Finite Group Databasebeta

← D61×#2230 #29834739

Subgroups — D61×#2230 #29834739

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#498×D61C211yesmaximal, characteristic, complemented
2#443×D61C211yesmaximal, characteristic
3#21447991C211yesmaximal, characteristic, complemented
4#21447990C211yesmaximal, characteristic, complemented
5#21447989C212yesmaximal, complemented
6#21447988C212yesmaximal, complemented
7#21447987C211yesmaximal, characteristic, complemented
8#365×D61C212yesmaximal, complemented
9#364×D61C211yesmaximal, characteristic, complemented
10#360×D61C212yesmaximal
11C61×#2230C211yesmaximal, characteristic, complemented
12#135×D61C2211yescharacteristic
13#131×D61—21no—
14C4⋊Q8×D61—21no—
15M32×D61C2212yes—
16#16840160C2211yescharacteristic, complemented
17#16840159—21no—
18#16840159C2212yescomplemented
19#16840158—21no—
20#16839880C2211yescharacteristic
21#16839879C2211yescharacteristic
22#16839878C2211yescharacteristic
23#16839877—21no—
24#16839876—21no—
25#108×D61C2211yescharacteristic
26#106×D61—21no—
27#106×D61C2212yes—
28#104×D61—21no—
29C4×C8×D61C2211yescharacteristic
30#16839586C2212yescomplemented
31#16839585C2212yescomplemented
32#16839584C2212yescomplemented
33#16839583C2211yescharacteristic, complemented
34#16839582C2212yescomplemented
35#16839573C2212yes—
36#16839572C2212yes—
37#16839571C2212yes—
38C61×#498C2211yescharacteristic, complemented
39C61×#443C2211yescharacteristic
40C61×#365C2212yescomplemented
41C61×#364C2211yescharacteristic, complemented
42C61×#360C2212yes—
43#41×D61—21no—
44C2×Q8×D61—41no—
45#14519800Q811yescharacteristic, complemented
46#14519799C2311yescharacteristic
47#14519798—21no—
48#14519797—21no—
49#14519796Q811yescharacteristic, complemented
50Q16×D61Q811yescharacteristic, complemented
51SD16×D61—21no—
52D8×D61Q811yescharacteristic, complemented
53#14519785—21no—
54#14519785—41no—
55#14519784—21no—
56#14519783—21no—
57#14519783—41no—
58M16×D61—21no—
59M16×D61—41no—
60C2×C8×D61—41no—
61C2×C8×D61D411yescharacteristic
62C2×C8×D61C2311yescharacteristic
63#14519777—21no—
64#14519776—22no—
65#14519776—41no—
66#14519775—41no—
67C4⋊C4×D61—22no—
68C4⋊C4×D61—41no—
69C42×D61D411yescharacteristic
70#14519717C2312yes—
71#14519716—22no—
72C16×D61—22no—
73#14519713C2311yescharacteristic
74#14519712—21no—
75#14519709—21no—
76#14519709C2312yes—
77#14519708—22no—
78#14519708—22no—
79#14519705—21no—
80#14519704—21no—
81#14519703—21no—
82C4×#92418D411yescharacteristic
83C8×Dic61D411yescharacteristic
84C8×Dic61C2311yescharacteristic
85#135×C61C2311yescharacteristic
86#131×C61—21no—
87C4⋊Q8×C61—21no—
88M32×C61C2312yes—
89#108×C61C2311yescharacteristic
90#106×C61—21no—
91#106×C61C2312yes—
92#104×C61—21no—
93C4×C8×C61C2311yescharacteristic
94#41×C61—21no—
95C2×Q8×C61—41no—
96#11758226—21no—
97Q8×D61—21no—
98Q8×D61—84no—
99#11758224—21no—
100#11758224—41no—
101D4×D61—21no—
102D4×D61—41no—
103#11758222—21no—
104#11758222—41no—
105C2×C4×D61—21no—
106C2×C4×D61—41no—
107C2×C4×D61—42no—
108C2×C4×D61C2×D411yescharacteristic
109C2×Dic122—42no—
110C2×Dic122—41no—
111Q16×C61C2×Q811yescharacteristic, complemented
112SD16×C61—21no—
113D8×C61C2×Q811yescharacteristic, complemented
114M16×C61—21no—
115M16×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2411yescharacteristic
119C4⋊C4×C61—22no—
120C4⋊C4×C61—41no—
121C42×C61C2×D411yescharacteristic
122#11758202—21no—
123#11758201—21no—
124#11758200—21no—
125#11758199—21no—
126C4⋊Dic61—22no—
127C4⋊Dic61—41no—
128#11758196—42no—
129#11758196—42no—
130C4×Dic61—21no—
131C4×Dic61C2×D411yescharacteristic
132#11758194—21no—
133#11758194—41no—
134C2×#92418—41no—
135C2×#92418C2×D411yescharacteristic
136C2×#92418C2×D411yescharacteristic
137Dic244C2×Q811yescharacteristic, complemented
138D488C2×Q811yescharacteristic, complemented
139#11758190—21no—
140#11758189—41no—
141#11758189—41no—
142#11758189—41no—
143C8×D61—41no—
144C8×D61—41no—
145C8×D61—41no—
146C8×D61SD1611yescharacteristic
147C8×D61SD1611yescharacteristic
148C8×D61SD1611yescharacteristic
149C8×D61SD1611yescharacteristic
150C8×D61C2×Q811yescharacteristic
151C8×D61C2×Q811yescharacteristic
152C8×D61#4111yescharacteristic
153C8×D61#4111yescharacteristic
154C16×C61—22no—
155#11758185—22no—
156C22×D61—41no—
157C22×D61AGL(1,ℤ/8)11yescharacteristic
158Q8×C61—21no—
159Q8×C61—82no—
160D4×C61—21no—
161D4×C61—41no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61C22×D411yescharacteristic
166C22⋊D61—41no—
167C22⋊D61—41no—
168C22⋊D61—41no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61AGL(1,ℤ/8)11yescharacteristic
173D244—21no—
174D244—41no—
175C4×D61—24no—
176C4×D61—41no—
177C4×D61—41no—
178C4×D61—41no—
179C4×D61—84no—
180C4×D61C22⋊Q811yescharacteristic
181C4×D61C22⋊Q811yescharacteristic
182C4×D61C2×SD1611yescharacteristic
183C4×D61C2×SD1611yescharacteristic
184Dic122—21no—
185Dic122—41no—
186Dic122—84no—
187Dic122—82no—
188C8×C61—41no—
189C8×C61C2×SD1611yescharacteristic
190C8×C61C2×SD1611yescharacteristic
191C8×C61C22×Q811yescharacteristic
192C8×C61C2×#4111yescharacteristic
193#92418—41no—
194#92418C22⋊Q811yescharacteristic
195#92418C22⋊Q811yescharacteristic
196#92418C2×SD1611yescharacteristic
197#92418C2×SD1611yescharacteristic
198C2×#2230—611nomaximal, Sylow
199C22×C61—41no—
200C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
201C2×D61—22no—
202C2×D61—41no—
203C2×D61—82no—
204C2×D61#47611yescharacteristic
205C2×D61#47611yescharacteristic
206C4×C61—22no—
207C4×C61—41no—
208C4×C61—82no—
209C4×C61C2×C22⋊Q811yescharacteristic
210C4×C61C22×SD1611yescharacteristic
211Dic61—22no—
212Dic61—41no—
213Dic61—82no—
214Dic61#47611yescharacteristic
215Dic61#47611yescharacteristic
216C2×#498—611no—
217C2×#443—611no—
218#2230—611no—
219#2230—611no—
220#2230—612no—
221#2230—611no—
222#2230—612no—
223#2230D6111yescharacteristic, direct product factor
224C2×#365—612no—
225C2×#364—611no—
226C2×#360—612no—
227C2×C61—21no—
228C2×C61—81no—
229C2×C61C2×#47611yescharacteristic
230D61—21no—
231D61—81no—
232D61#223012yesdirect product factor
233C2×#135—611no—
234C2×#131—1221no—
235C2×C4⋊Q8—1221no—
236C2×M32—612no—
237#498—612no—
238#498—611no—
239#498—1221no—
240#498—1221no—
241#498C2×D6111yescharacteristic, complemented
242#443—611no—
243#443—611no—
244#443—611no—
245#443—1221no—
246#443—1221no—
247#443C2×D6111yescharacteristic
248C2×#108—611no—
249C2×#106—612no—
250C2×#106—1221no—
251C2×#104—1221no—
252C2×C4×C8—611no—
253#365—612no—
254#365—612no—
255#365—612no—
256#365C2×D6112yescomplemented
257#364—612no—
258#364—611no—
259#364C2×D6111yescharacteristic, complemented
260#360—612no—
261#360—612no—
262#360—612no—
263#360C2×D6112yes—
264C61C2×#223011yescharacteristic, complemented, Sylow
265C2×#41—1221no—
266C22×Q8—2441no—
267#135—611no—
268#135—611no—
269#135—611no—
270#135—1221no—
271#135—1221no—
272#135C22×D6111yescharacteristic
273C2×Q16—611no—
274C2×SD16—1221no—
275C2×D8—611no—
276#131—21no—
277#131—1221no—
278#131—1221no—
279#131—1221no—
280#131—2441no—
281#131—2441no—
282C2×M16—1221no—
283C2×M16—2441no—
284C22×C8—611no—
285C22×C8—611no—
286C22×C8—2441no—
287C4⋊Q8—21no—
288C4⋊Q8—1222no—
289C4⋊Q8—1221no—
290C4⋊Q8—2441no—
291C4⋊Q8—2441no—
292C2×C4⋊C4—1222no—
293C2×C4⋊C4—2441no—
294C2×C42—611no—
295M32—612no—
296M32—1222no—
297M32C22×D6112yes—
298C2×C16—1222no—
299#108—611no—
300#108—1221no—
301#108C22×D6111yescharacteristic
302#106—21no—
303#106—612no—
304#106—1222no—
305#106—1222no—
306#106—1221no—
307#106C22×D6112yes—
308#104—21no—
309#104—1221no—
310#104—1221no—
311#104—1221no—
312C4×C8—611no—
313C4×C8—611no—
314C4×C8—611no—
315C4×C8C22×D6111yescharacteristic
316#41—21no—
317#41—1221no—
318#41—1221no—
319#41—1221no—
320#41—2441no—
321#41—2441no—
322C2×Q8—41no—
323C2×Q8—1221no—
324C2×Q8—4884no—
325C2×Q8—2441no—
326C2×Q8—2442no—
327C2×D4—1221no—
328C2×D4—2441no—
329C22×C4—611no—
330C22×C4—1221no—
331C22×C4—2441no—
332C22×C4—2442no—
333Q16—611no—
334Q16—1221no—
335Q16Q8×D6111yescharacteristic, complemented
336SD16—21no—
337SD16—1221no—
338SD16—1221no—
339SD16—1221no—
340D8—611no—
341D8—1221no—
342D8Q8×D6111yescharacteristic, complemented
343M16—21no—
344M16—41no—
345M16—1221no—
346M16—2441no—
347M16—2441no—
348M16—2441no—
349M16—2441no—
350C2×C8—41no—
351C2×C8—611no—
352C2×C8—611no—
353C2×C8—611no—
354C2×C8—611no—
355C2×C8—611no—
356C2×C8—611no—
357C2×C8—611no—
358C2×C8—611no—
359C2×C8—611no—
360C2×C8—611no—
361C2×C8—2441no—
362C2×C8—2441no—
363C2×C8—2441no—
364C2×C8—2441no—
365C2×C8D4×D6111yescharacteristic
366C2×C8C23×D6111yescharacteristic
367C4⋊C4—22no—
368C4⋊C4—41no—
369C4⋊C4—1222no—
370C4⋊C4—2441no—
371C4⋊C4—2442no—
372C4⋊C4—2442no—
373C42—611no—
374C42—1221no—
375C42D4×D6111yescharacteristic
376C16—22no—
377C16—1222no—
378C23—611no—
379C23—2441no—
380Q8—21no—
381Q8—82no—
382Q8—1221no—
383Q8—4882no—
384Q8—4884no—
385Q8—2441no—
386D4—21no—
387D4—41no—
388D4—1221no—
389D4—2441no—
390D4—2441no—
391D4—2441no—
392D4—2441no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—611no—
397C2×C4—611no—
398C2×C4—611no—
399C2×C4—611no—
400C2×C4—611no—
401C2×C4—1224no—
402C2×C4—1221no—
403C2×C4—4884no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2442no—
408C2×C4—2441no—
409C2×C4C2×D4×D6111yescharacteristic
410C8—41no—
411C8—611no—
412C8—611no—
413C8—611no—
414C8—611no—
415C8—2441no—
416C8SD16×D6111yescharacteristic
417C8SD16×D6111yescharacteristic
418C8C2×Q8×D6111yescharacteristic
419C8#41×D6111yescharacteristic
420C22—41no—
421C22—611no—
422C22—611no—
423C22—1222no—
424C22—4882no—
425C22—2441no—
426C22AGL(1,ℤ/8)×D6111yescharacteristic
427C4—22no—
428C4—41no—
429C4—82no—
430C4—611no—
431C4—611no—
432C4—1222no—
433C4—4882no—
434C4—2441no—
435C4C22⋊Q8×D6111yescharacteristic
436C4C2×SD16×D6111yescharacteristic
437C2—21no—
438C2—81no—
439C2—612no—
440C2—1221no—
441C2—4881no—
442C2#476×D6111yescharacteristic
subgroupG/H
centerC2#476×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2230C2
socleC2×C61C2×#476
prime radical#135×D61C22
hypercenter#2230D61
hypocenterC61C2×#2230
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2230

Complements

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

NH ≅ G/Ntype
1. #498×D61C2semidirect
3. #21447991C2semidirect
4. #21447990C2semidirect
5. #21447989C2semidirect
6. #21447988C2semidirect
7. #21447987C2semidirect
8. #365×D61C2semidirect
9. #364×D61C2semidirect
11. C61×#2230C2semidirect
16. #16840160C22semidirect
18. #16840159C22semidirect
30. #16839586C22semidirect
31. #16839585C22semidirect
32. #16839584C22semidirect
33. #16839583C22semidirect
34. #16839582C22semidirect
38. C61×#498C22semidirect
40. C61×#365C22semidirect
41. C61×#364C22semidirect
45. #14519800Q8semidirect
49. #14519796Q8semidirect
50. Q16×D61Q8semidirect
52. D8×D61Q8semidirect
111. Q16×C61C2×Q8semidirect
113. D8×C61C2×Q8semidirect
137. Dic244C2×Q8semidirect
138. D488C2×Q8semidirect
223. #2230D61direct (N × H)
232. D61#2230direct (N × H)
241. #498C2×D61semidirect
256. #365C2×D61semidirect
259. #364C2×D61semidirect
264. C61C2×#2230semidirect
335. Q16Q8×D61semidirect
342. D8Q8×D61semidirect

Maximal subgroups

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

subgroupindex
#498×D612
#443×D612
#214479912
#214479902
#214479892
#214479882
#214479872
#365×D612
#364×D612
#360×D612
C61×#22302
C2×#223061