Finite Group Databasebeta

← #25166558

Subgroups — #25166558

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144960C211yesmaximal, characteristic
2#19144558C211yesmaximal, characteristic
3#19144439C211yesmaximal, characteristic, complemented
4#19143439C211yesmaximal, characteristic
5#19135958C211yesmaximal, characteristic, complemented
6#19135939C211yesmaximal, characteristic, complemented
7#19135891C211yesmaximal, characteristic
8#19135398C211yesmaximal, characteristic, complemented
9#19135296C211yesmaximal, characteristic
10#19135253C211yesmaximal, characteristic, complemented
11#19135252C211yesmaximal, characteristic, complemented
12#19134989C211yesmaximal, characteristic, complemented
13#19134823C211yesmaximal, characteristic
14#19134473C211yesmaximal, characteristic, complemented
15C43×#2005C211yesmaximal, characteristic
16#14583527C2211yescharacteristic
17#14583382C2211yescharacteristic
18#14583377C2211yescharacteristic
19#14583267—21no—
20#14583258—21no—
21#14583253—21no—
22#14583249—21no—
23#14583237—21no—
24#14583237—21no—
25#14583232—21no—
26#14583227—21no—
27#14583208—21no—
28#14583204—21no—
29#14583192—21no—
30#14583182—21no—
31#14583006—21no—
32#14583000—21no—
33Q16×Dic43—21no—
34SD16×Dic43—21no—
35C2×#13063260C2211yescharacteristic
36#14582942C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582935C2211yescharacteristic
40#14582927C2211yescharacteristic
41#14582908C2211yescharacteristic
42#14582908C2211yescharacteristic
43#14582900C2211yescharacteristic
44#14582895C2211yescharacteristic
45C2×#13063249C2211yescharacteristic
46C2×#13063249C2211yescharacteristic
47C2×#13063249C2211yescharacteristic
48C2×#13063249C2211yescharacteristic
49C2×#13063244C2211yescharacteristic
50#14582866C2211yescharacteristic
51#14582857C2211yescharacteristic
52#14582855C2211yescharacteristic
53C2×C4×C43⋊C8C2211yescharacteristic
54#14582769C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582663C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582659C2211yescharacteristic
60C2×#137×C43C2211yescharacteristic
61C43×#536C2211yescharacteristic
62C2×C4⋊Q8×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C43×#419C2211yescharacteristic
65C2×#101×C43C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063325—21no—
72#13063324—21no—
73#13063317—21no—
74#13063316—21no—
75#13063302—41no—
76Q8×Dic43—21no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80Q8×Dic43—21no—
81D4×Dic43—21no—
82D4×Dic43—41no—
83#13063284—21no—
84#13063284—41no—
85#13063284C2311yescharacteristic
86#13063284C2311yescharacteristic
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—41no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91#13063260—22no—
92#13063259—21no—
93#13063259—21no—
94#13063258—21no—
95#13063258D411yescharacteristic
96#13063258D411yescharacteristic
97#13063257—21no—
98#13063257—21no—
99#13063256—21no—
100#13063256D411yescharacteristic
101#13063256D411yescharacteristic
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104#13063249—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063249—21no—
109#13063249—21no—
110#13063249—21no—
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063249—21no—
115#13063249—21no—
116#13063249—21no—
117#13063249D411yescharacteristic
118#13063249D411yescharacteristic
119#13063246—21no—
120#13063246D411yescharacteristic
121#13063246D411yescharacteristic
122#13063244—22no—
123C22⋊(C43⋊C8)—21no—
124C22⋊(C43⋊C8)—21no—
125#13063236—21no—
126#13063235—21no—
127C4×C43⋊C8—22no—
128C4×C43⋊C8—21no—
129C8×Dic43—21no—
130C2×#41×C43C2311yescharacteristic
131C22×Q8×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133#137×C43—22no—
134#137×C43—22no—
135C2×Q16×C43—21no—
136C2×SD16×C43—21no—
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C4⋊Q8×C43—21no—
140C4⋊Q8×C43—22no—
141C4⋊Q8×C43—22no—
142#124×C43—21no—
143#123×C43—41no—
144C22⋊Q8×C43—21no—
145C22⋊Q8×C43—21no—
146#117×C43C2311yescharacteristic
147C2×C4⋊C4×C43—41no—
148C2×C42×C43C2311yescharacteristic
149#104×C43—22no—
150#103×C43—21no—
151#103×C43—21no—
152#101×C43—22no—
153#41×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43C2×D411yescharacteristic
169C2×Q8×C43#4112yes—
170C2×D4×C43—21no—
171C2×D4×C43C2×D411yescharacteristic
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43C2411yescharacteristic
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—41no—
180C2×Dic86—41no—
181Q16×C43—24no—
182SD16×C43—24no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43—21no—
186M16×C43#4112yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C4⋊C4×C43—44no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—41no—
196C22⋊C4×C43—41no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43#4112yes—
200C22⋊Dic43—21no—
201C22⋊Dic43—21no—
202C22⋊Dic43—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—41no—
208C4⋊Dic43—41no—
209C4⋊Dic43—41no—
210C4⋊Dic43—41no—
211C4⋊Dic43—82no—
212C4⋊Dic43C2×D411yescharacteristic
213C4⋊Dic43C2×D411yescharacteristic
214C4⋊Dic43C2×D411yescharacteristic
215C4⋊Dic43C2×D411yescharacteristic
216Dic43⋊C4—41no—
217Dic43⋊C4—41no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—41no—
221C4×Dic43—41no—
222C4×Dic43—41no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8C2×D411yescharacteristic
234C2×C43⋊C8C2×D411yescharacteristic
235C2×C43⋊C8C2×D411yescharacteristic
236C2×C43⋊C8C2×D411yescharacteristic
237C23×C43—21no—
238C23×C43H(5,𝔽2)11yescharacteristic
239Q8×C43—22no—
240Q8×C43—21no—
241Q8×C43—21no—
242Q8×C43—22no—
243Q8×C43—41no—
244Q8×C43—41no—
245Q8×C43—41no—
246Q8×C43—41no—
247Q8×C43—41no—
248Q8×C43—41no—
249D4×C43—21no—
250D4×C43—21no—
251D4×C43—41no—
252D4×C43—41no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—22no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C432−1+411yescharacteristic
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—81no—
280C2×Dic43—81no—
281C2×Dic43—161no—
282Dic86—161no—
283C8×C43—22no—
284C8×C43—41no—
285C43⋊C8—21no—
286C43⋊C8—21no—
287C43⋊C8—21no—
288C43⋊C8—21no—
289C43⋊C8—41no—
290C43⋊C8—41no—
291#26849—431nomaximal, Sylow
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43#54211yescharacteristic
298C22×C43D4211yescharacteristic
299C22×C43#55111yescharacteristic
300C4×C43—24no—
301C4×C43—41no—
302C4×C43—42no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43#52511yescharacteristic
307C4×C43#53211yescharacteristic
308C4×C43#54711yescharacteristic
309C4×C43#54811yescharacteristic
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313Dic43—41no—
314Dic43—81no—
315Dic43—81no—
316#3137—431no—
317#3097—431no—
318#3082—431no—
319#2947—431no—
320#2064—431no—
321#2060—431no—
322#2052—431no—
323#2005D4311yescharacteristic
324#1956—431no—
325#1937—431no—
326#1930—431no—
327#1930—431no—
328#1886—431no—
329#1859—431no—
330#1772—431no—
331C2×C43—21no—
332C2×C43—21no—
333C2×C43—81no—
334C2×C43#246111yescharacteristic
335C2×C43#329111yescharacteristic
336C2×C43#329311yescharacteristic
337C2×#137C2×D4311yescharacteristic
338#544—431no—
339#536C2×D4311yescharacteristic
340C2×C4⋊Q8C2×D4311yescharacteristic
341#520—431no—
342#519—431no—
343#491—861no—
344#489—861no—
345#488—861no—
346#487—861no—
347#485—861no—
348#485—861no—
349#484—861no—
350#483—861no—
351#479—861no—
352#479—861no—
353#477—861no—
354#475—861no—
355#441—861no—
356#440—861no—
357C4×Q16—861no—
358C4×SD16—861no—
359C2×#108—431no—
360#428—431no—
361#428—431no—
362#428—431no—
363#427—431no—
364#424—431no—
365C2×#104C2×D4311yescharacteristic
366#419—431no—
367#419—431no—
368#419C2×D4311yescharacteristic
369#417—431no—
370#416—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×#101—431no—
376C2×#101C2×D4311yescharacteristic
377#408—431no—
378#405—431no—
379#405—431no—
380C2×C4×C8—431no—
381#384—431no—
382#343—431no—
383#343—431no—
384#341—431no—
385#339—431no—
386#339—431no—
387#339C2×D4311yescharacteristic
388C43#2684911yescharacteristic, complemented, Sylow
389C2×#41C22×D4311yescharacteristic
390C22×Q8C22×D4311yescharacteristic
391C22×Q8C22×D4311yescharacteristic
392#137—22no—
393#137—22no—
394C2×Q16—21no—
395C2×SD16—21no—
396C2×M16—431no—
397C2×M16—431no—
398C2×M16C22×D4311yescharacteristic
399C2×M16C22×D4311yescharacteristic
400C22×C8—431no—
401C22×C8—431no—
402C4⋊Q8—21no—
403C4⋊Q8—22no—
404C4⋊Q8—22no—
405C4⋊Q8—861no—
406C4⋊Q8—861no—
407#125—861no—
408#125—861no—
409#124—21no—
410#123—41no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—1721no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×Q8—861no—
419C4×D4—861no—
420C4×D4—1721no—
421#117—431no—
422#117—431no—
423#117—861no—
424#117—1721no—
425#117C22×D4311yescharacteristic
426C2×C4⋊C4—41no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—1721no—
431C2×C42C22×D4311yescharacteristic
432#108—862no—
433#107—431no—
434#107—431no—
435#107—861no—
436#107—861no—
437#107—861no—
438#106—431no—
439#106—431no—
440#106—861no—
441#106—861no—
442#106—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445#104—22no—
446#103—21no—
447#103—21no—
448#103—431no—
449#103—431no—
450#103—861no—
451#103—861no—
452#103—861no—
453#103—861no—
454#103—861no—
455#103—861no—
456#103—861no—
457#103—861no—
458#103—861no—
459#103—861no—
460#103—861no—
461#103—861no—
462#103—861no—
463#102—431no—
464#102—431no—
465#102—861no—
466#101—22no—
467#101—862no—
468C22⋊C8—861no—
469C22⋊C8—861no—
470#97—861no—
471#97—861no—
472C4×C8—861no—
473C4×C8—861no—
474C4×C8—862no—
475#41—21no—
476#41—21no—
477#41—21no—
478#41—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—1721no—
491C2×Q8D4×D4311yescharacteristic
492C2×Q8#1062190012yes—
493C2×D4—21no—
494C2×D4D4×D4311yescharacteristic
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—1721no—
502C22×C4C23×D4311yescharacteristic
503Q16—24no—
504SD16—24no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16—861no—
509M16—861no—
510M16—861no—
511M16—861no—
512M16#1062190012yes—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—431no—
516C2×C8—431no—
517C2×C8—431no—
518C2×C8—431no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C4⋊C4—44no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—431no—
529C4⋊C4—431no—
530C4⋊C4—431no—
531C4⋊C4—431no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—3442no—
537C4⋊C4—1721no—
538C4⋊C4—1721no—
539C4⋊C4—1721no—
540C4⋊C4—1721no—
541C4⋊C4—1721no—
542C4⋊C4—1721no—
543C4⋊C4D4×D4311yescharacteristic
544C4⋊C4D4×D4311yescharacteristic
545C22⋊C4—21no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—861no—
549C22⋊C4—861no—
550C22⋊C4—1721no—
551C42—21no—
552C42—21no—
553C42—861no—
554C42—861no—
555C42—1721no—
556C42—1721no—
557C42—1721no—
558C42#1062190012yes—
559C23—21no—
560C23#1306337011yescharacteristic
561Q8—22no—
562Q8—22no—
563Q8—21no—
564Q8—21no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570Q8—41no—
571Q8—6881no—
572D4—21no—
573D4—21no—
574D4—41no—
575D4—41no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—3441no—
595C2×C4—3441no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—6881no—
599C2×C4C2×D4×D4311yescharacteristic
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C2×#1062190011yescharacteristic
602C2×C4C2×#1062190011yescharacteristic
603C2×C4C2×#1062190011yescharacteristic
604C2×C4#1306337211yescharacteristic
605C8—22no—
606C8—41no—
607C8—861no—
608C8—861no—
609C8—861no—
610C8—861no—
611C8—1721no—
612C8—1721no—
613C22—21no—
614C22—21no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22#1458351611yescharacteristic
619C22#1458353111yescharacteristic
620C22#1458358011yescharacteristic
621C4—24no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—42no—
626C4—81no—
627C4—3441no—
628C4—3441no—
629C4—1721no—
630C4—1721no—
631C4—1721no—
632C4—1721no—
633C4#1458340511yescharacteristic
634C4#1458344711yescharacteristic
635C4#1458354911yescharacteristic
636C4#1458355511yescharacteristic
637C2—21no—
638C2—21no—
639C2—81no—
640C2#1913855711yescharacteristic
641C2#1914638511yescharacteristic
642C2#1914639611yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2005C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#2005D43
hypocenterC43#26849
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2005

Complements

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

NH ≅ G/Ntype
3. #19144439C2semidirect
5. #19135958C2semidirect
6. #19135939C2semidirect
8. #19135398C2semidirect
10. #19135253C2semidirect
11. #19135252C2semidirect
12. #19134989C2semidirect
14. #19134473C2semidirect
388. C43#26849semidirect

Maximal subgroups

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

subgroupindex
#191449602
#191445582
#191444392
#191434392
#191359582
#191359392
#191358912
#191353982
#191352962
#191352532
#191352522
#191349892
#191348232
#191344732
C43×#20052
#2684943