Finite Group Databasebeta

← #25081752

Subgroups — #25081752

Order 11008.

738 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#19145532C211yesmaximal, characteristic, complemented
2#19144387C211yesmaximal, characteristic, complemented
3#459×D43C211yesmaximal, characteristic
4#19143616C211yesmaximal, characteristic, complemented
5#19134005C211yesmaximal, characteristic, complemented
6#19134004C211yesmaximal, characteristic, complemented
7#19134003C211yesmaximal, characteristic, complemented
8#19134002C211yesmaximal, characteristic, complemented
9#19133939C211yesmaximal, characteristic, complemented
10#19133938C211yesmaximal, characteristic, complemented
11#19133933C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133261C211yesmaximal, characteristic, complemented
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16C2×D8×D43—21no—
17#14583454C2211yescharacteristic
18#127×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583273C2211yescharacteristic, complemented
21#14583246C2211yescharacteristic, complemented
22#14583245C2211yescharacteristic, complemented
23#14583202—21no—
24#14583201—21no—
25#14583190C2211yescharacteristic, complemented
26#14583189C2211yescharacteristic, complemented
27#14583176C2211yescharacteristic, complemented
28#14583097—21no—
29#14583097—21no—
30#14583095C2211yescharacteristic
31#14583094C2211yescharacteristic
32#14583093—21no—
33#14583092—21no—
34#14583091C2211yescharacteristic
35#14583048—21no—
36#14583048—21no—
37C8×D172C2211yescharacteristic, complemented
38D4×C43⋊C8C2211yescharacteristic, complemented
39#14582964C2211yescharacteristic, complemented
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582940—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582902—21no—
48#102×D43—21no—
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#492C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic, complemented
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×D4×D43—21no—
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43D411yescharacteristic
71C22×C4×D43—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×D344—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77D8×D43—44no—
78C2×#10621872—21no—
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83#13063325C2311yescharacteristic
84#13063322C2311yescharacteristic
85#13063321—21no—
86#13063321—21no—
87#13063321—21no—
88#13063316—21no—
89#13063305—21no—
90#13063301—21no—
91Q8×Dic43—21no—
92#13063290—21no—
93C4×D172C2311yescharacteristic
94D4×Dic43D411yescharacteristic
95#13063287D411yescharacteristic
96C4×C22⋊D43—21no—
97(C22⋊D43)⋊C4—21no—
98#13063283—21no—
99C4⋊C4×D43D411yescharacteristic
100C22⋊C4×D43—21no—
101C42×D43C2311yescharacteristic
102#13063258—21no—
103#13063257—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8D411yescharacteristic
111Dic43⋊C8D411yescharacteristic
112#13063247—21no—
113#13063247—21no—
114#13063247—21no—
115#13063247—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120#13063245—21no—
121#13063245—21no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8D411yescharacteristic
127(C2×D43)⋊C8D411yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43—21no—
130C2×SD16×C43—21no—
131C2×SD16×C43—21no—
132C2×D8×C43—21no—
133C22×C8×C43—21no—
134C4⋊Q8×C43C2311yescharacteristic
135#127×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137#107×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C23×D43—41no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C22×Dic43—21no—
158D4×D43—22no—
159D4×D43—42no—
160D4×D43—42no—
161D4×D43—81no—
162D4×D43—81no—
163D4×D43—82no—
164D4×D43SD1614yescomplemented
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172C2×D411yescharacteristic
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—81no—
173C2×C4×D43—81no—
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43#4111yescharacteristic
177C2×Dic86—21no—
178SD16×C43—81no—
179SD16×C43—81no—
180D8×C43—42no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—81no—
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C42×C43C2411yescharacteristic
192C22⋊Dic43—21no—
193#10621884—81no—
194#10621884—81no—
195#10621882—42no—
196#10621882—42no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—41no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—41no—
206C4×Dic43—41no—
207C4×Dic43C2×D411yescharacteristic
208C4×Dic43C2×D411yescharacteristic
209C4×Dic43#4111yescharacteristic
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—81no—
214C2×C43⋊C8C2×D411yescharacteristic
215C2×C43⋊C8C2×D411yescharacteristic
216D344—42no—
217#10621872—42no—
218C8×D43—42no—
219C8×D43—81no—
220C8×D43—81no—
221C23×C43—21no—
222C23×C43—41no—
223C22×D43—21no—
224C22×D43—24no—
225C22×D43—41no—
226C22×D43—81no—
227C22×D43—81no—
228C22×D43—82no—
229C22×D43—82no—
230C22×D43—82no—
231C22×D43#12111yescharacteristic
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—21no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—81no—
240D4×C43C2×SD1612yes—
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—24no—
249C22⋊D43—82no—
250C22⋊D43—82no—
251C22⋊D43—82no—
252C2×Dic43—21no—
253C2×Dic43—41no—
254C2×Dic43—81no—
255C2×Dic43#12111yescharacteristic
256C2×Dic43#12111yescharacteristic
257C2×Dic43#12111yescharacteristic
258D172—21no—
259D172—41no—
260D172—41no—
261D172—41no—
262D172—41no—
263D172—81no—
264D172C2×SD1612yes—
265C4×D43—21no—
266C4×D43—21no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—41no—
270C4×D43—81no—
271C4×D43—81no—
272C4×D43C2×SD1612yes—
273C4×D43#13512yes—
274Dic86—81no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—41no—
278C8×C43—41no—
279C8×C43—41no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285#19384—431nomaximal, Sylow
286C22×C43—22no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43C2×#12111yescharacteristic
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—22no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—84no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—164no—
303C2×D43#46512yes—
304C4×C43—21no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43C22×SD1611yescharacteristic
308C4×C43C2×#13511yescharacteristic
309C4×C43#57611yescharacteristic
310C4×C43#57611yescharacteristic
311Dic43—21no—
312Dic43—21no—
313Dic43—41no—
314Dic43—81no—
315Dic43#46512yes—
316#3208—431no—
317#3077—431no—
318C2×#459—431no—
319#2972—431no—
320#1677—431no—
321#1677—431no—
322#1677—431no—
323#1677—431no—
324#1665—431no—
325#1665—431no—
326#1665—431no—
327#1665D4311yescharacteristic, complemented
328#1570—431no—
329#1545—431no—
330#1542—431no—
331C2×C43—42no—
332C2×C43—161no—
333C2×C43#304111yescharacteristic
334C2×C43C2×#46511yescharacteristic
335C2×C43#306811yescharacteristic
336D43—22no—
337D43—42no—
338D43—161no—
339C22×D8—861no—
340#533—431no—
341C2×#127—431no—
342C2×C4×D4—431no—
343#492—431no—
344#492C2×D4311yescharacteristic, complemented
345#486—431no—
346#486—431no—
347#478—861no—
348#478—861no—
349#476—431no—
350#476—431no—
351#474—431no—
352#474C2×D4311yescharacteristic, complemented
353#460—861no—
354#460—861no—
355#459—431no—
356#459—431no—
357#459—431no—
358#459—861no—
359#459—861no—
360#459C2×D4311yescharacteristic
361#450—861no—
362#450—861no—
363C8×D4—431no—
364C8×D4—431no—
365C8×D4—431no—
366C8×D4—861no—
367C8×D4—861no—
368C8×D4C2×D4311yescharacteristic, complemented
369#431—431no—
370#431—431no—
371#428—861no—
372#423—431no—
373C2×C4⋊C8—431no—
374#418—861no—
375C2×#102—861no—
376C2×C22⋊C8—861no—
377C2×C22⋊C8—861no—
378#334—431no—
379#334—431no—
380#334—431no—
381#334C2×D4311yescharacteristic, complemented
382#333—431no—
383#333—431no—
384#332—431no—
385#332C2×D4311yescharacteristic, complemented
386#331—431no—
387#331—431no—
388#331—431no—
389#331C2×D4311yescharacteristic, complemented
390C43#1938411yescharacteristic, complemented, Sylow
391C22×D4—431no—
392C22×D4—861no—
393C22×D4—861no—
394C22×D4—861no—
395C23×C4—861no—
396C2×SD16—21no—
397C2×SD16—21no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×D8—21no—
401C2×D8—861no—
402C2×D8—861no—
403C2×D8—861no—
404C2×D8—1724no—
405C2×M16—861no—
406C22×C8—21no—
407C22×C8—861no—
408C22×C8—861no—
409C22×C8—861no—
410C22×C8—861no—
411C4⋊Q8—431no—
412C4⋊Q8C22×D4311yescharacteristic
413#127—431no—
414#127—861no—
415#127—861no—
416#127—861no—
417#127C22×D4311yescharacteristic
418#125—861no—
419C22⋊Q8—861no—
420C22⋊Q8—861no—
421C4×Q8—861no—
422C4×Q8—861no—
423C4×D4—431no—
424C4×D4—431no—
425C4×D4—431no—
426C4×D4—861no—
427C4×D4—861no—
428C4×D4C22×D4311yescharacteristic
429#117—861no—
430C2×C4⋊C4—431no—
431C2×C22⋊C4—861no—
432C2×C42—431no—
433#107—21no—
434#107—861no—
435#106—861no—
436#106—861no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8C22×D4311yescharacteristic
445C4⋊C8C22×D4311yescharacteristic
446C4⋊C8C22×D4311yescharacteristic
447#102—21no—
448#102—21no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102—861no—
458#102—861no—
459C22⋊C8—21no—
460C22⋊C8—431no—
461C22⋊C8—431no—
462C22⋊C8—861no—
463C22⋊C8—861no—
464C22⋊C8—861no—
465C22⋊C8—861no—
466C4×C8—431no—
467C4×C8—861no—
468C4×C8C22×D4311yescharacteristic
469C24—861no—
470C24—1721no—
471C2×Q8—21no—
472C2×Q8—861no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—434no—
477C2×D4—431no—
478C2×D4—862no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—3441no—
484C2×D4—3441no—
485C2×D4—3442no—
486C2×D4—1722no—
487C2×D4—1722no—
488C2×D4—1721no—
489C2×D4—1721no—
490C2×D4—1721no—
491C2×D4D4×D4311yescharacteristic
492C22×C4—21no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—3441no—
501C22×C4—3441no—
502SD16—81no—
503SD16—81no—
504SD16—3441no—
505SD16—3441no—
506D8—42no—
507D8—1722no—
508D8—1722no—
509D8—1722no—
510M16—1722no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—81no—
515C2×C8—431no—
516C2×C8—431no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—3441no—
521C2×C8—3441no—
522C2×C8—3441no—
523C2×C8—1722no—
524C2×C8D4×D4311yescharacteristic
525C2×C8D4×D4311yescharacteristic
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—431no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—1721no—
533C4⋊C4—1721no—
534C4⋊C4D4×D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C22⋊C4—1721no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—1721no—
544C42C23×D4311yescharacteristic
545C23—21no—
546C23—41no—
547C23—431no—
548C23—864no—
549C23—861no—
550C23—3441no—
551C23—3441no—
552C23—3442no—
553C23—3442no—
554C23—3442no—
555C23—1721no—
556Q8—41no—
557Q8—41no—
558Q8—3441no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—81no—
565D4—432no—
566D4—864no—
567D4—861no—
568D4—3441no—
569D4—3442no—
570D4—3442no—
571D4—3442no—
572D4—1721no—
573D4—1721no—
574D4—1721no—
575D4—1721no—
576D4SD16×D4312yes—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—431no—
582C2×C4—432no—
583C2×C4—432no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—3441no—
590C2×C4—3441no—
591C2×C4—3441no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4C2×D4×D4311yescharacteristic
597C2×C4C2×D4×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C8—21no—
600C8—21no—
601C8—41no—
602C8—41no—
603C8—41no—
604C8—861no—
605C8—861no—
606C8—1721no—
607C8—1721no—
608C8—1721no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—432no—
616C22—861no—
617C22—861no—
618C22—862no—
619C22—3444no—
620C22—3441no—
621C22—3441no—
622C22—3441no—
623C22—1721no—
624C22—1721no—
625C22—6884no—
626C22#121×D4311yescharacteristic
627C4—21no—
628C4—41no—
629C4—81no—
630C4—432no—
631C4—861no—
632C4—861no—
633C4—3441no—
634C4—1721no—
635C4C2×SD16×D4311yescharacteristic
636C4#135×D4311yescharacteristic
637C4#1458370011yescharacteristic
638C4#1458370311yescharacteristic
639C2—42no—
640C2—161no—
641C2—862no—
642C2—1722no—
643C2—6881no—
644C2#1914409311yescharacteristic
645C2#465×D4311yescharacteristic
646C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#459×D43C2
hypercenter#1665D43
hypocenterC43#19384
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. #19145532C2semidirect
2. #19144387C2semidirect
4. #19143616C2semidirect
5. #19134005C2semidirect
6. #19134004C2semidirect
7. #19134003C2semidirect
8. #19134002C2semidirect
9. #19133939C2semidirect
10. #19133938C2semidirect
11. #19133933C2semidirect
12. #19133364C2semidirect
13. #19133261C2semidirect
14. #19133251C2semidirect
15. C43×#1665C2semidirect
20. #14583273C22semidirect
21. #14583246C22semidirect
22. #14583245C22semidirect
25. #14583190C22semidirect
26. #14583189C22semidirect
27. #14583176C22semidirect
37. C8×D172C22semidirect
38. D4×C43⋊C8C22semidirect
39. #14582964C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582645C22semidirect
57. #14582643C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#492C22semidirect
61. C43×#474C22semidirect
63. C8×D4×C43C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
66. C43×#331C22semidirect
164. D4×D43SD16semidirect
327. #1665D43semidirect
344. #492C2×D43semidirect
352. #474C2×D43semidirect
368. C8×D4C2×D43semidirect
381. #334C2×D43semidirect
385. #332C2×D43semidirect
389. #331C2×D43semidirect
390. C43#19384semidirect

Maximal subgroups

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

subgroupindex
#191455322
#191443872
#459×D432
#191436162
#191340052
#191340042
#191340032
#191340022
#191339392
#191339382
#191339332
#191333642
#191332612
#191332512
C43×#16652
#1938443