Finite Group Databasebeta

← #25253066

Subgroups — #25253066

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583335C211yesmaximal, characteristic, complemented
2C22×#13063269C211yesmaximal, characteristic, complemented
3#19146338C211yesmaximal, characteristic, complemented
4#19136859C211yesmaximal, characteristic, complemented
5#19136706C211yesmaximal, characteristic, complemented
6#19136679C211yesmaximal, characteristic, complemented
7#19136650C211yesmaximal, characteristic, complemented
8#19136632C211yesmaximal, characteristic, complemented
9#19136524C211yesmaximal, characteristic, complemented
10#19136516C211yesmaximal, characteristic, complemented
11#19136511C211yesmaximal, characteristic, complemented
12#19136507C211yesmaximal, characteristic, complemented
13#19136459C211yesmaximal, characteristic, complemented
14#19136421C211yesmaximal, characteristic, complemented
15D4×D8×C43C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic, complemented
17C22×Dic172C2211yescharacteristic, complemented
18#14583558—21no—
19#14583335—24no—
20C2×#13063269—24no—
21C2×#13063269C2211yescharacteristic
22C2×#13063269C2211yescharacteristic
23C2×#13063269C2211yescharacteristic, complemented
24C2×#13063269C2211yescharacteristic, complemented
25C2×#13063269C2211yescharacteristic, complemented
26C2×#13063269C2211yescharacteristic, complemented
27C2×#13063266C2211yescharacteristic
28C2×#13063266C2211yescharacteristic, complemented
29C2×#13063266C2211yescharacteristic, complemented
30C2×#13063265C2211yescharacteristic, complemented
31C22×C43⋊C16C2211yescharacteristic, complemented
32#14583283C2211yescharacteristic, complemented
33#14583140C2211yescharacteristic, complemented
34#14583135C2211yescharacteristic, complemented
35#14583122—21no—
36#14583063—21no—
37#14583040—21no—
38C4×Dic172C2211yescharacteristic, complemented
39#14582724C2211yescharacteristic, complemented
40C4⋊(C43⋊C16)C2211yescharacteristic, complemented
41#14582702C2211yescharacteristic, complemented
42#14582702C2211yescharacteristic, complemented
43#14582700C2211yescharacteristic
44#14582700C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic, complemented
46#14582699C2211yescharacteristic, complemented
47C22⋊(C43⋊C16)C2211yescharacteristic, complemented
48C22⋊(C43⋊C16)C2211yescharacteristic, complemented
49#14582675C2211yescharacteristic, complemented
50C22×D8×C43C2211yescharacteristic
51C22×D8×C43C2211yescharacteristic
52D42×C43—21no—
53C43×#493C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#459—21no—
57C43×#447—21no—
58C43×#447—21no—
59C4×D8×C43C2211yescharacteristic
60C8×D4×C43C2211yescharacteristic
61C2×#10621898—21no—
62C22×Dic86—21no—
63#13063347—22no—
64#13063347—41no—
65C2×Dic172—22no—
66C2×Dic172—21no—
67C2×Dic172—41no—
68C2×Dic172C2311yescharacteristic
69C2×Dic172C2311yescharacteristic
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×D344C2311yescharacteristic
73#13063313—21no—
74#13063311—41no—
75#13063304—21no—
76#13063303—41no—
77#13063299—21no—
78#13063297—41no—
79C4×Dic86—21no—
80(C22⋊D43)⋊C4—41no—
81#13063269—22no—
82#13063269—22no—
83#13063269—22no—
84#13063269—22no—
85#13063269—41no—
86#13063269D414yescomplemented
87#13063266—22no—
88#13063266—22no—
89#13063266—41no—
90#13063265—22no—
91C2×C43⋊C16—22no—
92C2×C43⋊C16C2311yescharacteristic
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C2×C43⋊C16C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063247—21no—
100C22×D4×C43—21no—
101C22×D4×C43—21no—
102C22×D4×C43—41no—
103C2×D8×C43—22no—
104C2×D8×C43—22no—
105C2×D8×C43—21no—
106C2×D8×C43—21no—
107C2×D8×C43—21no—
108C2×D8×C43—41no—
109C2×D8×C43—41no—
110C2×D8×C43C2311yescharacteristic
111C2×D8×C43C2311yescharacteristic
112C2×D8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#127×C43—21no—
116#121×C43—21no—
117#121×C43—21no—
118#121×C43—41no—
119#120×C43—41no—
120#120×C43—41no—
121C4×D4×C43—21no—
122C4×D4×C43D411yescharacteristic
123#107×C43C2311yescharacteristic
124C4⋊C8×C43D411yescharacteristic
125#102×C43—21no—
126#102×C43—21no—
127#102×C43—21no—
128C22⋊C8×C43D411yescharacteristic
129C22⋊C8×C43D411yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C24×C43—41no—
132C24×C43—41no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—41no—
137C2×D4×C43—41no—
138C2×D4×C43—41no—
139C2×D4×C43—41no—
140C2×D4×C43—41no—
141C2×D4×C43—41no—
142C2×D4×C43—42no—
143C2×D4×C43—42no—
144C2×D4×C43—81no—
145C2×D4×C43—81no—
146C2×D4×C43—84no—
147C2×D4×C43D811yescharacteristic
148C22×C4×C43—41no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153C22×Dic43—41no—
154#10621898—42no—
155#10621898—81no—
156C2×D172—21no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—42no—
161C2×Dic86—41no—
162C2×Dic86—81no—
163D8×C43—21no—
164D8×C43—21no—
165D8×C43—21no—
166D8×C43—21no—
167D8×C43—21no—
168D8×C43—42no—
169D8×C43—42no—
170D8×C43—81no—
171D8×C43C2×D412yes—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43D811yescharacteristic
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43D811yescharacteristic
186C22⋊C4×C43D811yescharacteristic
187C42×C43C2×D411yescharacteristic
188C22⋊Dic43—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—41no—
196Dic172—21no—
197Dic172—21no—
198Dic172—21no—
199Dic172—42no—
200Dic172C2×D412yescomplemented
201D344—21no—
202D344—21no—
203#10621873—42no—
204#10621873—81no—
205C43⋊C16—21no—
206C43⋊C16—21no—
207C43⋊C16—21no—
208C43⋊C16C2×D412yescomplemented
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—82no—
213C23×C43—82no—
214C23×C43—82no—
215C23×C43—82no—
216C23×C43—161no—
217C23×C43—161no—
218C23×C43C2×D811yescharacteristic
219C23×C43C2×D811yescharacteristic
220C22×D43—41no—
221D4×C43—22no—
222D4×C43—22no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—82no—
229D4×C43—82no—
230D4×C43—82no—
231D4×C43—82no—
232D4×C43—82no—
233D4×C43—161no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—82no—
240C2×C4×C43C2×D811yescharacteristic
241C2×C4×C43C2×D811yescharacteristic
242C2×C4×C43C2×D811yescharacteristic
243C2×C4×C43C2×D811yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C22⋊D43—82no—
246C22⋊D43—82no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—82no—
251D172—41no—
252D172—41no—
253C4×D43—82no—
254Dic86—22no—
255Dic86—41no—
256Dic86—41no—
257Dic86—41no—
258Dic86—82no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43C22×D411yescharacteristic
263C8×C43H(5,𝔽2)11yescharacteristic
264#33831—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—42no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—164no—
280C22×C43—164no—
281C22×C43#50912yescomplemented
282C22×C43C22×D811yescharacteristic
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—81no—
291C4×C43D4211yescharacteristic
292C4×C43#57611yescharacteristic
293Dic43—42no—
294Dic43—81no—
295Dic43—81no—
296C2×#509—431no—
297C22×SD32—431no—
298#3285—431no—
299D4×D8D4311yescharacteristic, complemented
300#2250—431no—
301#2220—431no—
302#2215—431no—
303#2210—431no—
304#2207—431no—
305#2187—431no—
306#2186—431no—
307#2185—431no—
308#2184—431no—
309#2175—431no—
310#2168—431no—
311C2×C43—22no—
312C2×C43—41no—
313C2×C43—82no—
314C2×C43—161no—
315C2×C43—161no—
316C2×C43D4×D811yescharacteristic
317C2×C43C2×#50911yescharacteristic
318C2×C43#341611yescharacteristic
319D43—161no—
320C2×#135—431no—
321C22×Q16—431no—
322C22×D8C2×D4311yescharacteristic
323C22×D8C2×D4311yescharacteristic
324#548—861no—
325D42—21no—
326#509—864no—
327C2×SD32—431no—
328C2×SD32—431no—
329C2×SD32—431no—
330C2×SD32—431no—
331C2×SD32—431no—
332C2×SD32—431no—
333C2×SD32—864no—
334C2×D16—431no—
335C2×D16—431no—
336C2×D16—431no—
337C2×M32—431no—
338C22×C16—431no—
339#495—431no—
340#493C2×D4311yescharacteristic
341#467—431no—
342#466—431no—
343#466C2×D4311yescharacteristic
344#466C2×D4311yescharacteristic
345#464—861no—
346#459—21no—
347#452—861no—
348#448—861no—
349#447—21no—
350#447—21no—
351C4×Q16—431no—
352C4×D8C2×D4311yescharacteristic
353C8×D4C2×D4311yescharacteristic
354#366—431no—
355C4⋊C16—431no—
356#358—431no—
357#358—431no—
358#357—431no—
359#357—431no—
360#357—431no—
361#357—431no—
362C22⋊C16—431no—
363C22⋊C16—431no—
364#346—431no—
365C43#3383111yescharacteristic, complemented, Sylow
366C2×#41—861no—
367C22×Q8—861no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—41no—
371#135—862no—
372#135—1721no—
373C2×Q16—431no—
374C2×Q16—431no—
375C2×Q16—862no—
376C2×Q16—861no—
377C2×Q16—1721no—
378C2×SD16—861no—
379C2×SD16—861no—
380C2×D8—22no—
381C2×D8—22no—
382C2×D8—21no—
383C2×D8—21no—
384C2×D8—21no—
385C2×D8—41no—
386C2×D8—41no—
387C2×D8—431no—
388C2×D8C22×D4311yescharacteristic
389C2×D8C22×D4311yescharacteristic
390C2×D8C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392C22×C8C22×D4311yescharacteristic
393#127—21no—
394#124—861no—
395#124—1721no—
396C22⋊Q8—861no—
397C22⋊Q8—1721no—
398#121—21no—
399#121—21no—
400#121—41no—
401#121—861no—
402#121—1721no—
403#120—41no—
404#120—41no—
405C4×Q8—861no—
406C4×D4—21no—
407C4×D4—1721no—
408C4×D4C22⋊D4311yescharacteristic
409SD32—434no—
410SD32—862no—
411SD32—862no—
412SD32—862no—
413SD32—862no—
414SD32—1721no—
415D16—862no—
416D16—862no—
417D16—1721no—
418M32—862no—
419C2×C16—431no—
420C2×C16—431no—
421C2×C16—431no—
422C2×C16—431no—
423C2×C16—862no—
424#107—431no—
425#107C22×D4311yescharacteristic
426C4⋊C8C22⋊D4311yescharacteristic
427#103—861no—
428#103—861no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—861no—
433C22⋊C8C22⋊D4311yescharacteristic
434C22⋊C8C22⋊D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436C24—41no—
437C24—41no—
438#41—3441no—
439#41—1722no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—3441no—
443C2×Q8—1722no—
444C2×Q8—1721no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—81no—
457C2×D4—81no—
458C2×D4—84no—
459C2×D4—861no—
460C2×D4—1721no—
461C2×D4—1721no—
462C2×D4#1062188211yescharacteristic
463C22×C4—41no—
464C22×C4—1721no—
465C22×C4—1721no—
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C2×C22⋊D4311yescharacteristic
468Q16—432no—
469Q16—861no—
470Q16—861no—
471Q16—861no—
472Q16—1722no—
473SD16—3441no—
474SD16—1722no—
475D8—21no—
476D8—21no—
477D8—21no—
478D8—21no—
479D8—21no—
480D8—42no—
481D8—42no—
482D8—81no—
483D8—861no—
484D8—861no—
485D8D4×D4312yes—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8C2×C22⋊D4311yescharacteristic
491C2×C8C2×C22⋊D4311yescharacteristic
492C2×C8C2×C22⋊D4311yescharacteristic
493C2×C8C23×D4311yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—861no—
496C4⋊C4—1721no—
497C4⋊C4—1721no—
498C4⋊C4#1062188211yescharacteristic
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C22⋊C4—1721no—
505C22⋊C4—1721no—
506C22⋊C4#1062188211yescharacteristic
507C22⋊C4#1062188211yescharacteristic
508C42—1721no—
509C42C2×C22⋊D4311yescharacteristic
510C16—432no—
511C16—861no—
512C16—861no—
513C16—861no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—82no—
518C23—82no—
519C23—82no—
520C23—82no—
521C23—161no—
522C23—161no—
523C23—1721no—
524C23C2×#1062188211yescharacteristic
525C23C2×#1062188211yescharacteristic
526Q8—862no—
527Q8—3442no—
528Q8—1721no—
529Q8—1721no—
530Q8—1721no—
531D4—22no—
532D4—22no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—82no—
539D4—82no—
540D4—82no—
541D4—82no—
542D4—82no—
543D4—161no—
544D4—3442no—
545D4—3442no—
546D4—1721no—
547D4—1721no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—3442no—
555C2×C4—3442no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4C2×#1062188211yescharacteristic
560C2×C4C2×#1062188211yescharacteristic
561C2×C4C2×#1062188211yescharacteristic
562C2×C4C2×#1062188211yescharacteristic
563C2×C4C22×C22⋊D4311yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8C2×D4×D4311yescharacteristic
568C8#1306337011yescharacteristic
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—164no—
584C22—164no—
585C22—3441no—
586C22—3441no—
587C22—3441no—
588C22#1458333512yescomplemented
589C22C22×#1062188211yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—81no—
595C4—3441no—
596C4—3441no—
597C4—1722no—
598C4D4×C22⋊D4311yescharacteristic
599C4#1458370211yescharacteristic
600C2—22no—
601C2—41no—
602C2—82no—
603C2—161no—
604C2—161no—
605C2—6881no—
606C2D4×#1062188211yescharacteristic
607C2C2×#1458333511yescharacteristic
608C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingD4×D8×C43C2
socleC22×C43C22×D8
hypercenterD4×D8D43
hypocenterC43#33831
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14583335C2semidirect
2. C22×#13063269C2semidirect
3. #19146338C2semidirect
4. #19136859C2semidirect
5. #19136706C2semidirect
6. #19136679C2semidirect
7. #19136650C2semidirect
8. #19136632C2semidirect
9. #19136524C2semidirect
10. #19136516C2semidirect
11. #19136511C2semidirect
12. #19136507C2semidirect
13. #19136459C2semidirect
14. #19136421C2semidirect
15. D4×D8×C43C2semidirect
16. C2×#13063347C22semidirect
17. C22×Dic172C22semidirect
23. C2×#13063269C22semidirect
24. C2×#13063269C22semidirect
25. C2×#13063269C22semidirect
26. C2×#13063269C22semidirect
28. C2×#13063266C22semidirect
29. C2×#13063266C22semidirect
30. C2×#13063265C22semidirect
31. C22×C43⋊C16C22semidirect
32. #14583283C22semidirect
33. #14583140C22semidirect
34. #14583135C22semidirect
38. C4×Dic172C22semidirect
39. #14582724C22semidirect
40. C4⋊(C43⋊C16)C22semidirect
41. #14582702C22semidirect
42. #14582702C22semidirect
44. #14582700C22semidirect
45. #14582700C22semidirect
46. #14582699C22semidirect
47. C22⋊(C43⋊C16)C22semidirect
48. C22⋊(C43⋊C16)C22semidirect
49. #14582675C22semidirect
86. #13063269D4semidirect
200. Dic172C2×D4semidirect
208. C43⋊C16C2×D4semidirect
281. C22×C43#509semidirect
299. D4×D8D43semidirect
365. C43#33831semidirect
588. C22#14583335semidirect

Maximal subgroups

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

subgroupindex
C2×#145833352
C22×#130632692
#191463382
#191368592
#191367062
#191366792
#191366502
#191366322
#191365242
#191365162
#191365112
#191365072
#191364592
#191364212
D4×D8×C432
#3383143