Finite Group Databasebeta

← #25081904

Subgroups — #25081904

Order 11008.

610 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145546C211yesmaximal, characteristic
2#19144727C211yesmaximal, characteristic, complemented
3#19144625C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic, complemented
5#19134038C211yesmaximal, characteristic, complemented
6#19134037C211yesmaximal, characteristic, complemented
7#19134026C211yesmaximal, characteristic, complemented
8#19134025C211yesmaximal, characteristic, complemented
9#19133964C211yesmaximal, characteristic, complemented
10#19133963C211yesmaximal, characteristic, complemented
11#19133940C211yesmaximal, characteristic, complemented
12#19133372C211yesmaximal, characteristic, complemented
13#19133297C211yesmaximal, characteristic
14#19133258C211yesmaximal, characteristic, complemented
15C43×#1666C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583278C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583231—21no—
23#14583216—21no—
24#14583185C2211yescharacteristic
25#14583184C2211yescharacteristic
26#14583181C2211yescharacteristic
27#14583119—21no—
28#14583119—21no—
29#14583110C2211yescharacteristic
30#14583109C2211yescharacteristic
31#14583096C2211yescharacteristic
32#14583058—21no—
33#14583058—21no—
34#14583056—21no—
35#14583036—21no—
36Q8×C43⋊C8C2211yescharacteristic
37C8×Dic86—21no—
38C8×Dic86C2211yescharacteristic
39#14583023—21no—
40#14583023C2211yescharacteristic
41#14583005—21no—
42#14583003—21no—
43#14582990—21no—
44SD16×Dic43—21no—
45#14582955C2211yescharacteristic
46#14582951—21no—
47#14582951C2211yescharacteristic
48#14582951C2211yescharacteristic
49#14582950—21no—
50#14582950C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#475C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43D411yescharacteristic
69C2×Dic172—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063316—21no—
77#13063312—21no—
78#13063305—21no—
79#13063301—21no—
80#13063296—21no—
81#13063296—21no—
82Q8×Dic43—21no—
83Q8×Dic43D411yescharacteristic
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86#13063290—21no—
87#13063290—21no—
88#13063290D411yescharacteristic
89D4×Dic43—21no—
90D4×Dic43—21no—
91#13063283—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43D411yescharacteristic
94C42×D43—21no—
95C42×D43C2311yescharacteristic
96#13063257—21no—
97#13063256—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133#127×C43C2311yescharacteristic
134C4×Q8×C43C2311yescharacteristic
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C2×D411yescharacteristic
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×C22⋊D43—41no—
150C22×Dic43—41no—
151Q8×D43—22no—
152Q8×D43—22no—
153#10621900—81no—
154#10621900—81no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164SD16×C43—42no—
165SD16×C43—81no—
166SD16×C43—81no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C42×C43—21no—
177C42×C43C2411yescharacteristic
178C22⋊Dic43—41no—
179C22⋊Dic43—41no—
180#10621885—42no—
181#10621885—81no—
182#10621885—81no—
183#10621883—42no—
184(C2×D43)⋊C4—41no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43#4111yescharacteristic
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208Dic172—42no—
209C23×C43—41no—
210C22×D43#12111yescharacteristic
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43#13512yes—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—81no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—82no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—82no—
232C2×Dic43#12111yescharacteristic
233C2×Dic43#12111yescharacteristic
234C2×Dic43#12111yescharacteristic
235C4×D43—24no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—41no—
241C4×D43—81no—
242Dic86—24no—
243Dic86—21no—
244Dic86—41no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86#13512yes—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#19400—431nomaximal, Sylow
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43C2×#12111yescharacteristic
264C2×D43—21no—
265C2×D43—21no—
266C2×D43—21no—
267C4×C43—22no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13511yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57711yescharacteristic
275Dic43—21no—
276Dic43—21no—
277Dic43—22no—
278Dic43—21no—
279Dic43—41no—
280Dic43—81no—
281Dic43—81no—
282#3210—431no—
283#3113—431no—
284#3103—431no—
285#2982—431no—
286#1682—431no—
287#1682—431no—
288#1680—431no—
289#1680—431no—
290#1670—431no—
291#1670—431no—
292#1666—431no—
293#1666D4311yescharacteristic, complemented
294#1572—431no—
295#1553—431no—
296#1544—431no—
297C2×C43—161no—
298C2×C43#304311yescharacteristic
299C2×C43#305011yescharacteristic
300C2×C43#306911yescharacteristic
301D43—41no—
302#533—431no—
303#532—431no—
304C2×C4×Q8—431no—
305#494—431no—
306#492C2×D4311yescharacteristic
307#487—431no—
308#486—431no—
309#483—861no—
310#481—861no—
311#475—431no—
312#475—431no—
313#475—431no—
314#475C2×D4311yescharacteristic
315#464—861no—
316#464—861no—
317#462—431no—
318#462—431no—
319#460—431no—
320#460C2×D4311yescharacteristic
321#452—861no—
322#452—861no—
323#451—861no—
324#448—861no—
325C8×Q8—431no—
326C8×Q8—431no—
327C8×Q8—431no—
328C8×Q8—861no—
329C8×Q8—861no—
330C8×Q8C2×D4311yescharacteristic
331#441—861no—
332#441—861no—
333C4×SD16—861no—
334C4×SD16—861no—
335#432—431no—
336#431—431no—
337#431—431no—
338#431—431no—
339#431—861no—
340#431—861no—
341#335—431no—
342#335—431no—
343#334—431no—
344#334C2×D4311yescharacteristic
345#332—431no—
346#332—431no—
347#332—431no—
348#332—431no—
349#332—431no—
350#332C2×D4311yescharacteristic
351#331—431no—
352#331C2×D4311yescharacteristic
353C43#1940011yescharacteristic, complemented, Sylow
354C2×#41—861no—
355C22×Q8—431no—
356C2×Q16—861no—
357C2×Q16—861no—
358C2×Q16—861no—
359C2×Q16—861no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8C22×D4311yescharacteristic
367#127C22×D4311yescharacteristic
368#125—861no—
369#124—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—861no—
373#121—861no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—431no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8C22×D4311yescharacteristic
382C4×D4—861no—
383C4×D4—861no—
384#117—861no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—861no—
387C2×C42—431no—
388C2×C42—861no—
389#106—21no—
390#106—861no—
391#106—861no—
392#106—861no—
393C4⋊C8—21no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405#103—21no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—21no—
414#102—861no—
415#102—861no—
416#102—861no—
417C22⋊C8—431no—
418C22⋊C8—431no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—861no—
423C4×C8—21no—
424C4×C8—431no—
425C4×C8—861no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8C22×D4311yescharacteristic
431#41—3441no—
432#41—3441no—
433C2×Q8—21no—
434C2×Q8—431no—
435C2×Q8—861no—
436C2×Q8—862no—
437C2×Q8—862no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8D4×D4311yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—1721no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—1721no—
451Q16—3441no—
452Q16—3441no—
453Q16—1722no—
454Q16—1722no—
455SD16—42no—
456SD16—81no—
457SD16—81no—
458SD16—1722no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8D4×D4311yescharacteristic
468C2×C8D4×D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—431no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4D4×D4311yescharacteristic
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—21no—
488C42—431no—
489C42—431no—
490C42—431no—
491C42—861no—
492C42—861no—
493C42—861no—
494C42—1721no—
495C42C23×D4311yescharacteristic
496C23—41no—
497C23—431no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—432no—
502Q8—864no—
503Q8—861no—
504Q8—1721no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508Q8#1306334612yes—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—81no—
514D4—3442no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—431no—
519C2×C4—431no—
520C2×C4—431no—
521C2×C4—864no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—3441no—
529C2×C4—3442no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4#41×D4311yescharacteristic
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—861no—
550C22—861no—
551C22—861no—
552C22#121×D4311yescharacteristic
553C4—21no—
554C4—22no—
555C4—41no—
556C4—81no—
557C4—861no—
558C4—861no—
559C4—861no—
560C4—862no—
561C4—3441no—
562C4—3441no—
563C4—1721no—
564C4#135×D4311yescharacteristic
565C4C2×#1306334611yescharacteristic
566C4#1458370511yescharacteristic
567C4#1458370911yescharacteristic
568C2—161no—
569C2—1721no—
570C2#1914411111yescharacteristic
571C2#1914417111yescharacteristic
572C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1666C2
socleC22×C43C2×#121
prime radical#14583447C22
hypercenter#1666D43
hypocenterC43#19400
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1666

Complements

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

NH ≅ G/Ntype
2. #19144727C2semidirect
4. #19143674C2semidirect
5. #19134038C2semidirect
6. #19134037C2semidirect
7. #19134026C2semidirect
8. #19134025C2semidirect
9. #19133964C2semidirect
10. #19133963C2semidirect
11. #19133940C2semidirect
12. #19133372C2semidirect
14. #19133258C2semidirect
15. C43×#1666C2semidirect
293. #1666D43semidirect
353. C43#19400semidirect

Maximal subgroups

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

subgroupindex
#191455462
#191447272
#191446252
#191436742
#191340382
#191340372
#191340262
#191340252
#191339642
#191339632
#191339402
#191333722
#191332972
#191332582
C43×#16662
#1940043