Finite Group Databasebeta

← #25079042

Subgroups — #25079042

Order 11008.

618 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#19145180C211yesmaximal, characteristic, complemented
2#19144384C211yesmaximal, characteristic
3#19144376C211yesmaximal, characteristic
4C8×#10621900C211yesmaximal, characteristic
5#19134054C211yesmaximal, characteristic, complemented
6#19134050C211yesmaximal, characteristic, complemented
7#19134046C211yesmaximal, characteristic, complemented
8#19133998C211yesmaximal, characteristic, complemented
9#19133992C211yesmaximal, characteristic, complemented
10#19133964C211yesmaximal, characteristic, complemented
11#19133958C211yesmaximal, characteristic, complemented
12#335×D43C211yesmaximal, characteristic, complemented
13#19133251C211yesmaximal, characteristic, complemented
14#19133249C211yesmaximal, characteristic, complemented
15C43×#1683C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583209—21no—
23#14583205—21no—
24#14583201—21no—
25#14583197—21no—
26#14583195C2211yescharacteristic
27#14583191C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583185C2211yescharacteristic
30#14583181C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583139—21no—
33#14583139—21no—
34C8×Dic86C2211yescharacteristic
35#14583023C2211yescharacteristic
36#14582991—21no—
37#14582991—21no—
38D4×C43⋊C8C2211yescharacteristic
39C8×C22⋊D43—21no—
40(C22⋊D43)⋊C8—21no—
41#14582951C2211yescharacteristic
42#14582949—21no—
43#14582936—21no—
44#14582934—21no—
45C4⋊C8×D43C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582892—21no—
48#14582892—21no—
49C2×C8×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621885—21no—
70C22×C43⋊C8—21no—
71C2×C8×D43—21no—
72C2×C8×D43—21no—
73C2×C8×D43D411yescharacteristic
74C2×C8×D43D411yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063316—21no—
78#13063316—21no—
79#13063305—21no—
80#13063305—21no—
81#13063301—21no—
82#13063301—21no—
83Q8×Dic43—21no—
84Q8×Dic43—21no—
85C4×Dic86C2311yescharacteristic
86#13063290—21no—
87#13063290—21no—
88#13063290D411yescharacteristic
89D4×Dic43D411yescharacteristic
90C4×C22⋊D43—21no—
91(C22⋊D43)⋊C4—21no—
92#13063283—21no—
93#13063283—21no—
94#13063283D411yescharacteristic
95#13063281—21no—
96C2×C4×Dic43—21no—
97C42×D43C2311yescharacteristic
98#13063259—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063257—21no—
104#13063256—21no—
105#13063256—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063248—21no—
118#13063248—21no—
119#13063246—21no—
120#13063246—21no—
121C22⋊(C43⋊C8)—21no—
122(C2×D43)⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C22×C8×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#107×C43—21no—
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×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—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621900—22no—
152#10621900Q1614yescomplemented
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43#4111yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C2×D411yescharacteristic
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—42no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C2×D411yescharacteristic
170C22⋊C4×C43—21no—
171C42×C43C2411yescharacteristic
172C22⋊Dic43—21no—
173#10621885—42no—
174#10621885—42no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—41no—
177(C2×D43)⋊C4—41no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—41no—
183C4⋊Dic43—41no—
184C4⋊Dic43C2×D411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—41no—
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
203C8×D43—22no—
204C8×D43—41no—
205C8×D43—42no—
206C8×D43—42no—
207C23×C43—21no—
208C22×D43#12111yescharacteristic
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—81no—
212D4×C43—21no—
213D4×C43C2×Q1612yes—
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—24no—
223C2×Dic43—21no—
224C2×Dic43—24no—
225C2×Dic43—21no—
226C2×Dic43—42no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43#12111yescharacteristic
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—41no—
235C4×D43C2×Q1612yes—
236C4×D43#13512yes—
237Dic86—21no—
238Dic86—41no—
239Dic86—41no—
240Dic86—81no—
241Dic86C2×Q1612yes—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8#13512yes—
252#19126—431nomaximal, Sylow
253C22×C43—22no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43C2×#12111yescharacteristic
257C2×D43—21no—
258C2×D43—21no—
259C2×D43#46712yes—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43C22×Q1611yescharacteristic
265C4×C43C2×#13511yescharacteristic
266C4×C43C2×#13511yescharacteristic
267C4×C43#57511yescharacteristic
268Dic43—21no—
269Dic43—22no—
270Dic43—21no—
271Dic43—41no—
272Dic43—81no—
273Dic43—81no—
274Dic43#46712yes—
275#3170—431no—
276#3076—431no—
277#3076—431no—
278C8×#41—431no—
279#1684—431no—
280#1684—431no—
281#1683—431no—
282#1683D4311yescharacteristic, complemented
283#1676—431no—
284#1675—431no—
285#1670—431no—
286#1669—431no—
287C2×#335—431no—
288#1542—431no—
289#1542—431no—
290C2×C43—42no—
291C2×C43#303511yescharacteristic
292C2×C43C2×#46711yescharacteristic
293C2×C43#306711yescharacteristic
294D43—22no—
295#533—431no—
296#533—431no—
297C4×#41—431no—
298#500—431no—
299#494—431no—
300#487—431no—
301#487C2×D4311yescharacteristic
302#479—861no—
303#479—861no—
304#478—861no—
305#478—861no—
306#477—431no—
307#477—431no—
308#476—431no—
309#476C2×D4311yescharacteristic
310#475—431no—
311#475—431no—
312#474—431no—
313#474C2×D4311yescharacteristic
314#467—861no—
315#467—861no—
316C8×Q8—431no—
317C8×Q8—431no—
318C4×Q16—861no—
319C4×Q16—861no—
320C8×D4—431no—
321C8×D4—861no—
322C8×D4—861no—
323C8×D4C2×D4311yescharacteristic
324#431—431no—
325#431—861no—
326#427—861no—
327#427—861no—
328C2×C4⋊C8—431no—
329C2×C4⋊C8—431no—
330#416—861no—
331#416—861no—
332C2×C4×C8—431no—
333C2×C4×C8—861no—
334#335—431no—
335#335—431no—
336#335—431no—
337#335C2×D4311yescharacteristic
338#333—431no—
339#333—431no—
340#333—431no—
341#333C2×D4311yescharacteristic
342#332—431no—
343#332—431no—
344#332—431no—
345#332C2×D4311yescharacteristic
346C43#1912611yescharacteristic, complemented, Sylow
347C2×#41—431no—
348C2×Q16—861no—
349C2×Q16—861no—
350C22×C8—21no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8—861no—
354C22×C8—861no—
355C22×C8—861no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#125—861no—
361#125—861no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C22⋊Q8—861no—
365C22⋊Q8—861no—
366C4×Q8—431no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×D4—431no—
373C4×D4—861no—
374C4×D4—861no—
375C4×D4C22×D4311yescharacteristic
376#117—431no—
377#117—861no—
378#117—861no—
379#117—861no—
380C2×C42—431no—
381C2×C42—861no—
382#107—21no—
383#107—861no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—861no—
388#106—21no—
389#106—861no—
390#106—861no—
391#106—861no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—21no—
403#103—21no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#102—21no—
411#102—21no—
412#102—861no—
413#102—861no—
414C22⋊C8—21no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424#41—434no—
425#41—862no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—431no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×D4—861no—
432C2×D4D4×D4311yescharacteristic
433C22×C4—21no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—861no—
438C22×C4—861no—
439Q16—1722no—
440Q16—1722no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—42no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—862no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—1721no—
452C2×C8—1722no—
453C2×C8—1722no—
454C2×C8—1722no—
455C2×C8D4×D4311yescharacteristic
456C2×C8D4×D4311yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—431no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4D4×D4311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—1721no—
477C22⋊C4—1721no—
478C42—431no—
479C42—431no—
480C42—431no—
481C42—861no—
482C42—861no—
483C42—861no—
484C42—1721no—
485C42—1721no—
486C42C23×D4311yescharacteristic
487C23—21no—
488C23—431no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—432no—
493Q8—861no—
494Q8—3441no—
495Q8—1721no—
496Q8—1721no—
497D4—21no—
498D4—864no—
499D4Q16×D4312yes—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—431no—
506C2×C4—432no—
507C2×C4—432no—
508C2×C4—431no—
509C2×C4—431no—
510C2×C4—864no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—1721no—
516C2×C4—1722no—
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—432no—
528C8—861no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—22no—
533C22—41no—
534C22—41no—
535C22—432no—
536C22—861no—
537C22—861no—
538C22#121×D4311yescharacteristic
539C4—21no—
540C4—41no—
541C4—81no—
542C4—81no—
543C4—432no—
544C4—861no—
545C4—861no—
546C4—862no—
547C4—3441no—
548C4—3441no—
549C4—1721no—
550C4C2×Q16×D4311yescharacteristic
551C4#135×D4311yescharacteristic
552C4#135×D4311yescharacteristic
553C4#1458369511yescharacteristic
554C2—42no—
555C2—862no—
556C2#1914404711yescharacteristic
557C2#467×D4311yescharacteristic
558C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1683C2
socleC22×C43C2×#121
prime radicalC2×#10621900D4
hypercenter#1683D43
hypocenterC43#19126
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1683

Complements

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

NH ≅ G/Ntype
1. #19145180C2semidirect
5. #19134054C2semidirect
6. #19134050C2semidirect
7. #19134046C2semidirect
8. #19133998C2semidirect
9. #19133992C2semidirect
10. #19133964C2semidirect
11. #19133958C2semidirect
12. #335×D43C2semidirect
13. #19133251C2semidirect
14. #19133249C2semidirect
15. C43×#1683C2semidirect
152. #10621900Q16semidirect
282. #1683D43semidirect
346. C43#19126semidirect

Maximal subgroups

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

subgroupindex
#191451802
#191443842
#191443762
C8×#106219002
#191340542
#191340502
#191340462
#191339982
#191339922
#191339642
#191339582
#335×D432
#191332512
#191332492
C43×#16832
#1912643