Finite Group Databasebeta

← #25075222

Subgroups — #25075222

Order 11008.

964 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145723C211yesmaximal, characteristic, complemented
2#19144595C211yesmaximal, characteristic
3#19144067C211yesmaximal, characteristic, complemented
4#19133865C214yesmaximal, complemented
5#19133705C214yesmaximal, complemented
6#19133280C211yesmaximal, characteristic, complemented
7#19133020C211yesmaximal, characteristic, complemented
8#19132990C211yesmaximal, characteristic, complemented
9C2×C43×#556C211yesmaximal, characteristic, complemented
10C2×#13063356—21no—
11#14583449C2211yescharacteristic
12#14583295C2212yescomplemented
13#14583247C2212yescomplemented
14#14583217—22no—
15#14583212—21no—
16#14583186—22no—
17#14583179C2212yes—
18#14583121—22no—
19#14583109C2212yescomplemented
20#14583099C2212yescomplemented
21#14583094C2212yes—
22#14583033—21no—
23C4×#10621882—22no—
24#14582952C2211yescharacteristic
25#14582952C2211yescharacteristic
26#14582923C2211yescharacteristic
27#14582898—21no—
28#14582645C2214yescomplemented
29Q8⋊(C43⋊C8)C2214yescomplemented
30D4⋊(C43⋊C8)C2214yes—
31C43×#556—22no—
32C43×#556—22no—
33C43×#556—22no—
34C43×#556C2214yes—
35C2×C4⋊Q8×C43C2211yescharacteristic
36C2×#126×C43—22no—
37C2×#124×C43—21no—
38C2×C22⋊Q8×C43—21no—
39C2×C4×Q8×C43—21no—
40C2×C4×Q8×C43C2211yescharacteristic
41C2×C4×D4×C43C2211yescharacteristic
42C2×#117×C43—21no—
43C2×#10621898—21no—
44#13063356—44no—
45C2×#10621885—22no—
46C2×#10621884—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—
71C22×Q8×C43—21no—
72C22×Q8×C43D411yescharacteristic
73C22×D4×C43D411yescharacteristic
74C23×C4×C43—21no—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43—21no—
77C4⋊Q8×C43D412yes—
78C4⋊Q8×C43C2312yes—
79#126×C43—28no—
80#126×C43—28no—
81#124×C43—24no—
82#124×C43—24no—
83C22⋊Q8×C43—24no—
84C22⋊Q8×C43—24no—
85C4×Q8×C43—24no—
86C4×Q8×C43—24no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43D412yes—
90C4×Q8×C43C2312yes—
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43D412yes—
94C4×D4×C43C2312yes—
95#117×C43—24no—
96#117×C43—24no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43D412yes—
103C2×C22⋊C4×C43—22no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43—21no—
106C2×C42×C43—22no—
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—22no—
115C2×Q8×C43—44no—
116C2×Q8×C43C2×D412yes—
117C2×D4×C43—21no—
118C2×D4×C43—42no—
119C2×D4×C43C2×D412yes—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C2×C22⋊D43—41no—
132#10621898—42no—
133#10621898—42no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×C4×D43—41no—
138C2×Dic86—21no—
139C4⋊C4×C43—28no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43C2×D412yes—
148C4⋊C4×C43C2×D412yes—
149C4⋊C4×C43C2×D414yes—
150C22⋊C4×C43—28no—
151C22⋊C4×C43—28no—
152C22⋊C4×C43—22no—
153C22⋊C4×C43—22no—
154C42×C43—28no—
155C42×C43—22no—
156C42×C43—22no—
157C42×C43C2×D411yescharacteristic
158C42×C43C2×D411yescharacteristic
159C42×C43C2×D411yescharacteristic
160C42×C43C2411yescharacteristic
161#10621885—44no—
162#10621884—44no—
163#10621882—44no—
164(C2×D43)⋊C4—41no—
165(C2×D43)⋊C4—41no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168#10621877—42no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—22no—
172C23×C43—22no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43#12011yescharacteristic
177C22×D43—41no—
178Q8×C43—22no—
179Q8×C43—22no—
180Q8×C43—44no—
181Q8×C43—44no—
182Q8×C43—42no—
183D4×C43—22no—
184D4×C43—22no—
185D4×C43—42no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—24no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—44no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—44no—
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#12011yescharacteristic
201C2×C4×C43#12011yescharacteristic
202C2×C4×C43#13512yes—
203C2×C4×C43AGL(1,ℤ/8)12yes—
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C22⋊D43—82no—
208C2×Dic43—41no—
209D172—42no—
210D172—41no—
211D172—41no—
212D172—42no—
213C4×D43—82no—
214Dic86—41no—
215Dic86—41no—
216C43⋊C8—42no—
217C43⋊C8—42no—
218C43⋊C8—42no—
219#18762—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—42no—
223C22×C43—42no—
224C22×C43—42no—
225C22×C43—84no—
226C22×C43#44912yes—
227C22×C43C2×#12011yescharacteristic
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—42no—
235C4×C43—42no—
236C4×C43—44no—
237C4×C43—42no—
238C4×C43#44912yes—
239C4×C43C2×#13511yescharacteristic
240C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
241C4×C43#57512yes—
242Dic43—81no—
243C2×#556D4311yescharacteristic, complemented
244#3227—431no—
245#3100—431no—
246#3037—431no—
247#1652—434no—
248#1628—434no—
249#1549—431no—
250#1486—431no—
251#1479—431no—
252C2×C43—22no—
253C2×C43—82no—
254C2×C43C2×#44911yescharacteristic
255C2×C43#300511yescharacteristic
256C2×C43#302011yescharacteristic
257D43—161no—
258C2×#137—861no—
259#556—22no—
260#556—22no—
261#556—22no—
262#556C2×D4314yes—
263#532—431no—
264C2×C4⋊Q8C2×D4311yescharacteristic
265C2×#126—22no—
266C2×#124—21no—
267C2×C22⋊Q8—21no—
268C2×C4×Q8—21no—
269C2×C4×Q8C2×D4311yescharacteristic
270C2×C4×D4C2×D4311yescharacteristic
271C2×#117—21no—
272#498—432no—
273#486—432no—
274#481—862no—
275#480—861no—
276#476—862no—
277#474—432no—
278#464—862no—
279#462—432no—
280#460—432no—
281#459—432no—
282#447—861no—
283C4×D8—862no—
284#431—431no—
285#431—431no—
286#423—431no—
287#417—861no—
288#332—434no—
289Q8⋊C8—434no—
290D4⋊C8—434no—
291C43#1876211yescharacteristic, complemented, Sylow
292C2×#41—861no—
293C22×Q8—21no—
294C22×Q8C22⋊D4311yescharacteristic
295C22×D4C22⋊D4311yescharacteristic
296C23×C4—21no—
297#137—1724no—
298C2×Q16—862no—
299C2×SD16—862no—
300C2×D8—862no—
301C2×M16—861no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—431no—
305C4⋊Q8C22⋊D4312yes—
306C4⋊Q8C22×D4312yes—
307#127—431no—
308#126—28no—
309#126—28no—
310#124—24no—
311#124—24no—
312#124—861no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315#121—861no—
316#121—861no—
317C4×Q8—24no—
318C4×Q8—24no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8C22⋊D4312yes—
322C4×Q8C22×D4312yes—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—861no—
326C4×D4—861no—
327C4×D4C22⋊D4312yes—
328C4×D4C22×D4312yes—
329#117—24no—
330#117—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4C22⋊D4311yescharacteristic
335C2×C4⋊C4C22⋊D4311yescharacteristic
336C2×C4⋊C4C22⋊D4312yes—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—21no—
340C2×C42—22no—
341C2×C42—21no—
342C2×C42C22×D4311yescharacteristic
343#107—862no—
344#106—864no—
345C4⋊C8—432no—
346C4⋊C8—432no—
347C4⋊C8—861no—
348C4⋊C8—861no—
349#103—862no—
350#102—862no—
351#102—862no—
352#102—862no—
353#102—864no—
354C22⋊C8—861no—
355C22⋊C8—861no—
356C4×C8—432no—
357C4×C8—861no—
358C24—21no—
359#41—1722no—
360#41—1722no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—44no—
367C2×Q8—861no—
368C2×Q8C2×C22⋊D4312yes—
369C2×D4—21no—
370C2×D4—42no—
371C2×D4—861no—
372C2×D4—861no—
373C2×D4—861no—
374C2×D4—1721no—
375C2×D4C2×C22⋊D4312yes—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—1721no—
385C22×C4C2×C22⋊D4311yescharacteristic
386C22×C4C2×C22⋊D4311yescharacteristic
387C22×C4C2×C22⋊D4311yescharacteristic
388Q16—1724no—
389SD16—1724no—
390D8—1724no—
391M16—1722no—
392C2×C8—862no—
393C2×C8—862no—
394C2×C8—862no—
395C4⋊C4—28no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C4⋊C4C2×C22⋊D4312yes—
406C4⋊C4C2×C22⋊D4314yes—
407C4⋊C4C2×C22⋊D4312yes—
408C22⋊C4—28no—
409C22⋊C4—28no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C42—28no—
415C42—22no—
416C42—22no—
417C42C2×C22⋊D4311yescharacteristic
418C42C2×C22⋊D4311yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—22no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—1721no—
426C23#1306329411yescharacteristic
427Q8—22no—
428Q8—22no—
429Q8—44no—
430Q8—42no—
431Q8—44no—
432Q8—1721no—
433Q8—1721no—
434D4—22no—
435D4—22no—
436D4—42no—
437D4—3442no—
438D4—1722no—
439D4—1721no—
440D4—1721no—
441D4—1722no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—41no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—3442no—
456C2×C4—1721no—
457C2×C4#1306329411yescharacteristic
458C2×C4#1306329411yescharacteristic
459C2×C4#1306329411yescharacteristic
460C2×C4#1306334512yes—
461C2×C4#1306335012yes—
462C2×C4C22×C22⋊D4311yescharacteristic
463C2×C4C22×C22⋊D4311yescharacteristic
464C2×C4C22×C22⋊D4311yescharacteristic
465C8—1722no—
466C8—1722no—
467C8—1722no—
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—84no—
474C22—3441no—
475C22—3441no—
476C22—3441no—
477C22#1458304412yes—
478C22C2×#1306329411yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—44no—
486C4—3441no—
487C4#1458304412yes—
488C4C2×#1306334511yescharacteristic
489C4C2×#1306335011yescharacteristic
490C4#1458369712yes—
491C2—22no—
492C2—82no—
493C2—6881no—
494C2C2×#1458304411yescharacteristic
495C2#1914383711yescharacteristic
496C2#1914395911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#556C2
socleC22×C43C2×#120
prime radical#19144595C2
hypercenterC2×#556D43
hypocenterC43#18762
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #19145723C2semidirect
3. #19144067C2semidirect
4. #19133865C2semidirect
5. #19133705C2semidirect
6. #19133280C2semidirect
7. #19133020C2semidirect
8. #19132990C2semidirect
9. C2×C43×#556C2semidirect
12. #14583295C22semidirect
13. #14583247C22semidirect
19. #14583109C22semidirect
20. #14583099C22semidirect
28. #14582645C22semidirect
29. Q8⋊(C43⋊C8)C22semidirect
243. C2×#556D43semidirect
291. C43#18762semidirect

Maximal subgroups

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

subgroupindex
#191457232
#191445952
#191440672
#191338652
#191337052
#191332802
#191330202
#191329902
C2×C43×#5562
#1876243