Finite Group Databasebeta

← #25964279

Subgroups — #25964279

Order 11008.

2054 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148417C211yesmaximal, characteristic, complemented
2H(5,𝔽2)×Dic43C211yesmaximal, characteristic
3#19144455C213yesmaximal, complemented
4#19144450C213yesmaximal, complemented
5#19144428C213yesmaximal, complemented
6#19144422C213yesmaximal, complemented
7#19144415C213yesmaximal, complemented
8#19144389C213yesmaximal, complemented
9#19144379C213yesmaximal, complemented
10C2×#14583201C213yesmaximal, complemented
11#19143193C211yesmaximal, characteristic, complemented
12#19143190C211yesmaximal, characteristic, complemented
13#19143161C211yesmaximal, characteristic, complemented
14#19143121C211yesmaximal, characteristic
15C43×#2897C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17#14583628—21no—
18#14583625—21no—
19#14583608—23no—
20#14583606—23no—
21#14583530C2213yescomplemented
22#14583527C2213yescomplemented
23#14583452C2213yescomplemented
24C2×#13063316C2213yescomplemented
25#14583382—21no—
26#14583382C2213yes—
27#14583382C2211yescharacteristic
28#14583382C2211yescharacteristic
29#14583374—23no—
30#14583374C2213yes—
31#41×Dic43—21no—
32#41×Dic43C2213yes—
33#41×Dic43C2211yescharacteristic
34C2×D4×Dic43—23no—
35C2×D4×Dic43C2213yes—
36#14583208C2213yescomplemented
37#14583204C2216yescomplemented
38#14583204C2211yescharacteristic, complemented
39#14583201C2216yescomplemented
40#14583201C2216yescomplemented
41#14583201C2213yescomplemented
42#14583201C2216yescomplemented
43#14583197C2213yescomplemented
44#14583197C2216yescomplemented
45#14583192C2213yescomplemented
46#14583187C2216yescomplemented
47#14583187C2213yescomplemented
48#14583182C2213yescomplemented
49#14583177C2216yescomplemented
50#14583177C2213yescomplemented
51#14582942C2213yescomplemented
52#14582941C2213yescomplemented
53#14582941C2213yescomplemented
54#14582939C2213yescomplemented
55#14582937C2213yescomplemented
56#14582935C2213yescomplemented
57C2×#13063258C2213yescomplemented
58C2×#13063257C2213yescomplemented
59#14582927C2213yescomplemented
60#14582925C2213yescomplemented
61#14582922C2213yescomplemented
62C2×Dic43⋊C8C2213yescomplemented
63#14582904C2213yes—
64#14582900C2213yes—
65#14582895C2213yes—
66C2×#13063246C2213yes—
67C2×H(5,𝔽2)×C43C2211yescharacteristic
68C2×#131×C43C2211yescharacteristic
69C43×#520C2211yescharacteristic
70C43×#418C2213yes—
71C43×#417C2213yes—
72C43×#416C2213yes—
73C2×#102×C43C2213yes—
74C23×Dic43—23no—
75#13063332—24no—
76C2×#10621877C2313yes—
77C22×C43⋊C8C2313yes—
78#13063325—23no—
79#13063324—23no—
80#13063324C2313yes—
81#13063324C2313yes—
82#13063317—23no—
83#13063316—23no—
84#13063316—23no—
85#13063316—23no—
86#13063316C2313yes—
87#13063316C2316yes—
88#13063316C2311yescharacteristic
89#13063304—26no—
90#13063302—23no—
91#13063302—23no—
92#13063302—26no—
93Q8×Dic43—21no—
94Q8×Dic43—21no—
95Q8×Dic43D411yescharacteristic
96Q8×Dic43D411yescharacteristic
97Q8×Dic43C2311yescharacteristic
98Q8×Dic43C2313yes—
99C4×Dic86—23no—
100C4×Dic86—23no—
101D4×Dic43—23no—
102D4×Dic43—23no—
103D4×Dic43—23no—
104D4×Dic43—23no—
105D4×Dic43—26no—
106D4×Dic43—23no—
107D4×Dic43—23no—
108D4×Dic43—23no—
109D4×Dic43—23no—
110D4×Dic43D413yes—
111D4×Dic43D413yes—
112D4×Dic43C2313yes—
113D4×Dic43C2316yes—
114D4×Dic43C2313yes—
115#13063284—23no—
116#13063284—23no—
117#13063284C2313yes—
118#13063284C2313yes—
119#13063284C2313yes—
120C2×C4⋊Dic43—23no—
121C2×C4⋊Dic43—23no—
122C2×C4⋊Dic43C2313yes—
123C2×C4⋊Dic43C2313yes—
124C2×Dic43⋊C4—23no—
125C2×C22⋊Dic43—23no—
126C2×C22⋊Dic43—26no—
127C2×C4×Dic43—23no—
128C2×C4×Dic43C2313yes—
129#13063259C2313yes—
130#13063259C2313yes—
131#13063258C2311yescharacteristic
132#13063258C2316yes—
133#13063258C2313yes—
134#13063257C2313yes—
135#13063257C2316yes—
136#13063257C2311yescharacteristic
137#13063256C2313yes—
138#13063256C2313yes—
139Dic43⋊C8C2311yescharacteristic
140Dic43⋊C8C2313yes—
141Dic43⋊C8C2313yes—
142Dic43⋊C8C2313yes—
143Dic43⋊C8C2316yes—
144#13063249C2311yescharacteristic
145#13063249C2313yes—
146#13063246C2313yes—
147#13063246C2316yes—
148#13063246C2313yes—
149H(5,𝔽2)×C43—24no—
150H(5,𝔽2)×C43Q818yescomplemented
151C2×#41×C43—21no—
152C2×#41×C43C2313yes—
153C2×#41×C43C2311yescharacteristic
154C22×D4×C43—23no—
155C22×D4×C43C2313yes—
156#131×C43—24no—
157C2×M16×C43C2313yes—
158C22×C8×C43C2313yes—
159C4×Q8×C43—21no—
160C4×D4×C43—23no—
161#117×C43C2313yes—
162C2×C4⋊C4×C43C2313yes—
163#103×C43C2311yescharacteristic
164#103×C43C2313yes—
165#102×C43C2313yes—
166#102×C43C2316yes—
167#102×C43C2313yes—
168C24×C43—23no—
169#41×C43—28no—
170#41×C43—26no—
171#41×C43C2×Q8112yes—
172#41×C43C2×Q814yes—
173#41×C43#4114yes—
174C2×Q8×C43C2×D411yescharacteristic
175C2×Q8×C43C2411yescharacteristic
176C2×D4×C43—224no—
177C2×D4×C43—23no—
178C2×D4×C43—26no—
179C2×D4×C43—23no—
180C2×D4×C43C2×D413yes—
181C2×D4×C43C2×Q8112yes—
182C2×D4×C43C2413yes—
183C22×C4×C43—23no—
184C22×C4×C43—23no—
185C22×C4×C43C2413yes—
186C22×Dic43—23no—
187C22×Dic43—23no—
188C22×Dic43—26no—
189C22×Dic43—23no—
190C22×Dic43—23no—
191C22×Dic43—86no—
192C22×Dic43C2×D413yes—
193C22×Dic43C2×D413yes—
194C2×Dic86—23no—
195C2×Dic86—23no—
196M16×C43—26no—
197C2×C8×C43—26no—
198C2×C8×C43C2411yescharacteristic
199C2×C8×C43C2413yes—
200C4⋊C4×C43—23no—
201C4⋊C4×C43C2413yes—
202C4⋊C4×C43C2411yescharacteristic
203C22⋊C4×C43—23no—
204C42×C43—23no—
205C22⋊Dic43—23no—
206C22⋊Dic43—26no—
207C22⋊Dic43—23no—
208C22⋊Dic43—23no—
209C22⋊Dic43—23no—
210C22⋊Dic43C2×D416yes—
211C4⋊Dic43—23no—
212C4⋊Dic43—23no—
213C4⋊Dic43—23no—
214C4⋊Dic43—23no—
215C4⋊Dic43—26no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43C2×D413yes—
219C4⋊Dic43C2×D413yes—
220C4⋊Dic43C2413yes—
221C4⋊Dic43C2411yescharacteristic
222C4⋊Dic43C2411yescharacteristic
223C4⋊Dic43C2413yes—
224Dic43⋊C4—23no—
225Dic43⋊C4—26no—
226Dic43⋊C4—21no—
227Dic43⋊C4—23no—
228Dic43⋊C4—23no—
229C4×Dic43—23no—
230C4×Dic43—23no—
231C4×Dic43—21no—
232C4×Dic43—23no—
233C4×Dic43C2×D413yes—
234C4×Dic43C2×D413yes—
235C4×Dic43C2411yescharacteristic
236C4×Dic43C2413yes—
237#10621877—26no—
238C2×C43⋊C8—26no—
239C2×C43⋊C8C2413yes—
240C2×C43⋊C8C2411yescharacteristic
241C23×C43—23no—
242C23×C43—212no—
243C23×C43—83no—
244C23×C43—83no—
245C23×C43C22×D413yes—
246Q8×C43—21no—
247Q8×C43C22⋊Q814yes—
248Q8×C43C22×Q812yes—
249D4×C43—212no—
250D4×C43—212no—
251D4×C43—23no—
252D4×C43C22⋊Q8112yes—
253D4×C43C22×Q816yes—
254C2×C4×C43—21no—
255C2×C4×C43—212no—
256C2×C4×C43—23no—
257C2×C4×C43—21no—
258C2×C4×C43—83no—
259C2×C4×C43C22×D413yes—
260C2×C4×C43C22×Q816yes—
261C2×C4×C43C2×#4116yes—
262C2×C4×C43C2511yescharacteristic
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—23no—
266C2×Dic43—23no—
267C2×Dic43—43no—
268C2×Dic43—43no—
269C2×Dic43—46no—
270C2×Dic43—83no—
271C2×Dic43—86no—
272C2×Dic43—83no—
273C2×Dic43—83no—
274C2×Dic43C22×D411yescharacteristic
275C2×Dic43C22×D413yes—
276C2×Dic43C22×D411yescharacteristic
277C2×Dic43C22×D413yes—
278Dic86—83no—
279Dic86—83no—
280C8×C43—21no—
281C8×C43—23no—
282C43⋊C8—21no—
283C43⋊C8—23no—
284#60496—431nomaximal, Sylow
285C22×C43—23no—
286C22×C43—23no—
287C22×C43—26no—
288C22×C43—43no—
289C22×C43—43no—
290C22×C43—812no—
291C22×C43C2×C22⋊Q816yes—
292C22×C43C23×D411yescharacteristic
293C4×C43—22no—
294C4×C43—41no—
295C4×C43—43no—
296C4×C43C2×C22⋊Q816yes—
297C4×C43C23×Q811yescharacteristic
298C4×C43C22×#4111yescharacteristic
299Dic43—23no—
300Dic43—21no—
301Dic43—23no—
302Dic43—21no—
303Dic43—43no—
304Dic43—41no—
305Dic43—41no—
306Dic43—43no—
307#3504—431no—
308C4×H(5,𝔽2)—431no—
309#3084—433no—
310#3083—433no—
311#3081—433no—
312#3081—433no—
313#3080—433no—
314#3077—433no—
315#3076—433no—
316C2×#478—433no—
317#2913—431no—
318#2912—431no—
319#2906—431no—
320#2897—431no—
321#2897D4311yescharacteristic
322C2×C43—26no—
323C2×C43—46no—
324C2×C43C22×C22⋊Q811yescharacteristic
325C2×C43#358411yescharacteristic
326C2×C43#358511yescharacteristic
327C2×H(5,𝔽2)C2×D4311yescharacteristic
328C2×#131—431no—
329C2×#131C2×D4311yescharacteristic
330#557—861no—
331#557—861no—
332#554—863no—
333#554—863no—
334#544—433no—
335#544—433no—
336#533—433no—
337C2×#125—433no—
338#520—431no—
339#520—431no—
340#520—433no—
341#520—861no—
342#520C2×D4311yescharacteristic
343#518—433no—
344#518—863no—
345C4×#41—431no—
346C4×#41—433no—
347C4×#41—861no—
348C2×C4×D4—433no—
349C2×C4×D4—863no—
350#479—431no—
351#479—433no—
352#479—436no—
353#478—433no—
354#478—436no—
355#478—436no—
356#478—436no—
357#478—433no—
358#478—436no—
359#477—433no—
360#476—433no—
361#476—436no—
362#475—433no—
363#474—433no—
364#474—436no—
365#428—433no—
366#428—433no—
367#428—433no—
368#428—433no—
369#427—433no—
370#427—433no—
371C2×#107—433no—
372C2×#106—433no—
373#424—433no—
374#424—433no—
375#423—433no—
376C2×C4⋊C8—433no—
377#418—433no—
378#418C2×D4313yes—
379#417—433no—
380#417C2×D4313yes—
381#416—433no—
382#416C2×D4313yes—
383C2×#102—433no—
384C2×#102C2×D4313yes—
385C43#6049611yescharacteristic, complemented, Sylow
386H(5,𝔽2)—24no—
387H(5,𝔽2)Dic8618yescomplemented
388C2×#41—21no—
389C2×#41C22×D4313yes—
390C2×#41C22×D4311yescharacteristic
391C22×D4—23no—
392C22×D4C22×D4313yes—
393C23×C4—863no—
394#131—24no—
395#131—864no—
396C2×M16—433no—
397C2×M16C22×D4313yes—
398C22×C8—433no—
399C22×C8C22×D4313yes—
400C4⋊Q8—433no—
401C4⋊Q8—433no—
402C4⋊Q8—863no—
403C4⋊Q8—863no—
404#125—433no—
405#125—436no—
406#125—431no—
407#125—863no—
408#125—863no—
409#125—863no—
410#125—863no—
411C22⋊Q8—866no—
412C22⋊Q8—863no—
413C22⋊Q8—863no—
414C22⋊Q8—866no—
415C4×Q8—21no—
416C4×Q8—431no—
417C4×Q8—431no—
418C4×Q8—431no—
419C4×Q8—433no—
420C4×Q8—863no—
421C4×Q8—863no—
422C4×Q8—861no—
423C4×Q8—861no—
424C4×D4—23no—
425C4×D4—433no—
426C4×D4—433no—
427C4×D4—433no—
428C4×D4—436no—
429C4×D4—433no—
430C4×D4—863no—
431C4×D4—863no—
432C4×D4—866no—
433C4×D4—863no—
434C4×D4—863no—
435C4×D4—863no—
436C4×D4—863no—
437C4×D4—863no—
438C4×D4—863no—
439#117—433no—
440#117—433no—
441#117—433no—
442#117—863no—
443#117—863no—
444#117C22×D4313yes—
445C2×C4⋊C4—433no—
446C2×C4⋊C4—433no—
447C2×C4⋊C4—863no—
448C2×C4⋊C4—863no—
449C2×C4⋊C4—863no—
450C2×C4⋊C4C22×D4313yes—
451C2×C22⋊C4—866no—
452C2×C22⋊C4—863no—
453C2×C42—433no—
454C2×C42—863no—
455#107—433no—
456#107—433no—
457#107—433no—
458#107—436no—
459#107—431no—
460#106—433no—
461#106—436no—
462#106—431no—
463#106—433no—
464#106—433no—
465C4⋊C8—431no—
466C4⋊C8—433no—
467C4⋊C8—433no—
468C4⋊C8—433no—
469C4⋊C8—436no—
470#103—431no—
471#103—433no—
472#103C22×D4311yescharacteristic
473#103C22×D4313yes—
474#102—433no—
475#102—436no—
476#102—433no—
477#102C22×D4313yes—
478#102C22×D4316yes—
479#102C22×D4313yes—
480C24—23no—
481#41—28no—
482#41—26no—
483#41C2×Dic86112yes—
484#41C2×Dic8614yes—
485#41#1062190014yes—
486C2×Q8—863no—
487C2×Q8—863no—
488C2×Q8D4×D4311yescharacteristic
489C2×Q8C23×D4311yescharacteristic
490C2×D4—23no—
491C2×D4—224no—
492C2×D4—23no—
493C2×D4—26no—
494C2×D4C2×Dic86112yes—
495C2×D4D4×D4313yes—
496C2×D4C23×D4313yes—
497C22×C4—23no—
498C22×C4—23no—
499C22×C4—433no—
500C22×C4—433no—
501C22×C4—863no—
502C22×C4—866no—
503C22×C4—863no—
504C22×C4—863no—
505C22×C4—863no—
506C22×C4—3446no—
507C22×C4C23×D4313yes—
508M16—26no—
509M16—866no—
510C2×C8—26no—
511C2×C8—433no—
512C2×C8—431no—
513C2×C8—866no—
514C2×C8C23×D4311yescharacteristic
515C2×C8C23×D4313yes—
516C4⋊C4—23no—
517C4⋊C4—433no—
518C4⋊C4—433no—
519C4⋊C4—433no—
520C4⋊C4—431no—
521C4⋊C4—433no—
522C4⋊C4—431no—
523C4⋊C4—863no—
524C4⋊C4—863no—
525C4⋊C4—863no—
526C4⋊C4—866no—
527C4⋊C4—866no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—863no—
532C4⋊C4—863no—
533C4⋊C4—863no—
534C4⋊C4—863no—
535C4⋊C4C23×D4311yescharacteristic
536C4⋊C4C23×D4313yes—
537C22⋊C4—23no—
538C22⋊C4—436no—
539C22⋊C4—863no—
540C22⋊C4—866no—
541C22⋊C4—863no—
542C22⋊C4—863no—
543C22⋊C4—863no—
544C42—23no—
545C42—433no—
546C42—433no—
547C42—431no—
548C42—433no—
549C42—861no—
550C42—863no—
551C42—863no—
552C42—863no—
553C23—23no—
554C23—212no—
555C23—83no—
556C23—83no—
557C23C2×D4×D4313yes—
558Q8—21no—
559Q8—3443no—
560Q8—3443no—
561Q8#1306330214yes—
562Q8C22×Dic8612yes—
563D4—212no—
564D4—212no—
565D4—23no—
566D4#13063302112yes—
567D4C22×Dic8616yes—
568C2×C4—21no—
569C2×C4—212no—
570C2×C4—21no—
571C2×C4—23no—
572C2×C4—83no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—433no—
576C2×C4—433no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—863no—
580C2×C4—863no—
581C2×C4—3446no—
582C2×C4—3443no—
583C2×C4—3443no—
584C2×C4—3443no—
585C2×C4—1723no—
586C2×C4—1723no—
587C2×C4—1726no—
588C2×C4C2×D4×D4313yes—
589C2×C4C22×Dic8616yes—
590C2×C4C2×#1062190016yes—
591C2×C4C24×D4311yescharacteristic
592C8—21no—
593C8—23no—
594C8—861no—
595C8—863no—
596C22—23no—
597C22—23no—
598C22—26no—
599C22—43no—
600C22—43no—
601C22—812no—
602C22C2×#1306330216yes—
603C22C22×D4×D4311yescharacteristic
604C4—22no—
605C4—41no—
606C4—43no—
607C4—863no—
608C4—861no—
609C4—863no—
610C4—861no—
611C4—1721no—
612C4—1723no—
613C4—1723no—
614C4—1721no—
615C4C2×#1306330216yes—
616C4C23×Dic8611yescharacteristic
617C4C22×#1062190011yescharacteristic
618C2—26no—
619C2—46no—
620C2C22×#1306330211yescharacteristic
621C2#1914936711yescharacteristic
622C2#1914937011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2897C2
socleC22×C43C23×D4
prime radicalC2×H(5,𝔽2)×C43C22
hypercenter#2897D43
hypocenterC43#60496
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2897

Complements

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

NH ≅ G/Ntype
1. #19148417C2semidirect
3. #19144455C2semidirect
4. #19144450C2semidirect
5. #19144428C2semidirect
6. #19144422C2semidirect
7. #19144415C2semidirect
8. #19144389C2semidirect
9. #19144379C2semidirect
10. C2×#14583201C2semidirect
11. #19143193C2semidirect
12. #19143190C2semidirect
13. #19143161C2semidirect
21. #14583530C22semidirect
22. #14583527C22semidirect
23. #14583452C22semidirect
24. C2×#13063316C22semidirect
36. #14583208C22semidirect
37. #14583204C22semidirect
38. #14583204C22semidirect
39. #14583201C22semidirect
40. #14583201C22semidirect
41. #14583201C22semidirect
42. #14583201C22semidirect
43. #14583197C22semidirect
44. #14583197C22semidirect
45. #14583192C22semidirect
46. #14583187C22semidirect
47. #14583187C22semidirect
48. #14583182C22semidirect
49. #14583177C22semidirect
50. #14583177C22semidirect
51. #14582942C22semidirect
52. #14582941C22semidirect
53. #14582941C22semidirect
54. #14582939C22semidirect
55. #14582937C22semidirect
56. #14582935C22semidirect
57. C2×#13063258C22semidirect
58. C2×#13063257C22semidirect
59. #14582927C22semidirect
60. #14582925C22semidirect
61. #14582922C22semidirect
62. C2×Dic43⋊C8C22semidirect
150. H(5,𝔽2)×C43Q8semidirect
385. C43#60496semidirect
387. H(5,𝔽2)Dic86semidirect

Maximal subgroups

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

subgroupindex
#191484172
H(5,𝔽2)×Dic432
#191444552
#191444502
#191444282
#191444222
#191444152
#191443892
#191443792
C2×#145832012
#191431932
#191431902
#191431612
#191431212
C43×#28972
#6049643