Finite Group Databasebeta

← D61×#2214 #29834395

Subgroups — D61×#2214 #29834395

Order 15616.

686 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#510×D61C212yesmaximal
2#494×D61C211yesmaximal, characteristic, complemented
3#443×D61C211yesmaximal, characteristic
4#21447901C211yesmaximal, characteristic, complemented
5#21447900C211yesmaximal, characteristic, complemented
6#21447899C212yesmaximal, complemented
7#21447898C212yesmaximal, complemented
8#21447897C211yesmaximal, characteristic, complemented
9#364×D61C211yesmaximal, characteristic, complemented
10#362×D61C212yesmaximal, complemented
11C61×#2214C211yesmaximal, characteristic, complemented
12#135×D61C2211yescharacteristic
13C2×Q16×D61—21no—
14C2×Q16×D61C2212yes—
15#131×D61—21no—
16C4⋊Q8×D61—21no—
17#16840205C2212yes—
18#16840204—22no—
19#16840203C2212yes—
20#16840202C2212yes—
21#16840201—22no—
22Q32×D61—22no—
23SD32×D61—22no—
24M32×D61C2212yes—
25#16840142C2211yescharacteristic, complemented
26#16840141—21no—
27#16840140—21no—
28#16840140C2212yescomplemented
29#16839880C2211yescharacteristic
30#16839879C2211yescharacteristic
31#16839878C2211yescharacteristic
32#16839877—21no—
33#16839876—21no—
34#108×D61C2211yescharacteristic
35#104×D61—21no—
36C4×C8×D61C2211yescharacteristic
37#16839583C2211yescharacteristic, complemented
38#16839582C2212yescomplemented
39#16839579C2212yescomplemented
40#16839578C2212yescomplemented
41#16839577C2212yescomplemented
42C61×#510C2212yes—
43C61×#494C2211yescharacteristic, complemented
44C61×#443C2211yescharacteristic
45C61×#364C2211yescharacteristic, complemented
46C61×#362C2212yescomplemented
47#41×D61—21no—
48C2×Q8×D61—22no—
49#14519800D411yescharacteristic
50#14519799C2311yescharacteristic
51#14519798—21no—
52#14519797—21no—
53#14519796D411yescharacteristic
54C2×Dic244—21no—
55C2×Dic244C2312yes—
56C2×#11758202—22no—
57C2×#11758202—22no—
58Q16×D61—22no—
59Q16×D61—22no—
60Q16×D61—22no—
61Q16×D61—22no—
62Q16×D61—41no—
63Q16×D61—41no—
64Q16×D61—41no—
65Q16×D61—41no—
66Q16×D61D411yescharacteristic
67SD16×D61—21no—
68D8×D61D411yescharacteristic
69#14519785—21no—
70#14519785—41no—
71#14519784—21no—
72#14519783—21no—
73#14519783—41no—
74M16×D61—21no—
75M16×D61—41no—
76C2×C8×D61—41no—
77C2×C8×D61D411yescharacteristic
78C2×C8×D61C2311yescharacteristic
79#14519777—21no—
80#14519776—42no—
81#14519775—22no—
82C4⋊C4×D61—42no—
83C42×D61D411yescharacteristic
84Dic488—22no—
85#14519723—22no—
86#14519723—22no—
87#14519722—22no—
88#14519721—22no—
89#14519720—22no—
90#14519717C2312yes—
91#14519716—22no—
92C16×D61—22no—
93#14519713C2311yescharacteristic
94#14519712—21no—
95#14519705—21no—
96#14519704—21no—
97#14519703—21no—
98C4×#92418D411yescharacteristic
99C8×Dic61D411yescharacteristic
100C8×Dic61C2311yescharacteristic
101#135×C61C2311yescharacteristic
102C2×Q16×C61—21no—
103C2×Q16×C61C2312yes—
104#131×C61—21no—
105C4⋊Q8×C61—21no—
106Q32×C61—22no—
107SD32×C61—22no—
108M32×C61C2312yes—
109#108×C61C2311yescharacteristic
110#104×C61—21no—
111C4×C8×C61C2311yescharacteristic
112#41×C61—21no—
113C2×Q8×C61—22no—
114#11758226—21no—
115Q8×D61—21no—
116Q8×D61—42no—
117Q8×D61—42no—
118Q8×D61—42no—
119Q8×D61—42no—
120#11758224—21no—
121#11758224—41no—
122D4×D61—21no—
123D4×D61—41no—
124#11758222—21no—
125#11758222—41no—
126C2×C4×D61—21no—
127C2×C4×D61—41no—
128C2×C4×D61—42no—
129C2×C4×D61C2×D411yescharacteristic
130C2×Dic122—22no—
131C2×Dic122—42no—
132Q16×C61—22no—
133Q16×C61—22no—
134Q16×C61—41no—
135Q16×C61—41no—
136Q16×C61C2×D411yescharacteristic
137SD16×C61—21no—
138D8×C61C2×D411yescharacteristic
139M16×C61—21no—
140M16×C61—41no—
141C2×C8×C61—41no—
142C2×C8×C61C2×D411yescharacteristic
143C2×C8×C61C2411yescharacteristic
144C4⋊C4×C61—42no—
145C42×C61C2×D411yescharacteristic
146#11758202—21no—
147#11758202—42no—
148#11758202—42no—
149#11758202—42no—
150#11758202—42no—
151#11758201—21no—
152#11758200—21no—
153#11758199—21no—
154C4⋊Dic61—42no—
155#11758196—44no—
156C4×Dic61—21no—
157C4×Dic61C2×D411yescharacteristic
158#11758194—21no—
159#11758194—41no—
160C2×#92418—41no—
161C2×#92418C2×D411yescharacteristic
162C2×#92418C2×D411yescharacteristic
163Dic244—22no—
164Dic244—22no—
165Dic244—41no—
166Dic244—41no—
167Dic244C2×D411yescharacteristic
168D488C2×D411yescharacteristic
169#11758190—21no—
170#11758189—41no—
171#11758189—41no—
172#11758189—41no—
173C8×D61—41no—
174C8×D61—41no—
175C8×D61—41no—
176C8×D61D811yescharacteristic
177C8×D61D811yescharacteristic
178C8×D61D811yescharacteristic
179C8×D61D811yescharacteristic
180C8×D61C2×D411yescharacteristic
181C8×D61C2×D411yescharacteristic
182C8×D61#4111yescharacteristic
183C8×D61#4111yescharacteristic
184C16×C61—22no—
185#11758185—22no—
186C22×D61—41no—
187C22×D61AGL(1,ℤ/8)11yescharacteristic
188Q8×C61—21no—
189Q8×C61—42no—
190Q8×C61—42no—
191D4×C61—21no—
192D4×C61—41no—
193C2×C4×C61—21no—
194C2×C4×C61—41no—
195C2×C4×C61—42no—
196C2×C4×C61C22×D411yescharacteristic
197C22⋊D61—41no—
198C22⋊D61—41no—
199C22⋊D61—41no—
200C2×Dic61—21no—
201C2×Dic61—41no—
202C2×Dic61—42no—
203C2×Dic61AGL(1,ℤ/8)11yescharacteristic
204D244—21no—
205D244—41no—
206C4×D61—24no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—41no—
210C4×D61—82no—
211C4×D61—82no—
212C4×D61#12111yescharacteristic
213C4×D61#12111yescharacteristic
214C4×D61C2×D811yescharacteristic
215C4×D61C2×D811yescharacteristic
216Dic122—21no—
217Dic122—41no—
218Dic122—42no—
219Dic122—42no—
220Dic122—82no—
221Dic122—82no—
222C8×C61—41no—
223C8×C61C2×D811yescharacteristic
224C8×C61C2×D811yescharacteristic
225C8×C61C22×D411yescharacteristic
226C8×C61C2×#4111yescharacteristic
227#92418—41no—
228#92418#12111yescharacteristic
229#92418#12111yescharacteristic
230#92418C2×D811yescharacteristic
231#92418C2×D811yescharacteristic
232C2×#2214—611nomaximal, Sylow
233C22×C61—41no—
234C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
235C2×D61—22no—
236C2×D61—41no—
237C2×D61—82no—
238C2×D61#45911yescharacteristic
239C2×D61#45911yescharacteristic
240C4×C61—22no—
241C4×C61—41no—
242C4×C61—82no—
243C4×C61C2×#12111yescharacteristic
244C4×C61C22×D811yescharacteristic
245Dic61—22no—
246Dic61—41no—
247Dic61—82no—
248Dic61#45911yescharacteristic
249Dic61#45911yescharacteristic
250C2×#510—612no—
251C2×#494—611no—
252C2×#443—611no—
253#2214—612no—
254#2214—611no—
255#2214—611no—
256#2214—611no—
257#2214—612no—
258#2214D6111yescharacteristic, direct product factor
259C2×#364—611no—
260C2×#362—612no—
261C2×C61—21no—
262C2×C61—81no—
263C2×C61C2×#45911yescharacteristic
264D61—21no—
265D61—81no—
266D61#221412yesdirect product factor
267C2×#135—611no—
268C22×Q16—612no—
269C22×Q16—1221no—
270C2×#131—1221no—
271C2×C4⋊Q8—1221no—
272#510—612no—
273#510—612no—
274#510—612no—
275#510—1222no—
276#510—1222no—
277#510C2×D6112yes—
278C2×Q32—1222no—
279C2×SD32—1222no—
280C2×M32—612no—
281#494—612no—
282#494—611no—
283#494—1221no—
284#494—1221no—
285#494C2×D6111yescharacteristic, complemented
286#443—611no—
287#443—611no—
288#443—611no—
289#443—1221no—
290#443—1221no—
291#443C2×D6111yescharacteristic
292C2×#108—611no—
293C2×#104—1221no—
294C2×C4×C8—611no—
295#364—612no—
296#364—611no—
297#364C2×D6111yescharacteristic, complemented
298#362—612no—
299#362—612no—
300#362—612no—
301#362C2×D6112yescomplemented
302C61C2×#221411yescharacteristic, complemented, Sylow
303C2×#41—1221no—
304C22×Q8—1222no—
305#135—611no—
306#135—611no—
307#135—611no—
308#135—1221no—
309#135—1221no—
310#135C22×D6111yescharacteristic
311C2×Q16—21no—
312C2×Q16—611no—
313C2×Q16—612no—
314C2×Q16—1222no—
315C2×Q16—1222no—
316C2×Q16—1222no—
317C2×Q16—1222no—
318C2×Q16—1222no—
319C2×Q16—1222no—
320C2×Q16—1221no—
321C2×Q16—2441no—
322C2×Q16—2441no—
323C2×Q16—2441no—
324C2×Q16—2441no—
325C2×Q16C22×D6112yes—
326C2×SD16—1221no—
327C2×D8—611no—
328#131—21no—
329#131—1221no—
330#131—1221no—
331#131—1221no—
332#131—2441no—
333#131—2441no—
334C2×M16—1221no—
335C2×M16—2441no—
336C22×C8—611no—
337C22×C8—611no—
338C22×C8—2441no—
339C4⋊Q8—21no—
340C4⋊Q8—1222no—
341C4⋊Q8—1221no—
342C4⋊Q8—2442no—
343C2×C4⋊C4—2442no—
344C2×C42—611no—
345Q32—22no—
346Q32—1222no—
347Q32—1222no—
348Q32—1222no—
349SD32—22no—
350SD32—1222no—
351SD32—1222no—
352SD32—1222no—
353M32—612no—
354M32—1222no—
355M32C22×D6112yes—
356C2×C16—1222no—
357#108—611no—
358#108—1221no—
359#108C22×D6111yescharacteristic
360#104—21no—
361#104—1221no—
362#104—1221no—
363#104—1221no—
364C4×C8—611no—
365C4×C8—611no—
366C4×C8—611no—
367C4×C8C22×D6111yescharacteristic
368#41—21no—
369#41—1221no—
370#41—1221no—
371#41—1221no—
372#41—2441no—
373#41—2441no—
374C2×Q8—22no—
375C2×Q8—1221no—
376C2×Q8—1222no—
377C2×Q8—2442no—
378C2×Q8—2442no—
379C2×Q8—2442no—
380C2×Q8—2442no—
381C2×Q8—2442no—
382C2×D4—1221no—
383C2×D4—2441no—
384C22×C4—611no—
385C22×C4—1221no—
386C22×C4—2441no—
387C22×C4—2442no—
388Q16—22no—
389Q16—22no—
390Q16—41no—
391Q16—41no—
392Q16—611no—
393Q16—1221no—
394Q16—1222no—
395Q16—1222no—
396Q16—2442no—
397Q16—2442no—
398Q16—2442no—
399Q16—2442no—
400Q16—2441no—
401Q16—2441no—
402Q16D4×D6111yescharacteristic
403SD16—21no—
404SD16—1221no—
405SD16—1221no—
406SD16—1221no—
407D8—611no—
408D8—1221no—
409D8D4×D6111yescharacteristic
410M16—21no—
411M16—41no—
412M16—1221no—
413M16—2441no—
414M16—2441no—
415M16—2441no—
416M16—2441no—
417C2×C8—41no—
418C2×C8—611no—
419C2×C8—611no—
420C2×C8—611no—
421C2×C8—611no—
422C2×C8—611no—
423C2×C8—611no—
424C2×C8—611no—
425C2×C8—611no—
426C2×C8—611no—
427C2×C8—611no—
428C2×C8—2441no—
429C2×C8—2441no—
430C2×C8—2441no—
431C2×C8—2441no—
432C2×C8D4×D6111yescharacteristic
433C2×C8C23×D6111yescharacteristic
434C4⋊C4—42no—
435C4⋊C4—2442no—
436C4⋊C4—2444no—
437C42—611no—
438C42—1221no—
439C42D4×D6111yescharacteristic
440C16—22no—
441C16—1222no—
442C23—611no—
443C23—2441no—
444Q8—21no—
445Q8—42no—
446Q8—42no—
447Q8—1221no—
448Q8—4882no—
449Q8—4882no—
450Q8—2441no—
451Q8—2442no—
452Q8—2442no—
453D4—21no—
454D4—41no—
455D4—1221no—
456D4—2441no—
457D4—2441no—
458D4—2441no—
459D4—2441no—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—611no—
464C2×C4—611no—
465C2×C4—611no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—1224no—
469C2×C4—1221no—
470C2×C4—4882no—
471C2×C4—4882no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2442no—
476C2×C4—2441no—
477C2×C4C2×D4×D6111yescharacteristic
478C8—41no—
479C8—611no—
480C8—611no—
481C8—611no—
482C8—611no—
483C8—2441no—
484C8D8×D6111yescharacteristic
485C8D8×D6111yescharacteristic
486C8C2×D4×D6111yescharacteristic
487C8#41×D6111yescharacteristic
488C22—41no—
489C22—611no—
490C22—611no—
491C22—1222no—
492C22—4882no—
493C22—2441no—
494C22AGL(1,ℤ/8)×D6111yescharacteristic
495C4—22no—
496C4—41no—
497C4—82no—
498C4—611no—
499C4—611no—
500C4—1222no—
501C4—4882no—
502C4—2441no—
503C4#121×D6111yescharacteristic
504C4C2×D8×D6111yescharacteristic
505C2—21no—
506C2—81no—
507C2—612no—
508C2—1221no—
509C2—4881no—
510C2#459×D6111yescharacteristic
subgroupG/H
centerC2#459×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2214C2
socleC2×C61C2×#459
prime radical#135×D61C22
hypercenter#2214D61
hypocenterC61C2×#2214
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2214

Complements

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

NH ≅ G/Ntype
2. #494×D61C2semidirect
4. #21447901C2semidirect
5. #21447900C2semidirect
6. #21447899C2semidirect
7. #21447898C2semidirect
8. #21447897C2semidirect
9. #364×D61C2semidirect
10. #362×D61C2semidirect
11. C61×#2214C2semidirect
25. #16840142C22semidirect
28. #16840140C22semidirect
37. #16839583C22semidirect
38. #16839582C22semidirect
39. #16839579C22semidirect
40. #16839578C22semidirect
41. #16839577C22semidirect
43. C61×#494C22semidirect
45. C61×#364C22semidirect
46. C61×#362C22semidirect
258. #2214D61direct (N × H)
266. D61#2214direct (N × H)
285. #494C2×D61semidirect
297. #364C2×D61semidirect
301. #362C2×D61semidirect
302. C61C2×#2214semidirect

Maximal subgroups

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

subgroupindex
#510×D612
#494×D612
#443×D612
#214479012
#214479002
#214478992
#214478982
#214478972
#364×D612
#362×D612
C61×#22142
C2×#221461