Finite Group Databasebeta

← #25253424

Subgroups — #25253424

Order 11008.

622 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146984C211yesmaximal, characteristic, complemented
2D8×C22⋊D43C211yesmaximal, characteristic
3#19136817C211yesmaximal, characteristic, complemented
4#19136781C211yesmaximal, characteristic, complemented
5#19136779C211yesmaximal, characteristic, complemented
6#19136740C211yesmaximal, characteristic, complemented
7#19136693C211yesmaximal, characteristic, complemented
8#19136688C211yesmaximal, characteristic, complemented
9#19136633C211yesmaximal, characteristic, complemented
10#19136522C211yesmaximal, characteristic, complemented
11SD32×Dic43C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C16C211yesmaximal, characteristic, complemented
13C2×#14582700C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2187C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583607—21no—
18D4×C22⋊D43—21no—
19C2×#13063268C2211yescharacteristic, complemented
20C22×C43⋊C16C2211yescharacteristic, complemented
21C2×C16×D43C2211yescharacteristic, complemented
22#14583303C2211yescharacteristic, complemented
23#14583274C2211yescharacteristic
24#14583233—21no—
25#14583232—21no—
26#14583192—21no—
27#14583137C2211yescharacteristic, complemented
28#14583135C2211yescharacteristic
29#14583132C2211yescharacteristic
30#14583092—21no—
31#14583033—21no—
32#14583031—21no—
33Q16×Dic43C2211yescharacteristic, complemented
34D8×Dic43C2211yescharacteristic
35C8×C22⋊D43C2211yescharacteristic
36C2×#13063259C2211yescharacteristic, complemented
37#107×D43C2211yescharacteristic, complemented
38#14582727C2211yescharacteristic, complemented
39#14582727C2211yescharacteristic, complemented
40#14582726C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42#14582703C2211yescharacteristic, complemented
43#14582701C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582700C2211yescharacteristic, complemented
48#14582700C2211yescharacteristic, complemented
49#14582699C2211yescharacteristic, complemented
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C22×D8×C43C2211yescharacteristic
53C2×SD32×C43C2211yescharacteristic
54C2×SD32×C43C2211yescharacteristic, complemented
55C43×#467C2211yescharacteristic, complemented
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic, complemented
58C43×C22⋊C16C2211yescharacteristic, complemented
59C22×C22⋊D43—41no—
60C2×D4×D43—21no—
61C2×D344C2311yescharacteristic
62C2×#10621882—21no—
63C2×#10621882—21no—
64D8×D43—22no—
65D8×D43—41no—
66C2×C8×D43C2311yescharacteristic
67#13063324—21no—
68#13063321—21no—
69#13063315—41no—
70#13063305—41no—
71#13063302—41no—
72#13063301—21no—
73#13063299—21no—
74#13063297—41no—
75#13063296—21no—
76#13063294—41no—
77#13063293—41no—
78Q8×Dic43—21no—
79D4×Dic43—21no—
80C4×C22⋊D43D411yescharacteristic
81(C22⋊D43)⋊C4—41no—
82C2×C4⋊Dic43—21no—
83C4⋊C4×D43—21no—
84#13063268—41no—
85C2×C43⋊C16—41no—
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88C16×D43—41no—
89#13063259—21no—
90#13063259C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95Dic43⋊C8D411yescharacteristic
96#13063249—21no—
97#13063249—21no—
98#13063247—21no—
99#13063246—21no—
100#13063246—21no—
101C22⋊(C43⋊C8)D411yescharacteristic
102(C2×D43)⋊C8D411yescharacteristic
103C8×Dic43C2311yescharacteristic
104C22×D4×C43—21no—
105C2×Q16×C43C2311yescharacteristic
106C2×D8×C43—22no—
107C2×D8×C43—21no—
108C2×D8×C43—41no—
109C2×D8×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22⋊Q8×C43—21no—
113SD32×C43—22no—
114SD32×C43—41no—
115C2×C16×C43C2311yescharacteristic
116C2×C16×C43C2311yescharacteristic
117#107×C43C2311yescharacteristic
118#103×C43—21no—
119C24×C43—41no—
120C23×D43—41no—
121C2×Q8×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—41no—
125C2×D4×C43—42no—
126C2×D4×C43—81no—
127C22×C4×C43C2×D411yescharacteristic
128C2×C22⋊D43—41no—
129C2×C22⋊D43—41no—
130C2×C22⋊D43—41no—
131C2×C22⋊D43—41no—
132C2×C22⋊D43—41no—
133C2×C22⋊D43—84no—
134C2×C22⋊D43D811yescharacteristic
135C22×Dic43—41no—
136C22×Dic43—41no—
137D4×D43—42no—
138D4×D43—81no—
139C2×D172—21no—
140C2×C4×D43—41no—
141C2×C4×D43C2×D411yescharacteristic
142C2×Dic86—41no—
143Q16×C43—21no—
144Q16×C43—21no—
145D8×C43—21no—
146D8×C43—21no—
147D8×C43—21no—
148D8×C43—42no—
149D8×C43#4112yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43C2×D411yescharacteristic
153C2×C8×C43C2411yescharacteristic
154C4⋊C4×C43—21no—
155C4⋊C4×C43—41no—
156C22⋊C4×C43—41no—
157C22⋊Dic43—41no—
158C22⋊Dic43—41no—
159C22⋊Dic43D811yescharacteristic
160#10621882—42no—
161#10621882—81no—
162(C2×D43)⋊C4—41no—
163(C2×D43)⋊C4—41no—
164(C2×D43)⋊C4D811yescharacteristic
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—41no—
169C4⋊Dic43—41no—
170Dic43⋊C4—41no—
171Dic43⋊C4—41no—
172Dic43⋊C4—41no—
173Dic43⋊C4D811yescharacteristic
174C4×Dic43—41no—
175C4×Dic43C2×D411yescharacteristic
176C2×C43⋊C8C2×D411yescharacteristic
177C2×C43⋊C8C2×D411yescharacteristic
178D344—21no—
179D344—21no—
180C8×D43—21no—
181C8×D43—21no—
182C16×C43—21no—
183C16×C43—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—82no—
189C23×C43—82no—
190C23×C43—161no—
191C23×C43C2×D811yescharacteristic
192C22×D43—41no—
193C22×D43—82no—
194C22×D43—82no—
195C22×D43—161no—
196C22×D43C2×D811yescharacteristic
197Q8×C43—41no—
198Q8×C43—41no—
199D4×C43—22no—
200D4×C43—41no—
201D4×C43—41no—
202D4×C43—41no—
203D4×C43—82no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43C2×D811yescharacteristic
209C2×C4×C43C22×D411yescharacteristic
210C22⋊D43—82no—
211C22⋊D43—82no—
212C22⋊D43—82no—
213C22⋊D43—82no—
214C22⋊D43—161no—
215C22⋊D43SD3214yescomplemented
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—82no—
220C2×Dic43—161no—
221C2×Dic43C2×D811yescharacteristic
222C2×Dic43C2×D811yescharacteristic
223C2×Dic43C2×D811yescharacteristic
224D172—41no—
225D172—41no—
226C4×D43—21no—
227C4×D43—21no—
228C4×D43—161no—
229Dic86—161no—
230C8×C43—21no—
231C8×C43C2×#4111yescharacteristic
232C8×C43H(5,𝔽2)11yescharacteristic
233C43⋊C8—21no—
234C43⋊C8—21no—
235#33862—431nomaximal, Sylow
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—42no—
239C22×C43—81no—
240C22×C43—81no—
241C22×C43—81no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43—164no—
245C22×C43C2×SD3212yes—
246C22×C43C22×D811yescharacteristic
247C2×D43—21no—
248C2×D43—21no—
249C2×D43—81no—
250C2×D43—81no—
251C2×D43—81no—
252C2×D43—164no—
253C2×D43C2×SD3212yes—
254C4×C43—21no—
255C4×C43—81no—
256C4×C43—81no—
257C4×C43#54611yescharacteristic
258C4×C43#57711yescharacteristic
259Dic43—21no—
260Dic43—21no—
261Dic43—81no—
262Dic43—81no—
263Dic43—81no—
264Dic43C2×SD3212yes—
265#3338—431no—
266D4×D8—431no—
267#2240—431no—
268#2233—431no—
269#2233—431no—
270#2226—431no—
271#2217—431no—
272#2217—431no—
273#2207—431no—
274#2187—431no—
275#2187D4311yescharacteristic, complemented
276C4×SD32—431no—
277D4×C16—431no—
278C2×#357—431no—
279C2×#357—431no—
280C2×C43—22no—
281C2×C43—82no—
282C2×C43—161no—
283C2×C43#329411yescharacteristic
284C2×C43C22×SD3211yescharacteristic
285C2×C43#341511yescharacteristic
286D43—22no—
287D43—161no—
288C22×D8—431no—
289C22×D8C2×D4311yescharacteristic
290#554—861no—
291D42—861no—
292C2×SD32—431no—
293C2×SD32C2×D4311yescharacteristic
294C2×SD32C2×D4311yescharacteristic, complemented
295C22×C16—431no—
296C22×C16—431no—
297#500—431no—
298#493—431no—
299#484—861no—
300#484—861no—
301#477—861no—
302#467—431no—
303#467C2×D4311yescharacteristic, complemented
304#466—431no—
305#466—431no—
306#459—861no—
307#447—861no—
308#447—861no—
309C4×Q16—431no—
310C4×D8—431no—
311C8×D4—431no—
312C2×#107—431no—
313C2×#107—431no—
314#367—431no—
315#367—431no—
316#367—431no—
317C4⋊C16—431no—
318#358—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322#357—431no—
323#357—431no—
324#357—431no—
325#357—431no—
326#357C2×D4311yescharacteristic
327#357C2×D4311yescharacteristic, complemented
328C22⋊C16—431no—
329C22⋊C16C2×D4311yescharacteristic, complemented
330C4×C16—431no—
331C43#3386211yescharacteristic, complemented, Sylow
332C22×D4—21no—
333C22×D4—861no—
334C22×D4—1721no—
335C2×Q16C22×D4311yescharacteristic
336C2×D8—22no—
337C2×D8—21no—
338C2×D8—41no—
339C2×D8—431no—
340C2×D8—861no—
341C2×D8—861no—
342C2×D8—862no—
343C2×D8—1721no—
344C2×D8C22×D4311yescharacteristic
345C2×D8C22×D4311yescharacteristic
346C22×C8—431no—
347C22×C8C22×D4311yescharacteristic
348C4⋊Q8—861no—
349#127—861no—
350#125—1721no—
351C22⋊Q8—21no—
352C22⋊Q8—861no—
353C22⋊Q8—1721no—
354C22⋊Q8—1721no—
355#121—861no—
356#121—861no—
357#121—1721no—
358#120—1721no—
359#120—1721no—
360C4×Q8—861no—
361C4×D4—431no—
362C4×D4—861no—
363C4×D4—1721no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366SD32—22no—
367SD32—41no—
368SD32—1721no—
369C2×C16—431no—
370C2×C16—431no—
371C2×C16—1721no—
372C2×C16—1721no—
373C2×C16C22×D4311yescharacteristic
374C2×C16C22×D4311yescharacteristic
375#107—431no—
376#107—431no—
377#107—431no—
378#107—861no—
379#107—861no—
380#107—861no—
381#107C22×D4311yescharacteristic
382C4⋊C8—431no—
383#103—21no—
384#103—861no—
385#103—861no—
386#102—861no—
387#102—861no—
388#102—861no—
389C22⋊C8—431no—
390C22⋊C8—431no—
391C4×C8—431no—
392C24—41no—
393C24—1721no—
394C2×Q8—21no—
395C2×Q8—1721no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—81no—
401C2×D4—431no—
402C2×D4—861no—
403C2×D4—3441no—
404C2×D4—3444no—
405C2×D4—1721no—
406C2×D4—1721no—
407C2×D4—1721no—
408C2×D4—1722no—
409C2×D4—1721no—
410C2×D4—1721no—
411C22×C4—431no—
412C22×C4—1721no—
413C22×C4—1721no—
414C22×C4—1721no—
415C22×C4D4×D4311yescharacteristic
416Q16—21no—
417Q16—21no—
418D8—21no—
419D8—21no—
420D8—21no—
421D8—42no—
422D8—861no—
423D8—861no—
424D8—3441no—
425D8—1722no—
426D8#1062190012yes—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—431no—
430C2×C8—431no—
431C2×C8—861no—
432C2×C8—861no—
433C2×C8D4×D4311yescharacteristic
434C2×C8C23×D4311yescharacteristic
435C4⋊C4—21no—
436C4⋊C4—41no—
437C4⋊C4—431no—
438C4⋊C4—861no—
439C4⋊C4—861no—
440C4⋊C4—861no—
441C4⋊C4—1721no—
442C4⋊C4—1721no—
443C4⋊C4—1721no—
444C4⋊C4—1721no—
445C4⋊C4—1721no—
446C22⋊C4—41no—
447C22⋊C4—431no—
448C22⋊C4—431no—
449C22⋊C4—1721no—
450C22⋊C4—1721no—
451C22⋊C4—1721no—
452C22⋊C4—1721no—
453C42—431no—
454C42—1721no—
455C16—21no—
456C16—21no—
457C16—861no—
458C16—861no—
459C23—41no—
460C23—41no—
461C23—82no—
462C23—82no—
463C23—161no—
464C23—431no—
465C23—3442no—
466C23—3442no—
467C23—1721no—
468C23—6881no—
469C23D8×D4311yescharacteristic
470Q8—41no—
471Q8—41no—
472Q8—6881no—
473D4—22no—
474D4—41no—
475D4—41no—
476D4—41no—
477D4—82no—
478D4—434no—
479D4—3442no—
480D4—3442no—
481D4—3442no—
482D4—3442no—
483D4—1721no—
484D4—1721no—
485D4—6881no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—431no—
491C2×C4—431no—
492C2×C4—431no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—3442no—
496C2×C4—1721no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4—6881no—
500C2×C4—6881no—
501C2×C4D8×D4311yescharacteristic
502C2×C4C2×D4×D4311yescharacteristic
503C8—21no—
504C8—861no—
505C8—861no—
506C8C2×#1062190011yescharacteristic
507C8#1306337011yescharacteristic
508C22—21no—
509C22—21no—
510C22—42no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—164no—
517C22—432no—
518C22—861no—
519C22—861no—
520C22—3441no—
521C22—3441no—
522C22—3441no—
523C22—6884no—
524C22SD32×D4312yes—
525C22C2×D8×D4311yescharacteristic
526C4—21no—
527C4—81no—
528C4—81no—
529C4—432no—
530C4—861no—
531C4—861no—
532C4—3441no—
533C4—3441no—
534C4—3441no—
535C4#1458353611yescharacteristic
536C4#1458370911yescharacteristic
537C2—22no—
538C2—82no—
539C2—161no—
540C2—862no—
541C2—6881no—
542C2#1914640111yescharacteristic
543C2C2×SD32×D4311yescharacteristic
544C2#1914773511yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2187C2
socleC22×C43C22×D8
prime radicalD8×C22⋊D43C2
hypercenter#2187D43
hypocenterC43#33862
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #19146984C2semidirect
3. #19136817C2semidirect
4. #19136781C2semidirect
5. #19136779C2semidirect
6. #19136740C2semidirect
7. #19136693C2semidirect
8. #19136688C2semidirect
9. #19136633C2semidirect
10. #19136522C2semidirect
11. SD32×Dic43C2semidirect
12. (C22⋊D43)⋊C16C2semidirect
13. C2×#14582700C2semidirect
14. #357×D43C2semidirect
15. C43×#2187C2semidirect
19. C2×#13063268C22semidirect
20. C22×C43⋊C16C22semidirect
21. C2×C16×D43C22semidirect
22. #14583303C22semidirect
27. #14583137C22semidirect
33. Q16×Dic43C22semidirect
36. C2×#13063259C22semidirect
37. #107×D43C22semidirect
38. #14582727C22semidirect
39. #14582727C22semidirect
40. #14582726C22semidirect
41. Dic43⋊C16C22semidirect
42. #14582703C22semidirect
43. #14582701C22semidirect
44. #14582701C22semidirect
47. #14582700C22semidirect
48. #14582700C22semidirect
49. #14582699C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. C16×Dic43C22semidirect
54. C2×SD32×C43C22semidirect
55. C43×#467C22semidirect
57. C43×#357C22semidirect
58. C43×C22⋊C16C22semidirect
215. C22⋊D43SD32semidirect
275. #2187D43semidirect
294. C2×SD32C2×D43semidirect
303. #467C2×D43semidirect
327. #357C2×D43semidirect
329. C22⋊C16C2×D43semidirect
331. C43#33862semidirect

Maximal subgroups

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

subgroupindex
#191469842
D8×C22⋊D432
#191368172
#191367812
#191367792
#191367402
#191366932
#191366882
#191366332
#191365222
SD32×Dic432
(C22⋊D43)⋊C162
C2×#145827002
#357×D432
C43×#21872
#3386243