Finite Group Databasebeta

← D61⋊#2180 #30624317

Subgroups — D61⋊#2180 #30624317

Order 15616.

646 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#444C211yesmaximal, characteristic
2C2×#16840802C211yesmaximal, characteristic, complemented
3#21462227C212yesmaximal, complemented
4#21462226C212yesmaximal, complemented
5#21462225C212yesmaximal, complemented
6#21462224C212yesmaximal, complemented
7D61⋊#365C211yesmaximal, characteristic, complemented
8D61⋊#362C211yesmaximal, characteristic, complemented
9D61⋊#360C211yesmaximal, characteristic
10#21462034C211yesmaximal, characteristic, complemented
11#510×D61C211yesmaximal, characteristic
12D61⋊#131—21no—
13C2×Q8×#6923—21no—
14D61⋊M32C2211yescharacteristic
15#16840809C2211yescharacteristic
16#16840809C2211yescharacteristic
17#16840808C2211yescharacteristic
18#16840808C2211yescharacteristic
19#16840807—21no—
20#16840807—21no—
21#16840802—21no—
22#16840802—21no—
23#16840802C2212yescomplemented
24#16840802C2212yescomplemented
25D61⋊#108C2211yescharacteristic
26C2×#14519845C2211yescharacteristic
27D61⋊#104—21no—
28C2×#14519840—21no—
29C2×#14519831C2211yescharacteristic
30#16840687C2212yescomplemented
31#16840686C2212yescomplemented
32#16840681C2212yescomplemented
33#16840681C2212yescomplemented
34#16840679C2212yes—
35#16840678C2212yes—
36#16840653C2212yescomplemented
37#16840652C2212yescomplemented
38#135×D61C2211yescharacteristic
39C2×Q16×D61C2211yescharacteristic
40#16840205C411yescharacteristic, complemented
41#16840204C2212yes—
42#16840203C411yescharacteristic, complemented
43#16840202C411yescharacteristic, complemented
44#16840201C2212yes—
45Q32×D61C412yescomplemented
46SD32×D61C412yescomplemented
47M32×D61C2211yescharacteristic
48C61×#510C411yescharacteristic, complemented
49#14519865—21no—
50#14519865—21no—
51#14519864—21no—
52#14519864—21no—
53#14519864—41no—
54#14519864—41no—
55D61⋊M16—21no—
56D61⋊M16—41no—
57C2×D61⋊C8—41no—
58C2×D61⋊C8D411yescharacteristic
59Q8×#6923—22no—
60Q8×#6923—22no—
61Q8×#6923—41no—
62Q8×#6923—41no—
63C2×C4⋊#6923—21no—
64C2×C4⋊#6923—41no—
65C2×C4×#6923—41no—
66C2×C4×#6923D411yescharacteristic
67#14519852C2312yes—
68#14519851—21no—
69D61⋊C16—21no—
70#14519848—21no—
71#14519847C2311yescharacteristic
72#14519847C2311yescharacteristic
73#14519845—21no—
74#14519845C2312yes—
75#14519842—21no—
76#14519842—21no—
77#14519841—21no—
78#14519841—21no—
79#14519840—22no—
80#14519840—22no—
81#14519831D411yescharacteristic
82#14519831D411yescharacteristic
83#14519831C2311yescharacteristic
84#14519831C2311yescharacteristic
85#41×D61—21no—
86C2×Q8×D61—21no—
87#14519800C2311yescharacteristic
88#14519799C2×C411yescharacteristic
89#14519798—21no—
90#14519797—21no—
91#14519796C2311yescharacteristic
92C2×Dic244C2×C411yescharacteristic
93C2×#11758202—21no—
94Q16×D61—21no—
95Q16×D61—21no—
96Q16×D61C2×C412yes—
97Q16×D61C2×C411yescharacteristic
98Q16×D61C2312yes—
99SD16×D61—21no—
100D8×D61C2×C411yescharacteristic
101C2×C8×D61C2311yescharacteristic
102Dic488C2×C412yescomplemented
103#14519723C2×C412yescomplemented
104#14519723C2×C412yescomplemented
105#14519722C2×C412yescomplemented
106#14519721C2×C412yescomplemented
107#14519720C2×C412yescomplemented
108#14519717C2×C411yescharacteristic
109#14519716C2312yes—
110C16×D61C2×C412yes—
111#135×C61C2×C411yescharacteristic
112C2×Q16×C61C2×C411yescharacteristic
113Q32×C61C2×C412yescomplemented
114SD32×C61C2×C412yescomplemented
115M32×C61C2×C411yescharacteristic
116C22×#6923—21no—
117C22×#6923—41no—
118#41×C61—21no—
119C2×Q8×C61—21no—
120#11758226—21no—
121Q8×D61—22no—
122Q8×D61—21no—
123Q8×D61—22no—
124Q8×D61—41no—
125Q8×D61—41no—
126#11758224—21no—
127#11758224—41no—
128D4×D61—21no—
129D4×D61—41no—
130#11758222—21no—
131#11758222—41no—
132C2×C4×D61—41no—
133C2×C4×D61—41no—
134C2×C4×D61C2×D411yescharacteristic
135C2×Dic122—21no—
136C2×Dic122—41no—
137#11758217—41no—
138#11758217—41no—
139#11758217—41no—
140C2×#92420—21no—
141C2×#92420—41no—
142C2×#92420—41no—
143C4⋊#6923—22no—
144C4⋊#6923—42no—
145C4⋊#6923—42no—
146C4⋊#6923—41no—
147C4×#6923—21no—
148C4×#6923—42no—
149C4×#6923—42no—
150C4×#6923C2×D411yescharacteristic
151C4×#6923C2×D411yescharacteristic
152#11758213—21no—
153#11758213—21no—
154#11758213—41no—
155#11758213—41no—
156D61⋊C8—21no—
157D61⋊C8—41no—
158D61⋊C8—41no—
159D61⋊C8—41no—
160D61⋊C8C2×D411yescharacteristic
161D61⋊C8C2×D411yescharacteristic
162Q16×C61—21no—
163Q16×C61C22×C412yes—
164Q16×C61C22×C411yescharacteristic
165SD16×C61—21no—
166D8×C61C22×C411yescharacteristic
167C2×C8×C61C22×C411yescharacteristic
168#11758202—22no—
169#11758202—21no—
170#11758202—22no—
171#11758201—21no—
172#11758200—21no—
173#11758199—21no—
174C2×#92418#4111yescharacteristic
175Dic244—21no—
176Dic244C22×C412yes—
177Dic244C22×C411yescharacteristic
178D488C22×C411yescharacteristic
179#11758190—21no—
180C8×D61C22×C411yescharacteristic
181C8×D61C2×D411yescharacteristic
182C8×D61#4111yescharacteristic
183C8×D61C2411yescharacteristic
184#11758187—22no—
185C16×C61C22×C412yes—
186#11758185C22×C412yes—
187C22×D61—41no—
188C22×D61AGL(1,ℤ/8)11yescharacteristic
189C2×#6923—21no—
190C2×#6923—21no—
191C2×#6923—42no—
192C2×#6923—42no—
193C2×#6923—82no—
194Q8×C61—21no—
195Q8×C61—22no—
196Q8×C61—41no—
197D4×C61—21no—
198D4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61C4×D411yescharacteristic
202C22⋊D61—41no—
203C22⋊D61—41no—
204C22⋊D61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61AGL(1,ℤ/8)11yescharacteristic
208D244—21no—
209D244—41no—
210C4×D61—42no—
211C4×D61—41no—
212C4×D61—42no—
213C4×D61—41no—
214C4×D61—41no—
215C4×D61C4×D411yescharacteristic
216C4×D61AGL(1,ℤ/8)11yescharacteristic
217C4×D61AGL(1,ℤ/8)11yescharacteristic
218C4×D61C22×D411yescharacteristic
219Dic122—21no—
220Dic122—22no—
221Dic122—41no—
222Dic122—42no—
223Dic122—42no—
224Dic122—41no—
225#92420—21no—
226#92420—21no—
227#92420—41no—
228#92420—41no—
229C8×C61C4×D411yescharacteristic
230C8×C61C23×C411yescharacteristic
231#92418C4×D411yescharacteristic
232#92418C2×#4111yescharacteristic
233C2×#2180—611nomaximal, Sylow
234C22×C61—41no—
235C22×C61#44211yescharacteristic
236C2×D61—22no—
237C2×D61—41no—
238C2×D61—82no—
239C2×D61#44211yescharacteristic
240C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
241#6923—41no—
242#6923—41no—
243#6923—82no—
244C4×C61—42no—
245C4×C61—41no—
246C4×C61#44211yescharacteristic
247C4×C61C2×C4×D411yescharacteristic
248Dic61—42no—
249Dic61—41no—
250Dic61#44211yescharacteristic
251Dic61C2×AGL(1,ℤ/8)11yescharacteristic
252C2×#510—611no—
253C2×#444—611no—
254C2×#441—611no—
255#2180—612no—
256#2180—612no—
257#2180—612no—
258#2180—612no—
259C2×#365—611no—
260C2×#362—611no—
261C2×#360—611no—
262C2×#347—611no—
263C2×C61—21no—
264C2×C61—81no—
265C2×C61C2×#44211yescharacteristic
266D61—21no—
267D61—81no—
268D61#218012yescomplemented
269C2×#135—611no—
270C22×Q16—611no—
271C2×#131—1221no—
272C2×C4×Q8—1221no—
273#510—611no—
274#510—611no—
275#510—612no—
276#510—612no—
277#510—611no—
278#510#692311yescharacteristic, complemented
279C2×Q32—612no—
280C2×SD32—612no—
281C2×M32—611no—
282C2×M32—611no—
283#444—611no—
284#444—611no—
285#444—611no—
286#444—611no—
287#444—1221no—
288#444—1221no—
289#441—612no—
290#441—612no—
291#441—1221no—
292#441—1221no—
293C2×#108—611no—
294C2×#106—611no—
295C2×#104—1221no—
296C2×#103—1221no—
297C2×#97—611no—
298#365—612no—
299#365—612no—
300#362—612no—
301#362—612no—
302#360—612no—
303#360—612no—
304#347—612no—
305#347—612no—
306C61C2×#218011yescharacteristic, complemented, Sylow
307C2×#41—1221no—
308C22×Q8—1221no—
309#135—611no—
310#135—611no—
311#135—611no—
312#135—1221no—
313#135—1221no—
314#135C2×#692311yescharacteristic
315C2×Q16—612no—
316C2×Q16—612no—
317C2×Q16—611no—
318C2×Q16—611no—
319C2×Q16—1221no—
320C2×Q16—1221no—
321C2×Q16—1221no—
322C2×Q16C2×#692311yescharacteristic
323C2×SD16—1221no—
324C2×D8—611no—
325#131—1221no—
326#131—1221no—
327#131—1221no—
328#131—1221no—
329#131—2441no—
330#131—2441no—
331C2×M16—1221no—
332C2×M16—2441no—
333C22×C8—611no—
334C22×C8—611no—
335C22×C8—2441no—
336C4×Q8—1222no—
337C4×Q8—1222no—
338C4×Q8—2441no—
339C4×Q8—2441no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4—2441no—
342C2×C42—611no—
343C2×C42—2441no—
344Q32—612no—
345Q32—612no—
346Q32—612no—
347Q32C2×#692312yescomplemented
348SD32—612no—
349SD32—612no—
350SD32—612no—
351SD32C2×#692312yescomplemented
352M32—611no—
353M32—612no—
354M32—612no—
355M32—1221no—
356M32C2×#692311yescharacteristic
357C2×C16—612no—
358C2×C16—1221no—
359#108—611no—
360#108—611no—
361#108—1221no—
362#106—612no—
363#106—1221no—
364#104—1221no—
365#104—1221no—
366#104—1221no—
367#104—1221no—
368#103—1222no—
369#103—1222no—
370#97—611no—
371#97—611no—
372#97—611no—
373#97—611no—
374#41—21no—
375#41—1221no—
376#41—1221no—
377#41—1221no—
378#41—2441no—
379#41—2441no—
380C2×Q8—21no—
381C2×Q8—1222no—
382C2×Q8—1221no—
383C2×Q8—1222no—
384C2×Q8—1221no—
385C2×Q8—2441no—
386C2×Q8—2441no—
387C2×Q8—2441no—
388C2×D4—1221no—
389C2×D4—2441no—
390C22×C4—611no—
391C22×C4—1221no—
392C22×C4—2441no—
393C22×C4—2441no—
394C22×C4—2441no—
395Q16—21no—
396Q16—612no—
397Q16—611no—
398Q16—1222no—
399Q16—1222no—
400Q16—1221no—
401Q16—1221no—
402Q16C22×#692312yes—
403Q16C22×#692311yescharacteristic
404SD16—21no—
405SD16—1221no—
406SD16—1221no—
407SD16—1221no—
408D8—611no—
409D8—1221no—
410D8C22×#692311yescharacteristic
411M16—1221no—
412M16—1221no—
413M16—2441no—
414M16—2441no—
415M16—2441no—
416M16—2441no—
417M16—2441no—
418C2×C8—611no—
419C2×C8—611no—
420C2×C8—611no—
421C2×C8—611no—
422C2×C8—611no—
423C2×C8—611no—
424C2×C8—611no—
425C2×C8—1221no—
426C2×C8—1221no—
427C2×C8—2441no—
428C2×C8—2441no—
429C2×C8—2441no—
430C2×C8—2441no—
431C2×C8—2441no—
432C2×C8C22×#692311yescharacteristic
433C4⋊C4—1222no—
434C4⋊C4—2441no—
435C4⋊C4—2442no—
436C4⋊C4—2442no—
437C42—611no—
438C42—611no—
439C42—1221no—
440C42—2442no—
441C42—2442no—
442C16—612no—
443C16—1222no—
444C16C22×#692312yes—
445C23—611no—
446C23—2441no—
447Q8—21no—
448Q8—22no—
449Q8—41no—
450Q8—1221no—
451Q8—1222no—
452Q8—2442no—
453Q8—2442no—
454Q8—2441no—
455Q8—2441no—
456D4—21no—
457D4—41no—
458D4—1221no—
459D4—2441no—
460D4—2441no—
461D4—2441no—
462D4—2441no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—611no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—611no—
469C2×C4—611no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—4882no—
473C2×C4—2441no—
474C2×C4—2442no—
475C2×C4—2441no—
476C2×C4—2442no—
477C2×C4—2441no—
478C2×C4—2442no—
479C2×C4—2442no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4D4×#692311yescharacteristic
483C8—611no—
484C8—611no—
485C8—1221no—
486C8—1221no—
487C8—2441no—
488C8—2441no—
489C8D4×#692311yescharacteristic
490C8C23×#692311yescharacteristic
491C22—41no—
492C22—611no—
493C22—611no—
494C22—1222no—
495C22—4882no—
496C22—2441no—
497C22#1684080311yescharacteristic
498C4—41no—
499C4—42no—
500C4—611no—
501C4—611no—
502C4—4882no—
503C4—2441no—
504C4—2441no—
505C4—2441no—
506C4—2442no—
507C4#1684080311yescharacteristic
508C4C2×D4×#692311yescharacteristic
509C2—21no—
510C2—81no—
511C2—612no—
512C2—1221no—
513C2—4881no—
514C2C2×#1684080311yescharacteristic
subgroupG/H
centerC2C2×#16840803
commutatorC8×C61C23×C4
FrattiniC8C23×#6923
FittingC61×#510C4
socleC2×C61C2×#442
prime radical#135×D61C22
cosocleC8×D61C24
hypercenter#510#6923
hypocenterC61C2×#2180
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C2×#16840802C2semidirect
3. #21462227C2semidirect
4. #21462226C2semidirect
5. #21462225C2semidirect
6. #21462224C2semidirect
7. D61⋊#365C2semidirect
8. D61⋊#362C2semidirect
10. #21462034C2semidirect
23. #16840802C22semidirect
24. #16840802C22semidirect
30. #16840687C22semidirect
31. #16840686C22semidirect
32. #16840681C22semidirect
33. #16840681C22semidirect
36. #16840653C22semidirect
37. #16840652C22semidirect
40. #16840205C4semidirect
42. #16840203C4semidirect
43. #16840202C4semidirect
45. Q32×D61C4semidirect
46. SD32×D61C4semidirect
48. C61×#510C4semidirect
102. Dic488C2×C4semidirect
103. #14519723C2×C4semidirect
104. #14519723C2×C4semidirect
105. #14519722C2×C4semidirect
106. #14519721C2×C4semidirect
107. #14519720C2×C4semidirect
113. Q32×C61C2×C4semidirect
114. SD32×C61C2×C4semidirect
268. D61#2180semidirect
278. #510#6923semidirect
306. C61C2×#2180semidirect
347. Q32C2×#6923semidirect
351. SD32C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4442
C2×#168408022
#214622272
#214622262
#214622252
#214622242
D61⋊#3652
D61⋊#3622
D61⋊#3602
#214620342
#510×D612
C2×#218061