Finite Group Databasebeta

← #25097428

Subgroups — #25097428

Order 11008.

1394 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147793C211yesmaximal, characteristic
2#428×D43C212yesmaximal, complemented
3C2×#14582880C211yesmaximal, characteristic
4#19137185C211yesmaximal, characteristic
5#19134811C212yesmaximal, complemented
6#19134808C212yesmaximal, complemented
7#19134807C211yesmaximal, characteristic, complemented
8#19134805C211yesmaximal, characteristic, complemented
9#19134804C211yesmaximal, characteristic, complemented
10#19134303C212yesmaximal, 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×#13063282C2211yescharacteristic
22C2×#13063281—22no—
23#117×D43C2212yes—
24C2×C4⋊C4×D43C2211yescharacteristic
25#14582942C2212yes—
26#14582941C2212yes—
27#14582940—22no—
28#14582939C2212yes—
29#14582938—22no—
30#107×D43—22no—
31#106×D43—22no—
32#14582880C418yescomplemented
33C2×#13063243C2212yes—
34C2×#13063242C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582804C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582775—22no—
39#14582757—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#13063283D412yes—
75#13063283D412yes—
76#13063282—22no—
77#13063282—24no—
78#13063281—24no—
79#13063281—24no—
80#13063281—22no—
81#13063281—24no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—22no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—22no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43D412yes—
90C4⋊C4×D43D412yes—
91C2×C22⋊Dic43—22no—
92C2×C22⋊Dic43—22no—
93C2×(C2×D43)⋊C4—21no—
94C22⋊C4×D43—22no—
95C2×C4×Dic43—22no—
96C2×C4×Dic43—22no—
97C2×C4×Dic43C2311yescharacteristic
98C42×D43—22no—
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—82no—
153C2×C4×D43C22×C412yes—
154C2×C4×D43C2×D412yes—
155C2×C4×D43C2×D412yes—
156C2×C4×D43C2×Q812yes—
157C2×C4×D43#4114yes—
158C2×Dic86—22no—
159C2×Dic86—22no—
160C2×Dic86C22×C412yes—
161C2×Dic86C2×Q812yes—
162M16×C43—22no—
163M16×C43C22×C414yes—
164C2×C8×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43C2×D412yes—
167C4⋊C4×C43C2×D412yes—
168C22⋊C4×C43—24no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—82no—
171C42×C43—22no—
172C42×C43—22no—
173C22⋊Dic43—24no—
174C22⋊Dic43—22no—
175C22⋊Dic43—82no—
176(C2×D43)⋊C4—22no—
177(C2×D43)⋊C4—22no—
178(C2×D43)⋊C4—42no—
179C4⋊Dic43—22no—
180C4⋊Dic43C2×D412yes—
181C4⋊Dic43C2×D412yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188Dic43⋊C4—42no—
189C4×Dic43—24no—
190C4×Dic43—24no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195#10621877—22no—
196#10621877C22×C414yes—
197C2×C43⋊C8—22no—
198#10621872—28no—
199C8×D43—28no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43C2×C4⋊C414yes—
205C23×C43C22×D411yescharacteristic
206C22×D43—41no—
207C22×D43—41no—
208C22×D43C2×C4⋊C412yes—
209C22×D43#12012yes—
210C22×D43#12312yes—
211D4×C43—24no—
212D4×C43—24no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—82no—
221C2×C4×C43—82no—
222C2×C4×C43C23×C411yescharacteristic
223C2×C4×C43C22×D412yes—
224C2×C4×C43C22×Q811yescharacteristic
225C2×C4×C43C2×#4112yes—
226C22⋊D43—216no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—28no—
230C2×Dic43—28no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—41no—
234C2×Dic43—42no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—82no—
239C2×Dic43—82no—
240C2×Dic43C2×C4⋊C414yes—
241C2×Dic43C2×C4⋊C412yes—
242C2×Dic43#12011yescharacteristic
243C2×Dic43#12011yescharacteristic
244C2×Dic43#12312yes—
245C4×D43—82no—
246C4×D43—82no—
247C4×D43—84no—
248C4×D43C4×D414yes—
249C4×D43C4×D414yes—
250C4×D43C22⋊Q814yes—
251C4×D43C22⋊Q814yes—
252Dic86—24no—
253Dic86—24no—
254C8×C43—24no—
255C43⋊C8—24no—
256#20858—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—24no—
260C22×C43—44no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—82no—
264C22×C43C22×C4⋊C411yescharacteristic
265C22×C43C2×#12011yescharacteristic
266C22×C43C2×#12311yescharacteristic
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—42no—
270C2×D43—42no—
271C2×D43#38514yes—
272C4×C43—42no—
273C4×C43—42no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43C2×C4×D412yes—
277C4×C43C2×C22⋊Q812yes—
278Dic43—24no—
279Dic43—42no—
280Dic43—42no—
281Dic43—81no—
282Dic43—81no—
283Dic43#38512yes—
284Dic43#38512yes—
285#3428—431no—
286C2×#428—432no—
287C2×#413—431no—
288#2311—431no—
289#1857—432no—
290#1857—432no—
291#1856—431no—
292#1856—431no—
293#1856—431no—
294#1856D4311yescharacteristic, complemented
295#1733—432no—
296C2×C43—21no—
297C2×C43—21no—
298C2×C43—44no—
299C2×C43C2×#38511yescharacteristic
300C2×C43#302111yescharacteristic
301C2×C43#302211yescharacteristic
302D43—24no—
303C22×#41—431no—
304C22×M16—432no—
305#520—862no—
306#520—862no—
307#519—432no—
308#518—431no—
309#518—862no—
310#518C2×D4311yescharacteristic
311C4×#41—862no—
312C4×#41—862no—
313C2×#117—431no—
314C2×#117—432no—
315C2×#117—862no—
316C22×C4⋊C4—431no—
317#428—432no—
318#428—432no—
319#428—432no—
320#428—862no—
321#428—862no—
322#428C2×D4312yes—
323C2×#107—862no—
324C2×#106—862no—
325#413—438no—
326C2×#101—432no—
327C2×#100—431no—
328C2×#100C2×D4311yescharacteristic
329#391—431no—
330#391—431no—
331#390—431no—
332#390C2×D4311yescharacteristic
333#386—862no—
334#380—862no—
335#339—432no—
336#339—432no—
337#339—432no—
338#339C2×D4312yes—
339C43#2085811yescharacteristic, complemented, Sylow
340C2×#41—434no—
341C2×#41—434no—
342C2×#41—862no—
343C2×#41—862no—
344C2×#41—864no—
345C22×Q8—431no—
346C22×D4—432no—
347C22×D4C22×D4311yescharacteristic
348C23×C4—431no—
349C23×C4—432no—
350C23×C4—861no—
351C2×M16—432no—
352C2×M16—438no—
353C2×M16—862no—
354C2×M16—864no—
355C2×M16C22×D4312yes—
356C22×C8—862no—
357C4×Q8—862no—
358C4×Q8—862no—
359C4×Q8—862no—
360C4×Q8—862no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—864no—
364C4×D4—864no—
365C4×D4—862no—
366C4×D4—862no—
367C4×D4—864no—
368C4×D4—864no—
369#117—432no—
370#117—432no—
371#117—432no—
372#117—862no—
373#117—864no—
374#117—862no—
375#117—864no—
376#117—864no—
377#117—864no—
378#117C22×D4312yes—
379C2×C4⋊C4—432no—
380C2×C4⋊C4—432no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—862no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—862no—
392C2×C22⋊C4—862no—
393C2×C22⋊C4—862no—
394C2×C22⋊C4—861no—
395C2×C42—431no—
396C2×C42—862no—
397C2×C42—862no—
398C2×C42—862no—
399C2×C42C22×D4311yescharacteristic
400#107—22no—
401#107—862no—
402#107—862no—
403#107—862no—
404#106—22no—
405#106—862no—
406#106—862no—
407#106—862no—
408#101—438no—
409#100—434no—
410#100C4×D4314yescomplemented
411#95—862no—
412#95—862no—
413C24—431no—
414C24D4×D4312yes—
415#41—868no—
416#41—868no—
417#41—868no—
418#41—868no—
419C2×Q8—432no—
420C2×Q8—432no—
421C2×Q8—862no—
422C2×Q8—862no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—438no—
426C2×D4—864no—
427C2×D4—864no—
428C2×D4C2×C4×D4312yes—
429C2×D4Q8×D4312yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—431no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—432no—
439C22×C4—434no—
440C22×C4—438no—
441C22×C4—432no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—864no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—3442no—
452C22×C4—1722no—
453C22×C4C23×D4311yescharacteristic
454M16—22no—
455M16—434no—
456M16—868no—
457M16—862no—
458M16C2×C4×D4314yes—
459C2×C8—22no—
460C2×C8—868no—
461C2×C8—862no—
462C4⋊C4—22no—
463C4⋊C4—432no—
464C4⋊C4—432no—
465C4⋊C4—862no—
466C4⋊C4—862no—
467C4⋊C4—864no—
468C4⋊C4—864no—
469C4⋊C4—862no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1722no—
473C4⋊C4D4×D4312yes—
474C4⋊C4D4×D4312yes—
475C22⋊C4—24no—
476C22⋊C4—22no—
477C22⋊C4—82no—
478C22⋊C4—862no—
479C22⋊C4—862no—
480C22⋊C4—864no—
481C22⋊C4—862no—
482C22⋊C4—3442no—
483C22⋊C4—1722no—
484C42—22no—
485C42—22no—
486C42—862no—
487C42—862no—
488C42—864no—
489C42—864no—
490C42—862no—
491C42—862no—
492C23—22no—
493C23—22no—
494C23—42no—
495C23—42no—
496C23—432no—
497C23—432no—
498C23—432no—
499C23—1721no—
500C23—1721no—
501C23C4⋊C4×D4314yes—
502C23C2×D4×D4311yescharacteristic
503Q8—864no—
504Q8—864no—
505D4—24no—
506D4—24no—
507D4—8616no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—432no—
518C2×C4—431no—
519C2×C4—431no—
520C2×C4—432no—
521C2×C4—434no—
522C2×C4—434no—
523C2×C4—434no—
524C2×C4—434no—
525C2×C4—434no—
526C2×C4—868no—
527C2×C4—868no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—3442no—
533C2×C4—3442no—
534C2×C4—3444no—
535C2×C4—3442no—
536C2×C4—3442no—
537C2×C4—1721no—
538C2×C4—1722no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4C22×C4×D4311yescharacteristic
543C2×C4C2×D4×D4312yes—
544C2×C4C2×Q8×D4311yescharacteristic
545C2×C4#41×D4312yes—
546C8—24no—
547C8—864no—
548C22—21no—
549C22—21no—
550C22—24no—
551C22—44no—
552C22—42no—
553C22—42no—
554C22—82no—
555C22—434no—
556C22—862no—
557C22—862no—
558C22—1722no—
559C22—1722no—
560C22C2×C4⋊C4×D4311yescharacteristic
561C22#120×D4311yescharacteristic
562C22#123×D4311yescharacteristic
563C4—42no—
564C4—42no—
565C4—81no—
566C4—81no—
567C4—432no—
568C4—432no—
569C4—864no—
570C4—3441no—
571C4—3441no—
572C4—1722no—
573C4—1722no—
574C4C4×D4×D4312yes—
575C4C22⋊Q8×D4312yes—
576C2—21no—
577C2—21no—
578C2—44no—
579C2—864no—
580C2#385×D4311yescharacteristic
581C2#1914396311yescharacteristic
582C2#1914397011yescharacteristic
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#20858
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. #428×D43C2semidirect
5. #19134811C2semidirect
6. #19134808C2semidirect
7. #19134807C2semidirect
8. #19134805C2semidirect
9. #19134804C2semidirect
10. #19134303C2semidirect
11. C43×#1856C2semidirect
32. #14582880C4semidirect
61. M16×D43C2×C4semidirect
105. #13063243C2×C4semidirect
106. #13063242C2×C4semidirect
120. #100×C43C2×C4semidirect
294. #1856D43semidirect
339. C43#20858semidirect
410. #100C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191477932
#428×D432
C2×#145828802
#191371852
#191348112
#191348082
#191348072
#191348052
#191348042
#191343032
C43×#18562
#2085843