Finite Group Databasebeta

← #25253627

Subgroups — #25253627

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#19146962C211yesmaximal, characteristic, complemented
2#19146270C211yesmaximal, characteristic
3#19136784C211yesmaximal, characteristic, complemented
4#19136774C211yesmaximal, characteristic, complemented
5#19136749C211yesmaximal, characteristic, complemented
6#19136707C211yesmaximal, characteristic, complemented
7#19136690C211yesmaximal, characteristic, complemented
8#19136632C211yesmaximal, characteristic, complemented
9#19136525C211yesmaximal, characteristic, complemented
10#19136525C211yesmaximal, characteristic, complemented
11#19136461C211yesmaximal, characteristic, complemented
12#19136422C211yesmaximal, characteristic, complemented
13#19136309C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2244C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583587—21no—
19#14583534—21no—
20C2×#13063270C2211yescharacteristic
21C2×#13063269C2211yescharacteristic, complemented
22C2×#13063269C2211yescharacteristic, complemented
23C2×#13063264C2211yescharacteristic, complemented
24C2×C16×D43C2211yescharacteristic, complemented
25#14583243—21no—
26#14583231—21no—
27#14583203—21no—
28#14583141C2211yescharacteristic, complemented
29#14583141C2211yescharacteristic, complemented
30#14583132C2211yescharacteristic
31#14583132C2211yescharacteristic
32#14583091—21no—
33#14583031—21no—
34#14583031—21no—
35C4×Dic172C2211yescharacteristic, complemented
36C4×D344C2211yescharacteristic
37C8×D172C2211yescharacteristic
38#14582936C2211yescharacteristic, complemented
39#107×D43C2211yescharacteristic, complemented
40#14582726C2211yescharacteristic, complemented
41#14582725C2211yescharacteristic, complemented
42#14582724C2211yescharacteristic, complemented
43C4⋊(C43⋊C16)C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic
46#14582700C2211yescharacteristic, complemented
47#14582700C2211yescharacteristic, complemented
48#14582699C2211yescharacteristic
49#14582699C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51(C2×D43)⋊C16C2211yescharacteristic, complemented
52C43×#499C2211yescharacteristic, complemented
53C43×#493C2211yescharacteristic
54C43×#357C2211yescharacteristic, complemented
55C43×#357C2211yescharacteristic, complemented
56C43×#357C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic, complemented
58C43×#346C2211yescharacteristic, complemented
59C2×D4×D43—21no—
60C2×D4×D43—21no—
61C2×D4×D43—41no—
62C2×Dic172C2311yescharacteristic
63C2×D344C2311yescharacteristic
64C2×#10621882—21no—
65C2×#10621882—21no—
66D8×D43—22no—
67D8×D43—22no—
68D8×D43—41no—
69D8×D43—41no—
70C2×C8×D43C2311yescharacteristic
71C2×C8×D43C2311yescharacteristic
72#13063320—41no—
73#13063316—41no—
74#13063310—41no—
75#13063305—21no—
76#13063305—21no—
77#13063296—21no—
78#13063296—21no—
79#13063296—41no—
80#13063293—41no—
81#13063293—41no—
82C4×Dic86—21no—
83C4×D172—21no—
84C4×D172D411yescharacteristic
85#13063283—21no—
86#13063283—41no—
87C4⋊C4×D43—21no—
88#13063270—22no—
89#13063269—41no—
90#13063269—41no—
91#13063264—41no—
92C2×C43⋊C16C2311yescharacteristic
93C2×C43⋊C16C2311yescharacteristic
94C16×D43—41no—
95#13063259C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063258—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)D411yescharacteristic
100#13063250—21no—
101#13063248—21no—
102#13063248—21no—
103#13063247—21no—
104#13063246—21no—
105#13063246—21no—
106(C2×D43)⋊C8D411yescharacteristic
107(C2×D43)⋊C8D411yescharacteristic
108C2×D8×C43—21no—
109C2×D8×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111#127×C43—21no—
112#125×C43—21no—
113C2×C16×C43C2311yescharacteristic
114C2×C16×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#106×C43—21no—
118C4×C8×C43C2311yescharacteristic
119C23×D43—41no—
120C23×D43—41no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—41no—
124C2×D4×C43—41no—
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C2×C22⋊D43—41no—
129D4×D43—42no—
130D4×D43—42no—
131D4×D43—81no—
132D4×D43—81no—
133D4×D43—84no—
134C2×D172—21no—
135C2×D172D811yescharacteristic
136C2×C4×D43—41no—
137C2×C4×D43—41no—
138C2×C4×D43C2×D411yescharacteristic
139C2×C4×D43C2×D411yescharacteristic
140C2×Dic86—21no—
141D8×C43—21no—
142D8×C43—21no—
143D8×C43—21no—
144D8×C43—21no—
145D8×C43—81no—
146C2×C8×C43C2×D411yescharacteristic
147C2×C8×C43C2411yescharacteristic
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—41no—
151C4⋊C4×C43—41no—
152C42×C43C2×D411yescharacteristic
153C22⋊Dic43—41no—
154C22⋊Dic43—41no—
155#10621882—42no—
156#10621882—42no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4D811yescharacteristic
162(C2×D43)⋊C4D811yescharacteristic
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—41no—
166C4⋊Dic43—41no—
167C4⋊Dic43D811yescharacteristic
168Dic43⋊C4—41no—
169Dic43⋊C4—41no—
170C4×Dic43—41no—
171C4×Dic43—41no—
172C2×C43⋊C8C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174Dic172—21no—
175Dic172—21no—
176D344—21no—
177D344#4112yes—
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—
187C23×C43—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
197D4×C43—41no—
198D4×C43—41no—
199D4×C43—41no—
200D4×C43—41no—
201D4×C43—82no—
202D4×C43—161no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43C2×D811yescharacteristic
206C2×C4×C43C2×D811yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C22⋊D43—82no—
209C22⋊D43—82no—
210C22⋊D43—82no—
211C22⋊D43—82no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43C2×D811yescharacteristic
216C2×Dic43C2×D811yescharacteristic
217D172—22no—
218D172—22no—
219D172—41no—
220C4×D43—21no—
221C4×D43—21no—
222C4×D43—21no—
223C4×D43—21no—
224C4×D43—82no—
225C4×D43—82no—
226Dic86—41no—
227Dic86—41no—
228C8×C43—21no—
229C8×C43C2×#4111yescharacteristic
230C8×C43H(5,𝔽2)11yescharacteristic
231C43⋊C8—21no—
232C43⋊C8—21no—
233#33877—431nomaximal, Sylow
234C22×C43—81no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43C22×D811yescharacteristic
241C2×D43—21no—
242C2×D43—21no—
243C2×D43—21no—
244C2×D43—21no—
245C2×D43—21no—
246C2×D43—42no—
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#54611yescharacteristic
257C4×C43#57711yescharacteristic
258Dic43—21no—
259Dic43—21no—
260Dic43—81no—
261Dic43—81no—
262Dic43—81no—
263#3336—431no—
264D4×D8—431no—
265#2244D4311yescharacteristic, complemented
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#2175—431no—
275#2168—431no—
276#2140—431no—
277C2×#357—431no—
278C2×C43—161no—
279C2×C43—161no—
280C2×C43#329411yescharacteristic
281C2×C43C2×#50911yescharacteristic
282C2×C43#341611yescharacteristic
283D43—22no—
284D43—41no—
285D43—82no—
286C22×D8—431no—
287C22×D8—431no—
288#552—861no—
289D42—861no—
290C2×SD32—431no—
291C2×SD32—431no—
292C2×SD32—431no—
293C2×M32—431no—
294C22×C16—431no—
295#499C2×D4311yescharacteristic, complemented
296#493C2×D4311yescharacteristic
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×Q16—431no—
308C4×D8—431no—
309C8×D4—431no—
310#427—431no—
311C2×#107—431no—
312#367—431no—
313#366—431no—
314#366—431no—
315C4⋊C16—431no—
316#358—431no—
317#357—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322#357C2×D4311yescharacteristic, complemented
323#357C2×D4311yescharacteristic, complemented
324#357C2×D4311yescharacteristic, complemented
325#357C2×D4311yescharacteristic, complemented
326C22⋊C16—431no—
327C22⋊C16—431no—
328#346C2×D4311yescharacteristic, complemented
329C43#3387711yescharacteristic, complemented, Sylow
330C22×D4—861no—
331C22×D4—861no—
332C22×D4—1721no—
333C2×Q16—431no—
334C2×D8—21no—
335C2×D8—431no—
336C2×D8—861no—
337C2×D8—861no—
338C2×D8—862no—
339C2×D8—862no—
340C2×D8—1721no—
341C2×D8—1721no—
342C2×D8C22×D4311yescharacteristic
343C2×D8C22×D4311yescharacteristic
344C22×C8—431no—
345C22×C8—431no—
346#127—21no—
347#126—1721no—
348#125—21no—
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—861no—
359C4×D4—431no—
360C4×D4—861no—
361#117—861no—
362#117—1721no—
363C2×C4⋊C4—861no—
364SD32—862no—
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—21no—
379#106—861no—
380C4⋊C8—431no—
381#103—861no—
382#103—861no—
383#103—861no—
384#102—861no—
385#102—861no—
386#102—861no—
387C22⋊C8—431no—
388C22⋊C8—431no—
389C4×C8C22×D4311yescharacteristic
390C24—1721no—
391C24—1721no—
392C2×Q8—861no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—431no—
398C2×D4—861no—
399C2×D4—3441no—
400C2×D4—3441no—
401C2×D4—3444no—
402C2×D4—1721no—
403C2×D4—1721no—
404C2×D4—1722no—
405C2×D4—1722no—
406C2×D4—1721no—
407C2×D4—1721no—
408C22×C4—431no—
409C22×C4—431no—
410C22×C4—1721no—
411C22×C4—1721no—
412Q16—861no—
413Q16—861no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—21no—
418D8—81no—
419D8—432no—
420D8—861no—
421D8—1722no—
422D8—1722no—
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—41no—
435C4⋊C4—431no—
436C4⋊C4—861no—
437C4⋊C4—861no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4—1721no—
441C4⋊C4—1721no—
442C22⋊C4—431no—
443C22⋊C4—431no—
444C22⋊C4—1721no—
445C22⋊C4—1721no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C22⋊C4—1721no—
450C42—1721no—
451C42—1721no—
452C42D4×D4311yescharacteristic
453C16—21no—
454C16—21no—
455C16—861no—
456C16—861no—
457C23—41no—
458C23—41no—
459C23—431no—
460C23—431no—
461C23—3442no—
462C23—3442no—
463C23—3442no—
464C23—3442no—
465C23—1721no—
466C23—6881no—
467C23—6881no—
468Q8—1721no—
469Q8—1721no—
470D4—41no—
471D4—41no—
472D4—41no—
473D4—41no—
474D4—82no—
475D4—161no—
476D4—862no—
477D4—862no—
478D4—3442no—
479D4—3442no—
480D4—3442no—
481D4—3442no—
482D4—1721no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—431no—
486C2×C4—431no—
487C2×C4—861no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—3442no—
492C2×C4—3442no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4—1721no—
496C2×C4D8×D4311yescharacteristic
497C2×C4D8×D4311yescharacteristic
498C2×C4C2×D4×D4311yescharacteristic
499C8—21no—
500C8—861no—
501C8—861no—
502C8#41×D4311yescharacteristic
503C8#1306337111yescharacteristic
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—432no—
511C22—861no—
512C22—861no—
513C22—861no—
514C22—861no—
515C22—861no—
516C22—3441no—
517C22—3441no—
518C22—1722no—
519C22—6884no—
520C22—6884no—
521C22C2×D8×D4311yescharacteristic
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—861no—
527C4—861no—
528C4—3441no—
529C4—3441no—
530C4—3441no—
531C4#1458354211yescharacteristic
532C4#1458370511yescharacteristic
533C2—161no—
534C2—161no—
535C2—862no—
536C2—3442no—
537C2—1721no—
538C2#1914640711yescharacteristic
539C2#509×D4311yescharacteristic
540C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2244C2
socleC22×C43C22×D8
prime radical#19146270C2
hypercenter#2244D43
hypocenterC43#33877
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #19146962C2semidirect
3. #19136784C2semidirect
4. #19136774C2semidirect
5. #19136749C2semidirect
6. #19136707C2semidirect
7. #19136690C2semidirect
8. #19136632C2semidirect
9. #19136525C2semidirect
10. #19136525C2semidirect
11. #19136461C2semidirect
12. #19136422C2semidirect
13. #19136309C2semidirect
14. #357×D43C2semidirect
15. C43×#2244C2semidirect
21. C2×#13063269C22semidirect
22. C2×#13063269C22semidirect
23. C2×#13063264C22semidirect
24. C2×C16×D43C22semidirect
28. #14583141C22semidirect
29. #14583141C22semidirect
35. C4×Dic172C22semidirect
38. #14582936C22semidirect
39. #107×D43C22semidirect
40. #14582726C22semidirect
41. #14582725C22semidirect
42. #14582724C22semidirect
43. C4⋊(C43⋊C16)C22semidirect
44. #14582704C22semidirect
46. #14582700C22semidirect
47. #14582700C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. (C2×D43)⋊C16C22semidirect
52. C43×#499C22semidirect
54. C43×#357C22semidirect
55. C43×#357C22semidirect
56. C43×#357C22semidirect
57. C43×#357C22semidirect
58. C43×#346C22semidirect
265. #2244D43semidirect
295. #499C2×D43semidirect
322. #357C2×D43semidirect
323. #357C2×D43semidirect
324. #357C2×D43semidirect
325. #357C2×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
#191469622
#191462702
#191367842
#191367742
#191367492
#191367072
#191366902
#191366322
#191365252
#191364612
#191364222
#191363092
#357×D432
C43×#22442
#3387743