Finite Group Databasebeta

← #25125529

Subgroups — #25125529

Order 11008.

892 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143158C211yesmaximal, characteristic, complemented
2C2×#14582915C211yesmaximal, characteristic
3#19143115C211yesmaximal, characteristic
4C2×#14582881C211yesmaximal, characteristic
5#19136051C218yesmaximal, complemented
6C2×#14582670C211yesmaximal, characteristic, complemented
7C2×#14582656C211yesmaximal, characteristic, complemented
8C43×#1738C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12C2×#13063284C2211yescharacteristic
13#14582927—22no—
14#14582925C2214yescomplemented
15#14582922—22no—
16#14582915—22no—
17#14582915C2214yes—
18C2×#13063251—22no—
19#14582909—21no—
20#14582905—21no—
21#14582901—22no—
22#14582896C2214yes—
23#14582881—22no—
24#14582881C2214yes—
25C2×#13063243—21no—
26C2×#13063241—21no—
27#14582670C2214yescomplemented
28#14582656C2214yescomplemented
29C22×M16×C43C2211yescharacteristic
30C22×M16×C43C2211yescharacteristic
31C22×M16×C43C2211yescharacteristic
32C43×#341C2214yescomplemented
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898D412yes—
44C2×#10621898C2312yes—
45C22×Dic86D411yescharacteristic
46C22×D172D411yescharacteristic
47C22×C22⋊D43—21no—
48C22×C4×D43—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877C2312yes—
55C22×C43⋊C8—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284—21no—
59#13063284—21no—
60#13063284—21no—
61#13063284D412yes—
62#13063284C2312yes—
63#13063284C2312yes—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C4×Dic43—21no—
69C2×C4×Dic43D412yes—
70Dic43⋊C8—28no—
71#13063251—28no—
72#13063250—24no—
73#13063247—24no—
74#13063243—24no—
75#13063241—24no—
76C23×C4×C43C2311yescharacteristic
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C2×M16×C43—21no—
86C2×M16×C43—21no—
87C2×M16×C43—21no—
88C2×M16×C43—21no—
89C2×M16×C43—21no—
90C2×M16×C43—21no—
91C2×M16×C43—21no—
92C2×M16×C43—21no—
93C2×M16×C43C2312yes—
94C2×M16×C43C2312yes—
95C22×C8×C43—21no—
96C22×C8×C43—21no—
97C22×C8×C43C2312yes—
98C24×C43#4111yescharacteristic
99C23×D43—21no—
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×C4×C43#4111yescharacteristic
106C22×C4×C43#4111yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43C2411yescharacteristic
114C2×C22⋊D43—22no—
115C2×C22⋊D43—22no—
116C2×C22⋊D43—41no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C22×Dic43—21no—
121C22×Dic43—22no—
122C22×Dic43—41no—
123#10621898—22no—
124#10621898—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—22no—
131#10621898—41no—
132#10621898—41no—
133#10621898—41no—
134#10621898—41no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172C2×D412yes—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—41no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86C2×D412yes—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—22no—
160M16×C43—22no—
161M16×C43—41no—
162M16×C43—41no—
163M16×C43—41no—
164M16×C43—41no—
165M16×C43—41no—
166M16×C43—41no—
167M16×C43—41no—
168M16×C43—41no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—41no—
175C2×C8×C43—41no—
176C2×C8×C43—41no—
177C2×C8×C43—41no—
178C22⋊Dic43—22no—
179C22⋊Dic43—22no—
180C22⋊Dic43—22no—
181C22⋊Dic43—41no—
182C4⋊Dic43—22no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43—41no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C4×Dic43—41no—
189C4×Dic43C2×D414yes—
190#10621877—22no—
191#10621877—22no—
192#10621877—41no—
193#10621877—41no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—41no—
197C23×C43—81no—
198C23×C43#12311yescharacteristic
199C23×C43#12311yescharacteristic
200C23×C43#12311yescharacteristic
201C23×C43#12311yescharacteristic
202C23×C43#12611yescharacteristic
203C23×C43#12611yescharacteristic
204C23×C43C2×#4111yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—82no—
209C2×C4×C43#12111yescharacteristic
210C2×C4×C43#12111yescharacteristic
211C2×C4×C43#12111yescharacteristic
212C2×C4×C43#12111yescharacteristic
213C2×C4×C43#12311yescharacteristic
214C2×C4×C43#12311yescharacteristic
215C2×C4×C43#12311yescharacteristic
216C2×C4×C43#12311yescharacteristic
217C2×C4×C43#12311yescharacteristic
218C2×C4×C43#12311yescharacteristic
219C2×C4×C43#12311yescharacteristic
220C2×C4×C43#12311yescharacteristic
221C2×C4×C43#12411yescharacteristic
222C2×C4×C43#12411yescharacteristic
223C2×C4×C43#12411yescharacteristic
224C2×C4×C43#12411yescharacteristic
225C2×C4×C43#12611yescharacteristic
226C2×C4×C43#12611yescharacteristic
227C2×C4×C43#12611yescharacteristic
228C2×C4×C43#12611yescharacteristic
229C2×C4×C43#12611yescharacteristic
230C2×C4×C43#12611yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—42no—
238C22⋊D43—42no—
239C22⋊D43—42no—
240C22⋊D43—42no—
241C2×Dic43—24no—
242C2×Dic43—22no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—82no—
247C2×Dic43—82no—
248D172—22no—
249D172—22no—
250D172—41no—
251D172—41no—
252C4×D43—42no—
253C4×D43—42no—
254C4×D43—42no—
255C4×D43—42no—
256Dic86—22no—
257Dic86—22no—
258Dic86—41no—
259Dic86—41no—
260C8×C43—42no—
261C8×C43—42no—
262C8×C43—42no—
263C43⋊C8—42no—
264#23649—431nomaximal, Sylow
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43#39711yescharacteristic
273C22×C43#39711yescharacteristic
274C22×C43#39711yescharacteristic
275C22×C43#39711yescharacteristic
276C22×C43C2×#12311yescharacteristic
277C22×C43C2×#12311yescharacteristic
278C22×C43C2×#12611yescharacteristic
279C2×D43—42no—
280C2×D43—82no—
281C2×D43—82no—
282C2×D43—82no—
283C4×C43#39711yescharacteristic
284C4×C43#39711yescharacteristic
285C4×C43#39711yescharacteristic
286C4×C43#39711yescharacteristic
287C4×C43C2×#12111yescharacteristic
288C4×C43C2×#12311yescharacteristic
289C4×C43C2×#12411yescharacteristic
290C4×C43C2×#12611yescharacteristic
291Dic43—44no—
292Dic43—42no—
293Dic43—82no—
294#2905—431no—
295C2×#421—431no—
296#2896—431no—
297C2×#413—431no—
298#2080—438no—
299C2×#344—431no—
300#1738D4311yescharacteristic, complemented
301C2×H(3,ℤ/4)—431no—
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—21no—
309C2×C43C2×#39711yescharacteristic
310D43—82no—
311C22×#41—431no—
312C22×M16—431no—
313C22×M16C2×D4311yescharacteristic
314C22×M16C2×D4311yescharacteristic
315C22×M16C2×D4311yescharacteristic
316C2×#117—431no—
317C2×#117—431no—
318#424—434no—
319#424—862no—
320#423—862no—
321#421—434no—
322#421—862no—
323C2×#104—862no—
324#419—861no—
325#418—861no—
326#417—862no—
327#416—434no—
328#413—434no—
329#413—862no—
330C2×#101—861no—
331C2×#100—861no—
332#344—434no—
333#341C2×D4314yescomplemented
334H(3,ℤ/4)—434no—
335C43#2364911yescharacteristic, complemented, Sylow
336C2×#41—432no—
337C2×#41—432no—
338C2×#41—861no—
339C2×#41—861no—
340C2×#41—861no—
341C2×#41—861no—
342C2×#41—861no—
343C2×#41—861no—
344C2×#41—861no—
345C2×#41—861no—
346C2×#41—861no—
347C2×#41—861no—
348C22×Q8—431no—
349C22×D4—431no—
350C22×D4—861no—
351C23×C4—861no—
352C23×C4C22×D4311yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—432no—
370C2×M16—861no—
371C2×M16—861no—
372C2×M16—861no—
373C2×M16—861no—
374C2×M16—861no—
375C2×M16C22×D4312yes—
376C2×M16C22×D4312yes—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—861no—
380C22×C8C22×D4312yes—
381#117—432no—
382#117—432no—
383#117—432no—
384#117—861no—
385#117—861no—
386#117—861no—
387#117—861no—
388#117—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C42—432no—
394C2×C42—861no—
395C4⋊C8—868no—
396#104—868no—
397#103—864no—
398#102—864no—
399#101—864no—
400#100—864no—
401C24—861no—
402C24#1062190211yescharacteristic
403#41—862no—
404#41—862no—
405#41—862no—
406#41—862no—
407#41—862no—
408#41—862no—
409#41—862no—
410#41—862no—
411#41—1721no—
412#41—1721no—
413#41—1721no—
414#41—1721no—
415#41—1721no—
416#41—1721no—
417#41—1721no—
418#41—1721no—
419C2×Q8—432no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×D4—432no—
426C2×D4—862no—
427C2×D4—862no—
428C2×D4—861no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—1721no—
434C2×D4—1721no—
435C2×D4—1721no—
436C2×D4—1721no—
437C22×C4—862no—
438C22×C4—861no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—1721no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4#1062189811yescharacteristic
447C22×C4#1062189811yescharacteristic
448C22×C4#1062189811yescharacteristic
449C22×C4#1062189811yescharacteristic
450C22×C4#1062189811yescharacteristic
451C22×C4#1062189811yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4#1062190011yescharacteristic
457C22×C4#1062190011yescharacteristic
458C22×C4#1062190211yescharacteristic
459C22×C4C23×D4311yescharacteristic
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472M16—862no—
473M16—862no—
474M16—1721no—
475M16—1721no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—862no—
486C2×C8—1721no—
487C2×C8—1721no—
488C4⋊C4—862no—
489C4⋊C4—862no—
490C4⋊C4—862no—
491C4⋊C4—1721no—
492C22⋊C4—862no—
493C22⋊C4—862no—
494C22⋊C4—862no—
495C22⋊C4—1721no—
496C42—434no—
497C42—862no—
498C42—862no—
499C42—1721no—
500C23—81no—
501C23—862no—
502C23—3442no—
503C23—1721no—
504C23—1721no—
505C23#1306331011yescharacteristic
506C23#1306331011yescharacteristic
507C23#1306331011yescharacteristic
508C23#1306331011yescharacteristic
509C23#1306332011yescharacteristic
510C23#1306332011yescharacteristic
511C23C2×#1062190211yescharacteristic
512Q8—862no—
513Q8—862no—
514Q8—1721no—
515Q8—1721no—
516D4—862no—
517D4—862no—
518D4—1722no—
519D4—1722no—
520D4—1722no—
521D4—1722no—
522D4—1721no—
523D4—1721no—
524C2×C4—864no—
525C2×C4—862no—
526C2×C4—3442no—
527C2×C4—3442no—
528C2×C4—1722no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4#1306329811yescharacteristic
536C2×C4#1306329811yescharacteristic
537C2×C4#1306329811yescharacteristic
538C2×C4#1306329811yescharacteristic
539C2×C4#1306330711yescharacteristic
540C2×C4#1306330711yescharacteristic
541C2×C4#1306330711yescharacteristic
542C2×C4#1306330711yescharacteristic
543C2×C4#1306331011yescharacteristic
544C2×C4#1306331011yescharacteristic
545C2×C4#1306331011yescharacteristic
546C2×C4#1306331011yescharacteristic
547C2×C4#1306331111yescharacteristic
548C2×C4#1306331111yescharacteristic
549C2×C4#1306331111yescharacteristic
550C2×C4#1306331111yescharacteristic
551C2×C4#1306331911yescharacteristic
552C2×C4#1306331911yescharacteristic
553C2×C4#1306331911yescharacteristic
554C2×C4#1306331911yescharacteristic
555C2×C4#1306332011yescharacteristic
556C2×C4#1306332011yescharacteristic
557C2×C4C2×D4×D4311yescharacteristic
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×#1062190011yescharacteristic
560C2×C4C2×#1062189811yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C2×C4C2×#1062189811yescharacteristic
563C8—42no—
564C8—42no—
565C8—42no—
566C8—1722no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—3442no—
575C22—3442no—
576C22—3442no—
577C22—1722no—
578C22#1458282811yescharacteristic
579C22#1458282811yescharacteristic
580C22#1458282811yescharacteristic
581C22#1458282811yescharacteristic
582C22C2×#1306331011yescharacteristic
583C22C2×#1306331011yescharacteristic
584C22C2×#1306332011yescharacteristic
585C4—3442no—
586C4—1724no—
587C4—1722no—
588C4#1458282811yescharacteristic
589C4#1458282811yescharacteristic
590C4#1458282811yescharacteristic
591C4#1458282811yescharacteristic
592C4C2×#1306329811yescharacteristic
593C4C2×#1306330711yescharacteristic
594C4C2×#1306331111yescharacteristic
595C4C2×#1306331911yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—3442no—
604C2C2×#1458282811yescharacteristic
subgroupG/H
centerC4C2×#13063311
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1738C2
socleC2×C43C2×#397
prime radicalC22×#10621898C22
hypercenter#1738D43
hypocenterC43#23649
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1738

Complements

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

NH ≅ G/Ntype
1. #19143158C2semidirect
5. #19136051C2semidirect
6. C2×#14582670C2semidirect
7. C2×#14582656C2semidirect
8. C43×#1738C2semidirect
14. #14582925C22semidirect
27. #14582670C22semidirect
28. #14582656C22semidirect
32. C43×#341C22semidirect
300. #1738D43semidirect
333. #341C2×D43semidirect
335. C43#23649semidirect

Maximal subgroups

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

subgroupindex
#191431582
C2×#145829152
#191431152
C2×#145828812
#191360512
C2×#145826702
C2×#145826562
C43×#17382
#2364943