Finite Group Databasebeta

← #25125723

Subgroups — #25125723

Order 11008.

774 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143182C211yesmaximal, characteristic
2C2×#14582940C211yesmaximal, characteristic
3#428×D43C211yesmaximal, characteristic
4#19143156C211yesmaximal, characteristic
5#19136109C211yesmaximal, characteristic, complemented
6#19136108C211yesmaximal, characteristic, complemented
7#19136107C211yesmaximal, characteristic, complemented
8#19136105C211yesmaximal, characteristic, complemented
9#19136104C211yesmaximal, characteristic, complemented
10#19136103C211yesmaximal, characteristic, complemented
11#19136101C211yesmaximal, characteristic, complemented
12#19134332C211yesmaximal, characteristic
13#343×D43C211yesmaximal, characteristic
14#19134320C211yesmaximal, characteristic
15C43×#2089C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21#117×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582942C2211yescharacteristic
24#14582942C2211yescharacteristic
25#14582941C2211yescharacteristic
26#14582941C2211yescharacteristic
27#14582940—22no—
28#14582940—22no—
29#14582940—21no—
30#14582940—21no—
31#14582939C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582938—21no—
34#14582938—21no—
35#14582936—21no—
36#14582934—21no—
37C2×#13063258C2211yescharacteristic
38#107×D43—21no—
39C2×#13063257C2211yescharacteristic
40C2×#13063256C2211yescharacteristic
41#106×D43—21no—
42#14582927C2211yescharacteristic
43#14582926C2211yescharacteristic
44#14582925C2211yescharacteristic
45#14582924—22no—
46#14582921—22no—
47#14582668C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582664C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C43×#428C2211yescharacteristic
57C43×#428C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C43×#424C2211yescharacteristic
60C43×#343C2211yescharacteristic
61C43×#343C2211yescharacteristic
62C43×#341C2211yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43C2311yescharacteristic
65C2×#10621877C2311yescharacteristic
66C2×#10621877C2311yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621872—21no—
69C2×#10621872—21no—
70C2×#10621872—22no—
71C2×#10621872—22no—
72C2×#10621872—21no—
73C2×#10621872D412yes—
74C2×#10621872D412yes—
75M16×D43—22no—
76M16×D43—22no—
77M16×D43—22no—
78M16×D43—22no—
79M16×D43Q814yes—
80M16×D43Q814yes—
81C22×C43⋊C8C2311yescharacteristic
82C2×C8×D43—21no—
83C2×C8×D43—21no—
84C2×C8×D43—21no—
85#13063284C2311yescharacteristic
86#13063283—21no—
87#13063283—21no—
88#13063283—21no—
89#13063283—21no—
90#13063283D411yescharacteristic
91#13063283D411yescharacteristic
92#13063282—21no—
93#13063281—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43—21no—
101C4⋊C4×D43D411yescharacteristic
102C4⋊C4×D43D411yescharacteristic
103C2×(C2×D43)⋊C4—21no—
104C22⋊C4×D43—21no—
105C2×C4×Dic43—21no—
106C42×D43—21no—
107#13063259—21no—
108#13063259—21no—
109#13063258—21no—
110#13063258—21no—
111#13063258—21no—
112#13063258—21no—
113#13063258—22no—
114#13063257—22no—
115#13063257—21no—
116#13063257—21no—
117#13063256—21no—
118#13063256—21no—
119#13063256—21no—
120#13063256—21no—
121#13063256—22no—
122C4⋊(C43⋊C8)—22no—
123Dic43⋊C8—22no—
124Dic43⋊C8—22no—
125C2×M16×C43C2311yescharacteristic
126C2×M16×C43C2311yescharacteristic
127C2×M16×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129#117×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132#107×C43—22no—
133#107×C43—21no—
134#107×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—22no—
138C23×D43#4111yescharacteristic
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43#4111yescharacteristic
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—82no—
150C2×C4×D43C2×D411yescharacteristic
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43C2×Q812yes—
155C2×C4×D43C2×Q812yes—
156C2×C4×D43#4112yes—
157C2×C4×D43#4112yes—
158M16×C43—21no—
159M16×C43—21no—
160M16×C43—21no—
161M16×C43—21no—
162M16×C43C2×Q812yes—
163M16×C43C2×Q812yes—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D412yes—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C42×C43—21no—
178C22⋊Dic43—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C2×D411yescharacteristic
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198#10621877—21no—
199#10621877—21no—
200#10621877—21no—
201#10621877—21no—
202#10621877C2×Q812yes—
203#10621877C2×Q812yes—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×D412yes—
210#10621872—24no—
211#10621872—24no—
212#10621872—24no—
213#10621872—24no—
214#10621872—42no—
215C8×D43—24no—
216C8×D43—24no—
217C8×D43—42no—
218C23×C43C2×#4111yescharacteristic
219C22×D43—41no—
220C22×D43—41no—
221C22×D43#12111yescharacteristic
222C22×D43#12111yescharacteristic
223C22×D43#12512yes—
224C22×D43#12512yes—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—81no—
230C2×C4×C43—81no—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×Q811yescharacteristic
234C2×C4×C43C22×Q811yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—81no—
242C2×Dic43—81no—
243C2×Dic43#12111yescharacteristic
244C2×Dic43#12111yescharacteristic
245C2×Dic43#12512yes—
246C2×Dic43#12512yes—
247C4×D43—81no—
248C4×D43—81no—
249C4×D43—82no—
250C4×D43—82no—
251C4×D43C22⋊Q812yes—
252C4×D43C22⋊Q812yes—
253C4×D43C22⋊Q812yes—
254C4×D43C22⋊Q812yes—
255C4×D43#12312yes—
256C4×D43#12312yes—
257C4×D43C4⋊Q812yes—
258C4×D43C4⋊Q812yes—
259C8×C43—22no—
260C8×C43—22no—
261C8×C43—22no—
262C8×C43—41no—
263C43⋊C8—22no—
264C43⋊C8—22no—
265C43⋊C8—22no—
266C43⋊C8—41no—
267#23675—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43C2×#12111yescharacteristic
271C22×C43C2×#12511yescharacteristic
272C22×C43C2×#12511yescharacteristic
273C2×D43—21no—
274C2×D43—21no—
275C2×D43—21no—
276C2×D43—21no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43#39812yes—
280C2×D43#39812yes—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43C2×C22⋊Q811yescharacteristic
286C4×C43C2×C22⋊Q811yescharacteristic
287C4×C43C2×#12311yescharacteristic
288C4×C43C2×C4⋊Q811yescharacteristic
289Dic43—41no—
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293Dic43#39812yes—
294Dic43#39812yes—
295#2911—431no—
296C2×#428—431no—
297C2×#428—431no—
298#2905—431no—
299#2090—431no—
300#2090—431no—
301#2090—431no—
302#2090—431no—
303#2089—431no—
304#2089—431no—
305#2089—431no—
306#2089D4311yescharacteristic, complemented
307#1742—431no—
308C2×#343—431no—
309#1738—431no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43C2×#39811yescharacteristic
313C2×C43#306811yescharacteristic
314C2×C43#306911yescharacteristic
315D43—22no—
316D43—22no—
317C22×M16—431no—
318C22×M16—431no—
319C22×M16—431no—
320C22×M16—431no—
321C2×#117—431no—
322C2×#117—431no—
323C22×C4⋊C4—431no—
324#428—431no—
325#428—431no—
326#428—431no—
327#428—431no—
328#428—431no—
329#428—431no—
330#428—861no—
331#428—861no—
332#428—861no—
333#428—861no—
334#428—862no—
335#428—862no—
336#428C2×D4311yescharacteristic
337#428C2×D4311yescharacteristic
338#427—861no—
339#427—861no—
340C2×#107—431no—
341C2×#107—861no—
342C2×#107C2×D4311yescharacteristic
343C2×#106—431no—
344C2×#106—431no—
345C2×#106—861no—
346#424—431no—
347#424—431no—
348#424—431no—
349#424—862no—
350#424C2×D4311yescharacteristic
351#423—862no—
352#343—431no—
353#343—431no—
354#343—431no—
355#343—431no—
356#343—431no—
357#343—431no—
358#343C2×D4311yescharacteristic
359#343C2×D4311yescharacteristic
360#341—431no—
361#341—431no—
362#341—431no—
363#341C2×D4311yescharacteristic
364C43#2367511yescharacteristic, complemented, Sylow
365C23×C4—431no—
366C23×C4—861no—
367C2×M16—432no—
368C2×M16—432no—
369C2×M16—431no—
370C2×M16—431no—
371C2×M16—434no—
372C2×M16—434no—
373C2×M16—431no—
374C2×M16—862no—
375C2×M16—862no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16—861no—
379C2×M16—862no—
380C2×M16—862no—
381C2×M16—862no—
382C2×M16—862no—
383C2×M16C22×D4311yescharacteristic
384C2×M16C22×D4311yescharacteristic
385C2×M16C22×D4311yescharacteristic
386C22×C8—431no—
387C22×C8—861no—
388C22×C8—861no—
389C22×C8—861no—
390C22×C8C22×D4311yescharacteristic
391#117—431no—
392#117—431no—
393#117—431no—
394#117—861no—
395#117—861no—
396#117—861no—
397#117—861no—
398#117—861no—
399#117—861no—
400#117C22×D4311yescharacteristic
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—861no—
415C2×C42—861no—
416#107—22no—
417#107—21no—
418#107—21no—
419#107—861no—
420#107—861no—
421#107—862no—
422#107—861no—
423#107—861no—
424#107—861no—
425#107—861no—
426#106—21no—
427#106—21no—
428#106—861no—
429#106—861no—
430#106—862no—
431#106—861no—
432#106—861no—
433#106—862no—
434#106—861no—
435#106—861no—
436C4⋊C8—22no—
437C4⋊C8—862no—
438C4⋊C8—862no—
439C4⋊C8—862no—
440C24—431no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—432no—
449C22×C4—432no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—3442no—
457C22×C4—1721no—
458C22×C4—1721no—
459C22×C4C23×D4311yescharacteristic
460M16—21no—
461M16—21no—
462M16—21no—
463M16—21no—
464M16—432no—
465M16—432no—
466M16—864no—
467M16—864no—
468M16—864no—
469M16—864no—
470M16—861no—
471M16—861no—
472M16—861no—
473M16—861no—
474M16—1722no—
475M16Q8×D4312yes—
476M16Q8×D4312yes—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—432no—
483C2×C8—864no—
484C2×C8—864no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—1722no—
491C2×C8D4×D4312yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—431no—
497C4⋊C4—431no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4D4×D4311yescharacteristic
507C4⋊C4D4×D4311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C22⋊C4—1721no—
513C22⋊C4—1721no—
514C42—21no—
515C42—861no—
516C42—861no—
517C42—861no—
518C42—1721no—
519C42—1721no—
520C23—431no—
521C23—431no—
522C23—432no—
523C23—432no—
524C23—1721no—
525C23—1721no—
526C23#41×D4311yescharacteristic
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—431no—
534C2×C4—431no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—432no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—3441no—
548C2×C4—3441no—
549C2×C4—3442no—
550C2×C4—3442no—
551C2×C4—3441no—
552C2×C4—3441no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4C2×Q8×D4311yescharacteristic
558C2×C4C2×Q8×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C2×C4#41×D4311yescharacteristic
561C8—22no—
562C8—22no—
563C8—22no—
564C8—41no—
565C8—862no—
566C8—862no—
567C8—862no—
568C8—1721no—
569C22—21no—
570C22—21no—
571C22—432no—
572C22—432no—
573C22—861no—
574C22—861no—
575C22—861no—
576C22—861no—
577C22—1722no—
578C22—1722no—
579C22#121×D4311yescharacteristic
580C22#125×D4311yescharacteristic
581C22#125×D4311yescharacteristic
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—432no—
587C4—432no—
588C4—3441no—
589C4—3441no—
590C4—1721no—
591C4—1721no—
592C4C22⋊Q8×D4311yescharacteristic
593C4C22⋊Q8×D4311yescharacteristic
594C4#123×D4311yescharacteristic
595C4C4⋊Q8×D4311yescharacteristic
596C2—21no—
597C2—21no—
598C2—862no—
599C2—862no—
600C2#398×D4311yescharacteristic
601C2#1914432111yescharacteristic
602C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2089C2
socleC22×C43C2×#121
prime radicalC23×D43#41
hypercenter#2089D43
hypocenterC43#23675
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2089

Complements

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

NH ≅ G/Ntype
5. #19136109C2semidirect
6. #19136108C2semidirect
7. #19136107C2semidirect
8. #19136105C2semidirect
9. #19136104C2semidirect
10. #19136103C2semidirect
11. #19136101C2semidirect
15. C43×#2089C2semidirect
306. #2089D43semidirect
364. C43#23675semidirect

Maximal subgroups

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

subgroupindex
#191431822
C2×#145829402
#428×D432
#191431562
#191361092
#191361082
#191361072
#191361052
#191361042
#191361032
#191361012
#191343322
#343×D432
#191343202
C43×#20892
#2367543