Finite Group Databasebeta

← #25075426

Subgroups — #25075426

Order 11008.

1224 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145723C211yesmaximal, characteristic, complemented
2#19144595C211yesmaximal, characteristic, complemented
3#19144059C211yesmaximal, characteristic, complemented
4#19133879C214yesmaximal, complemented
5#19133684C214yesmaximal, complemented
6#19133280C211yesmaximal, characteristic, complemented
7#19133020C211yesmaximal, characteristic, complemented
8#19132986C211yesmaximal, characteristic, complemented
9C2×C43×#547C211yesmaximal, characteristic, complemented
10C2×#13063351—21no—
11#14583449C2211yescharacteristic
12#14583295C2212yescomplemented
13#14583247C2212yescomplemented
14#14583217—22no—
15#14583212—21no—
16#14583186—22no—
17#14583179C2212yescomplemented
18#14583114—22no—
19#14583104C2212yescomplemented
20#14583094C2212yescomplemented
21#14583094C2212yescomplemented
22#14583033—21no—
23C4×#10621882—22no—
24#14582952C2211yescharacteristic
25#14582952C2211yescharacteristic
26#14582923C2211yescharacteristic
27#14582898—21no—
28#14582645C2214yescomplemented
29D4⋊(C43⋊C8)C2214yescomplemented
30D4⋊(C43⋊C8)C2214yescomplemented
31C22×#41×C43—21no—
32C43×#547—22no—
33C43×#547—22no—
34C43×#547—22no—
35C43×#547C2214yes—
36C2×C4⋊Q8×C43C2211yescharacteristic
37C2×#123×C43—22no—
38C2×C22⋊Q8×C43—21no—
39C2×#121×C43—21no—
40C2×C4×D4×C43C2211yescharacteristic
41C2×C4×D4×C43C2211yescharacteristic
42C22×C4⋊C4×C43—21no—
43C2×#10621898—21no—
44#13063351—44no—
45C2×#10621883—22no—
46C2×#10621882—22no—
47C2×#10621882—22no—
48C2×#10621877—21no—
49#13063325C2311yescharacteristic
50#13063322C2311yescharacteristic
51#13063313—21no—
52#13063299—21no—
53#13063299—21no—
54C4×D172—21no—
55C4×D172—21no—
56#13063258—22no—
57#13063256—24no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)C2312yes—
61C4⋊(C43⋊C8)C2312yes—
62#13063248—22no—
63#13063246—22no—
64#13063245—22no—
65#13063245—22no—
66#13063245—24no—
67C22⋊(C43⋊C8)—21no—
68C22⋊(C43⋊C8)—21no—
69C4×C43⋊C8—21no—
70C4×C43⋊C8C2312yes—
71C2×#41×C43—24no—
72C2×#41×C43—24no—
73C2×#41×C43—48no—
74C22×Q8×C43—21no—
75C22×D4×C43—22no—
76C22×D4×C43D411yescharacteristic
77C22×D4×C43D411yescharacteristic
78C23×C4×C43—22no—
79C23×C4×C43—21no—
80C23×C4×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43—21no—
83C4⋊Q8×C43D412yes—
84C4⋊Q8×C43C2312yes—
85#123×C43—28no—
86#123×C43—28no—
87C22⋊Q8×C43—24no—
88C22⋊Q8×C43—24no—
89#121×C43—24no—
90#121×C43—24no—
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43D412yes—
96C4×D4×C43D412yes—
97C4×D4×C43C2312yes—
98C4×D4×C43C2312yes—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—24no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—24no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43D412yes—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C42×C43C2311yescharacteristic
110C24×C43—21no—
111C24×C43—21no—
112#41×C43—416no—
113#41×C43—48no—
114#41×C43—48no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43—44no—
118C2×D4×C43—24no—
119C2×D4×C43—28no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—48no—
125C2×D4×C43C2×D412yes—
126C2×D4×C43C2×D412yes—
127C22×C4×C43—28no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43—48no—
136C22×C4×C43—44no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C2×C22⋊D43—41no—
143#10621898—42no—
144#10621898—42no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×C4×D43—41no—
149C2×Dic86—21no—
150C4⋊C4×C43—28no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43C2×D412yes—
157C4⋊C4×C43C2×D412yes—
158C4⋊C4×C43C2×D414yes—
159C22⋊C4×C43—28no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C42×C43C2×D411yescharacteristic
165C42×C43C2×D411yescharacteristic
166C42×C43C2×D411yescharacteristic
167C42×C43C2411yescharacteristic
168#10621883—44no—
169#10621882—44no—
170#10621882—44no—
171(C2×D43)⋊C4—41no—
172(C2×D43)⋊C4—41no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175#10621877—42no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C23×C43—24no—
180C23×C43—22no—
181C23×C43—22no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43#12011yescharacteristic
188C22×D43—41no—
189Q8×C43—44no—
190Q8×C43—44no—
191D4×C43—24no—
192D4×C43—22no—
193D4×C43—22no—
194D4×C43—22no—
195D4×C43—416no—
196D4×C43—42no—
197D4×C43AGL(1,ℤ/8)14yescomplemented
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—24no—
202C2×C4×C43—41no—
203C2×C4×C43—44no—
204C2×C4×C43—42no—
205C2×C4×C43—44no—
206C2×C4×C43—416no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—44no—
211C2×C4×C43—44no—
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#12011yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#13512yes—
216C2×C4×C43AGL(1,ℤ/8)12yes—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C22⋊D43—82no—
221C2×Dic43—41no—
222D172—42no—
223D172—41no—
224D172—41no—
225D172—42no—
226C4×D43—82no—
227Dic86—41no—
228Dic86—41no—
229C43⋊C8—42no—
230C43⋊C8—42no—
231C43⋊C8—42no—
232#18782—431nomaximal, Sylow
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—24no—
236C22×C43—48no—
237C22×C43—42no—
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—42no—
241C22×C43—42no—
242C22×C43—84no—
243C22×C43#44912yes—
244C22×C43C2×#12011yescharacteristic
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—42no—
252C4×C43—42no—
253C4×C43—44no—
254C4×C43#44912yes—
255C4×C43C2×#13511yescharacteristic
256C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
257C4×C43C2×AGL(1,ℤ/8)12yes—
258Dic43—81no—
259C2×#547D4311yescharacteristic, complemented
260#3227—431no—
261#3100—431no—
262#3036—431no—
263#1654—434no—
264#1625—434no—
265#1549—431no—
266#1486—431no—
267#1478—431no—
268C2×C43—22no—
269C2×C43—44no—
270C2×C43—82no—
271C2×C43C2×#44911yescharacteristic
272C2×C43#300311yescharacteristic
273C2×C43#302011yescharacteristic
274D43—161no—
275C22×#41—21no—
276C2×AGL(1,ℤ/8)—861no—
277#547—22no—
278#547—22no—
279#547—22no—
280#547C2×D4314yes—
281#532—431no—
282C2×C4⋊Q8C2×D4311yescharacteristic
283C2×#123—22no—
284C2×C22⋊Q8—21no—
285C2×#121—21no—
286C2×C4×D4C2×D4311yescharacteristic
287C2×C4×D4C2×D4311yescharacteristic
288C22×C4⋊C4—21no—
289#498—432no—
290#486—432no—
291#481—862no—
292#480—861no—
293#476—862no—
294#474—432no—
295#463—862no—
296#461—432no—
297#459—432no—
298#459—432no—
299#447—861no—
300C4×D8—862no—
301#431—431no—
302#431—431no—
303#423—431no—
304#417—861no—
305#332—434no—
306D4⋊C8—434no—
307D4⋊C8—434no—
308C43#1878211yescharacteristic, complemented, Sylow
309C2×#41—24no—
310C2×#41—24no—
311C2×#41—48no—
312C2×#41—861no—
313C22×Q8—21no—
314C22×D4—22no—
315C22×D4C22⋊D4311yescharacteristic
316C22×D4C22⋊D4311yescharacteristic
317C23×C4—22no—
318C23×C4—21no—
319C23×C4—21no—
320AGL(1,ℤ/8)—1724no—
321C2×SD16—862no—
322C2×D8—862no—
323C2×D8—862no—
324C2×M16—861no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—431no—
328C4⋊Q8C22⋊D4312yes—
329C4⋊Q8C22×D4312yes—
330#127—431no—
331#124—861no—
332#123—28no—
333#123—28no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336#121—24no—
337#121—24no—
338#121—861no—
339#121—861no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—861no—
345C4×D4—861no—
346C4×D4C22⋊D4312yes—
347C4×D4C22⋊D4312yes—
348C4×D4C22×D4312yes—
349C4×D4C22×D4312yes—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4C22⋊D4311yescharacteristic
355C2×C4⋊C4C22⋊D4311yescharacteristic
356C2×C4⋊C4C22⋊D4312yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C42C22×D4311yescharacteristic
361#107—862no—
362#106—864no—
363C4⋊C8—432no—
364C4⋊C8—432no—
365C4⋊C8—861no—
366C4⋊C8—861no—
367#103—862no—
368#102—862no—
369#102—862no—
370#102—862no—
371#102—864no—
372C22⋊C8—861no—
373C22⋊C8—861no—
374C4×C8—432no—
375C4×C8—861no—
376C24—21no—
377C24—21no—
378#41—416no—
379#41—48no—
380#41—48no—
381#41—1722no—
382#41—1722no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—44no—
386C2×Q8—861no—
387C2×D4—24no—
388C2×D4—28no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—48no—
394C2×D4—861no—
395C2×D4—861no—
396C2×D4—861no—
397C2×D4—1721no—
398C2×D4C2×C22⋊D4312yes—
399C2×D4C2×C22⋊D4312yes—
400C22×C4—28no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—44no—
409C22×C4—48no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—1721no—
413C22×C4C2×C22⋊D4311yescharacteristic
414C22×C4C2×C22⋊D4311yescharacteristic
415C22×C4C2×C22⋊D4311yescharacteristic
416SD16—1724no—
417D8—1724no—
418D8—1724no—
419M16—1722no—
420C2×C8—862no—
421C2×C8—862no—
422C2×C8—862no—
423C4⋊C4—28no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4C2×C22⋊D4312yes—
432C4⋊C4C2×C22⋊D4314yes—
433C4⋊C4C2×C22⋊D4312yes—
434C22⋊C4—28no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C42C2×C22⋊D4311yescharacteristic
442C42C2×C22⋊D4311yescharacteristic
443C42C2×C22⋊D4311yescharacteristic
444C42C23×D4311yescharacteristic
445C23—24no—
446C23—22no—
447C23—22no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23—1721no—
454C23#1306329411yescharacteristic
455Q8—44no—
456Q8—44no—
457Q8—1721no—
458Q8—1721no—
459D4—24no—
460D4—22no—
461D4—22no—
462D4—22no—
463D4—416no—
464D4—42no—
465D4—3442no—
466D4—1722no—
467D4—1721no—
468D4—1721no—
469D4—1722no—
470D4#1306335114yescomplemented
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—41no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4—416no—
480C2×C4—42no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—3442no—
486C2×C4—1721no—
487C2×C4#1306329411yescharacteristic
488C2×C4#1306329411yescharacteristic
489C2×C4#1306329411yescharacteristic
490C2×C4#1306334512yes—
491C2×C4#1306335012yes—
492C2×C4C22×C22⋊D4311yescharacteristic
493C2×C4C22×C22⋊D4311yescharacteristic
494C2×C4C22×C22⋊D4311yescharacteristic
495C8—1722no—
496C8—1722no—
497C8—1722no—
498C22—21no—
499C22—21no—
500C22—24no—
501C22—48no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—84no—
508C22—3441no—
509C22—3441no—
510C22—3441no—
511C22#1458304412yes—
512C22C2×#1306329411yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—42no—
518C4—44no—
519C4—3441no—
520C4#1458304412yes—
521C4C2×#1306334511yescharacteristic
522C4C2×#1306335011yescharacteristic
523C4C2×#1306335112yes—
524C2—22no—
525C2—44no—
526C2—82no—
527C2—6881no—
528C2C2×#1458304411yescharacteristic
529C2#1914382211yescharacteristic
530C2#1914395911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#547C2
socleC22×C43C2×#120
hypercenterC2×#547D43
hypocenterC43#18782
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #19145723C2semidirect
2. #19144595C2semidirect
3. #19144059C2semidirect
4. #19133879C2semidirect
5. #19133684C2semidirect
6. #19133280C2semidirect
7. #19133020C2semidirect
8. #19132986C2semidirect
9. C2×C43×#547C2semidirect
12. #14583295C22semidirect
13. #14583247C22semidirect
17. #14583179C22semidirect
19. #14583104C22semidirect
20. #14583094C22semidirect
21. #14583094C22semidirect
28. #14582645C22semidirect
29. D4⋊(C43⋊C8)C22semidirect
30. D4⋊(C43⋊C8)C22semidirect
197. D4×C43AGL(1,ℤ/8)semidirect
259. C2×#547D43semidirect
308. C43#18782semidirect
470. D4#13063351semidirect

Maximal subgroups

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

subgroupindex
#191457232
#191445952
#191440592
#191338792
#191336842
#191332802
#191330202
#191329862
C2×C43×#5472
#1878243