Finite Group Databasebeta

← #25148753

Subgroups — #25148753

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145147C211yesmaximal, characteristic, complemented
2#19144392C211yesmaximal, characteristic
3C2×#14583199C211yesmaximal, characteristic
4#19143542C211yesmaximal, characteristic, complemented
5#19136109C211yesmaximal, characteristic, complemented
6#19136104C211yesmaximal, characteristic, complemented
7#19135951C211yesmaximal, characteristic
8#19135951C211yesmaximal, characteristic
9#19135588C211yesmaximal, characteristic, complemented
10#19135379C211yesmaximal, characteristic, complemented
11#19135374C211yesmaximal, characteristic, complemented
12#19135370C211yesmaximal, characteristic, complemented
13#19135259C211yesmaximal, characteristic
14#19135259C211yesmaximal, characteristic
15C4×#100×C43C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18#14583308—21no—
19#14583308—21no—
20#14583301—21no—
21#14583301—21no—
22#14583199—21no—
23#14583199—21no—
24#14583199—21no—
25#14583199—21no—
26#14583199—21no—
27#14583199—21no—
28#14583189—21no—
29#14583179—21no—
30#14583029—21no—
31#14583027—21no—
32#14583027—21no—
33C8×Dic86—21no—
34C2×#13063260C2211yescharacteristic
35C2×#13063260C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582941C2211yescharacteristic
40#14582939C2211yescharacteristic
41#14582939C2211yescharacteristic
42C2×#13063258C2211yescharacteristic
43C2×#13063256C2211yescharacteristic
44#14582927C2211yescharacteristic
45#14582927C2211yescharacteristic
46#14582923C2211yescharacteristic
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48#14582904C2211yescharacteristic
49#14582904C2211yescharacteristic
50C2×#13063246C2211yescharacteristic
51C2×#13063246C2211yescharacteristic
52#14582857C2211yescharacteristic
53#14582857C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582663C2211yescharacteristic
59#14582663C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×#100×C43C2211yescharacteristic
62C2×#100×C43C2211yescharacteristic
63C4×M16×C43C2211yescharacteristic
64C4×M16×C43C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063325D411yescharacteristic
72#13063325D411yescharacteristic
73#13063317—21no—
74#13063317—21no—
75#13063317—21no—
76#13063317—21no—
77#13063317D411yescharacteristic
78#13063317D411yescharacteristic
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83#13063284C2311yescharacteristic
84#13063284C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89#13063260—22no—
90#13063260—22no—
91#13063259—21no—
92#13063259—21no—
93#13063259—21no—
94#13063259—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063257—21no—
101#13063257—21no—
102#13063257—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256—21no—
106#13063256—21no—
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)D411yescharacteristic
110C4⋊(C43⋊C8)D411yescharacteristic
111C4⋊(C43⋊C8)D411yescharacteristic
112C4⋊(C43⋊C8)D411yescharacteristic
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063246—21no—
122#13063246—21no—
123#13063246—21no—
124#13063246—21no—
125#13063235—21no—
126#13063235—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131C2×M16×C43C2311yescharacteristic
132C2×M16×C43C2311yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137C4×D4×C43—21no—
138C4×D4×C43—21no—
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C42×C43C2311yescharacteristic
142#100×C43—22no—
143#100×C43Q814yescomplemented
144#97×C43—21no—
145#97×C43—21no—
146C4×C8×C43—21no—
147C4×C8×C43—21no—
148C24×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43C2×Q812yes—
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43—82no—
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166M16×C43—21no—
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43—21no—
171M16×C43C2×Q812yes—
172M16×C43C2×Q812yes—
173M16×C43#4112yes—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C22⋊Dic43—21no—
187C22⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×D411yescharacteristic
195C4⋊Dic43C2×D411yescharacteristic
196C4⋊Dic43C2×D411yescharacteristic
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208#10621877—21no—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222C23×C43—22no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—81no—
226C23×C43—81no—
227C23×C43C2×#4111yescharacteristic
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—41no—
231D4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—82no—
236C2×C4×C43—82no—
237C2×C4×C43—81no—
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×Q811yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—81no—
255C2×Dic43—81no—
256Dic86—42no—
257Dic86—81no—
258C8×C43—22no—
259C8×C43—22no—
260C8×C43—22no—
261C8×C43—41no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#25493—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—42no—
272C22×C43—82no—
273C22×C43—82no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43C2×#12111yescharacteristic
277C22×C43#53311yescharacteristic
278C22×C43#54111yescharacteristic
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—81no—
284C4×C43#54711yescharacteristic
285C4×C43#54811yescharacteristic
286C4×C43D4×Q811yescharacteristic
287C4×C43D4×Q811yescharacteristic
288Dic43—41no—
289Dic43—41no—
290Dic43—41no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294#3166—431no—
295#3077—431no—
296C2×#478—431no—
297#2962—431no—
298#2090—431no—
299#2089—431no—
300#2063—431no—
301#2063—431no—
302#1998—431no—
303#1952—431no—
304#1951—431no—
305#1950—431no—
306#1931—431no—
307#1931—431no—
308C4×#100D4311yescharacteristic
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—82no—
312C2×C43#242911yescharacteristic
313C2×C43#306711yescharacteristic
314C2×C43#306811yescharacteristic
315#533—431no—
316C2×#125—431no—
317C2×C4×D4C2×D4311yescharacteristic
318#501—861no—
319#501—861no—
320#499—861no—
321#499—861no—
322#478—861no—
323#478—861no—
324#478—861no—
325#478—861no—
326#478—861no—
327#478—861no—
328#476—861no—
329#474—861no—
330#446—861no—
331#446—861no—
332#446—861no—
333C8×Q8—861no—
334C2×#108—431no—
335C2×#108—431no—
336#428—431no—
337#428—431no—
338#428—431no—
339#428—431no—
340#428—431no—
341#428—431no—
342C2×#107—431no—
343C2×#106—431no—
344#424—431no—
345#424—431no—
346#423—431no—
347C2×C4⋊C8—431no—
348#418—431no—
349#418—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#100C2×D4311yescharacteristic
353C2×#100C2×D4311yescharacteristic
354#405—431no—
355#405—431no—
356C4×M16C2×D4311yescharacteristic
357C4×M16C2×D4311yescharacteristic
358#343—431no—
359#343—431no—
360#343—431no—
361#343—431no—
362#343C2×D4311yescharacteristic
363#343C2×D4311yescharacteristic
364#341—431no—
365#341—431no—
366C43#2549311yescharacteristic, complemented, Sylow
367C22×D4C22×D4311yescharacteristic
368C23×C4—21no—
369C2×M16—431no—
370C2×M16—431no—
371C2×M16C22×D4311yescharacteristic
372C2×M16C22×D4311yescharacteristic
373C2×M16C22×D4311yescharacteristic
374C2×M16C22×D4311yescharacteristic
375C22×C8—431no—
376C22×C8—431no—
377C4⋊Q8—431no—
378C4⋊Q8—431no—
379#125—431no—
380#125—431no—
381#125—861no—
382#125—861no—
383#125—861no—
384#125—861no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387C4×Q8—861no—
388C4×Q8—861no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393#117—431no—
394#117—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C22×D4311yescharacteristic
402#108—862no—
403#108—862no—
404#107—861no—
405#107—861no—
406#107—861no—
407#107—861no—
408#107—861no—
409#107—861no—
410#107—861no—
411#107—861no—
412#106—861no—
413#106—861no—
414#106—861no—
415#106—861no—
416#106—861no—
417#106—861no—
418#106—861no—
419#106—861no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8—861no—
427C4⋊C8—861no—
428C4⋊C8—861no—
429C4⋊C8—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#100—22no—
439#100Dic8614yescomplemented
440#97—21no—
441#97—21no—
442#97—861no—
443#97—861no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8—861no—
447C4×C8—861no—
448C24—21no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4C2×Dic8612yes—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—82no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4#1062189811yescharacteristic
464C22×C4#1062189811yescharacteristic
465C22×C4C23×D4311yescharacteristic
466M16—21no—
467M16—21no—
468M16—21no—
469M16—21no—
470M16—21no—
471M16—861no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16C2×Dic8612yes—
476M16C2×Dic8612yes—
477M16#1062189812yes—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—431no—
495C4⋊C4—431no—
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—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4—1721no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C42—861no—
517C42—861no—
518C42D4×D4311yescharacteristic
519C42D4×D4311yescharacteristic
520C42D4×D4311yescharacteristic
521C42D4×D4311yescharacteristic
522C23—22no—
523C23—41no—
524C23—41no—
525C23—81no—
526C23—81no—
527C23C2×#1062189811yescharacteristic
528Q8—3441no—
529Q8—1722no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—81no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—3441no—
545C2×C4—3441no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4#1306329811yescharacteristic
549C2×C4#1306329811yescharacteristic
550C2×C4#1306329811yescharacteristic
551C2×C4#1306329811yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C22×Dic8611yescharacteristic
555C2×C4C2×#1062189811yescharacteristic
556C2×C4#1306337211yescharacteristic
557C2×C4#1306337211yescharacteristic
558C8—22no—
559C8—22no—
560C8—22no—
561C8—41no—
562C8—861no—
563C8—861no—
564C8—861no—
565C8—861no—
566C8—1721no—
567C8—1721no—
568C22—21no—
569C22—21no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—81no—
574C22—81no—
575C22C2×#1306329811yescharacteristic
576C22#1458345611yescharacteristic
577C22#1458351111yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—81no—
583C4—3441no—
584C4—3441no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4—1721no—
589C4#1458355411yescharacteristic
590C4#1458355811yescharacteristic
591C4D4×Dic8611yescharacteristic
592C4D4×Dic8611yescharacteristic
593C2—21no—
594C2—21no—
595C2—82no—
596C2#1913819411yescharacteristic
597C2#1914431411yescharacteristic
598C2#1914432211yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#100×C43C2
socleC22×C43C2×#121
prime radicalC22×D4×C43C23
hypercenterC4×#100D43
hypocenterC43#25493
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
1. #19145147C2semidirect
4. #19143542C2semidirect
5. #19136109C2semidirect
6. #19136104C2semidirect
9. #19135588C2semidirect
10. #19135379C2semidirect
11. #19135374C2semidirect
12. #19135370C2semidirect
143. #100×C43Q8semidirect
366. C43#25493semidirect
439. #100Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451472
#191443922
C2×#145831992
#191435422
#191361092
#191361042
#191359512
#191355882
#191353792
#191353742
#191353702
#191352592
C4×#100×C432
#2549343