Finite Group Databasebeta

← #29836829

Subgroups — #29836829

Order 15616.

654 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458163C211yesmaximal, characteristic, complemented
2D8×C22⋊D61C211yesmaximal, characteristic, complemented
3#21448041C211yesmaximal, characteristic, complemented
4#21448000C211yesmaximal, characteristic, complemented
5#21447998C211yesmaximal, characteristic, complemented
6#21447954C211yesmaximal, characteristic, complemented
7#21447903C211yesmaximal, characteristic, complemented
8#21447902C211yesmaximal, characteristic, complemented
9#21447852C211yesmaximal, characteristic, complemented
10#21447729C211yesmaximal, characteristic, complemented
11D16×Dic61C211yesmaximal, characteristic, complemented
12#21447636C211yesmaximal, characteristic, complemented
13C2×#16839563C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2184C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17#16840412—21no—
18D4×C22⋊D61—21no—
19C2×#14519718C2211yescharacteristic, complemented
20C22×#11758185C2211yescharacteristic, complemented
21C2×C16×D61C2211yescharacteristic, complemented
22#16840166C2211yescharacteristic, complemented
23#16840137C2211yescharacteristic
24#16840074—21no—
25#16840073—21no—
26#16840040—21no—
27#16839998C2211yescharacteristic
28#16839995C2211yescharacteristic
29#16839995C2211yescharacteristic, complemented
30#16839955—21no—
31#16839896—21no—
32#16839894—21no—
33D8×Dic61C2211yescharacteristic
34D8×Dic61C2211yescharacteristic, complemented
35C8×C22⋊D61C2211yescharacteristic
36C2×#14519711C2211yescharacteristic, complemented
37#107×D61C2211yescharacteristic, complemented
38#16839588C2211yescharacteristic, complemented
39#16839588C2211yescharacteristic, complemented
40#16839587C2211yescharacteristic, complemented
41#16839580C2211yescharacteristic, complemented
42#16839564C2211yescharacteristic, complemented
43#16839564C2211yescharacteristic, complemented
44#16839563C2211yescharacteristic
45#16839563C2211yescharacteristic
46#16839563C2211yescharacteristic, complemented
47#16839563C2211yescharacteristic, complemented
48#16839563C2211yescharacteristic, complemented
49#16839562C2211yescharacteristic, complemented
50#16839541C2211yescharacteristic, complemented
51C16×Dic61C2211yescharacteristic, complemented
52C22×D8×C61C2211yescharacteristic
53C2×D16×C61C2211yescharacteristic
54C2×D16×C61C2211yescharacteristic, complemented
55C61×#466C2211yescharacteristic, complemented
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic, complemented
58C61×C22⋊C16C2211yescharacteristic, complemented
59C2×#11758224—41no—
60C22×C22⋊D61—41no—
61C2×D4×D61—21no—
62C2×D488C2311yescharacteristic
63C2×#11758199—21no—
64C2×#11758199—21no—
65D8×D61—22no—
66D8×D61—41no—
67C2×C8×D61C2311yescharacteristic
68#14519776—21no—
69#14519773—21no—
70#14519759—41no—
71#14519758—41no—
72#14519754—41no—
73#14519751—21no—
74#14519749—41no—
75#14519748—21no—
76#14519748—21no—
77#14519746—41no—
78#14519745—41no—
79D4×Dic61—21no—
80D4×Dic61—21no—
81C4×C22⋊D61D411yescharacteristic
82C2×C4⋊Dic61—21no—
83C4⋊C4×D61—21no—
84#14519718—41no—
85C2×#11758185—41no—
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88C16×D61—41no—
89#14519711—21no—
90#14519711C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519710—21no—
95#14519706D411yescharacteristic
96#14519699—21no—
97#14519698—21no—
98#14519698—21no—
99#14519698—21no—
100#14519698—21no—
101C22⋊#92418D411yescharacteristic
102#14519689D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C22×D4×C61—21no—
105C2×D8×C61—22no—
106C2×D8×C61—21no—
107C2×D8×C61—41no—
108C2×D8×C61C2311yescharacteristic
109C2×D8×C61C2311yescharacteristic
110C2×D8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112#121×C61—21no—
113D16×C61—22no—
114D16×C61—41no—
115C2×C16×C61C2311yescharacteristic
116C2×C16×C61C2311yescharacteristic
117#107×C61C2311yescharacteristic
118#102×C61—21no—
119C24×C61—41no—
120C23×D61—41no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—42no—
125C2×D4×C61—41no—
126C2×D4×C61—41no—
127C2×D4×C61—81no—
128C22×C4×C61C2×D411yescharacteristic
129C2×C22⋊D61—41no—
130C2×C22⋊D61—41no—
131C2×C22⋊D61—41no—
132C2×C22⋊D61—41no—
133C2×C22⋊D61—41no—
134C2×C22⋊D61—41no—
135C2×C22⋊D61—84no—
136C2×C22⋊D61D811yescharacteristic
137C22×Dic61—41no—
138C22×Dic61—41no—
139C22×Dic61—41no—
140#11758224—84no—
141D4×D61—42no—
142D4×D61—81no—
143C2×D244—21no—
144C2×C4×D61—41no—
145C2×C4×D61C2×D411yescharacteristic
146C2×Dic122—41no—
147D8×C61—21no—
148D8×C61—21no—
149D8×C61—21no—
150D8×C61—21no—
151D8×C61—21no—
152D8×C61—42no—
153D8×C61#4112yescomplemented
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61C2×D411yescharacteristic
157C2×C8×C61C2411yescharacteristic
158C4⋊C4×C61—21no—
159C22⋊C4×C61—41no—
160C22⋊Dic61—41no—
161C22⋊Dic61—41no—
162C22⋊Dic61—41no—
163C22⋊Dic61—41no—
164C22⋊Dic61D811yescharacteristic
165#11758199—42no—
166#11758199—81no—
167#11758198—41no—
168#11758198D811yescharacteristic
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—41no—
173#11758196—41no—
174#11758196—41no—
175#11758196D811yescharacteristic
176C4×Dic61C2×D411yescharacteristic
177C2×#92418C2×D411yescharacteristic
178C2×#92418C2×D411yescharacteristic
179D488—21no—
180D488—21no—
181C8×D61—21no—
182C8×D61—21no—
183C16×C61—21no—
184C16×C61—21no—
185#11758185—21no—
186#11758185—21no—
187C23×C61—41no—
188C23×C61—41no—
189C23×C61—41no—
190C23×C61—82no—
191C23×C61—82no—
192C23×C61—161no—
193C23×C61C2×D811yescharacteristic
194C22×D61—41no—
195C22×D61—82no—
196C22×D61—82no—
197C22×D61—161no—
198C22×D61C2×D811yescharacteristic
199D4×C61—22no—
200D4×C61—41no—
201D4×C61—41no—
202D4×C61—41no—
203D4×C61—41no—
204D4×C61—41no—
205D4×C61—82no—
206D4×C61—82no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—41no—
210C2×C4×C61C2×D811yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C22⋊D61—82no—
213C22⋊D61—82no—
214C22⋊D61—82no—
215C22⋊D61—82no—
216C22⋊D61—82no—
217C22⋊D61—161no—
218C22⋊D61D1614yescomplemented
219C2×Dic61—41no—
220C2×Dic61—41no—
221C2×Dic61—41no—
222C2×Dic61—82no—
223C2×Dic61—82no—
224C2×Dic61—82no—
225C2×Dic61C2×D811yescharacteristic
226C2×Dic61C2×D811yescharacteristic
227C2×Dic61C2×D811yescharacteristic
228D244—41no—
229D244—41no—
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—82no—
233Dic122—82no—
234C8×C61—21no—
235C8×C61C2×#4111yescharacteristic
236C8×C61H(5,𝔽2)11yescharacteristic
237#92418—21no—
238#92418—21no—
239#33861—611nomaximal, Sylow
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—42no—
243C22×C61—81no—
244C22×C61—81no—
245C22×C61—81no—
246C22×C61—81no—
247C22×C61—81no—
248C22×C61—81no—
249C22×C61—81no—
250C22×C61—81no—
251C22×C61—164no—
252C22×C61C2×D1612yes—
253C22×C61C22×D811yescharacteristic
254C2×D61—21no—
255C2×D61—21no—
256C2×D61—81no—
257C2×D61—81no—
258C2×D61—81no—
259C2×D61—164no—
260C2×D61C2×D1612yes—
261C4×C61—21no—
262C4×C61—81no—
263C4×C61#54611yescharacteristic
264C4×C61#57711yescharacteristic
265Dic61—21no—
266Dic61—21no—
267Dic61—81no—
268Dic61—81no—
269Dic61—81no—
270Dic61C2×D1612yes—
271#3334—611no—
272D4×D8—611no—
273#2240—611no—
274#2232—611no—
275#2232—611no—
276#2224—611no—
277#2215—611no—
278#2215—611no—
279#2206—611no—
280#2184—611no—
281#2184D6111yescharacteristic, complemented
282C4×D16—611no—
283D4×C16—611no—
284C2×#357—611no—
285C2×#357—611no—
286C2×C61—22no—
287C2×C61—82no—
288C2×C61—161no—
289C2×C61—161no—
290C2×C61#329411yescharacteristic
291C2×C61C22×D1611yescharacteristic
292C2×C61#341611yescharacteristic
293D61—22no—
294D61—161no—
295C22×D8—611no—
296C22×D8C2×D6111yescharacteristic
297#547—1221no—
298D42—1221no—
299C2×D16—611no—
300C2×D16C2×D6111yescharacteristic
301C2×D16C2×D6111yescharacteristic, complemented
302C22×C16—611no—
303C22×C16—611no—
304#500—611no—
305#493—611no—
306#480—1221no—
307#480—1221no—
308#474—1221no—
309#466—611no—
310#466—611no—
311#466—611no—
312#466C2×D6111yescharacteristic, complemented
313#459—1221no—
314#447—1221no—
315#447—1221no—
316C4×D8—611no—
317C4×D8—611no—
318C8×D4—611no—
319C2×#107—611no—
320C2×#107—611no—
321#366—611no—
322#366—611no—
323#366—611no—
324C4⋊C16—611no—
325#357—611no—
326#357—611no—
327#357—611no—
328#357—611no—
329#357—611no—
330#357—611no—
331#357—611no—
332#357—611no—
333#357C2×D6111yescharacteristic
334#357C2×D6111yescharacteristic, complemented
335C22⋊C16—611no—
336C22⋊C16C2×D6111yescharacteristic, complemented
337C4×C16—611no—
338C61#3386111yescharacteristic, complemented, Sylow
339C2×#41—2441no—
340C22×D4—21no—
341C22×D4—1221no—
342C22×D4—2441no—
343C2×D8—22no—
344C2×D8—21no—
345C2×D8—41no—
346C2×D8—611no—
347C2×D8—1221no—
348C2×D8—1221no—
349C2×D8—1222no—
350C2×D8—2441no—
351C2×D8C22×D6111yescharacteristic
352C2×D8C22×D6111yescharacteristic
353C2×D8C22×D6111yescharacteristic
354C22×C8—611no—
355C22×C8C22×D6111yescharacteristic
356C4⋊Q8—1221no—
357#127—1221no—
358#123—2441no—
359#123—2441no—
360C22⋊Q8—2441no—
361#121—21no—
362#121—1221no—
363#121—1221no—
364#121—1221no—
365#121—2441no—
366#120—2441no—
367#120—2441no—
368C4×D4—611no—
369C4×D4—1221no—
370C4×D4—1221no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1221no—
373D16—22no—
374D16—41no—
375D16—2441no—
376C2×C16—611no—
377C2×C16—611no—
378C2×C16—2441no—
379C2×C16—2441no—
380C2×C16C22×D6111yescharacteristic
381C2×C16C22×D6111yescharacteristic
382#107—611no—
383#107—611no—
384#107—611no—
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#107C22×D6111yescharacteristic
389C4⋊C8—611no—
390#102—21no—
391#102—1221no—
392#102—1221no—
393#102—1221no—
394#102—1221no—
395#102—1221no—
396C22⋊C8—611no—
397C22⋊C8—611no—
398C4×C8—611no—
399C24—41no—
400C24—2441no—
401#41—4884no—
402C2×Q8—2441no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—42no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—81no—
410C2×D4—611no—
411C2×D4—1221no—
412C2×D4—4881no—
413C2×D4—4884no—
414C2×D4—2441no—
415C2×D4—2441no—
416C2×D4—2441no—
417C2×D4—2442no—
418C2×D4—2441no—
419C2×D4—2441no—
420C2×D4—2441no—
421C22×C4—611no—
422C22×C4—2441no—
423C22×C4—2441no—
424C22×C4—2441no—
425C22×C4—2441no—
426C22×C4D4×D6111yescharacteristic
427D8—21no—
428D8—21no—
429D8—21no—
430D8—21no—
431D8—21no—
432D8—42no—
433D8—1221no—
434D8—1221no—
435D8—4881no—
436D8—2442no—
437D8#1175822412yescomplemented
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—611no—
441C2×C8—611no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8D4×D6111yescharacteristic
445C2×C8C23×D6111yescharacteristic
446C4⋊C4—21no—
447C4⋊C4—611no—
448C4⋊C4—1221no—
449C4⋊C4—1221no—
450C4⋊C4—1221no—
451C4⋊C4—2441no—
452C4⋊C4—2441no—
453C4⋊C4—2441no—
454C22⋊C4—41no—
455C22⋊C4—611no—
456C22⋊C4—611no—
457C22⋊C4—2441no—
458C22⋊C4—2441no—
459C22⋊C4—2441no—
460C22⋊C4—2441no—
461C22⋊C4—2441no—
462C42—611no—
463C16—21no—
464C16—21no—
465C16—1221no—
466C16—1221no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—82no—
471C23—82no—
472C23—161no—
473C23—611no—
474C23—9761no—
475C23—4882no—
476C23—4882no—
477C23—2441no—
478C23D8×D6111yescharacteristic
479Q8—4882no—
480D4—22no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—41no—
485D4—41no—
486D4—82no—
487D4—82no—
488D4—614no—
489D4—9761no—
490D4—4882no—
491D4—4882no—
492D4—4882no—
493D4—4882no—
494D4—4882no—
495D4—2441no—
496D4—2441no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—611no—
501C2×C4—611no—
502C2×C4—611no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—4882no—
506C2×C4—4882no—
507C2×C4—4882no—
508C2×C4—4882no—
509C2×C4—2441no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4D8×D6111yescharacteristic
513C2×C4C2×D4×D6111yescharacteristic
514C8—21no—
515C8—1221no—
516C8—1221no—
517C8C2×#1175822411yescharacteristic
518C8#1451982211yescharacteristic
519C22—21no—
520C22—21no—
521C22—42no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—164no—
531C22—612no—
532C22—1221no—
533C22—1221no—
534C22—9764no—
535C22—4881no—
536C22—4881no—
537C22—4881no—
538C22D16×D6112yes—
539C22C2×D8×D6111yescharacteristic
540C4—21no—
541C4—81no—
542C4—612no—
543C4—1221no—
544C4—1221no—
545C4—4881no—
546C4—4881no—
547C4—4881no—
548C4#1684039911yescharacteristic
549C4#1684057211yescharacteristic
550C2—22no—
551C2—82no—
552C2—161no—
553C2—161no—
554C2—1222no—
555C2—9761no—
556C2#2145762511yescharacteristic
557C2C2×D16×D6111yescharacteristic
558C2#2145896511yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2184C2
socleC22×C61C22×D8
hypercenter#2184D61
hypocenterC61#33861
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #21458163C2semidirect
2. D8×C22⋊D61C2semidirect
3. #21448041C2semidirect
4. #21448000C2semidirect
5. #21447998C2semidirect
6. #21447954C2semidirect
7. #21447903C2semidirect
8. #21447902C2semidirect
9. #21447852C2semidirect
10. #21447729C2semidirect
11. D16×Dic61C2semidirect
12. #21447636C2semidirect
13. C2×#16839563C2semidirect
14. #357×D61C2semidirect
15. C61×#2184C2semidirect
19. C2×#14519718C22semidirect
20. C22×#11758185C22semidirect
21. C2×C16×D61C22semidirect
22. #16840166C22semidirect
29. #16839995C22semidirect
34. D8×Dic61C22semidirect
36. C2×#14519711C22semidirect
37. #107×D61C22semidirect
38. #16839588C22semidirect
39. #16839588C22semidirect
40. #16839587C22semidirect
41. #16839580C22semidirect
42. #16839564C22semidirect
43. #16839564C22semidirect
46. #16839563C22semidirect
47. #16839563C22semidirect
48. #16839563C22semidirect
49. #16839562C22semidirect
50. #16839541C22semidirect
51. C16×Dic61C22semidirect
54. C2×D16×C61C22semidirect
55. C61×#466C22semidirect
57. C61×#357C22semidirect
58. C61×C22⋊C16C22semidirect
153. D8×C61#41semidirect
218. C22⋊D61D16semidirect
281. #2184D61semidirect
301. C2×D16C2×D61semidirect
312. #466C2×D61semidirect
334. #357C2×D61semidirect
336. C22⋊C16C2×D61semidirect
338. C61#33861semidirect
437. D8#11758224semidirect

Maximal subgroups

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

subgroupindex
#214581632
D8×C22⋊D612
#214480412
#214480002
#214479982
#214479542
#214479032
#214479022
#214478522
#214477292
D16×Dic612
#214476362
C2×#168395632
#357×D612
C61×#21842
#3386161