Finite Group Databasebeta

← #25964277

Subgroups — #25964277

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
2#19144457C213yesmaximal, complemented
3#19144446C213yesmaximal, complemented
4#19144426C213yesmaximal, complemented
5#19144426C213yesmaximal, complemented
6#19144417C213yesmaximal, complemented
7#19144392C213yesmaximal, complemented
8#19144383C213yesmaximal, complemented
9C2×#14583199C213yesmaximal, complemented
10#19143193C211yesmaximal, characteristic, complemented
11#19143188C211yesmaximal, characteristic, complemented
12#19143163C211yesmaximal, characteristic, complemented
13#19143121C211yesmaximal, characteristic
14#19143121C211yesmaximal, characteristic
15C4×H(5,𝔽2)×C43C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583625—21no—
19#14583625—21no—
20#14583608—23no—
21#14583608—23no—
22#14583527C2213yescomplemented
23#14583527C2213yescomplemented
24#14583456C2213yescomplemented
25C2×#13063317C2213yescomplemented
26#14583382C2211yescharacteristic
27#14583382C2211yescharacteristic
28#14583206C2216yescomplemented
29#14583206C2211yescharacteristic, complemented
30#14583206C2213yescomplemented
31#14583199C2216yescomplemented
32#14583199C2213yescomplemented
33#14583199C2216yescomplemented
34#14583199C2216yescomplemented
35#14583199C2213yescomplemented
36#14583199C2216yescomplemented
37#14583194C2213yescomplemented
38#14583189C2216yescomplemented
39#14583189C2213yescomplemented
40#14583184C2213yescomplemented
41#14583179C2213yescomplemented
42#14583179C2216yescomplemented
43#14582942C2213yescomplemented
44#14582942C2213yescomplemented
45#14582939C2213yescomplemented
46#14582939C2213yescomplemented
47#14582935C2213yescomplemented
48#14582935C2213yescomplemented
49C2×#13063258C2213yescomplemented
50C2×#13063256C2213yescomplemented
51#14582926C2213yescomplemented
52#14582926C2213yescomplemented
53#14582923C2213yescomplemented
54C2×C4⋊(C43⋊C8)C2213yescomplemented
55#14582904C2213yes—
56#14582904C2213yes—
57#14582900C2213yes—
58#14582900C2213yes—
59#14582895C2213yes—
60#14582895C2213yes—
61C2×#13063246C2213yes—
62C2×#13063246C2213yes—
63C2×H(5,𝔽2)×C43C2211yescharacteristic
64C43×#520—21no—
65C43×#520C2213yes—
66C43×#520C2211yescharacteristic
67C43×#518—23no—
68C43×#518C2213yes—
69C4×#41×C43—21no—
70C4×#41×C43C2213yes—
71C4×#41×C43C2211yescharacteristic
72C2×C4×D4×C43—23no—
73C2×C4×D4×C43C2213yes—
74#13063332—24no—
75#13063332—24no—
76C2×#10621877C2313yes—
77C2×#10621877C2313yes—
78C22×C43⋊C8C2313yes—
79C22×C43⋊C8C2313yes—
80#13063325C2313yes—
81#13063325C2313yes—
82#13063324—23no—
83#13063324—23no—
84#13063317—23no—
85#13063317—23no—
86#13063317C2313yes—
87#13063317C2316yes—
88#13063317C2311yescharacteristic
89#13063316—23no—
90#13063316—23no—
91#13063304—23no—
92#13063304—23no—
93#13063302—26no—
94#13063302—26no—
95Q8×Dic43—21no—
96Q8×Dic43—21no—
97C4×Dic86—23no—
98C4×Dic86—23no—
99D4×Dic43—23no—
100D4×Dic43—23no—
101#13063284C2313yes—
102#13063284C2313yes—
103C2×C4⋊Dic43C2313yes—
104C2×C4⋊Dic43C2313yes—
105C2×Dic43⋊C4—23no—
106C2×Dic43⋊C4—23no—
107#13063258C2311yescharacteristic
108#13063258C2313yes—
109#13063258C2316yes—
110#13063258C2313yes—
111#13063258C2313yes—
112#13063256C2313yes—
113#13063256C2313yes—
114#13063256C2316yes—
115#13063256C2311yescharacteristic
116#13063256C2313yes—
117C4⋊(C43⋊C8)C2311yescharacteristic
118C4⋊(C43⋊C8)C2313yes—
119C4⋊(C43⋊C8)C2313yes—
120C4⋊(C43⋊C8)C2313yes—
121C4⋊(C43⋊C8)C2316yes—
122#13063249C2311yescharacteristic
123#13063249C2311yescharacteristic
124#13063249C2313yes—
125#13063249C2313yes—
126#13063246C2313yes—
127#13063246C2313yes—
128#13063246C2316yes—
129#13063246C2316yes—
130#13063246C2313yes—
131#13063246C2313yes—
132H(5,𝔽2)×C43—24no—
133H(5,𝔽2)×C43Q818yescomplemented
134C2×#41×C43—21no—
135C2×#41×C43C2313yes—
136C2×#41×C43C2311yescharacteristic
137C22×D4×C43—23no—
138C22×D4×C43C2313yes—
139C23×C4×C43—23no—
140C4×Q8×C43—21no—
141C4×Q8×C43D411yescharacteristic
142C4×Q8×C43D411yescharacteristic
143C4×Q8×C43C2311yescharacteristic
144C4×Q8×C43C2313yes—
145C4×D4×C43—23no—
146C4×D4×C43—23no—
147C4×D4×C43—23no—
148C4×D4×C43—23no—
149C4×D4×C43—23no—
150C4×D4×C43—26no—
151C4×D4×C43—23no—
152C4×D4×C43—23no—
153C4×D4×C43D413yes—
154C4×D4×C43D413yes—
155C4×D4×C43C2313yes—
156C4×D4×C43C2316yes—
157C4×D4×C43C2313yes—
158#117×C43—23no—
159#117×C43—23no—
160#117×C43C2313yes—
161#117×C43C2313yes—
162C2×C4⋊C4×C43—23no—
163C2×C4⋊C4×C43C2313yes—
164C2×C22⋊C4×C43—23no—
165C2×C22⋊C4×C43—26no—
166C2×C42×C43—23no—
167C2×C42×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×C43—23no—
186C22×C4×C43—26no—
187C22×C4×C43—23no—
188C22×C4×C43—86no—
189C22×C4×C43C2×D413yes—
190C22×C4×C43C2×D413yes—
191C22×C4×C43C2413yes—
192C22×Dic43—23no—
193C22×Dic43—23no—
194C2×Dic86—23no—
195C2×Dic86—23no—
196C4⋊C4×C43—23no—
197C4⋊C4×C43—23no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43C2×D413yes—
200C4⋊C4×C43C2×D413yes—
201C4⋊C4×C43C2413yes—
202C4⋊C4×C43C2411yescharacteristic
203C22⋊C4×C43—23no—
204C22⋊C4×C43—23no—
205C22⋊C4×C43—26no—
206C22⋊C4×C43—23no—
207C22⋊C4×C43C2×D416yes—
208C42×C43—21no—
209C42×C43—23no—
210C42×C43—23no—
211C42×C43C2×D413yes—
212C42×C43C2×D413yes—
213C42×C43C2411yescharacteristic
214C42×C43C2413yes—
215C22⋊Dic43—23no—
216C22⋊Dic43—23no—
217C4⋊Dic43—23no—
218C4⋊Dic43—23no—
219C4⋊Dic43—23no—
220C4⋊Dic43—23no—
221C4⋊Dic43C2413yes—
222C4⋊Dic43C2411yescharacteristic
223C4⋊Dic43C2413yes—
224C4⋊Dic43C2411yescharacteristic
225Dic43⋊C4—23no—
226Dic43⋊C4—23no—
227Dic43⋊C4—26no—
228Dic43⋊C4—26no—
229Dic43⋊C4—21no—
230Dic43⋊C4—21no—
231C4×Dic43—23no—
232C4×Dic43—23no—
233#10621877—26no—
234#10621877—26no—
235C2×C43⋊C8—26no—
236C2×C43⋊C8—26no—
237C2×C43⋊C8C2411yescharacteristic
238C2×C43⋊C8C2413yes—
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—21no—
257C2×C4×C43—23no—
258C2×C4×C43—43no—
259C2×C4×C43—43no—
260C2×C4×C43—46no—
261C2×C4×C43—83no—
262C2×C4×C43—86no—
263C2×C4×C43—83no—
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D413yes—
267C2×C4×C43C22×D413yes—
268C2×C4×C43C22×D413yes—
269C2×C4×C43C22×Q816yes—
270C2×C4×C43C2×#4116yes—
271C2×C4×C43C2511yescharacteristic
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—23no—
275C2×Dic43—23no—
276C2×Dic43—83no—
277C2×Dic43—83no—
278Dic86—83no—
279Dic86—83no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—23no—
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—23no—
294C4×C43—21no—
295C4×C43—23no—
296C4×C43—21no—
297C4×C43—22no—
298C4×C43—41no—
299C4×C43—43no—
300C4×C43C2×C22⋊Q816yes—
301C4×C43C23×Q811yescharacteristic
302C4×C43C22×#4111yescharacteristic
303Dic43—41no—
304Dic43—43no—
305Dic43—41no—
306Dic43—43no—
307#3504—431no—
308C4×H(5,𝔽2)D4311yescharacteristic
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#2897—431no—
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×#131—431no—
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—21no—
339#520—431no—
340#520—431no—
341#520C2×D4313yes—
342#520C2×D4311yescharacteristic
343#518—23no—
344#518C2×D4313yes—
345C4×#41—21no—
346C4×#41C2×D4313yes—
347C4×#41C2×D4311yescharacteristic
348C2×C4×D4—23no—
349C2×C4×D4C2×D4313yes—
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#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)—24no—
387H(5,𝔽2)Dic8618yescomplemented
388C2×#41—21no—
389C2×#41C22×D4313yes—
390C2×#41C22×D4311yescharacteristic
391C22×D4—23no—
392C22×D4C22×D4313yes—
393C23×C4—23no—
394#131—864no—
395#131—864no—
396C2×M16—433no—
397C2×M16—433no—
398C22×C8—433no—
399C22×C8—433no—
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—21no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×Q8—863no—
419C4×Q8—863no—
420C4×Q8C22⋊D4311yescharacteristic
421C4×Q8C22⋊D4311yescharacteristic
422C4×Q8C22×D4311yescharacteristic
423C4×Q8C22×D4313yes—
424C4×D4—23no—
425C4×D4—23no—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4—23no—
429C4×D4—26no—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—863no—
433C4×D4—863no—
434C4×D4C22⋊D4313yes—
435C4×D4C22⋊D4313yes—
436C4×D4C22×D4313yes—
437C4×D4C22×D4316yes—
438C4×D4C22×D4313yes—
439#117—23no—
440#117—23no—
441#117—433no—
442#117—433no—
443#117C22×D4313yes—
444#117C22×D4313yes—
445C2×C4⋊C4—23no—
446C2×C4⋊C4—433no—
447C2×C4⋊C4—433no—
448C2×C4⋊C4—863no—
449C2×C4⋊C4—863no—
450C2×C4⋊C4C22×D4313yes—
451C2×C22⋊C4—23no—
452C2×C22⋊C4—26no—
453C2×C42—23no—
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⋊C8—431no—
466C4⋊C8—433no—
467C4⋊C8—433no—
468C4⋊C8—433no—
469C4⋊C8—436no—
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—23no—
481#41—28no—
482#41—26no—
483#41C2×Dic86112yes—
484#41C2×Dic8614yes—
485#41#1062189814yes—
486C2×Q8—863no—
487C2×Q8—863no—
488C2×Q8C2×C22⋊D4311yescharacteristic
489C2×Q8C23×D4311yescharacteristic
490C2×D4—23no—
491C2×D4—224no—
492C2×D4—23no—
493C2×D4—26no—
494C2×D4C2×Dic86112yes—
495C2×D4C2×C22⋊D4313yes—
496C2×D4C23×D4313yes—
497C22×C4—23no—
498C22×C4—23no—
499C22×C4—23no—
500C22×C4—23no—
501C22×C4—26no—
502C22×C4—86no—
503C22×C4—863no—
504C22×C4—863no—
505C22×C4C2×C22⋊D4313yes—
506C22×C4C2×C22⋊D4313yes—
507C22×C4C23×D4313yes—
508M16—866no—
509M16—866no—
510C2×C8—431no—
511C2×C8—433no—
512C2×C8—433no—
513C2×C8—431no—
514C2×C8—866no—
515C2×C8—866no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—21no—
519C4⋊C4—433no—
520C4⋊C4—431no—
521C4⋊C4—433no—
522C4⋊C4—431no—
523C4⋊C4—863no—
524C4⋊C4—863no—
525C4⋊C4—863no—
526C4⋊C4—863no—
527C4⋊C4—866no—
528C4⋊C4—866no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—863no—
532C4⋊C4—863no—
533C4⋊C4C2×C22⋊D4313yes—
534C4⋊C4C2×C22⋊D4313yes—
535C4⋊C4C23×D4313yes—
536C4⋊C4C23×D4311yescharacteristic
537C22⋊C4—23no—
538C22⋊C4—23no—
539C22⋊C4—26no—
540C22⋊C4—23no—
541C22⋊C4—863no—
542C22⋊C4—863no—
543C22⋊C4C2×C22⋊D4316yes—
544C42—21no—
545C42—23no—
546C42—23no—
547C42—863no—
548C42—863no—
549C42C2×C22⋊D4313yes—
550C42C2×C22⋊D4313yes—
551C42C23×D4311yescharacteristic
552C42C23×D4313yes—
553C23—23no—
554C23—212no—
555C23—83no—
556C23—83no—
557C23C22×C22⋊D4313yes—
558Q8—21no—
559Q8—3443no—
560Q8—3443no—
561Q8#1306330414yes—
562Q8C22×Dic8612yes—
563D4—212no—
564D4—212no—
565D4—23no—
566D4#13063304112yes—
567D4C22×Dic8616yes—
568C2×C4—21no—
569C2×C4—212no—
570C2×C4—21no—
571C2×C4—23no—
572C2×C4—43no—
573C2×C4—43no—
574C2×C4—46no—
575C2×C4—86no—
576C2×C4—83no—
577C2×C4—83no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—863no—
581C2×C4—863no—
582C2×C4—3443no—
583C2×C4—3443no—
584C2×C4C22×C22⋊D4311yescharacteristic
585C2×C4C22×C22⋊D4313yes—
586C2×C4C22×C22⋊D4311yescharacteristic
587C2×C4C22×C22⋊D4313yes—
588C2×C4C22×C22⋊D4313yes—
589C2×C4C22×Dic8616yes—
590C2×C4C2×#1062189816yes—
591C2×C4C24×D4311yescharacteristic
592C8—861no—
593C8—861no—
594C8—863no—
595C8—863no—
596C22—23no—
597C22—23no—
598C22—26no—
599C22—43no—
600C22—43no—
601C22—812no—
602C22C2×#1306330416yes—
603C22C23×C22⋊D4311yescharacteristic
604C4—22no—
605C4—21no—
606C4—23no—
607C4—21no—
608C4—23no—
609C4—41no—
610C4—43no—
611C4—1723no—
612C4—1721no—
613C4—1723no—
614C4—1721no—
615C4C2×#1306330416yes—
616C4C23×Dic8611yescharacteristic
617C4C22×#1062189811yescharacteristic
618C2—26no—
619C2—46no—
620C2C22×#1306330411yescharacteristic
621C2#1914936611yescharacteristic
622C2#1914937511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC4×H(5,𝔽2)×C43C2
socleC22×C43C23×D4
prime radicalC2×H(5,𝔽2)×C43C22
hypercenterC4×H(5,𝔽2)D43
hypocenterC43#60496
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #19148421C2semidirect
2. #19144457C2semidirect
3. #19144446C2semidirect
4. #19144426C2semidirect
5. #19144426C2semidirect
6. #19144417C2semidirect
7. #19144392C2semidirect
8. #19144383C2semidirect
9. C2×#14583199C2semidirect
10. #19143193C2semidirect
11. #19143188C2semidirect
12. #19143163C2semidirect
22. #14583527C22semidirect
23. #14583527C22semidirect
24. #14583456C22semidirect
25. C2×#13063317C22semidirect
28. #14583206C22semidirect
29. #14583206C22semidirect
30. #14583206C22semidirect
31. #14583199C22semidirect
32. #14583199C22semidirect
33. #14583199C22semidirect
34. #14583199C22semidirect
35. #14583199C22semidirect
36. #14583199C22semidirect
37. #14583194C22semidirect
38. #14583189C22semidirect
39. #14583189C22semidirect
40. #14583184C22semidirect
41. #14583179C22semidirect
42. #14583179C22semidirect
43. #14582942C22semidirect
44. #14582942C22semidirect
45. #14582939C22semidirect
46. #14582939C22semidirect
47. #14582935C22semidirect
48. #14582935C22semidirect
49. C2×#13063258C22semidirect
50. C2×#13063256C22semidirect
51. #14582926C22semidirect
52. #14582926C22semidirect
53. #14582923C22semidirect
54. C2×C4⋊(C43⋊C8)C22semidirect
133. 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
#191484212
#191444572
#191444462
#191444262
#191444172
#191443922
#191443832
C2×#145831992
#191431932
#191431882
#191431632
#191431212
C4×H(5,𝔽2)×C432
#6049643