Finite Group Databasebeta

← #25079287

Subgroups — #25079287

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145150C211yesmaximal, characteristic, complemented
2#19144383C211yesmaximal, characteristic, complemented
3#19143562C211yesmaximal, characteristic, complemented
4#19134151C211yesmaximal, characteristic, complemented
5#19134144C211yesmaximal, characteristic, complemented
6#19134133C211yesmaximal, characteristic, complemented
7#19134126C211yesmaximal, characteristic, complemented
8#19134099C211yesmaximal, characteristic, complemented
9#19134092C211yesmaximal, characteristic, complemented
10#19134065C211yesmaximal, characteristic, complemented
11#19134058C211yesmaximal, characteristic, complemented
12C2×#14582651C211yesmaximal, characteristic, complemented
13#19133253C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3035C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583271C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583206—21no—
22#14583199—21no—
23#14583194C2211yescharacteristic
24#14583189C2211yescharacteristic
25#14583184C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583126—21no—
28#14583126—21no—
29#14583030C2211yescharacteristic
30#14583030C2211yescharacteristic
31C4×#10621883—21no—
32C4×#10621883—21no—
33#14582977C2211yescharacteristic
34#14582977C2211yescharacteristic
35#14582971—21no—
36#14582971—21no—
37#14582952—21no—
38#14582952C2211yescharacteristic
39#14582935—21no—
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41#14582895—21no—
42C4×#10621877—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582651C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C2×#135×C43—21no—
57C43×#532C2211yescharacteristic
58C4×#41×C43C2211yescharacteristic
59C43×#464—21no—
60C43×#463—21no—
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#460C2211yescharacteristic
64C43×#459C2211yescharacteristic
65C2×C4⋊C8×C43C2211yescharacteristic
66C43×#416—21no—
67C2×#10621883—21no—
68C2×#10621883—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C22×C43⋊C8—21no—
72C22×C43⋊C8D411yescharacteristic
73C22×C43⋊C8D411yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063317—21no—
77#13063304—21no—
78#13063304—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81#13063284—21no—
82#13063258—21no—
83#13063258—21no—
84#13063256—21no—
85#13063256—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063249—21no—
97#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×#41×C43D411yescharacteristic
115#135×C43—44no—
116C2×Q16×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43—21no—
119C2×D8×C43—21no—
120C22×C8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#124×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126C4×Q8×C43D411yescharacteristic
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43D411yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#117×C43—21no—
135#117×C43D411yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#103×C43—21no—
143#102×C43—21no—
144#102×C43—21no—
145#41×C43—22no—
146#41×C43—22no—
147#41×C43—42no—
148#41×C43—42no—
149C2×Q8×C43—21no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43#4111yescharacteristic
164C2×Dic86—21no—
165C2×Dic86—21no—
166Q16×C43—42no—
167SD16×C43—42no—
168SD16×C43—42no—
169D8×C43—42no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—42no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43#4111yescharacteristic
190C42×C43C2411yescharacteristic
191C22⋊Dic43—41no—
192#10621883—42no—
193#10621883—42no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—41no—
201#10621877—42no—
202#10621877—42no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—41no—
209C2×C43⋊C8—42no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C23×C43—21no—
215C23×C43—41no—
216C23×C43#12111yescharacteristic
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—41no—
220Q8×C43—41no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—42no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43—82no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—41no—
241C2×C4×C43—82no—
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43AGL(1,ℤ/8)12yes—
246C2×C4×C43#13712yes—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×Dic43—41no—
251C2×Dic43—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—81no—
255C8×C43—41no—
256C8×C43—41no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8#13512yescomplemented
265#19156—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43#46812yes—
275C22×C43C2×#12111yescharacteristic
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—81no—
283C4×C43#46812yes—
284C4×C43C2×#13511yescharacteristic
285C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C43C2×#13711yescharacteristic
287C4×C43#57511yescharacteristic
288Dic43—81no—
289Dic43—81no—
290#3167—431no—
291#3076—431no—
292#3035D4311yescharacteristic
293#2965—431no—
294#1700—431no—
295#1699—431no—
296#1698—431no—
297#1697—431no—
298#1692—431no—
299#1691—431no—
300#1686—431no—
301#1685—431no—
302C2×#335—431no—
303#1542—431no—
304#1540—431no—
305C2×C43—22no—
306C2×C43—81no—
307C2×C43—161no—
308C2×C43#303511yescharacteristic
309C2×C43C2×#46811yescharacteristic
310C2×C43#306711yescharacteristic
311C2×#135—21no—
312#533—431no—
313#532C2×D4311yescharacteristic
314C4×#41C2×D4311yescharacteristic
315#498—431no—
316#492—431no—
317#487—431no—
318#486—431no—
319#479—861no—
320#478—861no—
321#477—431no—
322#476—431no—
323#475—431no—
324#474—431no—
325#465—861no—
326#465—861no—
327#464—21no—
328#463—21no—
329#462C2×D4311yescharacteristic
330#461C2×D4311yescharacteristic
331#460C2×D4311yescharacteristic
332#459C2×D4311yescharacteristic
333#446—431no—
334#446—431no—
335C4×SD16—861no—
336C4×SD16—861no—
337#436—431no—
338#436—431no—
339#435—861no—
340#435—861no—
341#431—431no—
342#431—861no—
343#427—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8C2×D4311yescharacteristic
346#416—21no—
347#416—861no—
348C4×M16—861no—
349C2×C4×C8—431no—
350#335—431no—
351#335—431no—
352#335—431no—
353#335—431no—
354#333—431no—
355#333—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#332—431no—
360#331—431no—
361#331—431no—
362C43#1915611yescharacteristic, complemented, Sylow
363C2×#41—21no—
364C2×#41C22⋊D4311yescharacteristic
365#135—44no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—21no—
372C2×M16—861no—
373C2×M16—861no—
374C22×C8—21no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8—861no—
378C4⋊Q8—431no—
379C4⋊Q8—431no—
380C4⋊Q8C22×D4311yescharacteristic
381#127C22×D4311yescharacteristic
382#125—861no—
383#124—21no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386#121—21no—
387#121—21no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8C22⋊D4311yescharacteristic
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C22⋊D4311yescharacteristic
397C4×D4C22×D4311yescharacteristic
398#117—21no—
399#117—861no—
400#117C22⋊D4311yescharacteristic
401C2×C42—21no—
402C2×C42C22×D4311yescharacteristic
403#107—861no—
404#107—861no—
405#106—861no—
406#106—861no—
407#106—861no—
408#106—861no—
409C4⋊C8—21no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—21no—
420#103—21no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#102—21no—
426#102—21no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434#97—861no—
435#97—861no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—861no—
441#41—22no—
442#41—22no—
443#41—42no—
444#41—42no—
445C2×Q8—21no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8C2×C22⋊D4311yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4C2×C22⋊D4311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4D4×D4311yescharacteristic
460C22×C4#1062190011yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462Q16—42no—
463SD16—42no—
464SD16—42no—
465SD16—1722no—
466SD16—1722no—
467D8—42no—
468M16—1722no—
469M16—1722no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—862no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—1721no—
483C2×C8—1722no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4C2×C22⋊D4311yescharacteristic
495C4⋊C4C2×C22⋊D4311yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—1721no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—1721no—
506C42D4×D4311yescharacteristic
507C42#1062190011yescharacteristic
508C42C2×C22⋊D4311yescharacteristic
509C42C23×D4311yescharacteristic
510C23—21no—
511C23—41no—
512C23#1306329711yescharacteristic
513Q8—21no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—3441no—
518Q8—1721no—
519Q8—1721no—
520D4—21no—
521D4—21no—
522D4—42no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—81no—
528D4—82no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329711yescharacteristic
544C2×C4#1306329711yescharacteristic
545C2×C4#1306329711yescharacteristic
546C2×C4#1306335112yes—
547C2×C4#1306335512yes—
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4C22×C22⋊D4311yescharacteristic
550C2×C4C2×#1062190011yescharacteristic
551C8—41no—
552C8—41no—
553C8—432no—
554C8—861no—
555C8—861no—
556C8—861no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C8—1721no—
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1458314312yes—
570C22C2×#1306329711yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—3441no—
579C4—3441no—
580C4#1458314312yes—
581C4#135×D4311yescharacteristic
582C4C2×#1306335111yescharacteristic
583C4C2×#1306335511yescharacteristic
584C4#1458369611yescharacteristic
585C2—22no—
586C2—81no—
587C2—161no—
588C2#1914404611yescharacteristic
589C2C2×#1458314311yescharacteristic
590C2#1914431211yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3035C2
socleC22×C43C2×#121
hypercenter#3035D43
hypocenterC43#19156
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #19145150C2semidirect
2. #19144383C2semidirect
3. #19143562C2semidirect
4. #19134151C2semidirect
5. #19134144C2semidirect
6. #19134133C2semidirect
7. #19134126C2semidirect
8. #19134099C2semidirect
9. #19134092C2semidirect
10. #19134065C2semidirect
11. #19134058C2semidirect
12. C2×#14582651C2semidirect
13. #19133253C2semidirect
14. #19133244C2semidirect
264. C43⋊C8#135semidirect
362. C43#19156semidirect

Maximal subgroups

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

subgroupindex
#191451502
#191443832
#191435622
#191341512
#191341442
#191341332
#191341262
#191340992
#191340922
#191340652
#191340582
C2×#145826512
#191332532
#191332442
C43×#30352
#1915643