Finite Group Databasebeta

← #25077859

Subgroups — #25077859

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145801C211yesmaximal, characteristic, complemented
2#19145598C211yesmaximal, characteristic, complemented
3#19144981C211yesmaximal, characteristic, complemented
4#19133918C214yesmaximal, complemented
5#19133912C214yesmaximal, complemented
6#19133219C211yesmaximal, characteristic, complemented
7#19133197C211yesmaximal, characteristic, complemented
8#19133193C211yesmaximal, characteristic, complemented
9C2×C43×#562C211yesmaximal, characteristic
10#14583456C2211yescharacteristic
11#14583309C2212yescomplemented
12#14583294C2212yescomplemented
13#14583269C2212yescomplemented
14#14583258C2212yescomplemented
15#14583258C2212yescomplemented
16#14583258C2212yescomplemented
17#14583253—22no—
18#14583234—21no—
19#14583229—21no—
20#14583203—22no—
21#14583118—22no—
22#14583055—21no—
23#14583050—21no—
24#14582956C2211yescharacteristic
25#14582956C2211yescharacteristic
26#14582908—21no—
27#14582904—21no—
28C4×#10621877C2211yescharacteristic
29#14582641C2214yescomplemented
30#14582639C2214yescomplemented
31#14582639C2214yescomplemented
32C43×#562—22no—
33C43×#562—22no—
34C43×#562—22no—
35C43×#562C2214yes—
36C2×#125×C43C2211yescharacteristic
37C2×#124×C43C2211yescharacteristic
38C2×#124×C43C2211yescharacteristic
39C2×#123×C43—21no—
40C2×#123×C43—21no—
41C2×C22⋊Q8×C43—21no—
42C2×C22⋊Q8×C43—21no—
43C2×#121×C43—21no—
44C2×#121×C43—21no—
45C2×#10621885—22no—
46C2×#10621883—22no—
47C2×#10621877—21no—
48#13063325C2311yescharacteristic
49#13063325C2311yescharacteristic
50#13063317—21no—
51#13063304—21no—
52#13063304—21no—
53C4×Dic86—21no—
54C4×Dic86—21no—
55#13063284—21no—
56#13063258—22no—
57#13063256—22no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)—21no—
60#13063249—22no—
61#13063249—22no—
62#13063249—22no—
63#13063248—22no—
64#13063248—22no—
65#13063246—22no—
66#13063246—22no—
67#13063246—22no—
68C22⋊(C43⋊C8)—21no—
69C22⋊(C43⋊C8)—21no—
70#13063236C2312yes—
71#13063236C2312yes—
72#13063236C2312yes—
73C4×C43⋊C8—21no—
74C22×Q8×C43D411yescharacteristic
75C22×Q8×C43D411yescharacteristic
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43D411yescharacteristic
79C22×D4×C43D411yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43—21no—
82#125×C43—21no—
83#125×C43—21no—
84#125×C43D412yes—
85#125×C43C2312yes—
86#124×C43—21no—
87#124×C43—21no—
88#124×C43—21no—
89#124×C43—21no—
90#124×C43D412yes—
91#124×C43D412yes—
92#124×C43C2312yes—
93#124×C43C2312yes—
94#123×C43—24no—
95#123×C43—24no—
96#123×C43—24no—
97#123×C43—24no—
98C22⋊Q8×C43—24no—
99C22⋊Q8×C43—24no—
100C22⋊Q8×C43—24no—
101C22⋊Q8×C43—24no—
102#121×C43—24no—
103#121×C43—24no—
104#121×C43—24no—
105#121×C43—24no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43C2311yescharacteristic
119C24×C43—21no—
120C24×C43—21no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—42no—
124C2×Q8×C43—81no—
125C2×Q8×C43C2×D412yes—
126C2×Q8×C43C2×D412yes—
127C2×D4×C43—24no—
128C2×D4×C43—24no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—42no—
132C2×D4×C43—81no—
133C2×D4×C43—82no—
134C2×D4×C43—82no—
135C2×D4×C43C2×D412yes—
136C2×D4×C43C2×D412yes—
137C22×C4×C43—24no—
138C22×C4×C43—24no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—82no—
144C22×C4×C43—82no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C2×Dic86—21no—
149C2×Dic86—21no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43C2×D412yes—
159C4⋊C4×C43C2×D412yes—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C42×C43C2×D411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43C2411yescharacteristic
174C22⋊Dic43—41no—
175#10621885—82no—
176#10621883—82no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183C4×Dic43—41no—
184#10621877—42no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43#12011yescharacteristic
197Q8×C43—42no—
198Q8×C43—42no—
199Q8×C43—81no—
200Q8×C43—81no—
201D4×C43—42no—
202D4×C43—42no—
203D4×C43—81no—
204D4×C43—81no—
205D4×C43—84no—
206D4×C43—84no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—84no—
219C2×C4×C43—84no—
220C2×C4×C43#12011yescharacteristic
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×Dic43—41no—
227C2×Dic43—41no—
228Dic86—42no—
229Dic86—42no—
230C43⋊C8—42no—
231C43⋊C8—42no—
232C43⋊C8—42no—
233#18998—431nomaximal, Sylow
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—42no—
237C22×C43—42no—
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—42no—
241C22×C43—42no—
242C22×C43—84no—
243C22×C43—84no—
244C22×C43#45512yes—
245C22×C43C2×#12011yescharacteristic
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—42no—
253C4×C43—42no—
254C4×C43—42no—
255C4×C43—42no—
256Dic43—81no—
257Dic43—81no—
258C2×#562D4311yescharacteristic
259#3236—431no—
260#3215—431no—
261#3140—431no—
262#1662—434no—
263#1661—434no—
264#1533—431no—
265#1528—431no—
266#1527—431no—
267C2×C43—22no—
268C2×C43—82no—
269C2×C43—82no—
270C2×C43C2×#45511yescharacteristic
271C2×C43#301911yescharacteristic
272C2×C43#302011yescharacteristic
273#562—22no—
274#562—22no—
275#562—22no—
276#562C2×D4314yes—
277#533—431no—
278C2×#125C2×D4311yescharacteristic
279C2×#124C2×D4311yescharacteristic
280C2×#124C2×D4311yescharacteristic
281C2×#123—21no—
282C2×#123—21no—
283C2×C22⋊Q8—21no—
284C2×C22⋊Q8—21no—
285C2×#121—21no—
286C2×#121—21no—
287#501—432no—
288#497—432no—
289#491—432no—
290#489—432no—
291#489—432no—
292#489—432no—
293#488—862no—
294#484—861no—
295#483—861no—
296#479—862no—
297#464—862no—
298#451—861no—
299#450—861no—
300#432—431no—
301#432—431no—
302#419—861no—
303#418—861no—
304C4×M16—431no—
305#330—434no—
306#329—434no—
307#329—434no—
308C43#1899811yescharacteristic, complemented, Sylow
309C22×Q8C22⋊D4311yescharacteristic
310C22×Q8C22⋊D4311yescharacteristic
311C22×D4—21no—
312C22×D4—21no—
313C22×D4C22⋊D4311yescharacteristic
314C22×D4C22⋊D4311yescharacteristic
315C23×C4—21no—
316C23×C4—21no—
317C2×Q16—862no—
318C2×SD16—862no—
319C2×M16—861no—
320C4⋊Q8—431no—
321C4⋊Q8—431no—
322#125—21no—
323#125—21no—
324#125—861no—
325#125C22⋊D4312yes—
326#125C22×D4312yes—
327#124—21no—
328#124—21no—
329#124—21no—
330#124—21no—
331#124C22⋊D4312yes—
332#124C22⋊D4312yes—
333#124C22×D4312yes—
334#124C22×D4312yes—
335#123—24no—
336#123—24no—
337#123—24no—
338#123—24no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—24no—
343C22⋊Q8—861no—
344C22⋊Q8—861no—
345#121—24no—
346#121—24no—
347#121—24no—
348#121—24no—
349C4×Q8—861no—
350C4×Q8—861no—
351#117—861no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4C22⋊D4311yescharacteristic
357C2×C4⋊C4C22⋊D4311yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C42C22×D4311yescharacteristic
365#107—862no—
366#106—862no—
367C4⋊C8—861no—
368C4⋊C8—861no—
369#103—862no—
370#103—862no—
371#103—862no—
372#103—862no—
373#103—862no—
374#102—862no—
375#102—862no—
376#102—862no—
377C22⋊C8—861no—
378C22⋊C8—861no—
379#97—432no—
380#97—432no—
381#97—432no—
382C4×C8—861no—
383C24—21no—
384C24—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—42no—
388C2×Q8—81no—
389C2×Q8—861no—
390C2×Q8—861no—
391C2×Q8C2×C22⋊D4312yes—
392C2×Q8C2×C22⋊D4312yes—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—81no—
399C2×D4—82no—
400C2×D4—82no—
401C2×D4C2×C22⋊D4312yes—
402C2×D4C2×C22⋊D4312yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—82no—
410C22×C4—82no—
411C22×C4C2×C22⋊D4311yescharacteristic
412C22×C4C2×C22⋊D4311yescharacteristic
413C22×C4C2×C22⋊D4311yescharacteristic
414Q16—3442no—
415SD16—3442no—
416M16—1722no—
417C2×C8—862no—
418C2×C8—862no—
419C2×C8—862no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C4⋊C4C2×C22⋊D4312yes—
435C4⋊C4C2×C22⋊D4312yes—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—1721no—
447C42—1721no—
448C42C2×C22⋊D4311yescharacteristic
449C42C2×C22⋊D4311yescharacteristic
450C42C2×C22⋊D4311yescharacteristic
451C42C23×D4311yescharacteristic
452C23—22no—
453C23—22no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23#1306329411yescharacteristic
461Q8—42no—
462Q8—42no—
463Q8—81no—
464Q8—81no—
465Q8—1722no—
466Q8—1722no—
467D4—42no—
468D4—42no—
469D4—81no—
470D4—81no—
471D4—84no—
472D4—84no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—84no—
485C2×C4—84no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4#1306329411yescharacteristic
489C2×C4#1306329411yescharacteristic
490C2×C4#1306329411yescharacteristic
491C2×C4C22×C22⋊D4311yescharacteristic
492C2×C4C22×C22⋊D4311yescharacteristic
493C2×C4C22×C22⋊D4311yescharacteristic
494C8—1722no—
495C8—1722no—
496C8—1722no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—84no—
506C22—84no—
507C22#1458307712yes—
508C22C2×#1306329411yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—3441no—
520C4—3441no—
521C2—22no—
522C2—82no—
523C2—82no—
524C2C2×#1458307711yescharacteristic
525C2#1914395211yescharacteristic
526C2#1914395911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC2×C43×#562C2
socleC22×C43C2×#120
hypercenterC2×#562D43
hypocenterC43#18998
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #19145801C2semidirect
2. #19145598C2semidirect
3. #19144981C2semidirect
4. #19133918C2semidirect
5. #19133912C2semidirect
6. #19133219C2semidirect
7. #19133197C2semidirect
8. #19133193C2semidirect
11. #14583309C22semidirect
12. #14583294C22semidirect
13. #14583269C22semidirect
14. #14583258C22semidirect
15. #14583258C22semidirect
16. #14583258C22semidirect
29. #14582641C22semidirect
30. #14582639C22semidirect
31. #14582639C22semidirect
308. C43#18998semidirect

Maximal subgroups

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

subgroupindex
#191458012
#191455982
#191449812
#191339182
#191339122
#191332192
#191331972
#191331932
C2×C43×#5622
#1899843