Finite Group Databasebeta

← #25079407

Subgroups — #25079407

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144969C211yesmaximal, characteristic, complemented
2#19144604C211yesmaximal, characteristic, complemented
3C2×#14583091C211yesmaximal, characteristic
4#19143330C211yesmaximal, characteristic, complemented
5#19134155C212yesmaximal, complemented
6#19134127C212yesmaximal, complemented
7#19134031C212yesmaximal, complemented
8#19134003C212yesmaximal, complemented
9#19133348C211yesmaximal, characteristic, complemented
10#19133286C211yesmaximal, characteristic, complemented
11C43×#1545C211yesmaximal, characteristic, complemented
12C22×#10621882—21no—
13C2×M16×D43—21no—
14#14583456C2211yescharacteristic
15C2×C4×D172C2211yescharacteristic
16#14583263—22no—
17#14583245C2212yescomplemented
18#14583245C2212yescomplemented
19#14583230—21no—
20#14583190C2211yescharacteristic, complemented
21#14583190C2211yescharacteristic, complemented
22#14583105C2211yescharacteristic, complemented
23#14583105C2211yescharacteristic, complemented
24#14583091—21no—
25#14583091—21no—
26#14583091C2212yes—
27#14583091C2212yes—
28#14583052—21no—
29C4×#10621873—21no—
30C4×#10621873—21no—
31#14582976C2212yescomplemented
32#14582969—22no—
33#14582964C2212yescomplemented
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35#14582904—21no—
36#14582904—21no—
37C2×#13063246—21no—
38#14582862—21no—
39C4×#10621877C2211yescharacteristic
40#14582651C2212yescomplemented
41#14582649C2212yescomplemented
42#14582647C2212yescomplemented
43#14582644C2212yescomplemented
44C2×#127×C43C2211yescharacteristic
45C43×#431C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C43×#331C2212yescomplemented
48C43×#331C2212yescomplemented
49C22×D172D411yescharacteristic
50C22×C4×D43—21no—
51C2×#10621873—21no—
52C2×#10621873—21no—
53C2×#10621882—22no—
54C2×#10621882—22no—
55C2×#10621882—44no—
56C2×#10621877D411yescharacteristic
57C2×#10621877D411yescharacteristic
58C2×#10621872—22no—
59M16×D43—44no—
60C22×C43⋊C8—21no—
61C2×C8×D43—22no—
62#13063325C2311yescharacteristic
63#13063325C2311yescharacteristic
64#13063317—21no—
65#13063304—21no—
66#13063304—21no—
67C4×Dic86—21no—
68C4×Dic86—21no—
69C4×D172—21no—
70C4×D172—21no—
71C4×D172D411yescharacteristic
72C4×D172D411yescharacteristic
73C4×D172C2311yescharacteristic
74C4×D172C2311yescharacteristic
75#13063284—21no—
76C2×C4⋊Dic43D411yescharacteristic
77C2×(C2×D43)⋊C4—21no—
78#13063257—21no—
79#13063257—21no—
80C4⋊(C43⋊C8)—21no—
81C4⋊(C43⋊C8)C2312yes—
82#13063250—21no—
83#13063250—21no—
84#13063247—21no—
85#13063247—21no—
86#13063246—22no—
87#13063246—22no—
88#13063246—22no—
89#13063246—22no—
90#13063246—22no—
91#13063246—22no—
92(C2×D43)⋊C8—22no—
93(C2×D43)⋊C8—22no—
94#13063236D412yes—
95C4×C43⋊C8C2312yes—
96C22×D4×C43—21no—
97C22×D4×C43—21no—
98C22×D4×C43—21no—
99C2×M16×C43—21no—
100#127×C43—21no—
101#127×C43—21no—
102#127×C43—21no—
103#127×C43C2312yes—
104C2×C42×C43C2311yescharacteristic
105C4⋊C8×C43—21no—
106C4⋊C8×C43C2311yescharacteristic
107C4⋊C8×C43C2311yescharacteristic
108C4⋊C8×C43C2312yes—
109C22⋊C8×C43—21no—
110C4×C8×C43—21no—
111C24×C43—41no—
112C23×D43—21no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—41no—
117C2×D4×C43—41no—
118C2×D4×C43—41no—
119C2×D4×C43—42no—
120C2×D4×C43—42no—
121C2×D4×C43—42no—
122C2×D4×C43—42no—
123C2×D4×C43—82no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C22×Dic43—21no—
128C2×D172—21no—
129C2×D172—22no—
130C2×D172—41no—
131C2×D172C2×D411yescharacteristic
132C2×D172C2×D411yescharacteristic
133C2×C4×D43—21no—
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—42no—
138C2×C4×D43—42no—
139C2×Dic86—21no—
140C2×Dic86—21no—
141M16×C43—42no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—22no—
145C42×C43C2×D411yescharacteristic
146C42×C43C2×D411yescharacteristic
147C42×C43#4111yescharacteristic
148C42×C43C2411yescharacteristic
149C22⋊Dic43—41no—
150#10621882—44no—
151#10621882—44no—
152(C2×D43)⋊C4—21no—
153(C2×D43)⋊C4—21no—
154(C2×D43)⋊C4—21no—
155(C2×D43)⋊C4—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43C2×D411yescharacteristic
162C4⋊Dic43C2×D411yescharacteristic
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165C4×Dic43—41no—
166#10621877—22no—
167#10621877—22no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—42no—
170C2×C43⋊C8C2×D412yes—
171C2×C43⋊C8C2×D412yes—
172#10621873—42no—
173#10621873—42no—
174#10621872—44no—
175C8×D43—44no—
176C23×C43—42no—
177C23×C43—82no—
178C23×C43—82no—
179C23×C43—82no—
180C23×C43#12111yescharacteristic
181C22×D43—21no—
182C22×D43—21no—
183C22×D43—42no—
184C22×D43—42no—
185C22×D43—81no—
186D4×C43—42no—
187D4×C43—42no—
188D4×C43—42no—
189D4×C43—42no—
190D4×C43—82no—
191D4×C43—82no—
192D4×C43—82no—
193D4×C43—82no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—41no—
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#12111yescharacteristic
199C2×C4×C43#12111yescharacteristic
200C2×C4×C43#13512yes—
201C2×C4×C43AGL(1,ℤ/8)12yes—
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×C4×C43C2×#4111yescharacteristic
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—42no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210D172—21no—
211D172—21no—
212D172—21no—
213D172—42no—
214D172AGL(1,ℤ/8)12yes—
215C4×D43—41no—
216C4×D43—41no—
217C4×D43—41no—
218C4×D43—41no—
219C4×D43—42no—
220C4×D43—42no—
221Dic86—41no—
222Dic86—41no—
223Dic86—81no—
224C8×C43—42no—
225C8×C43—41no—
226C8×C43—41no—
227C43⋊C8—22no—
228C43⋊C8—22no—
229C43⋊C8—42no—
230#19166—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—82no—
234C22×C43—82no—
235C22×C43—82no—
236C22×C43—164no—
237C22×C43#46312yes—
238C22×C43C2×#12111yescharacteristic
239C2×D43—22no—
240C2×D43—41no—
241C2×D43—41no—
242C2×D43—41no—
243C2×D43—41no—
244C2×D43—41no—
245C2×D43—84no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—21no—
249C4×C43#46312yes—
250C4×C43C2×#13511yescharacteristic
251C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
253C4×C43#57511yescharacteristic
254Dic43—41no—
255Dic43—41no—
256Dic43—81no—
257Dic43—81no—
258#3138—431no—
259#3101—431no—
260C2×#459—431no—
261D4×M16—431no—
262#1701—432no—
263#1697—432no—
264#1681—432no—
265#1677—432no—
266#1565—431no—
267#1550—431no—
268#1545D4311yescharacteristic, complemented
269C2×C43—22no—
270C2×C43—162no—
271C2×C43C2×#46311yescharacteristic
272C2×C43#305511yescharacteristic
273C2×C43#306811yescharacteristic
274D43—42no—
275D43—81no—
276C22×D8—861no—
277C22×M16—861no—
278#533—431no—
279C2×#127C2×D4311yescharacteristic
280C2×C4×D4—431no—
281#490—862no—
282#486—432no—
283#486—432no—
284#483—861no—
285#476—431no—
286#476—431no—
287#461—431no—
288#461—431no—
289#459—432no—
290#459—432no—
291#459—861no—
292#459—861no—
293#450—861no—
294C4×SD16—861no—
295C4×SD16—861no—
296#436—432no—
297#435—862no—
298C8×D4—432no—
299#431C2×D4311yescharacteristic
300#423C2×D4311yescharacteristic
301C2×C4⋊C8—431no—
302#418—861no—
303#418—861no—
304C2×#102—861no—
305#407—861no—
306C4×M16—431no—
307#335—432no—
308#334—432no—
309#333—432no—
310#332—432no—
311#331C2×D4312yescomplemented
312#331C2×D4312yescomplemented
313C43#1916611yescharacteristic, complemented, Sylow
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—431no—
318C23×C4—861no—
319C2×SD16—861no—
320C2×SD16—861no—
321C2×D8—862no—
322C2×D8—862no—
323C2×D8—1724no—
324C2×M16—21no—
325C2×M16—431no—
326C2×M16—431no—
327C2×M16—862no—
328C2×M16—1724no—
329C22×C8—862no—
330C22×C8—861no—
331C4⋊Q8—431no—
332C4⋊Q8—431no—
333#127—21no—
334#127—21no—
335#127—21no—
336#127C22×D4312yes—
337#125—861no—
338C22⋊Q8—861no—
339C22⋊Q8—861no—
340C4×Q8—861no—
341C4×Q8—861no—
342C4×D4—431no—
343C4×D4—431no—
344C4×D4—431no—
345C4×D4—431no—
346C4×D4—861no—
347C4×D4—861no—
348#117—861no—
349C2×C4⋊C4—431no—
350C2×C22⋊C4—861no—
351C2×C42C22×D4311yescharacteristic
352#106—861no—
353#106—861no—
354C4⋊C8—21no—
355C4⋊C8—432no—
356C4⋊C8—861no—
357C4⋊C8C22×D4312yes—
358C4⋊C8C22×D4311yescharacteristic
359C4⋊C8C22×D4311yescharacteristic
360#103—861no—
361#103—861no—
362#102—862no—
363#102—862no—
364#102—861no—
365#102—861no—
366#102—862no—
367#102—862no—
368#102—862no—
369#102—862no—
370C22⋊C8—21no—
371C22⋊C8—862no—
372C22⋊C8—862no—
373#97—432no—
374C4×C8—21no—
375C4×C8—432no—
376C24—41no—
377C24—861no—
378C2×Q8—861no—
379C2×Q8—861no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—82no—
391C2×D4—431no—
392C2×D4—431no—
393C2×D4—862no—
394C2×D4—861no—
395C2×D4—1721no—
396C22×C4—861no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—861no—
400C22×C4—861no—
401C22×C4—1722no—
402C22×C4—1722no—
403C22×C4#1062189811yescharacteristic
404C22×C4D4×D4311yescharacteristic
405C22×C4D4×D4311yescharacteristic
406SD16—1722no—
407SD16—1722no—
408D8—1724no—
409D8—1724no—
410M16—42no—
411M16—862no—
412M16—862no—
413M16—1724no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—22no—
417C2×C8—432no—
418C2×C8—432no—
419C2×C8—862no—
420C2×C8—1724no—
421C2×C8—1722no—
422C4⋊C4—431no—
423C4⋊C4—431no—
424C4⋊C4—861no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—1721no—
430C4⋊C4—1721no—
431C22⋊C4—861no—
432C22⋊C4—861no—
433C22⋊C4—861no—
434C22⋊C4—861no—
435C22⋊C4—1721no—
436C42—1721no—
437C42#1062189811yescharacteristic
438C42D4×D4311yescharacteristic
439C42D4×D4311yescharacteristic
440C42C23×D4311yescharacteristic
441C23—42no—
442C23—82no—
443C23—82no—
444C23—82no—
445C23—861no—
446C23—861no—
447C23—3441no—
448C23—1722no—
449C23—1722no—
450C23#1306329811yescharacteristic
451Q8—3441no—
452Q8—1721no—
453Q8—1721no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—82no—
460D4—82no—
461D4—82no—
462D4—432no—
463D4—861no—
464D4—861no—
465D4—861no—
466D4—1722no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—861no—
471C2×C4—861no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1722no—
475C2×C4—1722no—
476C2×C4—1722no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4#1306329811yescharacteristic
482C2×C4#1306329811yescharacteristic
483C2×C4#1306329811yescharacteristic
484C2×C4#1306334612yes—
485C2×C4#1306334912yes—
486C2×C4C2×D4×D4311yescharacteristic
487C2×C4C2×D4×D4311yescharacteristic
488C2×C4C2×#1062189811yescharacteristic
489C8—41no—
490C8—42no—
491C8—41no—
492C8—862no—
493C8—862no—
494C8—1722no—
495C22—21no—
496C22—21no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—164no—
501C22—862no—
502C22—3444no—
503C22—1721no—
504C22—1721no—
505C22—1721no—
506C22—1721no—
507C22—1721no—
508C22#1458311312yes—
509C22C2×#1306329811yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—3441no—
514C4—3441no—
515C4—1721no—
516C4—1721no—
517C4#1458311312yes—
518C4C2×#1306334611yescharacteristic
519C4AGL(1,ℤ/8)×D4311yescharacteristic
520C4C2×#1306334911yescharacteristic
521C4#1458369511yescharacteristic
522C2—22no—
523C2—162no—
524C2—3441no—
525C2—1722no—
526C2C2×#1458311311yescharacteristic
527C2#1914421211yescharacteristic
528C2#1914432211yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1545C2
socleC22×C43C2×#121
prime radicalC2×#14583091C2
hypercenter#1545D43
hypocenterC43#19166
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
1. #19144969C2semidirect
2. #19144604C2semidirect
4. #19143330C2semidirect
5. #19134155C2semidirect
6. #19134127C2semidirect
7. #19134031C2semidirect
8. #19134003C2semidirect
9. #19133348C2semidirect
10. #19133286C2semidirect
11. C43×#1545C2semidirect
17. #14583245C22semidirect
18. #14583245C22semidirect
20. #14583190C22semidirect
21. #14583190C22semidirect
22. #14583105C22semidirect
23. #14583105C22semidirect
31. #14582976C22semidirect
33. #14582964C22semidirect
40. #14582651C22semidirect
41. #14582649C22semidirect
42. #14582647C22semidirect
43. #14582644C22semidirect
47. C43×#331C22semidirect
48. C43×#331C22semidirect
268. #1545D43semidirect
311. #331C2×D43semidirect
312. #331C2×D43semidirect
313. C43#19166semidirect

Maximal subgroups

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

subgroupindex
#191449692
#191446042
C2×#145830912
#191433302
#191341552
#191341272
#191340312
#191340032
#191333482
#191332862
C43×#15452
#1916643