Finite Group Databasebeta

← #29836977

Subgroups — #29836977

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458163C211yesmaximal, characteristic, complemented
2#21457498C211yesmaximal, characteristic, complemented
3#21448057C211yesmaximal, characteristic, complemented
4#21448015C211yesmaximal, characteristic, complemented
5#21448005C211yesmaximal, characteristic, complemented
6#21447964C211yesmaximal, characteristic, complemented
7#21447920C211yesmaximal, characteristic, complemented
8#21447912C211yesmaximal, characteristic, complemented
9#21447876C211yesmaximal, characteristic, complemented
10#21447729C211yesmaximal, characteristic, complemented
11#21447695C211yesmaximal, characteristic, complemented
12#21447647C211yesmaximal, characteristic, complemented
13#21447531C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic, complemented
15C61×#2186C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17#16840412—21no—
18#16840400—21no—
19C2×#14519718C2211yescharacteristic
20C2×#14519717C2211yescharacteristic, complemented
21C2×C16×D61C2211yescharacteristic
22#16840166C2211yescharacteristic, complemented
23#16840147C2211yescharacteristic
24#16840074—21no—
25#16840073—21no—
26#16840040—21no—
27#16840000C2211yescharacteristic
28#16839998C2211yescharacteristic
29#16839995C2211yescharacteristic
30#16839979—21no—
31#16839911—21no—
32#16839907—21no—
33D8×Dic61C2211yescharacteristic
34D8×Dic61C2211yescharacteristic, complemented
35C8×C22⋊D61C2211yescharacteristic
36C2×#14519711C2211yescharacteristic, complemented
37#107×D61C2211yescharacteristic
38#16839590C2211yescharacteristic, complemented
39#16839590C2211yescharacteristic, complemented
40#16839589C2211yescharacteristic, complemented
41#16839580C2211yescharacteristic, complemented
42#16839566C2211yescharacteristic, complemented
43#16839566C2211yescharacteristic, complemented
44#16839564C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839563C2211yescharacteristic, complemented
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839537C2211yescharacteristic, complemented
52C2×#135×C61C2211yescharacteristic
53C2×SD32×C61C2211yescharacteristic, complemented
54C2×D16×C61C2211yescharacteristic
55C61×#466C2211yescharacteristic, complemented
56C61×#358C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic, complemented
59C2×#11758224—41no—
60C2×D4×D61—21no—
61C2×#11758201—21no—
62C2×D488C2311yescharacteristic
63C2×#11758199—21no—
64D8×D61—22no—
65D8×D61—41no—
66C2×C8×D61C2311yescharacteristic
67#14519776—21no—
68#14519766—21no—
69#14519760—41no—
70#14519759—41no—
71#14519758—41no—
72#14519754—41no—
73#14519753—21no—
74#14519751—21no—
75#14519749—41no—
76#14519748—21no—
77#14519745—41no—
78D4×Dic61—21no—
79D4×Dic61—21no—
80C4×C22⋊D61D411yescharacteristic
81C2×C4⋊Dic61—21no—
82C4⋊C4×D61—21no—
83C2×#11758198—41no—
84#14519718—41no—
85#14519717—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#14519701—21no—
97#14519699—21no—
98#14519698—21no—
99#14519698—21no—
100#14519698—21no—
101C22⋊#92418D411yescharacteristic
102#14519689D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×#41×C61—21no—
105#135×C61—22no—
106#135×C61—41no—
107C2×Q16×C61C2311yescharacteristic
108C2×SD16×C61—21no—
109C2×D8×C61C2311yescharacteristic
110C2×D8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112#121×C61—21no—
113SD32×C61—41no—
114D16×C61—22no—
115C2×C16×C61C2311yescharacteristic
116C2×C16×C61C2311yescharacteristic
117#107×C61C2311yescharacteristic
118#102×C61—21no—
119C23×D61—41no—
120#41×C61—42no—
121#41×C61—81no—
122C2×Q8×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—41no—
126C2×D4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61C2×D411yescharacteristic
129C2×C22⋊D61—41no—
130C2×C22⋊D61—41no—
131C2×C22⋊D61—41no—
132C2×C22⋊D61D811yescharacteristic
133C22×Dic61—41no—
134C22×Dic61—41no—
135C22×Dic61—41no—
136#11758224—84no—
137D4×D61—42no—
138D4×D61—81no—
139C2×D244—21no—
140C2×C4×D61—41no—
141C2×C4×D61C2×D411yescharacteristic
142C2×Dic122—41no—
143Q16×C61—21no—
144Q16×C61—21no—
145SD16×C61—42no—
146D8×C61—21no—
147D8×C61—21no—
148D8×C61—21no—
149D8×C61#4112yescomplemented
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61C2×D411yescharacteristic
153C2×C8×C61C2411yescharacteristic
154C4⋊C4×C61—21no—
155C22⋊C4×C61—41no—
156C22⋊Dic61—41no—
157C22⋊Dic61—41no—
158C22⋊Dic61—41no—
159C22⋊Dic61D811yescharacteristic
160#11758201—81no—
161#11758199—42no—
162#11758198—41no—
163#11758198—41no—
164#11758198—41no—
165#11758198—41no—
166#11758198D811yescharacteristic
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—41no—
171#11758196—41no—
172#11758196—41no—
173#11758196—41no—
174#11758196D811yescharacteristic
175C4×Dic61C2×D411yescharacteristic
176C2×#92418C2×D411yescharacteristic
177C2×#92418C2×D411yescharacteristic
178D488—21no—
179D488—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—
188C23×C61C2×D811yescharacteristic
189C22×D61—41no—
190C22×D61—82no—
191C22×D61—82no—
192C22×D61—161no—
193C22×D61C2×D811yescharacteristic
194Q8×C61—41no—
195Q8×C61—41no—
196D4×C61—22no—
197D4×C61—41no—
198D4×C61—41no—
199D4×C61—41no—
200D4×C61—82no—
201D4×C61—82no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—82no—
207C2×C4×C61C2×D811yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C22⋊D61—22no—
210C22⋊D61—82no—
211C22⋊D61—82no—
212C22⋊D61—161no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—82no—
217C2×Dic61—82no—
218C2×Dic61—161no—
219C2×Dic61C2×D811yescharacteristic
220C2×Dic61C2×D811yescharacteristic
221C2×Dic61C2×D811yescharacteristic
222D244—41no—
223D244—41no—
224C4×D61—21no—
225C4×D61—21no—
226C4×D61—82no—
227Dic122—82no—
228C8×C61—21no—
229C8×C61C2×#4111yescharacteristic
230C8×C61H(5,𝔽2)11yescharacteristic
231#92418—21no—
232#92418—21no—
233#33873—611nomaximal, Sylow
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—42no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61—81no—
241C22×C61—81no—
242C22×C61—81no—
243C22×C61C22×D811yescharacteristic
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—81no—
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—164no—
250C2×D61#50912yes—
251C4×C61—21no—
252C4×C61—81no—
253C4×C61—81no—
254C4×C61#54611yescharacteristic
255C4×C61#57711yescharacteristic
256Dic61—21no—
257Dic61—21no—
258Dic61—21no—
259Dic61—81no—
260Dic61—81no—
261Dic61—81no—
262#3334—611no—
263#3280—611no—
264#2243—611no—
265#2235—611no—
266#2233—611no—
267#2226—611no—
268#2218—611no—
269#2217—611no—
270#2210—611no—
271#2186D6111yescharacteristic, complemented
272#2184—611no—
273#2177—611no—
274#2168—611no—
275#2139—611no—
276C2×#357—611no—
277C2×C61—41no—
278C2×C61—82no—
279C2×C61—161no—
280C2×C61#329411yescharacteristic
281C2×C61C2×#50911yescharacteristic
282C2×C61#341611yescharacteristic
283D61—22no—
284D61—161no—
285C2×#135C2×D6111yescharacteristic
286C22×D8—611no—
287#547—1221no—
288#546—1221no—
289C2×SD32C2×D6111yescharacteristic, complemented
290C2×D16—611no—
291C2×D16C2×D6111yescharacteristic
292C2×M32—611no—
293C22×C16—611no—
294#500—611no—
295#495—611no—
296#480—1221no—
297#480—1221no—
298#474—1221no—
299#467—611no—
300#466—611no—
301#466—611no—
302#466C2×D6111yescharacteristic, complemented
303#463—1221no—
304#450—1221no—
305#449—1221no—
306C4×D8—611no—
307C4×D8—611no—
308C8×D4—611no—
309C2×#107—611no—
310C2×#107—611no—
311#367—611no—
312#367—611no—
313#367—611no—
314C4⋊C16—611no—
315#358—611no—
316#358—611no—
317#358C2×D6111yescharacteristic, complemented
318#357—611no—
319#357—611no—
320#357—611no—
321#357—611no—
322#357—611no—
323#357—611no—
324#357C2×D6111yescharacteristic
325C22⋊C16—611no—
326C22⋊C16C2×D6111yescharacteristic, complemented
327#346—611no—
328C61#3387311yescharacteristic, complemented, Sylow
329C2×#41—21no—
330C2×#41—2441no—
331C22×D4—1221no—
332#135—22no—
333#135—41no—
334C2×Q16C22×D6111yescharacteristic
335C2×SD16—21no—
336C2×SD16—1221no—
337C2×D8—611no—
338C2×D8—1221no—
339C2×D8—1222no—
340C2×D8—2441no—
341C2×D8C22×D6111yescharacteristic
342C2×D8C22×D6111yescharacteristic
343C22×C8—611no—
344C22×C8C22×D6111yescharacteristic
345C4⋊Q8—1221no—
346#124—1221no—
347#123—2441no—
348#123—2441no—
349#123—2441no—
350C22⋊Q8—1221no—
351C22⋊Q8—2441no—
352#121—21no—
353#121—1221no—
354#121—1221no—
355#121—2441no—
356#120—2441no—
357C4×D4—611no—
358C4×D4—1221no—
359C4×D4—1221no—
360C2×C4⋊C4—1221no—
361C2×C4⋊C4—1221no—
362C2×C22⋊C4—2441no—
363SD32—41no—
364D16—22no—
365D16—2441no—
366M32—2441no—
367C2×C16—611no—
368C2×C16—611no—
369C2×C16—2441no—
370C2×C16C22×D6111yescharacteristic
371C2×C16C22×D6111yescharacteristic
372#107—611no—
373#107—611no—
374#107—611no—
375#107—1221no—
376#107—1221no—
377#107—1221no—
378#107C22×D6111yescharacteristic
379C4⋊C8—611no—
380#103—1221no—
381#102—21no—
382#102—1221no—
383#102—1221no—
384#102—1221no—
385#102—1221no—
386C22⋊C8—611no—
387C22⋊C8—611no—
388C4×C8—611no—
389C24—2441no—
390#41—42no—
391#41—81no—
392#41—4884no—
393C2×Q8—21no—
394C2×Q8—2441no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—611no—
400C2×D4—1221no—
401C2×D4—4881no—
402C2×D4—2441no—
403C2×D4—2442no—
404C2×D4—2441no—
405C2×D4—2441no—
406C22×C4—41no—
407C22×C4—611no—
408C22×C4—2441no—
409C22×C4—2441no—
410C22×C4—2441no—
411C22×C4—2441no—
412C22×C4D4×D6111yescharacteristic
413Q16—21no—
414Q16—21no—
415SD16—42no—
416SD16—4881no—
417D8—21no—
418D8—21no—
419D8—21no—
420D8—1221no—
421D8—1221no—
422D8—2442no—
423D8#1175822412yescomplemented
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—611no—
427C2×C8—611no—
428C2×C8—1221no—
429C2×C8—1221no—
430C2×C8D4×D6111yescharacteristic
431C2×C8C23×D6111yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—611no—
434C4⋊C4—1221no—
435C4⋊C4—1221no—
436C4⋊C4—1221no—
437C4⋊C4—2441no—
438C4⋊C4—2441no—
439C4⋊C4—2441no—
440C4⋊C4—2441no—
441C22⋊C4—41no—
442C22⋊C4—611no—
443C22⋊C4—611no—
444C22⋊C4—2441no—
445C22⋊C4—2441no—
446C22⋊C4—2441no—
447C22⋊C4—2441no—
448C22⋊C4—2441no—
449C22⋊C4—2441no—
450C22⋊C4—2441no—
451C42—611no—
452C16—21no—
453C16—21no—
454C16—1221no—
455C16—1221no—
456C23—41no—
457C23—41no—
458C23—611no—
459C23—9761no—
460C23—4882no—
461C23—4882no—
462C23—2441no—
463C23D8×D6111yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—4882no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—41no—
471D4—82no—
472D4—82no—
473D4—1222no—
474D4—9761no—
475D4—4882no—
476D4—4882no—
477D4—2441no—
478D4—2441no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—611no—
485C2×C4—611no—
486C2×C4—611no—
487C2×C4—1221no—
488C2×C4—1221no—
489C2×C4—9761no—
490C2×C4—4882no—
491C2×C4—4882no—
492C2×C4—4882no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4D8×D6111yescharacteristic
497C2×C4C2×D4×D6111yescharacteristic
498C8—21no—
499C8—1221no—
500C8—1221no—
501C8C2×#1175822411yescharacteristic
502C8#1451982211yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—42no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—612no—
513C22—1221no—
514C22—1221no—
515C22—9764no—
516C22—4881no—
517C22—4881no—
518C22—4881no—
519C22C2×D8×D6111yescharacteristic
520C4—21no—
521C4—81no—
522C4—81no—
523C4—1221no—
524C4—1221no—
525C4—1221no—
526C4—4881no—
527C4—4881no—
528C4—4881no—
529C4#1684039911yescharacteristic
530C4#1684057211yescharacteristic
531C2—41no—
532C2—82no—
533C2—161no—
534C2—1222no—
535C2—9761no—
536C2#2145762511yescharacteristic
537C2#509×D6111yescharacteristic
538C2#2145896211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2186C2
socleC22×C61C22×D8
hypercenter#2186D61
hypocenterC61#33873
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2186

Complements

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

NH ≅ G/Ntype
1. #21458163C2semidirect
2. #21457498C2semidirect
3. #21448057C2semidirect
4. #21448015C2semidirect
5. #21448005C2semidirect
6. #21447964C2semidirect
7. #21447920C2semidirect
8. #21447912C2semidirect
9. #21447876C2semidirect
10. #21447729C2semidirect
11. #21447695C2semidirect
12. #21447647C2semidirect
13. #21447531C2semidirect
14. #357×D61C2semidirect
15. C61×#2186C2semidirect
20. C2×#14519717C22semidirect
22. #16840166C22semidirect
34. D8×Dic61C22semidirect
36. C2×#14519711C22semidirect
38. #16839590C22semidirect
39. #16839590C22semidirect
40. #16839589C22semidirect
41. #16839580C22semidirect
42. #16839566C22semidirect
43. #16839566C22semidirect
48. #16839563C22semidirect
51. #16839537C22semidirect
53. C2×SD32×C61C22semidirect
55. C61×#466C22semidirect
56. C61×#358C22semidirect
58. C61×C22⋊C16C22semidirect
149. D8×C61#41semidirect
271. #2186D61semidirect
289. C2×SD32C2×D61semidirect
302. #466C2×D61semidirect
317. #358C2×D61semidirect
326. C22⋊C16C2×D61semidirect
328. C61#33873semidirect
423. D8#11758224semidirect

Maximal subgroups

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

subgroupindex
#214581632
#214574982
#214480572
#214480152
#214480052
#214479642
#214479202
#214479122
#214478762
#214477292
#214476952
#214476472
#214475312
#357×D612
C61×#21862
#3387361