Finite Group Databasebeta

← #25130448

Subgroups — #25130448

Order 11008.

1068 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic
2C2×#14583229C211yesmaximal, characteristic, complemented
3C2×#14582939C211yesmaximal, characteristic, complemented
4#19135933C212yesmaximal, complemented
5#19135798C212yesmaximal, complemented
6#19135026C211yesmaximal, characteristic, complemented
7#19134893C211yesmaximal, characteristic
8#19134862C212yesmaximal, complemented
9#19134787C212yesmaximal, complemented
10#19134687C211yesmaximal, characteristic, complemented
11C43×#2487C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13#14583589—24no—
14#14583589—24no—
15C2×#13063318—21no—
16C2×#13063317C2211yescharacteristic
17C2×#13063315—21no—
18C2×#13063306—21no—
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23C2×#13063281—21no—
24C22×C4⋊Dic43C2211yescharacteristic
25#14583229—24no—
26#14582939—24no—
27C2×#13063258C2212yes—
28C2×#13063256C2212yes—
29C2×#13063256C2212yes—
30C2×#13063248C2212yes—
31C2×#13063248C2212yes—
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2212yes—
34#14582661C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37#14582654C2212yes—
38C2×C4×D4×C43C2211yescharacteristic
39C22×C4⋊C4×C43C2211yescharacteristic
40C43×#400—21no—
41C43×#399—21no—
42C43×#389C2212yes—
43C43×#386—21no—
44C43×#385—21no—
45C43×#380C2211yescharacteristic
46C43×#380C2212yes—
47C22×Dic86C2311yescharacteristic
48C23×Dic43—21no—
49C2×#10621877—22no—
50C2×#10621877—24no—
51C22×C43⋊C8C2312yes—
52C22×C43⋊C8C2312yes—
53#13063318—28no—
54#13063317—22no—
55#13063317—22no—
56#13063315—28no—
57#13063306—28no—
58#13063304—22no—
59#13063304—22no—
60#13063304—22no—
61#13063304D414yes—
62C4×Dic86—22no—
63C4×Dic86—22no—
64#13063284—22no—
65#13063284D414yes—
66#13063281—28no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—22no—
69C2×C4⋊Dic43—22no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
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—
82C2×C4×Dic43—21no—
83#13063258—24no—
84#13063256—24no—
85#13063256—24no—
86#13063248—24no—
87#13063248—24no—
88C22⋊(C43⋊C8)—22no—
89C22⋊(C43⋊C8)—24no—
90C22×D4×C43D411yescharacteristic
91C23×C4×C43—21no—
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43C2312yes—
102C2×C4⋊C4×C43C2312yes—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43D411yescharacteristic
106C2×C22⋊C4×C43D411yescharacteristic
107C2×C42×C43C2311yescharacteristic
108#95×C43—22no—
109#95×C43—21no—
110#95×C43—22no—
111C24×C43C2×D411yescharacteristic
112C24×C43C2×D411yescharacteristic
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—41no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—42no—
125C22×C4×C43—82no—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—24no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—42no—
139C22×Dic43—42no—
140C2×Dic86—22no—
141C2×Dic86—22no—
142C2×Dic86—21no—
143C2×Dic86C2×D412yes—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—42no—
150C4⋊C4×C43—82no—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—22no—
153C22⋊C4×C43—42no—
154C22⋊C4×C43—82no—
155C42×C43—21no—
156C42×C43—21no—
157C22⋊Dic43—24no—
158C22⋊Dic43—24no—
159C22⋊Dic43—24no—
160C4⋊Dic43—24no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43C2×D412yes—
165C4⋊Dic43C2×D412yes—
166C4⋊Dic43C2×D412yes—
167Dic43⋊C4—24no—
168Dic43⋊C4—24no—
169Dic43⋊C4—24no—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172C4×Dic43—24no—
173C4×Dic43—24no—
174#10621877—28no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8#4114yes—
181C23×C43—21no—
182C23×C43—22no—
183C23×C43—22no—
184C23×C43—21no—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43#12012yes—
190C23×C43#13712yes—
191C23×C43C22×D411yescharacteristic
192D4×C43—44no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—24no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—22no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—22no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—84no—
214C2×C4×C43#12012yes—
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C2×#4112yes—
218C2×C4×C432−1+412yes—
219C2×Dic43—22no—
220C2×Dic43—22no—
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—48no—
224C2×Dic43—42no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—42no—
230Dic86—24no—
231Dic86—41no—
232Dic86—41no—
233C43⋊C8—24no—
234C43⋊C8—42no—
235#24111—431nomaximal, Sylow
236C22×C43—24no—
237C22×C43—22no—
238C22×C43—22no—
239C22×C43—22no—
240C22×C43—22no—
241C22×C43—42no—
242C22×C43—42no—
243C22×C43—42no—
244C22×C43—41no—
245C22×C43—41no—
246C22×C43C2×#12011yescharacteristic
247C22×C43#54712yes—
248C22×C43C2×#13711yescharacteristic
249C22×C43#57511yescharacteristic
250C22×C43#57712yes—
251C4×C43—22no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—82no—
256C4×C43—82no—
257C4×C43#52511yescharacteristic
258C4×C43#53611yescharacteristic
259C4×C43#54712yes—
260Dic43—42no—
261Dic43—42no—
262Dic43—42no—
263Dic43—42no—
264C2×#552—431no—
265C2×#483—431no—
266C2×#428—431no—
267#2487D4311yescharacteristic
268#2059—432no—
269#2036—432no—
270#1894—431no—
271#1870—431no—
272#1865—432no—
273#1853—432no—
274#1825—431no—
275C2×C43—42no—
276C2×C43—42no—
277C2×C43#240611yescharacteristic
278C2×C43#300711yescharacteristic
279C2×C43#301011yescharacteristic
280C2×C43#334412yes—
281C2×C43#335112yes—
282C22×M16—431no—
283#552—864no—
284#552—864no—
285C2×#126—861no—
286C2×#125—431no—
287C2×#125—861no—
288C2×#123—861no—
289C2×C22⋊Q8—431no—
290C2×C22⋊Q8—431no—
291C2×C4×Q8—431no—
292C2×C4×D4C2×D4311yescharacteristic
293C2×#117—431no—
294C2×#117—861no—
295C22×C4⋊C4—431no—
296C22×C4⋊C4C2×D4311yescharacteristic
297#483—864no—
298#428—864no—
299C2×#107—432no—
300C2×#106—432no—
301C2×#106—432no—
302C2×#103—432no—
303C2×#103—432no—
304C2×C22⋊C8—431no—
305C2×C22⋊C8—432no—
306#400—21no—
307#399—21no—
308#389C2×D4312yes—
309#386—21no—
310#385—21no—
311#380C2×D4311yescharacteristic
312#380C2×D4312yes—
313#340—432no—
314#340—432no—
315#340—432no—
316#336—432no—
317C43#2411111yescharacteristic, complemented, Sylow
318C22×Q8—431no—
319C22×D4C22⋊D4311yescharacteristic
320C23×C4—21no—
321C23×C4—861no—
322C23×C4C22×D4311yescharacteristic
323C23×C4C22×D4311yescharacteristic
324C2×M16—864no—
325C2×M16—862no—
326C22×C8—432no—
327C22×C8—432no—
328#126—868no—
329#125—862no—
330#125—862no—
331#125—868no—
332#123—868no—
333C22⋊Q8—434no—
334C22⋊Q8—862no—
335C22⋊Q8—862no—
336C22⋊Q8—862no—
337C4×Q8—862no—
338C4×Q8—862no—
339C4×D4—22no—
340C4×D4—22no—
341#117—434no—
342#117—868no—
343#117—862no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—431no—
349C2×C4⋊C4—431no—
350C2×C4⋊C4—431no—
351C2×C4⋊C4—862no—
352C2×C4⋊C4—862no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—861no—
359C2×C4⋊C4C22⋊D4311yescharacteristic
360C2×C4⋊C4C22×D4312yes—
361C2×C4⋊C4C22×D4312yes—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—861no—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4C22⋊D4311yescharacteristic
368C2×C22⋊C4C22⋊D4311yescharacteristic
369C2×C42—861no—
370C2×C42—861no—
371C2×C42C22×D4311yescharacteristic
372#107—864no—
373#106—864no—
374#106—864no—
375#103—864no—
376#103—864no—
377C22⋊C8—864no—
378C22⋊C8—862no—
379#95—22no—
380#95—21no—
381#95—22no—
382C24C2×C22⋊D4311yescharacteristic
383C24C2×C22⋊D4311yescharacteristic
384C2×Q8—432no—
385C2×Q8—861no—
386C2×Q8—862no—
387C2×Q8—862no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—41no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—82no—
401C22×C4—864no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—861no—
405C22×C4—861no—
406C22×C4—1722no—
407C22×C4—1722no—
408C22×C4D4×D4312yes—
409C22×C4D4×D4312yes—
410C22×C4C2×C22⋊D4311yescharacteristic
411C22×C4C2×C22⋊D4311yescharacteristic
412C22×C4C2×C22⋊D4311yescharacteristic
413C22×C4C2×C22⋊D4311yescharacteristic
414C22×C4C23×D4311yescharacteristic
415M16—868no—
416C2×C8—434no—
417C2×C8—862no—
418C2×C8—862no—
419C2×C8—862no—
420C2×C8—862no—
421C2×C8—862no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—42no—
428C4⋊C4—82no—
429C4⋊C4—432no—
430C4⋊C4—432no—
431C4⋊C4—432no—
432C4⋊C4—864no—
433C4⋊C4—864no—
434C4⋊C4—864no—
435C4⋊C4—864no—
436C4⋊C4—864no—
437C4⋊C4—864no—
438C4⋊C4—861no—
439C4⋊C4—861no—
440C4⋊C4—861no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—42no—
444C22⋊C4—82no—
445C22⋊C4—864no—
446C22⋊C4—864no—
447C22⋊C4—864no—
448C42—21no—
449C42—21no—
450C42—864no—
451C42—864no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23#1306329312yes—
461C23#1306335612yes—
462C23C22×C22⋊D4311yescharacteristic
463Q8—864no—
464Q8—1721no—
465Q8—1721no—
466D4—44no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
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—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—84no—
488C2×C4—862no—
489C2×C4—862no—
490C2×C4—862no—
491C2×C4—862no—
492C2×C4—1728no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4—1721no—
496C2×C4—1721no—
497C2×C4—1722no—
498C2×C4—1722no—
499C2×C4#1306329312yes—
500C2×C4C2×D4×D4311yescharacteristic
501C2×C4C2×D4×D4311yescharacteristic
502C2×C4#41×D4312yes—
503C2×C4#1306337212yes—
504C8—864no—
505C8—1722no—
506C22—24no—
507C22—22no—
508C22—22no—
509C22—22no—
510C22—22no—
511C22—42no—
512C22—41no—
513C22—42no—
514C22—42no—
515C22—41no—
516C22C2×#1306329311yescharacteristic
517C22#1458354812yes—
518C22C2×#1306335611yescharacteristic
519C22#1458369711yescharacteristic
520C22#1458371012yes—
521C4—22no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—82no—
526C4—82no—
527C4—1722no—
528C4—1722no—
529C4—1722no—
530C4—1722no—
531C4#1458340711yescharacteristic
532C4#1458347111yescharacteristic
533C4#1458354712yes—
534C2—42no—
535C2—42no—
536C2#1913792711yescharacteristic
537C2#1914385311yescharacteristic
538C2#1914387911yescharacteristic
539C2#1914704412yes—
540C2#1914714912yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2487C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#2487D43
hypocenterC43#24111
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
2. C2×#14583229C2semidirect
3. C2×#14582939C2semidirect
4. #19135933C2semidirect
5. #19135798C2semidirect
6. #19135026C2semidirect
8. #19134862C2semidirect
9. #19134787C2semidirect
10. #19134687C2semidirect
317. C43#24111semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
C2×#145832292
C2×#145829392
#191359332
#191357982
#191350262
#191348932
#191348622
#191347872
#191346872
C43×#24872
#2411143