Finite Group Databasebeta

← #25079369

Subgroups — #25079369

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145049C211yesmaximal, characteristic, complemented
2#19144594C211yesmaximal, characteristic
3#474×D43C211yesmaximal, characteristic, complemented
4D4×#10621872C211yesmaximal, characteristic, complemented
5#19134085C211yesmaximal, characteristic, complemented
6#19134083C211yesmaximal, characteristic, complemented
7#19134059C211yesmaximal, characteristic, complemented
8#19134057C211yesmaximal, characteristic, complemented
9#19133960C211yesmaximal, characteristic, complemented
10#19133958C211yesmaximal, characteristic, complemented
11#19133934C211yesmaximal, characteristic, complemented
12#19133344C211yesmaximal, characteristic, complemented
13#19133269C211yesmaximal, characteristic, complemented
14#19133265C211yesmaximal, characteristic, complemented
15C43×#1665C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17C2×#13063354—21no—
18C22×#10621872—21no—
19#14583447C2211yescharacteristic
20C4⋊Q8×D43C2211yescharacteristic
21C4×D4×D43C2211yescharacteristic
22#14583290—21no—
23#14583290—21no—
24#14583279C2211yescharacteristic, complemented
25#14583278C2211yescharacteristic, complemented
26#14583271C2211yescharacteristic, complemented
27#14583211—21no—
28#14583180C2211yescharacteristic
29#14583180C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583178—21no—
33#14583177—21no—
34#14583176C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583031—21no—
37D8×Dic43—21no—
38#14582979—21no—
39#14582978C2211yescharacteristic
40#14582976C2211yescharacteristic
41#14582970—21no—
42#14582967—21no—
43D4×C43⋊C8C2211yescharacteristic
44#14582951C2211yescharacteristic
45#107×D43—21no—
46#14582921C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48#102×D43—21no—
49#14582861—21no—
50C4×#10621872C2211yescharacteristic
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582644C2211yescharacteristic, complemented
58#14582644C2211yescharacteristic, complemented
59#14582643C2211yescharacteristic, complemented
60C43×#492C2211yescharacteristic, complemented
61C43×#474C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic, complemented
65C43×#332C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69C2×D4×D43D411yescharacteristic
70C22×C4×D43—21no—
71#13063354—44no—
72#13063354—44no—
73C2×Dic172—21no—
74C2×Dic172—21no—
75C2×#10621885—21no—
76C2×#10621885—21no—
77C2×#10621883—21no—
78C2×#10621883—21no—
79C2×#10621882—21no—
80C2×#10621872—21no—
81C2×#10621872—21no—
82C2×#10621872—21no—
83C2×#10621872—44no—
84C2×#10621872D411yescharacteristic
85C2×#10621872D411yescharacteristic
86C22×C43⋊C8—21no—
87C2×C8×D43—21no—
88#13063325C2311yescharacteristic
89#13063325C2311yescharacteristic
90#13063324—21no—
91#13063324—21no—
92#13063323—21no—
93#13063312—21no—
94#13063296—21no—
95#13063296—21no—
96C4×D172C2311yescharacteristic
97D4×Dic43—21no—
98D4×Dic43—21no—
99D4×Dic43D411yescharacteristic
100#13063287D411yescharacteristic
101C4×C22⋊D43—21no—
102(C22⋊D43)⋊C4—21no—
103C4⋊C4×D43—21no—
104C4⋊C4×D43—21no—
105C4⋊C4×D43D411yescharacteristic
106C22⋊C4×D43—21no—
107C42×D43C2311yescharacteristic
108#13063259—21no—
109#13063259—21no—
110#13063258—21no—
111#13063258—21no—
112#13063258—21no—
113C4⋊(C43⋊C8)C2311yescharacteristic
114C4⋊(C43⋊C8)C2311yescharacteristic
115C4⋊(C43⋊C8)C2311yescharacteristic
116Dic43⋊C8—21no—
117Dic43⋊C8—21no—
118#13063247—21no—
119#13063247—21no—
120#13063246—21no—
121#13063246—21no—
122#13063246—21no—
123#13063245—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128#13063235D411yescharacteristic
129#13063235D411yescharacteristic
130C4×C43⋊C8C2311yescharacteristic
131C8×Dic43—21no—
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—21no—
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—
156C22×Dic43—21no—
157C22×Dic43—41no—
158Q8×D43—42no—
159Q8×D43—42no—
160#10621900—42no—
161#10621900—42no—
162D4×D43—22no—
163D4×D43—41no—
164C2×D172C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43—41no—
171C2×C4×D43C2×D411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43#4111yescharacteristic
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—41no—
177SD16×C43—42no—
178SD16×C43—42no—
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—
192C22⋊Dic43—41no—
193C22⋊Dic43—41no—
194#10621885—42no—
195#10621885—42no—
196#10621883—42no—
197#10621883—42no—
198#10621882—42no—
199(C2×D43)⋊C4—21no—
200(C2×D43)⋊C4—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—41no—
208Dic43⋊C4—41no—
209C4×Dic43C2×D411yescharacteristic
210C4×Dic43C2×D411yescharacteristic
211C4×Dic43#4111yescharacteristic
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—42no—
216C2×C43⋊C8C2×D411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218Dic172—42no—
219Dic172—42no—
220#10621872—22no—
221#10621872—42no—
222#10621872—42no—
223#10621872—42no—
224#10621872D814yescomplemented
225C8×D43—42no—
226C23×C43—21no—
227C23×C43—41no—
228C22×D43—21no—
229C22×D43—42no—
230C22×D43—42no—
231C22×D43—81no—
232C22×D43#12111yescharacteristic
233Q8×C43—41no—
234Q8×C43—41no—
235D4×C43—21no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—81no—
241D4×C43#13712yescomplemented
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C22⋊D43—42no—
250C22⋊D43—82no—
251C2×Dic43—21no—
252C2×Dic43—42no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—82no—
256C2×Dic43#12111yescharacteristic
257C2×Dic43#12111yescharacteristic
258C2×Dic43#12111yescharacteristic
259D172—21no—
260D172—21no—
261C4×D43—21no—
262C4×D43—21no—
263C4×D43—41no—
264C4×D43—42no—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—42no—
268C4×D43—82no—
269C4×D43C2×D812yes—
270C4×D43AGL(1,ℤ/8)12yes—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274Dic86—41no—
275Dic86—82no—
276C8×C43—21no—
277C8×C43—41no—
278C8×C43—41no—
279C8×C43—41no—
280C8×C43C2×D812yes—
281C43⋊C8—21no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8C2×D812yes—
286#19163—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#45912yes—
301C4×C43—21no—
302C4×C43—41no—
303C4×C43—81no—
304C4×C43C22×D811yescharacteristic
305C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C43C2×#13711yescharacteristic
307C4×C43#57511yescharacteristic
308Dic43—21no—
309Dic43—21no—
310Dic43—41no—
311Dic43—81no—
312Dic43—81no—
313Dic43#45912yes—
314#3152—431no—
315#3100—431no—
316C2×#474—431no—
317D4×M16—431no—
318#1689—431no—
319#1689—431no—
320#1685—431no—
321#1685—431no—
322#1669—431no—
323#1669—431no—
324#1665—431no—
325#1665D4311yescharacteristic, complemented
326#1565—431no—
327#1547—431no—
328#1546—431no—
329C2×C43—42no—
330C2×C43—161no—
331C2×C43C2×#45911yescharacteristic
332C2×C43#305611yescharacteristic
333C2×C43#306911yescharacteristic
334D43—22no—
335D43—81no—
336C2×#137—861no—
337C2×#137—861no—
338C22×M16—861no—
339#532—431no—
340C2×C4⋊Q8—431no—
341C2×C4×D4—431no—
342#497—861no—
343#497—861no—
344#494—431no—
345#494—431no—
346#492—431no—
347#492C2×D4311yescharacteristic, complemented
348#480—861no—
349#474—431no—
350#474—431no—
351#474—431no—
352#474—431no—
353#474—431no—
354#474—861no—
355#474—861no—
356#474C2×D4311yescharacteristic
357#459—431no—
358#459C2×D4311yescharacteristic
359#447—861no—
360C4×D8—861no—
361C4×D8—861no—
362#436—431no—
363#436—431no—
364#435—861no—
365#435—861no—
366C8×D4—431no—
367C8×D4C2×D4311yescharacteristic
368#431—431no—
369C2×#107—861no—
370#423—431no—
371C2×C4⋊C8—431no—
372C2×#102—861no—
373#407—861no—
374C4×M16—431no—
375#335—431no—
376#335—431no—
377#334—431no—
378#334C2×D4311yescharacteristic, complemented
379#332—431no—
380#332—431no—
381#332—431no—
382#332—431no—
383#332—431no—
384#332C2×D4311yescharacteristic, complemented
385#331—431no—
386#331C2×D4311yescharacteristic, complemented
387C43#1916311yescharacteristic, complemented, Sylow
388C2×#41—861no—
389C22×Q8—861no—
390C22×D4—431no—
391C23×C4—861no—
392#137—1724no—
393#137—1724no—
394C2×Q16—861no—
395C2×Q16—861no—
396C2×Q16—861no—
397C2×Q16—861no—
398C2×SD16—21no—
399C2×SD16—21no—
400C2×SD16—861no—
401C2×SD16—861no—
402C2×D8—21no—
403C2×D8—861no—
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⋊Q8—431no—
415C4⋊Q8—861no—
416C4⋊Q8—861no—
417C4⋊Q8—861no—
418C4⋊Q8C22×D4311yescharacteristic
419#127C22×D4311yescharacteristic
420#124—861no—
421#121—861no—
422#121—861no—
423C4×D4—431no—
424C4×D4—431no—
425C4×D4—431no—
426C4×D4—861no—
427C4×D4—861no—
428C4×D4—861no—
429C4×D4—861no—
430C4×D4C22×D4311yescharacteristic
431C2×C4⋊C4—431no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—431no—
436#107—21no—
437#107—861no—
438#107—861no—
439#107—861no—
440#107—861no—
441#107—861no—
442C4⋊C8—431no—
443C4⋊C8—431no—
444C4⋊C8—431no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8C22×D4311yescharacteristic
448C4⋊C8C22×D4311yescharacteristic
449C4⋊C8C22×D4311yescharacteristic
450#102—21no—
451#102—21no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102—861no—
458C22⋊C8—21no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463#97—431no—
464#97—431no—
465C4×C8—431no—
466C4×C8—861no—
467C4×C8C22×D4311yescharacteristic
468C24—861no—
469#41—1722no—
470#41—1722no—
471C2×Q8—21no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—1721no—
475C2×Q8—1722no—
476C2×Q8—1722no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—431no—
481C2×D4—861no—
482C2×D4—862no—
483C2×D4—1721no—
484C2×D4—1721no—
485C2×D4D4×D4311yescharacteristic
486C22×C4—21no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1721no—
497C22×C4—1721no—
498Q16—1722no—
499Q16—1722no—
500Q16—1722no—
501Q16—1722no—
502SD16—42no—
503SD16—42no—
504SD16—1722no—
505SD16—1722no—
506D8—42no—
507D8—1722no—
508M16—434no—
509M16—862no—
510M16—1722no—
511M16—1722no—
512M16—1722no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—42no—
517C2×C8—431no—
518C2×C8—431no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—1722no—
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—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—
542C22⋊C4—1721no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42C23×D4311yescharacteristic
547C23—21no—
548C23—41no—
549C23—431no—
550C23—861no—
551C23—3441no—
552C23—1722no—
553C23—1722no—
554Q8—41no—
555Q8—41no—
556Q8—3442no—
557Q8—1721no—
558Q8—1721no—
559Q8—1721no—
560Q8—1721no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—81no—
567D4—861no—
568D4—861no—
569D4—3442no—
570D4—1722no—
571D4#1306335412yescomplemented
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—431no—
577C2×C4—432no—
578C2×C4—432no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—3442no—
585C2×C4—3442no—
586C2×C4—1721no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4C2×D4×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C8—21no—
598C8—41no—
599C8—41no—
600C8—41no—
601C8—432no—
602C8—861no—
603C8—1721no—
604C8—1721no—
605C8—1721no—
606C8D8×D4312yes—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—432no—
614C22—861no—
615C22—861no—
616C22—3444no—
617C22—1721no—
618C22—1721no—
619C22—1721no—
620C22#121×D4311yescharacteristic
621C4—21no—
622C4—41no—
623C4—81no—
624C4—432no—
625C4—861no—
626C4—861no—
627C4—3441no—
628C4—3441no—
629C4—1721no—
630C4C2×D8×D4311yescharacteristic
631C4AGL(1,ℤ/8)×D4311yescharacteristic
632C4C2×#1306335411yescharacteristic
633C4#1458369611yescharacteristic
634C2—42no—
635C2—161no—
636C2—862no—
637C2—3441no—
638C2#459×D4311yescharacteristic
639C2#1914421811yescharacteristic
640C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1665C2
socleC22×C43C2×#121
prime radical#19144594C2
hypercenter#1665D43
hypocenterC43#19163
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. #19145049C2semidirect
3. #474×D43C2semidirect
4. D4×#10621872C2semidirect
5. #19134085C2semidirect
6. #19134083C2semidirect
7. #19134059C2semidirect
8. #19134057C2semidirect
9. #19133960C2semidirect
10. #19133958C2semidirect
11. #19133934C2semidirect
12. #19133344C2semidirect
13. #19133269C2semidirect
14. #19133265C2semidirect
15. C43×#1665C2semidirect
24. #14583279C22semidirect
25. #14583278C22semidirect
26. #14583271C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582646C22semidirect
56. #14582645C22semidirect
57. #14582644C22semidirect
58. #14582644C22semidirect
59. #14582643C22semidirect
60. C43×#492C22semidirect
64. C43×#334C22semidirect
65. C43×#332C22semidirect
66. C43×#331C22semidirect
224. #10621872D8semidirect
241. D4×C43#137semidirect
325. #1665D43semidirect
347. #492C2×D43semidirect
378. #334C2×D43semidirect
384. #332C2×D43semidirect
386. #331C2×D43semidirect
387. C43#19163semidirect
571. D4#13063354semidirect

Maximal subgroups

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

subgroupindex
#191450492
#191445942
#474×D432
D4×#106218722
#191340852
#191340832
#191340592
#191340572
#191339602
#191339582
#191339342
#191333442
#191332692
#191332652
C43×#16652
#1916343