Finite Group Databasebeta

← #25079019

Subgroups — #25079019

Order 11008.

672 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#19145154C211yesmaximal, characteristic, complemented
2#19144383C211yesmaximal, characteristic, complemented
3#19144050C211yesmaximal, characteristic
4#19134025C211yesmaximal, characteristic, complemented
5#19134018C211yesmaximal, characteristic, complemented
6#19134011C211yesmaximal, characteristic, complemented
7#19134004C211yesmaximal, characteristic, complemented
8#19133977C211yesmaximal, characteristic, complemented
9#19133970C211yesmaximal, characteristic, complemented
10#19133943C211yesmaximal, characteristic, complemented
11#19133936C211yesmaximal, characteristic, complemented
12C2×#14582650C211yesmaximal, characteristic, complemented
13#19133250C211yesmaximal, characteristic, complemented
14#19133242C211yesmaximal, characteristic, complemented
15C8×#41×C43C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583456C2211yescharacteristic
18#14583449C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583206—21no—
24#14583199—21no—
25#14583194C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583128—21no—
30#14583128—21no—
31#14583121—21no—
32#14583114—21no—
33#14583109C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583099C2211yescharacteristic
36#14583094C2211yescharacteristic
37C4×#10621873—21no—
38C4×#10621873—21no—
39#14582935—21no—
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582895—21no—
43#14582893—21no—
44#14582650C2211yescharacteristic
45#14582650C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C8×D4×C43—21no—
60C8×D4×C43—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431—21no—
64C43×#431C2211yescharacteristic
65C2×C4×C8×C43—21no—
66C2×C4×C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68#13063345—44no—
69C2×#10621885—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063317—21no—
82#13063313—21no—
83#13063304—21no—
84#13063304—21no—
85#13063299—21no—
86#13063299—21no—
87C4×Dic86—21no—
88C4×Dic86—21no—
89C4×D172—21no—
90C4×D172—21no—
91#13063284—21no—
92#13063258—21no—
93#13063258—21no—
94#13063257—21no—
95#13063257—21no—
96#13063256—21no—
97#13063256—21no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104#13063250—21no—
105#13063250—21no—
106#13063249—21no—
107#13063249—21no—
108#13063248—21no—
109#13063248—21no—
110#13063247—21no—
111#13063247—21no—
112#13063246—21no—
113#13063246—21no—
114#13063245—21no—
115#13063245—21no—
116C2×#41×C43D411yescharacteristic
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119C22×C8×C43D411yescharacteristic
120C22×C8×C43D411yescharacteristic
121C4×Q8×C43D411yescharacteristic
122C4×Q8×C43C2311yescharacteristic
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125C4×D4×C43D411yescharacteristic
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128#117×C43D411yescharacteristic
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43D411yescharacteristic
142C4×C8×C43D411yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145#41×C43—22no—
146#41×C43SD1614yescomplemented
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—41no—
157#10621898—42no—
158#10621898—42no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×C8×C43—22no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—41no—
170C2×C8×C43—42no—
171C2×C8×C43—42no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43#4111yescharacteristic
189C42×C43C2411yescharacteristic
190C22⋊Dic43—41no—
191#10621885—42no—
192#10621884—42no—
193#10621883—42no—
194#10621882—42no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—41no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205C4×Dic43—41no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—42no—
211C2×C43⋊C8—42no—
212#10621873—42no—
213#10621873—42no—
214C23×C43—21no—
215C23×C43#12111yescharacteristic
216C22×D43—41no—
217Q8×C43—21no—
218Q8×C43C2×SD1612yes—
219D4×C43—24no—
220D4×C43—21no—
221D4×C43C2×SD1612yes—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—24no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43C2×SD1612yes—
236C2×C4×C43#13512yes—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—82no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—81no—
249C4×D43—82no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—81no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43#13512yescomplemented
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265#19124—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—22no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43#46512yes—
272C22×C43C2×#12111yescharacteristic
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C4×C43—21no—
277C4×C43—22no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43#46512yes—
283C4×C43C22×SD1611yescharacteristic
284C4×C43C2×#13511yescharacteristic
285C4×C43C2×#13511yescharacteristic
286C4×C43#57511yescharacteristic
287Dic43—81no—
288Dic43—81no—
289Dic43—81no—
290#3167—431no—
291#3076—431no—
292#3035—431no—
293C8×#41D4311yescharacteristic, complemented
294#1680—431no—
295#1679—431no—
296#1678—431no—
297#1677—431no—
298#1672—431no—
299#1671—431no—
300#1666—431no—
301#1665—431no—
302C2×#334—431no—
303#1542—431no—
304#1540—431no—
305C2×C43—22no—
306C2×C43—42no—
307C2×C43#303511yescharacteristic
308C2×C43C2×#46511yescharacteristic
309C2×C43#306711yescharacteristic
310D43—161no—
311C2×#135—861no—
312#533—431no—
313#532—431no—
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—861no—
328#463—861no—
329#462—431no—
330#461—431no—
331#460—431no—
332#459—431no—
333C8×Q8C2×D4311yescharacteristic
334C8×Q8C2×D4311yescharacteristic
335C4×SD16—861no—
336C4×SD16—861no—
337C8×D4—21no—
338C8×D4—21no—
339C8×D4C2×D4311yescharacteristic
340C8×D4C2×D4311yescharacteristic
341#431—21no—
342#431C2×D4311yescharacteristic
343#427—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8—431no—
346#416—861no—
347#416—861no—
348C2×C4×C8—21no—
349C2×C4×C8C2×D4311yescharacteristic
350#334—431no—
351#334—431no—
352#334—431no—
353#334—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#1912411yescharacteristic, complemented, Sylow
363C2×#41—861no—
364C2×#41D17211yescharacteristic
365#135—1724no—
366C2×Q16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—861no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—861no—
375C22×C8—861no—
376C22×C8C22⋊D4311yescharacteristic
377C22×C8C22⋊D4311yescharacteristic
378C4⋊Q8—431no—
379C4⋊Q8—431no—
380C4⋊Q8—431no—
381#127—431no—
382#125—861no—
383#124—861no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386#121—861no—
387#121—861no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8D17211yescharacteristic
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4D17211yescharacteristic
397C4×D4C22×D4311yescharacteristic
398#117—21no—
399#117—861no—
400#117D17211yescharacteristic
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—21no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—861no—
416C4⋊C8—861no—
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C22⋊D4311yescharacteristic
438C4×C8C22⋊D4311yescharacteristic
439C4×C8C22×D4311yescharacteristic
440C4×C8C22×D4311yescharacteristic
441#41—22no—
442#41—1722no—
443#41—1722no—
444#41#1062187314yescomplemented
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8C2×D17211yescharacteristic
449C2×D4—21no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—1721no—
454C2×D4C2×D17211yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—1721no—
459C22×C4C2×D17211yescharacteristic
460C22×C4#1062189811yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462Q16—1722no—
463SD16—1722no—
464SD16—1722no—
465SD16—1722no—
466SD16—1722no—
467D8—1722no—
468C2×C8—22no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—41no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—1722no—
479C2×C8—1722no—
480C2×C8C2×C22⋊D4311yescharacteristic
481C2×C8C2×C22⋊D4311yescharacteristic
482C2×C8C2×C22⋊D4311yescharacteristic
483C2×C8C2×C22⋊D4311yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4C2×D17211yescharacteristic
495C4⋊C4C2×D17211yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—1721no—
506C42C2×D17211yescharacteristic
507C42#1062189811yescharacteristic
508C42C2×C22⋊D4311yescharacteristic
509C42C23×D4311yescharacteristic
510C23—21no—
511C23—1721no—
512C23#1306329911yescharacteristic
513Q8—21no—
514Q8—3441no—
515Q8—1721no—
516Q8—1721no—
517Q8—1721no—
518Q8—1721no—
519Q8C2×#1062187312yes—
520D4—24no—
521D4—21no—
522D4—3441no—
523D4—3442no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528D4C2×#1062187312yes—
529C2×C4—21no—
530C2×C4—24no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—3442no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329911yescharacteristic
544C2×C4#1306329911yescharacteristic
545C2×C4#1306329911yescharacteristic
546C2×C4C2×#1062187312yes—
547C2×C4#1306334712yes—
548C2×C4C22×C22⋊D4311yescharacteristic
549C2×C4C22×D17211yescharacteristic
550C2×C4C2×#1062189811yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C8#1306334512yescomplemented
561C22—21no—
562C22—21no—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—3441no—
567C22—3441no—
568C22—3441no—
569C22#1458312812yes—
570C22C2×#1306329911yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—3441no—
578C4—3441no—
579C4—3441no—
580C4#1458312812yes—
581C4C22×#1062187311yescharacteristic
582C4C2×#1306334511yescharacteristic
583C4C2×#1306334711yescharacteristic
584C4#1458369711yescharacteristic
585C2—22no—
586C2—42no—
587C2—6881no—
588C2#1914405011yescharacteristic
589C2C2×#1458312811yescharacteristic
590C2#1914431511yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC8×#41×C43C2
socleC22×C43C2×#121
prime radical#19144050C2
hypercenterC8×#41D43
hypocenterC43#19124
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. #19145154C2semidirect
2. #19144383C2semidirect
4. #19134025C2semidirect
5. #19134018C2semidirect
6. #19134011C2semidirect
7. #19134004C2semidirect
8. #19133977C2semidirect
9. #19133970C2semidirect
10. #19133943C2semidirect
11. #19133936C2semidirect
12. C2×#14582650C2semidirect
13. #19133250C2semidirect
14. #19133242C2semidirect
15. C8×#41×C43C2semidirect
146. #41×C43SD16semidirect
260. C8×C43#135semidirect
293. C8×#41D43semidirect
362. C43#19124semidirect
444. #41#10621873semidirect
560. C8#13063345semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191443832
#191440502
#191340252
#191340182
#191340112
#191340042
#191339772
#191339702
#191339432
#191339362
C2×#145826502
#191332502
#191332422
C8×#41×C432
#1912443