Finite Group Databasebeta

← #25079402

Subgroups — #25079402

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144966C211yesmaximal, characteristic, complemented
2#19144605C211yesmaximal, characteristic, complemented
3#459×D43C211yesmaximal, characteristic
4D4×#10621872C211yesmaximal, characteristic, complemented
5#19134157C211yesmaximal, characteristic, complemented
6#19134155C211yesmaximal, characteristic, complemented
7#19134131C211yesmaximal, characteristic, complemented
8#19134125C211yesmaximal, characteristic, complemented
9#19134032C211yesmaximal, characteristic, complemented
10#19134030C211yesmaximal, characteristic, complemented
11#19134006C211yesmaximal, characteristic, complemented
12#19133344C211yesmaximal, characteristic, complemented
13#19133282C211yesmaximal, characteristic, complemented
14#19133261C211yesmaximal, characteristic, complemented
15C43×#1677C211yesmaximal, characteristic, complemented
16C2×D8×D43—21no—
17C22×#10621872—21no—
18#14583454C2211yescharacteristic
19#127×D43C2211yescharacteristic
20C4×D4×D43C2211yescharacteristic
21#14583262—21no—
22#14583262—21no—
23#14583247C2211yescharacteristic, complemented
24#14583246C2211yescharacteristic, complemented
25#14583245C2211yescharacteristic, complemented
26#14583231—21no—
27#14583186C2211yescharacteristic, complemented
28#14583105C2211yescharacteristic, complemented
29#14583104C2211yescharacteristic, complemented
30#14583095C2211yescharacteristic
31#14583094C2211yescharacteristic
32#14583093—21no—
33#14583092—21no—
34#14583091C2211yescharacteristic
35#14583051—21no—
36#14582990—21no—
37#14582986—21no—
38#14582978C2211yescharacteristic, complemented
39#14582976C2211yescharacteristic, complemented
40#14582970—21no—
41#14582967—21no—
42D4×C43⋊C8C2211yescharacteristic, complemented
43#14582951C2211yescharacteristic
44#14582921C2211yescharacteristic
45C4⋊C8×D43C2211yescharacteristic
46#14582902—21no—
47#14582902—21no—
48#102×D43—21no—
49#14582861—21no—
50C4×#10621872C2211yescharacteristic
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#486C2211yescharacteristic, complemented
61C43×#476C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic, complemented
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×D4×D43—21no—
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43D411yescharacteristic
71C22×C4×D43—21no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×D344—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77D8×D43—44no—
78C2×#10621872—21no—
79C2×#10621872—21no—
80C2×#10621872—21no—
81C2×#10621872—44no—
82C2×#10621872D411yescharacteristic
83C2×#10621872D411yescharacteristic
84C22×C43⋊C8—21no—
85C2×C8×D43—21no—
86#13063325C2311yescharacteristic
87#13063322C2311yescharacteristic
88#13063321—21no—
89#13063321—21no—
90#13063321—21no—
91#13063316—21no—
92#13063305—21no—
93#13063301—21no—
94Q8×Dic43—21no—
95#13063290—21no—
96C4×D172C2311yescharacteristic
97D4×Dic43D411yescharacteristic
98#13063287D411yescharacteristic
99C4×C22⋊D43—21no—
100(C22⋊D43)⋊C4—21no—
101#13063283—21no—
102C4⋊C4×D43D411yescharacteristic
103C22⋊C4×D43—21no—
104C42×D43C2311yescharacteristic
105#13063256—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063248—21no—
113#13063247—21no—
114#13063247—21no—
115#13063247—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063245—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127#13063235D411yescharacteristic
128#13063235D411yescharacteristic
129C4×C43⋊C8C2311yescharacteristic
130C8×Dic43—21no—
131C2×D8×C43—21no—
132C22×C8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
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—
159D4×D43—22no—
160D4×D43—41no—
161D4×D43—42no—
162D4×D43—42no—
163D4×D43—42no—
164D4×D43—42no—
165D4×D43—82no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×C4×D43#4111yescharacteristic
178C2×Dic86—21no—
179D8×C43—42no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—42no—
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—21no—
190C42×C43C2411yescharacteristic
191C22⋊Dic43—21no—
192#10621883—42no—
193#10621882—42no—
194#10621882—42no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—41no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—41no—
201C4⋊Dic43C2×D411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—41no—
204C4×Dic43—41no—
205C4×Dic43C2×D411yescharacteristic
206C4×Dic43C2×D411yescharacteristic
207C4×Dic43#4111yescharacteristic
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—42no—
212C2×C43⋊C8C2×D411yescharacteristic
213C2×C43⋊C8C2×D411yescharacteristic
214D344—42no—
215#10621873—42no—
216#10621872—22no—
217#10621872—22no—
218#10621872—42no—
219#10621872—42no—
220#10621872—42no—
221C8×D43—42no—
222C23×C43—21no—
223C23×C43—41no—
224C22×D43—21no—
225C22×D43—42no—
226C22×D43—42no—
227C22×D43—41no—
228C22×D43—81no—
229C22×D43—82no—
230C22×D43—82no—
231C22×D43—82no—
232C22×D43#12111yescharacteristic
233Q8×C43—81no—
234D4×C43—21no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—81no—
240D4×C43AGL(1,ℤ/8)12yes—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C22⋊D43—42no—
249C22⋊D43—82no—
250C22⋊D43—82no—
251C22⋊D43—82no—
252C2×Dic43—21no—
253C2×Dic43—42no—
254C2×Dic43—41no—
255C2×Dic43#12111yescharacteristic
256C2×Dic43#12111yescharacteristic
257C2×Dic43#12111yescharacteristic
258D172—21no—
259D172—21no—
260D172—41no—
261D172—41no—
262D172—41no—
263D172—41no—
264D172—81no—
265C4×D43—21no—
266C4×D43—21no—
267C4×D43—41no—
268C4×D43—42no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—42no—
272C4×D43#13512yes—
273C4×D43AGL(1,ℤ/8)12yes—
274Dic86—41no—
275Dic86—41no—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—41no—
279C8×C43—41no—
280C8×C43—41no—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#19166—431nomaximal, Sylow
287C22×C43—22no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43C2×#12111yescharacteristic
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—84no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—164no—
304C2×D43#46312yes—
305C4×C43—21no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43C2×#13511yescharacteristic
309C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
310C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
311C4×C43#57511yescharacteristic
312Dic43—21no—
313Dic43—21no—
314Dic43—41no—
315Dic43—81no—
316Dic43#46312yes—
317#3138—431no—
318#3101—431no—
319C2×#459—431no—
320D4×M16—431no—
321#1701—431no—
322#1701—431no—
323#1697—431no—
324#1697—431no—
325#1681—431no—
326#1681—431no—
327#1677—431no—
328#1677D4311yescharacteristic, complemented
329#1565—431no—
330#1550—431no—
331#1545—431no—
332C2×C43—42no—
333C2×C43—161no—
334C2×C43C2×#46311yescharacteristic
335C2×C43#305511yescharacteristic
336C2×C43#306811yescharacteristic
337D43—22no—
338D43—81no—
339D43—161no—
340C22×D8—861no—
341C22×M16—861no—
342#533—431no—
343C2×#127—431no—
344C2×C4×D4—431no—
345#490—861no—
346#490—861no—
347#486—431no—
348#486—431no—
349#486—431no—
350#486C2×D4311yescharacteristic, complemented
351#483—861no—
352#476—431no—
353#476C2×D4311yescharacteristic, complemented
354#461—431no—
355#461—431no—
356#459—431no—
357#459—431no—
358#459—431no—
359#459—861no—
360#459—861no—
361#459C2×D4311yescharacteristic
362#450—861no—
363C4×SD16—861no—
364C4×SD16—861no—
365#436—431no—
366#436—431no—
367#435—861no—
368#435—861no—
369C8×D4—431no—
370C8×D4C2×D4311yescharacteristic, complemented
371#431—431no—
372#423—431no—
373C2×C4⋊C8—431no—
374#418—861no—
375#418—861no—
376C2×#102—861no—
377#407—861no—
378C4×M16—431no—
379#335—431no—
380#335—431no—
381#334—431no—
382#334C2×D4311yescharacteristic, complemented
383#333—431no—
384#333C2×D4311yescharacteristic, complemented
385#332—431no—
386#332—431no—
387#331—431no—
388#331—431no—
389#331—431no—
390#331C2×D4311yescharacteristic, complemented
391C43#1916611yescharacteristic, complemented, Sylow
392C22×D4—431no—
393C22×D4—861no—
394C22×D4—861no—
395C22×D4—861no—
396C23×C4—861no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×D8—21no—
400C2×D8—861no—
401C2×D8—861no—
402C2×D8—861no—
403C2×D8—1724no—
404C2×M16—431no—
405C2×M16—431no—
406C2×M16—861no—
407C2×M16—861no—
408C2×M16—861no—
409C2×M16—1724no—
410C22×C8—21no—
411C22×C8—861no—
412C22×C8—861no—
413C4⋊Q8—431no—
414C4⋊Q8C22×D4311yescharacteristic
415#127—431no—
416#127—861no—
417#127—861no—
418#127—861no—
419#127C22×D4311yescharacteristic
420#125—861no—
421C22⋊Q8—861no—
422C22⋊Q8—861no—
423C4×Q8—861no—
424C4×Q8—861no—
425C4×D4—431no—
426C4×D4—431no—
427C4×D4—431no—
428C4×D4—861no—
429C4×D4—861no—
430C4×D4C22×D4311yescharacteristic
431#117—861no—
432C2×C4⋊C4—431no—
433C2×C22⋊C4—861no—
434C2×C42—431no—
435#106—21no—
436#106—861no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—861no—
441C4⋊C8—861no—
442C4⋊C8C22×D4311yescharacteristic
443C4⋊C8C22×D4311yescharacteristic
444C4⋊C8C22×D4311yescharacteristic
445#103—861no—
446#103—861no—
447#102—21no—
448#102—21no—
449#102—21no—
450#102—21no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102—861no—
458#102—861no—
459#102—861no—
460#102—861no—
461C22⋊C8—21no—
462C22⋊C8—861no—
463C22⋊C8—861no—
464C22⋊C8—861no—
465C22⋊C8—861no—
466#97—431no—
467#97—431no—
468C4×C8—431no—
469C4×C8—861no—
470C4×C8C22×D4311yescharacteristic
471C24—861no—
472C24—1721no—
473C2×Q8—21no—
474C2×Q8—861no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—431no—
479C2×D4—861no—
480C2×D4—862no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—3442no—
485C2×D4—1722no—
486C2×D4—1722no—
487C2×D4—1721no—
488C2×D4—1721no—
489C2×D4—1721no—
490C2×D4—1721no—
491C2×D4—1722no—
492C2×D4—1722no—
493C2×D4D4×D4311yescharacteristic
494C22×C4—21no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—1722no—
503C22×C4—1722no—
504SD16—1722no—
505SD16—1722no—
506D8—42no—
507D8—1722no—
508D8—1722no—
509D8—1722no—
510M16—862no—
511M16—862no—
512M16—1722no—
513M16—1722no—
514M16—1722no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—42no—
519C2×C8—431no—
520C2×C8—431no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—1722no—
525C2×C8—1722no—
526C2×C8D4×D4311yescharacteristic
527C2×C8D4×D4311yescharacteristic
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—431no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1721no—
535C4⋊C4—1721no—
536C4⋊C4D4×D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C22⋊C4—1721no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—1721no—
546C42C23×D4311yescharacteristic
547C23—21no—
548C23—41no—
549C23—431no—
550C23—861no—
551C23—3441no—
552C23—3442no—
553C23—3442no—
554C23—3442no—
555C23—1722no—
556C23—1722no—
557C23—1721no—
558Q8—81no—
559Q8—1721no—
560Q8—1721no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—81no—
567D4—861no—
568D4—861no—
569D4—3441no—
570D4—3442no—
571D4—3442no—
572D4—3442no—
573D4—1722no—
574D4—1721no—
575D4—1721no—
576D4—1721no—
577D4—1721no—
578D4#1306335212yes—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—431no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—1721no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4C2×D4×D4311yescharacteristic
599C2×C4C2×D4×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C8—21no—
602C8—21no—
603C8—41no—
604C8—41no—
605C8—41no—
606C8—861no—
607C8—861no—
608C8—1721no—
609C8—1721no—
610C8—1721no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—432no—
618C22—861no—
619C22—861no—
620C22—3444no—
621C22—3441no—
622C22—3441no—
623C22—3441no—
624C22—1721no—
625C22—1721no—
626C22—1721no—
627C22—6884no—
628C22#121×D4311yescharacteristic
629C4—21no—
630C4—41no—
631C4—81no—
632C4—432no—
633C4—861no—
634C4—861no—
635C4—3441no—
636C4—1721no—
637C4#135×D4311yescharacteristic
638C4AGL(1,ℤ/8)×D4311yescharacteristic
639C4C2×#1306335211yescharacteristic
640C4#1458369611yescharacteristic
641C2—42no—
642C2—161no—
643C2—862no—
644C2—3441no—
645C2—6881no—
646C2#463×D4311yescharacteristic
647C2#1914420711yescharacteristic
648C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1677C2
socleC22×C43C2×#121
prime radical#459×D43C2
hypercenter#1677D43
hypocenterC43#19166
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1677

Complements

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

NH ≅ G/Ntype
1. #19144966C2semidirect
2. #19144605C2semidirect
4. D4×#10621872C2semidirect
5. #19134157C2semidirect
6. #19134155C2semidirect
7. #19134131C2semidirect
8. #19134125C2semidirect
9. #19134032C2semidirect
10. #19134030C2semidirect
11. #19134006C2semidirect
12. #19133344C2semidirect
13. #19133282C2semidirect
14. #19133261C2semidirect
15. C43×#1677C2semidirect
23. #14583247C22semidirect
24. #14583246C22semidirect
25. #14583245C22semidirect
27. #14583186C22semidirect
28. #14583105C22semidirect
29. #14583104C22semidirect
38. #14582978C22semidirect
39. #14582976C22semidirect
42. D4×C43⋊C8C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582646C22semidirect
56. #14582644C22semidirect
57. #14582643C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#486C22semidirect
61. C43×#476C22semidirect
63. C8×D4×C43C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
66. C43×#331C22semidirect
328. #1677D43semidirect
350. #486C2×D43semidirect
353. #476C2×D43semidirect
370. C8×D4C2×D43semidirect
382. #334C2×D43semidirect
384. #333C2×D43semidirect
390. #331C2×D43semidirect
391. C43#19166semidirect

Maximal subgroups

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

subgroupindex
#191449662
#191446052
#459×D432
D4×#106218722
#191341572
#191341552
#191341312
#191341252
#191340322
#191340302
#191340062
#191333442
#191332822
#191332612
C43×#16772
#1916643