Finite Group Databasebeta

← D61×#2211 #29834265

Subgroups — D61×#2211 #29834265

Order 15616.

722 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q32×D61C211yesmaximal, characteristic, complemented
2C2×SD32×D61C211yesmaximal, characteristic
3#495×D61C211yesmaximal, characteristic
4C4×Q16×D61C211yesmaximal, characteristic, complemented
5#21447884C211yesmaximal, characteristic, complemented
6#21447883C211yesmaximal, characteristic, complemented
7#21447882C211yesmaximal, characteristic, complemented
8#21447881C211yesmaximal, characteristic, complemented
9#21447880C211yesmaximal, characteristic, complemented
10#21447879C211yesmaximal, characteristic, complemented
11#21447878C211yesmaximal, characteristic, complemented
12C4⋊C16×D61C211yesmaximal, characteristic, complemented
13#358×D61C211yesmaximal, characteristic, complemented
14#357×D61C211yesmaximal, characteristic
15C61×#2211C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17C2×Q16×D61C2211yescharacteristic
18C2×SD16×D61—21no—
19C2×D8×D61C2211yescharacteristic
20#124×D61—21no—
21C4×Q8×D61—21no—
22C2×Dic488C2211yescharacteristic, complemented
23C2×#14519723C2211yescharacteristic, complemented
24C2×#14519723C2211yescharacteristic, complemented
25Q32×D61—24no—
26C2×#14519722C2211yescharacteristic
27C2×#14519721C2211yescharacteristic
28C2×#14519720C2211yescharacteristic
29SD32×D61—24no—
30C2×C16×D61C2211yescharacteristic
31C2×C16×D61C2211yescharacteristic
32#16840147C2211yescharacteristic
33#16840146C2211yescharacteristic
34#16840145C2211yescharacteristic
35#16840144—21no—
36#16840143—21no—
37C4×Dic244C2211yescharacteristic, complemented
38Q16×Dic61C2211yescharacteristic, complemented
39#16839856C2211yescharacteristic, complemented
40C4×#11758202—21no—
41#16839854—21no—
42#107×D61C2211yescharacteristic
43#103×D61—21no—
44C4×C8×D61C2211yescharacteristic
45C4⋊#11758185C2211yescharacteristic, complemented
46#16839580C2211yescharacteristic, complemented
47#16839580C2211yescharacteristic, complemented
48#16839567C2211yescharacteristic, complemented
49#16839566C2211yescharacteristic, complemented
50#16839565C2211yescharacteristic, complemented
51#16839564C2211yescharacteristic
52#16839563C2211yescharacteristic
53#16839562C2211yescharacteristic
54C2×Q32×C61C2211yescharacteristic, complemented
55C2×SD32×C61C2211yescharacteristic
56C61×#495C2211yescharacteristic
57C4×Q16×C61C2211yescharacteristic, complemented
58C61×C4⋊C16C2211yescharacteristic, complemented
59C61×#358C2211yescharacteristic, complemented
60C61×#357C2211yescharacteristic
61C2×Q8×D61—21no—
62C2×Q8×D61—21no—
63C2×D4×D61—21no—
64C2×Dic244C2311yescharacteristic
65C2×Dic244C2311yescharacteristic
66C2×#11758202—21no—
67C2×#11758202—21no—
68Q16×D61—22no—
69Q16×D61—22no—
70Q16×D61—22no—
71Q16×D61D414yes—
72C2×#11758190—21no—
73C2×#11758200—21no—
74C2×#11758201—21no—
75SD16×D61—44no—
76C2×D488C2311yescharacteristic
77C2×#11758199—21no—
78D8×D61—22no—
79D8×D61—22no—
80C2×C8×D61D411yescharacteristic
81C2×C8×D61C2311yescharacteristic
82#14519766—21no—
83#14519765—21no—
84#14519764—21no—
85#14519763—41no—
86#14519763—41no—
87Q8×Dic61—21no—
88C4×Dic122—21no—
89C4×Dic122—41no—
90#14519742—21no—
91#14519742—41no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—41no—
94C22⋊C4×D61—41no—
95C22⋊C4×D61—41no—
96C42×D61—41no—
97C42×D61D411yescharacteristic
98Dic488—22no—
99#14519723—22no—
100#14519723—22no—
101#14519722—22no—
102#14519721—22no—
103#14519720—22no—
104C2×#11758185C2311yescharacteristic
105C2×#11758185C2311yescharacteristic
106C16×D61—22no—
107C16×D61—22no—
108#14519711C2311yescharacteristic
109#14519710—21no—
110#14519702—21no—
111#14519701—21no—
112#14519700—21no—
113C4×#92418D411yescharacteristic
114C8×Dic61D411yescharacteristic
115C8×Dic61C2311yescharacteristic
116C2×Q16×C61C2311yescharacteristic
117C2×Q16×C61C2311yescharacteristic
118C2×SD16×C61—21no—
119C2×D8×C61C2311yescharacteristic
120#124×C61—21no—
121C4×Q8×C61—21no—
122Q32×C61—22no—
123SD32×C61—22no—
124C2×C16×C61C2311yescharacteristic
125C2×C16×C61C2311yescharacteristic
126#107×C61C2311yescharacteristic
127#103×C61—21no—
128C4×C8×C61C2311yescharacteristic
129C23×D61—41no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×D4×C61—21no—
133C2×C22⋊D61—41no—
134Q8×D61—24no—
135Q8×D61—42no—
136Q8×D61—42no—
137Q8×D61—42no—
138D4×D61—42no—
139D4×D61—42no—
140C2×D244—21no—
141C2×C4×D61—41no—
142C2×C4×D61—41no—
143C2×C4×D61—41no—
144C2×C4×D61D811yescharacteristic
145C2×C4×D61D811yescharacteristic
146C2×C4×D61C2×D411yescharacteristic
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122—41no—
150C2×Dic122—41no—
151Q16×C61—21no—
152Q16×C61—21no—
153Q16×C61—21no—
154Q16×C61C2×D412yes—
155SD16×C61—42no—
156D8×C61—21no—
157D8×C61—21no—
158C2×C8×C61C2×D411yescharacteristic
159C2×C8×C61C2411yescharacteristic
160C4⋊C4×C61—21no—
161C4⋊C4×C61—41no—
162C22⋊C4×C61—41no—
163C22⋊C4×C61—41no—
164C42×C61—41no—
165C42×C61C2×D411yescharacteristic
166C22⋊Dic61—41no—
167C22⋊Dic61—41no—
168#11758202—24no—
169#11758202—42no—
170#11758201—42no—
171#11758200—42no—
172#11758199—42no—
173#11758198—41no—
174#11758198—41no—
175#11758198—41no—
176#11758198—41no—
177C4⋊Dic61—21no—
178C4⋊Dic61—41no—
179#11758196—41no—
180#11758196—41no—
181#11758196—41no—
182C4×Dic61—41no—
183C4×Dic61—41no—
184C4×Dic61—41no—
185C4×Dic61D811yescharacteristic
186C4×Dic61D811yescharacteristic
187C4×Dic61C2×D411yescharacteristic
188C2×#92418C2×D411yescharacteristic
189C2×#92418C2×D411yescharacteristic
190Dic244—21no—
191Dic244—21no—
192Dic244—21no—
193Dic244C2×D412yes—
194D488—21no—
195D488—21no—
196#11758190—42no—
197C8×D61—22no—
198C8×D61C2×D412yes—
199C8×D61#4112yes—
200C16×C61—21no—
201C16×C61—21no—
202#11758185—21no—
203#11758185—21no—
204C23×C61—41no—
205C22×D61—41no—
206C22×D61—82no—
207C22×D61—82no—
208C22×D61—82no—
209C22×D61C2×D811yescharacteristic
210Q8×C61—22no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—41no—
214D4×C61—41no—
215D4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61C2×D811yescharacteristic
220C2×C4×C61C2×D811yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C22⋊D61—82no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61C2×D811yescharacteristic
227C2×Dic61C2×D811yescharacteristic
228C2×Dic61C2×D811yescharacteristic
229D244—41no—
230D244—41no—
231C4×D61—22no—
232C4×D61—22no—
233C4×D61—44no—
234C4×D61—82no—
235C4×D61—82no—
236C4×D61#12112yes—
237C4×D61AGL(1,ℤ/8)12yes—
238Dic122—22no—
239Dic122—41no—
240Dic122—44no—
241Dic122—41no—
242Dic122—41no—
243Dic122—82no—
244C8×C61—21no—
245C8×C61C22×D411yescharacteristic
246C8×C61C2×#4111yescharacteristic
247#92418—21no—
248#92418#12112yes—
249C2×#2211—611nomaximal, Sylow
250C22×C61—81no—
251C22×C61—81no—
252C22×C61—81no—
253C22×C61C22×D811yescharacteristic
254C2×D61—81no—
255C2×D61—81no—
256C2×D61—81no—
257C2×D61—164no—
258C2×D61#45912yes—
259C2×D61#50812yes—
260C2×D61#51012yes—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—42no—
264C4×C61—81no—
265C4×C61—81no—
266C4×C61C2×#12111yescharacteristic
267C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
268Dic61—21no—
269Dic61—21no—
270Dic61—42no—
271Dic61—81no—
272Dic61—81no—
273Dic61#45912yes—
274C22×Q32—611no—
275C22×SD32—611no—
276C2×#495—611no—
277C2×C4×Q16—611no—
278#2211—611no—
279#2211—611no—
280#2211—611no—
281#2211—611no—
282#2211—611no—
283#2211—611no—
284#2211—611no—
285#2211D6111yescharacteristic, direct product factor
286C2×C4⋊C16—611no—
287C2×#358—611no—
288C2×#357—611no—
289C2×C61—161no—
290C2×C61C2×#45911yescharacteristic
291C2×C61C2×#50811yescharacteristic
292C2×C61C2×#51011yescharacteristic
293D61—161no—
294D61#221114yesdirect product factor
295C22×Q16—611no—
296C22×Q16—611no—
297C22×SD16—1221no—
298C22×D8—611no—
299C2×#124—1221no—
300C2×C4×Q8—1221no—
301C2×Q32—611no—
302C2×Q32—611no—
303C2×Q32—611no—
304C2×Q32—1224no—
305C2×Q32C2×D6111yescharacteristic, complemented
306C2×SD32—611no—
307C2×SD32—611no—
308C2×SD32—611no—
309C2×SD32—1224no—
310C2×SD32C2×D6111yescharacteristic
311C22×C16—611no—
312C22×C16—611no—
313#495—611no—
314#495—611no—
315#495—611no—
316#495—1221no—
317#495—1221no—
318#495C2×D6111yescharacteristic
319C4×Q16—611no—
320C4×Q16—611no—
321C4×Q16—611no—
322C4×Q16—1221no—
323C4×Q16—1221no—
324C4×Q16C2×D6111yescharacteristic, complemented
325C2×#107—611no—
326C2×#103—1221no—
327C2×C4×C8—611no—
328C4⋊C16—611no—
329C4⋊C16—611no—
330C4⋊C16—611no—
331C4⋊C16C2×D6111yescharacteristic, complemented
332#358—611no—
333#358—611no—
334#358—611no—
335#358C2×D6111yescharacteristic, complemented
336#357—611no—
337#357—611no—
338#357—611no—
339#357C2×D6111yescharacteristic
340C61C2×#221111yescharacteristic, complemented, Sylow
341C22×Q8—1221no—
342C22×Q8—1221no—
343C22×D4—1221no—
344C2×Q16—614no—
345C2×Q16—611no—
346C2×Q16—611no—
347C2×Q16—1222no—
348C2×Q16—1222no—
349C2×Q16—1222no—
350C2×Q16—1221no—
351C2×Q16—1221no—
352C2×Q16C22×D6111yescharacteristic
353C2×Q16C22×D6111yescharacteristic
354C2×SD16—21no—
355C2×SD16—1221no—
356C2×SD16—1221no—
357C2×SD16—1221no—
358C2×SD16—2444no—
359C2×D8—611no—
360C2×D8—1222no—
361C2×D8—1222no—
362C2×D8—1221no—
363C2×D8C22×D6111yescharacteristic
364C22×C8—611no—
365C22×C8—611no—
366#124—21no—
367#124—1221no—
368#124—1221no—
369#124—1221no—
370#124—2441no—
371#124—2441no—
372C4×Q8—21no—
373C4×Q8—1221no—
374C4×Q8—1221no—
375C4×Q8—1221no—
376C4×Q8—2441no—
377C4×Q8—2441no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—2441no—
380C2×C22⋊C4—2441no—
381C2×C22⋊C4—2441no—
382C2×C42—611no—
383C2×C42—2441no—
384Q32—22no—
385Q32—1222no—
386Q32—1222no—
387Q32—1222no—
388SD32—22no—
389SD32—1222no—
390SD32—1222no—
391SD32—1222no—
392C2×C16—611no—
393C2×C16—611no—
394C2×C16—1222no—
395C2×C16—1222no—
396C2×C16C22×D6111yescharacteristic
397C2×C16C22×D6111yescharacteristic
398#107—611no—
399#107—1221no—
400#107C22×D6111yescharacteristic
401#103—21no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405C4×C8—611no—
406C4×C8—611no—
407C4×C8—611no—
408C4×C8C22×D6111yescharacteristic
409C24—2441no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—1224no—
413C2×Q8—1221no—
414C2×Q8—1221no—
415C2×Q8—2441no—
416C2×Q8—2441no—
417C2×Q8—2442no—
418C2×Q8—2442no—
419C2×Q8—2442no—
420C2×D4—21no—
421C2×D4—1221no—
422C2×D4—2442no—
423C2×D4—2442no—
424C2×D4—2441no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—2441no—
429C22×C4—2441no—
430C22×C4—2441no—
431Q16—21no—
432Q16—21no—
433Q16—21no—
434Q16—612no—
435Q16—1224no—
436Q16—1221no—
437Q16—1221no—
438Q16—1221no—
439Q16—2442no—
440Q16D4×D6112yes—
441SD16—42no—
442SD16—2442no—
443SD16—2442no—
444SD16—2442no—
445D8—21no—
446D8—21no—
447D8—1221no—
448D8—1221no—
449D8—2442no—
450C2×C8—611no—
451C2×C8—612no—
452C2×C8—612no—
453C2×C8—611no—
454C2×C8—1222no—
455C2×C8D4×D6111yescharacteristic
456C2×C8C23×D6111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—1221no—
460C4⋊C4—2441no—
461C4⋊C4—2441no—
462C4⋊C4—2441no—
463C4⋊C4—2441no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—2441no—
467C22⋊C4—2441no—
468C22⋊C4—2441no—
469C22⋊C4—2441no—
470C22⋊C4—2441no—
471C22⋊C4—2441no—
472C42—41no—
473C42—611no—
474C42—611no—
475C42—611no—
476C42—2441no—
477C42—2441no—
478C42—2441no—
479C42D4×D6111yescharacteristic
480C16—21no—
481C16—21no—
482C16—1221no—
483C16—1221no—
484C23—41no—
485C23—611no—
486C23—4882no—
487C23—4882no—
488C23—4882no—
489C23—2441no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—1222no—
495Q8—4882no—
496Q8—2444no—
497Q8—2441no—
498Q8—2441no—
499Q8—2441no—
500D4—41no—
501D4—41no—
502D4—4882no—
503D4—2441no—
504D4—2441no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—611no—
509C2×C4—612no—
510C2×C4—612no—
511C2×C4—611no—
512C2×C4—611no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—4882no—
516C2×C4—4882no—
517C2×C4—2444no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4D8×D6111yescharacteristic
522C2×C4D8×D6111yescharacteristic
523C2×C4C2×D4×D6111yescharacteristic
524C8—21no—
525C8—612no—
526C8—1221no—
527C8C2×D4×D6111yescharacteristic
528C8#41×D6111yescharacteristic
529C22—81no—
530C22—81no—
531C22—81no—
532C22—612no—
533C22—612no—
534C22—612no—
535C22—9764no—
536C22—4881no—
537C22—4881no—
538C22—4881no—
539C22C2×D8×D6111yescharacteristic
540C4—21no—
541C4—21no—
542C4—42no—
543C4—81no—
544C4—81no—
545C4—612no—
546C4—1221no—
547C4—1221no—
548C4—4881no—
549C4—4881no—
550C4—2442no—
551C4#121×D6111yescharacteristic
552C4AGL(1,ℤ/8)×D6111yescharacteristic
553C2—161no—
554C2—614no—
555C2—9761no—
556C2#459×D6111yescharacteristic
557C2#508×D6111yescharacteristic
558C2#510×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2211C2
socleC22×C61C22×D8
prime radicalC2×D8×D61C22
hypercenter#2211D61
hypocenterC61C2×#2211
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2211

Complements

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

NH ≅ G/Ntype
1. C2×Q32×D61C2semidirect
4. C4×Q16×D61C2semidirect
5. #21447884C2semidirect
6. #21447883C2semidirect
7. #21447882C2semidirect
8. #21447881C2semidirect
9. #21447880C2semidirect
10. #21447879C2semidirect
11. #21447878C2semidirect
12. C4⋊C16×D61C2semidirect
13. #358×D61C2semidirect
15. C61×#2211C2semidirect
22. C2×Dic488C22semidirect
23. C2×#14519723C22semidirect
24. C2×#14519723C22semidirect
37. C4×Dic244C22semidirect
38. Q16×Dic61C22semidirect
39. #16839856C22semidirect
45. C4⋊#11758185C22semidirect
46. #16839580C22semidirect
47. #16839580C22semidirect
48. #16839567C22semidirect
49. #16839566C22semidirect
50. #16839565C22semidirect
54. C2×Q32×C61C22semidirect
57. C4×Q16×C61C22semidirect
58. C61×C4⋊C16C22semidirect
59. C61×#358C22semidirect
285. #2211D61direct (N × H)
294. D61#2211direct (N × H)
305. C2×Q32C2×D61semidirect
324. C4×Q16C2×D61semidirect
331. C4⋊C16C2×D61semidirect
335. #358C2×D61semidirect
340. C61C2×#2211semidirect

Maximal subgroups

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

subgroupindex
C2×Q32×D612
C2×SD32×D612
#495×D612
C4×Q16×D612
#214478842
#214478832
#214478822
#214478812
#214478802
#214478792
#214478782
C4⋊C16×D612
#358×D612
#357×D612
C61×#22112
C2×#221161