Finite Group Databasebeta

← #25130357

Subgroups — #25130357

Order 11008.

1146 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583613C211yesmaximal, characteristic
2C2×#14582939C211yesmaximal, characteristic, complemented
3#19138897C211yesmaximal, characteristic, complemented
4#19135926C212yesmaximal, complemented
5#19135782C212yesmaximal, complemented
6#19135034C211yesmaximal, characteristic, complemented
7#19134890C211yesmaximal, characteristic, complemented
8#19134840C212yesmaximal, complemented
9#19134793C212yesmaximal, complemented
10#19134691C211yesmaximal, characteristic, complemented
11C2×C43×#481C211yesmaximal, characteristic, complemented
12C22×#10621877C2211yescharacteristic
13#14583613—24no—
14#14583613—24no—
15C2×#13063324C2211yescharacteristic
16C2×#13063312—21no—
17C2×#13063311—21no—
18C2×#13063308—21no—
19C2×#13063297—21no—
20C2×#13063296C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23C2×#13063284C2211yescharacteristic
24C2×#13063283C2211yescharacteristic
25C2×#13063281—21no—
26#14582939—24no—
27C2×#13063258C2212yes—
28C2×#13063256C2212yes—
29C2×#13063246C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31#14582830—21no—
32#14582825—21no—
33#14582795C2212yes—
34#14582762—21no—
35#14582759C2211yescharacteristic
36#14582756C2212yes—
37#14582662C2212yes—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582653C2212yes—
41C2×#121×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C43×#481—24no—
44C2×#106×C43C2212yes—
45C2×#102×C43C2212yes—
46C2×C22⋊C8×C43C2211yescharacteristic
47C22×Dic86—21no—
48C22×C22⋊D43—21no—
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#13063312—28no—
58#13063311—28no—
59#13063308—44no—
60#13063297—28no—
61#13063296—22no—
62#13063296—22no—
63D4×Dic43—22no—
64D4×Dic43—22no—
65C4×C22⋊D43—22no—
66C4×C22⋊D43—22no—
67#13063284—22no—
68#13063284D414yes—
69#13063283—22no—
70#13063283—22no—
71#13063281—28no—
72C2×C4⋊Dic43C2312yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
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#13063258—24no—
90#13063256—24no—
91#13063246—24no—
92(C2×D43)⋊C8—24no—
93C43⋊#95—21no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C22×D4×C43—21no—
97C22×D4×C43C2311yescharacteristic
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100C22×C8×C43C2312yes—
101#121×C43—22no—
102#121×C43D414yes—
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#102×C43—24no—
111C22⋊C8×C43—22no—
112C24×C43—21no—
113C24×C43C2×D411yescharacteristic
114C23×D43C2×D411yescharacteristic
115C2×D4×C43—21no—
116C2×D4×C43—24no—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—82no—
120C2×D4×C43C2×D412yes—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C2×C22⋊D43—24no—
133C2×C22⋊D43—22no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—41no—
136C2×C22⋊D43—82no—
137C22×Dic43—24no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×Dic86—24no—
151C2×Dic86—82no—
152C2×C8×C43—22no—
153C2×C8×C43—22no—
154C2×C8×C43—22no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—42no—
159C4⋊C4×C43C2×D412yes—
160C22⋊C4×C43—24no—
161C22⋊Dic43—24no—
162C22⋊Dic43—24no—
163C22⋊Dic43—24no—
164C22⋊Dic43—22no—
165C22⋊Dic43—42no—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—22no—
168(C2×D43)⋊C4—44no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—22no—
172C4⋊Dic43—22no—
173C4⋊Dic43C2×D412yes—
174C4⋊Dic43C2×D412yes—
175Dic43⋊C4—24no—
176Dic43⋊C4—22no—
177Dic43⋊C4—44no—
178C4×Dic43—24no—
179C4×Dic43—24no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182#10621877—28no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8#4114yes—
186C23×C43—22no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—42no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—42no—
195C23×C43#12012yes—
196C23×C43C22×D411yescharacteristic
197C22×D43—21no—
198C22×D43—22no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—22no—
202D4×C43—24no—
203D4×C43—41no—
204D4×C43—41no—
205D4×C43—84no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—24no—
210C2×C4×C43—22no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—84no—
216C2×C4×C43#12012yes—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4112yes—
220C2×C4×C432−1+412yes—
221C22⋊D43—44no—
222C22⋊D43—84no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—21no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—48no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43AGL(1,ℤ/8)12yes—
239C4×D43—41no—
240C4×D43—41no—
241C4×D43—42no—
242Dic86—84no—
243C8×C43—42no—
244C43⋊C8—24no—
245#24104—431nomaximal, Sylow
246C22×C43—22no—
247C22×C43—22no—
248C22×C43—22no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43—42no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—82no—
255C22×C43—82no—
256C22×C43C2×#12011yescharacteristic
257C22×C43#54712yes—
258C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C43#57511yescharacteristic
260C22×C43#57712yes—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—41no—
266C4×C43—22no—
267C4×C43—42no—
268C4×C43—82no—
269C4×C43#52511yescharacteristic
270C4×C43#53611yescharacteristic
271C4×C43#54712yes—
272Dic43—22no—
273Dic43—41no—
274Dic43—42no—
275Dic43—41no—
276Dic43—42no—
277Dic43—82no—
278C2×#555—431no—
279C2×#481D4311yescharacteristic, complemented
280C2×#428—431no—
281#2486—431no—
282#2058—432no—
283#2034—432no—
284#1895—431no—
285#1870—431no—
286#1862—432no—
287#1854—432no—
288#1825—431no—
289C2×C43—42no—
290C2×C43—82no—
291C2×C43#240611yescharacteristic
292C2×C43#300611yescharacteristic
293C2×C43#300911yescharacteristic
294C2×C43#334812yes—
295C2×C43#335412yes—
296D43—81no—
297C22×M16—431no—
298#555—864no—
299#555—864no—
300C2×C4⋊Q8—431no—
301C2×#124—861no—
302C2×#124—861no—
303C2×#123—861no—
304C2×#121—431no—
305C2×#121—861no—
306C2×#121C2×D4311yescharacteristic
307C2×C4×D4—431no—
308C2×C4×D4—431no—
309C2×#117—431no—
310C2×#117—431no—
311C2×#117—861no—
312C22×C4⋊C4C2×D4311yescharacteristic
313#481—24no—
314#428—864no—
315C2×#107—432no—
316C2×#106—432no—
317C2×#106C2×D4312yes—
318C2×#102—432no—
319C2×#102C2×D4312yes—
320C2×C22⋊C8—432no—
321C2×C22⋊C8C2×D4311yescharacteristic
322#398—861no—
323#397—861no—
324#389—432no—
325#381—861no—
326#380—431no—
327#380—432no—
328#340—432no—
329#340—432no—
330#340—432no—
331#336—432no—
332C43#2410411yescharacteristic, complemented, Sylow
333C22×Q8—861no—
334C22×D4—21no—
335C22×D4—431no—
336C22×D4—861no—
337C22×D4C22×D4311yescharacteristic
338C23×C4—21no—
339C23×C4—431no—
340C23×C4—861no—
341C23×C4C22×D4311yescharacteristic
342C2×M16—864no—
343C2×M16—862no—
344C22×C8—432no—
345C22×C8C22×D4312yes—
346C4⋊Q8—862no—
347C4⋊Q8—862no—
348#124—868no—
349#124—868no—
350#123—1724no—
351#121—22no—
352#121—862no—
353#121—868no—
354#121—862no—
355#121C22⋊D4314yes—
356C4×D4—862no—
357C4×D4—862no—
358C4×D4—862no—
359C4×D4—862no—
360#117—434no—
361#117—868no—
362#117—862no—
363#117—862no—
364#117—862no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—432no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4C22×D4312yes—
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—431no—
378C2×C22⋊C4—431no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—862no—
384C2×C22⋊C4—861no—
385C2×C42—431no—
386C2×C42—861no—
387C2×C42—861no—
388#107—864no—
389#106—24no—
390#106—864no—
391#102—24no—
392#102—864no—
393C22⋊C8—22no—
394C22⋊C8—864no—
395#95—862no—
396#95—862no—
397#95—861no—
398C24—21no—
399C24—431no—
400C24D4×D4311yescharacteristic
401C2×Q8—864no—
402C2×Q8—3442no—
403C2×D4—24no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—82no—
408C2×D4—862no—
409C2×D4—864no—
410C2×D4—862no—
411C2×D4—3442no—
412C2×D4—1721no—
413C2×D4C2×C22⋊D4312yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—431no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—864no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—1722no—
433C22×C4—1722no—
434C22×C4D4×D4311yescharacteristic
435C22×C4D4×D4312yes—
436C22×C4C2×C22⋊D4312yes—
437C22×C4C23×D4311yescharacteristic
438M16—868no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—434no—
443C2×C8—862no—
444C2×C8—862no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4—432no—
450C4⋊C4—432no—
451C4⋊C4—864no—
452C4⋊C4—862no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—862no—
456C4⋊C4—862no—
457C4⋊C4—1724no—
458C4⋊C4C2×C22⋊D4312yes—
459C22⋊C4—24no—
460C22⋊C4—864no—
461C22⋊C4—864no—
462C22⋊C4—864no—
463C22⋊C4—862no—
464C22⋊C4—864no—
465C22⋊C4—862no—
466C22⋊C4—1724no—
467C22⋊C4—1722no—
468C42—864no—
469C42—864no—
470C42—861no—
471C42—861no—
472C23—21no—
473C23—21no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—42no—
481C23—861no—
482C23—861no—
483C23—861no—
484C23—862no—
485C23—862no—
486C23#1306329312yes—
487C23C2×D4×D4311yescharacteristic
488Q8—3444no—
489D4—24no—
490D4—41no—
491D4—41no—
492D4—84no—
493D4—3444no—
494D4—1724no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—84no—
505C2×C4—432no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—862no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—1728no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1722no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1722no—
524C2×C4#1306329312yes—
525C2×C4C2×D4×D4311yescharacteristic
526C2×C4C22×C22⋊D4311yescharacteristic
527C2×C4#41×D4312yes—
528C2×C4#1306337212yes—
529C8—42no—
530C8—864no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—82no—
540C22—82no—
541C22—1722no—
542C22—1721no—
543C22—1721no—
544C22—1722no—
545C22—1721no—
546C22C2×#1306329311yescharacteristic
547C22#1458354712yes—
548C22AGL(1,ℤ/8)×D4311yescharacteristic
549C22#1458369511yescharacteristic
550C22#1458370512yes—
551C4—22no—
552C4—42no—
553C4—82no—
554C4—862no—
555C4—3442no—
556C4—1721no—
557C4—1722no—
558C4—1721no—
559C4—1722no—
560C4#1458340711yescharacteristic
561C4#1458347111yescharacteristic
562C4#1458354812yes—
563C2—42no—
564C2—82no—
565C2—3441no—
566C2#1913792711yescharacteristic
567C2#1914384311yescharacteristic
568C2#1914386811yescharacteristic
569C2#1914711312yes—
570C2#1914718312yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#481C2
socleC23×C43C22×D4
prime radicalC2×#14583613C2
hypercenterC2×#481D43
hypocenterC43#24104
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#14582939C2semidirect
3. #19138897C2semidirect
4. #19135926C2semidirect
5. #19135782C2semidirect
6. #19135034C2semidirect
7. #19134890C2semidirect
8. #19134840C2semidirect
9. #19134793C2semidirect
10. #19134691C2semidirect
11. C2×C43×#481C2semidirect
279. C2×#481D43semidirect
332. C43#24104semidirect

Maximal subgroups

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

subgroupindex
C2×#145836132
C2×#145829392
#191388972
#191359262
#191357822
#191350342
#191348902
#191348402
#191347932
#191346912
C2×C43×#4812
#2410443