Finite Group Databasebeta

← #25130444

Subgroups — #25130444

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×#14583583C211yesmaximal, characteristic
2C2×#14583227C211yesmaximal, characteristic, complemented
3C2×#14582941C211yesmaximal, characteristic, complemented
4#19138913C211yesmaximal, characteristic
5#19135936C212yesmaximal, complemented
6#19135797C212yesmaximal, complemented
7#19134892C211yesmaximal, characteristic
8#19134865C212yesmaximal, complemented
9#19134789C212yesmaximal, complemented
10#19134687C211yesmaximal, characteristic, complemented
11C43×#1894C211yesmaximal, characteristic, complemented
12#14583583—24no—
13#14583583—24no—
14C2×#13063318—21no—
15C2×#13063316C2211yescharacteristic
16C2×#13063315—21no—
17C2×#13063307—21no—
18C2×#13063301C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22C2×#13063283—21no—
23C22×C4⋊Dic43C2211yescharacteristic
24C2×C4⋊C4×D43C2211yescharacteristic
25#14583227—24no—
26#14582941—24no—
27C2×#13063259C2212yes—
28C2×#13063257C2212yes—
29C2×#13063256C2212yes—
30C2×#13063249C2212yes—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×(C2×D43)⋊C8C2212yes—
33#14582839—21no—
34#14582836—21no—
35#14582798C2212yes—
36#14582776—21no—
37#14582774—21no—
38#14582756C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41#14582653C2212yes—
42C22×M16×C43C2211yescharacteristic
43C2×C22⋊Q8×C43C2211yescharacteristic
44C2×#103×C43C2212yes—
45C43×#380C2211yescharacteristic
46C43×#340C2212yes—
47C22×C22⋊D43D411yescharacteristic
48C23×Dic43—21no—
49C22×C4×D43—21no—
50C22×C4×D43C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063318—28no—
53#13063316—22no—
54#13063316—22no—
55#13063315—28no—
56#13063307—28no—
57#13063301—22no—
58#13063301—22no—
59Q8×Dic43—22no—
60Q8×Dic43—22no—
61C4×C22⋊D43—22no—
62C4×C22⋊D43—22no—
63#13063284—22no—
64#13063284D414yes—
65#13063283—28no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—22no—
69C2×C4⋊Dic43—22no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43C2312yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4D411yescharacteristic
79C4⋊C4×D43—22no—
80C4⋊C4×D43—22no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43D411yescharacteristic
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—22no—
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89#13063259—24no—
90#13063257—24no—
91#13063256—24no—
92#13063249—24no—
93C22⋊(C43⋊C8)—22no—
94(C2×D43)⋊C8—24no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C22×Q8×C43C2311yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C2×M16×C43—22no—
100C2×M16×C43—24no—
101C22×C8×C43C2312yes—
102C22⋊Q8×C43—22no—
103C22⋊Q8×C43D414yes—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109#103×C43—24no—
110#95×C43—21no—
111C24×C43C2×D411yescharacteristic
112C23×D43C2×D411yescharacteristic
113C2×Q8×C43—21no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43C2×D412yes—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
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×Dic43—42no—
133C22×Dic43—82no—
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C2×C4×D43—24no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144M16×C43—28no—
145C2×C8×C43—22no—
146C2×C8×C43—22no—
147C2×C8×C43#4114yes—
148C4⋊C4×C43—24no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43C2×D412yes—
153C22⋊C4×C43—24no—
154C22⋊C4×C43—42no—
155C22⋊Dic43—24no—
156C22⋊Dic43—22no—
157(C2×D43)⋊C4—24no—
158(C2×D43)⋊C4—22no—
159(C2×D43)⋊C4—82no—
160C4⋊Dic43—24no—
161C4⋊Dic43—24no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43—42no—
167C4⋊Dic43—82no—
168C4⋊Dic43C2×D412yes—
169C4⋊Dic43C2×D412yes—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—22no—
174C4×Dic43—24no—
175C4×Dic43—24no—
176C4×Dic43—21no—
177C4×Dic43—21no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C23×C43—22no—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43—22no—
185C23×C43#12012yes—
186C23×C43C22×D411yescharacteristic
187C22×D43—21no—
188C22×D43—22no—
189C22×D43—21no—
190C22×D43—22no—
191C22×D43#13712yes—
192Q8×C43—24no—
193Q8×C43—41no—
194Q8×C43—41no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—24no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—42no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
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—22no—
215C2×Dic43—21no—
216C2×Dic43—22no—
217C2×Dic43—21no—
218C2×Dic43—22no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—22no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—84no—
229C4×D43—48no—
230C4×D43—41no—
231C4×D43—41no—
232C4×D43—42no—
233C8×C43—24no—
234C43⋊C8—42no—
235#24111—431nomaximal, Sylow
236C22×C43—22no—
237C22×C43—22no—
238C22×C43—22no—
239C22×C43—42no—
240C22×C43—42no—
241C22×C43C2×#12011yescharacteristic
242C22×C43#54712yes—
243C22×C43C2×#13711yescharacteristic
244C22×C43#57511yescharacteristic
245C22×C43#57712yes—
246C2×D43—24no—
247C2×D43—22no—
248C2×D43—42no—
249C2×D43—41no—
250C2×D43—41no—
251C4×C43—22no—
252C4×C43—42no—
253C4×C43—42no—
254C4×C43—82no—
255C4×C43#52511yescharacteristic
256C4×C43#53611yescharacteristic
257C4×C43#54712yes—
258Dic43—41no—
259Dic43—42no—
260Dic43—41no—
261Dic43—41no—
262Dic43—42no—
263Dic43—82no—
264C2×#552—431no—
265C2×#483—431no—
266C2×#428—431no—
267#2487—431no—
268#2059—432no—
269#2036—432no—
270#1894D4311yescharacteristic, complemented
271#1870—431no—
272#1865—432no—
273#1853—432no—
274#1825—431no—
275C2×C43—42no—
276C2×C43#240611yescharacteristic
277C2×C43#300711yescharacteristic
278C2×C43#301011yescharacteristic
279C2×C43#334412yes—
280C2×C43#335112yes—
281D43—42no—
282C22×M16C2×D4311yescharacteristic
283#552—864no—
284#552—864no—
285C2×#126—861no—
286C2×#125—431no—
287C2×#125—861no—
288C2×#123—861no—
289C2×C22⋊Q8—431no—
290C2×C22⋊Q8C2×D4311yescharacteristic
291C2×C4×Q8—431no—
292C2×C4×D4—431no—
293C2×#117—431no—
294C2×#117—861no—
295C22×C4⋊C4—431no—
296C22×C4⋊C4—431no—
297#483—864no—
298#428—864no—
299C2×#107—432no—
300C2×#106—432no—
301C2×#106—432no—
302C2×#103—432no—
303C2×#103C2×D4312yes—
304C2×C22⋊C8—431no—
305C2×C22⋊C8—432no—
306#400—861no—
307#399—861no—
308#389—432no—
309#386—861no—
310#385—861no—
311#380—432no—
312#380C2×D4311yescharacteristic
313#340—432no—
314#340—432no—
315#340C2×D4312yes—
316#336—432no—
317C43#2411111yescharacteristic, complemented, Sylow
318C22×Q8C22×D4311yescharacteristic
319C22×D4—431no—
320C23×C4—431no—
321C23×C4—861no—
322C23×C4—861no—
323C23×C4C22×D4311yescharacteristic
324C2×M16—22no—
325C2×M16—24no—
326C22×C8—432no—
327C22×C8C22×D4312yes—
328#126—868no—
329#125—862no—
330#125—868no—
331#125—862no—
332#123—868no—
333C22⋊Q8—22no—
334C22⋊Q8—862no—
335C22⋊Q8—862no—
336C22⋊Q8D17214yes—
337C4×Q8—862no—
338C4×Q8—862no—
339C4×D4—862no—
340C4×D4—862no—
341#117—434no—
342#117—868no—
343#117—862no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—431no—
346C2×C4⋊C4—431no—
347C2×C4⋊C4—431no—
348C2×C4⋊C4—432no—
349C2×C4⋊C4—862no—
350C2×C4⋊C4—861no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4—861no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—862no—
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×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—431no—
365C2×C22⋊C4—431no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—862no—
369C2×C42—431no—
370C2×C42—861no—
371C2×C42—861no—
372#107—864no—
373#106—864no—
374#106—864no—
375#103—24no—
376#103—864no—
377C22⋊C8—862no—
378C22⋊C8—864no—
379#95—21no—
380#95—862no—
381#95—862no—
382C24—431no—
383C24D4×D4311yescharacteristic
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8C2×D17212yes—
388C2×D4—862no—
389C2×D4—862no—
390C2×D4—1721no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—864no—
400C22×C4—861no—
401C22×C4—861no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—862no—
405C22×C4—862no—
406C22×C4—862no—
407C22×C4—3442no—
408C22×C4—1722no—
409C22×C4—1722no—
410C22×C4—1722no—
411C22×C4C2×D17212yes—
412C22×C4D4×D4311yescharacteristic
413C22×C4D4×D4312yes—
414C22×C4C23×D4311yescharacteristic
415M16—28no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—862no—
419C2×C8—862no—
420C2×C8—862no—
421C2×C8#1062190014yes—
422C4⋊C4—24no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—432no—
427C4⋊C4—432no—
428C4⋊C4—864no—
429C4⋊C4—864no—
430C4⋊C4—864no—
431C4⋊C4—864no—
432C4⋊C4—864no—
433C4⋊C4—862no—
434C4⋊C4—861no—
435C4⋊C4—861no—
436C4⋊C4—862no—
437C4⋊C4—862no—
438C4⋊C4—3442no—
439C4⋊C4—1722no—
440C4⋊C4C2×D17212yes—
441C22⋊C4—24no—
442C22⋊C4—42no—
443C22⋊C4—864no—
444C22⋊C4—862no—
445C22⋊C4—864no—
446C22⋊C4—862no—
447C22⋊C4—3442no—
448C42—864no—
449C42—864no—
450C42—861no—
451C42—861no—
452C23—21no—
453C23—21no—
454C23—22no—
455C23—22no—
456C23—432no—
457C23—861no—
458C23—861no—
459C23—862no—
460C23—862no—
461C23#1306329512yes—
462C23C2×D4×D4311yescharacteristic
463Q8—24no—
464Q8—41no—
465Q8—41no—
466D4—1724no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—861no—
480C2×C4—862no—
481C2×C4—862no—
482C2×C4—861no—
483C2×C4—861no—
484C2×C4—861no—
485C2×C4—861no—
486C2×C4—862no—
487C2×C4—862no—
488C2×C4—3444no—
489C2×C4—1728no—
490C2×C4—1722no—
491C2×C4—1722no—
492C2×C4—1722no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4—1722no—
496C2×C4—1722no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4#1306329512yes—
500C2×C4C2×D4×D4311yescharacteristic
501C2×C4C22×D17211yescharacteristic
502C2×C4C2×#1062190012yes—
503C2×C4#1306337212yes—
504C8—24no—
505C8—1722no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—42no—
510C22—42no—
511C22—864no—
512C22—862no—
513C22—1721no—
514C22—1722no—
515C22—1721no—
516C22C2×#1306329511yescharacteristic
517C22#1458354912yes—
518C22#137×D4311yescharacteristic
519C22#1458369511yescharacteristic
520C22#1458370812yes—
521C4—22no—
522C4—42no—
523C4—42no—
524C4—82no—
525C4—3442no—
526C4—1721no—
527C4—1721no—
528C4—1722no—
529C4—1721no—
530C4—1722no—
531C4#1458340511yescharacteristic
532C4#1458347111yescharacteristic
533C4#1458355312yes—
534C2—42no—
535C2—1722no—
536C2#1913792911yescharacteristic
537C2#1914385611yescharacteristic
538C2#1914388211yescharacteristic
539C2#1914704512yes—
540C2#1914715012yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#1894D43
hypocenterC43#24111
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
2. C2×#14583227C2semidirect
3. C2×#14582941C2semidirect
5. #19135936C2semidirect
6. #19135797C2semidirect
8. #19134865C2semidirect
9. #19134789C2semidirect
10. #19134687C2semidirect
11. C43×#1894C2semidirect
270. #1894D43semidirect
317. C43#24111semidirect

Maximal subgroups

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

subgroupindex
C2×#145835832
C2×#145832272
C2×#145829412
#191389132
#191359362
#191357972
#191348922
#191348652
#191347892
#191346872
C43×#18942
#2411143