Finite Group Databasebeta

← #29836845

Subgroups — #29836845

Order 15616.

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#21458209C211yesmaximal, characteristic, complemented
2#21457493C211yesmaximal, characteristic
3#21448041C211yesmaximal, characteristic, complemented
4#21448006C211yesmaximal, characteristic, complemented
5#21447965C211yesmaximal, characteristic, complemented
6#21447916C211yesmaximal, characteristic, complemented
7#21447913C211yesmaximal, characteristic, complemented
8#21447858C211yesmaximal, characteristic, complemented
9#21447750C211yesmaximal, characteristic, complemented
10#21447749C211yesmaximal, characteristic, complemented
11#21447670C211yesmaximal, characteristic, complemented
12#21447636C211yesmaximal, characteristic, complemented
13C2×#16839562C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2233C211yesmaximal, characteristic, complemented
16C22×D488C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18#16840467—21no—
19#16840396—21no—
20C2×#14519722C2211yescharacteristic
21C2×#14519722C2211yescharacteristic, complemented
22C2×#14519721C2211yescharacteristic, complemented
23C22×#11758185C2211yescharacteristic, complemented
24C2×C16×D61C2211yescharacteristic, complemented
25#16840166C2211yescharacteristic, complemented
26#16840137C2211yescharacteristic
27#16840099—21no—
28#16840097—21no—
29#16840056—21no—
30#16840004C2211yescharacteristic, complemented
31#16840003C2211yescharacteristic, complemented
32#16839999C2211yescharacteristic
33#16839956—21no—
34#16839897—21no—
35#16839895—21no—
36#16839856C2211yescharacteristic, complemented
37#16839844C2211yescharacteristic
38C8×C22⋊D61C2211yescharacteristic
39#107×D61C2211yescharacteristic, complemented
40#16839589C2211yescharacteristic, complemented
41#16839580C2211yescharacteristic, complemented
42#16839565C2211yescharacteristic, complemented
43#16839564C2211yescharacteristic
44#16839564C2211yescharacteristic, complemented
45#16839563C2211yescharacteristic, complemented
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic, complemented
49#16839562C2211yescharacteristic, complemented
50#16839541C2211yescharacteristic, complemented
51C16×Dic61C2211yescharacteristic, complemented
52C61×#466C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic, complemented
54C61×#367C2211yescharacteristic, complemented
55C61×#367C2211yescharacteristic, complemented
56C61×#357C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic, complemented
58C61×C22⋊C16C2211yescharacteristic, complemented
59C22×D244—21no—
60C2×D4×D61—21no—
61C2×D4×D61—41no—
62C2×Dic244C2311yescharacteristic
63C2×D488—22no—
64C2×D488—21no—
65C2×D488—41no—
66C2×D488C2311yescharacteristic
67C2×D488C2311yescharacteristic
68C2×#11758199—21no—
69C2×#11758199—21no—
70D8×D61—22no—
71D8×D61—41no—
72C2×C8×D61C2311yescharacteristic
73#14519776—21no—
74#14519773—21no—
75#14519767—41no—
76#14519757—21no—
77#14519756—21no—
78#14519756—41no—
79#14519755—41no—
80#14519752—21no—
81#14519750—41no—
82#14519747—41no—
83#14519745—41no—
84#14519742—21no—
85#14519739—21no—
86C4×C22⋊D61—41no—
87C4×C22⋊D61D411yescharacteristic
88C4⋊C4×D61—21no—
89#14519722—22no—
90#14519722—41no—
91#14519721—41no—
92C2×#11758185—41no—
93C2×#11758185C2311yescharacteristic
94C2×#11758185C2311yescharacteristic
95C16×D61—41no—
96#14519711C2311yescharacteristic
97#14519710—21no—
98#14519710—21no—
99#14519706D411yescharacteristic
100#14519702—21no—
101#14519700—21no—
102#14519700—21no—
103#14519697—21no—
104#14519697—21no—
105C22⋊#92418D411yescharacteristic
106#14519689D411yescharacteristic
107C8×Dic61C2311yescharacteristic
108C2×D8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110#121×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C16×C61C2311yescharacteristic
113C2×C16×C61C2311yescharacteristic
114#107×C61—21no—
115#107×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#107×C61C2311yescharacteristic
118#102×C61—21no—
119C23×D61—41no—
120C23×D61—41no—
121C2×D4×C61—21no—
122C2×D4×C61—41no—
123C22×C4×C61—41no—
124C22×C4×C61C2×D411yescharacteristic
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C2×C22⋊D61D811yescharacteristic
129D4×D61—42no—
130D4×D61—81no—
131D4×D61—84no—
132C2×D244—21no—
133C2×D244—21no—
134C2×D244—42no—
135C2×D244—41no—
136C2×D244—41no—
137C2×D244—81no—
138C2×C4×D61—41no—
139C2×C4×D61—41no—
140C2×C4×D61C2×D411yescharacteristic
141C2×Dic122—21no—
142C2×Dic122—41no—
143D8×C61—21no—
144D8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61C2×D411yescharacteristic
148C2×C8×C61C2411yescharacteristic
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—41no—
153C22⋊C4×C61—41no—
154C22⋊Dic61—41no—
155C22⋊Dic61D811yescharacteristic
156#11758199—42no—
157#11758199—81no—
158#11758198—41no—
159#11758198—41no—
160#11758198—41no—
161#11758198D811yescharacteristic
162C4⋊Dic61—21no—
163C4⋊Dic61—41no—
164#11758196—41no—
165#11758196—41no—
166#11758196—41no—
167#11758196—41no—
168#11758196D811yescharacteristic
169C4×Dic61—41no—
170C4×Dic61C2×D411yescharacteristic
171C2×#92418C2×D411yescharacteristic
172C2×#92418C2×D411yescharacteristic
173Dic244—21no—
174Dic244—21no—
175D488—21no—
176D488—21no—
177D488—21no—
178D488—42no—
179D488#4112yes—
180C8×D61—21no—
181C8×D61—21no—
182C16×C61—21no—
183C16×C61—21no—
184#11758185—21no—
185#11758185—21no—
186C23×C61—41no—
187C23×C61C2×D811yescharacteristic
188C22×D61—41no—
189C22×D61—41no—
190C22×D61—82no—
191C22×D61—82no—
192C22×D61—82no—
193C22×D61—82no—
194C22×D61—161no—
195C22×D61—161no—
196C22×D61C2×D811yescharacteristic
197D4×C61—41no—
198D4×C61—41no—
199D4×C61—82no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—161no—
206C2×C4×C61C2×D811yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C22⋊D61—82no—
209C22⋊D61—82no—
210C22⋊D61—161no—
211C22⋊D61SD3214yescomplemented
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61C2×D811yescharacteristic
215C2×Dic61C2×D811yescharacteristic
216C2×Dic61C2×D811yescharacteristic
217D244—22no—
218D244—41no—
219D244—41no—
220D244—41no—
221D244—82no—
222D244—82no—
223C4×D61—21no—
224C4×D61—21no—
225C4×D61—82no—
226C4×D61—161no—
227Dic122—41no—
228Dic122—41no—
229Dic122—161no—
230C8×C61—21no—
231C8×C61C2×#4111yescharacteristic
232C8×C61H(5,𝔽2)11yescharacteristic
233#92418—21no—
234#92418—21no—
235#33862—611nomaximal, Sylow
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61—81no—
241C22×C61C2×SD3212yes—
242C22×C61C22×D811yescharacteristic
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—42no—
246C2×D61—81no—
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—81no—
250C2×D61—81no—
251C2×D61—164no—
252C2×D61—164no—
253C2×D61C2×SD3212yes—
254C4×C61—21no—
255C4×C61—81no—
256C4×C61—81no—
257C4×C61—81no—
258C4×C61#54611yescharacteristic
259C4×C61#57711yescharacteristic
260Dic61—21no—
261Dic61—21no—
262Dic61—81no—
263Dic61—81no—
264Dic61C2×SD3212yes—
265#3338—611no—
266D4×D8—611no—
267#2240—611no—
268#2233—611no—
269#2233D6111yescharacteristic, complemented
270#2226—611no—
271#2217—611no—
272#2217—611no—
273#2207—611no—
274#2187—611no—
275#2187—611no—
276C4×SD32—611no—
277D4×C16—611no—
278C2×#357—611no—
279C2×#357—611no—
280C2×C61—22no—
281C2×C61—161no—
282C2×C61#329411yescharacteristic
283C2×C61C22×SD3211yescharacteristic
284C2×C61#341511yescharacteristic
285D61—22no—
286D61—82no—
287D61—161no—
288C22×D8—611no—
289C22×D8—611no—
290#554—1221no—
291D42—1221no—
292C2×SD32—611no—
293C2×SD32—611no—
294C2×SD32—611no—
295C22×C16—611no—
296C22×C16—611no—
297#500—611no—
298#493—611no—
299#484—1221no—
300#484—1221no—
301#477—1221no—
302#467—611no—
303#467—611no—
304#466—611no—
305#466C2×D6111yescharacteristic
306#459—1221no—
307#447—1221no—
308#447—1221no—
309C4×Q16—611no—
310C4×D8—611no—
311C8×D4—611no—
312C2×#107—611no—
313C2×#107C2×D6111yescharacteristic, complemented
314#367—611no—
315#367C2×D6111yescharacteristic, complemented
316#367C2×D6111yescharacteristic, complemented
317C4⋊C16—611no—
318#358—611no—
319#357—611no—
320#357—611no—
321#357—611no—
322#357—611no—
323#357—611no—
324#357—611no—
325#357—611no—
326#357C2×D6111yescharacteristic, complemented
327#357C2×D6111yescharacteristic, complemented
328C22⋊C16—611no—
329C22⋊C16C2×D6111yescharacteristic, complemented
330C4×C16—611no—
331C61#3386211yescharacteristic, complemented, Sylow
332C22×D4—1221no—
333C22×D4—1221no—
334C22×D4—2441no—
335C2×Q16—611no—
336C2×D8—611no—
337C2×D8—611no—
338C2×D8—1222no—
339C2×D8—1221no—
340C2×D8—1221no—
341C2×D8—1222no—
342C2×D8—1221no—
343C2×D8—2441no—
344C2×D8—2441no—
345C2×D8C22×D6111yescharacteristic
346C22×C8—611no—
347C22×C8C22×D6111yescharacteristic
348C4⋊Q8—1221no—
349#127—1221no—
350#125—2441no—
351C22⋊Q8—1221no—
352C22⋊Q8—1221no—
353C22⋊Q8—2441no—
354C22⋊Q8—2441no—
355#121—21no—
356#121—1221no—
357#121—2441no—
358#120—2441no—
359#120—2441no—
360C4×Q8—1221no—
361C4×D4—611no—
362C4×D4—1221no—
363C4×D4—2441no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—1221no—
366SD32—1222no—
367SD32—2441no—
368SD32—2441no—
369C2×C16—611no—
370C2×C16—611no—
371C2×C16—2441no—
372C2×C16—2441no—
373C2×C16C22×D6111yescharacteristic
374C2×C16C22×D6111yescharacteristic
375#107—21no—
376#107—611no—
377#107—1221no—
378#107—1221no—
379#107C22×D6111yescharacteristic
380#107C22×D6111yescharacteristic
381#107C22×D6111yescharacteristic
382C4⋊C8—611no—
383#103—1221no—
384#103—1221no—
385#103—1221no—
386#102—21no—
387#102—1221no—
388#102—1221no—
389C22⋊C8—611no—
390C22⋊C8—611no—
391C4×C8—611no—
392C24—2441no—
393C24—2441no—
394C2×Q8—1221no—
395C2×Q8—2441no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—611no—
399C2×D4—1221no—
400C2×D4—1221no—
401C2×D4—4881no—
402C2×D4—4881no—
403C2×D4—4884no—
404C2×D4—2442no—
405C2×D4—2441no—
406C2×D4—2441no—
407C2×D4—2441no—
408C2×D4—2441no—
409C2×D4—2442no—
410C2×D4—2441no—
411C22×C4—41no—
412C22×C4—611no—
413C22×C4—2441no—
414C22×C4—2441no—
415C22×C4D4×D6111yescharacteristic
416Q16—1221no—
417Q16—1221no—
418D8—21no—
419D8—21no—
420D8—612no—
421D8—1221no—
422D8—1221no—
423D8—1221no—
424D8—4881no—
425D8—2442no—
426D8—2442no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—611no—
430C2×C8—611no—
431C2×C8—1221no—
432C2×C8—1221no—
433C2×C8D4×D6111yescharacteristic
434C2×C8C23×D6111yescharacteristic
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—41no—
439C4⋊C4—611no—
440C4⋊C4—1221no—
441C4⋊C4—2441no—
442C4⋊C4—2441no—
443C4⋊C4—2441no—
444C4⋊C4—2441no—
445C4⋊C4—2441no—
446C22⋊C4—41no—
447C22⋊C4—611no—
448C22⋊C4—611no—
449C22⋊C4—2441no—
450C22⋊C4—2441no—
451C22⋊C4—2441no—
452C22⋊C4—2441no—
453C42—611no—
454C42—2441no—
455C16—21no—
456C16—21no—
457C16—1221no—
458C16—1221no—
459C23—41no—
460C23—611no—
461C23—9761no—
462C23—9761no—
463C23—4882no—
464C23—4882no—
465C23—4882no—
466C23—4882no—
467C23—2441no—
468C23—2441no—
469C23D8×D6111yescharacteristic
470Q8—9761no—
471Q8—2441no—
472Q8—2441no—
473D4—41no—
474D4—41no—
475D4—82no—
476D4—614no—
477D4—1222no—
478D4—9761no—
479D4—4882no—
480D4—4882no—
481D4—4882no—
482D4—4882no—
483D4—2441no—
484D4—2441no—
485D4—2441no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—161no—
492C2×C4—611no—
493C2×C4—611no—
494C2×C4—611no—
495C2×C4—1221no—
496C2×C4—1221no—
497C2×C4—9761no—
498C2×C4—4882no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4D8×D6111yescharacteristic
502C2×C4C2×D4×D6111yescharacteristic
503C8—21no—
504C8—1221no—
505C8—1221no—
506C8#41×D6111yescharacteristic
507C8#1451982311yescharacteristic
508C22—21no—
509C22—21no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—612no—
514C22—1221no—
515C22—1221no—
516C22—9764no—
517C22—9764no—
518C22—4881no—
519C22—4881no—
520C22—4881no—
521C22—4881no—
522C22—4881no—
523C22—2442no—
524C22SD32×D6112yes—
525C22C2×D8×D6111yescharacteristic
526C4—21no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—612no—
531C4—1221no—
532C4—1221no—
533C4—4881no—
534C4—4881no—
535C4#1684040411yescharacteristic
536C4#1684057111yescharacteristic
537C2—22no—
538C2—161no—
539C2—1222no—
540C2—9761no—
541C2—4882no—
542C2#2145763011yescharacteristic
543C2C2×SD32×D6111yescharacteristic
544C2#2145895911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2233C2
socleC22×C61C22×D8
prime radical#21457493C2
hypercenter#2233D61
hypocenterC61#33862
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
1. #21458209C2semidirect
3. #21448041C2semidirect
4. #21448006C2semidirect
5. #21447965C2semidirect
6. #21447916C2semidirect
7. #21447913C2semidirect
8. #21447858C2semidirect
9. #21447750C2semidirect
10. #21447749C2semidirect
11. #21447670C2semidirect
12. #21447636C2semidirect
13. C2×#16839562C2semidirect
14. #357×D61C2semidirect
15. C61×#2233C2semidirect
21. C2×#14519722C22semidirect
22. C2×#14519721C22semidirect
23. C22×#11758185C22semidirect
24. C2×C16×D61C22semidirect
25. #16840166C22semidirect
30. #16840004C22semidirect
31. #16840003C22semidirect
36. #16839856C22semidirect
39. #107×D61C22semidirect
40. #16839589C22semidirect
41. #16839580C22semidirect
42. #16839565C22semidirect
44. #16839564C22semidirect
45. #16839563C22semidirect
48. #16839562C22semidirect
49. #16839562C22semidirect
50. #16839541C22semidirect
51. C16×Dic61C22semidirect
53. C2×#107×C61C22semidirect
54. C61×#367C22semidirect
55. C61×#367C22semidirect
56. C61×#357C22semidirect
57. C61×#357C22semidirect
58. C61×C22⋊C16C22semidirect
211. C22⋊D61SD32semidirect
269. #2233D61semidirect
313. C2×#107C2×D61semidirect
315. #367C2×D61semidirect
316. #367C2×D61semidirect
326. #357C2×D61semidirect
327. #357C2×D61semidirect
329. C22⋊C16C2×D61semidirect
331. C61#33862semidirect

Maximal subgroups

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

subgroupindex
#214582092
#214574932
#214480412
#214480062
#214479652
#214479162
#214479132
#214478582
#214477502
#214477492
#214476702
#214476362
C2×#168395622
#357×D612
C61×#22332
#3386261