306337212yes—
562C8—42no—
563C8—1722no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—42no—
569C22—42no—
570C22—41no—
571C22—42no—
572C22—1721no—
573C22—1722no—
574C22C2×C22⋊C4×D4311yescharacteristic
575C22#1458346411yescharacteristic
576C22#1458347111yescharacteristic
577C4—22no—
578C4—41no—
579C4—42no—
580C4—82no—
581C4—862no—
582C4—862no—
583C4—862no—
584C4—862no—
585C4—1724no—
586C4—1721no—
587C4—1722no—
588C4#1458337812yes—
589C4#1458347612yes—
590C2—21no—
591C2—21no—
592C2—42no—
593C2—81no—
594C2—3441no—
595C2#1913718211yescharacteristic
596C2#1914314112yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1897C2
socleC22×C43C22×C22⋊C4
prime radical#19147983C2
cosocleC22×C4×C43C24
hypercenter#1897D43
hypocenterC43#21901
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. #19143230C2semidirect
3. #19137077C2semidirect
4. #19135537C2semidirect
5. #19135512C2semidirect
6. #19135043C2semidirect
7. #19135039C2semidirect
8. #19135036C2semidirect
9. #19134614C2semidirect
10. #19134613C2semidirect
11. C43×#1897C2semidirect
12. #14583522C4semidirect
13. #14583516C4semidirect
14. #14583509C4semidirect
15. #14583502C4semidirect
50. #13063324C2×C4semidirect
51. #13063323C2×C4semidirect
52. #13063321C2×C4semidirect
58. #13063316C2×C4semidirect
60. #13063314C2×C4semidirect
62. #13063312C2×C4semidirect
78. Q8×Dic43C2×C4semidirect
80. #13063290C2×C4semidirect
82. D4×Dic43C2×C4semidirect
83. #13063287C2×C4semidirect
298. #1897D43semidirect
345. C43#21901semidirect

Maximal subgroups

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

subgroupindex
#191479832
#191432302
#191370772
#191355372
#191355122
#191350432
#191350392
#191350362
#191346142
#191346132
C43×#18972
#2190143