Finite Group Databasebeta

← #25964278

Subgroups — #25964278

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#19148421C211yesmaximal, characteristic, complemented
2C4×#13063371C211yesmaximal, characteristic
3#19144459C213yesmaximal, complemented
4#19144448C213yesmaximal, complemented
5#19144427C213yesmaximal, complemented
6#19144427C213yesmaximal, complemented
7#19144418C213yesmaximal, complemented
8#19144394C213yesmaximal, complemented
9#19144385C213yesmaximal, complemented
10C2×#14583200C213yesmaximal, complemented
11#19143195C211yesmaximal, characteristic, complemented
12#19143190C211yesmaximal, characteristic, complemented
13#19143122C211yesmaximal, characteristic
14#19143122C211yesmaximal, characteristic
15C43×#2906C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17#14583625—21no—
18#14583625—21no—
19#14583608—23no—
20#14583608—23no—
21#14583527C2213yescomplemented
22#14583527C2213yescomplemented
23#14583456C2213yescomplemented
24C2×#13063317C2213yescomplemented
25#14583382C2211yescharacteristic
26#14583382C2211yescharacteristic
27#14583382C2211yescharacteristic
28#14583381—21no—
29#14583379C2213yes—
30#14583373C2213yes—
31#14583371—23no—
32C4×#10621902—21no—
33C4×#10621898C2213yes—
34C2×C4×D172C2213yes—
35C4×D4×D43—23no—
36#14583207C2216yescomplemented
37#14583207C2211yescharacteristic, complemented
38#14583207C2213yescomplemented
39#14583200C2216yescomplemented
40#14583200C2216yescomplemented
41#14583200C2213yescomplemented
42#14583200C2216yescomplemented
43#14583200C2213yescomplemented
44#14583200C2216yescomplemented
45#14583195C2213yescomplemented
46#14583190C2216yescomplemented
47#14583190C2213yescomplemented
48#14583185C2213yescomplemented
49#14583180C2216yescomplemented
50#14583180C2213yescomplemented
51#14582941C2213yescomplemented
52#14582941C2213yescomplemented
53#14582941C2213yescomplemented
54#14582941C2213yescomplemented
55#14582937C2213yescomplemented
56#14582937C2213yescomplemented
57C2×#13063259C2213yescomplemented
58C2×#13063257C2213yescomplemented
59#14582905C2213yes—
60#14582905C2213yes—
61#14582901C2213yes—
62#14582901C2213yes—
63#14582896C2213yes—
64#14582896C2213yes—
65C2×#13063247C2213yes—
66C2×#13063247C2213yes—
67C2×#131×C43C2211yescharacteristic
68C2×#131×C43C2211yescharacteristic
69C4×#41×C43C2211yescharacteristic
70C43×#424C2213yescomplemented
71C43×#424C2213yescomplemented
72C43×#423C2213yescomplemented
73C2×C4⋊C8×C43C2213yescomplemented
74#13063371—24no—
75#13063371Q818yescomplemented
76C2×#10621902—21no—
77C2×#10621898C2313yes—
78C22×D172C2313yes—
79C2×D4×D43—23no—
80C22×C4×D43—23no—
81#13063325C2313yes—
82#13063325C2313yes—
83#13063324—23no—
84#13063324—23no—
85#13063317—23no—
86#13063317—23no—
87#13063317C2313yes—
88#13063317C2316yes—
89#13063317C2311yescharacteristic
90#13063316—23no—
91#13063316—23no—
92#13063304—23no—
93#13063304—23no—
94#13063302—26no—
95#13063302—26no—
96Q8×Dic43—21no—
97Q8×Dic43—21no—
98Q8×Dic43—21no—
99C4×Dic86—23no—
100C4×Dic86—23no—
101C4×Dic86C2311yescharacteristic
102C4×Dic86C2313yes—
103C4×D172—23no—
104C4×D172—23no—
105C4×D172C2313yes—
106C4×D172C2316yes—
107C4×D172C2313yes—
108D4×Dic43—23no—
109D4×Dic43—23no—
110D4×Dic43—23no—
111#13063287—23no—
112#13063287—23no—
113C4×C22⋊D43—23no—
114C4×C22⋊D43—23no—
115(C22⋊D43)⋊C4—26no—
116#13063284C2313yes—
117#13063284C2313yes—
118#13063284C2313yes—
119#13063283—23no—
120#13063282—23no—
121C2×C4⋊Dic43C2313yes—
122C2×C4⋊Dic43C2313yes—
123C2×C4⋊Dic43C2313yes—
124C2×Dic43⋊C4—23no—
125C2×Dic43⋊C4—23no—
126C4⋊C4×D43—23no—
127C2×(C2×D43)⋊C4—23no—
128C22⋊C4×D43—26no—
129C42×D43—23no—
130#13063259C2311yescharacteristic
131#13063259C2313yes—
132#13063259C2316yes—
133#13063259C2313yes—
134#13063259C2313yes—
135#13063257C2313yes—
136#13063257C2313yes—
137#13063257C2316yes—
138#13063257C2311yescharacteristic
139#13063257C2313yes—
140#13063250C2311yescharacteristic
141#13063250C2311yescharacteristic
142#13063250C2313yes—
143#13063250C2313yes—
144#13063247C2313yes—
145#13063247C2313yes—
146#13063247C2316yes—
147#13063247C2316yes—
148#13063247C2313yes—
149#13063247C2313yes—
150C2×#41×C43C2311yescharacteristic
151#131×C43—24no—
152#131×C43—24no—
153C2×M16×C43C2313yes—
154C2×M16×C43C2313yes—
155C22×C8×C43C2313yes—
156C22×C8×C43C2313yes—
157C4×Q8×C43D411yescharacteristic
158C4×Q8×C43D411yescharacteristic
159C4×D4×C43D413yes—
160C4×D4×C43D413yes—
161#117×C43C2313yes—
162C2×C42×C43C2313yes—
163C4⋊C8×C43C2316yes—
164C4⋊C8×C43C2313yes—
165C4⋊C8×C43C2313yes—
166C4⋊C8×C43C2311yescharacteristic
167C4⋊C8×C43C2313yes—
168C23×D43—23no—
169#41×C43C2×Q814yes—
170#41×C43#4114yes—
171C2×Q8×C43C2×D411yescharacteristic
172C2×D4×C43C2×D413yes—
173C22×C4×C43C2×D413yes—
174C22×C4×C43C2×D413yes—
175C22×C4×C43C2413yes—
176C2×C22⋊D43—23no—
177C22×Dic43—23no—
178C22×Dic43—23no—
179C22×Dic43—23no—
180#10621902—28no—
181D4×D43—224no—
182#10621898—26no—
183#10621898C2×Q8112yes—
184C2×D172—23no—
185C2×D172—26no—
186C2×D172C2×Q8112yes—
187C2×D172C2413yes—
188C2×C4×D43—23no—
189C2×C4×D43—23no—
190C2×C4×D43—23no—
191C2×C4×D43—26no—
192C2×C4×D43—86no—
193C2×Dic86—23no—
194C2×Dic86—23no—
195C2×Dic86C2411yescharacteristic
196M16×C43—26no—
197M16×C43—26no—
198C2×C8×C43—26no—
199C2×C8×C43—26no—
200C2×C8×C43C2411yescharacteristic
201C2×C8×C43C2411yescharacteristic
202C2×C8×C43C2413yes—
203C2×C8×C43C2413yes—
204C4⋊C4×C43C2×D413yes—
205C4⋊C4×C43C2×D413yes—
206C22⋊C4×C43C2×D416yes—
207C42×C43C2×D413yes—
208C42×C43C2×D413yes—
209C42×C43C2411yescharacteristic
210C42×C43C2413yes—
211C22⋊Dic43—23no—
212C22⋊Dic43—23no—
213C22⋊Dic43—23no—
214(C2×D43)⋊C4—23no—
215(C2×D43)⋊C4—26no—
216(C2×D43)⋊C4—23no—
217C4⋊Dic43—23no—
218C4⋊Dic43—23no—
219C4⋊Dic43—23no—
220C4⋊Dic43—23no—
221C4⋊Dic43—23no—
222C4⋊Dic43C2413yes—
223C4⋊Dic43C2411yescharacteristic
224C4⋊Dic43C2413yes—
225C4⋊Dic43C2411yescharacteristic
226C4⋊Dic43C2413yes—
227C4⋊Dic43C2411yescharacteristic
228Dic43⋊C4—23no—
229Dic43⋊C4—23no—
230Dic43⋊C4—23no—
231Dic43⋊C4—26no—
232Dic43⋊C4—26no—
233Dic43⋊C4—21no—
234Dic43⋊C4—21no—
235Dic43⋊C4—21no—
236C4×Dic43—21no—
237C4×Dic43—23no—
238C4×Dic43—23no—
239C4×Dic43—23no—
240C4×Dic43—23no—
241C23×C43C22×D413yes—
242C22×D43—23no—
243C22×D43—212no—
244C22×D43—83no—
245C22×D43—83no—
246Q8×C43C22⋊Q814yes—
247D4×C43C22⋊Q8112yes—
248C2×C4×C43—43no—
249C2×C4×C43—43no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D413yes—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D413yes—
254C2×C4×C43C22×D413yes—
255C2×C4×C43C22×Q816yes—
256C2×C4×C43C2×#4116yes—
257C2×C4×C43C2511yescharacteristic
258C22⋊D43—212no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—23no—
264C2×Dic43—23no—
265C2×Dic43—23no—
266C2×Dic43—83no—
267C2×Dic43—83no—
268C2×Dic43—83no—
269D172—212no—
270D172—23no—
271D172C22×Q816yes—
272C4×D43—212no—
273C4×D43—46no—
274C4×D43—83no—
275C4×D43—86no—
276Dic86—21no—
277Dic86—83no—
278Dic86—83no—
279Dic86C22×Q812yes—
280C8×C43—21no—
281C8×C43—21no—
282C8×C43—23no—
283C8×C43—23no—
284#60496—431nomaximal, Sylow
285C22×C43—23no—
286C22×C43—23no—
287C22×C43C2×C22⋊Q816yes—
288C22×C43C23×D411yescharacteristic
289C2×D43—26no—
290C2×D43—43no—
291C2×D43—43no—
292C2×D43—812no—
293C4×C43—23no—
294C4×C43—21no—
295C4×C43—23no—
296C4×C43—21no—
297C4×C43C2×C22⋊Q816yes—
298C4×C43C23×Q811yescharacteristic
299C4×C43C22×#4111yescharacteristic
300Dic43—22no—
301Dic43—41no—
302Dic43—43no—
303Dic43—41no—
304Dic43—41no—
305Dic43—43no—
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#2906D4311yescharacteristic, complemented
320#2897—431no—
321#2897—431no—
322C2×C43—26no—
323C2×C43C22×C22⋊Q811yescharacteristic
324C2×C43#358411yescharacteristic
325C2×C43#358511yescharacteristic
326D43—46no—
327C2×H(5,𝔽2)—431no—
328C2×#131C2×D4311yescharacteristic
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—431no—
341#520—433no—
342#520—861no—
343#518—433no—
344#518—863no—
345C4×#41—433no—
346C4×#41—861no—
347C4×#41C2×D4311yescharacteristic
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#424C2×D4313yescomplemented
374#424C2×D4313yescomplemented
375#423C2×D4313yescomplemented
376C2×C4⋊C8C2×D4313yescomplemented
377#418—433no—
378#418—433no—
379#417—433no—
380#417—433no—
381#416—433no—
382#416—433no—
383C2×#102—433no—
384C2×#102—433no—
385C43#6049611yescharacteristic, complemented, Sylow
386H(5,𝔽2)—438no—
387H(5,𝔽2)—864no—
388C2×#41—433no—
389C2×#41—861no—
390C2×#41C22×D4311yescharacteristic
391C22×D4—433no—
392C22×D4—863no—
393C23×C4—863no—
394#131—24no—
395#131—24no—
396C2×M16C22×D4313yes—
397C2×M16C22×D4313yes—
398C22×C8C22×D4313yes—
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—863no—
412C22⋊Q8—863no—
413C22⋊Q8—866no—
414C22⋊Q8—866no—
415C4×Q8—431no—
416C4×Q8—433no—
417C4×Q8—861no—
418C4×Q8—861no—
419C4×Q8—861no—
420C4×Q8—863no—
421C4×Q8—863no—
422C4×Q8D17211yescharacteristic
423C4×Q8D17211yescharacteristic
424C4×D4—433no—
425C4×D4—436no—
426C4×D4—433no—
427C4×D4—863no—
428C4×D4—863no—
429C4×D4—863no—
430C4×D4—863no—
431C4×D4—863no—
432C4×D4—863no—
433C4×D4—863no—
434C4×D4—866no—
435C4×D4—863no—
436C4×D4—863no—
437C4×D4D17213yes—
438C4×D4D17213yes—
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—433no—
448C2×C4⋊C4—863no—
449C2×C4⋊C4—863no—
450C2×C4⋊C4—863no—
451C2×C22⋊C4—863no—
452C2×C22⋊C4—866no—
453C2×C42—863no—
454C2×C42C22×D4313yes—
455#107—433no—
456#107—436no—
457#107—431no—
458#107—433no—
459#107—433no—
460#106—433no—
461#106—436no—
462#106—431no—
463#106—433no—
464#106—433no—
465C4⋊C8C22×D4311yescharacteristic
466C4⋊C8C22×D4313yes—
467C4⋊C8C22×D4313yes—
468C4⋊C8C22×D4313yes—
469C4⋊C8C22×D4316yes—
470#103—431no—
471#103—431no—
472#103—433no—
473#103—433no—
474#102—433no—
475#102—433no—
476#102—436no—
477#102—436no—
478#102—433no—
479#102—433no—
480C24—863no—
481#41—4312no—
482#41—868no—
483#41—866no—
484#41#1062190014yes—
485#41Q8×D4314yes—
486C2×Q8—431no—
487C2×Q8—863no—
488C2×Q8—863no—
489C2×Q8C2×D17211yescharacteristic
490C2×D4—4312no—
491C2×D4—433no—
492C2×D4—863no—
493C2×D4—8624no—
494C2×D4—863no—
495C2×D4—866no—
496C2×D4C2×D17213yes—
497C22×C4—863no—
498C22×C4—863no—
499C22×C4—863no—
500C22×C4—863no—
501C22×C4—863no—
502C22×C4—866no—
503C22×C4—863no—
504C22×C4—3446no—
505C22×C4C2×D17213yes—
506C22×C4C2×D17213yes—
507C22×C4C23×D4313yes—
508M16—26no—
509M16—26no—
510C2×C8—26no—
511C2×C8—26no—
512C2×C8C23×D4311yescharacteristic
513C2×C8C23×D4313yes—
514C2×C8C23×D4313yes—
515C2×C8C23×D4311yescharacteristic
516C4⋊C4—433no—
517C4⋊C4—431no—
518C4⋊C4—433no—
519C4⋊C4—431no—
520C4⋊C4—433no—
521C4⋊C4—431no—
522C4⋊C4—863no—
523C4⋊C4—863no—
524C4⋊C4—863no—
525C4⋊C4—863no—
526C4⋊C4—863no—
527C4⋊C4—863no—
528C4⋊C4—866no—
529C4⋊C4—866no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—863no—
534C4⋊C4—863no—
535C4⋊C4C2×D17213yes—
536C4⋊C4C2×D17213yes—
537C22⋊C4—863no—
538C22⋊C4—863no—
539C22⋊C4—863no—
540C22⋊C4—863no—
541C22⋊C4—866no—
542C22⋊C4—863no—
543C22⋊C4C2×D17216yes—
544C42—861no—
545C42—863no—
546C42—863no—
547C42—863no—
548C42—863no—
549C42C2×D17213yes—
550C42C2×D17213yes—
551C42C23×D4311yescharacteristic
552C42C23×D4313yes—
553C23—8612no—
554C23—863no—
555C23—3443no—
556C23—3443no—
557C23C22×D17213yes—
558Q8—432no—
559Q8—861no—
560Q8—3443no—
561Q8—3443no—
562Q8#1306330514yes—
563D4—436no—
564D4—8612no—
565D4—8612no—
566D4—863no—
567D4#13063305112yes—
568C2×C4—43no—
569C2×C4—43no—
570C2×C4—861no—
571C2×C4—8612no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—863no—
576C2×C4—863no—
577C2×C4—863no—
578C2×C4—3446no—
579C2×C4—3443no—
580C2×C4—3443no—
581C2×C4—3443no—
582C2×C4—3443no—
583C2×C4—1726no—
584C2×C4C22×D17211yescharacteristic
585C2×C4C22×D17213yes—
586C2×C4C22×D17211yescharacteristic
587C2×C4C22×D17213yes—
588C2×C4C22×D17213yes—
589C2×C4C2×Q8×D4316yes—
590C2×C4C2×#1062190016yes—
591C2×C4C24×D4311yescharacteristic
592C8—21no—
593C8—21no—
594C8—23no—
595C8—23no—
596C22—23no—
597C22—23no—
598C22—866no—
599C22—34412no—
600C22—1723no—
601C22—1723no—
602C22C2×#1306330516yes—
603C22C23×D17211yescharacteristic
604C4—21no—
605C4—23no—
606C4—21no—
607C4—23no—
608C4—862no—
609C4—1721no—
610C4—1723no—
611C4—1721no—
612C4—1723no—
613C4—1723no—
614C4—1721no—
615C4C2×#1306330516yes—
616C4C22×Q8×D4311yescharacteristic
617C4C22×#1062190011yescharacteristic
618C2—26no—
619C2—1726no—
620C2C22×#1306330511yescharacteristic
621C2#1914936911yescharacteristic
622C2#1914937611yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2906C2
socleC22×C43C23×D4
prime radicalC2×#13063371C22
hypercenter#2906D43
hypocenterC43#60496
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2906

Complements

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

NH ≅ G/Ntype
1. #19148421C2semidirect
3. #19144459C2semidirect
4. #19144448C2semidirect
5. #19144427C2semidirect
6. #19144427C2semidirect
7. #19144418C2semidirect
8. #19144394C2semidirect
9. #19144385C2semidirect
10. C2×#14583200C2semidirect
11. #19143195C2semidirect
12. #19143190C2semidirect
15. C43×#2906C2semidirect
21. #14583527C22semidirect
22. #14583527C22semidirect
23. #14583456C22semidirect
24. C2×#13063317C22semidirect
36. #14583207C22semidirect
37. #14583207C22semidirect
38. #14583207C22semidirect
39. #14583200C22semidirect
40. #14583200C22semidirect
41. #14583200C22semidirect
42. #14583200C22semidirect
43. #14583200C22semidirect
44. #14583200C22semidirect
45. #14583195C22semidirect
46. #14583190C22semidirect
47. #14583190C22semidirect
48. #14583185C22semidirect
49. #14583180C22semidirect
50. #14583180C22semidirect
51. #14582941C22semidirect
52. #14582941C22semidirect
53. #14582941C22semidirect
54. #14582941C22semidirect
55. #14582937C22semidirect
56. #14582937C22semidirect
57. C2×#13063259C22semidirect
58. C2×#13063257C22semidirect
70. C43×#424C22semidirect
71. C43×#424C22semidirect
72. C43×#423C22semidirect
73. C2×C4⋊C8×C43C22semidirect
75. #13063371Q8semidirect
319. #2906D43semidirect
373. #424C2×D43semidirect
374. #424C2×D43semidirect
375. #423C2×D43semidirect
376. C2×C4⋊C8C2×D43semidirect
385. C43#60496semidirect

Maximal subgroups

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

subgroupindex
#191484212
C4×#130633712
#191444592
#191444482
#191444272
#191444182
#191443942
#191443852
C2×#145832002
#191431952
#191431902
#191431222
C43×#29062
#6049643