Finite Group Databasebeta

← D61⋊#2129 #30623967

Subgroups — D61⋊#2129 #30623967

Order 15616.

1230 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#410C212yesmaximal
2#21462103C212yesmaximal, complemented
3#21462102C214yesmaximal, complemented
4#21462101C212yesmaximal, complemented
5D61⋊#354C214yesmaximal, complemented
6#536×D61C211yesmaximal, characteristic
7C2×#14519856—22no—
8#16840743C2214yes—
9#16840742—22no—
10#16840741—22no—
11#16840741C2214yes—
12D61⋊#99—22no—
13D61⋊#99C2214yes—
14#16840669C2218yescomplemented
15#16840668C2218yescomplemented
16C2×#41×D61C2211yescharacteristic
17C22×Q8×D61C411yescharacteristic, complemented
18#16840338C2211yescharacteristic
19#16840337C2212yes—
20#16840336C2211yescharacteristic
21#16840335—22no—
22#16840334—22no—
23#16840333C411yescharacteristic, complemented
24#16840332C412yescomplemented
25C4⋊Q8×D61C412yescomplemented
26#124×D61C2212yes—
27#123×D61—22no—
28C22⋊Q8×D61—22no—
29#117×D61C411yescharacteristic, complemented
30C61×#536C411yescharacteristic, complemented
31#14519856—24no—
32#14519856—24no—
33#14519856—42no—
34#14519856—42no—
35C2×C4⋊#6923—42no—
36C2×C22⋊#6923—24no—
37C2×C4×#6923—42no—
38#14519836—24no—
39#14519836C2318yes—
40#14519835—24no—
41#14519835—24no—
42C2×#11758226C2311yescharacteristic
43C2×#11758222D412yes—
44C2×#11758222C2311yescharacteristic
45C2×#11758224C2×C411yescharacteristic
46C2×#11758224D412yes—
47#41×D61—42no—
48#41×D61—42no—
49C22×Dic122—21no—
50C22×Dic122C2×C411yescharacteristic, complemented
51C2×Q8×D61—21no—
52C2×Q8×D61—21no—
53C2×Q8×D61—42no—
54C2×Q8×D61—42no—
55C2×Q8×D61C2×C412yes—
56C2×Q8×D61C2×C411yescharacteristic
57C2×Q8×D61C2×C412yescomplemented
58C2×D4×D61D412yes—
59C2×D4×D61C2311yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61D412yes—
63#14519777C2×C412yescomplemented
64#14519776—24no—
65#14519775C2×C412yescomplemented
66#14519775C2×C412yescomplemented
67#14519766C2312yes—
68#14519765C2312yes—
69#14519764C2×C412yes—
70#14519763—24no—
71#14519762—24no—
72#14519761—22no—
73#14519760—22no—
74#14519759—24no—
75#14519758—22no—
76#14519757—22no—
77#14519756—22no—
78#14519755—24no—
79#14519754—24no—
80#14519753—22no—
81#14519736C2×C411yescharacteristic, complemented
82#14519735—21no—
83#14519734C2×C412yescomplemented
84#14519733—21no—
85C4⋊C4×D61—21no—
86C4⋊C4×D61—24no—
87C22⋊C4×D61—21no—
88C22⋊C4×D61—24no—
89C42×D61C2×C412yes—
90C2×#41×C61C2×C411yescharacteristic
91C22×Q8×C61C2×C411yescharacteristic, complemented
92C4⋊Q8×C61C2×C412yescomplemented
93#124×C61C2×C412yes—
94#123×C61—22no—
95C22⋊Q8×C61—22no—
96#117×C61C2×C411yescharacteristic, complemented
97C23×D61C22⋊C411yescharacteristic
98C23×D61C2×D412yes—
99C22×#6923—44no—
100#41×C61—42no—
101C2×Q8×C61—21no—
102C2×Q8×C61—42no—
103C2×Q8×C61C22×C412yes—
104C2×Q8×C61C22×C411yescharacteristic
105C2×D4×C61C22⋊C412yes—
106C2×D4×C61C22×C411yescharacteristic
107C22×C4×C61—21no—
108C22×C4×C61C22⋊C412yes—
109C22×C4×C61C22×C411yescharacteristic
110C2×C22⋊D61C22⋊C412yes—
111C2×C22⋊D61C2×D412yes—
112C2×C22⋊D61C2×D412yes—
113C22×Dic61—21no—
114C22×Dic61C22⋊C411yescharacteristic
115C22×Dic61C22⋊C412yes—
116#11758226—42no—
117Q8×D61—41no—
118Q8×D61—41no—
119Q8×D61—44no—
120Q8×D61—42no—
121Q8×D61—42no—
122Q8×D61—42no—
123Q8×D61—42no—
124Q8×D61—44no—
125#11758224—42no—
126#11758224—42no—
127#11758224—42no—
128D4×D61—42no—
129D4×D61—42no—
130D4×D61—41no—
131D4×D61—41no—
132#11758222—42no—
133#11758222—42no—
134#11758222—42no—
135C2×D244C2×D412yes—
136C2×D244C2411yescharacteristic
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—42no—
147C2×C4×D61—42no—
148C2×C4×D61C22⋊C411yescharacteristic
149C2×C4×D61C22⋊C412yes—
150C2×C4×D61C22⋊C411yescharacteristic
151C2×C4×D61C22×C411yescharacteristic
152C2×C4×D61C22×C411yescharacteristic
153C2×C4×D61C2×D412yes—
154C2×C4×D61C2×D412yes—
155C2×Dic122—21no—
156C2×Dic122—22no—
157C2×Dic122—22no—
158C2×Dic122—44no—
159C2×Dic122—42no—
160C2×Dic122C22⋊C412yes—
161C2×Dic122C22×C412yes—
162C2×Dic122C22×C411yescharacteristic
163C22⋊#6923—28no—
164C22⋊#6923—44no—
165C4⋊#6923—44no—
166C4⋊#6923—44no—
167C4×#6923—44no—
168C4×#6923—44no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—24no—
171C22⋊C4×C61—21no—
172C22⋊C4×C61—24no—
173C42×C61C22×C412yes—
174C22⋊Dic61—21no—
175C22⋊Dic61—24no—
176#11758198—22no—
177#11758198—24no—
178#11758198—24no—
179C4⋊Dic61—21no—
180C4⋊Dic61—24no—
181#11758196—24no—
182#11758196—22no—
183#11758196—24no—
184C4×Dic61—22no—
185C4×Dic61C22×C412yes—
186C23×C61C2×C22⋊C412yes—
187C23×C61C2×C22⋊C411yescharacteristic
188C22×D61—21no—
189C22×D61—21no—
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—42no—
193C22×D61—44no—
194C22×D61C2×C22⋊C411yescharacteristic
195C22×D61C2×C22⋊C411yescharacteristic
196C22×D61C22×D412yes—
197C2×#6923—48no—
198C2×#6923—88no—
199Q8×C61—41no—
200Q8×C61—42no—
201Q8×C61—42no—
202D4×C61—42no—
203D4×C61—41no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—42no—
210C2×C4×C61C2×C22⋊C412yes—
211C2×C4×C61C2×C22⋊C411yescharacteristic
212C2×C4×C61C23×C411yescharacteristic
213C22⋊D61—42no—
214C22⋊D61—42no—
215C22⋊D61—42no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—42no—
222C2×Dic61C2×C22⋊C411yescharacteristic
223C2×Dic61C2×C22⋊C412yes—
224C2×Dic61C2×C22⋊C411yescharacteristic
225D244—42no—
226D244—41no—
227C4×D61—22no—
228C4×D61—22no—
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—22no—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—44no—
238C4×D61—44no—
239C4×D61—42no—
240C4×D61—42no—
241C4×D61#9912yes—
242C4×D61#9912yes—
243Dic122—42no—
244Dic122—41no—
245Dic122—44no—
246Dic122—42no—
247Dic122—44no—
248Dic122—42no—
249C2×#2129—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—22no—
252C22×C61—41no—
253C22×C61—42no—
254C22×C61C22×C22⋊C411yescharacteristic
255C2×D61—22no—
256C2×D61—21no—
257C2×D61—22no—
258C2×D61—42no—
259C2×D61—44no—
260C2×D61—42no—
261C2×D61—41no—
262C2×D61—42no—
263C2×D61—82no—
264C2×D61C2×#9911yescharacteristic
265C2×D61C2×#9911yescharacteristic
266#6923—88no—
267C4×C61—21no—
268C4×C61—22no—
269C4×C61—42no—
270C4×C61—42no—
271C4×C61C2×#9912yes—
272Dic61—21no—
273Dic61—22no—
274Dic61—42no—
275Dic61—42no—
276Dic61C2×#9912yes—
277C2×#536—611no—
278C2×#410—612no—
279#2129—612no—
280#2129—614no—
281#2129—612no—
282C2×#354—614no—
283C2×C61—21no—
284C2×C61—41no—
285C2×C61—42no—
286C2×C61C22×#9911yescharacteristic
287D61—21no—
288D61—42no—
289D61—41no—
290D61#212912yescomplemented
291C22×#41—611no—
292C23×Q8—611no—
293#536—611no—
294#536—611no—
295#536—612no—
296#536—612no—
297#536—611no—
298#536—1222no—
299#536—1222no—
300#536#692311yescharacteristic, complemented
301C2×C4⋊Q8—612no—
302C2×#124—612no—
303C2×#123—1222no—
304C2×C22⋊Q8—1222no—
305C2×#117—611no—
306C2×#117—1222no—
307#410—614no—
308#410—614no—
309#410—1222no—
310#410—1222no—
311C2×#99—614no—
312C2×#99—1222no—
313#354—618no—
314#354—618no—
315C61C2×#212911yescharacteristic, complemented, Sylow
316C2×#41—611no—
317C2×#41—612no—
318C2×#41—611no—
319C2×#41—612no—
320C2×#41—611no—
321C2×#41—2442no—
322C2×#41—2442no—
323C2×#41C2×#692311yescharacteristic
324C22×Q8—611no—
325C22×Q8—612no—
326C22×Q8—612no—
327C22×Q8—611no—
328C22×Q8—1221no—
329C22×Q8—1221no—
330C22×Q8—1221no—
331C22×Q8—2442no—
332C22×Q8—2442no—
333C22×Q8C2×#692311yescharacteristic, complemented
334C22×D4—612no—
335C22×D4—611no—
336C23×C4—612no—
337C23×C4—611no—
338C23×C4—1221no—
339C4⋊Q8—612no—
340C4⋊Q8—612no—
341C4⋊Q8—612no—
342C4⋊Q8—1224no—
343C4⋊Q8C2×#692312yescomplemented
344#124—612no—
345#124—612no—
346#124—612no—
347#124—1224no—
348#124C2×#692312yes—
349#123—22no—
350#123—1224no—
351#123—1222no—
352#123—1224no—
353#123—1222no—
354#123—1222no—
355C22⋊Q8—22no—
356C22⋊Q8—1224no—
357C22⋊Q8—1224no—
358C22⋊Q8—1222no—
359C22⋊Q8—1222no—
360C22⋊Q8—1222no—
361#117—611no—
362#117—612no—
363#117—1221no—
364#117—1221no—
365#117—1224no—
366#117—1224no—
367#117—2442no—
368#117—2442no—
369#117C2×#692311yescharacteristic, complemented
370C2×C4⋊C4—1221no—
371C2×C4⋊C4—1224no—
372C2×C4⋊C4—2442no—
373C2×C22⋊C4—1221no—
374C2×C22⋊C4—1224no—
375C2×C22⋊C4—1224no—
376C2×C42—612no—
377C2×C42—2442no—
378#99—618no—
379#99—1224no—
380#99—1224no—
381#99—1224no—
382C24—612no—
383C24—611no—
384#41—42no—
385#41—2442no—
386#41—2442no—
387#41—2442no—
388#41—2442no—
389#41—2442no—
390#41—2442no—
391#41—2442no—
392C2×Q8—21no—
393C2×Q8—42no—
394C2×Q8—612no—
395C2×Q8—611no—
396C2×Q8—612no—
397C2×Q8—1222no—
398C2×Q8—1222no—
399C2×Q8—1221no—
400C2×Q8—2442no—
401C2×Q8—2444no—
402C2×Q8—2442no—
403C2×Q8—2442no—
404C2×Q8—2441no—
405C2×Q8—2441no—
406C2×Q8—2444no—
407C2×Q8—2444no—
408C2×Q8—2442no—
409C2×Q8—2442no—
410C2×Q8C22×#692312yes—
411C2×Q8C22×#692311yescharacteristic
412C2×D4—612no—
413C2×D4—612no—
414C2×D4—612no—
415C2×D4—612no—
416C2×D4—611no—
417C2×D4—2442no—
418C2×D4—2442no—
419C2×D4—2441no—
420C2×D4—2441no—
421C2×D4C22⋊#692312yes—
422C2×D4C22×#692311yescharacteristic
423C22×C4—21no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—612no—
429C22×C4—612no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1221no—
443C22×C4—2442no—
444C22×C4—2442no—
445C22×C4—2444no—
446C22×C4C22⋊#692312yes—
447C22×C4C22×#692311yescharacteristic
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—1222no—
451C4⋊C4—1224no—
452C4⋊C4—1224no—
453C4⋊C4—1224no—
454C4⋊C4—1221no—
455C4⋊C4—2444no—
456C4⋊C4—2444no—
457C22⋊C4—21no—
458C22⋊C4—24no—
459C22⋊C4—1222no—
460C22⋊C4—1224no—
461C22⋊C4—1224no—
462C22⋊C4—1221no—
463C22⋊C4—1224no—
464C22⋊C4—1228no—
465C22⋊C4—2444no—
466C42—612no—
467C42—1222no—
468C42—2444no—
469C42—2444no—
470C42C22×#692312yes—
471C23—611no—
472C23—611no—
473C23—612no—
474C23—1222no—
475C23—1221no—
476C23—1221no—
477C23—1222no—
478C23—2444no—
479C23—2442no—
480C23C2×C22⋊#692312yes—
481C23C2×C22⋊#692311yescharacteristic
482Q8—41no—
483Q8—42no—
484Q8—42no—
485Q8—2442no—
486Q8—2441no—
487Q8—2442no—
488Q8—2444no—
489Q8—2444no—
490Q8—2442no—
491D4—42no—
492D4—41no—
493D4—2442no—
494D4—2441no—
495D4—2442no—
496D4—2442no—
497D4—2442no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—42no—
504C2×C4—611no—
505C2×C4—612no—
506C2×C4—612no—
507C2×C4—611no—
508C2×C4—612no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1222no—
512C2×C4—1222no—
513C2×C4—1222no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1222no—
517C2×C4—1222no—
518C2×C4—1222no—
519C2×C4—1222no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—4888no—
525C2×C4—2442no—
526C2×C4—2442no—
527C2×C4—2444no—
528C2×C4—2444no—
529C2×C4—2448no—
530C2×C4—2442no—
531C2×C4C2×C22⋊#692312yes—
532C2×C4C2×C22⋊#692311yescharacteristic
533C2×C4C23×#692311yescharacteristic
534C22—21no—
535C22—22no—
536C22—42no—
537C22—41no—
538C22—611no—
539C22—611no—
540C22—1222no—
541C22—1222no—
542C22—1221no—
543C22—4882no—
544C22—2442no—
545C22—2441no—
546C22—2444no—
547C22—2442no—
548C22—2442no—
549C22C22×C22⋊#692311yescharacteristic
550C4—22no—
551C4—21no—
552C4—42no—
553C4—42no—
554C4—612no—
555C4—1222no—
556C4—1221no—
557C4—4888no—
558C4—2442no—
559C4—2442no—
560C4D61⋊#9912yes—
561C2—21no—
562C2—42no—
563C2—41no—
564C2—612no—
565C2—1221no—
566C2—2442no—
567C2—2441no—
568C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC2C2×D61⋊#99
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#536C4
socleC2×C61C22×#99
prime radicalC2×#41×D61C22
cosocleC2×D244C24
hypercenter#536#6923
hypocenterC61C2×#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #21462103C2semidirect
3. #21462102C2semidirect
4. #21462101C2semidirect
5. D61⋊#354C2semidirect
14. #16840669C22semidirect
15. #16840668C22semidirect
17. C22×Q8×D61C4semidirect
23. #16840333C4semidirect
24. #16840332C4semidirect
25. C4⋊Q8×D61C4semidirect
29. #117×D61C4semidirect
30. C61×#536C4semidirect
50. C22×Dic122C2×C4semidirect
57. C2×Q8×D61C2×C4semidirect
63. #14519777C2×C4semidirect
65. #14519775C2×C4semidirect
66. #14519775C2×C4semidirect
81. #14519736C2×C4semidirect
83. #14519734C2×C4semidirect
91. C22×Q8×C61C2×C4semidirect
92. C4⋊Q8×C61C2×C4semidirect
96. #117×C61C2×C4semidirect
290. D61#2129semidirect
300. #536#6923semidirect
315. C61C2×#2129semidirect
333. C22×Q8C2×#6923semidirect
343. C4⋊Q8C2×#6923semidirect
369. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4102
#214621032
#214621022
#214621012
D61⋊#3542
#536×D612
C2×#212961