Finite Group Databasebeta

← #25102513

Subgroups — #25102513

Order 11008.

1486 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063370C211yesmaximal, characteristic, complemented
2C2×#14583066C211yesmaximal, characteristic
3C4×#13063351C212yesmaximal, complemented
4#19134994C211yesmaximal, characteristic, complemented
5#19134974C212yesmaximal, complemented
6#19134827C212yesmaximal, complemented
7#19134804C211yesmaximal, characteristic, complemented
8#19134548C211yesmaximal, characteristic, complemented
9#19134406C212yesmaximal, complemented
10C4×#13063242C211yesmaximal, characteristic, complemented
11C43×#2328C211yesmaximal, characteristic, complemented
12C2×#13063370C2211yescharacteristic
13C2×#13063351C2212yes—
14#14583380C2212yes—
15#14583378—22no—
16#14583374C2211yescharacteristic
17#14583372—22no—
18#14583371—22no—
19C4×#10621898C2212yes—
20C4×#10621900—22no—
21C2×C4×C22⋊D43—22no—
22C4×D4×D43—22no—
23#14583066C418yescomplemented
24#14583009—22no—
25#14582999—22no—
26C4×#10621883—22no—
27C4×#10621882—22no—
28#14582939C2212yescomplemented
29C2×#13063253C2212yes—
30C2×#13063253C2212yes—
31#14582904C2212yescomplemented
32#14582898C2212yes—
33C2×#13063242C2211yescharacteristic
34C2×#13063242C2211yescharacteristic
35C4×#10621877C2212yescomplemented
36#14582668C2212yescomplemented
37#14582659C2212yescomplemented
38#14582659C2212yescomplemented
39C2×#127×C43C2211yescharacteristic
40C2×C4×D4×C43C2211yescharacteristic
41C2×C4×D4×C43C2211yescharacteristic, complemented
42C43×#390C2211yescharacteristic
43C43×#390C2211yescharacteristic, complemented
44C43×#386—22no—
45C43×#386—22no—
46C43×#382C2211yescharacteristic, complemented
47C43×#376C2211yescharacteristic, complemented
48#13063370—22no—
49#13063370—24no—
50#13063370C2×C414yescomplemented
51C2×#10621898C2312yes—
52C2×#10621900—22no—
53C22×C22⋊D43—22no—
54C2×D4×D43—22no—
55C22×C4×D43—22no—
56#13063351—24no—
57#13063351C2×C418yescomplemented
58C2×#10621883—22no—
59C2×#10621882—22no—
60C2×#10621877C2312yes—
61C2×#10621877C2312yes—
62C4×Dic86D412yescomplemented
63C4×Dic86D412yescomplemented
64#13063290—22no—
65C4×D172D412yescomplemented
66C4×D172D412yescomplemented
67D4×Dic43—22no—
68D4×Dic43—22no—
69#13063287—22no—
70C4×C22⋊D43—24no—
71C4×C22⋊D43—24no—
72C4×C22⋊D43—22no—
73C4×C22⋊D43—24no—
74C4×C22⋊D43—22no—
75(C22⋊D43)⋊C4—24no—
76(C22⋊D43)⋊C4—24no—
77#13063284C2312yes—
78#13063283—22no—
79#13063282—22no—
80#13063281—24no—
81C2×Dic43⋊C4—22no—
82C4⋊C4×D43—22no—
83C2×C22⋊Dic43—22no—
84C2×(C2×D43)⋊C4—22no—
85C22⋊C4×D43—24no—
86C2×C4×Dic43—22no—
87C42×D43—22no—
88#13063258—22no—
89#13063256—22no—
90#13063253—24no—
91#13063253C2×C418yescomplemented
92#13063248—22no—
93#13063246—22no—
94#13063246—22no—
95#13063245—22no—
96#13063242—22no—
97#13063242C2×C414yescomplemented
98#13063236—22no—
99C4×C43⋊C8—22no—
100C22×D4×C43—22no—
101C22×D4×C43C2311yescharacteristic
102C22×D4×C43C2311yescharacteristic
103C23×C4×C43—21no—
104C23×C4×C43D412yes—
105#127×C43—22no—
106#127×C43C2×C414yescomplemented
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43—22no—
110C4×D4×C43—22no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43D412yes—
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—22no—
123C24×C43—21no—
124C24×C43C2×D412yes—
125C23×D43—22no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—21no—
129C2×D4×C43—28no—
130C2×D4×C43—22no—
131C2×D4×C43—22no—
132C2×D4×C43—82no—
133C2×D4×C43—82no—
134C2×D4×C43C22×C412yes—
135C2×D4×C43C22×C412yescomplemented
136C2×D4×C43#4112yes—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—42no—
143C22×C4×C43—82no—
144C22×C4×C43—82no—
145C22×C4×C43C2×D412yes—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—24no—
150C2×C22⋊D43—28no—
151C2×C22⋊D43—28no—
152C2×C22⋊D43—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156#10621900—28no—
157#10621900—28no—
158D4×D43—28no—
159D4×D43—28no—
160#10621898—22no—
161#10621898—22no—
162#10621898C22×C414yes—
163#10621898#4114yes—
164C2×D172C2×D412yes—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—24no—
168C2×C4×D43—22no—
169C2×C4×D43—84no—
170C2×Dic86C2×D412yes—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—82no—
177C22⋊C4×C43—82no—
178C42×C43—21no—
179C42×C43—22no—
180C42×C43C22×C412yescomplemented
181C42×C43C2×D412yes—
182C42×C43C2×D412yes—
183C22⋊Dic43—24no—
184C22⋊Dic43—22no—
185#10621883—28no—
186#10621882—28no—
187(C2×D43)⋊C4—24no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190C4⋊Dic43C2×D412yes—
191C4⋊Dic43C2×D412yes—
192Dic43⋊C4—24no—
193Dic43⋊C4—22no—
194Dic43⋊C4—22no—
195C4×Dic43—24no—
196C4×Dic43—22no—
197C4×Dic43—22no—
198C4×Dic43—22no—
199#10621877—22no—
200#10621877—22no—
201#10621877—22no—
202#10621877C22×C414yescomplemented
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43C4×D414yes—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—28no—
218C22×D43—82no—
219C22×D43—82no—
220D4×C43—24no—
221D4×C43—24no—
222D4×C43—24no—
223D4×C43—42no—
224D4×C43—88no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—44no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—82no—
239C2×C4×C43—84no—
240C2×C4×C43#12011yescharacteristic
241C2×C4×C43#12012yes—
242C2×C4×C43#12011yescharacteristic
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D412yes—
245C2×C4×C43C2×#4112yes—
246C2×C4×C43C2×#4111yescharacteristic
247C22⋊D43—216no—
248C22⋊D43—24no—
249C22⋊D43—24no—
250C2×Dic43—28no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—82no—
255C2×Dic43—82no—
256D172—22no—
257D172C4×D414yes—
258C4×D43—24no—
259C4×D43—24no—
260C4×D43—44no—
261C4×D43—82no—
262C4×D43—84no—
263Dic86—22no—
264Dic86C4×D414yes—
265C43⋊C8—24no—
266C43⋊C8—42no—
267#21473—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—24no—
271C22×C43—44no—
272C22×C43—44no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—82no—
277C22×C43—82no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C2×#12011yescharacteristic
282C22×C43#52511yescharacteristic
283C2×D43—24no—
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—88no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—22no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C2×C4×D412yes—
295C4×C43#52512yes—
296Dic43—24no—
297Dic43—42no—
298Dic43—42no—
299C4×H(5,𝔽2)—431no—
300C2×#453—431no—
301C4×AGL(1,ℤ/8)—432no—
302#2328D4311yescharacteristic, complemented
303#1887—431no—
304#1883—432no—
305#1860—432no—
306#1856—431no—
307#1792—431no—
308#1759—432no—
309C4×#100—431no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—44no—
313C2×C43—82no—
314C2×C43C4×#12011yescharacteristic
315C2×C43#301911yescharacteristic
316C2×C43#302111yescharacteristic
317D43—44no—
318C2×H(5,𝔽2)—431no—
319C2×AGL(1,ℤ/8)—432no—
320C2×#127C2×D4311yescharacteristic
321#520—432no—
322#520—862no—
323#518—431no—
324#518—862no—
325#518—862no—
326C4×#41—432no—
327C4×#41—862no—
328C2×C4×D4—862no—
329C2×C4×D4—862no—
330C2×C4×D4C2×D4311yescharacteristic
331C2×C4×D4C2×D4311yescharacteristic, complemented
332#453—438no—
333#442—862no—
334#440—862no—
335C4×SD16—862no—
336C4×D8—862no—
337#428—432no—
338C2×#104—432no—
339C2×#104—432no—
340#418—432no—
341#417—432no—
342C2×#100—431no—
343C2×#100—431no—
344C4×M16—432no—
345#390C2×D4311yescharacteristic
346#390C2×D4311yescharacteristic, complemented
347#386—22no—
348#386—22no—
349#382C2×D4311yescharacteristic, complemented
350#376C2×D4311yescharacteristic, complemented
351#343—432no—
352#339—432no—
353#339—432no—
354C43#2147311yescharacteristic, complemented, Sylow
355H(5,𝔽2)—434no—
356H(5,𝔽2)—864no—
357H(5,𝔽2)—862no—
358C2×#41—432no—
359C2×#41—862no—
360C22×D4—22no—
361C22×D4—862no—
362C22×D4—862no—
363C22×D4C22×D4311yescharacteristic
364C22×D4C22×D4311yescharacteristic
365C23×C4—21no—
366C23×C4—862no—
367C23×C4C22⋊D4312yes—
368AGL(1,ℤ/8)—438no—
369AGL(1,ℤ/8)—864no—
370C2×SD16—862no—
371C2×D8—862no—
372C2×M16—432no—
373C2×M16—432no—
374#127—22no—
375#127C4×D4314yescomplemented
376C4×Q8—432no—
377C4×Q8—432no—
378C4×Q8—862no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—432no—
384C4×D4—432no—
385C4×D4—864no—
386C4×D4—864no—
387C4×D4—862no—
388C4×D4—862no—
389C4×D4—862no—
390C4×D4—864no—
391C4×D4—864no—
392C4×D4—862no—
393C4×D4—864no—
394C4×D4—862no—
395#117—432no—
396#117—864no—
397#117—862no—
398#117—862no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—864no—
407C2×C22⋊C4—862no—
408C2×C22⋊C4—862no—
409C2×C22⋊C4C22⋊D4312yes—
410C2×C42—862no—
411C2×C42—862no—
412C2×C42C22×D4311yescharacteristic
413C2×C42C22×D4311yescharacteristic
414C2×C42C22×D4311yescharacteristic
415#107—862no—
416#106—862no—
417#104—438no—
418#104—864no—
419#103—862no—
420#102—862no—
421#102—862no—
422#102—862no—
423#100—434no—
424#100—862no—
425#97—862no—
426C4×C8—862no—
427#95—21no—
428#95—21no—
429#95—22no—
430C24—21no—
431C24—862no—
432C24C2×C22⋊D4312yes—
433#41—434no—
434#41—434no—
435#41—868no—
436#41—868no—
437#41—862no—
438#41—862no—
439C2×Q8—432no—
440C2×D4—28no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—82no—
447C2×D4—82no—
448C2×D4—432no—
449C2×D4—868no—
450C2×D4—868no—
451C2×D4—864no—
452C2×D4—868no—
453C2×D4—868no—
454C2×D4—862no—
455C2×D4C2×C4×D4312yes—
456C2×D4C2×C4×D4312yescomplemented
457C2×D4#1062189812yes—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—82no—
465C22×C4—82no—
466C22×C4—864no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—3444no—
474C22×C4C2×C22⋊D4312yes—
475C22×C4C2×C22⋊D4311yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—868no—
479D8—868no—
480M16—434no—
481M16—862no—
482M16—862no—
483M16—862no—
484C2×C8—862no—
485C2×C8—862no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—432no—
489C4⋊C4—432no—
490C4⋊C4—864no—
491C4⋊C4—862no—
492C4⋊C4—862no—
493C22⋊C4—24no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—82no—
497C22⋊C4—82no—
498C22⋊C4—864no—
499C22⋊C4—864no—
500C22⋊C4—862no—
501C22⋊C4—862no—
502C22⋊C4—862no—
503C42—21no—
504C42—22no—
505C42—864no—
506C42—862no—
507C42—862no—
508C42—862no—
509C42C2×C4×D4312yescomplemented
510C42D4×D4312yes—
511C42D4×D4312yes—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—868no—
522C23—862no—
523C23—3442no—
524C23—3442no—
525C23C4×C22⋊D4314yes—
526C23C22×C22⋊D4311yescharacteristic
527Q8—434no—
528Q8—862no—
529D4—24no—
530D4—24no—
531D4—24no—
532D4—42no—
533D4—88no—
534D4—434no—
535D4—8616no—
536D4—864no—
537D4—864no—
538D4—862no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—44no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—84no—
554C2×C4—868no—
555C2×C4—862no—
556C2×C4—864no—
557C2×C4—864no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—3442no—
561C2×C4—3444no—
562C2×C4—3442no—
563C2×C4—3442no—
564C2×C4—1724no—
565C2×C4#1306329311yescharacteristic
566C2×C4#1306329312yes—
567C2×C4#1306329311yescharacteristic
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4C2×D4×D4312yes—
570C2×C4#41×D4312yes—
571C2×C4C2×#1062189811yescharacteristic
572C8—864no—
573C8—1722no—
574C22—21no—
575C22—21no—
576C22—24no—
577C22—44no—
578C22—44no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—82no—
583C22—82no—
584C22—81no—
585C22—81no—
586C22—864no—
587C22—3448no—
588C22—1722no—
589C22—1722no—
590C22C2×C4×C22⋊D4311yescharacteristic
591C22C2×#1306329311yescharacteristic
592C22#1458340611yescharacteristic
593C4—21no—
594C4—21no—
595C4—22no—
596C4—42no—
597C4—42no—
598C4—81no—
599C4—81no—
600C4—864no—
601C4—1722no—
602C4—1722no—
603C4C4×D4×D4312yes—
604C4#1458340812yes—
605C2—21no—
606C2—21no—
607C2—44no—
608C2—82no—
609C2—1724no—
610C2C4×#1306329311yescharacteristic
611C2#1914395111yescharacteristic
612C2#1914396611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2328C2
socleC22×C43C2×#120
prime radicalC2×#14583066C2
cosocleC22×C4×C43C24
hypercenter#2328D43
hypocenterC43#21473
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2328

Complements

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

NH ≅ G/Ntype
1. C4×#13063370C2semidirect
3. C4×#13063351C2semidirect
4. #19134994C2semidirect
5. #19134974C2semidirect
6. #19134827C2semidirect
7. #19134804C2semidirect
8. #19134548C2semidirect
9. #19134406C2semidirect
10. C4×#13063242C2semidirect
11. C43×#2328C2semidirect
23. #14583066C4semidirect
28. #14582939C22semidirect
31. #14582904C22semidirect
35. C4×#10621877C22semidirect
36. #14582668C22semidirect
37. #14582659C22semidirect
38. #14582659C22semidirect
41. C2×C4×D4×C43C22semidirect
43. C43×#390C22semidirect
46. C43×#382C22semidirect
47. C43×#376C22semidirect
50. #13063370C2×C4semidirect
57. #13063351C2×C4semidirect
62. C4×Dic86D4semidirect
63. C4×Dic86D4semidirect
65. C4×D172D4semidirect
66. C4×D172D4semidirect
91. #13063253C2×C4semidirect
97. #13063242C2×C4semidirect
106. #127×C43C2×C4semidirect
135. C2×D4×C43C22×C4semidirect
180. C42×C43C22×C4semidirect
202. #10621877C22×C4semidirect
302. #2328D43semidirect
331. C2×C4×D4C2×D43semidirect
346. #390C2×D43semidirect
349. #382C2×D43semidirect
350. #376C2×D43semidirect
354. C43#21473semidirect
375. #127C4×D43semidirect
456. C2×D4C2×C4×D43semidirect
509. C42C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C4×#130633702
C2×#145830662
C4×#130633512
#191349942
#191349742
#191348272
#191348042
#191345482
#191344062
C4×#130632422
C43×#23282
#2147343