Finite Group Databasebeta

← #25097409

Subgroups — #25097409

Order 11008.

1422 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147793C211yesmaximal, characteristic
2#19143182C212yesmaximal, complemented
3C2×#14582880C211yesmaximal, characteristic
4#19137082C211yesmaximal, characteristic
5#19134811C212yesmaximal, complemented
6#19134808C212yesmaximal, complemented
7#19134807C211yesmaximal, characteristic, complemented
8#19134805C211yesmaximal, characteristic, complemented
9#19134804C211yesmaximal, characteristic, complemented
10#339×D43C212yesmaximal, complemented
11C43×#1856C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13C2×M16×D43C2212yes—
14#14583378—22no—
15#14583378—22no—
16#14583376C2212yes—
17#14583374C2211yescharacteristic
18#14583372—22no—
19C4×#10621900—22no—
20C4×#10621900—22no—
21C2×#13063283C2211yescharacteristic
22C2×#13063281—22no—
23#117×D43C2212yes—
24C2×C42×D43C2211yescharacteristic
25#14582942C2212yes—
26#14582941C2212yes—
27#14582940—22no—
28#14582939C2212yes—
29#14582938—22no—
30#14582936—22no—
31#14582934—22no—
32#14582880C418yescomplemented
33C2×#13063243C2212yes—
34C2×#13063242C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582804C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582775—22no—
39C22⋊C4×Dic43—22no—
40#14582660C2212yes—
41#14582659C2212yes—
42#14582658C2212yes—
43C43×#518C2211yescharacteristic
44C43×#428C2212yes—
45C2×#100×C43C2211yescharacteristic
46C43×#390C2211yescharacteristic
47C43×#339C2212yes—
48C2×#10621900—22no—
49C2×#10621900—22no—
50C2×#10621900—24no—
51C2×#10621900C2×C414yes—
52C2×#10621900Q814yes—
53C22×Dic86C2311yescharacteristic
54C22×C22⋊D43D412yes—
55C23×Dic43D412yes—
56C22×C4×D43—21no—
57C22×C4×D43C2311yescharacteristic
58C2×#10621877C2312yes—
59C2×#10621872—22no—
60M16×D43—24no—
61M16×D43C2×C418yescomplemented
62C2×C8×D43—22no—
63C4×Dic86—22no—
64C4×Dic86—22no—
65#13063290—22no—
66#13063290—22no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69C4×C22⋊D43—24no—
70C4×C22⋊D43—24no—
71(C22⋊D43)⋊C4—24no—
72(C22⋊D43)⋊C4—24no—
73#13063284C2312yes—
74#13063283—22no—
75#13063283—22no—
76#13063283D412yes—
77#13063283D412yes—
78#13063282—22no—
79#13063281—24no—
80#13063281—24no—
81#13063281—22no—
82#13063281—24no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—22no—
86C4⋊C4×D43D412yes—
87C4⋊C4×D43D412yes—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43—22no—
90C2×(C2×D43)⋊C4—21no—
91C22⋊C4×D43—22no—
92C2×C4×Dic43—22no—
93C2×C4×Dic43—22no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C42×D43—22no—
98C42×D43—24no—
99#13063259—22no—
100#13063258—22no—
101#13063258—22no—
102#13063257—22no—
103#13063256—22no—
104#13063256—22no—
105#13063243C2×C418yescomplemented
106#13063242C2×C414yescomplemented
107C43⋊#95—22no—
108C43⋊#95—22no—
109C22×D4×C43C2311yescharacteristic
110C2×M16×C43C2312yes—
111C4×D4×C43—22no—
112C4×D4×C43—22no—
113#117×C43C2312yes—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—22no—
117C2×C42×C43C2311yescharacteristic
118#107×C43—22no—
119#106×C43—22no—
120#100×C43C2×C414yescomplemented
121C24×C43C2×D412yes—
122C23×D43C2×D411yescharacteristic
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43C22×C412yes—
126C2×D4×C43C2×Q812yes—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2411yescharacteristic
132C2×C22⋊D43—24no—
133C2×C22⋊D43—24no—
134C2×C22⋊D43C4⋊C418yes—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—24no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43C4⋊C418yes—
143C22×Dic43C2×D412yes—
144C22×Dic43C2×D411yescharacteristic
145#10621900—28no—
146#10621900—28no—
147#10621900—28no—
148#10621900—28no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43C22×C412yes—
155C2×C4×D43C2×D412yes—
156C2×C4×D43C2×D412yes—
157C2×C4×D43C2×Q812yes—
158C2×C4×D43#4114yes—
159C2×Dic86—22no—
160C2×Dic86—22no—
161C2×Dic86C22×C412yes—
162C2×Dic86C2×Q812yes—
163M16×C43—22no—
164M16×C43C22×C414yes—
165C2×C8×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43C2×D412yes—
168C4⋊C4×C43C2×D412yes—
169C22⋊C4×C43—24no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—44no—
172C42×C43—22no—
173C42×C43—22no—
174C22⋊Dic43—24no—
175C22⋊Dic43—22no—
176C22⋊Dic43—44no—
177(C2×D43)⋊C4—22no—
178(C2×D43)⋊C4—22no—
179(C2×D43)⋊C4—42no—
180C4⋊Dic43—22no—
181C4⋊Dic43C2×D412yes—
182C4⋊Dic43C2×D412yes—
183Dic43⋊C4—24no—
184Dic43⋊C4—24no—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187C4×Dic43—24no—
188C4×Dic43—24no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—41no—
194C4×Dic43—41no—
195C4×Dic43—42no—
196#10621877—22no—
197#10621877C22×C414yes—
198C2×C43⋊C8—22no—
199#10621872—28no—
200C8×D43—28no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43C2×C4⋊C414yes—
206C23×C43C22×D411yescharacteristic
207C22×D43—41no—
208C22×D43—41no—
209C22×D43C2×C4⋊C412yes—
210C22×D43#12012yes—
211C22×D43#12312yes—
212D4×C43—24no—
213D4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—82no—
222C2×C4×C43—82no—
223C2×C4×C43C23×C411yescharacteristic
224C2×C4×C43C22×D412yes—
225C2×C4×C43C22×Q811yescharacteristic
226C2×C4×C43C2×#4112yes—
227C22⋊D43—216no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—28no—
231C2×Dic43—28no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—42no—
238C2×Dic43—41no—
239C2×Dic43—82no—
240C2×Dic43—82no—
241C2×Dic43C2×C4⋊C414yes—
242C2×Dic43C2×C4⋊C412yes—
243C2×Dic43#12011yescharacteristic
244C2×Dic43#12011yescharacteristic
245C2×Dic43#12312yes—
246C4×D43—48no—
247C4×D43—82no—
248C4×D43—82no—
249C4×D43C4×D414yes—
250C4×D43C4×D414yes—
251C4×D43C22⋊Q814yes—
252C4×D43C22⋊Q814yes—
253Dic86—24no—
254Dic86—24no—
255C8×C43—24no—
256C43⋊C8—24no—
257#20855—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—24no—
261C22×C43—44no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—82no—
265C22×C43C22×C4⋊C411yescharacteristic
266C22×C43C2×#12011yescharacteristic
267C22×C43C2×#12311yescharacteristic
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43#38514yes—
273C4×C43—42no—
274C4×C43—42no—
275C4×C43—42no—
276C4×C43—81no—
277C4×C43C2×C4×D412yes—
278C4×C43C2×C22⋊Q812yes—
279Dic43—24no—
280Dic43—42no—
281Dic43—42no—
282Dic43—42no—
283Dic43—81no—
284Dic43#38512yes—
285Dic43#38512yes—
286#3428—431no—
287#2911—432no—
288C2×#413—431no—
289#2297—431no—
290#1857—432no—
291#1857—432no—
292#1856—431no—
293#1856—431no—
294#1856—431no—
295#1856D4311yescharacteristic, complemented
296C2×#339—432no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—44no—
300C2×C43C2×#38511yescharacteristic
301C2×C43#301811yescharacteristic
302C2×C43#301811yescharacteristic
303D43—24no—
304C22×#41—431no—
305C22×M16—432no—
306#520—862no—
307#520—862no—
308#519—432no—
309#518—431no—
310#518—862no—
311#518C2×D4311yescharacteristic
312C4×#41—862no—
313C4×#41—862no—
314C2×#117—432no—
315C2×#117—431no—
316C2×#117—862no—
317C22×C42—431no—
318#428—432no—
319#428—432no—
320#428—432no—
321#428—862no—
322#428—862no—
323#428C2×D4312yes—
324#427—862no—
325#427—862no—
326#413—438no—
327C2×#101—432no—
328C2×#100—431no—
329C2×#100C2×D4311yescharacteristic
330#391—431no—
331#391—431no—
332#390—431no—
333#390C2×D4311yescharacteristic
334#386—862no—
335C4×C22⋊C4—862no—
336#339—432no—
337#339—432no—
338#339—432no—
339#339C2×D4312yes—
340C43#2085511yescharacteristic, complemented, Sylow
341C2×#41—434no—
342C2×#41—434no—
343C2×#41—862no—
344C2×#41—862no—
345C2×#41—864no—
346C22×Q8—431no—
347C22×D4—432no—
348C22×D4C22×D4311yescharacteristic
349C23×C4—431no—
350C23×C4—432no—
351C23×C4—861no—
352C2×M16—432no—
353C2×M16—438no—
354C2×M16—862no—
355C2×M16—864no—
356C2×M16C22×D4312yes—
357C22×C8—862no—
358C4×Q8—862no—
359C4×Q8—862no—
360C4×Q8—862no—
361C4×Q8—862no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—864no—
365C4×D4—864no—
366C4×D4—862no—
367C4×D4—862no—
368C4×D4—864no—
369C4×D4—864no—
370#117—432no—
371#117—432no—
372#117—432no—
373#117—862no—
374#117—862no—
375#117—864no—
376#117—864no—
377#117—864no—
378#117—862no—
379#117—862no—
380#117C22×D4312yes—
381C2×C4⋊C4—432no—
382C2×C4⋊C4—432no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—862no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—862no—
393C2×C42—431no—
394C2×C42—862no—
395C2×C42—864no—
396C2×C42—862no—
397C2×C42—862no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#107—22no—
402#107—862no—
403#107—862no—
404#107—862no—
405#106—22no—
406#106—862no—
407#106—862no—
408#106—862no—
409#101—438no—
410#100—434no—
411#100C4×D4314yescomplemented
412#95—862no—
413#95—862no—
414C24—431no—
415C24D4×D4312yes—
416#41—868no—
417#41—868no—
418#41—868no—
419#41—868no—
420C2×Q8—432no—
421C2×Q8—432no—
422C2×Q8—862no—
423C2×Q8—862no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—438no—
427C2×D4—864no—
428C2×D4—864no—
429C2×D4C2×C4×D4312yes—
430C2×D4Q8×D4312yes—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—431no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—432no—
439C22×C4—432no—
440C22×C4—434no—
441C22×C4—438no—
442C22×C4—432no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—864no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—1722no—
453C22×C4—1722no—
454C22×C4—1722no—
455C22×C4C23×D4311yescharacteristic
456M16—22no—
457M16—434no—
458M16—868no—
459M16—862no—
460M16C2×C4×D4314yes—
461C2×C8—22no—
462C2×C8—868no—
463C2×C8—862no—
464C4⋊C4—22no—
465C4⋊C4—432no—
466C4⋊C4—432no—
467C4⋊C4—862no—
468C4⋊C4—862no—
469C4⋊C4—864no—
470C4⋊C4—864no—
471C4⋊C4—862no—
472C4⋊C4D4×D4312yes—
473C4⋊C4D4×D4312yes—
474C22⋊C4—24no—
475C22⋊C4—22no—
476C22⋊C4—44no—
477C22⋊C4—862no—
478C22⋊C4—862no—
479C22⋊C4—864no—
480C22⋊C4—862no—
481C22⋊C4—1722no—
482C22⋊C4—1724no—
483C42—22no—
484C42—22no—
485C42—862no—
486C42—862no—
487C42—864no—
488C42—864no—
489C42—862no—
490C42—862no—
491C42—1722no—
492C42—1721no—
493C42—1721no—
494C23—22no—
495C23—22no—
496C23—42no—
497C23—42no—
498C23—432no—
499C23—432no—
500C23—432no—
501C23—1721no—
502C23—1721no—
503C23C4⋊C4×D4314yes—
504C23C2×D4×D4311yescharacteristic
505Q8—864no—
506Q8—864no—
507D4—24no—
508D4—24no—
509D4—8616no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—432no—
520C2×C4—431no—
521C2×C4—431no—
522C2×C4—432no—
523C2×C4—434no—
524C2×C4—434no—
525C2×C4—434no—
526C2×C4—434no—
527C2×C4—434no—
528C2×C4—868no—
529C2×C4—868no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—3442no—
536C2×C4—3442no—
537C2×C4—3442no—
538C2×C4—3442no—
539C2×C4—1728no—
540C2×C4—1722no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4C22×C4×D4311yescharacteristic
545C2×C4C2×D4×D4312yes—
546C2×C4C2×Q8×D4311yescharacteristic
547C2×C4#41×D4312yes—
548C8—24no—
549C8—864no—
550C22—21no—
551C22—21no—
552C22—24no—
553C22—44no—
554C22—42no—
555C22—42no—
556C22—82no—
557C22—434no—
558C22—862no—
559C22—862no—
560C22—1722no—
561C22—1722no—
562C22C2×C4⋊C4×D4311yescharacteristic
563C22#120×D4311yescharacteristic
564C22#123×D4311yescharacteristic
565C4—42no—
566C4—42no—
567C4—42no—
568C4—81no—
569C4—432no—
570C4—432no—
571C4—864no—
572C4—3441no—
573C4—1722no—
574C4—1722no—
575C4—1722no—
576C4C4×D4×D4312yes—
577C4C22⋊Q8×D4312yes—
578C2—21no—
579C2—21no—
580C2—44no—
581C2—864no—
582C2#385×D4311yescharacteristic
583C2#1914394011yescharacteristic
584C2#1914394511yescharacteristic
subgroupG/H
centerC22#120×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1856C2
socleC22×C43C2×#120
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1856D43
hypocenterC43#20855
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1856

Complements

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

NH ≅ G/Ntype
2. #19143182C2semidirect
5. #19134811C2semidirect
6. #19134808C2semidirect
7. #19134807C2semidirect
8. #19134805C2semidirect
9. #19134804C2semidirect
10. #339×D43C2semidirect
11. C43×#1856C2semidirect
32. #14582880C4semidirect
61. M16×D43C2×C4semidirect
105. #13063243C2×C4semidirect
106. #13063242C2×C4semidirect
120. #100×C43C2×C4semidirect
295. #1856D43semidirect
340. C43#20855semidirect
411. #100C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191477932
#191431822
C2×#145828802
#191370822
#191348112
#191348082
#191348072
#191348052
#191348042
#339×D432
C43×#18562
#2085543