Finite Group Databasebeta

← #29835342

Subgroups — #29835342

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456352C211yesmaximal, characteristic, complemented
2#21456301C211yesmaximal, characteristic
3#21448061C211yesmaximal, characteristic, complemented
4#21448059C211yesmaximal, characteristic, complemented
5#21448057C211yesmaximal, characteristic, complemented
6#21448052C211yesmaximal, characteristic, complemented
7#21448050C211yesmaximal, characteristic, complemented
8#21448044C211yesmaximal, characteristic, complemented
9#21448041C211yesmaximal, characteristic, complemented
10#21447533C211yesmaximal, characteristic, complemented
11#21447530C211yesmaximal, characteristic, complemented
12#21447525C211yesmaximal, characteristic, complemented
13#357×D61C211yesmaximal, characteristic, complemented
14#21447417C211yesmaximal, characteristic, complemented
15C61×#2243C211yesmaximal, characteristic, complemented
16C2×#14519804—21no—
17C2×#14519800C2211yescharacteristic
18C2×D8×D61C2211yescharacteristic
19#16840389—21no—
20#16840330—21no—
21C2×#14519716C2211yescharacteristic
22C2×C16×D61C2211yescharacteristic
23#16840170—21no—
24#16840168—21no—
25#16840166C2211yescharacteristic, complemented
26#16840164C2211yescharacteristic, complemented
27#16840163C2211yescharacteristic, complemented
28#16840152—21no—
29#16840148—21no—
30#16840147C2211yescharacteristic
31#16840139C2211yescharacteristic
32#16840137C2211yescharacteristic
33#16839803—21no—
34#16839799C2211yescharacteristic
35#107×D61C2211yescharacteristic
36#16839716C2211yescharacteristic
37#16839566C2211yescharacteristic, complemented
38#16839566C2211yescharacteristic, complemented
39#16839564C2211yescharacteristic
40#16839564C2211yescharacteristic
41#16839564C2211yescharacteristic, complemented
42#16839564C2211yescharacteristic, complemented
43#16839563C2211yescharacteristic
44#16839563C2211yescharacteristic
45#16839562C2211yescharacteristic
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic, complemented
48#16839562C2211yescharacteristic, complemented
49#16839537C2211yescharacteristic, complemented
50C4×#11758185C2211yescharacteristic, complemented
51C16×Dic61C2211yescharacteristic, complemented
52C61×#500C2211yescharacteristic, complemented
53C61×#495C2211yescharacteristic
54C61×#358C2211yescharacteristic, complemented
55C61×#358C2211yescharacteristic, complemented
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#346C2211yescharacteristic, complemented
59C2×#11758226—21no—
60C2×D4×D61—21no—
61#14519804—44no—
62#14519800—22no—
63#14519800—22no—
64C2×#11758201—21no—
65C2×#11758201—21no—
66C2×D488—21no—
67C2×D488C2311yescharacteristic
68C2×D488C2311yescharacteristic
69C2×#11758199—21no—
70C2×#11758199—21no—
71D8×D61—22no—
72D8×D61—22no—
73C2×#11758189D411yescharacteristic
74C2×C8×D61C2311yescharacteristic
75#14519776—21no—
76#14519775—41no—
77#14519774—21no—
78#14519773—21no—
79#14519769—21no—
80#14519768—21no—
81#14519767—41no—
82#14519766—21no—
83#14519755—41no—
84#14519753—41no—
85#14519750—41no—
86#14519750—41no—
87#14519747—41no—
88#14519747—41no—
89#14519735—21no—
90#14519734D411yescharacteristic
91C4⋊C4×D61—21no—
92#14519716—22no—
93C2×#11758185C2311yescharacteristic
94C2×#11758185C2311yescharacteristic
95C16×D61—22no—
96#14519711C2311yescharacteristic
97#14519711C2311yescharacteristic
98#14519710—21no—
99#14519710—21no—
100#14519709—21no—
101#14519708—21no—
102#14519708—21no—
103#14519688D411yescharacteristic
104#14519687D411yescharacteristic
105C8×Dic61C2311yescharacteristic
106C2×Q16×C61C2311yescharacteristic
107C2×SD16×C61—21no—
108C2×D8×C61C2311yescharacteristic
109C4⋊Q8×C61—21no—
110#124×C61—21no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113#107×C61—21no—
114#107×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116C4×C8×C61C2311yescharacteristic
117C23×D61—41no—
118C2×Q8×C61—21no—
119C2×Q8×C61—41no—
120C2×D4×C61—21no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124#11758226—42no—
125#11758226—42no—
126D4×D61—42no—
127D4×D61—42no—
128C2×D244—21no—
129C2×D244—21no—
130C2×D244—41no—
131C2×D244—41no—
132C2×D244—41no—
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61C2×D411yescharacteristic
136C2×Dic122—41no—
137Q16×C61—21no—
138Q16×C61—21no—
139SD16×C61—42no—
140D8×C61—21no—
141D8×C61—21no—
142C2×C8×C61C2×D411yescharacteristic
143C2×C8×C61C2411yescharacteristic
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C22⋊C4×C61—41no—
149C42×C61C2×D411yescharacteristic
150#11758201—42no—
151#11758201—42no—
152#11758199—42no—
153#11758199—42no—
154#11758198—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198D811yescharacteristic
158#11758198D811yescharacteristic
159C4⋊Dic61—21no—
160C4⋊Dic61—21no—
161C4⋊Dic61—41no—
162#11758196—41no—
163#11758196—41no—
164#11758196—41no—
165#11758196—41no—
166#11758196—41no—
167#11758196D811yescharacteristic
168#11758196D811yescharacteristic
169C4×Dic61—41no—
170C4×Dic61C2×D411yescharacteristic
171C2×#92418C2×D411yescharacteristic
172C2×#92418C2×D411yescharacteristic
173D488—21no—
174D488—21no—
175D488—21no—
176D488—21no—
177D488—42no—
178#11758189SD1614yes—
179C8×D61#4112yes—
180C8×D61#4112yes—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—82no—
189C22×D61—161no—
190C22×D61—161no—
191C22×D61C2×D811yescharacteristic
192Q8×C61—41no—
193Q8×C61—41no—
194Q8×C61—161no—
195D4×C61—41no—
196D4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61C2×D811yescharacteristic
201C2×C4×C61C2×D811yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C22⋊D61—82no—
204C22⋊D61—161no—
205C22⋊D61—161no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61C2×D811yescharacteristic
209C2×Dic61C2×D811yescharacteristic
210C2×Dic61C2×D811yescharacteristic
211D244—41no—
212D244—41no—
213D244—41no—
214D244—41no—
215D244—82no—
216D244—161no—
217D244—161no—
218C4×D61—82no—
219C4×D61—161no—
220C4×D61#12412yes—
221C4×D61C2×SD1612yes—
222Dic122—161no—
223C8×C61C2×SD1612yes—
224C8×C61C2×#4111yescharacteristic
225C8×C61C2×#4111yescharacteristic
226#92418#12412yes—
227#92418C2×SD1612yes—
228#33702—611nomaximal, Sylow
229C22×C61—81no—
230C22×C61—81no—
231C22×C61—81no—
232C22×C61C22×D811yescharacteristic
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—81no—
236C2×D61—81no—
237C2×D61—81no—
238C2×D61—81no—
239C2×D61—81no—
240C2×D61—81no—
241C2×D61—164no—
242C2×D61#48612yes—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—81no—
246C4×C61—81no—
247C4×C61—81no—
248C4×C61C2×#12411yescharacteristic
249C4×C61C22×SD1611yescharacteristic
250Dic61—21no—
251Dic61—21no—
252Dic61—81no—
253Dic61—81no—
254Dic61#48612yes—
255#3164—611no—
256#3155—611no—
257#2244—611no—
258#2244—611no—
259#2243—611no—
260#2243D6111yescharacteristic, complemented
261#2242—611no—
262#2242—611no—
263#2240—611no—
264#2240—611no—
265#2140—611no—
266#2139—611no—
267#2138—611no—
268C2×#357—611no—
269#2108—611no—
270C2×C61—161no—
271C2×C61C2×#48611yescharacteristic
272C2×C61#341511yescharacteristic
273C2×C61#341611yescharacteristic
274D61—22no—
275D61—161no—
276D61—161no—
277C2×AGL(1,ℤ/8)—1221no—
278C2×#135—611no—
279C22×D8—611no—
280#544—1221no—
281#535—1221no—
282C2×M32—611no—
283C22×C16—611no—
284#501—1221no—
285#501—1221no—
286#500—611no—
287#500C2×D6111yescharacteristic, complemented
288#499—611no—
289#499—611no—
290#496—1221no—
291#496—1221no—
292#495—611no—
293#495C2×D6111yescharacteristic
294#493—611no—
295#493—611no—
296#428—1221no—
297#427—611no—
298C2×#107—611no—
299#405—611no—
300#358—611no—
301#358—611no—
302#358C2×D6111yescharacteristic, complemented
303#358C2×D6111yescharacteristic, complemented
304#357—611no—
305#357—611no—
306#357—611no—
307#357—611no—
308#357—611no—
309#357—611no—
310#357—611no—
311#357—611no—
312#357—611no—
313#357—611no—
314#357C2×D6111yescharacteristic
315#357C2×D6111yescharacteristic
316#346—611no—
317#346C2×D6111yescharacteristic, complemented
318C4×C16—611no—
319C4×C16—611no—
320C61#3370211yescharacteristic, complemented, Sylow
321C2×#41—1221no—
322C22×D4—1221no—
323AGL(1,ℤ/8)—2444no—
324#135—1222no—
325#135—1222no—
326C2×Q16C22×D6111yescharacteristic
327C2×SD16—21no—
328C2×SD16—1221no—
329C2×SD16—1221no—
330C2×D8—611no—
331C2×D8—611no—
332C2×D8—1222no—
333C2×D8—1222no—
334C2×D8—1221no—
335C2×D8—1221no—
336C2×D8—1221no—
337C2×D8C22×D6111yescharacteristic
338C2×M16—611no—
339C22×C8—611no—
340C4⋊Q8—21no—
341C4⋊Q8—1221no—
342C4⋊Q8—2441no—
343#127—1221no—
344#127—1221no—
345#125—1221no—
346#125—1221no—
347#125—2441no—
348#124—21no—
349#124—1221no—
350C22⋊Q8—2441no—
351C22⋊Q8—2441no—
352#121—2441no—
353#121—2441no—
354#120—2441no—
355#120—2441no—
356#117—611no—
357#117—1221no—
358C2×C4⋊C4—1221no—
359M32—1222no—
360C2×C16—611no—
361C2×C16—611no—
362C2×C16—1222no—
363C2×C16C22×D6111yescharacteristic
364C2×C16C22×D6111yescharacteristic
365#107—21no—
366#107—611no—
367#107—611no—
368#107—1221no—
369#107—1221no—
370#107C22×D6111yescharacteristic
371#107C22×D6111yescharacteristic
372#106—1221no—
373#106—1221no—
374#106—1221no—
375#97—611no—
376#97—611no—
377C4×C8—611no—
378C4×C8C22×D6111yescharacteristic
379C24—2441no—
380#41—2442no—
381#41—2442no—
382C2×Q8—21no—
383C2×Q8—41no—
384C2×Q8—2441no—
385C2×D4—21no—
386C2×D4—1221no—
387C2×D4—1221no—
388C2×D4—2441no—
389C2×D4—2442no—
390C2×D4—2442no—
391C2×D4—2441no—
392C2×D4—2441no—
393C2×D4—2441no—
394C2×D4—2441no—
395C2×D4—2441no—
396C22×C4—611no—
397C22×C4—2441no—
398C22×C4—2441no—
399Q16—21no—
400Q16—21no—
401SD16—42no—
402SD16—2442no—
403SD16—2442no—
404D8—21no—
405D8—21no—
406D8—1221no—
407D8—1221no—
408D8—1221no—
409D8—1221no—
410D8—2442no—
411D8—2442no—
412D8—2442no—
413M16—614no—
414C2×C8—611no—
415C2×C8—611no—
416C2×C8—612no—
417C2×C8—612no—
418C2×C8D4×D6111yescharacteristic
419C2×C8C23×D6111yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—611no—
424C4⋊C4—611no—
425C4⋊C4—1221no—
426C4⋊C4—1221no—
427C4⋊C4—2441no—
428C4⋊C4—2441no—
429C4⋊C4—2441no—
430C4⋊C4—2441no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—611no—
436C22⋊C4—611no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C42—611no—
441C42—2441no—
442C42D4×D6111yescharacteristic
443C16—21no—
444C16—21no—
445C16—1221no—
446C16—1221no—
447C23—41no—
448C23—611no—
449C23—9761no—
450C23—9761no—
451C23—4882no—
452C23—2441no—
453C23—2441no—
454Q8—41no—
455Q8—41no—
456Q8—161no—
457Q8—9761no—
458D4—41no—
459D4—41no—
460D4—9761no—
461D4—9761no—
462D4—9761no—
463D4—9761no—
464D4—4882no—
465D4—4882no—
466D4—2441no—
467D4—2441no—
468D4—2441no—
469D4—2441no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—611no—
474C2×C4—612no—
475C2×C4—612no—
476C2×C4—611no—
477C2×C4—611no—
478C2×C4—9761no—
479C2×C4—4882no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4D8×D6111yescharacteristic
483C2×C4D8×D6111yescharacteristic
484C2×C4C2×D4×D6111yescharacteristic
485C8—612no—
486C8—612no—
487C8SD16×D6112yes—
488C8#41×D6111yescharacteristic
489C8#41×D6111yescharacteristic
490C22—81no—
491C22—81no—
492C22—81no—
493C22—612no—
494C22—1221no—
495C22—1221no—
496C22—9764no—
497C22—4881no—
498C22—4881no—
499C22—4881no—
500C22—4881no—
501C22—4881no—
502C22—4881no—
503C22C2×D8×D6111yescharacteristic
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—81no—
509C4—612no—
510C4—1221no—
511C4—1221no—
512C4—4881no—
513C4—4881no—
514C4#124×D6111yescharacteristic
515C4C2×SD16×D6111yescharacteristic
516C2—161no—
517C2—1222no—
518C2—9761no—
519C2—9761no—
520C2#486×D6111yescharacteristic
521C2#2145895911yescharacteristic
522C2#2145896411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2243C2
socleC22×C61C22×D8
prime radical#21456301C2
hypercenter#2243D61
hypocenterC61#33702
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
1. #21456352C2semidirect
3. #21448061C2semidirect
4. #21448059C2semidirect
5. #21448057C2semidirect
6. #21448052C2semidirect
7. #21448050C2semidirect
8. #21448044C2semidirect
9. #21448041C2semidirect
10. #21447533C2semidirect
11. #21447530C2semidirect
12. #21447525C2semidirect
13. #357×D61C2semidirect
14. #21447417C2semidirect
15. C61×#2243C2semidirect
25. #16840166C22semidirect
26. #16840164C22semidirect
27. #16840163C22semidirect
37. #16839566C22semidirect
38. #16839566C22semidirect
41. #16839564C22semidirect
42. #16839564C22semidirect
47. #16839562C22semidirect
48. #16839562C22semidirect
49. #16839537C22semidirect
50. C4×#11758185C22semidirect
51. C16×Dic61C22semidirect
52. C61×#500C22semidirect
54. C61×#358C22semidirect
55. C61×#358C22semidirect
58. C61×#346C22semidirect
260. #2243D61semidirect
287. #500C2×D61semidirect
302. #358C2×D61semidirect
303. #358C2×D61semidirect
317. #346C2×D61semidirect
320. C61#33702semidirect

Maximal subgroups

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

subgroupindex
#214563522
#214563012
#214480612
#214480592
#214480572
#214480522
#214480502
#214480442
#214480412
#214475332
#214475302
#214475252
#357×D612
#214474172
C61×#22432
#3370261