Finite Group Databasebeta

← #25080478

Subgroups — #25080478

Order 11008.

786 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#492×D43C211yesmaximal, characteristic, complemented
2#19144403C211yesmaximal, characteristic, complemented
3#19144070C211yesmaximal, characteristic
4C8×#10621900C211yesmaximal, characteristic, complemented
5#19133946C211yesmaximal, characteristic, complemented
6#19133944C211yesmaximal, characteristic, complemented
7#19133942C211yesmaximal, characteristic, complemented
8#19133940C211yesmaximal, characteristic, complemented
9#19133938C211yesmaximal, characteristic, complemented
10#19133936C211yesmaximal, characteristic, complemented
11#19133934C211yesmaximal, characteristic, complemented
12#19133349C211yesmaximal, characteristic, complemented
13#19133278C211yesmaximal, characteristic, complemented
14#19133261C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C2×SD16×D43—21no—
18C2×SD16×D43—21no—
19C4⋊Q8×D43C2211yescharacteristic
20#127×D43C2211yescharacteristic
21C4×#10621900C2211yescharacteristic
22#14583273C2211yescharacteristic
23#14583272C2211yescharacteristic
24#14583271C2211yescharacteristic
25#14583270—21no—
26#14583270—21no—
27#14583193—21no—
28#14583187—21no—
29#14583185C2211yescharacteristic, complemented
30#14583181C2211yescharacteristic, complemented
31#14583179C2211yescharacteristic, complemented
32#14583100C2211yescharacteristic
33#14583098—21no—
34#14583096C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583092—21no—
37C8×Dic86C2211yescharacteristic, complemented
38#14583023C2211yescharacteristic, complemented
39D4×C43⋊C8C2211yescharacteristic, complemented
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582951C2211yescharacteristic
43#14582949—21no—
44#14582940—21no—
45#14582921C2211yescharacteristic
46#14582921C2211yescharacteristic
47#14582902—21no—
48#14582897—21no—
49C2×C8×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582645C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#492C2211yescharacteristic
61C43×#474C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic, complemented
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×Q8×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43—21no—
72#13063349—44no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×#10621873—21no—
76C2×#10621883—21no—
77C2×#10621883—21no—
78C2×#10621883—21no—
79C2×#10621884—21no—
80C2×#10621884—21no—
81SD16×D43—44no—
82SD16×D43—44no—
83C2×#10621882—21no—
84C2×#10621872—21no—
85C2×#10621872—21no—
86C22×C43⋊C8—21no—
87C2×C8×D43D411yescharacteristic
88C2×C8×D43D411yescharacteristic
89#13063325C2311yescharacteristic
90#13063324—21no—
91#13063324—21no—
92#13063323—21no—
93#13063322C2311yescharacteristic
94#13063321—21no—
95#13063321—21no—
96#13063321—21no—
97C4×Dic86C2311yescharacteristic
98#13063290D411yescharacteristic
99D4×Dic43D411yescharacteristic
100C4×C22⋊D43—21no—
101(C22⋊D43)⋊C4—21no—
102#13063283D411yescharacteristic
103#13063281—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43—21no—
106C2×C4×Dic43—21no—
107C42×D43C2311yescharacteristic
108#13063258—21no—
109#13063257—21no—
110#13063256—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#13063248—21no—
120#13063247—21no—
121#13063246—21no—
122#13063246—21no—
123#13063245—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C8×Dic43D411yescharacteristic
131C8×Dic43D411yescharacteristic
132C2×SD16×C43—21no—
133C2×SD16×C43—21no—
134C2×D8×C43—21no—
135C22×C8×C43—21no—
136C4⋊Q8×C43C2311yescharacteristic
137#127×C43C2311yescharacteristic
138C4×D4×C43C2311yescharacteristic
139#107×C43—21no—
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143#102×C43—21no—
144#102×C43—21no—
145C22⋊C8×C43—21no—
146C4×C8×C43C2311yescharacteristic
147C23×D43—41no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C2×C22⋊D43—21no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C2×C22⋊D43—41no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160Q8×D43—42no—
161Q8×D43—42no—
162#10621900—22no—
163#10621900SD1614yescomplemented
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—41no—
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43#4111yescharacteristic
176C2×Dic86—21no—
177C2×Dic86—41no—
178C2×Dic86C2×D411yescharacteristic
179SD16×C43—42no—
180SD16×C43—42no—
181D8×C43—42no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—42no—
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43C2×D411yescharacteristic
191C22⋊C4×C43—21no—
192C42×C43C2411yescharacteristic
193C22⋊Dic43—21no—
194#10621884—42no—
195#10621884—42no—
196#10621883—42no—
197#10621883—42no—
198#10621883—42no—
199#10621882—42no—
200(C2×D43)⋊C4—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43C2×D411yescharacteristic
212C4×Dic43C2×D411yescharacteristic
213C4×Dic43#4111yescharacteristic
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—42no—
218C2×C43⋊C8C2×D411yescharacteristic
219C2×C43⋊C8C2×D411yescharacteristic
220#10621873—42no—
221#10621873—42no—
222#10621873—42no—
223#10621872—42no—
224#10621872—42no—
225C8×D43—22no—
226C8×D43—22no—
227C23×C43—21no—
228C23×C43—41no—
229C22×D43—41no—
230C22×D43—82no—
231C22×D43—82no—
232C22×D43—82no—
233C22×D43#12111yescharacteristic
234Q8×C43—41no—
235Q8×C43—41no—
236D4×C43—21no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—81no—
242D4×C43C2×SD1612yescomplemented
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C22⋊D43—24no—
251C22⋊D43—82no—
252C22⋊D43—82no—
253C22⋊D43—82no—
254C2×Dic43—21no—
255C2×Dic43—24no—
256C2×Dic43—21no—
257C2×Dic43—42no—
258C2×Dic43—41no—
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—22no—
270C4×D43—82no—
271C4×D43C2×SD1612yes—
272C4×D43#13512yes—
273Dic86—21no—
274Dic86—41no—
275Dic86—41no—
276Dic86—82no—
277Dic86C2×SD1612yescomplemented
278C8×C43—21no—
279C8×C43—41no—
280C8×C43—41no—
281C8×C43—41no—
282C8×C43AGL(1,ℤ/8)12yescomplemented
283C43⋊C8—21no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C43⋊C8AGL(1,ℤ/8)12yescomplemented
288#19266—431nomaximal, Sylow
289C22×C43—22no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43C2×#12111yescharacteristic
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—164no—
302C2×D43#46512yes—
303C4×C43—21no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43C22×SD1611yescharacteristic
307C4×C43C2×#13511yescharacteristic
308C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
309C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
310Dic43—21no—
311Dic43—22no—
312Dic43—41no—
313Dic43—81no—
314Dic43#46512yes—
315Dic43#47112yes—
316C2×#492—431no—
317#3079—431no—
318#3038—431no—
319C8×#41—431no—
320#1666—431no—
321#1666—431no—
322#1666—431no—
323#1666—431no—
324#1665—431no—
325#1665—431no—
326#1665—431no—
327#1665D4311yescharacteristic, complemented
328#1566—431no—
329#1549—431no—
330#1545—431no—
331C2×C43—42no—
332C2×C43—161no—
333C2×C43#303811yescharacteristic
334C2×C43C2×#46511yescharacteristic
335C2×C43C2×#47111yescharacteristic
336D43—22no—
337D43—161no—
338C2×AGL(1,ℤ/8)—861no—
339C22×SD16—861no—
340C22×SD16—861no—
341C2×C4⋊Q8—431no—
342C2×#127—431no—
343C4×#41—431no—
344#492—431no—
345#492—431no—
346#492—431no—
347#492—861no—
348#492—861no—
349#492C2×D4311yescharacteristic
350#477—861no—
351#476—861no—
352#475—431no—
353#475—431no—
354#474—431no—
355#474C2×D4311yescharacteristic, complemented
356#460—431no—
357#460—431no—
358#460—861no—
359#459—431no—
360#459—861no—
361#459C2×D4311yescharacteristic
362C8×Q8—431no—
363C8×Q8—431no—
364C8×D4—431no—
365C8×D4—861no—
366C8×D4—861no—
367C8×D4C2×D4311yescharacteristic, complemented
368#431—431no—
369#431—861no—
370#428—861no—
371#423—431no—
372#423—431no—
373#418—861no—
374#417—861no—
375C2×C4×C8—431no—
376C2×C4×C8—861no—
377#334—431no—
378#334—431no—
379#334—431no—
380#334C2×D4311yescharacteristic, complemented
381#332—431no—
382#332—431no—
383#332—431no—
384#332C2×D4311yescharacteristic, complemented
385#331—431no—
386#331—431no—
387#331—431no—
388#331C2×D4311yescharacteristic
389C43#1926611yescharacteristic, complemented, Sylow
390C2×#41—431no—
391C22×Q8—861no—
392C22×D4—861no—
393C22×D4—861no—
394C22×D4—861no—
395AGL(1,ℤ/8)—1724no—
396C2×SD16—21no—
397C2×SD16—21no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16—861no—
401C2×SD16—861no—
402C2×SD16—861no—
403C2×SD16—861no—
404C2×SD16—861no—
405C2×SD16—861no—
406C2×SD16—1724no—
407C2×SD16—1724no—
408C2×D8—21no—
409C2×D8—861no—
410C2×M16—861no—
411C2×M16—861no—
412C22×C8—21no—
413C22×C8—431no—
414C22×C8—431no—
415C22×C8—861no—
416C4⋊Q8—431no—
417C4⋊Q8—861no—
418C4⋊Q8—861no—
419C4⋊Q8—861no—
420C4⋊Q8C22×D4311yescharacteristic
421#127—431no—
422#127—861no—
423#127—861no—
424#127—861no—
425#127C22×D4311yescharacteristic
426C4×Q8—431no—
427C4×Q8—431no—
428C4×D4—431no—
429C4×D4—861no—
430C4×D4—861no—
431C4×D4C22×D4311yescharacteristic
432#117—431no—
433#117—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C42—431no—
437C2×C42—861no—
438#107—21no—
439#107—861no—
440#106—861no—
441#106—861no—
442C4⋊C8—431no—
443C4⋊C8—431no—
444C4⋊C8—431no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C4⋊C8—861no—
449C4⋊C8C22×D4311yescharacteristic
450C4⋊C8C22×D4311yescharacteristic
451C4⋊C8C22×D4311yescharacteristic
452#103—861no—
453#103—861no—
454#102—21no—
455#102—21no—
456#102—861no—
457#102—861no—
458#102—861no—
459#102—861no—
460C22⋊C8—21no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463C4×C8—431no—
464C4×C8—431no—
465C4×C8—431no—
466C4×C8—861no—
467C4×C8—861no—
468C4×C8—861no—
469C4×C8C22×D4311yescharacteristic
470C24—1721no—
471#41—434no—
472#41—862no—
473C2×Q8—21no—
474C2×Q8—431no—
475C2×Q8—861no—
476C2×Q8—1721no—
477C2×Q8—1722no—
478C2×Q8—1722no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—3442no—
487C2×D4—1722no—
488C2×D4—1722no—
489C2×D4—1721no—
490C2×D4—1721no—
491C2×D4—1721no—
492C2×D4—1722no—
493C2×D4—1722no—
494C2×D4D4×D4311yescharacteristic
495C22×C4—21no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—1721no—
502SD16—42no—
503SD16—42no—
504SD16—1722no—
505SD16—1722no—
506SD16—1722no—
507SD16—1722no—
508SD16—1722no—
509SD16—1722no—
510SD16—1722no—
511SD16—1722no—
512D8—42no—
513D8—1722no—
514M16—1722no—
515M16—1722no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—42no—
520C2×C8—431no—
521C2×C8—431no—
522C2×C8—862no—
523C2×C8—862no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—1722no—
528C2×C8D4×D4311yescharacteristic
529C2×C8D4×D4311yescharacteristic
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—431no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—1721no—
538C4⋊C4—1721no—
539C4⋊C4D4×D4311yescharacteristic
540C22⋊C4—21no—
541C22⋊C4—861no—
542C22⋊C4—861no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—861no—
547C42—861no—
548C42—861no—
549C42C23×D4311yescharacteristic
550C23—21no—
551C23—41no—
552C23—431no—
553C23—3442no—
554C23—3442no—
555C23—3442no—
556C23—1721no—
557Q8—41no—
558Q8—41no—
559Q8—432no—
560Q8—861no—
561Q8—3442no—
562Q8—1721no—
563Q8—1721no—
564D4—21no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—81no—
570D4—864no—
571D4—3441no—
572D4—3442no—
573D4—3442no—
574D4—3442no—
575D4—1721no—
576D4—1721no—
577D4—1721no—
578D4—1721no—
579D4SD16×D4312yescomplemented
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—431no—
589C2×C4—862no—
590C2×C4—864no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—3442no—
596C2×C4—1722no—
597C2×C4—1721no—
598C2×C4C2×D4×D4311yescharacteristic
599C2×C4C2×D4×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C8—21no—
602C8—41no—
603C8—41no—
604C8—41no—
605C8—432no—
606C8—861no—
607C8—1721no—
608C8—1721no—
609C8—1721no—
610C8#1306334912yescomplemented
611C22—22no—
612C22—41no—
613C22—41no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—432no—
618C22—861no—
619C22—861no—
620C22—3441no—
621C22—3441no—
622C22—3441no—
623C22—6884no—
624C22#121×D4311yescharacteristic
625C4—21no—
626C4—41no—
627C4—81no—
628C4—432no—
629C4—432no—
630C4—861no—
631C4—862no—
632C4—3441no—
633C4—1721no—
634C4C2×SD16×D4311yescharacteristic
635C4#135×D4311yescharacteristic
636C4AGL(1,ℤ/8)×D4311yescharacteristic
637C4C2×#1306334911yescharacteristic
638C2—42no—
639C2—161no—
640C2—862no—
641C2—6881no—
642C2#1914407011yescharacteristic
643C2#465×D4311yescharacteristic
644C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#19144070C2
hypercenter#1665D43
hypocenterC43#19266
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1665

Complements

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

NH ≅ G/Ntype
1. #492×D43C2semidirect
2. #19144403C2semidirect
4. C8×#10621900C2semidirect
5. #19133946C2semidirect
6. #19133944C2semidirect
7. #19133942C2semidirect
8. #19133940C2semidirect
9. #19133938C2semidirect
10. #19133936C2semidirect
11. #19133934C2semidirect
12. #19133349C2semidirect
13. #19133278C2semidirect
14. #19133261C2semidirect
15. C43×#1665C2semidirect
29. #14583185C22semidirect
30. #14583181C22semidirect
31. #14583179C22semidirect
37. C8×Dic86C22semidirect
38. #14583023C22semidirect
39. D4×C43⋊C8C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
61. C43×#474C22semidirect
63. C8×D4×C43C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
163. #10621900SD16semidirect
242. D4×C43C2×SD16semidirect
277. Dic86C2×SD16semidirect
282. C8×C43AGL(1,ℤ/8)semidirect
287. C43⋊C8AGL(1,ℤ/8)semidirect
327. #1665D43semidirect
355. #474C2×D43semidirect
367. C8×D4C2×D43semidirect
380. #334C2×D43semidirect
384. #332C2×D43semidirect
389. C43#19266semidirect
579. D4SD16×D43semidirect
610. C8#13063349semidirect

Maximal subgroups

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

subgroupindex
#492×D432
#191444032
#191440702
C8×#106219002
#191339462
#191339442
#191339422
#191339402
#191339382
#191339362
#191339342
#191333492
#191332782
#191332612
C43×#16652
#1926643