Finite Group Databasebeta

← #25077890

Subgroups — #25077890

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583649C211yesmaximal, characteristic, complemented
2#19145781C211yesmaximal, characteristic, complemented
3#19144995C211yesmaximal, characteristic, complemented
4#19133928C214yesmaximal, complemented
5#19133891C214yesmaximal, complemented
6#19133221C211yesmaximal, characteristic, complemented
7#19133198C211yesmaximal, characteristic, complemented
8#19133193C211yesmaximal, characteristic, complemented
9C43×#3213C211yesmaximal, characteristic
10#14583649—22no—
11#14583649—22no—
12#14583649—22no—
13#14583649C2214yes—
14C2×#13063323—21no—
15C2×#13063318—21no—
16C2×#13063318—21no—
17C2×#13063317C2211yescharacteristic
18C2×#13063317C2211yescharacteristic
19C2×#13063306—21no—
20C2×#13063302—21no—
21C2×#13063302—21no—
22#14583305C2212yescomplemented
23#14583267C2212yescomplemented
24#14583263C2212yescomplemented
25#14583263C2212yescomplemented
26#14583253—22no—
27#14583215—21no—
28#14583210—21no—
29#14583199—22no—
30#14582956C2211yescharacteristic
31#14582900—21no—
32#14582900—21no—
33C4×#10621877C2211yescharacteristic
34#14582640C2214yescomplemented
35#14582640C2214yescomplemented
36#14582639C2214yes—
37C43×#532C2211yescharacteristic
38C2×#124×C43C2211yescharacteristic
39C43×#496C2212yes—
40C43×#489C2212yes—
41C43×#463—22no—
42C43×#448—21no—
43C43×#447—21no—
44C43×#432C2211yescharacteristic
45C22×Dic86—21no—
46C23×Dic43—21no—
47C2×#10621877—21no—
48#13063323—24no—
49#13063323—24no—
50#13063318—24no—
51#13063318—24no—
52#13063318—24no—
53#13063318—24no—
54#13063317—21no—
55#13063317—21no—
56#13063317—21no—
57#13063317—21no—
58#13063317D412yes—
59#13063317D412yes—
60#13063317C2312yes—
61#13063317C2312yes—
62#13063306—24no—
63#13063306—24no—
64#13063302—24no—
65#13063302—24no—
66#13063302—24no—
67#13063302—24no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43D411yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82#13063258—22no—
83#13063256—22no—
84C4⋊(C43⋊C8)—21no—
85#13063249—22no—
86#13063249—22no—
87#13063246—22no—
88#13063246—22no—
89#13063246—22no—
90#13063246—22no—
91C22⋊(C43⋊C8)—21no—
92#13063236C2312yes—
93#13063236C2312yes—
94C4×C43⋊C8—21no—
95C2×#41×C43—21no—
96C22×Q8×C43D411yescharacteristic
97C22×D4×C43D411yescharacteristic
98C2×SD16×C43—22no—
99C2×D8×C43—22no—
100C4⋊Q8×C43C2311yescharacteristic
101#127×C43C2311yescharacteristic
102#124×C43—21no—
103#124×C43—21no—
104#124×C43—21no—
105#124×C43D412yes—
106#124×C43C2312yes—
107#121×C43—21no—
108#121×C43—21no—
109C4×D4×C43—21no—
110C4×D4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C42×C43C2311yescharacteristic
114C4⋊C8×C43—21no—
115#103×C43—22no—
116#102×C43—22no—
117C22⋊C8×C43—21no—
118#97×C43C2312yes—
119C24×C43—21no—
120#41×C43—44no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—81no—
124C2×Q8×C43C2×D412yes—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—41no—
130C2×D4×C43—81no—
131C2×D4×C43C2×D412yes—
132C22×C4×C43—21no—
133C22×C4×C43—41no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×Dic43—24no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—82no—
143C2×Dic86—24no—
144C2×Dic86—82no—
145SD16×C43—82no—
146D8×C43—82no—
147C2×C8×C43—22no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C22⋊C4×C43—22no—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—22no—
153C22⋊C4×C43—22no—
154C22⋊C4×C43—41no—
155C22⋊C4×C43—41no—
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C42×C43C2×D411yescharacteristic
159C42×C43C2411yescharacteristic
160C22⋊Dic43—24no—
161C22⋊Dic43—24no—
162C22⋊Dic43—24no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43C2×D412yes—
168C4⋊Dic43C2×D412yes—
169C4⋊Dic43C2×D412yes—
170C4⋊Dic43C2×D412yes—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175Dic43⋊C4—22no—
176Dic43⋊C4—22no—
177Dic43⋊C4—22no—
178Dic43⋊C4—22no—
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181C4×Dic43—24no—
182#10621877—42no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C23×C43—22no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—41no—
190C23×C43#12011yescharacteristic
191Q8×C43—42no—
192Q8×C43—42no—
193Q8×C43—81no—
194D4×C43—42no—
195D4×C43—42no—
196D4×C43—42no—
197D4×C43—42no—
198D4×C43—81no—
199D4×C43—82no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—42no—
205C2×C4×C43—41no—
206C2×C4×C43—82no—
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43C22×D411yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C2×C4×C43C22×D411yescharacteristic
213C2×Dic43—22no—
214C2×Dic43—22no—
215C2×Dic43—22no—
216C2×Dic43—22no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—42no—
220C2×Dic43—42no—
221C2×Dic43—84no—
222Dic86—84no—
223C8×C43—42no—
224C43⋊C8—42no—
225C43⋊C8—42no—
226#19002—431nomaximal, Sylow
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—42no—
230C22×C43—42no—
231C22×C43—42no—
232C22×C43—84no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43#45412yes—
237C22×C43C2×#12011yescharacteristic
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—42no—
245C4×C43—81no—
246Dic43—42no—
247Dic43—42no—
248Dic43—42no—
249Dic43—42no—
250C2×#563—431no—
251#3234—431no—
252#3213D4311yescharacteristic
253#3142—431no—
254#1664—434no—
255#1657—434no—
256#1534—431no—
257#1528—431no—
258#1527—431no—
259C2×C43—22no—
260C2×C43—82no—
261C2×C43—161no—
262C2×C43C2×#45411yescharacteristic
263C2×C43#301911yescharacteristic
264C2×C43#302011yescharacteristic
265#563—434no—
266#563—862no—
267#563—862no—
268#563—862no—
269#532C2×D4311yescharacteristic
270C2×C4⋊Q8—861no—
271C2×#126—861no—
272C2×#126—861no—
273C2×#125—431no—
274C2×#125—431no—
275C2×#124C2×D4311yescharacteristic
276C2×#123—861no—
277C2×C22⋊Q8—861no—
278C2×C22⋊Q8—861no—
279#501—432no—
280#496C2×D4312yes—
281#491—432no—
282#490—432no—
283#490—432no—
284#489C2×D4312yes—
285#488—862no—
286#481—861no—
287#480—861no—
288#478—862no—
289#463—22no—
290#448—21no—
291#447—21no—
292#432—431no—
293#432C2×D4311yescharacteristic
294#417—861no—
295#417—861no—
296C4×M16—431no—
297#330—434no—
298#330—434no—
299#329—434no—
300C43#1900211yescharacteristic, complemented, Sylow
301C2×#41—21no—
302C22×Q8—861no—
303C22×Q8C22⋊D4311yescharacteristic
304C22×D4C22⋊D4311yescharacteristic
305C23×C4—861no—
306C2×SD16—22no—
307C2×D8—22no—
308C2×M16—861no—
309C4⋊Q8—864no—
310C4⋊Q8—864no—
311C4⋊Q8C22×D4311yescharacteristic
312#127C22×D4311yescharacteristic
313#126—864no—
314#126—864no—
315#126—864no—
316#126—864no—
317#125—432no—
318#125—432no—
319#125—432no—
320#125—432no—
321#125—861no—
322#125—861no—
323#125—861no—
324#125—861no—
325#124—21no—
326#124—21no—
327#124—21no—
328#124C22⋊D4312yes—
329#124C22×D4312yes—
330#123—864no—
331#123—864no—
332C22⋊Q8—864no—
333C22⋊Q8—864no—
334C22⋊Q8—864no—
335C22⋊Q8—864no—
336#121—21no—
337#121—21no—
338C4×D4—21no—
339C4×D4—21no—
340C2×C4⋊C4—431no—
341C2×C4⋊C4—431no—
342C2×C4⋊C4—431no—
343C2×C4⋊C4—431no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4—861no—
348C2×C4⋊C4—861no—
349C2×C4⋊C4—861no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—861no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4—861no—
355C2×C42—861no—
356C2×C42C22×D4311yescharacteristic
357#107—862no—
358#106—862no—
359C4⋊C8—21no—
360C4⋊C8—861no—
361#103—22no—
362#103—862no—
363#103—862no—
364#102—22no—
365#102—862no—
366#102—862no—
367#102—862no—
368#102—862no—
369C22⋊C8—21no—
370C22⋊C8—861no—
371#97—432no—
372#97—432no—
373#97C22×D4312yes—
374C4×C8—861no—
375C24—21no—
376#41—44no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—81no—
380C2×Q8—864no—
381C2×Q8—3442no—
382C2×Q8C2×C22⋊D4312yes—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—81no—
389C2×D4C2×C22⋊D4312yes—
390C22×C4—21no—
391C22×C4—41no—
392C22×C4—864no—
393C22×C4—861no—
394C22×C4—861no—
395C22×C4—861no—
396C22×C4—861no—
397C22×C4—3442no—
398C22×C4D4×D4311yescharacteristic
399C22×C4D4×D4311yescharacteristic
400C22×C4C2×C22⋊D4311yescharacteristic
401SD16—82no—
402D8—82no—
403M16—1722no—
404C2×C8—22no—
405C2×C8—862no—
406C2×C8—862no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—432no—
410C4⋊C4—432no—
411C4⋊C4—432no—
412C4⋊C4—432no—
413C4⋊C4—864no—
414C4⋊C4—864no—
415C4⋊C4—861no—
416C4⋊C4—861no—
417C4⋊C4—861no—
418C4⋊C4—861no—
419C4⋊C4—862no—
420C4⋊C4—862no—
421C4⋊C4—862no—
422C4⋊C4—862no—
423C4⋊C4—862no—
424C4⋊C4—862no—
425C4⋊C4—862no—
426C4⋊C4—862no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—864no—
434C22⋊C4—864no—
435C22⋊C4—864no—
436C42—864no—
437C42D4×D4311yescharacteristic
438C42D4×D4311yescharacteristic
439C42C2×C22⋊D4311yescharacteristic
440C42C23×D4311yescharacteristic
441C23—22no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—41no—
446C23#1306329311yescharacteristic
447Q8—42no—
448Q8—42no—
449Q8—81no—
450Q8—3444no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—81no—
456D4—82no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—82no—
464C2×C4—862no—
465C2×C4—862no—
466C2×C4—862no—
467C2×C4—862no—
468C2×C4—3444no—
469C2×C4—1722no—
470C2×C4—1722no—
471C2×C4—1722no—
472C2×C4—1722no—
473C2×C4#1306329311yescharacteristic
474C2×C4#1306329311yescharacteristic
475C2×C4#1306329311yescharacteristic
476C2×C4C2×D4×D4311yescharacteristic
477C2×C4C2×D4×D4311yescharacteristic
478C2×C4C22×C22⋊D4311yescharacteristic
479C8—42no—
480C8—1722no—
481C8—1722no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—84no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22#1458307012yes—
492C22C2×#1306329311yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—42no—
500C4—81no—
501C4—1722no—
502C4—1722no—
503C4—1722no—
504C4—1722no—
505C2—22no—
506C2—82no—
507C2—161no—
508C2C2×#1458307011yescharacteristic
509C2#1914395111yescharacteristic
510C2#1914395711yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3213C2
socleC22×C43C2×#120
hypercenter#3213D43
hypocenterC43#19002
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3213

Complements

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

NH ≅ G/Ntype
1. C2×#14583649C2semidirect
2. #19145781C2semidirect
3. #19144995C2semidirect
4. #19133928C2semidirect
5. #19133891C2semidirect
6. #19133221C2semidirect
7. #19133198C2semidirect
8. #19133193C2semidirect
22. #14583305C22semidirect
23. #14583267C22semidirect
24. #14583263C22semidirect
25. #14583263C22semidirect
34. #14582640C22semidirect
35. #14582640C22semidirect
300. C43#19002semidirect

Maximal subgroups

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

subgroupindex
C2×#145836492
#191457812
#191449952
#191339282
#191338912
#191332212
#191331982
#191331932
C43×#32132
#1900243