Finite Group Databasebeta

← #25075324

Subgroups — #25075324

Order 11008.

1040 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145520C211yesmaximal, characteristic, complemented
2#19144595C211yesmaximal, characteristic, complemented
3#19144059C211yesmaximal, characteristic, complemented
4#19133823C214yesmaximal, complemented
5#19133678C214yesmaximal, complemented
6#19133276C211yesmaximal, characteristic, complemented
7#19133020C211yesmaximal, characteristic, complemented
8#19132986C211yesmaximal, characteristic, complemented
9C2×C43×#555C211yesmaximal, characteristic, complemented
10C2×#13063351—21no—
11#14583449C2211yescharacteristic
12#14583273C2212yescomplemented
13#14583249C2212yescomplemented
14#14583212—21no—
15#14583179C2212yescomplemented
16#14583114—22no—
17#14583104C2212yescomplemented
18#14583101—22no—
19#14583094C2212yescomplemented
20#14583094C2212yescomplemented
21#14583038—22no—
22#14583033—21no—
23C4×#10621882—22no—
24#14582952C2211yescharacteristic
25#14582952C2211yescharacteristic
26#14582923C2211yescharacteristic
27#14582898—21no—
28#14582648C2214yescomplemented
29D4⋊(C43⋊C8)C2214yescomplemented
30D4⋊(C43⋊C8)C2214yescomplemented
31C43×#555—22no—
32C43×#555—22no—
33C43×#555—22no—
34C43×#555C2214yes—
35C2×C4⋊Q8×C43C2211yescharacteristic
36C2×#124×C43—22no—
37C2×#121×C43—21no—
38C2×#121×C43—21no—
39C2×C4×D4×C43C2211yescharacteristic
40C2×C4×D4×C43C2211yescharacteristic
41C2×#117×C43—21no—
42C2×#117×C43—21no—
43C2×#10621898—21no—
44#13063351—44no—
45C2×#10621883—22no—
46C2×#10621884—24no—
47C2×#10621882—22no—
48C2×#10621882—22no—
49C2×#10621877—21no—
50#13063325C2311yescharacteristic
51#13063322C2311yescharacteristic
52#13063313—21no—
53#13063299—21no—
54#13063299—21no—
55C4×D172—21no—
56C4×D172—21no—
57#13063258—22no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)C2312yes—
61C4⋊(C43⋊C8)C2312yes—
62#13063249—24no—
63#13063248—22no—
64#13063246—22no—
65#13063245—22no—
66#13063245—22no—
67C22⋊(C43⋊C8)—21no—
68C22⋊(C43⋊C8)—21no—
69C4×C43⋊C8—21no—
70C4×C43⋊C8C2312yes—
71C22×Q8×C43D412yes—
72C22×D4×C43—22no—
73C22×D4×C43D411yescharacteristic
74C22×D4×C43D411yescharacteristic
75C23×C4×C43—21no—
76C23×C4×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43—21no—
79C4⋊Q8×C43D412yes—
80C4⋊Q8×C43C2312yes—
81#124×C43—28no—
82#124×C43—28no—
83#121×C43—24no—
84#121×C43—24no—
85#121×C43—24no—
86#121×C43—24no—
87C4×D4×C43—21no—
88C4×D4×C43—21no—
89C4×D4×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43D412yes—
92C4×D4×C43D412yes—
93C4×D4×C43C2312yes—
94C4×D4×C43C2312yes—
95#117×C43—24no—
96#117×C43—24no—
97#117×C43—24no—
98#117×C43—24no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C22⋊C4×C43—22no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C42×C43—22no—
108C2×C42×C43C2311yescharacteristic
109C24×C43—21no—
110C24×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—82no—
113C2×Q8×C43C2×D414yes—
114C2×D4×C43—28no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—42no—
120C2×D4×C43—84no—
121C2×D4×C43C2×D412yes—
122C2×D4×C43C2×D412yes—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43—44no—
131C22×C4×C43—42no—
132C22×C4×C43—42no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C2×C22⋊D43—41no—
137#10621898—42no—
138#10621898—42no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×C4×D43—41no—
143C2×Dic86—21no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43C2×D412yes—
151C4⋊C4×C43C2×D412yes—
152C22⋊C4×C43—28no—
153C22⋊C4×C43—28no—
154C22⋊C4×C43—22no—
155C22⋊C4×C43—22no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—22no—
158C42×C43—28no—
159C42×C43C2×D411yescharacteristic
160C42×C43C2×D411yescharacteristic
161C42×C43C2×D411yescharacteristic
162C42×C43C2411yescharacteristic
163#10621884—84no—
164#10621883—44no—
165#10621882—44no—
166#10621882—44no—
167(C2×D43)⋊C4—41no—
168(C2×D43)⋊C4—41no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171#10621877—42no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—22no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—42no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43#12011yescharacteristic
184C22×D43—41no—
185Q8×C43—44no—
186Q8×C43—82no—
187D4×C43—22no—
188D4×C43—22no—
189D4×C43—22no—
190D4×C43—22no—
191D4×C43—42no—
192D4×C43—42no—
193D4×C43—88no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—24no—
198C2×C4×C43—41no—
199C2×C4×C43—44no—
200C2×C4×C43—42no—
201C2×C4×C43—44no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—44no—
206C2×C4×C43—44no—
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#13512yes—
211C2×C4×C43AGL(1,ℤ/8)12yes—
212C2×C4×C43C22×D411yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C22⋊D43—82no—
216C2×Dic43—41no—
217D172—42no—
218D172—41no—
219D172—41no—
220D172—42no—
221C4×D43—82no—
222Dic86—41no—
223Dic86—41no—
224C43⋊C8—42no—
225C43⋊C8—42no—
226C43⋊C8—42no—
227#18772—431nomaximal, Sylow
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—42no—
231C22×C43—42no—
232C22×C43—42no—
233C22×C43—42no—
234C22×C43—42no—
235C22×C43—42no—
236C22×C43—84no—
237C22×C43—84no—
238C22×C43#44912yes—
239C22×C43C2×#12011yescharacteristic
240C2×D43—81no—
241C2×D43—81no—
242C2×D43—81no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—42no—
247C4×C43—42no—
248C4×C43—44no—
249C4×C43#44912yes—
250C4×C43C2×#13511yescharacteristic
251C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C43#57512yes—
253Dic43—81no—
254C2×#555D4311yescharacteristic, complemented
255#3206—431no—
256#3100—431no—
257#3036—431no—
258#1646—434no—
259#1624—434no—
260#1548—431no—
261#1486—431no—
262#1478—431no—
263C2×C43—22no—
264C2×C43—82no—
265C2×C43—82no—
266C2×C43C2×#44911yescharacteristic
267C2×C43#300511yescharacteristic
268C2×C43#301911yescharacteristic
269D43—161no—
270C2×AGL(1,ℤ/8)—861no—
271#555—22no—
272#555—22no—
273#555—22no—
274#555C2×D4314yes—
275#532—431no—
276C2×C4⋊Q8C2×D4311yescharacteristic
277C2×#124—22no—
278C2×#121—21no—
279C2×#121—21no—
280C2×C4×D4C2×D4311yescharacteristic
281C2×C4×D4C2×D4311yescharacteristic
282C2×#117—21no—
283C2×#117—21no—
284#492—432no—
285#487—432no—
286#480—861no—
287#474—432no—
288#463—862no—
289#461—432no—
290#461—862no—
291#459—432no—
292#459—432no—
293#448—862no—
294#447—861no—
295C4×D8—862no—
296#431—431no—
297#431—431no—
298#423—431no—
299#417—861no—
300#333—434no—
301D4⋊C8—434no—
302D4⋊C8—434no—
303C43#1877211yescharacteristic, complemented, Sylow
304C2×#41—861no—
305C22×Q8C22⋊D4312yes—
306C22×D4—22no—
307C22×D4C22⋊D4311yescharacteristic
308C22×D4C22⋊D4311yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311AGL(1,ℤ/8)—1724no—
312C2×SD16—864no—
313C2×SD16—862no—
314C2×D8—862no—
315C2×D8—862no—
316C2×M16—861no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—431no—
320C4⋊Q8C22⋊D4312yes—
321C4⋊Q8C22×D4312yes—
322#127—431no—
323#124—28no—
324#124—28no—
325#124—861no—
326#121—24no—
327#121—24no—
328#121—24no—
329#121—24no—
330#121—861no—
331#121—861no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—861no—
337C4×D4—861no—
338C4×D4C22⋊D4312yes—
339C4×D4C22⋊D4312yes—
340C4×D4C22×D4312yes—
341C4×D4C22×D4312yes—
342#117—24no—
343#117—24no—
344#117—24no—
345#117—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4C22⋊D4311yescharacteristic
349C2×C4⋊C4C22⋊D4311yescharacteristic
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C42—22no—
355C2×C42C22×D4311yescharacteristic
356#107—862no—
357C4⋊C8—432no—
358C4⋊C8—432no—
359C4⋊C8—861no—
360C4⋊C8—861no—
361#103—864no—
362#103—862no—
363#102—862no—
364#102—862no—
365#102—862no—
366C22⋊C8—861no—
367C22⋊C8—861no—
368C4×C8—432no—
369C4×C8—861no—
370C24—21no—
371C24—21no—
372#41—1722no—
373#41—1722no—
374C2×Q8—22no—
375C2×Q8—82no—
376C2×Q8—861no—
377C2×Q8C2×C22⋊D4314yes—
378C2×D4—28no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—42no—
384C2×D4—84no—
385C2×D4—861no—
386C2×D4—861no—
387C2×D4—861no—
388C2×D4—1721no—
389C2×D4C2×C22⋊D4312yes—
390C2×D4C2×C22⋊D4312yes—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—44no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—1721no—
402C22×C4C2×C22⋊D4311yescharacteristic
403C22×C4C2×C22⋊D4311yescharacteristic
404C22×C4C2×C22⋊D4311yescharacteristic
405SD16—3444no—
406SD16—1724no—
407D8—1724no—
408D8—1724no—
409M16—1722no—
410C2×C8—862no—
411C2×C8—862no—
412C2×C8—862no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—861no—
420C4⋊C4—861no—
421C4⋊C4C2×C22⋊D4312yes—
422C4⋊C4C2×C22⋊D4312yes—
423C22⋊C4—28no—
424C22⋊C4—28no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—1721no—
430C22⋊C4—1721no—
431C42—28no—
432C42C2×C22⋊D4311yescharacteristic
433C42C2×C22⋊D4311yescharacteristic
434C42C2×C22⋊D4311yescharacteristic
435C42C23×D4311yescharacteristic
436C23—22no—
437C23—22no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—1721no—
445C23#1306329411yescharacteristic
446Q8—44no—
447Q8—82no—
448Q8—1721no—
449Q8—1721no—
450D4—22no—
451D4—22no—
452D4—22no—
453D4—22no—
454D4—42no—
455D4—42no—
456D4—88no—
457D4—3442no—
458D4—1722no—
459D4—1721no—
460D4—1721no—
461D4—1722no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—41no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—3442no—
476C2×C4—1721no—
477C2×C4#1306329411yescharacteristic
478C2×C4#1306329411yescharacteristic
479C2×C4#1306329411yescharacteristic
480C2×C4#1306334512yes—
481C2×C4#1306335012yes—
482C2×C4C22×C22⋊D4311yescharacteristic
483C2×C4C22×C22⋊D4311yescharacteristic
484C2×C4C22×C22⋊D4311yescharacteristic
485C8—1722no—
486C8—1722no—
487C8—1722no—
488C22—21no—
489C22—21no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—84no—
497C22—84no—
498C22—3441no—
499C22—3441no—
500C22—3441no—
501C22#1458304412yes—
502C22C2×#1306329411yescharacteristic
503C4—21no—
504C4—21no—
505C4—21no—
506C4—44no—
507C4—42no—
508C4—42no—
509C4—3441no—
510C4#1458304412yes—
511C4C2×#1306334511yescharacteristic
512C4C2×#1306335011yescharacteristic
513C4#1458369712yes—
514C2—22no—
515C2—82no—
516C2—82no—
517C2—6881no—
518C2C2×#1458304411yescharacteristic
519C2#1914383711yescharacteristic
520C2#1914395211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#555C2
socleC22×C43C2×#120
hypercenterC2×#555D43
hypocenterC43#18772
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #19145520C2semidirect
2. #19144595C2semidirect
3. #19144059C2semidirect
4. #19133823C2semidirect
5. #19133678C2semidirect
6. #19133276C2semidirect
7. #19133020C2semidirect
8. #19132986C2semidirect
9. C2×C43×#555C2semidirect
12. #14583273C22semidirect
13. #14583249C22semidirect
15. #14583179C22semidirect
17. #14583104C22semidirect
19. #14583094C22semidirect
20. #14583094C22semidirect
28. #14582648C22semidirect
29. D4⋊(C43⋊C8)C22semidirect
30. D4⋊(C43⋊C8)C22semidirect
254. C2×#555D43semidirect
303. C43#18772semidirect

Maximal subgroups

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

subgroupindex
#191455202
#191445952
#191440592
#191338232
#191336782
#191332762
#191330202
#191329862
C2×C43×#5552
#1877243