Finite Group Databasebeta

← #25253075

Subgroups — #25253075

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×#14583337C211yesmaximal, characteristic, complemented
2C22×#13063270C211yesmaximal, characteristic, complemented
3#19146338C211yesmaximal, characteristic, complemented
4D4×D344C211yesmaximal, characteristic, complemented
5#19136861C211yesmaximal, characteristic, complemented
6#19136708C211yesmaximal, characteristic, complemented
7#19136681C211yesmaximal, characteristic, complemented
8#19136651C211yesmaximal, characteristic, complemented
9#19136636C211yesmaximal, characteristic, complemented
10#19136526C211yesmaximal, characteristic, complemented
11#19136520C211yesmaximal, characteristic, complemented
12#19136514C211yesmaximal, characteristic, complemented
13#19136509C211yesmaximal, characteristic, complemented
14#19136461C211yesmaximal, characteristic, complemented
15C43×#2168C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic, complemented
17C22×Dic172C2211yescharacteristic, complemented
18C22×D344C2211yescharacteristic
19C22×D344C2211yescharacteristic
20#14583558—21no—
21D4×D172—21no—
22#14583337—24no—
23C2×#13063270—24no—
24C2×#13063270C2211yescharacteristic
25C2×#13063270C2211yescharacteristic
26C2×#13063270C2211yescharacteristic, complemented
27C2×#13063270C2211yescharacteristic, complemented
28C2×#13063270C2211yescharacteristic, complemented
29C2×#13063270C2211yescharacteristic, complemented
30C2×D688C2211yescharacteristic
31C2×D688C2211yescharacteristic, complemented
32C2×D688C2211yescharacteristic, complemented
33#14583283C2211yescharacteristic, complemented
34#14583276C2211yescharacteristic
35#14583140C2211yescharacteristic, complemented
36#14583135C2211yescharacteristic
37#14583135C2211yescharacteristic
38#14583135C2211yescharacteristic, complemented
39#14583122—21no—
40#14583095—21no—
41#14583063—21no—
42#14583040—21no—
43#14583035—21no—
44#14583035—21no—
45C4×Dic172C2211yescharacteristic, complemented
46C4×D344C2211yescharacteristic
47#14582725C2211yescharacteristic, complemented
48#14582704C2211yescharacteristic, complemented
49#14582704C2211yescharacteristic, complemented
50#14582701C2211yescharacteristic
51#14582701C2211yescharacteristic, complemented
52#14582701C2211yescharacteristic, complemented
53#14582701C2211yescharacteristic, complemented
54C2×M32×C43C2211yescharacteristic, complemented
55C22×C16×C43C2211yescharacteristic, complemented
56C8×D4×C43C2211yescharacteristic
57C43×C4⋊C16C2211yescharacteristic, complemented
58C43×C22⋊C16C2211yescharacteristic, complemented
59C43×C22⋊C16C2211yescharacteristic, complemented
60C43×#346C2211yescharacteristic, complemented
61C2×#10621898—21no—
62C22×Dic86—21no—
63C22×D172—21no—
64C22×D172—21no—
65C2×D4×D43—41no—
66#13063347—22no—
67#13063347—41no—
68C2×Dic172—22no—
69C2×Dic172—21no—
70C2×Dic172—41no—
71C2×Dic172C2311yescharacteristic
72C2×Dic172C2311yescharacteristic
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×D344—22no—
76C2×D344—22no—
77C2×D344—21no—
78C2×D344—21no—
79C2×D344—21no—
80C2×D344—41no—
81C2×D344—41no—
82C2×D344C2311yescharacteristic
83C2×D344C2311yescharacteristic
84C2×D344C2311yescharacteristic
85C2×D344C2311yescharacteristic
86#13063322—21no—
87#13063313—21no—
88#13063311—41no—
89#13063304—21no—
90#13063303—41no—
91#13063300—41no—
92#13063299—21no—
93#13063299—21no—
94#13063299—21no—
95#13063297—41no—
96#13063295—41no—
97#13063295—41no—
98C4×Dic86—21no—
99C4×D172—21no—
100(C22⋊D43)⋊C4—41no—
101#13063270—22no—
102#13063270—22no—
103#13063270—22no—
104#13063270—22no—
105#13063270—41no—
106#13063270D414yescomplemented
107D688—22no—
108D688—22no—
109D688—41no—
110#13063259C2311yescharacteristic
111#13063259C2311yescharacteristic
112#13063250—21no—
113#13063250—21no—
114#13063247—21no—
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C4×D4×C43D411yescharacteristic
121M32×C43—22no—
122C2×C16×C43—22no—
123C2×C16×C43C2311yescharacteristic
124C2×C16×C43C2311yescharacteristic
125C2×C16×C43C2311yescharacteristic
126C2×C16×C43C2311yescharacteristic
127C4⋊C8×C43D411yescharacteristic
128C22⋊C8×C43D411yescharacteristic
129C22⋊C8×C43D411yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C23×D43—41no—
132C23×D43—41no—
133C2×D4×C43D811yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C2×C22⋊D43—41no—
137C2×C22⋊D43—41no—
138C2×C22⋊D43—41no—
139C2×C22⋊D43—41no—
140C22×Dic43—41no—
141D4×D43—84no—
142#10621898—42no—
143#10621898—81no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—41no—
149C2×D172—41no—
150C2×D172—41no—
151C2×D172—41no—
152C2×D172—42no—
153C2×D172—42no—
154C2×D172—81no—
155C2×D172—81no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—42no—
161C2×Dic86—41no—
162C2×Dic86—81no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2411yescharacteristic
171C4⋊C4×C43D811yescharacteristic
172C22⋊C4×C43D811yescharacteristic
173C22⋊C4×C43D811yescharacteristic
174C42×C43C2×D411yescharacteristic
175C22⋊Dic43—41no—
176(C2×D43)⋊C4—41no—
177(C2×D43)⋊C4—41no—
178(C2×D43)⋊C4—41no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—41no—
181(C2×D43)⋊C4—41no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184Dic43⋊C4—41no—
185Dic43⋊C4—41no—
186C4×Dic43—41no—
187Dic172—21no—
188Dic172—21no—
189Dic172—21no—
190Dic172—42no—
191Dic172C2×D412yescomplemented
192D344—21no—
193D344—21no—
194D344—21no—
195D344—21no—
196D344—21no—
197D344—21no—
198D344—21no—
199D344—42no—
200D344—42no—
201D344—81no—
202D344C2×D412yes—
203#10621873—42no—
204#10621873—81no—
205C16×C43—21no—
206C16×C43—21no—
207C16×C43—21no—
208C16×C43C2×D412yescomplemented
209C23×C43C2×D811yescharacteristic
210C23×C43C2×D811yescharacteristic
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—82no—
216C22×D43—82no—
217C22×D43—82no—
218C22×D43—82no—
219C22×D43—161no—
220C22×D43—161no—
221D4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43C2×D811yescharacteristic
227C2×C4×C43C2×D811yescharacteristic
228C2×C4×C43C2×D811yescharacteristic
229C2×C4×C43C2×D811yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C22⋊D43—82no—
232C22⋊D43—82no—
233C22⋊D43—82no—
234C22⋊D43—82no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—82no—
240D172—22no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—82no—
249D172—82no—
250D172—82no—
251D172—161no—
252C4×D43—82no—
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#50912yescomplemented
271C22×C43C22×D811yescharacteristic
272C2×D43—42no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—164no—
285C2×D43—164no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43D4211yescharacteristic
291C4×C43#57611yescharacteristic
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295Dic43—81no—
296C2×#509—431no—
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#2168D4311yescharacteristic, complemented
311C2×C43—22no—
312C2×C43—41no—
313C2×C43D4×D811yescharacteristic
314C2×C43C2×#50911yescharacteristic
315C2×C43#341611yescharacteristic
316D43—82no—
317D43—161no—
318D43—161no—
319D43—161no—
320C2×#135—431no—
321C22×Q16—431no—
322C22×D8—431no—
323C22×D8—431no—
324#548—861no—
325D42—861no—
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×M32C2×D4311yescharacteristic, complemented
338C22×C16C2×D4311yescharacteristic, complemented
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×D4C2×D4311yescharacteristic
354#366—431no—
355C4⋊C16C2×D4311yescharacteristic, complemented
356#358—431no—
357#358—431no—
358#357—431no—
359#357—431no—
360#357—431no—
361#357—431no—
362C22⋊C16C2×D4311yescharacteristic, complemented
363C22⋊C16C2×D4311yescharacteristic, complemented
364#346C2×D4311yescharacteristic, complemented
365C43#3383111yescharacteristic, complemented, Sylow
366C2×#41—861no—
367C22×Q8—861no—
368C22×D4—861no—
369C22×D4—861no—
370C22×D4—1721no—
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—431no—
381C2×D8—431no—
382C2×D8—431no—
383C2×D8—431no—
384C2×D8—862no—
385C2×D8—862no—
386C2×D8—861no—
387C2×D8—861no—
388C2×D8—861no—
389C2×D8—1721no—
390C2×D8—1721no—
391C22×C8C22×D4311yescharacteristic
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—861no—
407C4×D4—1721no—
408C4×D4D17211yescharacteristic
409SD32—434no—
410SD32—862no—
411SD32—862no—
412SD32—862no—
413SD32—862no—
414SD32—1721no—
415D16—862no—
416D16—862no—
417D16—1721no—
418M32—22no—
419C2×C16—22no—
420C2×C16C22×D4311yescharacteristic
421C2×C16C22×D4311yescharacteristic
422C2×C16C22×D4311yescharacteristic
423C2×C16C22×D4311yescharacteristic
424#107—431no—
425#107—431no—
426C4⋊C8D17211yescharacteristic
427#103—861no—
428#103—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433C22⋊C8D17211yescharacteristic
434C22⋊C8D17211yescharacteristic
435C4×C8C22×D4311yescharacteristic
436C24—1721no—
437C24—1721no—
438#41—3441no—
439#41—1722no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—3441no—
443C2×Q8—1722no—
444C2×Q8—1721no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—3441no—
450C2×D4—3441no—
451C2×D4—3444no—
452C2×D4—1722no—
453C2×D4—1722no—
454C2×D4—1721no—
455C2×D4—1721no—
456C2×D4—1721no—
457C2×D4—1721no—
458C2×D4—1721no—
459C2×D4—1721no—
460C2×D4—1721no—
461C2×D4—1721no—
462C2×D4D34411yescharacteristic
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4—1721no—
466C22×C4C2×D17211yescharacteristic
467C22×C4C2×D17211yescharacteristic
468Q16—432no—
469Q16—861no—
470Q16—861no—
471Q16—861no—
472Q16—1722no—
473SD16—3441no—
474SD16—1722no—
475D8—432no—
476D8—861no—
477D8—861no—
478D8—861no—
479D8—861no—
480D8—861no—
481D8—861no—
482D8—861no—
483D8—3441no—
484D8—1722no—
485D8—1722no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8C2×D17211yescharacteristic
491C2×C8C2×D17211yescharacteristic
492C2×C8C2×D17211yescharacteristic
493C2×C8C23×D4311yescharacteristic
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—1721no—
497C4⋊C4—1721no—
498C4⋊C4D34411yescharacteristic
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C22⋊C4—1721no—
505C22⋊C4—1721no—
506C22⋊C4D34411yescharacteristic
507C22⋊C4D34411yescharacteristic
508C42—1721no—
509C42C2×D17211yescharacteristic
510C16—21no—
511C16—21no—
512C16—21no—
513C16D4×D4312yescomplemented
514C23—3442no—
515C23—3442no—
516C23—3442no—
517C23—3442no—
518C23—1721no—
519C23—1721no—
520C23—1721no—
521C23—1721no—
522C23—6881no—
523C23—6881no—
524C23C2×D34411yescharacteristic
525C23C2×D34411yescharacteristic
526Q8—862no—
527Q8—3442no—
528Q8—1721no—
529Q8—1721no—
530Q8—1721no—
531D4—22no—
532D4—862no—
533D4—3442no—
534D4—3442no—
535D4—3442no—
536D4—3442no—
537D4—3442no—
538D4—3442no—
539D4—3442no—
540D4—1721no—
541D4—1721no—
542D4—1721no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546D4—1721no—
547D4—6881no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—3442no—
553C2×C4—3442no—
554C2×C4—3442no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4C2×D34411yescharacteristic
560C2×C4C2×D34411yescharacteristic
561C2×C4C2×D34411yescharacteristic
562C2×C4C2×D34411yescharacteristic
563C2×C4C22×D17211yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8C2×D4×D4311yescharacteristic
568C8#1306337111yescharacteristic
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—3441no—
584C22—3441no—
585C22—1722no—
586C22—6884no—
587C22—6884no—
588C22#1458333712yescomplemented
589C22C22×D34411yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—3441no—
595C4—3441no—
596C4—3441no—
597C4—1722no—
598C4D4×D17211yescharacteristic
599C4#1458370411yescharacteristic
600C2—22no—
601C2—41no—
602C2—3442no—
603C2—6881no—
604C2—6881no—
605C2—6881no—
606C2D4×D34411yescharacteristic
607C2C2×#1458333711yescharacteristic
608C2#1914774311yescharacteristic
subgroupG/H
centerC22C22×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2168C2
socleC22×C43C22×D8
hypercenter#2168D43
hypocenterC43#33831
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. C2×#14583337C2semidirect
2. C22×#13063270C2semidirect
3. #19146338C2semidirect
4. D4×D344C2semidirect
5. #19136861C2semidirect
6. #19136708C2semidirect
7. #19136681C2semidirect
8. #19136651C2semidirect
9. #19136636C2semidirect
10. #19136526C2semidirect
11. #19136520C2semidirect
12. #19136514C2semidirect
13. #19136509C2semidirect
14. #19136461C2semidirect
15. C43×#2168C2semidirect
16. C2×#13063347C22semidirect
17. C22×Dic172C22semidirect
26. C2×#13063270C22semidirect
27. C2×#13063270C22semidirect
28. C2×#13063270C22semidirect
29. C2×#13063270C22semidirect
31. C2×D688C22semidirect
32. C2×D688C22semidirect
33. #14583283C22semidirect
35. #14583140C22semidirect
38. #14583135C22semidirect
45. C4×Dic172C22semidirect
47. #14582725C22semidirect
48. #14582704C22semidirect
49. #14582704C22semidirect
51. #14582701C22semidirect
52. #14582701C22semidirect
53. #14582701C22semidirect
54. C2×M32×C43C22semidirect
55. C22×C16×C43C22semidirect
57. C43×C4⋊C16C22semidirect
58. C43×C22⋊C16C22semidirect
59. C43×C22⋊C16C22semidirect
60. C43×#346C22semidirect
106. #13063270D4semidirect
191. Dic172C2×D4semidirect
208. C16×C43C2×D4semidirect
270. C22×C43#509semidirect
310. #2168D43semidirect
337. C2×M32C2×D43semidirect
338. C22×C16C2×D43semidirect
355. C4⋊C16C2×D43semidirect
362. C22⋊C16C2×D43semidirect
363. C22⋊C16C2×D43semidirect
364. #346C2×D43semidirect
365. C43#33831semidirect
513. C16D4×D43semidirect
588. C22#14583337semidirect

Maximal subgroups

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

subgroupindex
C2×#145833372
C22×#130632702
#191463382
D4×D3442
#191368612
#191367082
#191366812
#191366512
#191366362
#191365262
#191365202
#191365142
#191365092
#191364612
C43×#21682
#3383143