Finite Group Databasebeta

← #25081895

Subgroups — #25081895

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145539C211yesmaximal, characteristic
2#19144395C211yesmaximal, characteristic
3#475×D43C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic
5#19134054C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134052C211yesmaximal, characteristic, complemented
8#19134051C211yesmaximal, characteristic, complemented
9#19133964C211yesmaximal, characteristic, complemented
10#19133963C211yesmaximal, characteristic, complemented
11#19133962C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic
13#19133278C211yesmaximal, characteristic
14#19133251C211yesmaximal, characteristic
15C43×#1670C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583278C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583209—21no—
23#14583208—21no—
24#14583195C2211yescharacteristic
25#14583194C2211yescharacteristic
26#14583185C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583183—21no—
29#14583182—21no—
30#14583181C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583107—21no—
33#14583107—21no—
34#14583053—21no—
35#14583053—21no—
36Q8×C43⋊C8C2211yescharacteristic
37C8×Dic86—21no—
38C8×Dic86C2211yescharacteristic
39#14583023—21no—
40#14583023C2211yescharacteristic
41#14582951—21no—
42#14582951C2211yescharacteristic
43#14582950—21no—
44#14582950C2211yescharacteristic
45#14582938—21no—
46#106×D43—21no—
47#14582921C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582906—21no—
50#103×D43—21no—
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#494C2211yescharacteristic
61C43×#475C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43D411yescharacteristic
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621872—21no—
72C2×C8×D43—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063324—21no—
76#13063324—21no—
77#13063323—21no—
78#13063316—21no—
79#13063305—21no—
80#13063301—21no—
81Q8×Dic43—21no—
82Q8×Dic43D411yescharacteristic
83C4×Dic86—21no—
84C4×Dic86C2311yescharacteristic
85#13063290—21no—
86#13063290—21no—
87#13063290D411yescharacteristic
88#13063283—21no—
89C4⋊C4×D43—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43D411yescharacteristic
93C42×D43—21no—
94C42×D43C2311yescharacteristic
95#13063259—21no—
96#13063258—21no—
97#13063257—21no—
98#13063256—21no—
99#13063256—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8D411yescharacteristic
110Dic43⋊C8D411yescharacteristic
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063249—21no—
118#13063249—21no—
119#13063248—21no—
120#13063248—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8D411yescharacteristic
123(C2×D43)⋊C8D411yescharacteristic
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×Q16×C43—21no—
130C2×Q16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147Q8×D43—22no—
148Q8×D43—81no—
149Q8×D43—81no—
150Q8×D43Q1614yescomplemented
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—41no—
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43C2×D411yescharacteristic
156C2×C4×D43#4111yescharacteristic
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—41no—
161C2×Dic86C2×D411yescharacteristic
162Q16×C43—81no—
163Q16×C43—81no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C42×C43—21no—
176C42×C43C2411yescharacteristic
177#10621885—81no—
178#10621885—81no—
179(C2×D43)⋊C4—41no—
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—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43#4111yescharacteristic
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621872—42no—
206C8×D43—42no—
207C22×D43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43C2×Q1612yes—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43#12111yescharacteristic
226C2×Dic43#12111yescharacteristic
227C2×Dic43#12111yescharacteristic
228C4×D43—24no—
229C4×D43—21no—
230C4×D43—21no—
231C4×D43—41no—
232C4×D43—81no—
233C4×D43—82no—
234C4×D43C2×Q1612yes—
235C4×D43#13512yes—
236Dic86—21no—
237Dic86—24no—
238Dic86—41no—
239Dic86—41no—
240Dic86—82no—
241Dic86—81no—
242Dic86C2×Q1612yes—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253#19399—431nomaximal, Sylow
254C22×C43C2×#12111yescharacteristic
255C2×D43—21no—
256C2×D43—21no—
257C2×D43#46712yes—
258C4×C43—22no—
259C4×C43—21no—
260C4×C43—41no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43C22×Q1611yescharacteristic
264C4×C43C2×#13511yescharacteristic
265C4×C43#57711yescharacteristic
266C4×C43#57711yescharacteristic
267Dic43—21no—
268Dic43—22no—
269Dic43—21no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273Dic43#46712yes—
274#3209—431no—
275#3078—431no—
276C2×#475—431no—
277#2982—431no—
278#1684—431no—
279#1684—431no—
280#1684—431no—
281#1684—431no—
282#1670—431no—
283#1670—431no—
284#1670—431no—
285#1670D4311yescharacteristic, complemented
286#1571—431no—
287#1549—431no—
288#1542—431no—
289C2×C43#304311yescharacteristic
290C2×C43C2×#46711yescharacteristic
291C2×C43#306911yescharacteristic
292D43—22no—
293#533—431no—
294C2×C4⋊Q8—431no—
295C2×C4×Q8—431no—
296#494—431no—
297#494C2×D4311yescharacteristic
298#487—431no—
299#487—431no—
300#479—861no—
301#479—861no—
302#477—431no—
303#477—431no—
304#475—431no—
305#475—431no—
306#475—431no—
307#475—431no—
308#475—861no—
309#475—861no—
310#475C2×D4311yescharacteristic
311#475C2×D4311yescharacteristic
312#462—861no—
313#462—861no—
314#451—861no—
315#451—861no—
316C8×Q8—431no—
317C8×Q8—431no—
318C8×Q8—431no—
319C8×Q8—861no—
320C8×Q8—861no—
321C8×Q8C2×D4311yescharacteristic
322#431—431no—
323#431—431no—
324#431—861no—
325#431—861no—
326#428—861no—
327C2×#106—861no—
328#423—431no—
329C2×C4⋊C8—431no—
330#419—861no—
331C2×#103—861no—
332#335—431no—
333#335—431no—
334#335—431no—
335#335C2×D4311yescharacteristic
336#333—431no—
337#333—431no—
338#332—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332C2×D4311yescharacteristic
343#332C2×D4311yescharacteristic
344C43#1939911yescharacteristic, complemented, Sylow
345C22×Q8—431no—
346C22×Q8—861no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—861no—
350C2×Q16—861no—
351C2×M16—861no—
352C22×C8—861no—
353C4⋊Q8—431no—
354C4⋊Q8—431no—
355C4⋊Q8—861no—
356C4⋊Q8—861no—
357C4⋊Q8—861no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#125—861no—
361C22⋊Q8—861no—
362C22⋊Q8—861no—
363C4×Q8—431no—
364C4×Q8—431no—
365C4×Q8—431no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8C22×D4311yescharacteristic
371#117—861no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C42—431no—
377C2×C42—861no—
378#107—861no—
379#107—861no—
380#106—21no—
381#106—21no—
382#106—861no—
383#106—861no—
384#106—861no—
385#106—861no—
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400#103—21no—
401#103—21no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412C22⋊C8—431no—
413C22⋊C8—431no—
414C22⋊C8—861no—
415C4×C8—21no—
416C4×C8—431no—
417C4×C8—861no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8C22×D4311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—434no—
425C2×Q8—431no—
426C2×Q8—861no—
427C2×Q8—862no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—3441no—
431C2×Q8—3441no—
432C2×Q8—1721no—
433C2×Q8D4×D4311yescharacteristic
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—1721no—
440Q16—81no—
441Q16—81no—
442Q16—3441no—
443Q16—3441no—
444M16—1722no—
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—21no—
461C4⋊C4—431no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C4⋊C4D4×D4311yescharacteristic
475C22⋊C4—1721no—
476C42—21no—
477C42—431no—
478C42—431no—
479C42—431no—
480C42—861no—
481C42—861no—
482C42—861no—
483C42—1721no—
484C42C23×D4311yescharacteristic
485C23—431no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—432no—
492Q8—864no—
493Q8—861no—
494Q8—3441no—
495Q8—3442no—
496Q8—1721no—
497Q8—1721no—
498Q8Q16×D4312yes—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—431no—
504C2×C4—432no—
505C2×C4—432no—
506C2×C4—431no—
507C2×C4—431no—
508C2×C4—864no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—3441no—
514C2×C4—3442no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4#41×D4311yescharacteristic
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—861no—
527C8—861no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C22—432no—
532C22—861no—
533C22—861no—
534C22#121×D4311yescharacteristic
535C4—21no—
536C4—22no—
537C4—41no—
538C4—81no—
539C4—81no—
540C4—432no—
541C4—861no—
542C4—861no—
543C4—862no—
544C4—3441no—
545C4—3441no—
546C4—1721no—
547C4C2×Q16×D4311yescharacteristic
548C4#135×D4311yescharacteristic
549C4#1458370511yescharacteristic
550C4#1458370911yescharacteristic
551C2—862no—
552C2#1914411111yescharacteristic
553C2#467×D4311yescharacteristic
554C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1670C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1670D43
hypocenterC43#19399
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1670

Complements

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

NH ≅ G/Ntype
5. #19134054C2semidirect
6. #19134053C2semidirect
7. #19134052C2semidirect
8. #19134051C2semidirect
9. #19133964C2semidirect
10. #19133963C2semidirect
11. #19133962C2semidirect
15. C43×#1670C2semidirect
150. Q8×D43Q16semidirect
285. #1670D43semidirect
344. C43#19399semidirect

Maximal subgroups

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

subgroupindex
#191455392
#191443952
#475×D432
#191436742
#191340542
#191340532
#191340522
#191340512
#191339642
#191339632
#191339622
#191333682
#191332782
#191332512
C43×#16702
#1939943