Finite Group Databasebeta

← #25084182

Subgroups — #25084182

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145935C211yesmaximal, characteristic
2#19145820C211yesmaximal, characteristic
3#19145735C211yesmaximal, characteristic, complemented
4#19143758C211yesmaximal, characteristic
5#19134169C211yesmaximal, characteristic, complemented
6#19134101C211yesmaximal, characteristic, complemented
7#19134097C211yesmaximal, characteristic, complemented
8#19134051C211yesmaximal, characteristic, complemented
9#19134043C211yesmaximal, characteristic, complemented
10#19133979C211yesmaximal, characteristic, complemented
11#19133971C211yesmaximal, characteristic, complemented
12#19133377C211yesmaximal, characteristic, complemented
13#19133294C211yesmaximal, characteristic, complemented
14#333×D43C211yesmaximal, characteristic, complemented
15C43×#1704C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18#14583436C2211yescharacteristic
19#14583307—21no—
20#14583297C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583260—21no—
23#14583249C2211yescharacteristic
24#14583228—21no—
25#14583228—21no—
26#14583228—21no—
27#14583214—21no—
28#14583209—21no—
29#14583194C2211yescharacteristic
30#14583190C2211yescharacteristic
31#14583186C2211yescharacteristic
32#14583182—21no—
33#14583182—21no—
34#14583176C2211yescharacteristic
35#14583139—21no—
36#14583129—21no—
37#14583124—21no—
38#14583109C2211yescharacteristic
39#14583105C2211yescharacteristic
40Q8×C43⋊C8C2211yescharacteristic
41#14582976C2211yescharacteristic
42#14582972—21no—
43C8×D172C2211yescharacteristic
44#14582964—21no—
45#14582961—21no—
46#14582955C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582924—21no—
49C4⋊C8×D43C2211yescharacteristic
50C4⋊C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C43×#446C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×#10621885—21no—
69C2×#10621873—21no—
70C2×#10621872—21no—
71C2×C8×D43—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—21no—
78#13063323—21no—
79#13063320—21no—
80#13063316—21no—
81#13063316D411yescharacteristic
82#13063314D411yescharacteristic
83#13063310—21no—
84#13063305—21no—
85#13063301—21no—
86#13063301D411yescharacteristic
87#13063300D411yescharacteristic
88Q8×Dic43—21no—
89#13063290—21no—
90C4×D172—21no—
91C4×D172C2311yescharacteristic
92#13063283—21no—
93#13063282—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C42×D43C2311yescharacteristic
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063257—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113#13063250—21no—
114#13063249—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063247—21no—
119#13063245—21no—
120#13063245—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8D411yescharacteristic
125(C2×D43)⋊C8D411yescharacteristic
126#13063235—21no—
127C4×C43⋊C8—21no—
128C4×C43⋊C8C2311yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130C4⋊Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147Q8×D43—82no—
148C2×D172—21no—
149C2×D172C2×D411yescharacteristic
150C2×C4×D43—21no—
151C2×C4×D43—41no—
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43#4111yescharacteristic
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—41no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C2×D411yescharacteristic
169C42×C43—21no—
170C42×C43C2411yescharacteristic
171#10621885—81no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—41no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—41no—
184C4⋊Dic43C2×D411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190C4×Dic43—41no—
191C4×Dic43C2×D411yescharacteristic
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43#4111yescharacteristic
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199#10621873—81no—
200#10621872—81no—
201C8×D43—81no—
202C8×D43—81no—
203C8×D43—81no—
204C22×D43—21no—
205C22×D43#12111yescharacteristic
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—81no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×Dic43—21no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43#12111yescharacteristic
222C2×Dic43#12111yescharacteristic
223C2×Dic43#12111yescharacteristic
224D172—21no—
225D172—21no—
226D172—42no—
227C4×D43—22no—
228C4×D43—21no—
229C4×D43—21no—
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—41no—
233C4×D43—41no—
234C4×D43—82no—
235Dic86—41no—
236Dic86—41no—
237Dic86—82no—
238Dic86—81no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#19588—431nomaximal, Sylow
250C22×C43C2×#12111yescharacteristic
251C2×D43—21no—
252C2×D43—21no—
253C2×D43—41no—
254C2×D43—41no—
255C2×D43—41no—
256C2×D43#47112yes—
257C4×C43—21no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43#57711yescharacteristic
263C4×C43#57711yescharacteristic
264C4×C43#57811yescharacteristic
265C4×C43#57811yescharacteristic
266Dic43—21no—
267Dic43—21no—
268Dic43—21no—
269Dic43—41no—
270Dic43—81no—
271Dic43—81no—
272#3248—431no—
273#3238—431no—
274#3229—431no—
275#2994—431no—
276#1704D4311yescharacteristic, complemented
277#1703—431no—
278#1692—431no—
279#1691—431no—
280#1684—431no—
281#1683—431no—
282#1672—431no—
283#1671—431no—
284#1573—431no—
285#1552—431no—
286C2×#333—431no—
287C2×C43#304611yescharacteristic
288C2×C43#306311yescharacteristic
289C2×C43C2×#47111yescharacteristic
290D43—22no—
291D43—81no—
292#533—431no—
293C2×C4⋊Q8—431no—
294#529—431no—
295#501—861no—
296#498—431no—
297#498—431no—
298#489—861no—
299#487—431no—
300#487C2×D4311yescharacteristic
301#483—861no—
302#483—861no—
303#483—861no—
304#480—861no—
305#479—861no—
306#477—431no—
307#477C2×D4311yescharacteristic
308#476—431no—
309#476—431no—
310#475—861no—
311#475—861no—
312#475C2×D4311yescharacteristic
313#474—431no—
314#467—861no—
315#465—861no—
316#464—861no—
317#462—431no—
318#461—431no—
319#446C2×D4311yescharacteristic
320C8×Q8—431no—
321#436—431no—
322#435—861no—
323C8×D4—431no—
324C8×D4—861no—
325#433—861no—
326#432—431no—
327#431—431no—
328#424—861no—
329C2×C4⋊C8—431no—
330C2×C4⋊C8—431no—
331#335—431no—
332#335—431no—
333#334—431no—
334#334C2×D4311yescharacteristic
335#333—431no—
336#333—431no—
337#333—431no—
338#333C2×D4311yescharacteristic
339#332—431no—
340#332—431no—
341#332—431no—
342#332C2×D4311yescharacteristic
343C43#1958811yescharacteristic, complemented, Sylow
344C22×Q8—861no—
345C2×Q16—861no—
346C2×SD16—861no—
347C2×M16—861no—
348C22×C8—861no—
349C22×C8—861no—
350C22×C8—861no—
351C4⋊Q8—431no—
352C4⋊Q8—431no—
353C4⋊Q8—861no—
354C4⋊Q8—861no—
355C4⋊Q8—861no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—861no—
359#125—431no—
360#125—861no—
361#124—431no—
362#123—861no—
363C22⋊Q8—431no—
364C22⋊Q8—861no—
365C22⋊Q8—861no—
366#121—431no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8C22×D4311yescharacteristic
370C4×D4—431no—
371C4×D4—861no—
372#117—861no—
373#117—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C42—431no—
377#107—21no—
378#107—861no—
379#107—861no—
380#106—21no—
381#106—861no—
382#106—861no—
383#106—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—21no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#102—861no—
409#102—861no—
410#102—861no—
411C22⋊C8—431no—
412C22⋊C8—431no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—21no—
417#97—861no—
418C4×C8—431no—
419C4×C8—861no—
420C4×C8C22×D4311yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—3442no—
426C2×Q8—1721no—
427C2×Q8D4×D4311yescharacteristic
428C2×D4—431no—
429C2×D4—861no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—861no—
434C22×C4—1721no—
435Q16—3441no—
436SD16—3441no—
437M16—3441no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—431no—
442C2×C8—431no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—3441no—
447C2×C8—3441no—
448C2×C8—3441no—
449C2×C8D4×D4311yescharacteristic
450C2×C8D4×D4311yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—431no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4D4×D4311yescharacteristic
469C22⋊C4—861no—
470C22⋊C4—861no—
471C22⋊C4—861no—
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—1721no—
475C42—21no—
476C42—431no—
477C42—431no—
478C42—431no—
479C42—1721no—
480C42C23×D4311yescharacteristic
481C23—431no—
482C23—861no—
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—81no—
488Q8—3441no—
489Q8—3442no—
490Q8—1721no—
491Q8—1721no—
492D4—861no—
493D4—861no—
494D4—1722no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—431no—
500C2×C4—431no—
501C2×C4—431no—
502C2×C4—862no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—3442no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4C2×D4×D4311yescharacteristic
514C2×C4C2×D4×D4311yescharacteristic
515C2×C4#41×D4311yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—861no—
522C8—861no—
523C8—1721no—
524C8—1721no—
525C8—1721no—
526C22—432no—
527C22—861no—
528C22—861no—
529C22—1721no—
530C22—1721no—
531C22—1721no—
532C22#121×D4311yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—81no—
537C4—81no—
538C4—861no—
539C4—861no—
540C4—861no—
541C4—3441no—
542C4—3441no—
543C4—1721no—
544C4#1458370611yescharacteristic
545C4#1458370811yescharacteristic
546C4#1458371511yescharacteristic
547C4#1458371511yescharacteristic
548C2—862no—
549C2—3441no—
550C2#1914414811yescharacteristic
551C2#1914428311yescharacteristic
552C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1704C2
socleC22×C43C2×#121
prime radical#13063300D4
hypercenter#1704D43
hypocenterC43#19588
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1704

Complements

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

NH ≅ G/Ntype
3. #19145735C2semidirect
5. #19134169C2semidirect
6. #19134101C2semidirect
7. #19134097C2semidirect
8. #19134051C2semidirect
9. #19134043C2semidirect
10. #19133979C2semidirect
11. #19133971C2semidirect
12. #19133377C2semidirect
13. #19133294C2semidirect
14. #333×D43C2semidirect
15. C43×#1704C2semidirect
276. #1704D43semidirect
343. C43#19588semidirect

Maximal subgroups

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

subgroupindex
#191459352
#191458202
#191457352
#191437582
#191341692
#191341012
#191340972
#191340512
#191340432
#191339792
#191339712
#191333772
#191332942
#333×D432
C43×#17042
#1958843