Finite Group Databasebeta

← #25082103

Subgroups — #25082103

Order 11008.

594 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#19144751C211yesmaximal, characteristic
2#19144660C211yesmaximal, characteristic
3#19143703C211yesmaximal, characteristic
4#19134050C211yesmaximal, characteristic, complemented
5#19134043C211yesmaximal, characteristic, complemented
6#19134022C211yesmaximal, characteristic, complemented
7#19134015C211yesmaximal, characteristic, complemented
8#19133986C211yesmaximal, characteristic, complemented
9#19133981C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#19133375C211yesmaximal, characteristic, complemented
13#19133295C211yesmaximal, characteristic, complemented
14#19133252C211yesmaximal, characteristic, complemented
15C43×#3231C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583237—21no—
18#14583237—21no—
19#14583191C2211yescharacteristic
20#14583186C2211yescharacteristic
21#14583181C2211yescharacteristic
22#14583176C2211yescharacteristic
23#14583106C2211yescharacteristic
24#14583106C2211yescharacteristic
25#14583101C2211yescharacteristic
26#14583101C2211yescharacteristic
27#14583059—21no—
28#14583059—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31#14583004—21no—
32#14582997—21no—
33C4×#10621885—21no—
34C4×#10621884—21no—
35C8×D172C2211yescharacteristic
36C8×D172C2211yescharacteristic
37(C22⋊D43)⋊C8—21no—
38(C22⋊D43)⋊C8—21no—
39#14582956C2211yescharacteristic
40#14582952C2211yescharacteristic
41#14582951—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C4⋊C8×D43—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582645C2211yescharacteristic
55#14582645C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#533C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#498C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#485—21no—
63C43×#485—21no—
64C43×#479—21no—
65C43×#479—21no—
66C43×#431C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75C4×Dic86D411yescharacteristic
76C4×Dic86C2311yescharacteristic
77C4×D172D411yescharacteristic
78C4×D172C2311yescharacteristic
79C4×C22⋊D43—21no—
80C4×C22⋊D43—21no—
81#13063284D411yescharacteristic
82#13063282—21no—
83C42×D43—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—21no—
103#13063245—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C8×Dic43—21no—
112C8×Dic43—21no—
113C4⋊Q8×C43C2311yescharacteristic
114C4⋊Q8×C43C2311yescharacteristic
115C4⋊Q8×C43C2311yescharacteristic
116C4⋊Q8×C43C2311yescharacteristic
117#125×C43—21no—
118#125×C43—21no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43—21no—
123C4×Q8×C43—21no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127#117×C43—21no—
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130#107×C43—21no—
131#107×C43—21no—
132#106×C43—21no—
133#106×C43—21no—
134C4⋊C8×C43D411yescharacteristic
135C4⋊C8×C43D411yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140C22⋊C8×C43D411yescharacteristic
141C22⋊C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—21no—
152#10621898—22no—
153#10621898—22no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×Dic86C2×D411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
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×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C42×C43—41no—
178C42×C43—41no—
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43#4111yescharacteristic
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184#10621885—42no—
185#10621885—42no—
186#10621884—42no—
187#10621884—42no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204C8×D43—81no—
205C8×D43—81no—
206C23×C43#12111yescharacteristic
207C22×D43—21no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—24no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234D172—21no—
235D172#13512yes—
236C4×D43—24no—
237C4×D43—41no—
238C4×D43—41no—
239C4×D43—81no—
240Dic86—21no—
241Dic86#13512yes—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19418—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43C2×#12111yescharacteristic
257C2×D43—22no—
258C2×D43—41no—
259C2×D43—41no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43C2×#13511yescharacteristic
269C4×C43C2×#13511yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272Dic43—22no—
273Dic43—41no—
274Dic43—41no—
275#3231D4311yescharacteristic, complemented
276#3116—431no—
277#3107—431no—
278#2988—431no—
279#1684—431no—
280#1683—431no—
281#1680—431no—
282#1679—431no—
283#1674—431no—
284#1673—431no—
285#1672—431no—
286#1671—431no—
287#1572—431no—
288#1552—431no—
289#1542—431no—
290C2×C43—41no—
291C2×C43#304611yescharacteristic
292C2×C43#305011yescharacteristic
293C2×C43#306911yescharacteristic
294D43—42no—
295#533C2×D4311yescharacteristic
296#533C2×D4311yescharacteristic
297C4×#41—431no—
298#500C2×D4311yescharacteristic
299#498C2×D4311yescharacteristic
300#487C2×D4311yescharacteristic
301#487C2×D4311yescharacteristic
302#485—21no—
303#485—21no—
304#485—861no—
305#485—861no—
306#479—21no—
307#479—21no—
308#477—431no—
309#476—431no—
310#475—431no—
311#474—431no—
312#462—431no—
313#462—431no—
314#461—431no—
315#461—431no—
316#452—861no—
317#452—861no—
318C8×Q8—431no—
319C8×Q8—431no—
320#441—861no—
321#440—861no—
322C4×Q16—861no—
323C4×SD16—861no—
324C8×D4—431no—
325C8×D4—431no—
326C8×D4—861no—
327C8×D4—861no—
328#432—431no—
329#431—431no—
330#431—861no—
331#431C2×D4311yescharacteristic
332C2×C4⋊C8—431no—
333C2×C4⋊C8—861no—
334#335—431no—
335#335—431no—
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#332—431no—
345#332—431no—
346C43#1941811yescharacteristic, complemented, Sylow
347C2×#41—431no—
348C2×Q16—861no—
349C2×Q16—861no—
350C2×SD16—861no—
351C2×SD16—861no—
352C22×C8—861no—
353C22×C8—861no—
354C22×C8—861no—
355C4⋊Q8C22×D4311yescharacteristic
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358C4⋊Q8C22×D4311yescharacteristic
359#125—21no—
360#125—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—431no—
370C4×Q8—431no—
371C4×D4—431no—
372C4×D4—431no—
373C4×D4—861no—
374C4×D4—861no—
375#117—21no—
376#117—21no—
377#117—431no—
378#117—861no—
379C2×C42—861no—
380C2×C42C22×D4311yescharacteristic
381#107—21no—
382#107—21no—
383#107—861no—
384#107—861no—
385#106—21no—
386#106—21no—
387#106—861no—
388#106—861no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8C22⋊D4311yescharacteristic
399C4⋊C8C22⋊D4311yescharacteristic
400#103—21no—
401#103—21no—
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—861no—
411#102—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8C22⋊D4311yescharacteristic
417C22⋊C8C22⋊D4311yescharacteristic
418#97—861no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C4×C8C22×D4311yescharacteristic
424#41—862no—
425#41—862no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—431no—
431C2×D4—431no—
432C2×D4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4D4×D4311yescharacteristic
437C22×C4#1062190011yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439Q16—1722no—
440Q16—1722no—
441SD16—1722no—
442SD16—1722no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—3441no—
450C2×C8—3441no—
451C2×C8—3441no—
452C2×C8C2×C22⋊D4311yescharacteristic
453C2×C8C2×C22⋊D4311yescharacteristic
454C2×C8C2×C22⋊D4311yescharacteristic
455C2×C8C2×C22⋊D4311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—431no—
469C4⋊C4—431no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C42—41no—
478C42—41no—
479C42—861no—
480C42—861no—
481C42—861no—
482C42D4×D4311yescharacteristic
483C42#1062190011yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C42C23×D4311yescharacteristic
486C23—861no—
487C23#1306329611yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—432no—
496Q8—861no—
497D4—432no—
498D4—864no—
499D4—861no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—864no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—3441no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306329611yescharacteristic
517C2×C4#1306329611yescharacteristic
518C2×C4#1306329611yescharacteristic
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C22×C22⋊D4311yescharacteristic
521C2×C4C2×#1062190011yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—1721no—
527C8—1721no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—862no—
536C22—1721no—
537C22—1721no—
538C22C2×#1306329611yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—862no—
548C4—1721no—
549C4—1721no—
550C4#135×D4311yescharacteristic
551C4#135×D4311yescharacteristic
552C4#1458370711yescharacteristic
553C4#1458371411yescharacteristic
554C2—41no—
555C2—1722no—
556C2#1914414111yescharacteristic
557C2#1914417211yescharacteristic
558C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3231C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#3231D43
hypocenterC43#19418
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
4. #19134050C2semidirect
5. #19134043C2semidirect
6. #19134022C2semidirect
7. #19134015C2semidirect
8. #19133986C2semidirect
9. #19133981C2semidirect
10. #19133974C2semidirect
11. #19133967C2semidirect
12. #19133375C2semidirect
13. #19133295C2semidirect
14. #19133252C2semidirect
15. C43×#3231C2semidirect
275. #3231D43semidirect
346. C43#19418semidirect

Maximal subgroups

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

subgroupindex
#191447512
#191446602
#191437032
#191340502
#191340432
#191340222
#191340152
#191339862
#191339812
#191339742
#191339672
#191333752
#191332952
#191332522
C43×#32312
#1941843