Finite Group Databasebeta

← #25086780

Subgroups — #25086780

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#19147490C211yesmaximal, characteristic
2Q8×#10621882C211yesmaximal, characteristic
3#19146473C211yesmaximal, characteristic, complemented
4#19134270C211yesmaximal, characteristic, complemented
5#19134111C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19133975C211yesmaximal, characteristic, complemented
8#19133957C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic, complemented
10#19133842C211yesmaximal, characteristic, complemented
11#19133807C211yesmaximal, characteristic, complemented
12#19133760C211yesmaximal, characteristic, complemented
13#19133446C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic
15D4×Q16×C43C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17Q8×D172C2211yescharacteristic
18#14583305—21no—
19#14583302—21no—
20#14583302C2211yescharacteristic
21#14583302C2211yescharacteristic
22#14583295C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583236—21no—
26#14583199—21no—
27#14583194C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583186—21no—
30#14583179—21no—
31#14583179C2211yescharacteristic
32#14583176—21no—
33#14583176C2211yescharacteristic
34#14583176C2211yescharacteristic
35#14583139—21no—
36#14583109C2211yescharacteristic
37#14583053—21no—
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14583009—21no—
41C4×#10621882—21no—
42C4×#10621882C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#103×D43—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56C22×Q16×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58D4×Q8×C43C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#467—21no—
61C43×#462C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C43×#451—21no—
64C43×#451—21no—
65C4×Q16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×#10621885—21no—
69C2×#10621882D411yescharacteristic
70C2×C8×D43—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063317—21no—
75#13063305—21no—
76#13063305—41no—
77#13063303—41no—
78#13063301—21no—
79C4×D172—21no—
80C4×D172—21no—
81C4×D172C2311yescharacteristic
82C4⋊C4×D43—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—41no—
90#13063258D411yescharacteristic
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063248—21no—
103#13063248—41no—
104#13063246—21no—
105#13063246—21no—
106#13063246D411yescharacteristic
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111#13063236—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C22×Q8×C43—21no—
117C2×Q16×C43—21no—
118C2×Q16×C43—21no—
119C2×Q16×C43—21no—
120C2×Q16×C43—21no—
121C2×Q16×C43—44no—
122C2×Q16×C43D411yescharacteristic
123C22×C8×C43—21no—
124C4⋊Q8×C43—21no—
125C4⋊Q8×C43—21no—
126C4⋊Q8×C43C2311yescharacteristic
127C4⋊Q8×C43C2311yescharacteristic
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—41no—
131C22⋊Q8×C43—41no—
132C4×Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137#107×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
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—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43—81no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159Q8×D43—42no—
160Q8×D43—81no—
161C2×D172C2×D411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—41no—
164C2×C4×D43—41no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—41no—
168Q16×C43—22no—
169Q16×C43—42no—
170Q16×C43—42no—
171Q16×C43—42no—
172Q16×C43—81no—
173C2×C8×C43—21no—
174C2×C8×C43—42no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43C2411yescharacteristic
194#10621885—81no—
195#10621882Q1614yescomplemented
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—41no—
198(C2×D43)⋊C4—41no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—41no—
204C4⋊Dic43C2×D411yescharacteristic
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C8×D43—81no—
214C23×C43—21no—
215C22×D43—21no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—82no—
224Q8×C43—82no—
225Q8×C43AGL(1,ℤ/8)12yes—
226D4×C43—21no—
227D4×C43C2×Q1612yes—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—82no—
238C2×C4×C43—82no—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245D172—21no—
246D172C2×Q1612yescomplemented
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—82no—
250C4×D43—161no—
251Dic86—41no—
252Dic86—41no—
253Dic86—82no—
254Dic86—81no—
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#3299—431no—
290D4×Q16D4311yescharacteristic, complemented
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—21no—
308#554—431no—
309D4×Q8—431no—
310D4×Q8C2×D4311yescharacteristic
311D4×Q8C2×D4311yescharacteristic
312#501—861no—
313#500—431no—
314#500—431no—
315#500—861no—
316#498—431no—
317#494C2×D4311yescharacteristic
318#487—431no—
319#487—431no—
320#484—861no—
321#478—861no—
322#477—431no—
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#462C2×D4311yescharacteristic
334#462C2×D4311yescharacteristic
335#451—21no—
336#451—21no—
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—861no—
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—21no—
361C22×Q8—861no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—44no—
367C2×Q16—861no—
368C2×Q16C22⋊D4311yescharacteristic
369C2×D8—431no—
370C22×C8—21no—
371C22×C8—861no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8—861no—
377C4⋊Q8C22×D4311yescharacteristic
378C4⋊Q8C22×D4311yescharacteristic
379#125—861no—
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—861no—
397#107—431no—
398#107—861no—
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—861no—
418#103—861no—
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—41no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8—81no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—3441no—
448C2×Q8—1721no—
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—42no—
462Q16—42no—
463Q16—42no—
464Q16—81no—
465Q16—3441no—
466D8—434no—
467C2×C8—21no—
468C2×C8—42no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—3441no—
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—431no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—1721no—
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—41no—
514Q8—41no—
515Q8—82no—
516Q8—82no—
517Q8—3441no—
518Q8—3442no—
519Q8—1721no—
520Q8—1721no—
521Q8#1306335112yes—
522D4—21no—
523D4—432no—
524D4—861no—
525D4Q16×D4312yes—
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—82no—
537C2×C4—861no—
538C2×C4—3442no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—6881no—
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×#1306335111yescharacteristic
576C4#1458370211yescharacteristic
577C4#1458371211yescharacteristic
578C2—42no—
579C2—1722no—
580C2#1914607111yescharacteristic
581C2Q16×C22⋊D4311yescharacteristic
582C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×Q16×C43C2
socleC22×C43D42
prime radicalC2×#10621882D4
hypercenterD4×Q16D43
hypocenterC43#19811
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
3. #19146473C2semidirect
4. #19134270C2semidirect
5. #19134111C2semidirect
6. #19134046C2semidirect
7. #19133975C2semidirect
8. #19133957C2semidirect
9. #19133844C2semidirect
10. #19133842C2semidirect
11. #19133807C2semidirect
12. #19133760C2semidirect
13. #19133446C2semidirect
15. D4×Q16×C43C2semidirect
195. #10621882Q16semidirect
246. D172C2×Q16semidirect
263. C43⋊C8C2×Q16semidirect
290. D4×Q16D43semidirect
358. C43#19811semidirect

Maximal subgroups

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

subgroupindex
#191474902
Q8×#106218822
#191464732
#191342702
#191341112
#191340462
#191339752
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