Finite Group Databasebeta

← D61×#2138 #29832891

Subgroups — D61×#2138 #29832891

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#135×D61C211yesmaximal, characteristic
2C22×C16×D61C211yesmaximal, characteristic, complemented
3#427×D61C211yesmaximal, characteristic, complemented
4#21447527C211yesmaximal, characteristic, complemented
5#21447526C211yesmaximal, characteristic, complemented
6#21447525C212yesmaximal, complemented
7#21447524C211yesmaximal, characteristic, complemented
8#21447523C212yesmaximal, complemented
9#358×D61C212yesmaximal, complemented
10#357×D61C212yesmaximal, complemented
11C61×#2138C211yesmaximal, characteristic, complemented
12C2×#41×D61—21no—
13C2×#14519800C2211yescharacteristic
14C2×#14519799C2211yescharacteristic
15C2×#14519798—21no—
16C2×#14519797—21no—
17C2×#14519796C2211yescharacteristic
18#135×D61—24no—
19#135×D61C418yescomplemented
20C2×Q16×D61C2211yescharacteristic
21C2×SD16×D61—21no—
22C2×D8×D61C2211yescharacteristic
23C22×C8×D61C2211yescharacteristic
24#117×D61—21no—
25C22×#11758185C2211yescharacteristic, complemented
26C2×C16×D61—24no—
27C2×C16×D61C2212yes—
28C2×C16×D61C2212yescomplemented
29#16839800C2211yescharacteristic, complemented
30#16839799C2212yescomplemented
31#16839798—21no—
32#16839797—21no—
33#107×D61C2212yes—
34#106×D61—21no—
35#16839567C2212yescomplemented
36#16839566C2212yescomplemented
37#16839565C2212yescomplemented
38#16839564C2212yescomplemented
39#16839563C2212yescomplemented
40#16839562C2212yescomplemented
41C2×#135×C61C2211yescharacteristic
42C22×C16×C61C2211yescharacteristic, complemented
43C61×#427C2211yescharacteristic, complemented
44C61×#358C2212yescomplemented
45C61×#357C2212yescomplemented
46C2×#11758226—21no—
47C2×#11758222—21no—
48C2×#11758222—41no—
49C2×#11758224—21no—
50C2×#11758224—41no—
51#41×D61—28no—
52#41×D61—44no—
53C2×Q8×D61—21no—
54C2×D4×D61—21no—
55C2×D4×D61—41no—
56C22×C4×D61—41no—
57C22×C4×D61D411yescharacteristic
58#14519800—22no—
59#14519800C2×C414yescomplemented
60#14519799—22no—
61#14519799C2×C414yescomplemented
62#14519798—28no—
63#14519797—28no—
64#14519796—22no—
65#14519796C2×C414yescomplemented
66C2×Dic244C2311yescharacteristic
67C2×#11758202—21no—
68Q16×D61—22no—
69Q16×D61C2×C414yes—
70C2×#11758190—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73SD16×D61—28no—
74C2×D488C2311yescharacteristic
75C2×#11758199—21no—
76D8×D61—22no—
77D8×D61C2×C414yes—
78C22×#92418D411yescharacteristic
79C2×C8×D61C2×C414yes—
80C2×C8×D61D411yescharacteristic
81C2×C8×D61D411yescharacteristic
82C2×C8×D61D414yes—
83C2×C8×D61C2311yescharacteristic
84C2×C8×D61C2311yescharacteristic
85#14519736—21no—
86#14519735—22no—
87#14519734—41no—
88#14519733—41no—
89C4⋊C4×D61—22no—
90C22⋊C4×D61—41no—
91C42×D61—41no—
92C2×#11758185—22no—
93C2×#11758185C2312yes—
94C16×D61—24no—
95C16×D61—24no—
96#14519711C2312yes—
97#14519710—22no—
98#14519709—21no—
99#14519708—22no—
100C2×#41×C61—21no—
101#135×C61—22no—
102#135×C61C2×C414yescomplemented
103C2×Q16×C61C2311yescharacteristic
104C2×SD16×C61—21no—
105C2×D8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107#117×C61—21no—
108C2×C16×C61—22no—
109C2×C16×C61C2312yes—
110#107×C61C2312yes—
111#106×C61—21no—
112C23×D61—41no—
113C23×D61D811yescharacteristic
114#41×C61—24no—
115#41×C61—42no—
116C2×Q8×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61C2×D411yescharacteristic
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C22×Dic61—41no—
125C22×Dic61D811yescharacteristic
126#11758226—24no—
127#11758226—42no—
128Q8×D61—24no—
129Q8×D61—42no—
130#11758224—24no—
131#11758224—48no—
132#11758224—42no—
133D4×D61—24no—
134D4×D61—48no—
135D4×D61—42no—
136#11758222—24no—
137#11758222—42no—
138#11758222—48no—
139C2×D244—21no—
140C2×D244—41no—
141C2×C4×D61—41no—
142C2×C4×D61—41no—
143C2×C4×D61—41no—
144C2×C4×D61—48no—
145C2×C4×D61—42no—
146C2×C4×D61C22⋊C414yes—
147C2×C4×D61D811yescharacteristic
148C2×C4×D61D811yescharacteristic
149C2×C4×D61SD1614yes—
150C2×C4×D61C2×D411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×Dic122—21no—
153C2×Dic122—41no—
154Q16×C61—21no—
155Q16×C61C22×C412yes—
156SD16×C61—24no—
157D8×C61—21no—
158D8×C61C22×C412yes—
159C2×C8×C61C22×C412yes—
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D412yes—
162C2×C8×C61C2411yescharacteristic
163C4⋊C4×C61—22no—
164C22⋊C4×C61—41no—
165C42×C61—41no—
166C22⋊Dic61—41no—
167#11758202—24no—
168#11758201—24no—
169#11758200—24no—
170#11758199—24no—
171#11758198—42no—
172C4⋊Dic61—22no—
173#11758196—42no—
174C4×Dic61—41no—
175C4×Dic61—42no—
176C2×#92418C22⋊C414yes—
177C2×#92418C2×D411yescharacteristic
178C2×#92418C2×D411yescharacteristic
179Dic244—21no—
180Dic244C22×C412yes—
181D488—21no—
182D488C22×C412yes—
183#11758190—24no—
184C8×D61C22⋊C414yes—
185C8×D61C22⋊C414yes—
186C8×D61C22×C412yes—
187C8×D61C22×C412yes—
188C8×D61C2×D412yes—
189C8×D61C2×D412yes—
190C16×C61—22no—
191#11758185—22no—
192C23×C61—41no—
193C23×C61C2×D811yescharacteristic
194C22×D61—24no—
195C22×D61—41no—
196C22×D61—44no—
197C22×D61—84no—
198C22×D61#10214yes—
199C22×D61C2×D811yescharacteristic
200C22×D61C2×D811yescharacteristic
201Q8×C61—22no—
202Q8×C61—41no—
203D4×C61—22no—
204D4×C61—44no—
205D4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—44no—
208C2×C4×C61—42no—
209C2×C4×C61C2×C22⋊C412yes—
210C2×C4×C61C2×D811yescharacteristic
211C2×C4×C61C2×SD1612yes—
212C2×C4×C61C22×D411yescharacteristic
213C22⋊D61—44no—
214C22⋊D61—44no—
215C22⋊D61—44no—
216C2×Dic61—41no—
217C2×Dic61—44no—
218C2×Dic61—42no—
219C2×Dic61#10214yes—
220C2×Dic61C2×D811yescharacteristic
221C2×Dic61C2×D811yescharacteristic
222D244—22no—
223D244—44no—
224D244—41no—
225C4×D61—44no—
226C4×D61—44no—
227C4×D61—44no—
228C4×D61—84no—
229C4×D61#10214yes—
230C4×D61#10214yes—
231C4×D61C2×C22⋊C412yes—
232C4×D61C2×C22⋊C412yes—
233C4×D61C2×SD1612yes—
234C4×D61C2×SD1612yes—
235Dic122—22no—
236Dic122—41no—
237Dic122—44no—
238C8×C61C2×C22⋊C412yes—
239C8×C61C23×C411yescharacteristic
240C8×C61C22×D411yescharacteristic
241#92418C2×C22⋊C412yes—
242#92418C2×C22⋊C412yes—
243C2×#2138—611nomaximal, Sylow
244C22×C61—22no—
245C22×C61—42no—
246C22×C61—82no—
247C22×C61C2×#10212yes—
248C22×C61C22×D811yescharacteristic
249C2×D61—22no—
250C2×D61—28no—
251C2×D61—42no—
252C2×D61—82no—
253C2×D61—88no—
254C2×D61C2×#10212yes—
255C2×D61C2×#10212yes—
256C2×D61#50814yes—
257C4×C61—42no—
258C4×C61—82no—
259C4×C61C2×#10212yes—
260C4×C61C22×C22⋊C411yescharacteristic
261C4×C61C22×SD1611yescharacteristic
262Dic61—42no—
263Dic61—82no—
264Dic61C2×#10212yes—
265Dic61C2×#10212yes—
266C22×#135—611no—
267C23×C16—611no—
268C2×#427—611no—
269#2138—611no—
270#2138—611no—
271#2138—612no—
272#2138—612no—
273#2138—611no—
274#2138D6111yescharacteristic, direct product factor
275C2×#358—612no—
276C2×#357—612no—
277C2×C61—22no—
278C2×C61—82no—
279C2×C61C22×#10211yescharacteristic
280C2×C61C2×#50812yes—
281D61—22no—
282D61—82no—
283D61#213814yesdirect product factor
284C22×#41—1221no—
285C2×#135—618no—
286C2×#135—611no—
287C2×#135—611no—
288C2×#135—611no—
289C2×#135—1221no—
290C2×#135—1224no—
291C2×#135—1221no—
292C2×#135C2×D6111yescharacteristic
293C22×Q16—611no—
294C22×SD16—1221no—
295C22×D8—611no—
296C23×C8—611no—
297C2×#117—1221no—
298C22×C16—611no—
299C22×C16—612no—
300C22×C16—612no—
301C22×C16—1224no—
302C22×C16C2×D6111yescharacteristic, complemented
303#427—611no—
304#427—612no—
305#427—1221no—
306#427—1221no—
307#427C2×D6111yescharacteristic, complemented
308C2×#107—612no—
309C2×#106—1221no—
310#358—612no—
311#358—612no—
312#358—612no—
313#358C2×D6112yescomplemented
314#357—612no—
315#357—612no—
316#357—612no—
317#357C2×D6112yescomplemented
318C61C2×#213811yescharacteristic, complemented, Sylow
319C2×#41—21no—
320C2×#41—1221no—
321C2×#41—1221no—
322C2×#41—1228no—
323C2×#41—1221no—
324C2×#41—2441no—
325C2×#41—2441no—
326C2×#41—2444no—
327C22×Q8—1221no—
328C22×D4—1221no—
329C22×D4—2441no—
330C23×C4—611no—
331C23×C4—2441no—
332#135—22no—
333#135—614no—
334#135—614no—
335#135—614no—
336#135—1222no—
337#135—1228no—
338#135—1222no—
339#135—1228no—
340#135—1222no—
341#135C4×D6114yescomplemented
342C2×Q16—614no—
343C2×Q16—611no—
344C2×Q16—1222no—
345C2×Q16—1221no—
346C2×Q16C22×D6111yescharacteristic
347C2×SD16—21no—
348C2×SD16—1228no—
349C2×SD16—1221no—
350C2×SD16—1221no—
351C2×SD16—1221no—
352C2×D8—614no—
353C2×D8—611no—
354C2×D8—1222no—
355C2×D8—1221no—
356C2×D8C22×D6111yescharacteristic
357C22×C8—611no—
358C22×C8—614no—
359C22×C8—611no—
360C22×C8—611no—
361C22×C8—614no—
362C22×C8—611no—
363C22×C8—611no—
364C22×C8C22×D6111yescharacteristic
365#117—21no—
366#117—1222no—
367#117—1221no—
368#117—2441no—
369#117—2441no—
370C2×C4⋊C4—1222no—
371C2×C22⋊C4—2441no—
372C2×C42—2441no—
373C2×C16—22no—
374C2×C16—612no—
375C2×C16—1224no—
376C2×C16—1224no—
377C2×C16—1222no—
378C2×C16C22×D6112yes—
379#107—612no—
380#107—1222no—
381#107C22×D6112yes—
382#106—21no—
383#106—1222no—
384#106—1221no—
385C24—611no—
386C24—2441no—
387#41—24no—
388#41—42no—
389#41—1224no—
390#41—1224no—
391#41—1224no—
392#41—2448no—
393#41—2448no—
394#41—2442no—
395#41—2442no—
396#41—2442no—
397C2×Q8—21no—
398C2×Q8—1224no—
399C2×Q8—1221no—
400C2×Q8—2441no—
401C2×Q8—2442no—
402C2×D4—21no—
403C2×D4—41no—
404C2×D4—1224no—
405C2×D4—1221no—
406C2×D4—2441no—
407C2×D4—2442no—
408C2×D4—2441no—
409C2×D4—2448no—
410C2×D4—2441no—
411C2×D4—2441no—
412C22×C4—41no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—611no—
416C22×C4—614no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—614no—
420C22×C4—2441no—
421C22×C4—2448no—
422C22×C4—2442no—
423C22×C4—2441no—
424C22×C4—2441no—
425C22×C4—2441no—
426C22×C4D4×D6111yescharacteristic
427Q16—21no—
428Q16—612no—
429Q16—1224no—
430Q16—1221no—
431Q16C2×C4×D6112yes—
432SD16—24no—
433SD16—1224no—
434SD16—1224no—
435SD16—1224no—
436D8—21no—
437D8—612no—
438D8—1224no—
439D8—1221no—
440D8C2×C4×D6112yes—
441C2×C8—611no—
442C2×C8—611no—
443C2×C8—614no—
444C2×C8—612no—
445C2×C8—612no—
446C2×C8—612no—
447C2×C8—612no—
448C2×C8—614no—
449C2×C8—614no—
450C2×C8C2×C4×D6112yes—
451C2×C8D4×D6112yes—
452C2×C8D4×D6111yescharacteristic
453C2×C8C23×D6111yescharacteristic
454C4⋊C4—22no—
455C4⋊C4—1222no—
456C4⋊C4—2442no—
457C22⋊C4—41no—
458C22⋊C4—2442no—
459C22⋊C4—2441no—
460C42—41no—
461C42—2442no—
462C42—2441no—
463C16—22no—
464C16—1222no—
465C23—41no—
466C23—611no—
467C23—614no—
468C23—611no—
469C23—1224no—
470C23—4884no—
471C23—2444no—
472C23—2441no—
473C23D8×D6111yescharacteristic
474Q8—22no—
475Q8—41no—
476Q8—1222no—
477Q8—2444no—
478Q8—2441no—
479D4—22no—
480D4—44no—
481D4—41no—
482D4—1222no—
483D4—2444no—
484D4—2444no—
485D4—2444no—
486D4—2444no—
487D4—2441no—
488C2×C4—41no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—614no—
492C2×C4—611no—
493C2×C4—611no—
494C2×C4—612no—
495C2×C4—612no—
496C2×C4—614no—
497C2×C4—614no—
498C2×C4—612no—
499C2×C4—612no—
500C2×C4—4884no—
501C2×C4—2444no—
502C2×C4—2444no—
503C2×C4—2444no—
504C2×C4—2442no—
505C2×C4—2441no—
506C2×C4—2444no—
507C2×C4C22⋊C4×D6112yes—
508C2×C4D8×D6111yescharacteristic
509C2×C4SD16×D6112yes—
510C2×C4C2×D4×D6111yescharacteristic
511C8—612no—
512C8—612no—
513C8C22⋊C4×D6112yes—
514C8C22×C4×D6111yescharacteristic
515C8C2×D4×D6111yescharacteristic
516C22—22no—
517C22—42no—
518C22—82no—
519C22—612no—
520C22—614no—
521C22—612no—
522C22—1228no—
523C22—1222no—
524C22—4888no—
525C22—4882no—
526C22—2442no—
527C22#102×D6112yes—
528C22C2×D8×D6111yescharacteristic
529C4—42no—
530C4—82no—
531C4—612no—
532C4—612no—
533C4—4882no—
534C4—2442no—
535C4#102×D6112yes—
536C4C2×C22⋊C4×D6111yescharacteristic
537C4C2×SD16×D6111yescharacteristic
538C2—22no—
539C2—82no—
540C2—614no—
541C2—1222no—
542C2—4882no—
543C2C2×#102×D6111yescharacteristic
544C2#508×D6112yes—
subgroupG/H
centerC2×C4D8×D61
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC61×#2138C2
socleC22×C61C22×D8
prime radicalC2×#135×D61C2
cosocleC2×C8×C61C24
hypercenter#2138D61
hypocenterC61C2×#2138
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
2. C22×C16×D61C2semidirect
3. #427×D61C2semidirect
4. #21447527C2semidirect
5. #21447526C2semidirect
6. #21447525C2semidirect
7. #21447524C2semidirect
8. #21447523C2semidirect
9. #358×D61C2semidirect
10. #357×D61C2semidirect
11. C61×#2138C2semidirect
19. #135×D61C4semidirect
25. C22×#11758185C22semidirect
28. C2×C16×D61C22semidirect
29. #16839800C22semidirect
30. #16839799C22semidirect
35. #16839567C22semidirect
36. #16839566C22semidirect
37. #16839565C22semidirect
38. #16839564C22semidirect
39. #16839563C22semidirect
40. #16839562C22semidirect
42. C22×C16×C61C22semidirect
43. C61×#427C22semidirect
44. C61×#358C22semidirect
45. C61×#357C22semidirect
59. #14519800C2×C4semidirect
61. #14519799C2×C4semidirect
65. #14519796C2×C4semidirect
102. #135×C61C2×C4semidirect
274. #2138D61direct (N × H)
283. D61#2138direct (N × H)
302. C22×C16C2×D61semidirect
307. #427C2×D61semidirect
313. #358C2×D61semidirect
317. #357C2×D61semidirect
318. C61C2×#2138semidirect
341. #135C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#135×D612
C22×C16×D612
#427×D612
#214475272
#214475262
#214475252
#214475242
#214475232
#358×D612
#357×D612
C61×#21382
C2×#213861