Finite Group Databasebeta

← #25079450

Subgroups — #25079450

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145046C211yesmaximal, characteristic
2#19144625C211yesmaximal, characteristic, complemented
3#460×D43C211yesmaximal, characteristic, complemented
4Q8×#10621872C211yesmaximal, characteristic, complemented
5#19134078C211yesmaximal, characteristic, complemented
6#19134076C211yesmaximal, characteristic, complemented
7#19134068C211yesmaximal, characteristic, complemented
8#19134066C211yesmaximal, characteristic, complemented
9#19133953C211yesmaximal, characteristic, complemented
10#19133943C211yesmaximal, characteristic, complemented
11#19133941C211yesmaximal, characteristic, complemented
12#19133346C211yesmaximal, characteristic, complemented
13#19133269C211yesmaximal, characteristic, complemented
14#19133261C211yesmaximal, characteristic, complemented
15C43×#1668C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C2×#13063349—21no—
18C2×SD16×D43—21no—
19#14583447C2211yescharacteristic
20#127×D43C2211yescharacteristic
21C4×Q8×D43C2211yescharacteristic
22#14583287—21no—
23#14583287—21no—
24#14583275C2211yescharacteristic
25#14583272C2211yescharacteristic
26#14583271C2211yescharacteristic
27#14583216—21no—
28#14583185C2211yescharacteristic, complemented
29#14583184C2211yescharacteristic, complemented
30#14583100C2211yescharacteristic
31#14583099C2211yescharacteristic
32#14583098—21no—
33#14583097—21no—
34#14583096C2211yescharacteristic
35#14583096C2211yescharacteristic, complemented
36#14583036—21no—
37#14583029—21no—
38#14583029C2211yescharacteristic, complemented
39#14583026—21no—
40#14583026C2211yescharacteristic, complemented
41Q8×C43⋊C8C2211yescharacteristic, complemented
42#14582990—21no—
43SD16×Dic43—21no—
44#14582951C2211yescharacteristic
45#14582921—21no—
46#14582921C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48#102×D43—21no—
49C4×#10621872—21no—
50C4×#10621872C2211yescharacteristic
51#14582651C2211yescharacteristic, complemented
52#14582650C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582644C2211yescharacteristic, complemented
56#14582643C2211yescharacteristic
57#14582643C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#493C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#460C2211yescharacteristic, complemented
63C8×Q8×C43C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×Q8×D43D411yescharacteristic
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43—21no—
72#13063349—44no—
73#13063349—44no—
74C2×#10621873—21no—
75C2×#10621873—21no—
76C2×#10621873—21no—
77C2×#10621883—21no—
78C2×#10621883—21no—
79C2×#10621883—21no—
80C2×#10621883—21no—
81C2×#10621884—21no—
82SD16×D43—44no—
83C2×#10621882—21no—
84C2×#10621882—21no—
85C2×#10621872—21no—
86C2×#10621872D411yescharacteristic
87C2×#10621872D411yescharacteristic
88C2×C8×D43—21no—
89#13063325C2311yescharacteristic
90#13063322C2311yescharacteristic
91#13063321—21no—
92#13063321—21no—
93#13063321—21no—
94#13063312—21no—
95#13063296—21no—
96#13063296—21no—
97Q8×Dic43D411yescharacteristic
98C4×Dic86—21no—
99C4×Dic86C2311yescharacteristic
100#13063290—21no—
101#13063290D411yescharacteristic
102D4×Dic43—21no—
103D4×Dic43—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43D411yescharacteristic
106C42×D43—21no—
107C42×D43C2311yescharacteristic
108#13063257—21no—
109#13063256—21no—
110C4⋊(C43⋊C8)—21no—
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113C4⋊(C43⋊C8)C2311yescharacteristic
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118#13063250—21no—
119#13063249—21no—
120#13063247—21no—
121#13063246—21no—
122#13063246—21no—
123#13063245—21no—
124(C2×D43)⋊C8—21no—
125#13063235—21no—
126#13063235—21no—
127#13063235D411yescharacteristic
128#13063235D411yescharacteristic
129C4×C43⋊C8—21no—
130C4×C43⋊C8C2311yescharacteristic
131C8×Dic43—21no—
132C2×SD16×C43—21no—
133C2×SD16×C43—21no—
134C2×D8×C43—21no—
135C2×D8×C43—21no—
136#127×C43C2311yescharacteristic
137#127×C43C2311yescharacteristic
138C4×Q8×C43C2311yescharacteristic
139C4⋊C8×C43—21no—
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143#102×C43—21no—
144#102×C43—21no—
145C4×C8×C43—21no—
146C4×C8×C43C2311yescharacteristic
147C23×D43—41no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C22×Dic43—41no—
160Q8×D43—22no—
161Q8×D43—41no—
162#10621900—42no—
163#10621900—42no—
164D4×D43—42no—
165D4×D43—42no—
166D4×D43—42no—
167D4×D43—42no—
168D4×D43—82no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43#4111yescharacteristic
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86C2×D411yescharacteristic
180SD16×C43—42no—
181SD16×C43—42no—
182D8×C43—42no—
183D8×C43—42no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C4⋊C4×C43—21no—
190C4⋊C4×C43C2×D411yescharacteristic
191C42×C43—21no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—41no—
194C22⋊Dic43—41no—
195#10621884—42no—
196#10621883—42no—
197#10621883—42no—
198#10621883—42no—
199#10621883—42no—
200#10621882—42no—
201#10621882—42no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208Dic43⋊C4—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43C2×D411yescharacteristic
213C4×Dic43C2×D411yescharacteristic
214C4×Dic43#4111yescharacteristic
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220#10621873—42no—
221#10621873—42no—
222#10621873—42no—
223#10621872—22no—
224#10621872—42no—
225#10621872SD1614yescomplemented
226C8×D43—42no—
227C23×C43—41no—
228C23×C43—41no—
229C22×D43—41no—
230C22×D43—82no—
231C22×D43—82no—
232C22×D43—82no—
233C22×D43#12111yescharacteristic
234Q8×C43—21no—
235Q8×C43AGL(1,ℤ/8)12yescomplemented
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—81no—
245D4×C43—81no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C22⋊D43—82no—
252C22⋊D43—82no—
253C22⋊D43—82no—
254C22⋊D43—82no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—82no—
259C2×Dic43#12111yescharacteristic
260C2×Dic43#12111yescharacteristic
261C2×Dic43#12111yescharacteristic
262D172—41no—
263D172—41no—
264D172—41no—
265D172—41no—
266D172—81no—
267C4×D43—21no—
268C4×D43—21no—
269C4×D43—41no—
270C4×D43—42no—
271C4×D43—81no—
272C4×D43C2×SD1612yes—
273C4×D43AGL(1,ℤ/8)12yes—
274Dic86—21no—
275Dic86—21no—
276Dic86—42no—
277Dic86—41no—
278Dic86—41no—
279C8×C43—21no—
280C8×C43—41no—
281C8×C43—41no—
282C8×C43—41no—
283C8×C43C2×SD1612yescomplemented
284C43⋊C8—21no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288C43⋊C8C2×SD1612yescomplemented
289#19170—431nomaximal, Sylow
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43C2×#12111yescharacteristic
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—164no—
303C2×D43#46012yes—
304C4×C43—22no—
305C4×C43—21no—
306C4×C43—41no—
307C4×C43C22×SD1611yescharacteristic
308C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
309C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
310C4×C43#57511yescharacteristic
311Dic43—21no—
312Dic43—21no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316Dic43#46012yes—
317#3151—431no—
318#3103—431no—
319C2×#460—431no—
320Q8×M16—431no—
321#1688—431no—
322#1688—431no—
323#1686—431no—
324#1686—431no—
325#1668—431no—
326#1668D4311yescharacteristic, complemented
327#1666—431no—
328#1666—431no—
329#1565—431no—
330#1547—431no—
331#1545—431no—
332C2×C43—161no—
333C2×C43—161no—
334C2×C43C2×#46011yescharacteristic
335C2×C43#305511yescharacteristic
336C2×C43#306811yescharacteristic
337D43—22no—
338D43—161no—
339C2×AGL(1,ℤ/8)—861no—
340C2×AGL(1,ℤ/8)—861no—
341C22×SD16—861no—
342#532—431no—
343C2×#127—431no—
344C2×C4×Q8—431no—
345#496—861no—
346#496—861no—
347#493—431no—
348#493C2×D4311yescharacteristic
349#492—431no—
350#492—431no—
351#481—861no—
352#475—431no—
353#475—431no—
354#460—431no—
355#460—431no—
356#460—431no—
357#460—431no—
358#460—861no—
359#460—861no—
360#460C2×D4311yescharacteristic
361#460C2×D4311yescharacteristic, complemented
362#448—861no—
363#446—431no—
364#446—431no—
365#446—861no—
366#446—861no—
367C8×Q8—431no—
368C8×Q8C2×D4311yescharacteristic, complemented
369C4×SD16—861no—
370C4×SD16—861no—
371#431—431no—
372#423—431no—
373#423—861no—
374C2×C4⋊C8—431no—
375C2×#102—861no—
376C4×M16—431no—
377C4×M16—861no—
378#335—431no—
379#335C2×D4311yescharacteristic, complemented
380#334—431no—
381#334—431no—
382#332—431no—
383#332—431no—
384#331—431no—
385#331—431no—
386#331—431no—
387#331—431no—
388#331C2×D4311yescharacteristic
389#331C2×D4311yescharacteristic, complemented
390C43#1917011yescharacteristic, complemented, Sylow
391C2×#41—861no—
392C22×Q8—431no—
393C22×D4—861no—
394C22×D4—861no—
395C22×D4—861no—
396AGL(1,ℤ/8)—1724no—
397AGL(1,ℤ/8)—1724no—
398C2×SD16—21no—
399C2×SD16—21no—
400C2×SD16—861no—
401C2×SD16—861no—
402C2×SD16—861no—
403C2×SD16—861no—
404C2×SD16—861no—
405C2×SD16—861no—
406C2×SD16—861no—
407C2×SD16—861no—
408C2×SD16—1724no—
409C2×D8—21no—
410C2×D8—21no—
411C2×D8—861no—
412C2×D8—861no—
413C2×M16—431no—
414C2×M16—431no—
415C2×M16—861no—
416C22×C8—861no—
417C4⋊Q8—431no—
418#127—431no—
419#127—861no—
420#127—861no—
421#127—861no—
422#127C22×D4311yescharacteristic
423#127C22×D4311yescharacteristic
424#124—861no—
425#121—861no—
426#121—861no—
427C4×Q8—431no—
428C4×Q8—431no—
429C4×Q8—431no—
430C4×Q8—861no—
431C4×Q8—861no—
432C4×Q8C22×D4311yescharacteristic
433C4×D4—861no—
434C4×D4—861no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—861no—
437C2×C42—431no—
438C2×C42—861no—
439#106—861no—
440#106—861no—
441C4⋊C8—21no—
442C4⋊C8—431no—
443C4⋊C8—431no—
444C4⋊C8—431no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C4⋊C8—861no—
449C4⋊C8—861no—
450C4⋊C8C22×D4311yescharacteristic
451C4⋊C8C22×D4311yescharacteristic
452C4⋊C8C22×D4311yescharacteristic
453#103—861no—
454#103—861no—
455#102—21no—
456#102—21no—
457#102—861no—
458#102—861no—
459#102—861no—
460#102—861no—
461C22⋊C8—861no—
462#97—431no—
463#97—431no—
464#97—861no—
465#97—861no—
466C4×C8—21no—
467C4×C8—431no—
468C4×C8—861no—
469C4×C8—861no—
470C4×C8C22×D4311yescharacteristic
471C24—1721no—
472#41—1722no—
473#41—1722no—
474C2×Q8—431no—
475C2×Q8—861no—
476C2×Q8—862no—
477C2×Q8—861no—
478C2×Q8—1721no—
479C2×Q8D4×D4311yescharacteristic
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—3442no—
490C2×D4—1722no—
491C2×D4—1722no—
492C2×D4—1721no—
493C2×D4—1721no—
494C2×D4—1721no—
495C2×D4—1722no—
496C2×D4—1722no—
497C2×D4—1721no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—1721no—
504SD16—42no—
505SD16—42no—
506SD16—1722no—
507SD16—1722no—
508SD16—1722no—
509SD16—1722no—
510SD16—1722no—
511SD16—1722no—
512SD16—1722no—
513SD16—1722no—
514D8—42no—
515D8—42no—
516D8—1722no—
517D8—1722no—
518M16—434no—
519M16—862no—
520M16—1722no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—431no—
525C2×C8—431no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—1722no—
530C2×C8D4×D4311yescharacteristic
531C2×C8D4×D4311yescharacteristic
532C4⋊C4—21no—
533C4⋊C4—431no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4D4×D4311yescharacteristic
541C22⋊C4—1721no—
542C22⋊C4—1721no—
543C42—21no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—861no—
548C42—861no—
549C42—861no—
550C42C23×D4311yescharacteristic
551C23—41no—
552C23—41no—
553C23—431no—
554C23—3442no—
555C23—3442no—
556C23—3442no—
557C23—1721no—
558Q8—21no—
559Q8—861no—
560Q8—861no—
561Q8—1722no—
562Q8—1721no—
563Q8—1721no—
564Q8#1306334912yescomplemented
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—81no—
574D4—81no—
575D4—3441no—
576D4—3442no—
577D4—3442no—
578D4—3442no—
579D4—3442no—
580D4—1721no—
581D4—1721no—
582D4—1721no—
583D4—1721no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—431no—
587C2×C4—432no—
588C2×C4—432no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—3441no—
596C2×C4—3442no—
597C2×C4—1721no—
598C2×C4—1722no—
599C2×C4—1721no—
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C8—21no—
604C8—41no—
605C8—41no—
606C8—41no—
607C8—432no—
608C8—861no—
609C8—1721no—
610C8—1721no—
611C8—1721no—
612C8SD16×D4312yescomplemented
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—432no—
620C22—861no—
621C22—861no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—6884no—
626C22#121×D4311yescharacteristic
627C4—22no—
628C4—21no—
629C4—41no—
630C4—432no—
631C4—861no—
632C4—861no—
633C4—3441no—
634C4—1721no—
635C4—1721no—
636C4C2×SD16×D4311yescharacteristic
637C4AGL(1,ℤ/8)×D4311yescharacteristic
638C4C2×#1306334911yescharacteristic
639C4#1458369611yescharacteristic
640C2—161no—
641C2—161no—
642C2—862no—
643C2—6881no—
644C2#460×D4311yescharacteristic
645C2#1914421111yescharacteristic
646C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1668C2
socleC22×C43C2×#121
prime radical#19145046C2
hypercenter#1668D43
hypocenterC43#19170
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1668

Complements

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

NH ≅ G/Ntype
2. #19144625C2semidirect
3. #460×D43C2semidirect
4. Q8×#10621872C2semidirect
5. #19134078C2semidirect
6. #19134076C2semidirect
7. #19134068C2semidirect
8. #19134066C2semidirect
9. #19133953C2semidirect
10. #19133943C2semidirect
11. #19133941C2semidirect
12. #19133346C2semidirect
13. #19133269C2semidirect
14. #19133261C2semidirect
15. C43×#1668C2semidirect
28. #14583185C22semidirect
29. #14583184C22semidirect
35. #14583096C22semidirect
38. #14583029C22semidirect
40. #14583026C22semidirect
41. Q8×C43⋊C8C22semidirect
51. #14582651C22semidirect
52. #14582650C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582644C22semidirect
57. #14582643C22semidirect
62. C43×#460C22semidirect
63. C8×Q8×C43C22semidirect
64. C43×#335C22semidirect
66. C43×#331C22semidirect
225. #10621872SD16semidirect
235. Q8×C43AGL(1,ℤ/8)semidirect
283. C8×C43C2×SD16semidirect
288. C43⋊C8C2×SD16semidirect
326. #1668D43semidirect
361. #460C2×D43semidirect
368. C8×Q8C2×D43semidirect
379. #335C2×D43semidirect
389. #331C2×D43semidirect
390. C43#19170semidirect
564. Q8#13063349semidirect
612. C8SD16×D43semidirect

Maximal subgroups

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

subgroupindex
#191450462
#191446252
#460×D432
Q8×#106218722
#191340782
#191340762
#191340682
#191340662
#191339532
#191339432
#191339412
#191333462
#191332692
#191332612
C43×#16682
#1917043