Finite Group Databasebeta

← #25086786

Subgroups — #25086786

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
2D8×Dic86C211yesmaximal, characteristic
3#19146472C211yesmaximal, characteristic, complemented
4D4×Dic172C211yesmaximal, characteristic, complemented
5#19134272C211yesmaximal, characteristic, complemented
6#19134114C211yesmaximal, characteristic, complemented
7#19134046C211yesmaximal, characteristic, complemented
8#19133978C211yesmaximal, characteristic, complemented
9#19133960C211yesmaximal, characteristic, complemented
10#19133847C211yesmaximal, characteristic, complemented
11#19133847C211yesmaximal, characteristic, complemented
12#19133812C211yesmaximal, characteristic, complemented
13#19133763C211yesmaximal, characteristic, complemented
14#19133447C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic
16C22×Dic172—21no—
17#14583606C2211yescharacteristic
18D4×Dic86C2211yescharacteristic
19D4×Dic86C2211yescharacteristic
20D4×Dic86C2211yescharacteristic
21#14583307—21no—
22#14583304C2211yescharacteristic
23#14583304C2211yescharacteristic
24#14583303—21no—
25#14583297C2211yescharacteristic
26#14583279C2211yescharacteristic
27#14583250C2211yescharacteristic
28#14583250C2211yescharacteristic
29#14583235—21no—
30#14583201—21no—
31#14583195C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583187—21no—
34#14583179C2211yescharacteristic
35#14583179C2211yescharacteristic
36#14583179C2211yescharacteristic
37#14583177—21no—
38#14583177—21no—
39#14583140—21no—
40#14583140—21no—
41#14583110C2211yescharacteristic
42#14583110C2211yescharacteristic
43#14583110C2211yescharacteristic
44#14583057—21no—
45#14583057—21no—
46#14583057—21no—
47#14583029C2211yescharacteristic
48C8×Dic86C2211yescharacteristic
49#14583011—21no—
50C4×Dic172C2211yescharacteristic
51D8×Dic43—21no—
52C2×#13063250—21no—
53#14582652C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582631C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C22×Dic86—21no—
68C22×Dic86—21no—
69C22×Dic86—21no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×Dic172—21no—
73C2×Dic172—21no—
74C2×Dic172—21no—
75C2×Dic172—44no—
76C2×Dic172D411yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063324—21no—
82#13063324—21no—
83#13063324—21no—
84#13063316—21no—
85#13063304—21no—
86#13063304—21no—
87#13063304—21no—
88#13063304—21no—
89#13063302—41no—
90#13063302—41no—
91#13063302—41no—
92#13063302—41no—
93C4×Dic86C2311yescharacteristic
94C4×Dic86C2311yescharacteristic
95D4×Dic43—21no—
96D4×Dic43—21no—
97D4×Dic43—21no—
98D4×Dic43—21no—
99C2×C4⋊Dic43—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—41no—
104#13063259D411yescharacteristic
105#13063258—21no—
106#13063258—21no—
107#13063258—21no—
108#13063257—21no—
109#13063257—21no—
110#13063256—21no—
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063250—21no—
121#13063250—41no—
122#13063250D411yescharacteristic
123#13063250D411yescharacteristic
124#13063246—21no—
125#13063246—21no—
126#13063246—21no—
127#13063246—21no—
128#13063235—21no—
129C8×Dic43—21no—
130C2×D8×C43D411yescharacteristic
131C22×C8×C43—21no—
132C22×C8×C43—21no—
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#102×C43D411yescharacteristic
139#102×C43D411yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×D4×C43C2×D411yescharacteristic
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×Dic43—41no—
150C22×Dic43—41no—
151C22×Dic43—41no—
152C22×Dic43—41no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—42no—
158C2×Dic86—42no—
159C2×Dic86—42no—
160C2×Dic86—41no—
161C2×Dic86—41no—
162C2×Dic86—41no—
163C2×Dic86—81no—
164C2×Dic86—81no—
165C2×Dic86—81no—
166C2×Dic86C2×D411yescharacteristic
167C2×Dic86C2×D411yescharacteristic
168D8×C43Q1614yescomplemented
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—42no—
173C2×C8×C43—81no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208Dic172—22no—
209Dic172—42no—
210Dic172—42no—
211Dic172—42no—
212Dic172—81no—
213Dic172—81no—
214C23×C43—21no—
215C23×C43—21no—
216D4×C43—21no—
217D4×C43—21no—
218D4×C43C2×Q1612yes—
219D4×C43C2×Q1612yescomplemented
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—82no—
238C2×Dic43—82no—
239C2×Dic43—82no—
240C2×Dic43—161no—
241Dic86—21no—
242Dic86—21no—
243Dic86—21no—
244Dic86—41no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—82no—
251Dic86—82no—
252Dic86—82no—
253Dic86—81no—
254Dic86AGL(1,ℤ/8)12yes—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43C2×Q1612yescomplemented
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—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43C22×Q1611yescharacteristic
276C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C43#57611yescharacteristic
278C4×C43#57811yescharacteristic
279Dic43—22no—
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287#3384—431no—
288Q8×D8—431no—
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#1580D4311yescharacteristic
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×Q8—431no—
311D4×Q8—431no—
312#501—861no—
313#500—431no—
314#500—431no—
315#500—861no—
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—431no—
326#474—431no—
327#474—431no—
328#474—861no—
329#474—861no—
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×Q8—431no—
340#442—861no—
341C4×Q16—431no—
342C4×D8—861no—
343C4×D8C2×D4311yescharacteristic
344C8×D4C2×D4311yescharacteristic
345C8×D4C2×D4311yescharacteristic
346C2×#103—861no—
347#335—431no—
348#334C2×D4311yescharacteristic
349#333—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353Q8⋊C8—431no—
354Q8⋊C8—431no—
355D4⋊C8C2×D4311yescharacteristic
356D4⋊C8C2×D4311yescharacteristic
357#322C2×D4311yescharacteristic
358C43#1981111yescharacteristic, complemented, Sylow
359C22×Q8—861no—
360C22×Q8—861no—
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×D8D17211yescharacteristic
370C22×C8—21no—
371C22×C8—21no—
372C4⋊Q8—431no—
373C4⋊Q8—431no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8—861no—
377C4⋊Q8—861no—
378C4⋊Q8—861no—
379#125—861no—
380C22⋊Q8—861no—
381C22⋊Q8—861no—
382C22⋊Q8—861no—
383C22⋊Q8—861no—
384C22⋊Q8—1721no—
385C22⋊Q8—1721no—
386C22⋊Q8—1721no—
387C22⋊Q8—1721no—
388C4×Q8—431no—
389C4×Q8—431no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4—861no—
394C4×D4C22×D4311yescharacteristic
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#107D17211yescharacteristic
406#106—861no—
407#106—861no—
408#106—861no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8C22×D4311yescharacteristic
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—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102D17211yescharacteristic
429#102D17211yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432#97—861no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436C4×C8C22×D4311yescharacteristic
437C2×Q8—431no—
438C2×Q8—431no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—3441no—
444C2×Q8—3441no—
445C2×Q8—3441no—
446C2×Q8—1721no—
447C2×Q8—1721no—
448C2×Q8—1721no—
449C2×Q8—1722no—
450C2×Q8—1722no—
451C2×Q8—1722no—
452C2×D4C2×D17211yescharacteristic
453C2×D4C2×D17211yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—1721no—
457C22×C4—1721no—
458C22×C4—1721no—
459C22×C4—1721no—
460Q16—862no—
461Q16—3441no—
462Q16—3441no—
463Q16—1722no—
464Q16—1722no—
465Q16—1722no—
466D8Dic17214yescomplemented
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—42no—
471C2×C8—81no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8C2×D17211yescharacteristic
475C2×C8C2×D17211yescharacteristic
476C2×C8D4×D4311yescharacteristic
477C2×C8D4×D4311yescharacteristic
478C4⋊C4—431no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C4⋊C4C2×D17211yescharacteristic
496C4⋊C4C2×D17211yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C42—861no—
504C42—861no—
505C42C23×D4311yescharacteristic
506C23—21no—
507C23—21no—
508Q8—432no—
509Q8—861no—
510Q8—861no—
511Q8—861no—
512Q8—3441no—
513Q8—3442no—
514Q8—3442no—
515Q8—3442no—
516Q8—1721no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520Q8—1721no—
521Q8—1721no—
522D4—21no—
523D4—21no—
524D4C2×Dic17212yes—
525D4C2×Dic17212yescomplemented
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—3442no—
537C2×C4—3442no—
538C2×C4—3442no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—6881no—
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C22×D17211yescharacteristic
546C2×C4#1306337111yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—1721no—
554C8—1721no—
555C8C2×Dic17212yescomplemented
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22D4×D17211yescharacteristic
563C4—21no—
564C4—41no—
565C4—41no—
566C4—862no—
567C4—3441no—
568C4—3441no—
569C4—3441no—
570C4—3441no—
571C4—1721no—
572C4—1721no—
573C4—1721no—
574C4C22×Dic17211yescharacteristic
575C4AGL(1,ℤ/8)×D4311yescharacteristic
576C4#1458370311yescharacteristic
577C4#1458371611yescharacteristic
578C2—42no—
579C2—42no—
580C2#1914607711yescharacteristic
581C2D4×Dic17211yescharacteristic
582C2#1914637111yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1580C2
socleC22×C43D42
prime radicalC2×D8×C43D4
hypercenter#1580D43
hypocenterC43#19811
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1580

Complements

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

NH ≅ G/Ntype
3. #19146472C2semidirect
4. D4×Dic172C2semidirect
5. #19134272C2semidirect
6. #19134114C2semidirect
7. #19134046C2semidirect
8. #19133978C2semidirect
9. #19133960C2semidirect
10. #19133847C2semidirect
11. #19133847C2semidirect
12. #19133812C2semidirect
13. #19133763C2semidirect
14. #19133447C2semidirect
168. D8×C43Q16semidirect
219. D4×C43C2×Q16semidirect
261. C8×C43C2×Q16semidirect
358. C43#19811semidirect
466. D8Dic172semidirect
525. D4C2×Dic172semidirect
555. C8C2×Dic172semidirect

Maximal subgroups

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

subgroupindex
#191474922
D8×Dic862
#191464722
D4×Dic1722
#191342722
#191341142
#191340462
#191339782
#191339602
#191338472
#191338122
#191337632
#191334472
C43×#15802
#1981143