Finite Group Databasebeta

← #25086784

Subgroups — #25086784

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#19147492C211yesmaximal, characteristic
2#19146471C211yesmaximal, characteristic, complemented
3D4×#10621885C211yesmaximal, characteristic, complemented
4#19134273C211yesmaximal, characteristic, complemented
5#19134110C211yesmaximal, characteristic, complemented
6#19134044C211yesmaximal, characteristic, complemented
7#19133977C211yesmaximal, characteristic, complemented
8#19133958C211yesmaximal, characteristic, complemented
9#19133844C211yesmaximal, characteristic, complemented
10#19133843C211yesmaximal, characteristic, complemented
11#19133808C211yesmaximal, characteristic, complemented
12#19133760C211yesmaximal, characteristic, complemented
13#19133445C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic
15Q8×D8×C43C211yesmaximal, characteristic
16C22×#10621885—21no—
17#14583606C2211yescharacteristic
18D4×Dic86C2211yescharacteristic
19#14583307—21no—
20#14583302C2211yescharacteristic
21#14583297C2211yescharacteristic
22#14583278C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583232—21no—
26#14583201—21no—
27#14583194C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583187—21no—
30#14583179C2211yescharacteristic
31#14583138—21no—
32#14583138—21no—
33#14583109C2211yescharacteristic
34#14583106C2211yescharacteristic
35#14583106C2211yescharacteristic
36#14583055—21no—
37#14583055—21no—
38#14583054—21no—
39#14583029C2211yescharacteristic
40#14583011—21no—
41C4×#10621885C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063249—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56D4×Q8×C43C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#500—21no—
59C43×#500C2211yescharacteristic
60C43×#474—21no—
61C43×#474—21no—
62C43×#474C2211yescharacteristic
63C43×#474C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×D8×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×#10621885—44no—
74C2×#10621885D411yescharacteristic
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063316—21no—
81#13063304—21no—
82#13063304—21no—
83#13063302—41no—
84#13063302—41no—
85C4×Dic86C2311yescharacteristic
86D4×Dic43—21no—
87D4×Dic43—21no—
88C2×C4⋊Dic43—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—41no—
92#13063258D411yescharacteristic
93#13063257—21no—
94#13063257—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249D411yescharacteristic
106#13063248—21no—
107#13063248—41no—
108#13063248D411yescharacteristic
109#13063246—21no—
110#13063246—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063235—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×Q8×C43—21no—
117C22×Q8×C43—21no—
118C2×D8×C43D411yescharacteristic
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136#107×C43D411yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C4×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×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×Dic43—41no—
161C22×Dic43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—42no—
165C2×Dic86—41no—
166C2×Dic86—81no—
167C2×Dic86C2×D411yescharacteristic
168D8×C43Q1614yescomplemented
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C42×C43—21no—
187C42×C43C2411yescharacteristic
188C22⋊Dic43—41no—
189C22⋊Dic43—41no—
190#10621885—22no—
191#10621885—42no—
192#10621885—42no—
193#10621885—42no—
194#10621885—81no—
195#10621885—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—41no—
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205C4×Dic43—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—42no—
211C2×C43⋊C8—81no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214C23×C43—21no—
215C23×C43—21no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—82no—
222Q8×C43—82no—
223Q8×C43AGL(1,ℤ/8)12yes—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43C2×Q1612yes—
227D4×C43C2×Q1612yescomplemented
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43—82no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—82no—
248C2×Dic43—161no—
249Dic86—21no—
250Dic86—21no—
251Dic86—41no—
252Dic86—41no—
253Dic86—82no—
254Dic86—81no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43C2×Q1612yescomplemented
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19811—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43D4211yescharacteristic
272C4×C43—22no—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43C22×Q1611yescharacteristic
280C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C43#57611yescharacteristic
282C4×C43#57811yescharacteristic
283Dic43—41no—
284Dic43—41no—
285Dic43—81no—
286Dic43—81no—
287#3384—431no—
288Q8×D8D4311yescharacteristic
289#3299—431no—
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—42no—
304C2×C43#326411yescharacteristic
305C2×C43D4×Q1611yescharacteristic
306C2×C43#328911yescharacteristic
307C22×Q16—861no—
308#554—431no—
309D4×Q8—431no—
310D4×Q8C2×D4311yescharacteristic
311D4×Q8C2×D4311yescharacteristic
312#501—861no—
313#500—21no—
314#500—431no—
315#500C2×D4311yescharacteristic
316#498—431no—
317#494—431no—
318#487—431no—
319#487—431no—
320#484—861no—
321#478—861no—
322#477—431no—
323#476—431no—
324#476—861no—
325#474—21no—
326#474—21no—
327#474—431no—
328#474C2×D4311yescharacteristic
329#474C2×D4311yescharacteristic
330#467—861no—
331#467—861no—
332#462—431no—
333#462—431no—
334#462—431no—
335#451—861no—
336#451—861no—
337#451—861no—
338#446—431no—
339C8×Q8C2×D4311yescharacteristic
340#442—861no—
341C4×Q16—431no—
342C4×D8—21no—
343C4×D8C2×D4311yescharacteristic
344C8×D4—431no—
345C8×D4—431no—
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—431no—
363C2×Q16—861no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×Q16—861no—
368C2×Q16—1724no—
369C2×D8C22⋊D4311yescharacteristic
370C22×C8—861no—
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×Q8—431no—
389C4×Q8C22×D4311yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—861no—
393C4×D4—861no—
394C4×D4C22×D4311yescharacteristic
395C4×D4C22×D4311yescharacteristic
396C2×C4⋊C4—861no—
397#107—21no—
398#107—21no—
399#107—21no—
400#107—21no—
401#107—431no—
402#107—861no—
403#107—861no—
404#107—1721no—
405#107C22⋊D4311yescharacteristic
406#106—861no—
407#106—861no—
408#106—861no—
409C4⋊C8—21no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415#103—431no—
416#103—431no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—1721no—
424#102—21no—
425#102—21no—
426#102—861no—
427#102—861no—
428#102C22⋊D4311yescharacteristic
429#102C22⋊D4311yescharacteristic
430C22⋊C8—861no—
431C22⋊C8—861no—
432#97—861no—
433C4×C8—21no—
434C4×C8—431no—
435C4×C8—431no—
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—431no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—3441no—
449C2×Q8—1721no—
450C2×Q8—1722no—
451C2×Q8D4×D4311yescharacteristic
452C2×D4C2×C22⋊D4311yescharacteristic
453C2×D4C2×C22⋊D4311yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—1721no—
459C22×C4—1721no—
460Q16—862no—
461Q16—3441no—
462Q16—3441no—
463Q16—1722no—
464Q16—1722no—
465Q16—1722no—
466D8#1062188514yescomplemented
467C2×C8—21no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—3441no—
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—41no—
484C4⋊C4—41no—
485C4⋊C4—431no—
486C4⋊C4—861no—
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—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C42—21no—
504C42—861no—
505C42C23×D4311yescharacteristic
506C23—21no—
507C23—21no—
508Q8—21no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—82no—
514Q8—82no—
515Q8—861no—
516Q8—861no—
517Q8—3441no—
518Q8—3442no—
519Q8—1721no—
520Q8—1721no—
521Q8#1306334912yes—
522D4—21no—
523D4—21no—
524D4C2×#1062188512yes—
525D4C2×#1062188512yescomplemented
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—3442no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—6881no—
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C22×C22⋊D4311yescharacteristic
546C2×C4#1306337011yescharacteristic
547C8—21no—
548C8—41no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C8C2×#1062188512yescomplemented
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22D4×C22⋊D4311yescharacteristic
563C4—22no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—3441no—
571C4—3441no—
572C4—1721no—
573C4—1721no—
574C4C22×#1062188511yescharacteristic
575C4C2×#1306334911yescharacteristic
576C4#1458370011yescharacteristic
577C4#1458371411yescharacteristic
578C2—42no—
579C2—42no—
580C2#1914607511yescharacteristic
581C2D4×#1062188511yescharacteristic
582C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×D8×C43C2
socleC22×C43D42
prime radicalC2×D8×C43D4
hypercenterQ8×D8D43
hypocenterC43#19811
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8×D8

Complements

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

NH ≅ G/Ntype
2. #19146471C2semidirect
3. D4×#10621885C2semidirect
4. #19134273C2semidirect
5. #19134110C2semidirect
6. #19134044C2semidirect
7. #19133977C2semidirect
8. #19133958C2semidirect
9. #19133844C2semidirect
10. #19133843C2semidirect
11. #19133808C2semidirect
12. #19133760C2semidirect
13. #19133445C2semidirect
168. D8×C43Q16semidirect
227. D4×C43C2×Q16semidirect
257. C8×C43C2×Q16semidirect
358. C43#19811semidirect
466. D8#10621885semidirect
525. D4C2×#10621885semidirect
555. C8C2×#10621885semidirect

Maximal subgroups

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

subgroupindex
#191474922
#191464712
D4×#106218852
#191342732
#191341102
#191340442
#191339772
#191339582
#191338442
#191338432
#191338082
#191337602
#191334452
#191334192
Q8×D8×C432
#1981143