Finite Group Databasebeta

← #29837049

Subgroups — #29837049

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#21458189C211yesmaximal, characteristic, complemented
2D8×D244C211yesmaximal, characteristic
3#21448061C211yesmaximal, characteristic, complemented
4#21448013C211yesmaximal, characteristic, complemented
5#21448001C211yesmaximal, characteristic, complemented
6#21447976C211yesmaximal, characteristic, complemented
7#21447935C211yesmaximal, characteristic, complemented
8#21447918C211yesmaximal, characteristic, complemented
9#21447859C211yesmaximal, characteristic, complemented
10#21447746C211yesmaximal, characteristic, complemented
11#21447746C211yesmaximal, characteristic, complemented
12#21447646C211yesmaximal, characteristic, complemented
13#21447533C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2175C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18#16840453—21no—
19D4×D244—21no—
20C2×#14519720C2211yescharacteristic, complemented
21C2×#14519720C2211yescharacteristic, complemented
22C2×#14519716C2211yescharacteristic, complemented
23C2×C16×D61C2211yescharacteristic, complemented
24#16840164C2211yescharacteristic, complemented
25#16840139C2211yescharacteristic
26#16840101—21no—
27#16840091—21no—
28#16840069—21no—
29#16840000C2211yescharacteristic, complemented
30#16840000C2211yescharacteristic, complemented
31#16839999C2211yescharacteristic
32#16839999C2211yescharacteristic
33#16839957—21no—
34#16839897—21no—
35#16839897—21no—
36C8×D244C2211yescharacteristic
37#16839799C2211yescharacteristic, complemented
38#107×D61C2211yescharacteristic, complemented
39#16839589C2211yescharacteristic, complemented
40#16839587C2211yescharacteristic, complemented
41C4⋊#11758185C2211yescharacteristic, complemented
42#16839564C2211yescharacteristic, complemented
43#16839564C2211yescharacteristic, complemented
44#16839564C2211yescharacteristic, complemented
45#16839564C2211yescharacteristic, complemented
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839562C2211yescharacteristic, complemented
49#16839562C2211yescharacteristic, complemented
50#16839541C2211yescharacteristic, complemented
51#16839541C2211yescharacteristic, complemented
52C2×SD32×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic, complemented
54C4×D8×C61C2211yescharacteristic
55C61×#366C2211yescharacteristic, complemented
56C61×#358C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic
58C61×#346C2211yescharacteristic, complemented
59C22×D244—41no—
60C2×D4×D61—21no—
61C2×D4×D61—21no—
62C2×D488—21no—
63C2×D488C2311yescharacteristic
64C2×D488C2311yescharacteristic
65C2×#11758199—21no—
66C2×#11758199—21no—
67D8×D61—22no—
68D8×D61—22no—
69D8×D61—41no—
70D8×D61—41no—
71C2×C8×D61C2311yescharacteristic
72C2×C8×D61C2311yescharacteristic
73#14519774—21no—
74#14519771—41no—
75#14519769—21no—
76#14519767—41no—
77#14519762—41no—
78#14519753—21no—
79#14519753—21no—
80#14519752—21no—
81#14519752—21no—
82#14519751—41no—
83#14519747—41no—
84#14519747—41no—
85C4×D244D411yescharacteristic
86#14519735—21no—
87#14519734—41no—
88C4⋊C4×D61—21no—
89#14519720—41no—
90#14519720—41no—
91#14519716—41no—
92C2×#11758185C2311yescharacteristic
93C2×#11758185C2311yescharacteristic
94C16×D61—41no—
95#14519711C2311yescharacteristic
96#14519711C2311yescharacteristic
97#14519710—21no—
98#14519709—21no—
99#14519708—21no—
100C4⋊#92418D411yescharacteristic
101#14519701—21no—
102#14519701—21no—
103#14519697—21no—
104#14519697—21no—
105#14519689D411yescharacteristic
106#14519689D411yescharacteristic
107C2×Q16×C61C2311yescharacteristic
108C2×D8×C61C2311yescharacteristic
109C4×Q8×C61—21no—
110C4×D4×C61—21no—
111SD32×C61—22no—
112C2×C16×C61C2311yescharacteristic
113C2×C16×C61C2311yescharacteristic
114#107×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116#103×C61—21no—
117#102×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C23×D61—41no—
120C23×D61—41no—
121C2×Q8×C61—21no—
122C2×D4×C61—21no—
123C22×C4×C61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126D4×D61—42no—
127D4×D61—42no—
128D4×D61—81no—
129D4×D61—81no—
130C2×D244—21no—
131C2×D244—21no—
132C2×D244—41no—
133C2×D244—41no—
134C2×D244—41no—
135C2×D244—41no—
136C2×D244—84no—
137C2×D244D811yescharacteristic
138C2×C4×D61—41no—
139C2×C4×D61C2×D411yescharacteristic
140C2×C4×D61C2×D411yescharacteristic
141Q16×C61—21no—
142Q16×C61—21no—
143D8×C61—21no—
144D8×C61#4112yes—
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2411yescharacteristic
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C42×C61—41no—
152C42×C61C2×D411yescharacteristic
153#11758199—42no—
154#11758199—42no—
155#11758198—41no—
156#11758198—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160#11758198D811yescharacteristic
161#11758198D811yescharacteristic
162C4⋊Dic61—21no—
163C4⋊Dic61—21no—
164C4⋊Dic61D811yescharacteristic
165#11758196—41no—
166#11758196—41no—
167#11758196—41no—
168#11758196—41no—
169#11758196—41no—
170C4×Dic61—41no—
171C2×#92418C2×D411yescharacteristic
172C2×#92418C2×D411yescharacteristic
173D488—21no—
174D488—21no—
175D488—21no—
176D488—21no—
177D488—81no—
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—
187C22×D61—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
197Q8×C61—41no—
198Q8×C61—41no—
199D4×C61—22no—
200D4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—82no—
205C2×C4×C61C2×D811yescharacteristic
206C2×C4×C61C2×D811yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C22⋊D61—82no—
209C22⋊D61—82no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61C2×D811yescharacteristic
213C2×Dic61C2×D811yescharacteristic
214D244—22no—
215D244—41no—
216D244—41no—
217D244—41no—
218D244—41no—
219D244—82no—
220D244—82no—
221D244—82no—
222D244—161no—
223C4×D61—21no—
224C4×D61—21no—
225C4×D61—21no—
226C4×D61—21no—
227C4×D61—82no—
228C8×C61—21no—
229C8×C61C2×#4111yescharacteristic
230C8×C61H(5,𝔽2)11yescharacteristic
231#92418—21no—
232#92418—21no—
233#33877—611nomaximal, Sylow
234C22×C61—42no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61C22×D811yescharacteristic
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
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—81no—
257C4×C61#54611yescharacteristic
258C4×C61#57711yescharacteristic
259Dic61—21no—
260Dic61—21no—
261Dic61—81no—
262Dic61—81no—
263#3336—611no—
264D4×D8—611no—
265#2244—611no—
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#2175D6111yescharacteristic, complemented
275#2168—611no—
276#2140—611no—
277C2×#357—611no—
278C2×C61—82no—
279C2×C61#329411yescharacteristic
280C2×C61C2×#50911yescharacteristic
281C2×C61#341611yescharacteristic
282D61—22no—
283D61—41no—
284D61—161no—
285D61—161no—
286C22×D8—611no—
287C22×D8—611no—
288#552—1221no—
289D42—1221no—
290C2×SD32—611no—
291C2×SD32—611no—
292C2×SD32C2×D6111yescharacteristic
293C2×M32—611no—
294C22×C16—611no—
295#499—611no—
296#493—611no—
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×Q16C2×D6111yescharacteristic, complemented
308C4×D8C2×D6111yescharacteristic
309C8×D4—611no—
310#427—611no—
311C2×#107—611no—
312#367—611no—
313#366—611no—
314#366C2×D6111yescharacteristic, complemented
315C4⋊C16—611no—
316#358C2×D6111yescharacteristic, complemented
317#357—611no—
318#357—611no—
319#357—611no—
320#357—611no—
321#357—611no—
322#357—611no—
323#357—611no—
324#357—611no—
325#357C2×D6111yescharacteristic
326C22⋊C16—611no—
327C22⋊C16—611no—
328#346C2×D6111yescharacteristic, complemented
329C61#3387711yescharacteristic, complemented, Sylow
330C22×D4—1221no—
331C22×D4—1221no—
332C22×D4—2441no—
333C2×Q16C22×D6111yescharacteristic
334C2×D8—611no—
335C2×D8—611no—
336C2×D8—1221no—
337C2×D8—1221no—
338C2×D8—1222no—
339C2×D8—1222no—
340C2×D8—1221no—
341C2×D8—2441no—
342C2×D8—2441no—
343C2×D8C22×D6111yescharacteristic
344C22×C8—611no—
345C22×C8—611no—
346#127—1221no—
347#126—2441no—
348#125—1221no—
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—21no—
359C4×D4—21no—
360C4×D4—611no—
361#117—1221no—
362#117—2441no—
363C2×C4⋊C4—1221no—
364SD32—22no—
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—1221no—
379#106—1221no—
380C4⋊C8—611no—
381#103—21no—
382#103—1221no—
383#103—1221no—
384#102—21no—
385#102—1221no—
386#102—1221no—
387C22⋊C8—611no—
388C22⋊C8—611no—
389C4×C8C22×D6111yescharacteristic
390C24—2441no—
391C24—2441no—
392C2×Q8—21no—
393C2×D4—21no—
394C2×D4—611no—
395C2×D4—1221no—
396C2×D4—1221no—
397C2×D4—4884no—
398C2×D4—4881no—
399C2×D4—4881no—
400C2×D4—2441no—
401C2×D4—2441no—
402C2×D4—2441no—
403C2×D4—2441no—
404C2×D4—2442no—
405C2×D4—2442no—
406C2×D4—2441no—
407C2×D4—2441no—
408C22×C4—41no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—2441no—
412Q16—21no—
413Q16—21no—
414D8—21no—
415D8—1221no—
416D8—1221no—
417D8—1221no—
418D8—1221no—
419D8—4881no—
420D8—2442no—
421D8—2442no—
422D8#1175822212yes—
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—611no—
435C4⋊C4—1221no—
436C4⋊C4—1221no—
437C4⋊C4—2441no—
438C4⋊C4—2441no—
439C4⋊C4—2441no—
440C4⋊C4—2441no—
441C4⋊C4—2441no—
442C22⋊C4—41no—
443C22⋊C4—611no—
444C22⋊C4—611no—
445C22⋊C4—2441no—
446C22⋊C4—2441no—
447C22⋊C4—2441no—
448C22⋊C4—2441no—
449C22⋊C4—2441no—
450C42—41no—
451C42—2441no—
452C42D4×D6111yescharacteristic
453C16—21no—
454C16—21no—
455C16—1221no—
456C16—1221no—
457C23—41no—
458C23—611no—
459C23—611no—
460C23—9761no—
461C23—9761no—
462C23—4882no—
463C23—4882no—
464C23—4882no—
465C23—4882no—
466C23—2441no—
467C23—2441no—
468Q8—41no—
469Q8—41no—
470D4—22no—
471D4—41no—
472D4—1222no—
473D4—9761no—
474D4—4882no—
475D4—4882no—
476D4—4882no—
477D4—4882no—
478D4—4882no—
479D4—2441no—
480D4—2441no—
481D4—2441no—
482D4—2441no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—611no—
488C2×C4—611no—
489C2×C4—1221no—
490C2×C4—1221no—
491C2×C4—1221no—
492C2×C4—1221no—
493C2×C4—4882no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4D8×D6111yescharacteristic
497C2×C4D8×D6111yescharacteristic
498C2×C4C2×D4×D6111yescharacteristic
499C8—21no—
500C8—1221no—
501C8—1221no—
502C8C2×#1175822211yescharacteristic
503C8#1451982311yescharacteristic
504C22—42no—
505C22—81no—
506C22—81no—
507C22—612no—
508C22—1221no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—1221no—
513C22—9764no—
514C22—9764no—
515C22—4881no—
516C22—4881no—
517C22—4881no—
518C22—4881no—
519C22—4881no—
520C22—4881no—
521C22C2×D8×D6111yescharacteristic
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—1221no—
528C4—1221no—
529C4—4881no—
530C4—4881no—
531C4#1684040811yescharacteristic
532C4#1684056911yescharacteristic
533C2—82no—
534C2—1222no—
535C2—9761no—
536C2—9761no—
537C2—2441no—
538C2#2145763411yescharacteristic
539C2#509×D6111yescharacteristic
540C2#2145896411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2175C2
socleC22×C61C22×D8
prime radicalD8×D244C2
hypercenter#2175D61
hypocenterC61#33877
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. #21458189C2semidirect
3. #21448061C2semidirect
4. #21448013C2semidirect
5. #21448001C2semidirect
6. #21447976C2semidirect
7. #21447935C2semidirect
8. #21447918C2semidirect
9. #21447859C2semidirect
10. #21447746C2semidirect
11. #21447746C2semidirect
12. #21447646C2semidirect
13. #21447533C2semidirect
14. #357×D61C2semidirect
15. C61×#2175C2semidirect
20. C2×#14519720C22semidirect
21. C2×#14519720C22semidirect
22. C2×#14519716C22semidirect
23. C2×C16×D61C22semidirect
24. #16840164C22semidirect
29. #16840000C22semidirect
30. #16840000C22semidirect
37. #16839799C22semidirect
38. #107×D61C22semidirect
39. #16839589C22semidirect
40. #16839587C22semidirect
41. C4⋊#11758185C22semidirect
42. #16839564C22semidirect
43. #16839564C22semidirect
44. #16839564C22semidirect
45. #16839564C22semidirect
48. #16839562C22semidirect
49. #16839562C22semidirect
50. #16839541C22semidirect
51. #16839541C22semidirect
53. C4×Q16×C61C22semidirect
55. C61×#366C22semidirect
56. C61×#358C22semidirect
58. C61×#346C22semidirect
274. #2175D61semidirect
307. C4×Q16C2×D61semidirect
314. #366C2×D61semidirect
316. #358C2×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
#214581892
D8×D2442
#214480612
#214480132
#214480012
#214479762
#214479352
#214479182
#214478592
#214477462
#214476462
#214475332
#357×D612
C61×#21752
#3387761