Finite Group Databasebeta

← #25130430

Subgroups — #25130430

Order 11008.

1088 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583232C211yesmaximal, characteristic, complemented
2C2×#14582942C211yesmaximal, characteristic, complemented
3#19138903C211yesmaximal, characteristic
4#19135930C212yesmaximal, complemented
5#19135788C212yesmaximal, complemented
6#19135029C211yesmaximal, characteristic, complemented
7#19134893C211yesmaximal, characteristic
8#19134849C212yesmaximal, complemented
9#19134783C212yesmaximal, complemented
10#19134690C211yesmaximal, characteristic, complemented
11C2×C43×#552C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13C2×#13063306—21no—
14C22×C4⋊Dic43C2211yescharacteristic
15#14583232—24no—
16#14582942—24no—
17C2×#13063258C2212yes—
18C2×#13063258C2212yes—
19C2×#13063256C2212yes—
20C2×#13063249C2212yes—
21C2×#13063249C2212yes—
22C2×C22⋊(C43⋊C8)C2212yes—
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24#14582829—21no—
25#14582824—21no—
26#14582797C2212yes—
27#14582760—21no—
28#14582759C2212yes—
29#14582759C2211yescharacteristic
30#14582661C2212yes—
31#14582661C2212yes—
32#14582661C2212yes—
33#14582654C2212yes—
34C43×#552—24no—
35C43×#552—24no—
36C2×#126×C43—21no—
37C2×#125×C43—21no—
38C2×#125×C43C2211yescharacteristic
39C2×#123×C43—21no—
40C2×C22⋊Q8×C43C2211yescharacteristic
41C2×C22⋊Q8×C43C2211yescharacteristic
42C2×C4×Q8×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C2×#117×C43—21no—
45C2×#117×C43C2211yescharacteristic
46C22×C4⋊C4×C43C2211yescharacteristic
47C23×Dic43—21no—
48C2×#10621877—22no—
49C2×#10621877—24no—
50C22×C43⋊C8C2312yes—
51C22×C43⋊C8C2312yes—
52#13063306—44no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43C2312yes—
57C2×C4⋊Dic43C2312yes—
58C2×Dic43⋊C4—22no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—21no—
61#13063258—24no—
62#13063258—24no—
63#13063256—24no—
64#13063249—24no—
65#13063249—24no—
66C22⋊(C43⋊C8)—22no—
67C22⋊(C43⋊C8)—24no—
68C43⋊#95—22no—
69C43⋊#95—21no—
70C43⋊#95—22no—
71C22×Q8×C43C2311yescharacteristic
72C22×D4×C43D411yescharacteristic
73C23×C4×C43—21no—
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76#126×C43—28no—
77#125×C43—28no—
78#125×C43—22no—
79#125×C43—22no—
80#123×C43—28no—
81C22⋊Q8×C43—22no—
82C22⋊Q8×C43—22no—
83C22⋊Q8×C43—22no—
84C22⋊Q8×C43D414yes—
85C4×Q8×C43—22no—
86C4×Q8×C43—22no—
87C4×D4×C43—22no—
88C4×D4×C43—22no—
89#117×C43—28no—
90#117×C43—22no—
91#117×C43D414yes—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43D411yescharacteristic
108C2×C22⋊C4×C43D411yescharacteristic
109C2×C42×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43C2311yescharacteristic
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C2×Q8×C43—21no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43C2×D412yes—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—41no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—24no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C4⋊C4×C43—24no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—24no—
149C4⋊C4×C43—24no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43C2×D412yes—
157C4⋊C4×C43C2×D412yes—
158C4⋊C4×C43C2×D412yes—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C22⋊C4×C43—22no—
164C42×C43—24no—
165C42×C43—24no—
166C42×C43—21no—
167C42×C43—21no—
168C22⋊Dic43—42no—
169C22⋊Dic43—44no—
170C4⋊Dic43—22no—
171C4⋊Dic43—22no—
172C4⋊Dic43—22no—
173C4⋊Dic43—22no—
174C4⋊Dic43—42no—
175Dic43⋊C4—44no—
176#10621877—28no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8#4114yes—
183C23×C43—21no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—21no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43#12012yes—
192C23×C43AGL(1,ℤ/8)12yes—
193C23×C43C22×D411yescharacteristic
194Q8×C43—24no—
195Q8×C43—41no—
196Q8×C43—41no—
197D4×C43—44no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—24no—
202C2×C4×C43—21no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—48no—
214C2×C4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—42no—
223C2×C4×C43#12012yes—
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4112yes—
227C2×C4×C432−1+412yes—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—84no—
235C43⋊C8—24no—
236C43⋊C8—42no—
237#24110—431nomaximal, Sylow
238C22×C43—24no—
239C22×C43—22no—
240C22×C43—22no—
241C22×C43—22no—
242C22×C43—22no—
243C22×C43—42no—
244C22×C43—42no—
245C22×C43—42no—
246C22×C43—41no—
247C22×C43—41no—
248C22×C43C2×#12011yescharacteristic
249C22×C43#54712yes—
250C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C43#57511yescharacteristic
252C22×C43#57812yes—
253C4×C43—22no—
254C4×C43—41no—
255C4×C43—42no—
256C4×C43—41no—
257C4×C43—42no—
258C4×C43—42no—
259C4×C43—41no—
260C4×C43—42no—
261C4×C43#52511yescharacteristic
262C4×C43#53611yescharacteristic
263C4×C43#54712yes—
264Dic43—82no—
265Dic43—82no—
266C2×#552D4311yescharacteristic
267C2×#484—431no—
268C2×#428—431no—
269#2486—431no—
270#2059—432no—
271#2035—432no—
272#1894—431no—
273#1870—431no—
274#1863—432no—
275#1852—432no—
276#1825—431no—
277C2×C43—42no—
278C2×C43—42no—
279C2×C43#240611yescharacteristic
280C2×C43#300611yescharacteristic
281C2×C43#301111yescharacteristic
282C2×C43#334312yes—
283C2×C43#335212yes—
284C22×M16—431no—
285#552—24no—
286#552—24no—
287C2×#126—21no—
288C2×#125—21no—
289C2×#125C2×D4311yescharacteristic
290C2×#123—21no—
291C2×#123—861no—
292C2×C22⋊Q8C2×D4311yescharacteristic
293C2×C22⋊Q8C2×D4311yescharacteristic
294C2×C4×Q8C2×D4311yescharacteristic
295C2×C4×D4C2×D4311yescharacteristic
296C2×#117—21no—
297C2×#117C2×D4311yescharacteristic
298C22×C4⋊C4—431no—
299C22×C4⋊C4C2×D4311yescharacteristic
300#484—864no—
301#428—864no—
302C2×#107—432no—
303C2×#107—432no—
304C2×#106—432no—
305C2×#103—432no—
306C2×#103—432no—
307C2×C22⋊C8—431no—
308C2×C22⋊C8—432no—
309#398—861no—
310#397—861no—
311#389—432no—
312#381—861no—
313#380—431no—
314#380—432no—
315#340—432no—
316#340—432no—
317#340—432no—
318#336—432no—
319C43#2411011yescharacteristic, complemented, Sylow
320C22×Q8C22×D4311yescharacteristic
321C22×D4C22⋊D4311yescharacteristic
322C23×C4—21no—
323C23×C4—861no—
324C23×C4C22×D4311yescharacteristic
325C23×C4C22×D4311yescharacteristic
326C2×M16—864no—
327C2×M16—862no—
328C22×C8—432no—
329C22×C8—432no—
330#126—28no—
331#125—28no—
332#125—22no—
333#125—22no—
334#123—28no—
335#123—1724no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8C22⋊D4314yes—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×D4—22no—
343C4×D4—22no—
344#117—28no—
345#117—22no—
346#117C22⋊D4314yes—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—432no—
356C2×C4⋊C4—432no—
357C2×C4⋊C4—862no—
358C2×C4⋊C4—862no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4—862no—
361C2×C4⋊C4C22⋊D4311yescharacteristic
362C2×C4⋊C4C22×D4311yescharacteristic
363C2×C4⋊C4C22×D4311yescharacteristic
364C2×C4⋊C4C22×D4311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—862no—
370C2×C22⋊C4C22⋊D4311yescharacteristic
371C2×C22⋊C4C22⋊D4311yescharacteristic
372C2×C42—21no—
373C2×C42—21no—
374C2×C42C22×D4311yescharacteristic
375#107—864no—
376#107—864no—
377#106—864no—
378#103—864no—
379#103—864no—
380C22⋊C8—864no—
381C22⋊C8—862no—
382#95—862no—
383#95—861no—
384#95—862no—
385C24C2×C22⋊D4311yescharacteristic
386C24C2×C22⋊D4311yescharacteristic
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8C2×C22⋊D4312yes—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—41no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—862no—
408C22×C4—862no—
409C22×C4—1722no—
410C22×C4—1722no—
411C22×C4—1722no—
412C22×C4C2×C22⋊D4311yescharacteristic
413C22×C4C2×C22⋊D4311yescharacteristic
414C22×C4C2×C22⋊D4311yescharacteristic
415C22×C4C2×C22⋊D4311yescharacteristic
416C22×C4C2×C22⋊D4312yes—
417C22×C4C2×C22⋊D4312yes—
418C22×C4C23×D4311yescharacteristic
419M16—868no—
420C2×C8—434no—
421C2×C8—862no—
422C2×C8—862no—
423C2×C8—862no—
424C2×C8—862no—
425C2×C8—862no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—862no—
437C4⋊C4—862no—
438C4⋊C4—862no—
439C4⋊C4—862no—
440C4⋊C4—1724no—
441C4⋊C4—1722no—
442C4⋊C4C2×C22⋊D4312yes—
443C4⋊C4C2×C22⋊D4312yes—
444C4⋊C4C2×C22⋊D4312yes—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—1722no—
451C22⋊C4—1724no—
452C42—24no—
453C42—24no—
454C42—21no—
455C42—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23#1306329412yes—
465C23#1306335012yes—
466C23C22×C22⋊D4311yescharacteristic
467Q8—24no—
468Q8—41no—
469Q8—41no—
470D4—44no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—48no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—3444no—
497C2×C4—1722no—
498C2×C4—1722no—
499C2×C4—1722no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4#1306329412yes—
504C2×C4C22×C22⋊D4311yescharacteristic
505C2×C4C22×C22⋊D4311yescharacteristic
506C2×C4#41×D4312yes—
507C2×C4#1306337212yes—
508C8—864no—
509C8—1722no—
510C22—24no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—42no—
516C22—41no—
517C22—42no—
518C22—42no—
519C22—41no—
520C22C2×#1306329411yescharacteristic
521C22#1458354812yes—
522C22C2×#1306335011yescharacteristic
523C22#1458369711yescharacteristic
524C22#1458371412yes—
525C4—22no—
526C4—41no—
527C4—42no—
528C4—41no—
529C4—42no—
530C4—42no—
531C4—41no—
532C4—42no—
533C4—3442no—
534C4—3442no—
535C4#1458340611yescharacteristic
536C4#1458347011yescharacteristic
537C4#1458354812yes—
538C2—42no—
539C2—42no—
540C2#1913792611yescharacteristic
541C2#1914384711yescharacteristic
542C2#1914389011yescharacteristic
543C2#1914703512yes—
544C2#1914716412yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#552C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenterC2×#552D43
hypocenterC43#24110
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#14583232C2semidirect
2. C2×#14582942C2semidirect
4. #19135930C2semidirect
5. #19135788C2semidirect
6. #19135029C2semidirect
8. #19134849C2semidirect
9. #19134783C2semidirect
10. #19134690C2semidirect
319. C43#24110semidirect

Maximal subgroups

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

subgroupindex
C2×#145832322
C2×#145829422
#191389032
#191359302
#191357882
#191350292
#191348932
#191348492
#191347832
#191346902
C2×C43×#5522
#2411043