Finite Group Databasebeta

← #25253633

Subgroups — #25253633

Order 11008.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146965C211yesmaximal, characteristic, complemented
2D8×D172C211yesmaximal, characteristic
3#19136837C211yesmaximal, characteristic, complemented
4#19136789C211yesmaximal, characteristic, complemented
5#19136777C211yesmaximal, characteristic, complemented
6#19136752C211yesmaximal, characteristic, complemented
7#19136711C211yesmaximal, characteristic, complemented
8#19136694C211yesmaximal, characteristic, complemented
9#19136635C211yesmaximal, characteristic, complemented
10#19136522C211yesmaximal, characteristic, complemented
11#19136522C211yesmaximal, characteristic, complemented
12#19136422C211yesmaximal, characteristic, complemented
13#19136309C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2175C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583590—21no—
19D4×D172—21no—
20C2×#13063268C2211yescharacteristic, complemented
21C2×#13063268C2211yescharacteristic, complemented
22C2×#13063264C2211yescharacteristic, complemented
23C2×C16×D43C2211yescharacteristic, complemented
24#14583301C2211yescharacteristic, complemented
25#14583276C2211yescharacteristic
26#14583238—21no—
27#14583228—21no—
28#14583206—21no—
29#14583137C2211yescharacteristic, complemented
30#14583137C2211yescharacteristic, complemented
31#14583136C2211yescharacteristic
32#14583136C2211yescharacteristic
33#14583094—21no—
34#14583034—21no—
35#14583034—21no—
36C8×D172C2211yescharacteristic
37#14582936C2211yescharacteristic, complemented
38#107×D43C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41C4⋊(C43⋊C16)C2211yescharacteristic, complemented
42#14582701C2211yescharacteristic, complemented
43#14582701C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic, complemented
46#14582700C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582699C2211yescharacteristic, complemented
49#14582699C2211yescharacteristic, complemented
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51(C2×D43)⋊C16C2211yescharacteristic, complemented
52C2×SD32×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic, complemented
54C4×D8×C43C2211yescharacteristic
55C43×#366C2211yescharacteristic, complemented
56C43×#358C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C43×#346C2211yescharacteristic, complemented
59C22×D172—41no—
60C2×D4×D43—21no—
61C2×D4×D43—21no—
62C2×D344—21no—
63C2×D344C2311yescharacteristic
64C2×D344C2311yescharacteristic
65C2×#10621882—21no—
66C2×#10621882—21no—
67D8×D43—22no—
68D8×D43—22no—
69D8×D43—41no—
70D8×D43—41no—
71C2×C8×D43C2311yescharacteristic
72C2×C8×D43C2311yescharacteristic
73#13063322—21no—
74#13063319—41no—
75#13063317—21no—
76#13063315—41no—
77#13063310—41no—
78#13063301—21no—
79#13063301—21no—
80#13063300—21no—
81#13063300—21no—
82#13063299—41no—
83#13063295—41no—
84#13063295—41no—
85C4×D172D411yescharacteristic
86#13063283—21no—
87#13063282—41no—
88C4⋊C4×D43—21no—
89#13063268—41no—
90#13063268—41no—
91#13063264—41no—
92C2×C43⋊C16C2311yescharacteristic
93C2×C43⋊C16C2311yescharacteristic
94C16×D43—41no—
95#13063259C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063258—21no—
98#13063257—21no—
99#13063256—21no—
100C4⋊(C43⋊C8)D411yescharacteristic
101#13063249—21no—
102#13063249—21no—
103#13063245—21no—
104#13063245—21no—
105(C2×D43)⋊C8D411yescharacteristic
106(C2×D43)⋊C8D411yescharacteristic
107C2×Q16×C43C2311yescharacteristic
108C2×D8×C43C2311yescharacteristic
109C4×Q8×C43—21no—
110C4×D4×C43—21no—
111SD32×C43—22no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#103×C43—21no—
117#102×C43—21no—
118C4×C8×C43C2311yescharacteristic
119C23×D43—41no—
120C23×D43—41no—
121C2×Q8×C43—21no—
122C2×D4×C43—21no—
123C22×C4×C43—41no—
124C2×C22⋊D43—41no—
125C2×C22⋊D43—41no—
126D4×D43—42no—
127D4×D43—42no—
128D4×D43—81no—
129D4×D43—81no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—41no—
133C2×D172—41no—
134C2×D172—41no—
135C2×D172—41no—
136C2×D172—84no—
137C2×D172D811yescharacteristic
138C2×C4×D43—41no—
139C2×C4×D43C2×D411yescharacteristic
140C2×C4×D43C2×D411yescharacteristic
141Q16×C43—21no—
142Q16×C43—21no—
143D8×C43—21no—
144D8×C43#4112yes—
145C2×C8×C43C2×D411yescharacteristic
146C2×C8×C43C2411yescharacteristic
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C42×C43—41no—
152C42×C43C2×D411yescharacteristic
153#10621882—42no—
154#10621882—42no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4D811yescharacteristic
161(C2×D43)⋊C4D811yescharacteristic
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43D811yescharacteristic
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169Dic43⋊C4—41no—
170C4×Dic43—41no—
171C2×C43⋊C8C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173D344—21no—
174D344—21no—
175D344—21no—
176D344—21no—
177D344—81no—
178C8×D43—21no—
179C8×D43—21no—
180C8×D43—21no—
181C8×D43—21no—
182C16×C43—21no—
183C16×C43—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C22×D43—41no—
188C22×D43—41no—
189C22×D43—82no—
190C22×D43—82no—
191C22×D43—82no—
192C22×D43—82no—
193C22×D43—161no—
194C22×D43—161no—
195C22×D43C2×D811yescharacteristic
196C22×D43C2×D811yescharacteristic
197Q8×C43—41no—
198Q8×C43—41no—
199D4×C43—22no—
200D4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—82no—
205C2×C4×C43C2×D811yescharacteristic
206C2×C4×C43C2×D811yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C22⋊D43—82no—
209C22⋊D43—82no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43C2×D811yescharacteristic
213C2×Dic43C2×D811yescharacteristic
214D172—22no—
215D172—41no—
216D172—41no—
217D172—41no—
218D172—41no—
219D172—82no—
220D172—82no—
221D172—82no—
222D172—161no—
223C4×D43—21no—
224C4×D43—21no—
225C4×D43—21no—
226C4×D43—21no—
227C4×D43—82no—
228C8×C43—21no—
229C8×C43C2×#4111yescharacteristic
230C8×C43H(5,𝔽2)11yescharacteristic
231C43⋊C8—21no—
232C43⋊C8—21no—
233#33877—431nomaximal, Sylow
234C22×C43—42no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43C22×D811yescharacteristic
238C2×D43—21no—
239C2×D43—21no—
240C2×D43—21no—
241C2×D43—21no—
242C2×D43—21no—
243C2×D43—81no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—164no—
250C2×D43—164no—
251C2×D43#50912yes—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—81no—
255C4×C43—81no—
256C4×C43—81no—
257C4×C43#54611yescharacteristic
258C4×C43#57711yescharacteristic
259Dic43—21no—
260Dic43—21no—
261Dic43—81no—
262Dic43—81no—
263#3336—431no—
264D4×D8—431no—
265#2244—431no—
266#2234—431no—
267#2232—431no—
268#2228—431no—
269#2220—431no—
270#2217—431no—
271#2207—431no—
272#2187—431no—
273#2187—431no—
274#2175D4311yescharacteristic, complemented
275#2168—431no—
276#2140—431no—
277C2×#357—431no—
278C2×C43—82no—
279C2×C43#329411yescharacteristic
280C2×C43C2×#50911yescharacteristic
281C2×C43#341611yescharacteristic
282D43—22no—
283D43—41no—
284D43—161no—
285D43—161no—
286C22×D8—431no—
287C22×D8—431no—
288#552—861no—
289D42—861no—
290C2×SD32—431no—
291C2×SD32—431no—
292C2×SD32C2×D4311yescharacteristic
293C2×M32—431no—
294C22×C16—431no—
295#499—431no—
296#493—431no—
297#485—861no—
298#483—861no—
299#479—861no—
300#467—431no—
301#467—431no—
302#466—431no—
303#466—431no—
304#459—861no—
305#447—861no—
306#447—861no—
307C4×Q16C2×D4311yescharacteristic, complemented
308C4×D8C2×D4311yescharacteristic
309C8×D4—431no—
310#427—431no—
311C2×#107—431no—
312#367—431no—
313#366—431no—
314#366C2×D4311yescharacteristic, complemented
315C4⋊C16—431no—
316#358C2×D4311yescharacteristic, complemented
317#357—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322#357—431no—
323#357—431no—
324#357—431no—
325#357C2×D4311yescharacteristic
326C22⋊C16—431no—
327C22⋊C16—431no—
328#346C2×D4311yescharacteristic, complemented
329C43#3387711yescharacteristic, complemented, Sylow
330C22×D4—861no—
331C22×D4—861no—
332C22×D4—1721no—
333C2×Q16C22×D4311yescharacteristic
334C2×D8—431no—
335C2×D8—431no—
336C2×D8—861no—
337C2×D8—861no—
338C2×D8—862no—
339C2×D8—862no—
340C2×D8—861no—
341C2×D8—1721no—
342C2×D8—1721no—
343C2×D8C22×D4311yescharacteristic
344C22×C8—431no—
345C22×C8—431no—
346#127—861no—
347#126—1721no—
348#125—861no—
349#125—1721no—
350#123—1721no—
351C22⋊Q8—861no—
352C22⋊Q8—861no—
353#121—861no—
354#121—861no—
355#121—1721no—
356#120—1721no—
357#120—1721no—
358C4×Q8—21no—
359C4×D4—21no—
360C4×D4—431no—
361#117—861no—
362#117—1721no—
363C2×C4⋊C4—861no—
364SD32—22no—
365SD32—1721no—
366SD32—1721no—
367M32—1721no—
368C2×C16—431no—
369C2×C16—431no—
370C2×C16—1721no—
371C2×C16C22×D4311yescharacteristic
372C2×C16C22×D4311yescharacteristic
373#107—431no—
374#107—431no—
375#107—861no—
376#107C22×D4311yescharacteristic
377#107C22×D4311yescharacteristic
378#106—861no—
379#106—861no—
380C4⋊C8—431no—
381#103—21no—
382#103—861no—
383#103—861no—
384#102—21no—
385#102—861no—
386#102—861no—
387C22⋊C8—431no—
388C22⋊C8—431no—
389C4×C8C22×D4311yescharacteristic
390C24—1721no—
391C24—1721no—
392C2×Q8—21no—
393C2×D4—21no—
394C2×D4—431no—
395C2×D4—861no—
396C2×D4—861no—
397C2×D4—3444no—
398C2×D4—3441no—
399C2×D4—3441no—
400C2×D4—1721no—
401C2×D4—1721no—
402C2×D4—1721no—
403C2×D4—1721no—
404C2×D4—1722no—
405C2×D4—1722no—
406C2×D4—1721no—
407C2×D4—1721no—
408C22×C4—41no—
409C22×C4—431no—
410C22×C4—431no—
411C22×C4—1721no—
412Q16—21no—
413Q16—21no—
414D8—21no—
415D8—861no—
416D8—861no—
417D8—861no—
418D8—861no—
419D8—3441no—
420D8—1722no—
421D8—1722no—
422D8#1062189812yes—
423C2×C8—431no—
424C2×C8—431no—
425C2×C8—861no—
426C2×C8—861no—
427C2×C8—861no—
428C2×C8—861no—
429C2×C8D4×D4311yescharacteristic
430C2×C8C23×D4311yescharacteristic
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—41no—
434C4⋊C4—431no—
435C4⋊C4—861no—
436C4⋊C4—861no—
437C4⋊C4—1721no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4—1721no—
441C4⋊C4—1721no—
442C22⋊C4—41no—
443C22⋊C4—431no—
444C22⋊C4—431no—
445C22⋊C4—1721no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C22⋊C4—1721no—
450C42—41no—
451C42—1721no—
452C42D4×D4311yescharacteristic
453C16—21no—
454C16—21no—
455C16—861no—
456C16—861no—
457C23—41no—
458C23—431no—
459C23—431no—
460C23—3442no—
461C23—3442no—
462C23—3442no—
463C23—3442no—
464C23—1721no—
465C23—1721no—
466C23—6881no—
467C23—6881no—
468Q8—41no—
469Q8—41no—
470D4—22no—
471D4—41no—
472D4—862no—
473D4—3442no—
474D4—3442no—
475D4—3442no—
476D4—3442no—
477D4—3442no—
478D4—1721no—
479D4—1721no—
480D4—1721no—
481D4—1721no—
482D4—6881no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—431no—
488C2×C4—431no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—861no—
492C2×C4—861no—
493C2×C4—3442no—
494C2×C4—1721no—
495C2×C4—1721no—
496C2×C4D8×D4311yescharacteristic
497C2×C4D8×D4311yescharacteristic
498C2×C4C2×D4×D4311yescharacteristic
499C8—21no—
500C8—861no—
501C8—861no—
502C8C2×#1062189811yescharacteristic
503C8#1306337111yescharacteristic
504C22—42no—
505C22—81no—
506C22—81no—
507C22—432no—
508C22—861no—
509C22—861no—
510C22—861no—
511C22—861no—
512C22—861no—
513C22—3441no—
514C22—3441no—
515C22—3441no—
516C22—3441no—
517C22—3441no—
518C22—3441no—
519C22—6884no—
520C22—6884no—
521C22C2×D8×D4311yescharacteristic
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—861no—
528C4—861no—
529C4—3441no—
530C4—3441no—
531C4#1458354511yescharacteristic
532C4#1458370611yescharacteristic
533C2—82no—
534C2—862no—
535C2—1721no—
536C2—6881no—
537C2—6881no—
538C2#1914641011yescharacteristic
539C2#509×D4311yescharacteristic
540C2#1914774011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2175C2
socleC22×C43C22×D8
prime radicalD8×D172C2
hypercenter#2175D43
hypocenterC43#33877
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. #19146965C2semidirect
3. #19136837C2semidirect
4. #19136789C2semidirect
5. #19136777C2semidirect
6. #19136752C2semidirect
7. #19136711C2semidirect
8. #19136694C2semidirect
9. #19136635C2semidirect
10. #19136522C2semidirect
11. #19136522C2semidirect
12. #19136422C2semidirect
13. #19136309C2semidirect
14. #357×D43C2semidirect
15. C43×#2175C2semidirect
20. C2×#13063268C22semidirect
21. C2×#13063268C22semidirect
22. C2×#13063264C22semidirect
23. C2×C16×D43C22semidirect
24. #14583301C22semidirect
29. #14583137C22semidirect
30. #14583137C22semidirect
37. #14582936C22semidirect
38. #107×D43C22semidirect
39. #14582726C22semidirect
40. #14582724C22semidirect
41. C4⋊(C43⋊C16)C22semidirect
42. #14582701C22semidirect
43. #14582701C22semidirect
44. #14582701C22semidirect
45. #14582701C22semidirect
48. #14582699C22semidirect
49. #14582699C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. (C2×D43)⋊C16C22semidirect
53. C4×Q16×C43C22semidirect
55. C43×#366C22semidirect
56. C43×#358C22semidirect
58. C43×#346C22semidirect
274. #2175D43semidirect
307. C4×Q16C2×D43semidirect
314. #366C2×D43semidirect
316. #358C2×D43semidirect
328. #346C2×D43semidirect
329. C43#33877semidirect

Maximal subgroups

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

subgroupindex
#191469652
D8×D1722
#191368372
#191367892
#191367772
#191367522
#191367112
#191366942
#191366352
#191365222
#191364222
#191363092
#357×D432
C43×#21752
#3387743