Finite Group Databasebeta

← #29836978

Subgroups — #29836978

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#21457506C211yesmaximal, characteristic, complemented
2#21448058C211yesmaximal, characteristic, complemented
3#21448016C211yesmaximal, characteristic, complemented
4#21448004C211yesmaximal, characteristic, complemented
5#21447963C211yesmaximal, characteristic, complemented
6#21447920C211yesmaximal, characteristic, complemented
7#21447913C211yesmaximal, characteristic, complemented
8#21447874C211yesmaximal, characteristic, complemented
9#21447740C211yesmaximal, characteristic, complemented
10#21447730C211yesmaximal, characteristic, complemented
11#21447693C211yesmaximal, characteristic, complemented
12#21447645C211yesmaximal, characteristic, complemented
13#21447529C211yesmaximal, characteristic, complemented
14C2×#16839562C211yesmaximal, characteristic, complemented
15C61×#3334C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C22×D488C2211yescharacteristic
18#16840408—21no—
19C2×#14519721C2211yescharacteristic, complemented
20C2×#14519718C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22C2×#14519717C2211yescharacteristic, complemented
23C22×#11758185C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840003C2211yescharacteristic
26#16839998C2211yescharacteristic
27#16839978—21no—
28#16839915—21no—
29#16839909—21no—
30C4×D488C2211yescharacteristic
31#16839589C2211yescharacteristic, complemented
32#16839589C2211yescharacteristic, complemented
33#16839589C2211yescharacteristic, complemented
34C4⋊#11758185C2211yescharacteristic, complemented
35#16839565C2211yescharacteristic, complemented
36#16839565C2211yescharacteristic, complemented
37#16839565C2211yescharacteristic, complemented
38#16839563C2211yescharacteristic, complemented
39#16839562C2211yescharacteristic
40#16839562C2211yescharacteristic
41#16839562C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44#16839562C2211yescharacteristic
45C22⋊#11758185C2211yescharacteristic
46C22⋊#11758185C2211yescharacteristic, complemented
47#16839538C2211yescharacteristic, complemented
48C61×#547—21no—
49C61×#500C2211yescharacteristic, complemented
50C61×#480—21no—
51C61×#480—21no—
52C61×#474—21no—
53C61×#466C2211yescharacteristic
54C61×#466C2211yescharacteristic, complemented
55C4×D8×C61C2211yescharacteristic, complemented
56C8×D4×C61C2211yescharacteristic
57C2×#107×C61C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic, complemented
59C2×#11758222—21no—
60C22×D244—21no—
61#14519799—22no—
62#14519799—41no—
63C2×Dic244C2311yescharacteristic
64C2×#11758190—21no—
65C2×#11758190—21no—
66C2×D488—22no—
67C2×D488—21no—
68C2×D488—41no—
69C2×D488C2311yescharacteristic
70C2×D488C2311yescharacteristic
71#14519765—21no—
72#14519762—41no—
73#14519756—21no—
74#14519751—21no—
75#14519750—41no—
76#14519745—41no—
77C4×D244—21no—
78C22⋊C4×D61—41no—
79#14519721—41no—
80#14519718—22no—
81#14519718—41no—
82#14519717—41no—
83C2×#11758185—41no—
84C2×#11758185C2311yescharacteristic
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519702—21no—
90#14519699—21no—
91#14519699—21no—
92C2×#41×C61—41no—
93C2×D8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96C4⋊Q8×C61—21no—
97#123×C61—41no—
98#123×C61—41no—
99C22⋊Q8×C61—41no—
100#121×C61—21no—
101#121×C61—21no—
102C4×D4×C61—21no—
103C4×D4×C61D411yescharacteristic
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106#107×C61—21no—
107#107×C61—21no—
108#107×C61—21no—
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112C4⋊C8×C61D411yescharacteristic
113#102×C61—21no—
114#102×C61—21no—
115#102×C61—21no—
116C22⋊C8×C61D411yescharacteristic
117C22⋊C8×C61D411yescharacteristic
118C4×C8×C61C2311yescharacteristic
119C23×D61—41no—
120#41×C61—84no—
121C2×Q8×C61—41no—
122C2×D4×C61—21no—
123C2×D4×C61—41no—
124C2×D4×C61—41no—
125C2×D4×C61D811yescharacteristic
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C2×C22⋊D61—41no—
132C2×C22⋊D61—41no—
133#11758222—42no—
134#11758222—81no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—42no—
138C2×D244—41no—
139C2×D244—81no—
140C2×C4×D61—41no—
141C2×C4×D61—41no—
142C2×Dic122—21no—
143D8×C61—21no—
144D8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61C2×D411yescharacteristic
150C2×C8×C61C2×D411yescharacteristic
151C2×C8×C61C2×D411yescharacteristic
152C2×C8×C61C2411yescharacteristic
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—41no—
157C4⋊C4×C61—41no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61D811yescharacteristic
160C22⋊C4×C61—41no—
161C22⋊C4×C61—41no—
162C22⋊C4×C61—41no—
163C22⋊C4×C61D811yescharacteristic
164C22⋊C4×C61D811yescharacteristic
165C42×C61C2×D411yescharacteristic
166C22⋊Dic61—41no—
167#11758198—41no—
168#11758198—41no—
169#11758198—41no—
170#11758198—41no—
171C4⋊Dic61—21no—
172#11758196—41no—
173Dic244—21no—
174Dic244—21no—
175D488—21no—
176D488—21no—
177D488—21no—
178D488—42no—
179D488#4112yescomplemented
180#11758190—42no—
181#11758190—81no—
182#11758185—21no—
183#11758185—21no—
184#11758185—21no—
185#11758185—21no—
186C23×C61—41no—
187C23×C61C2×D811yescharacteristic
188C23×C61C2×D811yescharacteristic
189C22×D61—41no—
190C22×D61—41no—
191C22×D61—82no—
192C22×D61—82no—
193C22×D61—161no—
194Q8×C61—82no—
195D4×C61—22no—
196D4×C61—41no—
197D4×C61—41no—
198D4×C61—82no—
199D4×C61—82no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—82no—
208C2×C4×C61—82no—
209C2×C4×C61—82no—
210C2×C4×C61C2×D811yescharacteristic
211C2×C4×C61C2×D811yescharacteristic
212C2×C4×C61C2×D811yescharacteristic
213C2×C4×C61C2×D811yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C22⋊D61—82no—
216C22⋊D61—161no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219D244—22no—
220D244—41no—
221D244—41no—
222D244—41no—
223D244—82no—
224C4×D61—82no—
225C4×D61—161no—
226Dic122—41no—
227Dic122—41no—
228C8×C61—21no—
229C8×C61—21no—
230C8×C61—21no—
231C8×C61C2×#4111yescharacteristic
232C8×C61H(5,𝔽2)11yescharacteristic
233#33873—611nomaximal, Sylow
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—81no—
240C22×C61—81no—
241C22×C61—81no—
242C22×C61#50912yes—
243C22×C61C22×D811yescharacteristic
244C2×D61—42no—
245C2×D61—81no—
246C2×D61—81no—
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—81no—
250C2×D61—164no—
251C4×C61—21no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—81no—
256C4×C61—81no—
257C4×C61—81no—
258C4×C61#54611yescharacteristic
259C4×C61#57711yescharacteristic
260Dic61—81no—
261Dic61—81no—
262#3334D6111yescharacteristic, complemented
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#2186—611no—
272#2184—611no—
273#2177—611no—
274#2168—611no—
275#2139—611no—
276C2×#357—611no—
277C2×C61—22no—
278C2×C61—41no—
279C2×C61—161no—
280C2×C61#329411yescharacteristic
281C2×C61C2×#50911yescharacteristic
282C2×C61#341611yescharacteristic
283D61—82no—
284D61—161no—
285C2×#135—611no—
286C22×D8—611no—
287#547—21no—
288#546—1221no—
289C2×SD32—611no—
290C2×D16—611no—
291C2×D16—611no—
292C2×M32—611no—
293C22×C16—611no—
294#500C2×D6111yescharacteristic, complemented
295#495—611no—
296#480—21no—
297#480—21no—
298#474—21no—
299#467—611no—
300#466—611no—
301#466C2×D6111yescharacteristic
302#466C2×D6111yescharacteristic, complemented
303#463—1221no—
304#450—1221no—
305#449—1221no—
306C4×D8—611no—
307C4×D8C2×D6111yescharacteristic, complemented
308C8×D4C2×D6111yescharacteristic
309C2×#107C2×D6111yescharacteristic
310C2×#107C2×D6111yescharacteristic, complemented
311#367—611no—
312#367—611no—
313#367—611no—
314C4⋊C16—611no—
315#358—611no—
316#358—611no—
317#358—611no—
318#357—611no—
319#357—611no—
320#357—611no—
321#357—611no—
322#357—611no—
323#357—611no—
324#357—611no—
325C22⋊C16—611no—
326C22⋊C16—611no—
327#346—611no—
328C61#3387311yescharacteristic, complemented, Sylow
329C2×#41—41no—
330C2×#41—1221no—
331C22×D4—1221no—
332#135—1222no—
333#135—2441no—
334C2×Q16—611no—
335C2×SD16—1221no—
336C2×SD16—1221no—
337C2×D8—611no—
338C2×D8—611no—
339C2×D8—1222no—
340C2×D8—1221no—
341C2×D8—2441no—
342C2×D8C22×D6111yescharacteristic
343C22×C8C22×D6111yescharacteristic
344C22×C8C22×D6111yescharacteristic
345C4⋊Q8—21no—
346#124—1221no—
347#123—41no—
348#123—41no—
349#123—2441no—
350C22⋊Q8—41no—
351C22⋊Q8—1221no—
352#121—21no—
353#121—21no—
354#121—1221no—
355#121—2441no—
356#120—2441no—
357C4×D4—21no—
358C4×D4—1221no—
359C4×D4C22⋊D6111yescharacteristic
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C22⋊C4—2441no—
363SD32—2441no—
364D16—1222no—
365D16—2441no—
366M32—2441no—
367C2×C16—611no—
368C2×C16—611no—
369C2×C16—611no—
370C2×C16—611no—
371C2×C16—2441no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—611no—
376#107C22×D6111yescharacteristic
377#107C22×D6111yescharacteristic
378#107C22×D6111yescharacteristic
379C4⋊C8C22⋊D6111yescharacteristic
380#103—1221no—
381#102—21no—
382#102—21no—
383#102—21no—
384#102—1221no—
385#102—1221no—
386C22⋊C8C22⋊D6111yescharacteristic
387C22⋊C8C22⋊D6111yescharacteristic
388C4×C8C22×D6111yescharacteristic
389C24—2441no—
390#41—84no—
391#41—4881no—
392#41—2442no—
393C2×Q8—41no—
394C2×Q8—1221no—
395C2×D4—21no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—1221no—
399C2×D4—1221no—
400C2×D4—4881no—
401C2×D4—2442no—
402C2×D4—2441no—
403C2×D4—2441no—
404C2×D4—2441no—
405C2×D4#1175819911yescharacteristic
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—2441no—
410C22×C4—2441no—
411C22×C4C2×C22⋊D6111yescharacteristic
412C22×C4C2×C22⋊D6111yescharacteristic
413Q16—1221no—
414Q16—1221no—
415SD16—4881no—
416SD16—2442no—
417D8—21no—
418D8—21no—
419D8—612no—
420D8—1221no—
421D8—1221no—
422D8—1221no—
423D8—2442no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8C2×C22⋊D6111yescharacteristic
429C2×C8C2×C22⋊D6111yescharacteristic
430C2×C8C2×C22⋊D6111yescharacteristic
431C2×C8C23×D6111yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—1221no—
439C4⋊C4—2441no—
440C4⋊C4#1175819911yescharacteristic
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—2441no—
445C22⋊C4—2441no—
446C22⋊C4—2441no—
447C22⋊C4—2441no—
448C22⋊C4—2441no—
449C22⋊C4#1175819911yescharacteristic
450C22⋊C4#1175819911yescharacteristic
451C42C2×C22⋊D6111yescharacteristic
452C16—1221no—
453C16—1221no—
454C16—1221no—
455C16—1221no—
456C23—41no—
457C23—9761no—
458C23—4882no—
459C23—4882no—
460C23—2441no—
461C23—2441no—
462C23C2×#1175819911yescharacteristic
463C23C2×#1175819911yescharacteristic
464Q8—82no—
465Q8—2441no—
466Q8—2441no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—82no—
471D4—82no—
472D4—1222no—
473D4—9761no—
474D4—4882no—
475D4—4882no—
476D4—2441no—
477D4—2441no—
478D4—2441no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4—9761no—
490C2×C4—4882no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4C2×#1175819911yescharacteristic
494C2×C4C2×#1175819911yescharacteristic
495C2×C4C2×#1175819911yescharacteristic
496C2×C4C2×#1175819911yescharacteristic
497C2×C4C22×C22⋊D6111yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8#41×D6111yescharacteristic
502C8#1451982311yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—9764no—
512C22—4881no—
513C22—4881no—
514C22—4881no—
515C22—4881no—
516C22—4881no—
517C22—2442no—
518C22#1684019812yes—
519C22C22×#1175819911yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—4881no—
528C4—4881no—
529C4#1684040011yescharacteristic
530C4#1684057011yescharacteristic
531C2—22no—
532C2—41no—
533C2—161no—
534C2—9761no—
535C2—4882no—
536C2#2145762611yescharacteristic
537C2C2×#1684019811yescharacteristic
538C2#2145896311yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3334C2
socleC22×C61C22×D8
hypercenter#3334D61
hypocenterC61#33873
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #21457506C2semidirect
2. #21448058C2semidirect
3. #21448016C2semidirect
4. #21448004C2semidirect
5. #21447963C2semidirect
6. #21447920C2semidirect
7. #21447913C2semidirect
8. #21447874C2semidirect
9. #21447740C2semidirect
10. #21447730C2semidirect
11. #21447693C2semidirect
12. #21447645C2semidirect
13. #21447529C2semidirect
14. C2×#16839562C2semidirect
15. C61×#3334C2semidirect
19. C2×#14519721C22semidirect
22. C2×#14519717C22semidirect
31. #16839589C22semidirect
32. #16839589C22semidirect
33. #16839589C22semidirect
34. C4⋊#11758185C22semidirect
35. #16839565C22semidirect
36. #16839565C22semidirect
37. #16839565C22semidirect
38. #16839563C22semidirect
46. C22⋊#11758185C22semidirect
47. #16839538C22semidirect
49. C61×#500C22semidirect
54. C61×#466C22semidirect
55. C4×D8×C61C22semidirect
58. C2×#107×C61C22semidirect
179. D488#41semidirect
262. #3334D61semidirect
294. #500C2×D61semidirect
302. #466C2×D61semidirect
307. C4×D8C2×D61semidirect
310. C2×#107C2×D61semidirect
328. C61#33873semidirect

Maximal subgroups

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

subgroupindex
#214575062
#214480582
#214480162
#214480042
#214479632
#214479202
#214479132
#214478742
#214477402
#214477302
#214476932
#214476452
#214475292
C2×#168395622
C61×#33342
#3387361