Finite Group Databasebeta

← D61×#2129 #29832803

Subgroups — D61×#2129 #29832803

Order 15616.

1230 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#536×D61C211yesmaximal, characteristic
2#410×D61C212yesmaximal
3#21447494C211yesmaximal, characteristic, complemented
4#21447493C212yesmaximal, complemented
5#21447492C214yesmaximal, complemented
6#354×D61C214yesmaximal, complemented
7C61×#2129C211yesmaximal, characteristic, complemented
8C2×#41×D61C2211yescharacteristic
9C22×Q8×D61C411yescharacteristic, complemented
10#16840338C411yescharacteristic, complemented
11#16840337C412yescomplemented
12#16840336C411yescharacteristic, complemented
13#16840335—22no—
14#16840334—22no—
15#16840333C2211yescharacteristic
16#16840332C2212yes—
17C4⋊Q8×D61C412yescomplemented
18#124×D61C2212yes—
19#123×D61—22no—
20C22⋊Q8×D61—22no—
21#117×D61—22no—
22#117×D61C411yescharacteristic, complemented
23#16839736C2212yes—
24#16839735—22no—
25#16839734—22no—
26#16839734C2214yes—
27#99×D61—22no—
28#99×D61C2214yes—
29#16839557C2214yescomplemented
30#16839556C2218yescomplemented
31C61×#536C2211yescharacteristic
32C61×#410C2212yes—
33C61×#354C2214yescomplemented
34C2×#11758226C2×C411yescharacteristic
35C2×#11758222C2×C411yescharacteristic
36C2×#11758222D412yes—
37C2×#11758224D412yes—
38C2×#11758224C2311yescharacteristic
39#41×D61—42no—
40#41×D61—42no—
41C22×Dic122—21no—
42C22×Dic122C2×C411yescharacteristic, complemented
43C2×Q8×D61—21no—
44C2×Q8×D61—21no—
45C2×Q8×D61—42no—
46C2×Q8×D61—42no—
47C2×Q8×D61C2×C412yes—
48C2×Q8×D61C2×C411yescharacteristic
49C2×Q8×D61C2×C412yescomplemented
50C2×D4×D61D412yes—
51C2×D4×D61C2311yescharacteristic
52C22×C4×D61—21no—
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61D412yes—
55#14519777C2×C412yescomplemented
56#14519776—24no—
57#14519775C2×C412yescomplemented
58#14519775C2×C412yescomplemented
59#14519766C2×C412yes—
60#14519765C2×C412yes—
61#14519764C2312yes—
62#14519763—24no—
63#14519762—24no—
64#14519761—22no—
65#14519760—22no—
66#14519759—24no—
67#14519758—22no—
68#14519757—22no—
69#14519756—22no—
70#14519755—24no—
71#14519754—24no—
72#14519753—22no—
73#14519736—22no—
74#14519736C2×C411yescharacteristic, complemented
75#14519735—21no—
76#14519735—42no—
77#14519734—42no—
78#14519734C2×C412yescomplemented
79#14519733—21no—
80#14519733—24no—
81C4⋊C4×D61—21no—
82C4⋊C4×D61—24no—
83C4⋊C4×D61—42no—
84C22⋊C4×D61—21no—
85C22⋊C4×D61—24no—
86C22⋊C4×D61—24no—
87C42×D61—42no—
88C42×D61C2×C412yes—
89#14519692—22no—
90#14519692C2314yes—
91#14519691—24no—
92#14519691—24no—
93C2×#41×C61C2311yescharacteristic
94C22×Q8×C61C2×C411yescharacteristic, complemented
95C4⋊Q8×C61C2×C412yescomplemented
96#124×C61C2312yes—
97#123×C61—22no—
98C22⋊Q8×C61—22no—
99#117×C61—22no—
100#117×C61C2×C411yescharacteristic, complemented
101#99×C61—22no—
102#99×C61C2314yes—
103C23×D61C22⋊C411yescharacteristic
104C23×D61C2×D412yes—
105#41×C61—42no—
106C2×Q8×C61—21no—
107C2×Q8×C61—42no—
108C2×Q8×C61C22×C412yes—
109C2×Q8×C61C22×C411yescharacteristic
110C2×D4×C61C2×D412yes—
111C2×D4×C61C2411yescharacteristic
112C22×C4×C61—21no—
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C2×D412yes—
115C2×C22⋊D61C22⋊C412yes—
116C2×C22⋊D61C2×D412yes—
117C2×C22⋊D61C2×D412yes—
118C22×Dic61—21no—
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C2×D412yes—
121#11758226—42no—
122Q8×D61—41no—
123Q8×D61—41no—
124Q8×D61—44no—
125Q8×D61—42no—
126Q8×D61—42no—
127Q8×D61—42no—
128Q8×D61—42no—
129Q8×D61—44no—
130#11758224—42no—
131#11758224—42no—
132#11758224—42no—
133D4×D61—42no—
134D4×D61—42no—
135D4×D61—41no—
136D4×D61—41no—
137#11758222—42no—
138#11758222—42no—
139#11758222—42no—
140C2×D244C22⋊C412yes—
141C2×D244C22×C411yescharacteristic
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—44no—
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C412yes—
156C2×C4×D61C22⋊C412yes—
157C2×C4×D61C22⋊C412yes—
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22×C411yescharacteristic
160C2×C4×D61C22×C411yescharacteristic
161C2×Dic122—21no—
162C2×Dic122—22no—
163C2×Dic122—22no—
164C2×Dic122—44no—
165C2×Dic122—42no—
166C2×Dic122C22⋊C412yes—
167C2×Dic122C22×C412yes—
168C2×Dic122C22×C411yescharacteristic
169C4⋊C4×C61—21no—
170C4⋊C4×C61—24no—
171C4⋊C4×C61—42no—
172C22⋊C4×C61—21no—
173C22⋊C4×C61—24no—
174C22⋊C4×C61—24no—
175C42×C61—42no—
176C42×C61C22×C412yes—
177C22⋊Dic61—21no—
178C22⋊Dic61—24no—
179C22⋊Dic61—24no—
180#11758198—22no—
181#11758198—24no—
182#11758198—24no—
183#11758198—44no—
184C4⋊Dic61—21no—
185C4⋊Dic61—24no—
186C4⋊Dic61—42no—
187#11758196—24no—
188#11758196—22no—
189#11758196—24no—
190#11758196—44no—
191C4×Dic61—22no—
192C4×Dic61—44no—
193C4×Dic61—42no—
194C4×Dic61C22×C412yes—
195C23×C61C2×C22⋊C411yescharacteristic
196C23×C61C22×D412yes—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—42no—
202C22×D61—44no—
203C22×D61C2×C22⋊C411yescharacteristic
204C22×D61C2×C22⋊C412yes—
205C22×D61C2×C22⋊C411yescharacteristic
206Q8×C61—41no—
207Q8×C61—42no—
208Q8×C61—42no—
209D4×C61—42no—
210D4×C61—41no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—42no—
217C2×C4×C61—44no—
218C2×C4×C61C2×C22⋊C412yes—
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C23×C411yescharacteristic
221C22⋊D61—42no—
222C22⋊D61—42no—
223C22⋊D61—42no—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—42no—
230C2×Dic61—44no—
231C2×Dic61C2×C22⋊C411yescharacteristic
232C2×Dic61C2×C22⋊C412yes—
233C2×Dic61C2×C22⋊C411yescharacteristic
234D244—42no—
235D244—41no—
236C4×D61—22no—
237C4×D61—22no—
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—22no—
241C4×D61—22no—
242C4×D61—22no—
243C4×D61—22no—
244C4×D61—22no—
245C4×D61—22no—
246C4×D61—44no—
247C4×D61—44no—
248C4×D61—42no—
249C4×D61—42no—
250C4×D61—88no—
251C4×D61#9912yes—
252C4×D61#9912yes—
253Dic122—42no—
254Dic122—41no—
255Dic122—44no—
256Dic122—42no—
257Dic122—44no—
258Dic122—42no—
259C2×#2129—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—22no—
262C22×C61—41no—
263C22×C61—42no—
264C22×C61C22×C22⋊C411yescharacteristic
265C2×D61—22no—
266C2×D61—21no—
267C2×D61—22no—
268C2×D61—42no—
269C2×D61—44no—
270C2×D61—42no—
271C2×D61—41no—
272C2×D61—42no—
273C2×D61—82no—
274C2×D61C2×#9911yescharacteristic
275C2×D61C2×#9911yescharacteristic
276C4×C61—21no—
277C4×C61—22no—
278C4×C61—42no—
279C4×C61—42no—
280C4×C61—84no—
281C4×C61C2×#9912yes—
282Dic61—21no—
283Dic61—22no—
284Dic61—42no—
285Dic61—42no—
286Dic61—84no—
287Dic61C2×#9912yes—
288C2×#536—611no—
289C2×#410—612no—
290#2129—612no—
291#2129—614no—
292#2129—611no—
293#2129D6111yescharacteristic, direct product factor
294C2×#354—614no—
295C2×C61—21no—
296C2×C61—42no—
297C2×C61—41no—
298C2×C61C22×#9911yescharacteristic
299D61—21no—
300D61—41no—
301D61—42no—
302D61#212912yesdirect product factor
303C22×#41—611no—
304C23×Q8—611no—
305#536—611no—
306#536—611no—
307#536—612no—
308#536—612no—
309#536—611no—
310#536—1222no—
311#536—1222no—
312#536C2×D6111yescharacteristic
313C2×C4⋊Q8—612no—
314C2×#124—612no—
315C2×#123—1222no—
316C2×C22⋊Q8—1222no—
317C2×#117—611no—
318C2×#117—1222no—
319#410—612no—
320#410—614no—
321#410—1222no—
322#410—1222no—
323#410C2×D6112yes—
324C2×#99—614no—
325C2×#99—1222no—
326#354—614no—
327#354—618no—
328#354C2×D6114yescomplemented
329C61C2×#212911yescharacteristic, complemented, Sylow
330C2×#41—611no—
331C2×#41—612no—
332C2×#41—611no—
333C2×#41—611no—
334C2×#41—612no—
335C2×#41—2442no—
336C2×#41—2442no—
337C2×#41C22×D6111yescharacteristic
338C22×Q8—611no—
339C22×Q8—612no—
340C22×Q8—612no—
341C22×Q8—611no—
342C22×Q8—1221no—
343C22×Q8—1221no—
344C22×Q8—1221no—
345C22×Q8—2442no—
346C22×Q8—2442no—
347C22×Q8C4×D6111yescharacteristic, complemented
348C22×D4—612no—
349C22×D4—611no—
350C23×C4—611no—
351C23×C4—612no—
352C23×C4—1221no—
353C4⋊Q8—612no—
354C4⋊Q8—612no—
355C4⋊Q8—612no—
356C4⋊Q8—1224no—
357C4⋊Q8C4×D6112yescomplemented
358#124—612no—
359#124—612no—
360#124—612no—
361#124—1224no—
362#124C22×D6112yes—
363#123—22no—
364#123—1224no—
365#123—1222no—
366#123—1224no—
367#123—1222no—
368#123—1222no—
369C22⋊Q8—22no—
370C22⋊Q8—1224no—
371C22⋊Q8—1224no—
372C22⋊Q8—1222no—
373C22⋊Q8—1222no—
374C22⋊Q8—1222no—
375#117—22no—
376#117—611no—
377#117—612no—
378#117—1221no—
379#117—1221no—
380#117—1224no—
381#117—1222no—
382#117—2442no—
383#117—2442no—
384#117C4×D6111yescharacteristic, complemented
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1224no—
387C2×C4⋊C4—2442no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1224no—
390C2×C22⋊C4—1224no—
391C2×C42—612no—
392C2×C42—2442no—
393#99—22no—
394#99—614no—
395#99—1224no—
396#99—1224no—
397#99—1222no—
398#99C22×D6114yes—
399C24—612no—
400C24—611no—
401#41—42no—
402#41—2442no—
403#41—2442no—
404#41—2442no—
405#41—2442no—
406#41—2442no—
407#41—2442no—
408#41—2442no—
409C2×Q8—21no—
410C2×Q8—42no—
411C2×Q8—611no—
412C2×Q8—612no—
413C2×Q8—612no—
414C2×Q8—1222no—
415C2×Q8—1222no—
416C2×Q8—1221no—
417C2×Q8—2442no—
418C2×Q8—2444no—
419C2×Q8—2442no—
420C2×Q8—2442no—
421C2×Q8—2441no—
422C2×Q8—2441no—
423C2×Q8—2444no—
424C2×Q8—2444no—
425C2×Q8—2442no—
426C2×Q8—2442no—
427C2×Q8C2×C4×D6112yes—
428C2×Q8C2×C4×D6111yescharacteristic
429C2×D4—612no—
430C2×D4—612no—
431C2×D4—612no—
432C2×D4—611no—
433C2×D4—612no—
434C2×D4—2442no—
435C2×D4—2442no—
436C2×D4—2441no—
437C2×D4—2441no—
438C2×D4D4×D6112yes—
439C2×D4C23×D6111yescharacteristic
440C22×C4—21no—
441C22×C4—611no—
442C22×C4—612no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—612no—
447C22×C4—612no—
448C22×C4—611no—
449C22×C4—612no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1221no—
460C22×C4—2444no—
461C22×C4—2442no—
462C22×C4—2442no—
463C22×C4C2×C4×D6111yescharacteristic
464C22×C4D4×D6112yes—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—42no—
468C4⋊C4—1222no—
469C4⋊C4—1224no—
470C4⋊C4—1224no—
471C4⋊C4—1224no—
472C4⋊C4—1221no—
473C4⋊C4—2442no—
474C4⋊C4—2444no—
475C22⋊C4—24no—
476C22⋊C4—21no—
477C22⋊C4—24no—
478C22⋊C4—1222no—
479C22⋊C4—1224no—
480C22⋊C4—1224no—
481C22⋊C4—1224no—
482C22⋊C4—1221no—
483C22⋊C4—1224no—
484C22⋊C4—2444no—
485C42—42no—
486C42—612no—
487C42—1222no—
488C42—2442no—
489C42—2444no—
490C42C2×C4×D6112yes—
491C23—611no—
492C23—612no—
493C23—611no—
494C23—1222no—
495C23—1222no—
496C23—1221no—
497C23—1221no—
498C23—2444no—
499C23—2442no—
500C23C22⋊C4×D6111yescharacteristic
501C23C2×D4×D6112yes—
502Q8—41no—
503Q8—42no—
504Q8—42no—
505Q8—2441no—
506Q8—2442no—
507Q8—2442no—
508Q8—2444no—
509Q8—2444no—
510Q8—2442no—
511D4—42no—
512D4—41no—
513D4—2441no—
514D4—2442no—
515D4—2442no—
516D4—2442no—
517D4—2442no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—611no—
526C2×C4—612no—
527C2×C4—612no—
528C2×C4—611no—
529C2×C4—612no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—4888no—
546C2×C4—2442no—
547C2×C4—2442no—
548C2×C4—2444no—
549C2×C4—2444no—
550C2×C4—2444no—
551C2×C4—2442no—
552C2×C4C22⋊C4×D6112yes—
553C2×C4C22⋊C4×D6111yescharacteristic
554C2×C4C22×C4×D6111yescharacteristic
555C22—22no—
556C22—21no—
557C22—42no—
558C22—41no—
559C22—611no—
560C22—611no—
561C22—1222no—
562C22—1221no—
563C22—1222no—
564C22—4882no—
565C22—2442no—
566C22—2441no—
567C22—2444no—
568C22—2442no—
569C22—2442no—
570C22C2×C22⋊C4×D6111yescharacteristic
571C4—21no—
572C4—22no—
573C4—42no—
574C4—42no—
575C4—84no—
576C4—612no—
577C4—1222no—
578C4—1221no—
579C4—4884no—
580C4—2442no—
581C4—2442no—
582C4#99×D6112yes—
583C2—21no—
584C2—42no—
585C2—41no—
586C2—612no—
587C2—1221no—
588C2—2442no—
589C2—2441no—
590C2C2×#99×D6111yescharacteristic
subgroupG/H
centerC2C2×#99×D61
commutatorC2×C4×C61C23×C4
FrattiniC2×D4C23×D61
FittingC61×#2129C2
socleC2×C61C22×#99
prime radicalC2×#41×D61C22
cosocleC2×D4×C61C24
hypercenter#2129D61
hypocenterC61C2×#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2129

Complements

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

NH ≅ G/Ntype
3. #21447494C2semidirect
4. #21447493C2semidirect
5. #21447492C2semidirect
6. #354×D61C2semidirect
7. C61×#2129C2semidirect
9. C22×Q8×D61C4semidirect
10. #16840338C4semidirect
11. #16840337C4semidirect
12. #16840336C4semidirect
17. C4⋊Q8×D61C4semidirect
22. #117×D61C4semidirect
29. #16839557C22semidirect
30. #16839556C22semidirect
33. C61×#354C22semidirect
42. C22×Dic122C2×C4semidirect
49. C2×Q8×D61C2×C4semidirect
55. #14519777C2×C4semidirect
57. #14519775C2×C4semidirect
58. #14519775C2×C4semidirect
74. #14519736C2×C4semidirect
78. #14519734C2×C4semidirect
94. C22×Q8×C61C2×C4semidirect
95. C4⋊Q8×C61C2×C4semidirect
100. #117×C61C2×C4semidirect
293. #2129D61direct (N × H)
302. D61#2129direct (N × H)
328. #354C2×D61semidirect
329. C61C2×#2129semidirect
347. C22×Q8C4×D61semidirect
357. C4⋊Q8C4×D61semidirect
384. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#536×D612
#410×D612
#214474942
#214474932
#214474922
#354×D612
C61×#21292
C2×#212961