Finite Group Databasebeta

← #25253064

Subgroups — #25253064

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×SD32×D43C211yesmaximal, characteristic, complemented
2#19146330C211yesmaximal, characteristic, complemented
3D8×C22⋊D43C211yesmaximal, characteristic, complemented
4#19136858C211yesmaximal, characteristic, complemented
5#19136708C211yesmaximal, characteristic, complemented
6#19136678C211yesmaximal, characteristic, complemented
7#19136648C211yesmaximal, characteristic, complemented
8#19136633C211yesmaximal, characteristic, complemented
9#19136524C211yesmaximal, characteristic, complemented
10#19136518C211yesmaximal, characteristic, complemented
11#19136510C211yesmaximal, characteristic, complemented
12#19136505C211yesmaximal, characteristic, complemented
13#19136460C211yesmaximal, characteristic, complemented
14#19136418C211yesmaximal, characteristic, complemented
15C2×C43×#509C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic, complemented
17C2×D8×D43C2211yescharacteristic
18#14583556—21no—
19D4×C22⋊D43—21no—
20C2×#13063270C2211yescharacteristic, complemented
21C2×#13063269C2211yescharacteristic
22C2×#13063269C2211yescharacteristic, complemented
23C2×#13063268C2211yescharacteristic, complemented
24SD32×D43—24no—
25C2×#13063266C2211yescharacteristic, complemented
26C2×C16×D43C2211yescharacteristic, complemented
27#14583282C2211yescharacteristic, complemented
28#14583274C2211yescharacteristic
29#14583140C2211yescharacteristic, complemented
30#14583135C2211yescharacteristic
31#14583132C2211yescharacteristic
32#14583132C2211yescharacteristic, complemented
33#14583119—21no—
34#14583092—21no—
35#14583061—21no—
36#14583036—21no—
37#14583033—21no—
38#14583031—21no—
39Q16×Dic43C2211yescharacteristic, complemented
40D8×Dic43C2211yescharacteristic
41C8×C22⋊D43C2211yescharacteristic
42#14582725C2211yescharacteristic, complemented
43Dic43⋊C16C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582703C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic, complemented
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic, complemented
49#14582700C2211yescharacteristic, complemented
50C22⋊(C43⋊C16)C2211yescharacteristic, complemented
51(C2×D43)⋊C16C2211yescharacteristic, complemented
52#14582674C2211yescharacteristic, complemented
53C2×#135×C43C2211yescharacteristic, complemented
54C22×D8×C43C2211yescharacteristic
55C43×#509—24no—
56C2×SD32×C43C2211yescharacteristic
57C2×SD32×C43C2211yescharacteristic, complemented
58C2×D16×C43C2211yescharacteristic
59C2×D16×C43C2211yescharacteristic, complemented
60C2×M32×C43C2211yescharacteristic, complemented
61C2×Q8×D43—21no—
62C22×C22⋊D43—41no—
63C2×D4×D43—21no—
64C2×Dic172C2311yescharacteristic
65C2×#10621885—21no—
66Q16×D43—22no—
67Q16×D43—41no—
68C2×#10621883—21no—
69C2×D344C2311yescharacteristic
70C2×#10621882—21no—
71C2×#10621882—21no—
72D8×D43—22no—
73D8×D43—41no—
74C2×C8×D43C2311yescharacteristic
75#13063321—21no—
76#13063312—21no—
77#13063312—41no—
78#13063304—21no—
79#13063304—41no—
80#13063299—21no—
81#13063297—41no—
82#13063296—21no—
83#13063296—21no—
84#13063296—41no—
85#13063294—41no—
86#13063293—41no—
87Q8×Dic43—21no—
88D4×Dic43—21no—
89C4×C22⋊D43—41no—
90C4×C22⋊D43D411yescharacteristic
91#13063270—22no—
92#13063269—22no—
93#13063269—41no—
94#13063268—22no—
95#13063266—41no—
96C2×C43⋊C16C2311yescharacteristic
97C2×C43⋊C16C2311yescharacteristic
98C16×D43—22no—
99#13063259C2311yescharacteristic
100#13063259C2311yescharacteristic
101Dic43⋊C8D411yescharacteristic
102#13063250—21no—
103#13063249—21no—
104#13063247—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108C22⋊(C43⋊C8)D411yescharacteristic
109(C2×D43)⋊C8D411yescharacteristic
110C8×Dic43C2311yescharacteristic
111C2×#41×C43—21no—
112C22×D4×C43—21no—
113#135×C43—22no—
114#135×C43—41no—
115C2×Q16×C43C2311yescharacteristic
116C2×SD16×C43—21no—
117C2×D8×C43—22no—
118C2×D8×C43—21no—
119C2×D8×C43—41no—
120C2×D8×C43C2311yescharacteristic
121C2×D8×C43C2311yescharacteristic
122C2×D8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124SD32×C43—22no—
125SD32×C43D414yescomplemented
126D16×C43—22no—
127D16×C43—22no—
128M32×C43—22no—
129C2×C16×C43C2311yescharacteristic
130C2×C16×C43C2311yescharacteristic
131C24×C43—41no—
132C23×D43—41no—
133#41×C43—42no—
134#41×C43—81no—
135C2×Q8×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—41no—
140C2×D4×C43—41no—
141C2×D4×C43—42no—
142C2×D4×C43—81no—
143C22×C4×C43—41no—
144C22×C4×C43C2×D411yescharacteristic
145C2×C22⋊D43—41no—
146C2×C22⋊D43—41no—
147C2×C22⋊D43—41no—
148C2×C22⋊D43—41no—
149C2×C22⋊D43—41no—
150C2×C22⋊D43—41no—
151C2×C22⋊D43—84no—
152C2×C22⋊D43D811yescharacteristic
153C22×Dic43—41no—
154Q8×D43—42no—
155Q8×D43—81no—
156D4×D43—42no—
157D4×D43—81no—
158C2×D172—21no—
159C2×C4×D43—41no—
160C2×C4×D43C2×D411yescharacteristic
161C2×Dic86—21no—
162C2×Dic86—41no—
163Q16×C43—21no—
164Q16×C43C2×D412yescomplemented
165SD16×C43—42no—
166D8×C43—21no—
167D8×C43—21no—
168D8×C43—21no—
169D8×C43—21no—
170D8×C43—21no—
171D8×C43—42no—
172D8×C43C2×D412yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2411yescharacteristic
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179C22⋊Dic43—41no—
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182C22⋊Dic43—41no—
183C22⋊Dic43D811yescharacteristic
184#10621885—42no—
185#10621883—81no—
186#10621882—42no—
187#10621882—81no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4D811yescharacteristic
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4D811yescharacteristic
195C4×Dic43—41no—
196C4×Dic43C2×D411yescharacteristic
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199Dic172—21no—
200Dic172—21no—
201D344—21no—
202D344—21no—
203C8×D43—21no—
204C8×D43—21no—
205C16×C43—21no—
206C16×C43C2×D412yescomplemented
207C43⋊C16—21no—
208C43⋊C16—21no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—82no—
213C23×C43—82no—
214C23×C43—161no—
215C23×C43C2×D811yescharacteristic
216C22×D43—41no—
217C22×D43—82no—
218C22×D43—82no—
219C22×D43—161no—
220C22×D43C2×D811yescharacteristic
221Q8×C43—22no—
222Q8×C43—41no—
223D4×C43—22no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—82no—
230D4×C43—82no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—82no—
235C2×C4×C43C2×D811yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C22⋊D43—22no—
238C22⋊D43—82no—
239C22⋊D43—82no—
240C22⋊D43—82no—
241C22⋊D43—82no—
242C22⋊D43—82no—
243C22⋊D43—161no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—82no—
248C2×Dic43C2×D811yescharacteristic
249C2×Dic43C2×D811yescharacteristic
250C2×Dic43C2×D811yescharacteristic
251D172—41no—
252D172—41no—
253C4×D43—21no—
254C4×D43—21no—
255C4×D43—82no—
256Dic86—41no—
257Dic86—41no—
258Dic86—82no—
259C8×C43—21no—
260C8×C43C22×D411yescharacteristic
261C8×C43H(5,𝔽2)11yescharacteristic
262C43⋊C8—21no—
263C43⋊C8—21no—
264#33831—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—42no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—164no—
278C22×C43C22×D811yescharacteristic
279C2×D43—21no—
280C2×D43—21no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—164no—
285C2×D43#50912yescomplemented
286C4×C43—21no—
287C4×C43—42no—
288C4×C43D4211yescharacteristic
289C4×C43#57611yescharacteristic
290Dic43—21no—
291Dic43—21no—
292Dic43—21no—
293Dic43—81no—
294Dic43—81no—
295Dic43—81no—
296C2×#509D4311yescharacteristic, complemented
297C22×SD32—431no—
298#3285—431no—
299D4×D8—431no—
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—41no—
312C2×C43—82no—
313C2×C43—161no—
314C2×C43—161no—
315C2×C43D4×D811yescharacteristic
316C2×C43C2×#50911yescharacteristic
317C2×C43#341611yescharacteristic
318D43—22no—
319D43—161no—
320C2×#135C2×D4311yescharacteristic, complemented
321C22×Q16—431no—
322C22×D8—431no—
323C22×D8C2×D4311yescharacteristic
324#548—861no—
325D42—861no—
326#509—24no—
327C2×SD32—431no—
328C2×SD32—431no—
329C2×SD32—431no—
330C2×SD32—431no—
331C2×SD32—864no—
332C2×SD32C2×D4311yescharacteristic
333C2×SD32C2×D4311yescharacteristic, complemented
334C2×D16—431no—
335C2×D16C2×D4311yescharacteristic
336C2×D16C2×D4311yescharacteristic, complemented
337C2×M32C2×D4311yescharacteristic, complemented
338C22×C16—431no—
339#495—431no—
340#493—431no—
341#467—431no—
342#466—431no—
343#466—431no—
344#466—431no—
345#464—861no—
346#459—861no—
347#452—861no—
348#448—861no—
349#447—861no—
350#447—861no—
351C4×Q16—431no—
352C4×D8—431no—
353C8×D4—431no—
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—21no—
367C22×Q8—861no—
368C22×D4—21no—
369C22×D4—861no—
370C22×D4—1721no—
371#135—22no—
372#135—41no—
373C2×Q16—431no—
374C2×Q16—861no—
375C2×Q16—862no—
376C2×Q16—1721no—
377C2×Q16C22×D4311yescharacteristic
378C2×SD16—21no—
379C2×SD16—861no—
380C2×D8—22no—
381C2×D8—21no—
382C2×D8—41no—
383C2×D8—431no—
384C2×D8—861no—
385C2×D8—861no—
386C2×D8—862no—
387C2×D8—1721no—
388C2×D8C22×D4311yescharacteristic
389C2×D8C22×D4311yescharacteristic
390C2×D8C22×D4311yescharacteristic
391C22×C8—431no—
392C22×C8C22×D4311yescharacteristic
393#127—861no—
394#124—861no—
395#124—1721no—
396C22⋊Q8—861no—
397C22⋊Q8—1721no—
398#121—861no—
399#121—861no—
400#121—861no—
401#121—1721no—
402#121—1721no—
403#120—1721no—
404#120—1721no—
405C4×Q8—861no—
406C4×D4—431no—
407C4×D4—861no—
408C4×D4—1721no—
409SD32—22no—
410SD32—862no—
411SD32—862no—
412SD32—862no—
413SD32—1721no—
414SD32C22⋊D4314yescomplemented
415D16—22no—
416D16—22no—
417D16—1721no—
418M32—22no—
419C2×C16—431no—
420C2×C16—431no—
421C2×C16—862no—
422C2×C16C22×D4311yescharacteristic
423C2×C16C22×D4311yescharacteristic
424#107—431no—
425#107—431no—
426C4⋊C8—431no—
427#103—861no—
428#103—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433C22⋊C8—431no—
434C22⋊C8—431no—
435C4×C8—431no—
436C24—41no—
437C24—1721no—
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—861no—
442C2×Q8—3441no—
443C2×Q8—1721no—
444C2×Q8—1722no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—42no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—81no—
452C2×D4—431no—
453C2×D4—861no—
454C2×D4—3441no—
455C2×D4—3444no—
456C2×D4—1721no—
457C2×D4—1721no—
458C2×D4—1721no—
459C2×D4—1722no—
460C2×D4—1721no—
461C2×D4—1721no—
462C2×D4—1721no—
463C22×C4—41no—
464C22×C4—431no—
465C22×C4—1721no—
466C22×C4—1721no—
467C22×C4D4×D4311yescharacteristic
468Q16—21no—
469Q16—861no—
470Q16—861no—
471Q16—1722no—
472Q16C2×C22⋊D4312yescomplemented
473SD16—42no—
474SD16—3441no—
475D8—21no—
476D8—21no—
477D8—21no—
478D8—21no—
479D8—21no—
480D8—42no—
481D8—861no—
482D8—861no—
483D8—3441no—
484D8—1722no—
485D8C2×C22⋊D4312yes—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—431no—
489C2×C8—431no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8D4×D4311yescharacteristic
493C2×C8C23×D4311yescharacteristic
494C4⋊C4—431no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1721no—
498C4⋊C4—1721no—
499C22⋊C4—431no—
500C22⋊C4—431no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C22⋊C4—1721no—
505C22⋊C4—1721no—
506C22⋊C4—1721no—
507C22⋊C4—1721no—
508C42—431no—
509C42—1721no—
510C16—21no—
511C16—861no—
512C16—861no—
513C16C2×C22⋊D4312yescomplemented
514C23—41no—
515C23—41no—
516C23—41no—
517C23—82no—
518C23—82no—
519C23—161no—
520C23—431no—
521C23—3442no—
522C23—3442no—
523C23—1721no—
524C23—6881no—
525C23D8×D4311yescharacteristic
526Q8—22no—
527Q8—41no—
528Q8—3442no—
529Q8—1721no—
530Q8—1721no—
531D4—22no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—82no—
538D4—82no—
539D4—862no—
540D4—3442no—
541D4—3442no—
542D4—3442no—
543D4—3442no—
544D4—3442no—
545D4—1721no—
546D4—1721no—
547D4—6881no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4—431no—
553C2×C4—431no—
554C2×C4—431no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—3442no—
558C2×C4—3442no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4D8×D4311yescharacteristic
563C2×C4C2×D4×D4311yescharacteristic
564C8—21no—
565C8—861no—
566C8—861no—
567C8C22×C22⋊D4311yescharacteristic
568C8#1306337011yescharacteristic
569C22—21no—
570C22—21no—
571C22—21no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—164no—
582C22—432no—
583C22—861no—
584C22—861no—
585C22—3441no—
586C22—3441no—
587C22—3441no—
588C22—6884no—
589C22C2×D8×D4311yescharacteristic
590C4—21no—
591C4—42no—
592C4—861no—
593C4—861no—
594C4—861no—
595C4—3441no—
596C4—3441no—
597C4—3441no—
598C4D4×C22⋊D4311yescharacteristic
599C4#1458370011yescharacteristic
600C2—41no—
601C2—82no—
602C2—161no—
603C2—161no—
604C2—862no—
605C2—6881no—
606C2D8×C22⋊D4311yescharacteristic
607C2#509×D4311yescharacteristic
608C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#509C2
socleC22×C43C22×D8
hypercenterC2×#509D43
hypocenterC43#33831
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×SD32×D43C2semidirect
2. #19146330C2semidirect
3. D8×C22⋊D43C2semidirect
4. #19136858C2semidirect
5. #19136708C2semidirect
6. #19136678C2semidirect
7. #19136648C2semidirect
8. #19136633C2semidirect
9. #19136524C2semidirect
10. #19136518C2semidirect
11. #19136510C2semidirect
12. #19136505C2semidirect
13. #19136460C2semidirect
14. #19136418C2semidirect
15. C2×C43×#509C2semidirect
16. C2×Q16×D43C22semidirect
20. C2×#13063270C22semidirect
22. C2×#13063269C22semidirect
23. C2×#13063268C22semidirect
25. C2×#13063266C22semidirect
26. C2×C16×D43C22semidirect
27. #14583282C22semidirect
29. #14583140C22semidirect
32. #14583132C22semidirect
39. Q16×Dic43C22semidirect
42. #14582725C22semidirect
43. Dic43⋊C16C22semidirect
44. #14582704C22semidirect
45. #14582703C22semidirect
46. #14582701C22semidirect
48. #14582700C22semidirect
49. #14582700C22semidirect
50. C22⋊(C43⋊C16)C22semidirect
51. (C2×D43)⋊C16C22semidirect
52. #14582674C22semidirect
53. C2×#135×C43C22semidirect
57. C2×SD32×C43C22semidirect
59. C2×D16×C43C22semidirect
60. C2×M32×C43C22semidirect
125. SD32×C43D4semidirect
164. Q16×C43C2×D4semidirect
206. C16×C43C2×D4semidirect
285. C2×D43#509semidirect
296. C2×#509D43semidirect
320. C2×#135C2×D43semidirect
333. C2×SD32C2×D43semidirect
336. C2×D16C2×D43semidirect
337. C2×M32C2×D43semidirect
365. C43#33831semidirect
414. SD32C22⋊D43semidirect
472. Q16C2×C22⋊D43semidirect
513. C16C2×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×D432
#191463302
D8×C22⋊D432
#191368582
#191367082
#191366782
#191366482
#191366332
#191365242
#191365182
#191365102
#191365052
#191364602
#191364182
C2×C43×#5092
#3383143