Finite Group Databasebeta

← #25081719

Subgroups — #25081719

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145964C211yesmaximal, characteristic
2#19145824C211yesmaximal, characteristic
3#19144972C211yesmaximal, characteristic, complemented
4#19143602C211yesmaximal, characteristic
5#19134176C211yesmaximal, characteristic, complemented
6#19134170C211yesmaximal, characteristic, complemented
7#19134152C211yesmaximal, characteristic, complemented
8#19134054C211yesmaximal, characteristic, complemented
9#19134044C211yesmaximal, characteristic, complemented
10#19134022C211yesmaximal, characteristic, complemented
11#19134020C211yesmaximal, characteristic, complemented
12#19133361C211yesmaximal, characteristic, complemented
13#19133302C211yesmaximal, characteristic, complemented
14#19133278C211yesmaximal, characteristic, complemented
15C43×#1699C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18#14583431C2211yescharacteristic
19#14583307—21no—
20#14583266—21no—
21#14583266—21no—
22#14583257—21no—
23#14583251C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583249C2211yescharacteristic
26#14583236—21no—
27#14583216—21no—
28#14583208—21no—
29#14583195C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583185C2211yescharacteristic
32#14583181C2211yescharacteristic
33#14583179C2211yescharacteristic
34#14583156—21no—
35#14583142—21no—
36#14583119—21no—
37#14583106C2211yescharacteristic
38#14583026C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14582975—21no—
41#14582967—21no—
42D4×C43⋊C8C2211yescharacteristic
43#14582957—21no—
44#14582955C2211yescharacteristic
45#14582951C2211yescharacteristic
46#14582921C2211yescharacteristic
47#14582906—21no—
48#14582906—21no—
49#14582857—21no—
50C4×#10621872C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582650C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×#10621885—21no—
69C2×#10621872—21no—
70C2×#10621872D411yescharacteristic
71C2×#10621872D411yescharacteristic
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063324—21no—
76#13063324—21no—
77#13063323—21no—
78#13063318—21no—
79#13063316—21no—
80#13063316D411yescharacteristic
81#13063312D411yescharacteristic
82#13063307—21no—
83#13063305—21no—
84#13063305D411yescharacteristic
85#13063301—21no—
86#13063296D411yescharacteristic
87Q8×Dic43—21no—
88C4×Dic86C2311yescharacteristic
89#13063290—21no—
90C4×C22⋊D43—21no—
91#13063284—21no—
92#13063283—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063258—21no—
98#13063257—21no—
99#13063256—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063248—21no—
115#13063248—21no—
116#13063248—21no—
117#13063246—21no—
118#13063246—21no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063235—21no—
123#13063235—21no—
124#13063235D411yescharacteristic
125#13063235D411yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×M16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149Q8×D43—42no—
150Q8×D43—42no—
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×Dic86C2×D411yescharacteristic
159SD16×C43—81no—
160M16×C43—42no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×D411yescharacteristic
171C22⋊C4×C43—21no—
172C42×C43C2411yescharacteristic
173C22⋊Dic43—21no—
174C22⋊Dic43—21no—
175C22⋊Dic43—21no—
176#10621885—81no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—41no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—41no—
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—21no—
193C4×Dic43—41no—
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43#4111yescharacteristic
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—42no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203#10621872—41no—
204#10621872—41no—
205#10621872—81no—
206C23×C43—21no—
207C22×D43#12111yescharacteristic
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212D4×C43—21no—
213D4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C22⋊D43—81no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43#12111yescharacteristic
228C2×Dic43#12111yescharacteristic
229C2×Dic43#12111yescharacteristic
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—41no—
235C4×D43—82no—
236Dic86—21no—
237Dic86—21no—
238Dic86—41no—
239Dic86—41no—
240Dic86—82no—
241Dic86—81no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19381—431nomaximal, Sylow
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43C2×#12111yescharacteristic
257C2×D43—21no—
258C2×D43—21no—
259C2×D43—21no—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43#57511yescharacteristic
265C4×C43#57511yescharacteristic
266C4×C43#57711yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—21no—
269Dic43—21no—
270Dic43—21no—
271Dic43—41no—
272Dic43—41no—
273Dic43—81no—
274Dic43—81no—
275#3252—431no—
276#3239—431no—
277#3139—431no—
278#2969—431no—
279#1704—431no—
280#1703—431no—
281#1700—431no—
282#1699D4311yescharacteristic, complemented
283#1684—431no—
284#1683—431no—
285#1680—431no—
286#1679—431no—
287#1569—431no—
288#1554—431no—
289#1549—431no—
290C2×C43—81no—
291C2×C43#304011yescharacteristic
292C2×C43#306311yescharacteristic
293C2×C43#306911yescharacteristic
294D43—41no—
295#533—431no—
296C2×C4⋊Q8—431no—
297#529—431no—
298#501—861no—
299#491—861no—
300#491—861no—
301#489—861no—
302#487—431no—
303#487—431no—
304#487—431no—
305#487C2×D4311yescharacteristic
306#484—861no—
307#481—861no—
308#479—861no—
309#477—431no—
310#476—431no—
311#475—431no—
312#475—431no—
313#474—431no—
314#474C2×D4311yescharacteristic
315#470—861no—
316#468—861no—
317#464—861no—
318#462—431no—
319#461C2×D4311yescharacteristic
320#446—431no—
321C8×Q8—431no—
322#436—861no—
323#436C2×D4311yescharacteristic
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#432—431no—
328#431—431no—
329#423—431no—
330#419—861no—
331#419—861no—
332#405—861no—
333C4×M16—431no—
334#335—431no—
335#335C2×D4311yescharacteristic
336#334—431no—
337#334—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332C2×D4311yescharacteristic
345#332C2×D4311yescharacteristic
346C43#1938111yescharacteristic, complemented, Sylow
347C22×Q8—861no—
348C2×Q16—861no—
349C2×SD16—21no—
350C2×M16—21no—
351C2×M16—431no—
352C2×M16—431no—
353C2×M16—861no—
354C22×C8—861no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—861no—
358C4⋊Q8—861no—
359C4⋊Q8—861no—
360C4⋊Q8C22×D4311yescharacteristic
361C4⋊Q8C22×D4311yescharacteristic
362#126—861no—
363#125—431no—
364#125—861no—
365#124—431no—
366#123—861no—
367C22⋊Q8—431no—
368C22⋊Q8—861no—
369C22⋊Q8—861no—
370#121—431no—
371C4×Q8—431no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×D4—861no—
375C4×D4C22×D4311yescharacteristic
376#117—861no—
377#117—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C42—431no—
381#107—21no—
382#107—861no—
383#107—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8C22×D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#102—21no—
410#102—861no—
411#102—861no—
412C22⋊C8—21no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—431no—
417#97—431no—
418#97—861no—
419#97—861no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—431no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—1721no—
430C2×Q8—1722no—
431C2×Q8—1722no—
432C2×D4—861no—
433C2×D4D4×D4311yescharacteristic
434C22×C4—21no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—1721no—
439Q16—3441no—
440SD16—81no—
441M16—42no—
442M16—3441no—
443M16—1721no—
444M16—1721no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—1722no—
454C2×C8D4×D4311yescharacteristic
455C2×C8D4×D4311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—431no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4D4×D4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—1721no—
480C42—431no—
481C42—431no—
482C42—431no—
483C42—861no—
484C42—1721no—
485C42C23×D4311yescharacteristic
486C23—21no—
487C23—431no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—861no—
493Q8—861no—
494Q8—3441no—
495Q8—3442no—
496Q8—1721no—
497Q8—1721no—
498D4—21no—
499D4—21no—
500D4—3441no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—431no—
507C2×C4—431no—
508C2×C4—431no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—3442no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4#41×D4311yescharacteristic
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—861no—
528C8—861no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—861no—
536C22—861no—
537C22—861no—
538C22#121×D4311yescharacteristic
539C4—21no—
540C4—41no—
541C4—81no—
542C4—81no—
543C4—861no—
544C4—861no—
545C4—861no—
546C4—3441no—
547C4—3441no—
548C4—1721no—
549C4—1721no—
550C4#1458369511yescharacteristic
551C4#1458369611yescharacteristic
552C4#1458370911yescharacteristic
553C4#1458371511yescharacteristic
554C2—81no—
555C2—1721no—
556C2#1914408411yescharacteristic
557C2#1914428111yescharacteristic
558C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1699C2
socleC22×C43C2×#121
prime radical#13063296D4
hypercenter#1699D43
hypocenterC43#19381
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1699

Complements

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

NH ≅ G/Ntype
3. #19144972C2semidirect
5. #19134176C2semidirect
6. #19134170C2semidirect
7. #19134152C2semidirect
8. #19134054C2semidirect
9. #19134044C2semidirect
10. #19134022C2semidirect
11. #19134020C2semidirect
12. #19133361C2semidirect
13. #19133302C2semidirect
14. #19133278C2semidirect
15. C43×#1699C2semidirect
282. #1699D43semidirect
346. C43#19381semidirect

Maximal subgroups

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

subgroupindex
#191459642
#191458242
#191449722
#191436022
#191341762
#191341702
#191341522
#191340542
#191340442
#191340222
#191340202
#191333612
#191333022
#191332782
C43×#16992
#1938143