Finite Group Databasebeta

← #29837043

Subgroups — #29837043

Order 15616.

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#21458186C211yesmaximal, characteristic, complemented
2#21457494C211yesmaximal, characteristic
3#21448008C211yesmaximal, characteristic, complemented
4#21447998C211yesmaximal, characteristic, complemented
5#21447973C211yesmaximal, characteristic, complemented
6#21447931C211yesmaximal, characteristic, complemented
7#21447914C211yesmaximal, characteristic, complemented
8#21447856C211yesmaximal, characteristic, complemented
9#21447749C211yesmaximal, characteristic, complemented
10#21447749C211yesmaximal, characteristic, complemented
11#21447685C211yesmaximal, characteristic, complemented
12#21447646C211yesmaximal, characteristic, complemented
13#21447533C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2244C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18#16840450—21no—
19#16840397—21no—
20C2×#14519722C2211yescharacteristic
21C2×#14519721C2211yescharacteristic, complemented
22C2×#14519721C2211yescharacteristic, complemented
23C2×#14519716C2211yescharacteristic, complemented
24C2×C16×D61C2211yescharacteristic, complemented
25#16840106—21no—
26#16840094—21no—
27#16840066—21no—
28#16840004C2211yescharacteristic, complemented
29#16840004C2211yescharacteristic, complemented
30#16839995C2211yescharacteristic
31#16839995C2211yescharacteristic
32#16839954—21no—
33#16839894—21no—
34#16839894—21no—
35C4×Dic244C2211yescharacteristic, complemented
36C4×D488C2211yescharacteristic
37C8×D244C2211yescharacteristic
38#16839799C2211yescharacteristic, complemented
39#107×D61C2211yescharacteristic, complemented
40#16839589C2211yescharacteristic, complemented
41#16839588C2211yescharacteristic, complemented
42#16839587C2211yescharacteristic, complemented
43C4⋊#11758185C2211yescharacteristic, complemented
44#16839567C2211yescharacteristic, complemented
45#16839564C2211yescharacteristic
46#16839563C2211yescharacteristic, complemented
47#16839563C2211yescharacteristic, complemented
48#16839562C2211yescharacteristic
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic, complemented
51#16839541C2211yescharacteristic, complemented
52C61×#499C2211yescharacteristic, complemented
53C61×#493C2211yescharacteristic
54C61×#357C2211yescharacteristic, complemented
55C61×#357C2211yescharacteristic, complemented
56C61×#357C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic, complemented
58C61×#346C2211yescharacteristic, complemented
59C2×D4×D61—21no—
60C2×D4×D61—21no—
61C2×D4×D61—41no—
62C2×Dic244C2311yescharacteristic
63C2×D488C2311yescharacteristic
64C2×#11758199—21no—
65C2×#11758199—21no—
66D8×D61—22no—
67D8×D61—22no—
68D8×D61—41no—
69D8×D61—41no—
70C2×C8×D61C2311yescharacteristic
71C2×C8×D61C2311yescharacteristic
72#14519772—41no—
73#14519768—41no—
74#14519762—41no—
75#14519757—21no—
76#14519757—21no—
77#14519748—21no—
78#14519748—21no—
79#14519748—41no—
80#14519745—41no—
81#14519745—41no—
82C4×Dic122—21no—
83C4×D244—21no—
84C4×D244D411yescharacteristic
85#14519735—21no—
86#14519735—41no—
87C4⋊C4×D61—21no—
88#14519722—22no—
89#14519721—41no—
90#14519721—41no—
91#14519716—41no—
92C2×#11758185C2311yescharacteristic
93C2×#11758185C2311yescharacteristic
94C16×D61—41no—
95#14519711C2311yescharacteristic
96#14519711C2311yescharacteristic
97#14519710—21no—
98#14519708—21no—
99C4⋊#92418D411yescharacteristic
100#14519702—21no—
101#14519700—21no—
102#14519700—21no—
103#14519699—21no—
104#14519698—21no—
105#14519698—21no—
106#14519689D411yescharacteristic
107#14519689D411yescharacteristic
108C2×D8×C61—21no—
109C2×D8×C61C2311yescharacteristic
110C2×D8×C61C2311yescharacteristic
111#127×C61—21no—
112#125×C61—21no—
113C2×C16×C61C2311yescharacteristic
114C2×C16×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#106×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C23×D61—41no—
120C23×D61—41no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—41no—
124C2×D4×C61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C2×C22⋊D61—41no—
129D4×D61—42no—
130D4×D61—42no—
131D4×D61—81no—
132D4×D61—81no—
133D4×D61—84no—
134C2×D244—21no—
135C2×D244D811yescharacteristic
136C2×C4×D61—41no—
137C2×C4×D61—41no—
138C2×C4×D61C2×D411yescharacteristic
139C2×C4×D61C2×D411yescharacteristic
140C2×Dic122—21no—
141D8×C61—21no—
142D8×C61—21no—
143D8×C61—21no—
144D8×C61—21no—
145D8×C61—81no—
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2411yescharacteristic
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—41no—
151C4⋊C4×C61—41no—
152C42×C61C2×D411yescharacteristic
153C22⋊Dic61—41no—
154C22⋊Dic61—41no—
155#11758199—42no—
156#11758199—42no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160#11758198—41no—
161#11758198D811yescharacteristic
162#11758198D811yescharacteristic
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61—41no—
166C4⋊Dic61—41no—
167C4⋊Dic61D811yescharacteristic
168#11758196—41no—
169#11758196—41no—
170C4×Dic61—41no—
171C4×Dic61—41no—
172C2×#92418C2×D411yescharacteristic
173C2×#92418C2×D411yescharacteristic
174Dic244—21no—
175Dic244—21no—
176D488—21no—
177D488#4112yes—
178C8×D61—21no—
179C8×D61—21no—
180C8×D61—21no—
181C8×D61—21no—
182C16×C61—21no—
183C16×C61—21no—
184#11758185—21no—
185#11758185—21no—
186C23×C61—41no—
187C23×C61—41no—
188C22×D61—41no—
189C22×D61—82no—
190C22×D61—82no—
191C22×D61—82no—
192C22×D61—82no—
193C22×D61—161no—
194C22×D61—161no—
195C22×D61C2×D811yescharacteristic
196C22×D61C2×D811yescharacteristic
197D4×C61—41no—
198D4×C61—41no—
199D4×C61—41no—
200D4×C61—41no—
201D4×C61—82no—
202D4×C61—161no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61C2×D811yescharacteristic
206C2×C4×C61C2×D811yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C22⋊D61—82no—
209C22⋊D61—82no—
210C22⋊D61—82no—
211C22⋊D61—82no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61C2×D811yescharacteristic
216C2×Dic61C2×D811yescharacteristic
217D244—22no—
218D244—22no—
219D244—41no—
220C4×D61—21no—
221C4×D61—21no—
222C4×D61—21no—
223C4×D61—21no—
224C4×D61—82no—
225C4×D61—82no—
226Dic122—41no—
227Dic122—41no—
228C8×C61—21no—
229C8×C61C2×#4111yescharacteristic
230C8×C61H(5,𝔽2)11yescharacteristic
231#92418—21no—
232#92418—21no—
233#33877—611nomaximal, Sylow
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61C22×D811yescharacteristic
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—42no—
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—164no—
250C2×D61—164no—
251C2×D61#50912yes—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—81no—
255C4×C61—81no—
256C4×C61#54611yescharacteristic
257C4×C61#57711yescharacteristic
258Dic61—21no—
259Dic61—21no—
260Dic61—81no—
261Dic61—81no—
262Dic61—81no—
263#3336—611no—
264D4×D8—611no—
265#2244D6111yescharacteristic, complemented
266#2234—611no—
267#2232—611no—
268#2228—611no—
269#2220—611no—
270#2217—611no—
271#2207—611no—
272#2187—611no—
273#2187—611no—
274#2175—611no—
275#2168—611no—
276#2140—611no—
277C2×#357—611no—
278C2×C61—161no—
279C2×C61—161no—
280C2×C61#329411yescharacteristic
281C2×C61C2×#50911yescharacteristic
282C2×C61#341611yescharacteristic
283D61—22no—
284D61—41no—
285D61—82no—
286C22×D8—611no—
287C22×D8—611no—
288#552—1221no—
289D42—1221no—
290C2×SD32—611no—
291C2×SD32—611no—
292C2×SD32—611no—
293C2×M32—611no—
294C22×C16—611no—
295#499C2×D6111yescharacteristic, complemented
296#493C2×D6111yescharacteristic
297#485—1221no—
298#483—1221no—
299#479—1221no—
300#467—611no—
301#467—611no—
302#466—611no—
303#466—611no—
304#459—1221no—
305#447—1221no—
306#447—1221no—
307C4×Q16—611no—
308C4×D8—611no—
309C8×D4—611no—
310#427—611no—
311C2×#107—611no—
312#367—611no—
313#366—611no—
314#366—611no—
315C4⋊C16—611no—
316#358—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357—611no—
321#357—611no—
322#357C2×D6111yescharacteristic, complemented
323#357C2×D6111yescharacteristic, complemented
324#357C2×D6111yescharacteristic, complemented
325#357C2×D6111yescharacteristic, complemented
326C22⋊C16—611no—
327C22⋊C16—611no—
328#346C2×D6111yescharacteristic, complemented
329C61#3387711yescharacteristic, complemented, Sylow
330C22×D4—1221no—
331C22×D4—1221no—
332C22×D4—2441no—
333C2×Q16—611no—
334C2×D8—21no—
335C2×D8—611no—
336C2×D8—1221no—
337C2×D8—1221no—
338C2×D8—1222no—
339C2×D8—1222no—
340C2×D8—2441no—
341C2×D8—2441no—
342C2×D8C22×D6111yescharacteristic
343C2×D8C22×D6111yescharacteristic
344C22×C8—611no—
345C22×C8—611no—
346#127—21no—
347#126—2441no—
348#125—21no—
349#125—2441no—
350#123—2441no—
351C22⋊Q8—1221no—
352C22⋊Q8—1221no—
353#121—1221no—
354#121—1221no—
355#121—2441no—
356#120—2441no—
357#120—2441no—
358C4×Q8—1221no—
359C4×D4—611no—
360C4×D4—1221no—
361#117—1221no—
362#117—2441no—
363C2×C4⋊C4—1221no—
364SD32—1222no—
365SD32—2441no—
366SD32—2441no—
367M32—2441no—
368C2×C16—611no—
369C2×C16—611no—
370C2×C16—2441no—
371C2×C16C22×D6111yescharacteristic
372C2×C16C22×D6111yescharacteristic
373#107—611no—
374#107—611no—
375#107—1221no—
376#107C22×D6111yescharacteristic
377#107C22×D6111yescharacteristic
378#106—21no—
379#106—1221no—
380C4⋊C8—611no—
381#103—1221no—
382#103—1221no—
383#103—1221no—
384#102—1221no—
385#102—1221no—
386#102—1221no—
387C22⋊C8—611no—
388C22⋊C8—611no—
389C4×C8C22×D6111yescharacteristic
390C24—2441no—
391C24—2441no—
392C2×Q8—1221no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—611no—
398C2×D4—1221no—
399C2×D4—4881no—
400C2×D4—4881no—
401C2×D4—4884no—
402C2×D4—2441no—
403C2×D4—2441no—
404C2×D4—2442no—
405C2×D4—2442no—
406C2×D4—2441no—
407C2×D4—2441no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—2441no—
411C22×C4—2441no—
412Q16—1221no—
413Q16—1221no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—21no—
418D8—81no—
419D8—612no—
420D8—1221no—
421D8—2442no—
422D8—2442no—
423C2×C8—611no—
424C2×C8—611no—
425C2×C8—1221no—
426C2×C8—1221no—
427C2×C8—1221no—
428C2×C8—1221no—
429C2×C8D4×D6111yescharacteristic
430C2×C8C23×D6111yescharacteristic
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—611no—
436C4⋊C4—1221no—
437C4⋊C4—1221no—
438C4⋊C4—2441no—
439C4⋊C4—2441no—
440C4⋊C4—2441no—
441C4⋊C4—2441no—
442C22⋊C4—611no—
443C22⋊C4—611no—
444C22⋊C4—2441no—
445C22⋊C4—2441no—
446C22⋊C4—2441no—
447C22⋊C4—2441no—
448C22⋊C4—2441no—
449C22⋊C4—2441no—
450C42—2441no—
451C42—2441no—
452C42D4×D6111yescharacteristic
453C16—21no—
454C16—21no—
455C16—1221no—
456C16—1221no—
457C23—41no—
458C23—41no—
459C23—611no—
460C23—611no—
461C23—9761no—
462C23—9761no—
463C23—4882no—
464C23—4882no—
465C23—4882no—
466C23—4882no—
467C23—2441no—
468Q8—2441no—
469Q8—2441no—
470D4—41no—
471D4—41no—
472D4—41no—
473D4—41no—
474D4—82no—
475D4—161no—
476D4—1222no—
477D4—1222no—
478D4—4882no—
479D4—4882no—
480D4—4882no—
481D4—4882no—
482D4—2441no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—611no—
486C2×C4—611no—
487C2×C4—1221no—
488C2×C4—1221no—
489C2×C4—1221no—
490C2×C4—1221no—
491C2×C4—4882no—
492C2×C4—4882no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4D8×D6111yescharacteristic
497C2×C4D8×D6111yescharacteristic
498C2×C4C2×D4×D6111yescharacteristic
499C8—21no—
500C8—1221no—
501C8—1221no—
502C8#41×D6111yescharacteristic
503C8#1451982311yescharacteristic
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—612no—
511C22—1221no—
512C22—1221no—
513C22—1221no—
514C22—1221no—
515C22—1221no—
516C22—9764no—
517C22—9764no—
518C22—4881no—
519C22—4881no—
520C22—2442no—
521C22C2×D8×D6111yescharacteristic
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—1221no—
527C4—1221no—
528C4—4881no—
529C4—4881no—
530C4—4881no—
531C4#1684040511yescharacteristic
532C4#1684056811yescharacteristic
533C2—161no—
534C2—161no—
535C2—1222no—
536C2—4882no—
537C2—2441no—
538C2#2145763111yescharacteristic
539C2#509×D6111yescharacteristic
540C2#2145896511yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2244C2
socleC22×C61C22×D8
prime radical#21457494C2
hypercenter#2244D61
hypocenterC61#33877
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #21458186C2semidirect
3. #21448008C2semidirect
4. #21447998C2semidirect
5. #21447973C2semidirect
6. #21447931C2semidirect
7. #21447914C2semidirect
8. #21447856C2semidirect
9. #21447749C2semidirect
10. #21447749C2semidirect
11. #21447685C2semidirect
12. #21447646C2semidirect
13. #21447533C2semidirect
14. #357×D61C2semidirect
15. C61×#2244C2semidirect
21. C2×#14519721C22semidirect
22. C2×#14519721C22semidirect
23. C2×#14519716C22semidirect
24. C2×C16×D61C22semidirect
28. #16840004C22semidirect
29. #16840004C22semidirect
35. C4×Dic244C22semidirect
38. #16839799C22semidirect
39. #107×D61C22semidirect
40. #16839589C22semidirect
41. #16839588C22semidirect
42. #16839587C22semidirect
43. C4⋊#11758185C22semidirect
44. #16839567C22semidirect
46. #16839563C22semidirect
47. #16839563C22semidirect
50. #16839541C22semidirect
51. #16839541C22semidirect
52. C61×#499C22semidirect
54. C61×#357C22semidirect
55. C61×#357C22semidirect
56. C61×#357C22semidirect
57. C61×#357C22semidirect
58. C61×#346C22semidirect
265. #2244D61semidirect
295. #499C2×D61semidirect
322. #357C2×D61semidirect
323. #357C2×D61semidirect
324. #357C2×D61semidirect
325. #357C2×D61semidirect
328. #346C2×D61semidirect
329. C61#33877semidirect

Maximal subgroups

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

subgroupindex
#214581862
#214574942
#214480082
#214479982
#214479732
#214479312
#214479142
#214478562
#214477492
#214476852
#214476462
#214475332
#357×D612
C61×#22442
#3387761