Finite Group Databasebeta

← #25130434

Subgroups — #25130434

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×#14583588C211yesmaximal, characteristic
2C2×#14583234C211yesmaximal, characteristic, complemented
3#19138897C211yesmaximal, characteristic
4#19135935C212yesmaximal, complemented
5#19135793C212yesmaximal, complemented
6#19135028C211yesmaximal, characteristic, complemented
7#19134892C211yesmaximal, characteristic
8#19134846C212yesmaximal, complemented
9#19134781C212yesmaximal, complemented
10#19134690C211yesmaximal, characteristic, complemented
11C2×C43×#428C211yesmaximal, characteristic, complemented
12#14583588—24no—
13#14583588—24no—
14C2×#13063318—21no—
15C2×#13063317—21no—
16C2×#13063316C2211yescharacteristic
17C2×#13063308—21no—
18C2×#13063307—21no—
19C2×#13063305C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23C2×#13063282—21no—
24C2×C4⋊C4×D43C2211yescharacteristic
25#14583234—24no—
26C2×#13063258C2212yes—
27C2×#13063250C2212yes—
28C2×#13063248C2212yes—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×(C2×D43)⋊C8C2212yes—
31#14582830—21no—
32#14582825—21no—
33#14582795C2212yes—
34#14582762—21no—
35#14582759C2211yescharacteristic
36#14582756C2212yes—
37#14582662C2212yes—
38#14582661C2212yes—
39#14582661C2212yes—
40#14582653C2212yes—
41C22×M16×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C22×C4⋊C4×C43C2211yescharacteristic
44C43×#428—24no—
45C2×#107×C43C2212yes—
46C2×#106×C43C2212yes—
47C22×Dic86C2311yescharacteristic
48C22×C22⋊D43D411yescharacteristic
49C22×C4×D43—21no—
50C22×C4×D43C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063318—28no—
53#13063317—28no—
54#13063316—22no—
55#13063316—22no—
56#13063308—44no—
57#13063307—28no—
58#13063305—22no—
59#13063305—22no—
60#13063304—22no—
61#13063304D414yes—
62#13063290—22no—
63#13063290—22no—
64C4×C22⋊D43—22no—
65C4×C22⋊D43—22no—
66#13063282—28no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2312yes—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4D411yescharacteristic
77C4⋊C4×D43—22no—
78C4⋊C4×D43—22no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43D411yescharacteristic
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—22no—
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87#13063258—24no—
88#13063250—24no—
89#13063248—24no—
90C22⋊(C43⋊C8)—22no—
91(C2×D43)⋊C8—24no—
92C43⋊#95—21no—
93C43⋊#95—22no—
94C43⋊#95—22no—
95C23×C4×C43—21no—
96C23×C4×C43C2311yescharacteristic
97C2×M16×C43—22no—
98C2×M16×C43—24no—
99C22×C8×C43C2312yes—
100#117×C43—22no—
101#117×C43D414yes—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C22⋊C4×C43—21no—
109C2×C42×C43—21no—
110#107×C43—24no—
111#106×C43—24no—
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×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43C2×D412yes—
123C22×C4×C43C2×D412yes—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C2×C22⋊D43—22no—
127C2×C22⋊D43—22no—
128C2×C22⋊D43—41no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—22no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×C4×D43—24no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—42no—
141C2×C4×D43—42no—
142C2×Dic86—22no—
143C2×Dic86—22no—
144C2×Dic86—21no—
145C2×Dic86C2×D412yes—
146M16×C43—28no—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C2×C8×C43#4114yes—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—42no—
155C4⋊C4×C43C2×D412yes—
156C4⋊C4×C43C2×D412yes—
157C22⋊C4×C43—24no—
158C42×C43—24no—
159C22⋊Dic43—24no—
160C22⋊Dic43—22no—
161C22⋊Dic43—42no—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—22no—
164(C2×D43)⋊C4—44no—
165C4⋊Dic43—24no—
166C4⋊Dic43—24no—
167C4⋊Dic43—21no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170C4⋊Dic43C2×D412yes—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—24no—
174Dic43⋊C4—24no—
175Dic43⋊C4—22no—
176Dic43⋊C4—44no—
177C4×Dic43—24no—
178C4×Dic43—21no—
179C4×Dic43—21no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
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—22no—
193C22×D43AGL(1,ℤ/8)12yes—
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—84no—
207C2×C4×C43#12012yes—
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C22×D411yescharacteristic
210C2×C4×C43C2×#4112yes—
211C2×C4×C432−1+412yes—
212C22⋊D43—44no—
213C2×Dic43—21no—
214C2×Dic43—21no—
215C2×Dic43—22no—
216C2×Dic43—21no—
217C2×Dic43—22no—
218C2×Dic43—22no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—22no—
222C2×Dic43—42no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C4×D43—48no—
229C4×D43—41no—
230C4×D43—41no—
231C4×D43—42no—
232Dic86—24no—
233Dic86—41no—
234Dic86—41no—
235C8×C43—24no—
236C43⋊C8—42no—
237#24110—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—24no—
249C2×D43—22no—
250C2×D43—42no—
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—42no—
261Dic43—41no—
262Dic43—42no—
263Dic43—41no—
264Dic43—41no—
265Dic43—82no—
266C2×#552—431no—
267C2×#484—431no—
268C2×#428D4311yescharacteristic, complemented
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#240611yescharacteristic
279C2×C43#300611yescharacteristic
280C2×C43#301111yescharacteristic
281C2×C43#334312yes—
282C2×C43#335212yes—
283D43—42no—
284C22×M16C2×D4311yescharacteristic
285#552—864no—
286#552—864no—
287C2×#126—861no—
288C2×#125—431no—
289C2×#125—861no—
290C2×#123—861no—
291C2×#123—861no—
292C2×C22⋊Q8—431no—
293C2×C22⋊Q8—431no—
294C2×C4×Q8—431no—
295C2×C4×D4—431no—
296C2×#117—861no—
297C2×#117C2×D4311yescharacteristic
298C22×C4⋊C4—431no—
299C22×C4⋊C4C2×D4311yescharacteristic
300#484—864no—
301#428—24no—
302C2×#107—432no—
303C2×#107C2×D4312yes—
304C2×#106C2×D4312yes—
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×Q8—431no—
321C22×D4—431no—
322C23×C4—21no—
323C23×C4—431no—
324C23×C4—861no—
325C23×C4C22×D4311yescharacteristic
326C2×M16—22no—
327C2×M16—24no—
328C22×C8—432no—
329C22×C8C22×D4312yes—
330#126—868no—
331#125—868no—
332#125—862no—
333#125—862no—
334#123—868no—
335#123—1724no—
336C22⋊Q8—434no—
337C22⋊Q8—862no—
338C22⋊Q8—862no—
339C22⋊Q8—862no—
340C4×Q8—862no—
341C4×Q8—862no—
342C4×D4—862no—
343C4×D4—862no—
344#117—22no—
345#117—868no—
346#117C22⋊D4314yes—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—431no—
351C2×C4⋊C4—431no—
352C2×C4⋊C4—432no—
353C2×C4⋊C4—862no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—861no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4—862no—
361C2×C4⋊C4—862no—
362C2×C4⋊C4C22×D4312yes—
363C2×C4⋊C4C22×D4311yescharacteristic
364C2×C4⋊C4C22×D4311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—431no—
367C2×C22⋊C4—431no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C22⋊C4—862no—
371C2×C22⋊C4—861no—
372C2×C42—21no—
373C2×C42—431no—
374C2×C42—861no—
375#107—24no—
376#107—864no—
377#106—24no—
378#103—864no—
379#103—864no—
380C22⋊C8—862no—
381C22⋊C8—864no—
382#95—862no—
383#95—862no—
384#95—861no—
385C24—431no—
386C24D4×D4311yescharacteristic
387C2×Q8—432no—
388C2×Q8—861no—
389C2×Q8—862no—
390C2×Q8—862no—
391C2×D4—862no—
392C2×D4—862no—
393C2×D4—1721no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—431no—
403C22×C4—431no—
404C22×C4—431no—
405C22×C4—864no—
406C22×C4—861no—
407C22×C4—861no—
408C22×C4—861no—
409C22×C4—861no—
410C22×C4—862no—
411C22×C4—862no—
412C22×C4—862no—
413C22×C4—1722no—
414C22×C4—1722no—
415C22×C4D4×D4311yescharacteristic
416C22×C4D4×D4312yes—
417C22×C4C2×C22⋊D4312yes—
418C22×C4C23×D4311yescharacteristic
419M16—28no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—862no—
423C2×C8—862no—
424C2×C8—862no—
425C2×C8#1062189814yes—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—42no—
431C4⋊C4—432no—
432C4⋊C4—864no—
433C4⋊C4—864no—
434C4⋊C4—864no—
435C4⋊C4—864no—
436C4⋊C4—864no—
437C4⋊C4—862no—
438C4⋊C4—864no—
439C4⋊C4—861no—
440C4⋊C4—862no—
441C4⋊C4—862no—
442C4⋊C4—1724no—
443C4⋊C4C2×C22⋊D4312yes—
444C4⋊C4C2×C22⋊D4312yes—
445C22⋊C4—24no—
446C22⋊C4—864no—
447C22⋊C4—862no—
448C22⋊C4—864no—
449C22⋊C4—862no—
450C22⋊C4—1724no—
451C22⋊C4—1722no—
452C42—24no—
453C42—864no—
454C42—861no—
455C42—861no—
456C23—21no—
457C23—21no—
458C23—22no—
459C23—22no—
460C23—432no—
461C23—861no—
462C23—861no—
463C23—862no—
464C23—862no—
465C23#1306329312yes—
466C23C2×D4×D4311yescharacteristic
467Q8—864no—
468Q8—1721no—
469Q8—1721no—
470D4—1724no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—84no—
484C2×C4—861no—
485C2×C4—862no—
486C2×C4—861no—
487C2×C4—862no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—862no—
492C2×C4—862no—
493C2×C4—1728no—
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#1306329312yes—
504C2×C4C2×D4×D4311yescharacteristic
505C2×C4C22×C22⋊D4311yescharacteristic
506C2×C4C2×#1062189812yes—
507C2×C4#1306337312yes—
508C8—24no—
509C8—1722no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—42no—
514C22—42no—
515C22—864no—
516C22—862no—
517C22—1721no—
518C22—1722no—
519C22—1721no—
520C22C2×#1306329311yescharacteristic
521C22#1458355012yes—
522C22AGL(1,ℤ/8)×D4311yescharacteristic
523C22#1458369511yescharacteristic
524C22#1458371512yes—
525C4—22no—
526C4—42no—
527C4—42no—
528C4—82no—
529C4—3442no—
530C4—1721no—
531C4—1722no—
532C4—1721no—
533C4—1722no—
534C4—1721no—
535C4#1458341011yescharacteristic
536C4#1458347311yescharacteristic
537C4#1458355012yes—
538C2—42no—
539C2—1722no—
540C2#1913793011yescharacteristic
541C2#1914384311yescharacteristic
542C2#1914388911yescharacteristic
543C2#1914703612yes—
544C2#1914716612yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#428C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#428D43
hypocenterC43#24110
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#14583234C2semidirect
4. #19135935C2semidirect
5. #19135793C2semidirect
6. #19135028C2semidirect
8. #19134846C2semidirect
9. #19134781C2semidirect
10. #19134690C2semidirect
11. C2×C43×#428C2semidirect
268. C2×#428D43semidirect
319. C43#24110semidirect

Maximal subgroups

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

subgroupindex
C2×#145835882
C2×#145832342
#191388972
#191359352
#191357932
#191350282
#191348922
#191348462
#191347812
#191346902
C2×C43×#4282
#2411043