Finite Group Databasebeta

← #25129888

Subgroups — #25129888

Order 11008.

1144 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic
2C2×#14583229C211yesmaximal, characteristic
3C2×#14582795C211yesmaximal, characteristic
4#19135926C212yesmaximal, complemented
5#19135839C212yesmaximal, complemented
6#19134903C211yesmaximal, characteristic
7#19134900C211yesmaximal, characteristic
8#19134861C212yesmaximal, complemented
9#19134860C212yesmaximal, complemented
10#19134661C211yesmaximal, characteristic
11C2×C43×#483C211yesmaximal, characteristic
12#14583451—24no—
13#14583451—24no—
14C2×#13063324C2211yescharacteristic
15C2×#13063323C2211yescharacteristic
16C2×#13063315—21no—
17C2×#13063304C2211yescharacteristic
18C2×#13063302—21no—
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063290—21no—
21C2×#13063290C2211yescharacteristic
22C2×#13063281—21no—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×Dic43⋊C4—21no—
25C22×C4×Dic43C2211yescharacteristic
26#14583229—24no—
27C2×#13063256C2212yes—
28C2×#13063250C2212yes—
29C2×#13063249C2212yes—
30C2×#13063248C2212yes—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32#14582795—21no—
33#14582795—21no—
34#14582795C2212yes—
35#14582795C2212yes—
36C2×C43⋊#95—21no—
37#14582662C2212yes—
38#14582661C2212yes—
39#14582653C2212yes—
40#14582653C2212yes—
41C2×C22⋊Q8×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C43×#483—24no—
44C2×#106×C43C2212yes—
45C2×#103×C43C2212yes—
46C2×C22⋊C8×C43C2211yescharacteristic
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C23×Dic43—21no—
50C23×Dic43D411yescharacteristic
51C23×Dic43D411yescharacteristic
52C22×C43⋊C8C2312yes—
53#13063324—22no—
54#13063324—22no—
55#13063323—22no—
56#13063323—22no—
57#13063315—28no—
58#13063304—22no—
59#13063304D414yes—
60#13063302—28no—
61Q8×Dic43—22no—
62Q8×Dic43—22no—
63#13063290—28no—
64#13063290—22no—
65#13063290—22no—
66#13063281—28no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—24no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2312yes—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—44no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—22no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063256—24no—
90#13063250—24no—
91#13063249—24no—
92#13063248—24no—
93C22⋊(C43⋊C8)—22no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C22×Q8×C43C2311yescharacteristic
97C23×C4×C43—21no—
98C23×C4×C43C2311yescharacteristic
99C22×C8×C43C2312yes—
100C22⋊Q8×C43—22no—
101C22⋊Q8×C43D414yes—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2312yes—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C22⋊C4×C43—21no—
109#106×C43—24no—
110#103×C43—24no—
111C22⋊C8×C43—22no—
112C24×C43C2×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×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43—42no—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—24no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—41no—
138C22×Dic43—42no—
139C22×Dic43—42no—
140C22×Dic43SD1614yes—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C2×Dic86—22no—
146C2×Dic86—22no—
147C2×Dic86—24no—
148C2×Dic86—21no—
149C2×Dic86—42no—
150C2×Dic86—42no—
151C2×Dic86C2×D412yes—
152C2×C8×C43—22no—
153C2×C8×C43—22no—
154C2×C8×C43—22no—
155C4⋊C4×C43—24no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43C2×D412yes—
161C22⋊C4×C43—24no—
162C22⋊Dic43—24no—
163C4⋊Dic43—24no—
164C4⋊Dic43—24no—
165C4⋊Dic43—21no—
166C4⋊Dic43—22no—
167C4⋊Dic43C2×D412yes—
168C4⋊Dic43#4114yes—
169Dic43⋊C4—24no—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—24no—
174Dic43⋊C4—44no—
175Dic43⋊C4—44no—
176C4×Dic43—24no—
177C4×Dic43—24no—
178C4×Dic43—22no—
179C4×Dic43—22no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43#12012yes—
192C23×C43C2×SD1612yes—
193C23×C43#13712yes—
194C23×C43C22×D411yescharacteristic
195Q8×C43—24no—
196Q8×C43—42no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—24no—
200C2×C4×C43—24no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—84no—
211C2×C4×C43#12012yes—
212C2×C4×C43C22×D411yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C2×#4112yes—
215C2×C4×C432−1+412yes—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—28no—
223C2×Dic43—21no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—24no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—44no—
230C2×Dic43—48no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—42no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—42no—
237C2×Dic43C2×SD1612yes—
238C2×Dic43C2×SD1612yes—
239C2×Dic43#13712yes—
240Dic86—24no—
241Dic86—48no—
242Dic86—42no—
243C8×C43—42no—
244C43⋊C8—42no—
245#24063—431nomaximal, Sylow
246C22×C43—22no—
247C22×C43—22no—
248C22×C43—22no—
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43#44814yes—
253C22×C43C2×#12011yescharacteristic
254C22×C43#52511yescharacteristic
255C22×C43#53611yescharacteristic
256C22×C43C22×SD1611yescharacteristic
257C22×C43C2×#13711yescharacteristic
258C22×C43C2×#13711yescharacteristic
259C22×C43#57511yescharacteristic
260C4×C43—22no—
261C4×C43—42no—
262C4×C43—42no—
263C4×C43—82no—
264C4×C43#54712yes—
265C4×C43#54712yes—
266Dic43—22no—
267Dic43—22no—
268Dic43—22no—
269Dic43—44no—
270Dic43—42no—
271Dic43—42no—
272Dic43—41no—
273C2×#533—431no—
274C2×#483—431no—
275C2×#483D4311yescharacteristic
276C2×#389—431no—
277#2058—432no—
278#2043—432no—
279#1872—431no—
280#1872—431no—
281#1865—432no—
282#1865—432no—
283#1817—431no—
284C2×C43—24no—
285C2×C43#240611yescharacteristic
286C2×C43C2×#44811yescharacteristic
287C2×C43#300711yescharacteristic
288C2×C43#310111yescharacteristic
289C2×C43#311311yescharacteristic
290C2×C43#322911yescharacteristic
291C2×C43#323611yescharacteristic
292#533—864no—
293#533—864no—
294C2×C4⋊Q8—431no—
295C2×C4⋊Q8—431no—
296C2×#125—861no—
297C2×C22⋊Q8—431no—
298C2×C22⋊Q8—861no—
299C2×C22⋊Q8C2×D4311yescharacteristic
300C2×C4×Q8—431no—
301C2×C4×Q8—431no—
302C2×C4×Q8—861no—
303C2×#117—861no—
304C22×C4⋊C4—431no—
305C22×C4⋊C4—861no—
306C22×C4⋊C4C2×D4311yescharacteristic
307C22×C42—431no—
308#483—24no—
309#483—864no—
310C2×#106—432no—
311C2×#106C2×D4312yes—
312C2×#103—432no—
313C2×#103—432no—
314C2×#103—432no—
315C2×#103C2×D4312yes—
316C2×C22⋊C8—431no—
317C2×C22⋊C8C2×D4311yescharacteristic
318#389—432no—
319#389—432no—
320#389—861no—
321#389—861no—
322C2×#95—861no—
323#340—432no—
324#340—432no—
325#336—432no—
326#336—432no—
327C43#2406311yescharacteristic, complemented, Sylow
328C22×Q8—431no—
329C22×Q8—861no—
330C22×Q8C22×D4311yescharacteristic
331C23×C4—21no—
332C23×C4—431no—
333C23×C4—431no—
334C23×C4—861no—
335C23×C4C22×D4311yescharacteristic
336C22×C8—432no—
337C22×C8C22×D4312yes—
338C4⋊Q8—862no—
339C4⋊Q8—862no—
340C4⋊Q8—862no—
341C4⋊Q8—862no—
342#125—868no—
343C22⋊Q8—22no—
344C22⋊Q8—434no—
345C22⋊Q8—868no—
346C22⋊Q8—862no—
347C22⋊Q8C22⋊D4314yes—
348C4×Q8—862no—
349C4×Q8—868no—
350C4×Q8—862no—
351C4×Q8—862no—
352C4×Q8—862no—
353#117—868no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—432no—
359C2×C4⋊C4—431no—
360C2×C4⋊C4—864no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—1724no—
371C2×C4⋊C4C22×D4312yes—
372C2×C4⋊C4C22×D4311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—861no—
375C2×C42—431no—
376C2×C42—431no—
377C2×C42—431no—
378C2×C42—431no—
379C2×C42—861no—
380C2×C42—861no—
381C2×C42—862no—
382C2×C42—862no—
383#106—24no—
384#106—864no—
385#103—24no—
386#103—864no—
387#103—864no—
388#103—864no—
389C22⋊C8—22no—
390C22⋊C8—862no—
391#95—862no—
392#95—862no—
393C24D4×D4311yescharacteristic
394C2×Q8—21no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—432no—
398C2×Q8—864no—
399C2×Q8—861no—
400C2×Q8—862no—
401C2×Q8—862no—
402C2×Q8—1722no—
403C2×Q8—1722no—
404C2×Q8C2×C22⋊D4312yes—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—434no—
414C22×C4—431no—
415C22×C4—431no—
416C22×C4—431no—
417C22×C4—431no—
418C22×C4—862no—
419C22×C4—862no—
420C22×C4—862no—
421C22×C4—864no—
422C22×C4—862no—
423C22×C4—862no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—1721no—
427C22×C4—1722no—
428C22×C4—1722no—
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4312yes—
431C22×C4C2×C22⋊D4312yes—
432C22×C4C23×D4311yescharacteristic
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—862no—
437C2×C8—862no—
438C2×C8—862no—
439C4⋊C4—24no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4—432no—
445C4⋊C4—434no—
446C4⋊C4—864no—
447C4⋊C4—864no—
448C4⋊C4—864no—
449C4⋊C4—864no—
450C4⋊C4—864no—
451C4⋊C4—864no—
452C4⋊C4—864no—
453C4⋊C4—861no—
454C4⋊C4—862no—
455C4⋊C4—1724no—
456C4⋊C4—1724no—
457C4⋊C4C2×C22⋊D4312yes—
458C22⋊C4—24no—
459C22⋊C4—864no—
460C42—864no—
461C42—864no—
462C42—862no—
463C42—862no—
464C42—861no—
465C42—861no—
466C42—861no—
467C42—861no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23#1306329312yes—
473C23SD16×D4312yes—
474C23#1306335412yes—
475C23C2×D4×D4311yescharacteristic
476Q8—24no—
477Q8—42no—
478Q8—864no—
479Q8—1728no—
480Q8—1722no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—84no—
495C2×C4—432no—
496C2×C4—432no—
497C2×C4—432no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—868no—
505C2×C4—861no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—864no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—1724no—
512C2×C4—1728no—
513C2×C4—1721no—
514C2×C4—1722no—
515C2×C4—1721no—
516C2×C4—1722no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4#1306329312yes—
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4C22×C22⋊D4311yescharacteristic
522C2×C4#41×D4312yes—
523C2×C4#1306337212yes—
524C8—42no—
525C8—1722no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22#1458303614yes—
533C22C2×#1306329311yescharacteristic
534C22#1458340711yescharacteristic
535C22#1458347111yescharacteristic
536C22C2×SD16×D4311yescharacteristic
537C22#137×D4311yescharacteristic
538C22C2×#1306335411yescharacteristic
539C22#1458369811yescharacteristic
540C4—22no—
541C4—42no—
542C4—42no—
543C4—82no—
544C4—862no—
545C4—862no—
546C4—862no—
547C4—1722no—
548C4—1724no—
549C4—1721no—
550C4—1722no—
551C4#1458354712yes—
552C4#1458354812yes—
553C2—24no—
554C2#1913792711yescharacteristic
555C2C2×#1458303611yescharacteristic
556C2#1914385111yescharacteristic
557C2#1914460011yescharacteristic
558C2#1914472211yescharacteristic
559C2#1914573711yescharacteristic
560C2#1914579811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#483C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC2×#483D43
hypocenterC43#24063
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
4. #19135926C2semidirect
5. #19135839C2semidirect
8. #19134861C2semidirect
9. #19134860C2semidirect
327. C43#24063semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
C2×#145832292
C2×#145827952
#191359262
#191358392
#191349032
#191349002
#191348612
#191348602
#191346612
C2×C43×#4832
#2406343