Finite Group Databasebeta

← #25964249

Subgroups — #25964249

Order 11008.

2090 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148408C211yesmaximal, characteristic, complemented
2H(5,𝔽2)×Dic43C211yesmaximal, characteristic
3#19144450C213yesmaximal, complemented
4#19144444C213yesmaximal, complemented
5#19144428C213yesmaximal, complemented
6#19144422C213yesmaximal, complemented
7#19144406C213yesmaximal, complemented
8#19144389C213yesmaximal, complemented
9#19144379C213yesmaximal, complemented
10C2×#14583177C213yesmaximal, complemented
11#19143195C211yesmaximal, characteristic, complemented
12#19143193C211yesmaximal, characteristic, complemented
13#19143161C211yesmaximal, characteristic, complemented
14#19143121C211yesmaximal, characteristic
15C43×#2897C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17Q8×Dic86—21no—
18#14583625—21no—
19#14583608—23no—
20D4×Dic86—23no—
21#14583530C2213yescomplemented
22#14583527C2213yescomplemented
23#14583452C2213yescomplemented
24C2×#13063324C2213yescomplemented
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#14583204C2213yescomplemented
38#14583201C2216yescomplemented
39#14583201C2213yescomplemented
40#14583197C2213yescomplemented
41#14583197C2216yescomplemented
42#14583192C2216yescomplemented
43#14583192C2211yescharacteristic, complemented
44#14583187C2213yescomplemented
45#14583187C2216yescomplemented
46#14583182C2213yescomplemented
47#14583177C2216yescomplemented
48#14583177C2213yescomplemented
49#14583177C2216yescomplemented
50#14583177C2216yescomplemented
51#14582942C2213yescomplemented
52#14582941C2213yescomplemented
53#14582941C2213yescomplemented
54#14582939C2213yescomplemented
55#14582937C2213yescomplemented
56#14582935C2213yescomplemented
57C2×#13063259C2213yescomplemented
58C2×#13063258C2213yescomplemented
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—
74C22×Dic86—23no—
75C23×Dic43—23no—
76#13063332—24no—
77C2×#10621877C2313yes—
78C22×C43⋊C8C2313yes—
79#13063325—23no—
80#13063324—23no—
81#13063324—23no—
82#13063324—23no—
83#13063324C2313yes—
84#13063324C2316yes—
85#13063324C2311yescharacteristic
86#13063317—23no—
87#13063316—23no—
88#13063316C2313yes—
89#13063316C2313yes—
90#13063304—26no—
91#13063302—23no—
92#13063302—23no—
93#13063302—26no—
94Q8×Dic43—21no—
95Q8×Dic43—21no—
96Q8×Dic43D411yescharacteristic
97Q8×Dic43D411yescharacteristic
98Q8×Dic43C2311yescharacteristic
99Q8×Dic43C2313yes—
100C4×Dic86—23no—
101C4×Dic86—23no—
102D4×Dic43—23no—
103D4×Dic43—23no—
104D4×Dic43—23no—
105D4×Dic43—23no—
106D4×Dic43—26no—
107D4×Dic43—23no—
108D4×Dic43—23no—
109D4×Dic43—23no—
110D4×Dic43—23no—
111D4×Dic43D413yes—
112D4×Dic43D413yes—
113D4×Dic43C2313yes—
114D4×Dic43C2316yes—
115D4×Dic43C2313yes—
116#13063284—23no—
117#13063284—23no—
118#13063284C2313yes—
119#13063284C2313yes—
120#13063284C2313yes—
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#13063259C2316yes—
131#13063259C2311yescharacteristic
132#13063258C2313yes—
133#13063258C2316yes—
134#13063258C2311yescharacteristic
135#13063257C2313yes—
136#13063257C2313yes—
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×C43C2313yes—
164#103×C43C2311yescharacteristic
165#102×C43C2313yes—
166#102×C43C2316yes—
167#102×C43C2313yes—
168C24×C43—23no—
169#41×C43—28no—
170#41×C43—26no—
171#41×C43C2×Q814yes—
172#41×C43C2×Q8112yescomplemented
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×Q8112yescomplemented
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—21no—
195C2×Dic86—23no—
196C2×Dic86—26no—
197C2×Dic86—86no—
198M16×C43—26no—
199C2×C8×C43—26no—
200C2×C8×C43C2411yescharacteristic
201C2×C8×C43C2413yes—
202C4⋊C4×C43—23no—
203C4⋊C4×C43C2413yes—
204C4⋊C4×C43C2411yescharacteristic
205C22⋊C4×C43—23no—
206C42×C43—23no—
207C22⋊Dic43—23no—
208C22⋊Dic43—26no—
209C22⋊Dic43—23no—
210C22⋊Dic43—23no—
211C22⋊Dic43—23no—
212C22⋊Dic43C2×D416yes—
213C4⋊Dic43—23no—
214C4⋊Dic43—23no—
215C4⋊Dic43—23no—
216C4⋊Dic43—21no—
217C4⋊Dic43—23no—
218C4⋊Dic43—23no—
219C4⋊Dic43C2×D413yes—
220C4⋊Dic43C2×D413yes—
221C4⋊Dic43C2411yescharacteristic
222C4⋊Dic43C2413yes—
223C4⋊Dic43C2411yescharacteristic
224C4⋊Dic43C2413yes—
225Dic43⋊C4—23no—
226Dic43⋊C4—26no—
227Dic43⋊C4—21no—
228Dic43⋊C4—23no—
229Dic43⋊C4—23no—
230C4×Dic43—23no—
231C4×Dic43—23no—
232C4×Dic43—21no—
233C4×Dic43—23no—
234C4×Dic43C2×D413yes—
235C4×Dic43C2×D413yes—
236C4×Dic43C2411yescharacteristic
237C4×Dic43C2413yes—
238#10621877—26no—
239C2×C43⋊C8—26no—
240C2×C43⋊C8C2413yes—
241C2×C43⋊C8C2411yescharacteristic
242C23×C43—23no—
243C23×C43—212no—
244C23×C43—83no—
245C23×C43—83no—
246C23×C43C22×D413yes—
247Q8×C43—21no—
248Q8×C43C22⋊Q814yes—
249Q8×C43C22×Q812yes—
250D4×C43—212no—
251D4×C43—212no—
252D4×C43—23no—
253D4×C43C22⋊Q8112yes—
254D4×C43C22×Q816yes—
255C2×C4×C43—21no—
256C2×C4×C43—212no—
257C2×C4×C43—21no—
258C2×C4×C43—23no—
259C2×C4×C43—83no—
260C2×C4×C43C22×D413yes—
261C2×C4×C43C22×Q816yes—
262C2×C4×C43C2×#4116yes—
263C2×C4×C43C2511yescharacteristic
264C2×Dic43—26no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—23no—
268C2×Dic43—23no—
269C2×Dic43—43no—
270C2×Dic43—46no—
271C2×Dic43—83no—
272C2×Dic43—86no—
273C2×Dic43—83no—
274C2×Dic43—83no—
275C2×Dic43C22×D413yes—
276C2×Dic43C22×D411yescharacteristic
277C2×Dic43C22×D413yes—
278C2×Dic43C22×D411yescharacteristic
279Dic86—42no—
280Dic86—46no—
281Dic86—86no—
282C8×C43—21no—
283C8×C43—23no—
284C43⋊C8—21no—
285C43⋊C8—23no—
286#60494—431nomaximal, Sylow
287C22×C43—23no—
288C22×C43—23no—
289C22×C43—26no—
290C22×C43—43no—
291C22×C43—43no—
292C22×C43—812no—
293C22×C43C2×C22⋊Q816yes—
294C22×C43C23×D411yescharacteristic
295C4×C43—22no—
296C4×C43—41no—
297C4×C43—43no—
298C4×C43C2×C22⋊Q816yes—
299C4×C43C23×Q811yescharacteristic
300C4×C43C22×#4111yescharacteristic
301Dic43—21no—
302Dic43—23no—
303Dic43—23no—
304Dic43—41no—
305Dic43—41no—
306Dic43—43no—
307Dic43—43no—
308Dic43#57612yes—
309#3503—431no—
310C4×H(5,𝔽2)—431no—
311#3083—433no—
312#3083—433no—
313#3081—433no—
314#3081—433no—
315#3079—433no—
316#3077—433no—
317#3076—433no—
318C2×#474—433no—
319#2913—431no—
320#2913—431no—
321#2906—431no—
322#2897—431no—
323#2897D4311yescharacteristic
324C2×C43—26no—
325C2×C43—46no—
326C2×C43C22×C22⋊Q811yescharacteristic
327C2×C43C2×#57611yescharacteristic
328C2×C43#358611yescharacteristic
329C2×H(5,𝔽2)C2×D4311yescharacteristic
330C2×#131—431no—
331C2×#131C2×D4311yescharacteristic
332Q82—861no—
333#557—861no—
334#554—863no—
335D4×Q8—863no—
336#544—433no—
337#544—433no—
338#533—433no—
339C2×C4⋊Q8—433no—
340#520—431no—
341#520—431no—
342#520—433no—
343#520—861no—
344#520C2×D4311yescharacteristic
345#518—433no—
346#518—863no—
347C4×#41—431no—
348C4×#41—433no—
349C4×#41—861no—
350C2×C4×D4—433no—
351C2×C4×D4—863no—
352#479—433no—
353#479—433no—
354#478—433no—
355#478—433no—
356#478—436no—
357#478—436no—
358#477—431no—
359#477—436no—
360#476—433no—
361#476—436no—
362#475—433no—
363#474—433no—
364#474—436no—
365#474—436no—
366#474—436no—
367#428—433no—
368#428—433no—
369#428—433no—
370#428—433no—
371#427—433no—
372#427—433no—
373C2×#107—433no—
374C2×#107—433no—
375#424—433no—
376#424—433no—
377#423—433no—
378C2×C4⋊C8—433no—
379#418—433no—
380#418C2×D4313yes—
381#417—433no—
382#417C2×D4313yes—
383#416—433no—
384#416C2×D4313yes—
385C2×#102—433no—
386C2×#102C2×D4313yes—
387C43#6049411yescharacteristic, complemented, Sylow
388H(5,𝔽2)—24no—
389H(5,𝔽2)Dic8618yescomplemented
390C2×#41—21no—
391C2×#41C22×D4313yes—
392C2×#41C22×D4311yescharacteristic
393C22×Q8—863no—
394C22×D4—23no—
395C22×D4C22×D4313yes—
396C23×C4—863no—
397#131—24no—
398#131—864no—
399C2×M16—433no—
400C2×M16C22×D4313yes—
401C22×C8—433no—
402C22×C8C22×D4313yes—
403C4⋊Q8—433no—
404C4⋊Q8—436no—
405C4⋊Q8—431no—
406C4⋊Q8—863no—
407C4⋊Q8—863no—
408C4⋊Q8—863no—
409C4⋊Q8—863no—
410#125—433no—
411#125—433no—
412#125—863no—
413#125—863no—
414C22⋊Q8—866no—
415C22⋊Q8—863no—
416C22⋊Q8—863no—
417C22⋊Q8—866no—
418C4×Q8—21no—
419C4×Q8—431no—
420C4×Q8—431no—
421C4×Q8—431no—
422C4×Q8—433no—
423C4×Q8—863no—
424C4×Q8—863no—
425C4×Q8—861no—
426C4×Q8—861no—
427C4×D4—23no—
428C4×D4—433no—
429C4×D4—433no—
430C4×D4—433no—
431C4×D4—436no—
432C4×D4—433no—
433C4×D4—863no—
434C4×D4—863no—
435C4×D4—866no—
436C4×D4—863no—
437C4×D4—863no—
438C4×D4—863no—
439C4×D4—863no—
440C4×D4—863no—
441C4×D4—863no—
442#117—433no—
443#117—433no—
444#117—433no—
445#117—863no—
446#117—863no—
447#117C22×D4313yes—
448C2×C4⋊C4—433no—
449C2×C4⋊C4—433no—
450C2×C4⋊C4—863no—
451C2×C4⋊C4—863no—
452C2×C4⋊C4C22×D4313yes—
453C2×C22⋊C4—866no—
454C2×C22⋊C4—863no—
455C2×C42—433no—
456C2×C42—863no—
457#107—433no—
458#107—436no—
459#107—431no—
460#107—433no—
461#107—436no—
462#107—431no—
463#106—433no—
464#106—433no—
465#106—433no—
466#106—433no—
467C4⋊C8—431no—
468C4⋊C8—433no—
469C4⋊C8—433no—
470C4⋊C8—433no—
471C4⋊C8—436no—
472#103—431no—
473#103—433no—
474#103C22×D4311yescharacteristic
475#103C22×D4313yes—
476#102—433no—
477#102—436no—
478#102—433no—
479#102C22×D4313yes—
480#102C22×D4316yes—
481#102C22×D4313yes—
482C24—23no—
483#41—28no—
484#41—26no—
485#41C2×Dic8614yes—
486#41C2×Dic86112yescomplemented
487#41#1062190014yes—
488C2×Q8—866no—
489C2×Q8—861no—
490C2×Q8—863no—
491C2×Q8—3446no—
492C2×Q8D4×D4311yescharacteristic
493C2×Q8C23×D4311yescharacteristic
494C2×D4—23no—
495C2×D4—224no—
496C2×D4—23no—
497C2×D4—26no—
498C2×D4C2×Dic86112yescomplemented
499C2×D4D4×D4313yes—
500C2×D4C23×D4313yes—
501C22×C4—23no—
502C22×C4—23no—
503C22×C4—433no—
504C22×C4—433no—
505C22×C4—863no—
506C22×C4—866no—
507C22×C4—863no—
508C22×C4—863no—
509C22×C4—863no—
510C22×C4—3446no—
511C22×C4C23×D4313yes—
512M16—26no—
513M16—866no—
514C2×C8—26no—
515C2×C8—433no—
516C2×C8—431no—
517C2×C8—866no—
518C2×C8C23×D4313yes—
519C2×C8C23×D4311yescharacteristic
520C4⋊C4—23no—
521C4⋊C4—433no—
522C4⋊C4—433no—
523C4⋊C4—431no—
524C4⋊C4—433no—
525C4⋊C4—431no—
526C4⋊C4—433no—
527C4⋊C4—863no—
528C4⋊C4—863no—
529C4⋊C4—866no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—863no—
533C4⋊C4—863no—
534C4⋊C4—863no—
535C4⋊C4—863no—
536C4⋊C4—863no—
537C4⋊C4—863no—
538C4⋊C4C23×D4311yescharacteristic
539C4⋊C4C23×D4313yes—
540C22⋊C4—23no—
541C22⋊C4—436no—
542C22⋊C4—863no—
543C22⋊C4—866no—
544C22⋊C4—863no—
545C22⋊C4—863no—
546C22⋊C4—863no—
547C42—23no—
548C42—433no—
549C42—433no—
550C42—431no—
551C42—433no—
552C42—861no—
553C42—863no—
554C42—863no—
555C42—863no—
556C23—23no—
557C23—212no—
558C23—83no—
559C23—83no—
560C23C2×D4×D4313yes—
561Q8—21no—
562Q8—3446no—
563Q8—1726no—
564Q8—1722no—
565Q8#1306330214yes—
566Q8C22×Dic8612yes—
567D4—212no—
568D4—212no—
569D4—23no—
570D4#13063302112yes—
571D4C22×Dic8616yes—
572C2×C4—21no—
573C2×C4—212no—
574C2×C4—21no—
575C2×C4—23no—
576C2×C4—83no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—433no—
580C2×C4—433no—
581C2×C4—866no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—863no—
585C2×C4—863no—
586C2×C4—3446no—
587C2×C4—3443no—
588C2×C4—3443no—
589C2×C4—3443no—
590C2×C4—1726no—
591C2×C4—1723no—
592C2×C4C2×D4×D4313yes—
593C2×C4C22×Dic8616yes—
594C2×C4C2×#1062190016yes—
595C2×C4C24×D4311yescharacteristic
596C8—21no—
597C8—23no—
598C8—861no—
599C8—863no—
600C22—23no—
601C22—23no—
602C22—26no—
603C22—43no—
604C22—43no—
605C22—812no—
606C22C2×#1306330216yes—
607C22C22×D4×D4311yescharacteristic
608C4—22no—
609C4—43no—
610C4—41no—
611C4—432no—
612C4—863no—
613C4—863no—
614C4—861no—
615C4—1723no—
616C4—1723no—
617C4—1721no—
618C4—1721no—
619C4C2×#1306330216yes—
620C4C23×Dic8611yescharacteristic
621C4C22×#1062190011yescharacteristic
622C2—26no—
623C2—46no—
624C2C22×#1306330211yescharacteristic
625C2#576×D4311yescharacteristic
626C2#1914937711yescharacteristic
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#60494
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. #19148408C2semidirect
3. #19144450C2semidirect
4. #19144444C2semidirect
5. #19144428C2semidirect
6. #19144422C2semidirect
7. #19144406C2semidirect
8. #19144389C2semidirect
9. #19144379C2semidirect
10. C2×#14583177C2semidirect
11. #19143195C2semidirect
12. #19143193C2semidirect
13. #19143161C2semidirect
21. #14583530C22semidirect
22. #14583527C22semidirect
23. #14583452C22semidirect
24. C2×#13063324C22semidirect
36. #14583208C22semidirect
37. #14583204C22semidirect
38. #14583201C22semidirect
39. #14583201C22semidirect
40. #14583197C22semidirect
41. #14583197C22semidirect
42. #14583192C22semidirect
43. #14583192C22semidirect
44. #14583187C22semidirect
45. #14583187C22semidirect
46. #14583182C22semidirect
47. #14583177C22semidirect
48. #14583177C22semidirect
49. #14583177C22semidirect
50. #14583177C22semidirect
51. #14582942C22semidirect
52. #14582941C22semidirect
53. #14582941C22semidirect
54. #14582939C22semidirect
55. #14582937C22semidirect
56. #14582935C22semidirect
57. C2×#13063259C22semidirect
58. C2×#13063258C22semidirect
59. #14582927C22semidirect
60. #14582925C22semidirect
61. #14582922C22semidirect
62. C2×Dic43⋊C8C22semidirect
150. H(5,𝔽2)×C43Q8semidirect
172. #41×C43C2×Q8semidirect
181. C2×D4×C43C2×Q8semidirect
387. C43#60494semidirect
389. H(5,𝔽2)Dic86semidirect
486. #41C2×Dic86semidirect
498. C2×D4C2×Dic86semidirect

Maximal subgroups

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

subgroupindex
#191484082
H(5,𝔽2)×Dic432
#191444502
#191444442
#191444282
#191444222
#191444062
#191443892
#191443792
C2×#145831772
#191431952
#191431932
#191431612
#191431212
C43×#28972
#6049443