Finite Group Databasebeta

← #25130399

Subgroups — #25130399

Order 11008.

1082 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×#14583617C211yesmaximal, characteristic
2C2×#14583235C211yesmaximal, characteristic, complemented
3C2×#14582942C211yesmaximal, characteristic, complemented
4#19138904C211yesmaximal, characteristic
5#19135922C212yesmaximal, complemented
6#19135801C212yesmaximal, complemented
7#19135026C211yesmaximal, characteristic, complemented
8#19134890C211yesmaximal, characteristic
9#19134864C212yesmaximal, complemented
10#19134797C212yesmaximal, complemented
11C43×#1825C211yesmaximal, characteristic, complemented
12C22×#10621877C2211yescharacteristic
13#14583617—24no—
14#14583617—24no—
15C2×#13063324C2211yescharacteristic
16C2×#13063319—21no—
17C2×#13063318—21no—
18C2×#13063311—21no—
19C2×#13063309—21no—
20C2×#13063305C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×C4×Dic86—21no—
23C2×#13063290C2211yescharacteristic
24C2×C4×C22⋊D43C2211yescharacteristic
25C2×#13063283C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27#14583235—24no—
28#14582942—24no—
29C2×#13063259C2212yes—
30C2×#13063258C2212yes—
31C2×#13063256C2212yes—
32C2×#13063250C2212yes—
33C2×#13063248C2212yes—
34C2×(C2×D43)⋊C8C2212yes—
35#14582831—21no—
36#14582826—21no—
37#14582798C2212yes—
38#14582760—21no—
39#14582756C2212yes—
40#14582661C2212yes—
41#14582653C2212yes—
42C2×#117×C43C2211yescharacteristic
43C2×C22⋊C8×C43C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C43×#340C2212yes—
46C43×#340C2212yes—
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C22×C22⋊D43D411yescharacteristic
50C23×Dic43—21no—
51C22×C4×D43C2311yescharacteristic
52C2×#10621877—22no—
53C2×#10621877—24no—
54C22×C43⋊C8C2312yes—
55#13063324—22no—
56#13063324—22no—
57#13063319—28no—
58#13063318—28no—
59#13063311—28no—
60#13063309—44no—
61#13063305—22no—
62#13063305—22no—
63#13063304—22no—
64#13063304D414yes—
65C4×Dic86—28no—
66#13063290—22no—
67#13063290—22no—
68C4×C22⋊D43—22no—
69C4×C22⋊D43—22no—
70#13063283—22no—
71#13063283—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43C2312yes—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43D411yescharacteristic
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92#13063259—24no—
93#13063258—24no—
94#13063256—24no—
95#13063250—24no—
96#13063248—24no—
97(C2×D43)⋊C8—24no—
98C43⋊#95—22no—
99C43⋊#95—22no—
100C23×C4×C43C2311yescharacteristic
101C22×C8×C43C2312yes—
102#117×C43—22no—
103#117×C43D414yes—
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C42×C43—21no—
110C22⋊C8×C43—22no—
111#95×C43—21no—
112C24×C43C2×D411yescharacteristic
113C23×D43C2×D411yescharacteristic
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43C2×D412yes—
120C22×C4×C43C2×D412yes—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2411yescharacteristic
123C2×C22⋊D43—22no—
124C2×C22⋊D43—22no—
125C2×C22⋊D43—41no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—22no—
129C22×Dic43—42no—
130C22×Dic43—42no—
131C22×Dic43—42no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×Dic86—22no—
140C2×Dic86—22no—
141C2×Dic86—24no—
142C2×Dic86—21no—
143C2×Dic86—42no—
144C2×Dic86—42no—
145C2×Dic86C2×D412yes—
146C2×C8×C43—22no—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43C2×D412yes—
154C4⋊C4×C43C2×D412yes—
155C22⋊C4×C43—24no—
156C22⋊C4×C43—42no—
157C42×C43—24no—
158C22⋊Dic43—24no—
159C22⋊Dic43—22no—
160(C2×D43)⋊C4—24no—
161(C2×D43)⋊C4—24no—
162(C2×D43)⋊C4—22no—
163(C2×D43)⋊C4—44no—
164C4⋊Dic43—24no—
165C4⋊Dic43—21no—
166C4⋊Dic43—22no—
167C4⋊Dic43—22no—
168C4⋊Dic43—42no—
169C4⋊Dic43—44no—
170C4⋊Dic43C2×D412yes—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—24no—
174Dic43⋊C4—22no—
175C4×Dic43—24no—
176C4×Dic43—24no—
177C4×Dic43—21no—
178C4×Dic43—21no—
179#10621877—28no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8#4114yes—
183C23×C43—22no—
184C23×C43—21no—
185C23×C43—21no—
186C23×C43—22no—
187C23×C43#12012yes—
188C23×C43C22×D411yescharacteristic
189C22×D43—21no—
190C22×D43—22no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—24no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43#12012yes—
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C2×#4112yes—
210C2×C4×C432−1+412yes—
211C22⋊D43—44no—
212C2×Dic43—21no—
213C2×Dic43—21no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—22no—
217C2×Dic43—22no—
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—42no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C2×Dic43—84no—
227C2×Dic43AGL(1,ℤ/8)12yes—
228C4×D43—41no—
229C4×D43—41no—
230C4×D43—42no—
231Dic86—24no—
232Dic86—48no—
233Dic86—41no—
234Dic86—41no—
235C8×C43—42no—
236C43⋊C8—24no—
237#24107—431nomaximal, Sylow
238C22×C43—22no—
239C22×C43—22no—
240C22×C43—22no—
241C22×C43—42no—
242C22×C43—42no—
243C22×C43C2×#12011yescharacteristic
244C22×C43#54712yes—
245C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
246C22×C43#57511yescharacteristic
247C22×C43#57812yes—
248C2×D43—42no—
249C2×D43—42no—
250C2×D43—41no—
251C2×D43—41no—
252C2×D43—41no—
253C4×C43—22no—
254C4×C43—42no—
255C4×C43—42no—
256C4×C43—82no—
257C4×C43#52511yescharacteristic
258C4×C43#53611yescharacteristic
259C4×C43#54712yes—
260Dic43—22no—
261Dic43—42no—
262Dic43—41no—
263Dic43—42no—
264Dic43—41no—
265Dic43—82no—
266C2×#556—431no—
267C2×#484—431no—
268C2×#428—431no—
269#2486—431no—
270#2057—432no—
271#2036—432no—
272#1894—431no—
273#1870—431no—
274#1865—432no—
275#1854—432no—
276#1825D4311yescharacteristic, complemented
277C2×C43—42no—
278C2×C43#240611yescharacteristic
279C2×C43#300611yescharacteristic
280C2×C43#301111yescharacteristic
281C2×C43#334912yes—
282C2×C43#335312yes—
283D43—81no—
284C22×M16—431no—
285#556—864no—
286#556—864no—
287C2×C4⋊Q8—431no—
288C2×#126—861no—
289C2×#126—861no—
290C2×#124—861no—
291C2×#123—861no—
292C2×C22⋊Q8—431no—
293C2×C22⋊Q8—431no—
294C2×C4×Q8—431no—
295C2×C4×Q8—861no—
296C2×C4×D4—431no—
297C2×#117—431no—
298C2×#117C2×D4311yescharacteristic
299C22×C4⋊C4—431no—
300#484—864no—
301#428—864no—
302C2×#107—432no—
303C2×#107—432no—
304C2×#106—432no—
305C2×#103—432no—
306C2×#103—432no—
307C2×C22⋊C8—432no—
308C2×C22⋊C8C2×D4311yescharacteristic
309#398—861no—
310#397—861no—
311#389—432no—
312#381—861no—
313#380—432no—
314#380C2×D4311yescharacteristic
315#340—432no—
316#340C2×D4312yes—
317#340C2×D4312yes—
318#336—432no—
319C43#2410711yescharacteristic, complemented, Sylow
320C22×Q8—431no—
321C22×Q8—861no—
322C22×D4—431no—
323C23×C4—431no—
324C23×C4—861no—
325C23×C4C22×D4311yescharacteristic
326C2×M16—864no—
327C2×M16—862no—
328C22×C8—432no—
329C22×C8C22×D4312yes—
330C4⋊Q8—862no—
331C4⋊Q8—862no—
332#126—868no—
333#126—868no—
334#124—868no—
335#123—1724no—
336C22⋊Q8—434no—
337C22⋊Q8—862no—
338C22⋊Q8—862no—
339C22⋊Q8—862no—
340C4×Q8—868no—
341C4×Q8—862no—
342C4×Q8—862no—
343C4×D4—862no—
344C4×D4—862no—
345#117—22no—
346#117—862no—
347#117—862no—
348#117D17214yes—
349C2×C4⋊C4—431no—
350C2×C4⋊C4—431no—
351C2×C4⋊C4—432no—
352C2×C4⋊C4—861no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—862no—
357C2×C4⋊C4—862no—
358C2×C4⋊C4—862no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4C22×D4312yes—
361C2×C4⋊C4C22×D4311yescharacteristic
362C2×C4⋊C4C22×D4311yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—431no—
366C2×C22⋊C4—431no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C22⋊C4—862no—
371C2×C42—21no—
372C2×C42—431no—
373C2×C42—861no—
374C2×C42—861no—
375#107—864no—
376#107—864no—
377#106—864no—
378#103—864no—
379#103—864no—
380C22⋊C8—22no—
381C22⋊C8—864no—
382#95—21no—
383#95—862no—
384#95—862no—
385C24—431no—
386C24D4×D4311yescharacteristic
387C2×Q8—432no—
388C2×Q8—864no—
389C2×Q8—861no—
390C2×Q8—862no—
391C2×Q8—862no—
392C2×Q8—1722no—
393C2×Q8—1722no—
394C2×D4—862no—
395C2×D4—862no—
396C2×D4—1721no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—431no—
403C22×C4—431no—
404C22×C4—431no—
405C22×C4—861no—
406C22×C4—861no—
407C22×C4—861no—
408C22×C4—861no—
409C22×C4—862no—
410C22×C4—862no—
411C22×C4—862no—
412C22×C4—1722no—
413C22×C4—1722no—
414C22×C4—1722no—
415C22×C4C2×D17212yes—
416C22×C4D4×D4311yescharacteristic
417C22×C4D4×D4312yes—
418C22×C4C23×D4311yescharacteristic
419M16—868no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—434no—
424C2×C8—862no—
425C2×C8—862no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—432no—
431C4⋊C4—864no—
432C4⋊C4—864no—
433C4⋊C4—864no—
434C4⋊C4—862no—
435C4⋊C4—864no—
436C4⋊C4—861no—
437C4⋊C4—862no—
438C4⋊C4—862no—
439C4⋊C4—1724no—
440C4⋊C4—1722no—
441C4⋊C4C2×D17212yes—
442C4⋊C4C2×D17212yes—
443C22⋊C4—24no—
444C22⋊C4—42no—
445C22⋊C4—864no—
446C22⋊C4—864no—
447C22⋊C4—862no—
448C22⋊C4—864no—
449C22⋊C4—862no—
450C22⋊C4—1724no—
451C42—24no—
452C42—864no—
453C42—864no—
454C42—861no—
455C42—861no—
456C23—21no—
457C23—21no—
458C23—22no—
459C23—22no—
460C23—861no—
461C23—861no—
462C23—861no—
463C23—862no—
464C23—862no—
465C23#1306329512yes—
466C23C2×D4×D4311yescharacteristic
467Q8—864no—
468Q8—1728no—
469Q8—1721no—
470Q8—1721no—
471D4—1724no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—432no—
485C2×C4—861no—
486C2×C4—861no—
487C2×C4—861no—
488C2×C4—862no—
489C2×C4—861no—
490C2×C4—862no—
491C2×C4—862no—
492C2×C4—862no—
493C2×C4—3444no—
494C2×C4—1722no—
495C2×C4—1722no—
496C2×C4—1722no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4—1722no—
500C2×C4—1721no—
501C2×C4—1721no—
502C2×C4—1722no—
503C2×C4#1306329512yes—
504C2×C4C2×D4×D4311yescharacteristic
505C2×C4C22×D17211yescharacteristic
506C2×C4#41×D4312yes—
507C2×C4#1306337212yes—
508C8—42no—
509C8—864no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—42no—
514C22—42no—
515C22—1722no—
516C22—1721no—
517C22—1721no—
518C22—1722no—
519C22—1721no—
520C22C2×#1306329511yescharacteristic
521C22#1458354712yes—
522C22AGL(1,ℤ/8)×D4311yescharacteristic
523C22#1458369811yescharacteristic
524C22#1458371312yes—
525C4—22no—
526C4—42no—
527C4—42no—
528C4—82no—
529C4—862no—
530C4—3442no—
531C4—1721no—
532C4—1722no—
533C4—1722no—
534C4—1721no—
535C4#1458341111yescharacteristic
536C4#1458347511yescharacteristic
537C4#1458354712yes—
538C2—42no—
539C2—3441no—
540C2#1913793211yescharacteristic
541C2#1914384811yescharacteristic
542C2#1914389311yescharacteristic
543C2#1914712812yes—
544C2#1914717712yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1825C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#1825D43
hypocenterC43#24107
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
2. C2×#14583235C2semidirect
3. C2×#14582942C2semidirect
5. #19135922C2semidirect
6. #19135801C2semidirect
7. #19135026C2semidirect
9. #19134864C2semidirect
10. #19134797C2semidirect
11. C43×#1825C2semidirect
276. #1825D43semidirect
319. C43#24107semidirect

Maximal subgroups

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

subgroupindex
C2×#145836172
C2×#145832352
C2×#145829422
#191389042
#191359222
#191358012
#191350262
#191348902
#191348642
#191347972
C43×#18252
#2410743