Finite Group Databasebeta

← #25084481

Subgroups — #25084481

Order 11008.

836 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145747C211yesmaximal, characteristic, complemented
2#19145509C211yesmaximal, characteristic
3#19145152C211yesmaximal, characteristic, complemented
4#492×D43C211yesmaximal, characteristic, complemented
5#19144985C211yesmaximal, characteristic, complemented
6#19144966C211yesmaximal, characteristic, complemented
7#19134251C211yesmaximal, characteristic, complemented
8#19134245C211yesmaximal, characteristic, complemented
9#19134235C211yesmaximal, characteristic, complemented
10#19134233C211yesmaximal, characteristic, complemented
11#19134196C211yesmaximal, characteristic, complemented
12#19134194C211yesmaximal, characteristic, complemented
13#19134185C211yesmaximal, characteristic, complemented
14C8×#10621872C211yesmaximal, characteristic, complemented
15C43×#1706C211yesmaximal, characteristic, complemented
16C2×SD16×D43—22no—
17#14583454C2211yescharacteristic
18#14583447C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#127×D43C2211yescharacteristic
21#14583302C2211yescharacteristic, complemented
22#14583297C2211yescharacteristic, complemented
23#14583275C2211yescharacteristic
24#14583273C2211yescharacteristic
25#14583272C2211yescharacteristic
26#14583271C2211yescharacteristic
27#14583270—22no—
28#14583262—22no—
29#14583257—22no—
30#14583251C2211yescharacteristic, complemented
31#14583251C2211yescharacteristic, complemented
32#14583250C2211yescharacteristic, complemented
33#14583250C2211yescharacteristic, complemented
34#14583249C2211yescharacteristic, complemented
35#14583247C2211yescharacteristic
36#14583246C2211yescharacteristic
37#14583246C2211yescharacteristic
38#14583245C2211yescharacteristic
39#14583245C2211yescharacteristic
40#14583245C2211yescharacteristic, complemented
41#14583245C2211yescharacteristic, complemented
42#14583236—22no—
43#14583193—22no—
44#14583125—22no—
45#14583092—22no—
46#14583031—22no—
47SD16×Dic43—22no—
48#14582950C2211yescharacteristic
49#14582902—22no—
50#14582897—22no—
51C4×#10621872C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic, complemented
54#14582620C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C43×#500C2211yescharacteristic, complemented
57C43×#493C2211yescharacteristic
58C43×#492C2211yescharacteristic
59C43×#492C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic
61C43×#486C2211yescharacteristic, complemented
62C82×C43C2211yescharacteristic, complemented
63C2×#10621900—21no—
64C2×Q8×D43—21no—
65C2×D4×D43—21no—
66C2×D4×D43—21no—
67C2×D4×D43—21no—
68C2×#10621873—22no—
69C2×#10621883—22no—
70C2×#10621884—22no—
71SD16×D43—48no—
72C2×#10621882—22no—
73C2×#10621872D412yes—
74C2×C8×D43D412yes—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063324—21no—
79#13063324—21no—
80#13063323—21no—
81#13063322C2311yescharacteristic
82#13063321—21no—
83#13063321—21no—
84#13063321—21no—
85#13063316—21no—
86#13063312—21no—
87#13063305—21no—
88#13063301—21no—
89#13063296—21no—
90#13063296—21no—
91Q8×Dic43—21no—
92#13063290—21no—
93D4×Dic43—21no—
94D4×Dic43—21no—
95#13063283—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C42×D43C2311yescharacteristic
99#13063258—22no—
100#13063257—22no—
101Dic43⋊C8D412yes—
102#13063250—22no—
103#13063250—22no—
104#13063249—22no—
105#13063248—22no—
106#13063248—22no—
107#13063247—22no—
108#13063247—22no—
109#13063246—22no—
110#13063246—22no—
111#13063246—22no—
112#13063246—22no—
113#13063245—22no—
114(C2×D43)⋊C8D412yes—
115#13063235D412yes—
116C4×C43⋊C8C2311yescharacteristic
117C4×C43⋊C8C2311yescharacteristic
118C4×C43⋊C8C2311yescharacteristic
119C8×Dic43D412yes—
120C2×SD16×C43—22no—
121C2×SD16×C43—22no—
122C2×D8×C43—22no—
123C4⋊Q8×C43C2311yescharacteristic
124C4⋊Q8×C43C2311yescharacteristic
125#127×C43C2311yescharacteristic
126#127×C43C2311yescharacteristic
127#107×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C4×C8×C43C2311yescharacteristic
133C23×D43—41no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×C22⋊D43—41no—
143C2×C22⋊D43—41no—
144C2×C22⋊D43—41no—
145C2×C22⋊D43—41no—
146C22×Dic43—41no—
147Q8×D43—44no—
148#10621900—44no—
149D4×D43—44no—
150D4×D43—44no—
151D4×D43—82no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×C4×D43—41no—
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163SD16×C43—44no—
164SD16×C43—44no—
165D8×C43—82no—
166C2×C8×C43C2×D412yes—
167C2×C8×C43C2×D412yes—
168C2×C8×C43C2×D412yes—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C42×C43C2411yescharacteristic
174C22⋊Dic43—41no—
175C22⋊Dic43—41no—
176#10621884—44no—
177#10621883—44no—
178#10621882—82no—
179(C2×D43)⋊C4—41no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—41no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190C4×Dic43—41no—
191C4×Dic43C2×D411yescharacteristic
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C2×C43⋊C8C2×D412yes—
195C2×C43⋊C8C2×D412yes—
196C2×C43⋊C8C2×D412yes—
197#10621873—44no—
198#10621872—24no—
199C8×D43—24no—
200C23×C43—41no—
201C23×C43—41no—
202C22×D43—41no—
203C22×D43—82no—
204C22×D43—82no—
205C22×D43—82no—
206C22×D43#12711yescharacteristic
207Q8×C43—42no—
208Q8×C43—42no—
209D4×C43—42no—
210D4×C43—42no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C22⋊D43—82no—
221C22⋊D43—82no—
222C22⋊D43—82no—
223C22⋊D43—82no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—82no—
228C2×Dic43#12711yescharacteristic
229C2×Dic43#12711yescharacteristic
230C2×Dic43#12711yescharacteristic
231D172—42no—
232D172—42no—
233D172—42no—
234C4×D43—22no—
235C4×D43—22no—
236C4×D43—82no—
237C4×D43#13514yes—
238Dic86—42no—
239Dic86—42no—
240Dic86—42no—
241Dic86—82no—
242C8×C43—22no—
243C8×C43—22no—
244C8×C43AGL(1,ℤ/8)14yes—
245C43⋊C8—22no—
246C43⋊C8—22no—
247C43⋊C8—22no—
248#19625—431nomaximal, Sylow
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43—81no—
255C22×C43C2×#12711yescharacteristic
256C2×D43—21no—
257C2×D43—21no—
258C2×D43—81no—
259C2×D43—81no—
260C2×D43—81no—
261C2×D43—164no—
262C2×D43#49512yes—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43C2×#13512yes—
266C4×C43C2×AGL(1,ℤ/8)12yes—
267C4×C43#57712yes—
268Dic43—21no—
269Dic43—21no—
270Dic43—81no—
271Dic43—81no—
272Dic43—81no—
273Dic43#49512yes—
274#3230—431no—
275#3205—431no—
276#3167—431no—
277C2×#492—431no—
278#3141—431no—
279#3138—431no—
280#1719—431no—
281#1719—431no—
282#1717—431no—
283#1717—431no—
284#1708—431no—
285#1708—431no—
286#1706—431no—
287#1706D4311yescharacteristic, complemented
288C8×M16—431no—
289C2×C43—161no—
290C2×C43—161no—
291C2×C43C2×#49511yescharacteristic
292C2×C43#315111yescharacteristic
293C2×C43#315411yescharacteristic
294D43—22no—
295D43—161no—
296C22×SD16—862no—
297#533—431no—
298#532—431no—
299C2×C4⋊Q8—431no—
300C2×#127—431no—
301#500—431no—
302#500C2×D4311yescharacteristic, complemented
303#498—431no—
304#493—431no—
305#493C2×D4311yescharacteristic
306#492—431no—
307#492—431no—
308#492—431no—
309#492—862no—
310#492C2×D4311yescharacteristic
311#492C2×D4311yescharacteristic, complemented
312#490—862no—
313#489—862no—
314#487—431no—
315#487—431no—
316#487—431no—
317#487—431no—
318#487—431no—
319#486—431no—
320#486—431no—
321#486—431no—
322#486—431no—
323#486—431no—
324#486—431no—
325#486—431no—
326#486C2×D4311yescharacteristic
327#486C2×D4311yescharacteristic, complemented
328#484—862no—
329#477—862no—
330#465—862no—
331#459—862no—
332#447—862no—
333C4×SD16—862no—
334#431—431no—
335#418—862no—
336#417—862no—
337C4×M16—431no—
338C2×C4×C8—431no—
339#322—431no—
340#322—431no—
341C82—431no—
342C82C2×D4311yescharacteristic, complemented
343C43#1962511yescharacteristic, complemented, Sylow
344C2×#41—861no—
345C22×Q8—861no—
346C22×D4—861no—
347C22×D4—861no—
348C22×D4—861no—
349C2×SD16—22no—
350C2×SD16—22no—
351C2×SD16—862no—
352C2×SD16—862no—
353C2×SD16—862no—
354C2×SD16—1728no—
355C2×D8—22no—
356C2×D8—862no—
357C2×M16—432no—
358C22×C8—432no—
359C4⋊Q8—431no—
360C4⋊Q8—431no—
361C4⋊Q8—431no—
362C4⋊Q8—861no—
363C4⋊Q8—861no—
364C4⋊Q8—861no—
365C4⋊Q8C22×D4311yescharacteristic
366C4⋊Q8C22×D4311yescharacteristic
367#127—431no—
368#127—861no—
369#127—861no—
370#127—861no—
371#127C22×D4311yescharacteristic
372#127C22×D4311yescharacteristic
373#125—861no—
374#124—861no—
375C22⋊Q8—861no—
376C22⋊Q8—861no—
377#121—861no—
378#121—861no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×D4—861no—
382C4×D4—861no—
383#117—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C42—431no—
387#107—22no—
388#107—862no—
389#106—862no—
390C4⋊C8—432no—
391#103—862no—
392#103—862no—
393#103—862no—
394#103—862no—
395#103—862no—
396#102—22no—
397#102—22no—
398#102—862no—
399#102—862no—
400#102—862no—
401#102—862no—
402#102—862no—
403#102—862no—
404#102—862no—
405C22⋊C8—432no—
406#97—432no—
407C4×C8—432no—
408C4×C8—431no—
409C4×C8—431no—
410C4×C8—431no—
411C4×C8C22×D4311yescharacteristic
412C4×C8C22×D4311yescharacteristic
413C4×C8C22×D4311yescharacteristic
414C24—1721no—
415#41—1724no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—1721no—
422C2×Q8—1724no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—3442no—
433C2×D4—1724no—
434C2×D4—1721no—
435C2×D4—1721no—
436C2×D4—1721no—
437C2×D4—1724no—
438C2×D4—1721no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—1721no—
443C22×C4—1721no—
444SD16—44no—
445SD16—44no—
446SD16—1724no—
447SD16—1724no—
448SD16—1724no—
449D8—82no—
450D8—3442no—
451M16—864no—
452C2×C8—432no—
453C2×C8—432no—
454C2×C8—432no—
455C2×C8—864no—
456C2×C8D4×D4312yes—
457C2×C8D4×D4312yes—
458C2×C8D4×D4312yes—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C22⋊C4—1721no—
474C22⋊C4—1721no—
475C22⋊C4—1721no—
476C42—431no—
477C42—431no—
478C42—431no—
479C42—1721no—
480C42C23×D4311yescharacteristic
481C23—41no—
482C23—41no—
483C23—431no—
484C23—3442no—
485C23—3442no—
486C23—3442no—
487C23—1721no—
488Q8—42no—
489Q8—42no—
490Q8—3442no—
491Q8—1722no—
492Q8—1722no—
493Q8—1722no—
494D4—42no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—3442no—
501D4—3442no—
502D4—3442no—
503D4—3442no—
504D4—1722no—
505D4—1722no—
506D4—1722no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—431no—
510C2×C4—434no—
511C2×C4—431no—
512C2×C4—431no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—3442no—
516C2×C4—3442no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4C2×D4×D4311yescharacteristic
522C2×C4C2×D4×D4311yescharacteristic
523C8—22no—
524C8—22no—
525C8—862no—
526C8—862no—
527C8—862no—
528C8#1306334914yes—
529C22—81no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—432no—
536C22—861no—
537C22—861no—
538C22—3441no—
539C22—3441no—
540C22—3441no—
541C22—6884no—
542C22#127×D4311yescharacteristic
543C4—81no—
544C4—81no—
545C4—432no—
546C4—861no—
547C4—861no—
548C4—3441no—
549C4—3441no—
550C4—3441no—
551C4#135×D4312yes—
552C4C2×#1306334912yes—
553C4#1458370512yes—
554C2—161no—
555C2—161no—
556C2—862no—
557C2—6881no—
558C2#495×D4311yescharacteristic
559C2#1914504611yescharacteristic
560C2#1914506411yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1706C2
socleC22×C43C2×#127
prime radical#19145509C2
hypercenter#1706D43
hypocenterC43#19625
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1706

Complements

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

NH ≅ G/Ntype
1. #19145747C2semidirect
3. #19145152C2semidirect
4. #492×D43C2semidirect
5. #19144985C2semidirect
6. #19144966C2semidirect
7. #19134251C2semidirect
8. #19134245C2semidirect
9. #19134235C2semidirect
10. #19134233C2semidirect
11. #19134196C2semidirect
12. #19134194C2semidirect
13. #19134185C2semidirect
14. C8×#10621872C2semidirect
15. C43×#1706C2semidirect
21. #14583302C22semidirect
22. #14583297C22semidirect
30. #14583251C22semidirect
31. #14583251C22semidirect
32. #14583250C22semidirect
33. #14583250C22semidirect
34. #14583249C22semidirect
40. #14583245C22semidirect
41. #14583245C22semidirect
53. #14582621C22semidirect
54. #14582620C22semidirect
55. C8×C43⋊C8C22semidirect
56. C43×#500C22semidirect
59. C43×#492C22semidirect
61. C43×#486C22semidirect
62. C82×C43C22semidirect
287. #1706D43semidirect
302. #500C2×D43semidirect
311. #492C2×D43semidirect
327. #486C2×D43semidirect
342. C82C2×D43semidirect
343. C43#19625semidirect

Maximal subgroups

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

subgroupindex
#191457472
#191455092
#191451522
#492×D432
#191449852
#191449662
#191342512
#191342452
#191342352
#191342332
#191341962
#191341942
#191341852
C8×#106218722
C43×#17062
#1962543