Finite Group Databasebeta

← #25086785

Subgroups — #25086785

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147494C211yesmaximal, characteristic
2Q8×#10621882C211yesmaximal, characteristic
3Q16×D172C211yesmaximal, characteristic, complemented
4#19134274C211yesmaximal, characteristic, complemented
5#19134111C211yesmaximal, characteristic, complemented
6#19134043C211yesmaximal, characteristic, complemented
7#19133979C211yesmaximal, characteristic, complemented
8#19133960C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic, complemented
10#19133842C211yesmaximal, characteristic, complemented
11#19133809C211yesmaximal, characteristic, complemented
12#19133758C211yesmaximal, characteristic, complemented
13#19133446C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic
15C43×#3299C211yesmaximal, characteristic, complemented
16C2×Q16×D43—21no—
17Q8×D172C2211yescharacteristic
18Q8×D172C2211yescharacteristic
19#14583309—21no—
20#14583302—21no—
21#14583302C2211yescharacteristic
22#14583302C2211yescharacteristic
23#14583295C2211yescharacteristic
24#14583279C2211yescharacteristic
25#14583249C2211yescharacteristic
26#14583196—21no—
27#14583189—21no—
28#14583186C2211yescharacteristic
29#14583179—21no—
30#14583179C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583176—21no—
33#14583176C2211yescharacteristic
34#14583141—21no—
35#14583109C2211yescharacteristic
36#14583109C2211yescharacteristic
37#14583056—21no—
38#14583056—21no—
39#14583030C2211yescharacteristic
40Q8×C43⋊C8C2211yescharacteristic
41#14583009—21no—
42C4×#10621882—21no—
43C4×#10621882C2211yescharacteristic
44C8×D172C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#554C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#484—21no—
60C43×#477C2211yescharacteristic
61C43×#467—21no—
62C43×#462C2211yescharacteristic
63C43×#451—21no—
64C4×Q16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#103×C43—21no—
67C2×Q8×D43—21no—
68C2×Q8×D43—21no—
69C2×Dic172—21no—
70C2×Dic172—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73Q16×D43—44no—
74C2×#10621882D411yescharacteristic
75C2×C8×D43—21no—
76#13063325—21no—
77#13063325—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063305—21no—
81#13063305—21no—
82#13063305—41no—
83#13063305—41no—
84C4×D172—21no—
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—41no—
93#13063258D411yescharacteristic
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102#13063249—41no—
103#13063248—21no—
104#13063248—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245—21no—
110#13063245D411yescharacteristic
111(C2×D43)⋊C8—21no—
112#13063236—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×Q8×C43—21no—
117C2×Q16×C43—21no—
118C2×Q16×C43D411yescharacteristic
119C22×C8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#125×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—41no—
127C22⋊Q8×C43—41no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134#107×C43—21no—
135#107×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#103×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×C4×C43—41no—
156Q8×D43—42no—
157Q8×D43—42no—
158Q8×D43—81no—
159Q8×D43—81no—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—41no—
163C2×C4×D43—41no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—41no—
167C2×Dic86—41no—
168Q16×C43—22no—
169Q16×C43—81no—
170C2×C8×C43—21no—
171C2×C8×C43—81no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43C2411yescharacteristic
192#10621885—42no—
193#10621885—42no—
194#10621882Q1614yescomplemented
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—41no—
197(C2×D43)⋊C4—41no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43—41no—
204C4⋊Dic43C2×D411yescharacteristic
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211Dic172—42no—
212Dic172—81no—
213C8×D43—42no—
214C23×C43—21no—
215C22×D43—21no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—82no—
222Q8×C43—81no—
223Q8×C43AGL(1,ℤ/8)12yes—
224D4×C43—21no—
225D4×C43C2×Q1612yescomplemented
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—82no—
236C2×C4×C43—161no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243D172—21no—
244D172C2×Q1612yes—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—82no—
248C4×D43—82no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—82no—
254Dic86—82no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—41no—
258C43⋊C8—21no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8C2×Q1612yescomplemented
264#19811—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43D4211yescharacteristic
269C2×D43—22no—
270C2×D43—41no—
271C2×D43—41no—
272C4×C43—22no—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43C22×Q1611yescharacteristic
281C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C4×C43#57611yescharacteristic
283C4×C43#57811yescharacteristic
284Dic43—41no—
285Dic43—81no—
286Dic43—81no—
287#3384—431no—
288Q8×D8—431no—
289#3299D4311yescharacteristic, complemented
290D4×Q16—431no—
291#1723—431no—
292#1694—431no—
293#1683—431no—
294#1672—431no—
295#1669—431no—
296#1649—431no—
297#1649—431no—
298#1644—431no—
299#1637—431no—
300#1584—431no—
301#1580—431no—
302C2×C43—42no—
303C2×C43#326411yescharacteristic
304C2×C43D4×Q1611yescharacteristic
305C2×C43#328911yescharacteristic
306D43—42no—
307C22×Q16—861no—
308#554C2×D4311yescharacteristic
309D4×Q8—431no—
310D4×Q8—431no—
311D4×Q8C2×D4311yescharacteristic
312#501—861no—
313#500—431no—
314#500—431no—
315#500—861no—
316#498—431no—
317#494—431no—
318#487—431no—
319#487C2×D4311yescharacteristic
320#484—21no—
321#478—861no—
322#477C2×D4311yescharacteristic
323#476—431no—
324#476—861no—
325#474—431no—
326#474—431no—
327#474—431no—
328#474—861no—
329#474—861no—
330#467—21no—
331#467—861no—
332#462—431no—
333#462—431no—
334#462C2×D4311yescharacteristic
335#451—21no—
336#451—861no—
337#451—861no—
338#446—431no—
339C8×Q8—431no—
340#442—861no—
341C4×Q16C2×D4311yescharacteristic
342C4×D8—431no—
343C4×D8—861no—
344C8×D4—431no—
345C8×D4C2×D4311yescharacteristic
346C2×#103—21no—
347#335—431no—
348#334—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353Q8⋊C8—431no—
354Q8⋊C8—431no—
355D4⋊C8—431no—
356D4⋊C8—431no—
357#322—431no—
358C43#1981111yescharacteristic, complemented, Sylow
359C22×Q8—21no—
360C22×Q8—861no—
361C22×Q8—861no—
362C2×Q16—21no—
363C2×Q16—861no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×Q16—1724no—
368C2×Q16C22⋊D4311yescharacteristic
369C2×D8—431no—
370C22×C8—21no—
371C22×C8—861no—
372C4⋊Q8—21no—
373C4⋊Q8—431no—
374C4⋊Q8—431no—
375C4⋊Q8—861no—
376C4⋊Q8—861no—
377C4⋊Q8C22×D4311yescharacteristic
378C4⋊Q8C22×D4311yescharacteristic
379#125—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—41no—
383C22⋊Q8—41no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386C22⋊Q8—1721no—
387C22⋊Q8—1721no—
388C4×Q8C22×D4311yescharacteristic
389C4×Q8C22×D4311yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4C22×D4311yescharacteristic
396C2×C4⋊C4—21no—
397#107—21no—
398#107—431no—
399#107—861no—
400#107—861no—
401#107—861no—
402#107—861no—
403#107—861no—
404#107—1721no—
405#107C22⋊D4311yescharacteristic
406#106—861no—
407#106—861no—
408#106—861no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—861no—
420#103—861no—
421#103—1721no—
422#103C22⋊D4311yescharacteristic
423#103C22⋊D4311yescharacteristic
424#102—431no—
425#102—431no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430C22⋊C8—21no—
431C22⋊C8—861no—
432#97—861no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—861no—
436C4×C8C22×D4311yescharacteristic
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—42no—
441C2×Q8—81no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—3441no—
445C2×Q8—3441no—
446C2×Q8—1721no—
447C2×Q8—1721no—
448C2×Q8—1722no—
449C2×Q8—1722no—
450C2×Q8C2×C22⋊D4311yescharacteristic
451C2×Q8C2×C22⋊D4311yescharacteristic
452C2×D4—431no—
453C2×D4D4×D4311yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—861no—
458C22×C4—1721no—
459C22×C4—1721no—
460Q16—22no—
461Q16—81no—
462Q16—3441no—
463Q16—1722no—
464Q16—1722no—
465Q16—1722no—
466D8—434no—
467C2×C8—21no—
468C2×C8—81no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—1722no—
476C2×C8C2×C22⋊D4311yescharacteristic
477C2×C8C2×C22⋊D4311yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—431no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4D4×D4311yescharacteristic
495C4⋊C4C2×C22⋊D4311yescharacteristic
496C4⋊C4C2×C22⋊D4311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—861no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C42—21no—
504C42—21no—
505C42C23×D4311yescharacteristic
506C23—21no—
507C23—861no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—82no—
514Q8—81no—
515Q8—3442no—
516Q8—3442no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520Q8—1721no—
521Q8#1306335012yes—
522D4—21no—
523D4—432no—
524D4—861no—
525D4Q16×D4312yescomplemented
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—161no—
537C2×C4—861no—
538C2×C4—3442no—
539C2×C4—3442no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C22×C22⋊D4311yescharacteristic
546C2×C4#1306337011yescharacteristic
547C8—21no—
548C8—21no—
549C8—41no—
550C8—432no—
551C8—861no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C8—1721no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—862no—
560C22—1721no—
561C22—1721no—
562C22D4×C22⋊D4311yescharacteristic
563C4—22no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—3441no—
572C4—3441no—
573C4—1721no—
574C4C2×Q16×D4311yescharacteristic
575C4C2×#1306335011yescharacteristic
576C4#1458370211yescharacteristic
577C4#1458371211yescharacteristic
578C2—42no—
579C2—1722no—
580C2#1914607611yescharacteristic
581C2Q16×C22⋊D4311yescharacteristic
582C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3299C2
socleC22×C43D42
prime radicalC2×#10621882D4
hypercenter#3299D43
hypocenterC43#19811
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3299

Complements

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

NH ≅ G/Ntype
3. Q16×D172C2semidirect
4. #19134274C2semidirect
5. #19134111C2semidirect
6. #19134043C2semidirect
7. #19133979C2semidirect
8. #19133960C2semidirect
9. #19133844C2semidirect
10. #19133842C2semidirect
11. #19133809C2semidirect
12. #19133758C2semidirect
13. #19133446C2semidirect
15. C43×#3299C2semidirect
194. #10621882Q16semidirect
225. D4×C43C2×Q16semidirect
263. C43⋊C8C2×Q16semidirect
289. #3299D43semidirect
358. C43#19811semidirect
525. D4Q16×D43semidirect

Maximal subgroups

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

subgroupindex
#191474942
Q8×#106218822
Q16×D1722
#191342742
#191341112
#191340432
#191339792
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