Finite Group Databasebeta

← #29837041

Subgroups — #29837041

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
2D8×D244C211yesmaximal, characteristic
3#21448062C211yesmaximal, characteristic, complemented
4#21448012C211yesmaximal, characteristic, complemented
5#21448001C211yesmaximal, characteristic, complemented
6#21447933C211yesmaximal, characteristic, complemented
7#21447916C211yesmaximal, characteristic, complemented
8#21447860C211yesmaximal, characteristic, complemented
9#21447749C211yesmaximal, characteristic, complemented
10#21447749C211yesmaximal, characteristic, complemented
11#21447683C211yesmaximal, characteristic, complemented
12#21447643C211yesmaximal, characteristic, complemented
13#21447533C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18#16840450—21no—
19D4×D244—21no—
20C2×#14519722C2211yescharacteristic, complemented
21C2×#14519722C2211yescharacteristic, complemented
22C2×#14519721C2211yescharacteristic
23C2×#14519716C2211yescharacteristic, complemented
24C2×C16×D61C2211yescharacteristic, complemented
25#16840139C2211yescharacteristic
26#16840106—21no—
27#16840094—21no—
28#16840066—21no—
29#16840004C2211yescharacteristic, complemented
30#16840004C2211yescharacteristic, complemented
31#16839999C2211yescharacteristic
32#16839999C2211yescharacteristic
33#16839957—21no—
34#16839897—21no—
35#16839897—21no—
36C4×Dic244C2211yescharacteristic, complemented
37C8×D244C2211yescharacteristic
38#16839799C2211yescharacteristic, complemented
39#107×D61C2211yescharacteristic, complemented
40#16839587C2211yescharacteristic, complemented
41#16839565C2211yescharacteristic, complemented
42#16839564C2211yescharacteristic, complemented
43#16839564C2211yescharacteristic, complemented
44#16839563C2211yescharacteristic
45#16839562C2211yescharacteristic, complemented
46#16839562C2211yescharacteristic, complemented
47#16839562C2211yescharacteristic, complemented
48#16839562C2211yescharacteristic, complemented
49#16839541C2211yescharacteristic, complemented
50#16839541C2211yescharacteristic, complemented
51#16839538C2211yescharacteristic, complemented
52C61×#499C2211yescharacteristic, complemented
53C4×D8×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic, complemented
55C61×#366C2211yescharacteristic, complemented
56C61×C4⋊C16C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C22×D244—41no—
60C2×D4×D61—21no—
61C2×D4×D61—21no—
62C2×Dic244C2311yescharacteristic
63C2×D488—21no—
64C2×D488C2311yescharacteristic
65C2×D488C2311yescharacteristic
66C2×#11758199—21no—
67C2×#11758199—21no—
68D8×D61—22no—
69D8×D61—22no—
70D8×D61—41no—
71D8×D61—41no—
72C2×C8×D61C2311yescharacteristic
73C2×C8×D61C2311yescharacteristic
74#14519774—21no—
75#14519772—41no—
76#14519768—41no—
77#14519762—41no—
78#14519757—21no—
79#14519757—21no—
80#14519752—21no—
81#14519752—21no—
82#14519751—41no—
83#14519747—41no—
84#14519747—41no—
85C4×Dic122—21no—
86C4×D244D411yescharacteristic
87#14519735—21no—
88#14519735—41no—
89C4⋊C4×D61—21no—
90#14519722—41no—
91#14519722—41no—
92#14519721—22no—
93#14519716—41no—
94C2×#11758185C2311yescharacteristic
95C2×#11758185C2311yescharacteristic
96C16×D61—41no—
97#14519711C2311yescharacteristic
98#14519710—21no—
99#14519708—21no—
100C4⋊#92418D411yescharacteristic
101#14519702—21no—
102#14519700—21no—
103#14519700—21no—
104#14519697—21no—
105#14519697—21no—
106#14519689D411yescharacteristic
107#14519689D411yescharacteristic
108C2×D8×C61C2311yescharacteristic
109#125×C61—21no—
110C4×D4×C61—21no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#107×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116#106×C61—21no—
117#102×C61—21no—
118C4×C8×C61C2311yescharacteristic
119C23×D61—41no—
120C23×D61—41no—
121C2×D4×C61—21no—
122C22×C4×C61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125D4×D61—42no—
126D4×D61—42no—
127D4×D61—81no—
128D4×D61—81no—
129C2×D244—21no—
130C2×D244—21no—
131C2×D244—41no—
132C2×D244—41no—
133C2×D244—41no—
134C2×D244—41no—
135C2×D244—84no—
136C2×D244D811yescharacteristic
137C2×C4×D61—41no—
138C2×C4×D61C2×D411yescharacteristic
139C2×C4×D61C2×D411yescharacteristic
140C2×Dic122—21no—
141D8×C61—21no—
142D8×C61#4112yes—
143C2×C8×C61C2×D411yescharacteristic
144C2×C8×C61C2411yescharacteristic
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—41no—
149C4⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C42×C61C2×D411yescharacteristic
152#11758199—42no—
153#11758199—42no—
154#11758198—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198D811yescharacteristic
160#11758198D811yescharacteristic
161C4⋊Dic61—21no—
162C4⋊Dic61—41no—
163C4⋊Dic61—41no—
164C4⋊Dic61D811yescharacteristic
165#11758196—41no—
166#11758196—41no—
167C4×Dic61—41no—
168C4×Dic61—41no—
169C2×#92418C2×D411yescharacteristic
170C2×#92418C2×D411yescharacteristic
171Dic244—21no—
172Dic244—21no—
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
197D4×C61—22no—
198D4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—82no—
203C2×C4×C61C2×D811yescharacteristic
204C2×C4×C61C2×D811yescharacteristic
205C2×C4×C61C22×D411yescharacteristic
206C22⋊D61—82no—
207C22⋊D61—82no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61C2×D811yescharacteristic
211C2×Dic61C2×D811yescharacteristic
212D244—22no—
213D244—41no—
214D244—41no—
215D244—41no—
216D244—41no—
217D244—82no—
218D244—82no—
219D244—82no—
220D244—161no—
221C4×D61—21no—
222C4×D61—21no—
223C4×D61—21no—
224C4×D61—21no—
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—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#2228D6111yescharacteristic, complemented
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—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×SD32—611no—
293C2×M32—611no—
294C22×C16—611no—
295#499C2×D6111yescharacteristic, complemented
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×Q16—611no—
308C4×D8C2×D6111yescharacteristic
309C8×D4—611no—
310#427—611no—
311C2×#107—611no—
312#367C2×D6111yescharacteristic, complemented
313#366—611no—
314#366C2×D6111yescharacteristic, complemented
315C4⋊C16C2×D6111yescharacteristic, complemented
316#358—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357—611no—
321#357—611no—
322#357—611no—
323#357—611no—
324#357C2×D6111yescharacteristic
325#357C2×D6111yescharacteristic
326C22⋊C16—611no—
327C22⋊C16—611no—
328#346—611no—
329C61#3387711yescharacteristic, complemented, Sylow
330C22×D4—1221no—
331C22×D4—1221no—
332C22×D4—2441no—
333C2×Q16—611no—
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—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—21no—
360C4×D4—611no—
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—1221no—
375#107C22×D6111yescharacteristic
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—21no—
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—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—1221no—
413Q16—1221no—
414D8—21no—
415D8—1221no—
416D8—1221no—
417D8—1221no—
418D8—1221no—
419D8—4881no—
420D8—2442no—
421D8—2442no—
422D8#1175822612yes—
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—21no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—611no—
437C4⋊C4—1221no—
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—2441no—
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—2441no—
469Q8—2441no—
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×#1175822611yescharacteristic
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#1684040311yescharacteristic
532C4#1684057111yescharacteristic
533C2—82no—
534C2—1222no—
535C2—9761no—
536C2—9761no—
537C2—2441no—
538C2#2145762911yescharacteristic
539C2#509×D6111yescharacteristic
540C2#2145896211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2228C2
socleC22×C61C22×D8
prime radicalD8×D244C2
hypercenter#2228D61
hypocenterC61#33877
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #21458186C2semidirect
3. #21448062C2semidirect
4. #21448012C2semidirect
5. #21448001C2semidirect
6. #21447933C2semidirect
7. #21447916C2semidirect
8. #21447860C2semidirect
9. #21447749C2semidirect
10. #21447749C2semidirect
11. #21447683C2semidirect
12. #21447643C2semidirect
13. #21447533C2semidirect
14. #357×D61C2semidirect
15. C61×#2228C2semidirect
20. C2×#14519722C22semidirect
21. C2×#14519722C22semidirect
23. C2×#14519716C22semidirect
24. C2×C16×D61C22semidirect
29. #16840004C22semidirect
30. #16840004C22semidirect
36. C4×Dic244C22semidirect
38. #16839799C22semidirect
39. #107×D61C22semidirect
40. #16839587C22semidirect
41. #16839565C22semidirect
42. #16839564C22semidirect
43. #16839564C22semidirect
45. #16839562C22semidirect
46. #16839562C22semidirect
47. #16839562C22semidirect
48. #16839562C22semidirect
49. #16839541C22semidirect
50. #16839541C22semidirect
51. #16839538C22semidirect
52. C61×#499C22semidirect
54. C61×#367C22semidirect
55. C61×#366C22semidirect
56. C61×C4⋊C16C22semidirect
268. #2228D61semidirect
295. #499C2×D61semidirect
312. #367C2×D61semidirect
314. #366C2×D61semidirect
315. C4⋊C16C2×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
D8×D2442
#214480622
#214480122
#214480012
#214479332
#214479162
#214478602
#214477492
#214476832
#214476432
#214475332
#357×D612
C61×#22282
#3387761