Finite Group Databasebeta

← #25075120

Subgroups — #25075120

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145520C211yesmaximal, characteristic, complemented
2#19144595C211yesmaximal, characteristic
3#19144067C211yesmaximal, characteristic, complemented
4#19133809C214yesmaximal, complemented
5#19133667C214yesmaximal, complemented
6#19133276C211yesmaximal, characteristic, complemented
7#19133020C211yesmaximal, characteristic, complemented
8#19132990C211yesmaximal, characteristic, complemented
9C2×C43×#554C211yesmaximal, characteristic, complemented
10C2×#13063356—21no—
11#14583449C2211yescharacteristic
12#14583273C2212yescomplemented
13#14583249C2212yescomplemented
14#14583212—21no—
15#14583179C2212yes—
16#14583121—22no—
17#14583109C2212yescomplemented
18#14583101—22no—
19#14583099C2212yescomplemented
20#14583094C2212yes—
21#14583038—22no—
22#14583033—21no—
23C4×#10621882—22no—
24#14582952C2211yescharacteristic
25#14582952C2211yescharacteristic
26#14582923C2211yescharacteristic
27#14582898—21no—
28#14582648C2214yescomplemented
29Q8⋊(C43⋊C8)C2214yescomplemented
30D4⋊(C43⋊C8)C2214yes—
31C43×#554—22no—
32C43×#554—22no—
33C43×#554—22no—
34C43×#554C2214yes—
35C2×C4⋊Q8×C43C2211yescharacteristic
36C2×#125×C43—21no—
37C2×C22⋊Q8×C43—21no—
38C2×C22⋊Q8×C43—22no—
39C2×C4×Q8×C43C2211yescharacteristic
40C2×C4×D4×C43—21no—
41C2×C4×D4×C43C2211yescharacteristic
42C22×C4⋊C4×C43—21no—
43C2×#10621898—21no—
44#13063356—44no—
45C2×#10621885—22no—
46C2×#10621884—22no—
47C2×#10621884—24no—
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×C43D411yescharacteristic
72C22×Q8×C43D412yes—
73C22×D4×C43D411yescharacteristic
74C23×C4×C43—22no—
75C23×C4×C43—21no—
76C4⋊Q8×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43D412yes—
79C4⋊Q8×C43C2312yes—
80#125×C43—24no—
81#125×C43—24no—
82C22⋊Q8×C43—24no—
83C22⋊Q8×C43—28no—
84C22⋊Q8×C43—24no—
85C22⋊Q8×C43—28no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43D412yes—
89C4×Q8×C43C2312yes—
90C4×D4×C43—24no—
91C4×D4×C43—24no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43D412yes—
95C4×D4×C43C2312yes—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—24no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—24no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43C2311yescharacteristic
109C24×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—22no—
113C2×Q8×C43—22no—
114C2×Q8×C43—82no—
115C2×Q8×C43C2×D412yes—
116C2×Q8×C43C2×D414yes—
117C2×D4×C43—24no—
118C2×D4×C43—21no—
119C2×D4×C43C2×D412yes—
120C22×C4×C43—28no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—84no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C2×C22⋊D43—41no—
134#10621898—42no—
135#10621898—42no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×C4×D43—41no—
140C2×Dic86—21no—
141C4⋊C4×C43—28no—
142C4⋊C4×C43—28no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43C2×D412yes—
152C4⋊C4×C43C2×D412yes—
153C22⋊C4×C43—28no—
154C22⋊C4×C43—22no—
155C22⋊C4×C43—22no—
156C42×C43—22no—
157C42×C43—22no—
158C42×C43C2×D411yescharacteristic
159C42×C43C2×D411yescharacteristic
160C42×C43C2×D411yescharacteristic
161C42×C43C2411yescharacteristic
162#10621885—44no—
163#10621884—44no—
164#10621884—84no—
165#10621882—44no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170#10621877—42no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—22no—
174C23×C43—24no—
175C23×C43—22no—
176C23×C43—42no—
177C23×C43—42no—
178C23×C43#12011yescharacteristic
179C22×D43—41no—
180Q8×C43—22no—
181Q8×C43—22no—
182Q8×C43—44no—
183Q8×C43—42no—
184Q8×C43—82no—
185D4×C43—24no—
186D4×C43—22no—
187D4×C43#13714yescomplemented
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—24no—
193C2×C4×C43—41no—
194C2×C4×C43—42no—
195C2×C4×C43—44no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—44no—
201C2×C4×C43—88no—
202C2×C4×C43#12011yescharacteristic
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43#12011yescharacteristic
205C2×C4×C43#13512yes—
206C2×C4×C43AGL(1,ℤ/8)12yes—
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C22×D411yescharacteristic
210C22⋊D43—82no—
211C2×Dic43—41no—
212D172—42no—
213D172—41no—
214D172—41no—
215D172—42no—
216C4×D43—82no—
217Dic86—41no—
218Dic86—41no—
219C43⋊C8—42no—
220C43⋊C8—42no—
221C43⋊C8—42no—
222#18752—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—24no—
226C22×C43—48no—
227C22×C43—42no—
228C22×C43—42no—
229C22×C43#44912yes—
230C22×C43C2×#12011yescharacteristic
231C2×D43—81no—
232C2×D43—81no—
233C2×D43—81no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—42no—
238C4×C43—42no—
239C4×C43—42no—
240C4×C43—44no—
241C4×C43#44912yes—
242C4×C43C2×#13511yescharacteristic
243C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C43C2×#13712yes—
245Dic43—81no—
246C2×#554D4311yescharacteristic, complemented
247#3206—431no—
248#3100—431no—
249#3037—431no—
250#1644—434no—
251#1622—434no—
252#1548—431no—
253#1486—431no—
254#1479—431no—
255C2×C43—22no—
256C2×C43—44no—
257C2×C43C2×#44911yescharacteristic
258C2×C43#300411yescharacteristic
259C2×C43#301911yescharacteristic
260D43—161no—
261C2×#137—861no—
262#554—22no—
263#554—22no—
264#554—22no—
265#554C2×D4314yes—
266#532—431no—
267C2×C4⋊Q8C2×D4311yescharacteristic
268C2×#125—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8—22no—
271C2×C4×Q8C2×D4311yescharacteristic
272C2×C4×D4—21no—
273C2×C4×D4C2×D4311yescharacteristic
274C22×C4⋊C4—21no—
275#492—432no—
276#487—432no—
277#480—861no—
278#474—432no—
279#464—862no—
280#462—432no—
281#461—862no—
282#460—432no—
283#459—432no—
284#448—862no—
285#447—861no—
286C4×D8—862no—
287#431—431no—
288#431—431no—
289#423—431no—
290#417—861no—
291#333—434no—
292Q8⋊C8—434no—
293D4⋊C8—434no—
294C43#1875211yescharacteristic, complemented, Sylow
295C2×#41—861no—
296C22×Q8C22⋊D4311yescharacteristic
297C22×Q8C22⋊D4312yes—
298C22×D4C22⋊D4311yescharacteristic
299C23×C4—22no—
300C23×C4—21no—
301#137—1724no—
302C2×Q16—862no—
303C2×SD16—864no—
304C2×SD16—862no—
305C2×D8—862no—
306C2×M16—861no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—431no—
310C4⋊Q8C22⋊D4312yes—
311C4⋊Q8C22×D4312yes—
312#127—431no—
313#125—24no—
314#125—24no—
315#124—861no—
316C22⋊Q8—24no—
317C22⋊Q8—28no—
318C22⋊Q8—24no—
319C22⋊Q8—28no—
320#121—861no—
321#121—861no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8C22⋊D4312yes—
325C4×Q8C22×D4312yes—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—861no—
331C4×D4—861no—
332C4×D4C22⋊D4312yes—
333C4×D4C22×D4312yes—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4C22⋊D4311yescharacteristic
342C2×C4⋊C4C22⋊D4311yescharacteristic
343C2×C22⋊C4—22no—
344C2×C22⋊C4—21no—
345C2×C42—21no—
346C2×C42C22×D4311yescharacteristic
347#107—862no—
348C4⋊C8—432no—
349C4⋊C8—432no—
350C4⋊C8—861no—
351C4⋊C8—861no—
352#103—864no—
353#103—862no—
354#102—862no—
355#102—862no—
356#102—862no—
357C22⋊C8—861no—
358C22⋊C8—861no—
359C4×C8—432no—
360C4×C8—861no—
361C24—21no—
362#41—1722no—
363#41—1722no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—82no—
369C2×Q8—861no—
370C2×Q8C2×C22⋊D4312yes—
371C2×Q8C2×C22⋊D4314yes—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—861no—
375C2×D4—861no—
376C2×D4—861no—
377C2×D4—1721no—
378C2×D4C2×C22⋊D4312yes—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—28no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—84no—
389C22×C4—1721no—
390C22×C4C2×C22⋊D4311yescharacteristic
391C22×C4C2×C22⋊D4311yescharacteristic
392C22×C4C2×C22⋊D4311yescharacteristic
393Q16—1724no—
394SD16—3444no—
395SD16—1724no—
396D8—1724no—
397M16—1722no—
398C2×C8—862no—
399C2×C8—862no—
400C2×C8—862no—
401C4⋊C4—28no—
402C4⋊C4—28no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—861no—
412C4⋊C4—861no—
413C4⋊C4C2×C22⋊D4312yes—
414C4⋊C4C2×C22⋊D4312yes—
415C22⋊C4—28no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C42—22no—
421C42—22no—
422C42C2×C22⋊D4311yescharacteristic
423C42C2×C22⋊D4311yescharacteristic
424C42C2×C22⋊D4311yescharacteristic
425C42C23×D4311yescharacteristic
426C23—24no—
427C23—22no—
428C23—42no—
429C23—42no—
430C23—1721no—
431C23#1306329411yescharacteristic
432Q8—22no—
433Q8—22no—
434Q8—44no—
435Q8—42no—
436Q8—82no—
437Q8—1721no—
438Q8—1721no—
439D4—24no—
440D4—22no—
441D4—3442no—
442D4—1722no—
443D4—1721no—
444D4—1721no—
445D4—1722no—
446D4#1306335614yescomplemented
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—88no—
461C2×C4—3442no—
462C2×C4—1721no—
463C2×C4#1306329411yescharacteristic
464C2×C4#1306329411yescharacteristic
465C2×C4#1306329411yescharacteristic
466C2×C4#1306334512yes—
467C2×C4#1306335012yes—
468C2×C4C22×C22⋊D4311yescharacteristic
469C2×C4C22×C22⋊D4311yescharacteristic
470C2×C4C22×C22⋊D4311yescharacteristic
471C8—1722no—
472C8—1722no—
473C8—1722no—
474C22—21no—
475C22—21no—
476C22—24no—
477C22—48no—
478C22—42no—
479C22—42no—
480C22—3441no—
481C22—3441no—
482C22—3441no—
483C22#1458304412yes—
484C22C2×#1306329411yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—44no—
490C4—42no—
491C4—42no—
492C4—3441no—
493C4#1458304412yes—
494C4C2×#1306334511yescharacteristic
495C4C2×#1306335011yescharacteristic
496C4C2×#1306335612yes—
497C2—22no—
498C2—44no—
499C2—6881no—
500C2C2×#1458304411yescharacteristic
501C2#1914382911yescharacteristic
502C2#1914395211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#554C2
socleC22×C43C2×#120
prime radical#19144595C2
hypercenterC2×#554D43
hypocenterC43#18752
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #19145520C2semidirect
3. #19144067C2semidirect
4. #19133809C2semidirect
5. #19133667C2semidirect
6. #19133276C2semidirect
7. #19133020C2semidirect
8. #19132990C2semidirect
9. C2×C43×#554C2semidirect
12. #14583273C22semidirect
13. #14583249C22semidirect
17. #14583109C22semidirect
19. #14583099C22semidirect
28. #14582648C22semidirect
29. Q8⋊(C43⋊C8)C22semidirect
187. D4×C43#137semidirect
246. C2×#554D43semidirect
294. C43#18752semidirect
446. D4#13063356semidirect

Maximal subgroups

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

subgroupindex
#191455202
#191445952
#191440672
#191338092
#191336672
#191332762
#191330202
#191329902
C2×C43×#5542
#1875243