Finite Group Databasebeta

← #25075221

Subgroups — #25075221

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
1C2×#14583619C211yesmaximal, characteristic, complemented
2#19145720C211yesmaximal, characteristic, complemented
3#19144063C211yesmaximal, characteristic, complemented
4#19133864C214yesmaximal, complemented
5#19133703C214yesmaximal, complemented
6#19133279C211yesmaximal, characteristic, complemented
7#19133020C211yesmaximal, characteristic, complemented
8#19132989C211yesmaximal, characteristic, complemented
9C43×#3100C211yesmaximal, characteristic
10C2×#13063355—21no—
11#14583619—22no—
12#14583619—22no—
13#14583619—22no—
14#14583619C2214yes—
15C2×#13063325C2211yescharacteristic
16C2×#13063318—22no—
17C2×#13063312—21no—
18C2×#13063304—21no—
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290—21no—
21C2×#13063284—21no—
22#14583295C2212yescomplemented
23#14583245C2212yescomplemented
24#14583215—22no—
25#14583189—22no—
26#14583118—22no—
27#14583106C2212yescomplemented
28#14583096C2212yescomplemented
29#14582952C2211yescharacteristic
30#14582923C2211yescharacteristic
31#14582900—21no—
32#14582646C2214yescomplemented
33#14582629C2214yescomplemented
34D4⋊(C43⋊C8)C2214yes—
35C43×#532C2211yescharacteristic
36C2×C4×D4×C43C2211yescharacteristic
37C43×#480—21no—
38C43×#474C2212yes—
39C43×#459C2212yes—
40C43×#447—21no—
41C4×D8×C43—22no—
42C43×#431C2211yescharacteristic
43C22×Dic86—21no—
44C22×Dic86D411yescharacteristic
45#13063355—44no—
46C2×#10621885—22no—
47C2×#10621883—22no—
48C2×#10621877—21no—
49#13063325—21no—
50#13063325—21no—
51#13063325D412yes—
52#13063325C2312yes—
53#13063318—28no—
54#13063318—28no—
55#13063312—24no—
56#13063312—24no—
57#13063304—24no—
58#13063304—24no—
59C4×Dic86—21no—
60C4×Dic86—21no—
61C4×Dic86D412yes—
62C4×Dic86C2312yes—
63#13063290—24no—
64#13063290—24no—
65#13063284—24no—
66#13063284—24no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D412yes—
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—21no—
72C2×C22⋊Dic43—22no—
73C2×C22⋊Dic43—22no—
74C2×C4×Dic43—22no—
75C2×C4×Dic43—21no—
76#13063256—24no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)—21no—
79C4⋊(C43⋊C8)C2312yes—
80#13063249—22no—
81#13063246—22no—
82#13063246—24no—
83C22⋊(C43⋊C8)—21no—
84C4×C43⋊C8C2312yes—
85C2×#41×C43—21no—
86C22×D4×C43D411yescharacteristic
87C23×C4×C43—21no—
88C2×D8×C43—22no—
89C4⋊Q8×C43C2311yescharacteristic
90#127×C43C2311yescharacteristic
91#124×C43—21no—
92#121×C43—21no—
93#121×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43D412yes—
99C4×D4×C43C2312yes—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C22⋊C4×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#107×C43—22no—
104C4⋊C8×C43C2312yes—
105#102×C43—22no—
106#102×C43—22no—
107C22⋊C8×C43—21no—
108C4×C8×C43—21no—
109C24×C43—21no—
110#41×C43—42no—
111#41×C43—42no—
112C2×Q8×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—42no—
118C2×D4×C43—41no—
119C2×D4×C43C2×D412yes—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—42no—
124C22×C4×C43—42no—
125C22×C4×C43—41no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—22no—
132C2×Dic86—22no—
133C2×Dic86—22no—
134C2×Dic86—22no—
135C2×Dic86—21no—
136C2×Dic86—22no—
137C2×Dic86—44no—
138C2×Dic86C2×D412yes—
139D8×C43—44no—
140C2×C8×C43—22no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43C2×D412yes—
145C22⋊C4×C43—22no—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—41no—
148C22⋊C4×C43—41no—
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43C2411yescharacteristic
153C22⋊Dic43—28no—
154C22⋊Dic43—28no—
155#10621885—44no—
156#10621883—44no—
157C4⋊Dic43—22no—
158C4⋊Dic43—21no—
159C4⋊Dic43—22no—
160C4⋊Dic43—22no—
161C4⋊Dic43C2×D412yes—
162C4⋊Dic43C2×D414yes—
163Dic43⋊C4—28no—
164Dic43⋊C4—22no—
165Dic43⋊C4—22no—
166C4×Dic43—28no—
167C4×Dic43—22no—
168C4×Dic43—22no—
169#10621877—42no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—22no—
172C23×C43—22no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43—41no—
177C23×C43#12011yescharacteristic
178Q8×C43—41no—
179Q8×C43—41no—
180D4×C43—22no—
181D4×C43—22no—
182D4×C43—42no—
183D4×C43—42no—
184D4×C43—41no—
185D4×C43—41no—
186D4×C43—42no—
187D4×C43—82no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—41no—
191C2×C4×C43—42no—
192C2×C4×C43—42no—
193C2×C4×C43—42no—
194C2×C4×C43—44no—
195C2×C4×C43—41no—
196C2×C4×C43—82no—
197C2×C4×C43#12011yescharacteristic
198C2×C4×C43#12011yescharacteristic
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#13512yes—
201C2×C4×C43AGL(1,ℤ/8)12yes—
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C2×Dic43—22no—
206C2×Dic43—22no—
207C2×Dic43—24no—
208C2×Dic43—44no—
209C2×Dic43—42no—
210C2×Dic43—42no—
211Dic86—22no—
212Dic86—22no—
213Dic86—44no—
214Dic86—44no—
215Dic86—42no—
216C8×C43—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—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43#44912yes—
230C22×C43C2×#12011yescharacteristic
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—42no—
235C4×C43—81no—
236C4×C43#44912yes—
237C4×C43C2×#13511yescharacteristic
238C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C43#57512yes—
240Dic43—42no—
241Dic43—44no—
242Dic43—42no—
243C2×#556—431no—
244#3227—431no—
245#3100D4311yescharacteristic
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×C43—161no—
255C2×C43C2×#44911yescharacteristic
256C2×C43#300511yescharacteristic
257C2×C43#302011yescharacteristic
258C2×#137—861no—
259#556—434no—
260#556—862no—
261#556—862no—
262#556—862no—
263#532C2×D4311yescharacteristic
264C2×C4⋊Q8—431no—
265C2×#126—862no—
266C2×#124—861no—
267C2×C22⋊Q8—861no—
268C2×C4×Q8—431no—
269C2×C4×Q8—861no—
270C2×C4×D4C2×D4311yescharacteristic
271C2×#117—861no—
272#498—432no—
273#486—432no—
274#481—862no—
275#480—21no—
276#476—862no—
277#474C2×D4312yes—
278#464—862no—
279#462—432no—
280#460—432no—
281#459C2×D4312yes—
282#447—21no—
283C4×D8—22no—
284#431—431no—
285#431C2×D4311yescharacteristic
286#423—431no—
287#417—861no—
288#332—434no—
289Q8⋊C8—434no—
290D4⋊C8—434no—
291C43#1876211yescharacteristic, complemented, Sylow
292C2×#41—21no—
293C22×Q8—431no—
294C22×Q8—861no—
295C22×D4C22⋊D4311yescharacteristic
296C23×C4—21no—
297#137—1724no—
298C2×Q16—862no—
299C2×SD16—862no—
300C2×D8—22no—
301C2×M16—861no—
302C4⋊Q8—432no—
303C4⋊Q8—432no—
304C4⋊Q8—861no—
305C4⋊Q8—861no—
306C4⋊Q8C22×D4311yescharacteristic
307#127C22×D4311yescharacteristic
308#126—868no—
309#126—868no—
310#124—21no—
311#124—864no—
312#124—864no—
313C22⋊Q8—864no—
314C22⋊Q8—864no—
315#121—21no—
316#121—21no—
317C4×Q8—432no—
318C4×Q8—432no—
319C4×Q8—864no—
320C4×Q8—864no—
321C4×Q8—861no—
322C4×Q8—861no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4C22⋊D4312yes—
328C4×D4C22×D4312yes—
329#117—864no—
330#117—864no—
331C2×C4⋊C4—431no—
332C2×C4⋊C4—432no—
333C2×C4⋊C4—862no—
334C2×C4⋊C4—861no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4C22⋊D4311yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—862no—
339C2×C22⋊C4—862no—
340C2×C42—862no—
341C2×C42—861no—
342C2×C42C22×D4311yescharacteristic
343#107—22no—
344#106—864no—
345C4⋊C8—432no—
346C4⋊C8—861no—
347C4⋊C8—861no—
348C4⋊C8C22×D4312yes—
349#103—862no—
350#102—22no—
351#102—22no—
352#102—862no—
353#102—864no—
354C22⋊C8—21no—
355C22⋊C8—861no—
356C4×C8—21no—
357C4×C8—432no—
358C24—21no—
359#41—42no—
360#41—42no—
361C2×Q8—21no—
362C2×Q8—432no—
363C2×Q8—861no—
364C2×Q8—862no—
365C2×Q8—862no—
366C2×Q8—862no—
367C2×Q8—862no—
368C2×Q8—1724no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—42no—
374C2×D4—41no—
375C2×D4C2×C22⋊D4312yes—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—41no—
382C22×C4—861no—
383C22×C4—862no—
384C22×C4—861no—
385C22×C4D4×D4311yescharacteristic
386C22×C4D4×D4311yescharacteristic
387C22×C4C2×C22⋊D4311yescharacteristic
388Q16—1724no—
389SD16—1724no—
390D8—44no—
391M16—1722no—
392C2×C8—22no—
393C2×C8—862no—
394C2×C8—862no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—432no—
399C4⋊C4—434no—
400C4⋊C4—868no—
401C4⋊C4—861no—
402C4⋊C4—862no—
403C4⋊C4—862no—
404C4⋊C4—862no—
405C4⋊C4—862no—
406C4⋊C4—862no—
407C4⋊C4C2×C22⋊D4312yes—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—868no—
413C22⋊C4—868no—
414C42—868no—
415C42—862no—
416C42—862no—
417C42D4×D4311yescharacteristic
418C42D4×D4311yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—22no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—41no—
426C23#1306329311yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—862no—
430Q8—862no—
431Q8—1724no—
432Q8—1722no—
433Q8—1724no—
434D4—22no—
435D4—22no—
436D4—42no—
437D4—42no—
438D4—41no—
439D4—41no—
440D4—42no—
441D4—82no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—82no—
451C2×C4—862no—
452C2×C4—864no—
453C2×C4—862no—
454C2×C4—1724no—
455C2×C4—1722no—
456C2×C4—1722no—
457C2×C4#1306329311yescharacteristic
458C2×C4#1306329311yescharacteristic
459C2×C4#1306329311yescharacteristic
460C2×C4#1306334412yes—
461C2×C4#1306334912yes—
462C2×C4C2×D4×D4311yescharacteristic
463C2×C4C2×D4×D4311yescharacteristic
464C2×C4C22×C22⋊D4311yescharacteristic
465C8—42no—
466C8—1722no—
467C8—1722no—
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—84no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22#1458304112yes—
478C22C2×#1306329311yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—1722no—
485C4—1722no—
486C4—1724no—
487C4#1458304112yes—
488C4C2×#1306334411yescharacteristic
489C4C2×#1306334911yescharacteristic
490C4#1458369712yes—
491C2—22no—
492C2—82no—
493C2—161no—
494C2C2×#1458304111yescharacteristic
495C2#1914383511yescharacteristic
496C2#1914395711yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3100C2
socleC22×C43C2×#120
hypercenter#3100D43
hypocenterC43#18762
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. C2×#14583619C2semidirect
2. #19145720C2semidirect
3. #19144063C2semidirect
4. #19133864C2semidirect
5. #19133703C2semidirect
6. #19133279C2semidirect
7. #19133020C2semidirect
8. #19132989C2semidirect
22. #14583295C22semidirect
23. #14583245C22semidirect
27. #14583106C22semidirect
28. #14583096C22semidirect
32. #14582646C22semidirect
33. #14582629C22semidirect
291. C43#18762semidirect

Maximal subgroups

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

subgroupindex
C2×#145836192
#191457202
#191440632
#191338642
#191337032
#191332792
#191330202
#191329892
C43×#31002
#1876243