Finite Group Databasebeta

← D61×#1305 #29570341

Subgroups — D61×#1305 #29570341

Order 15616.

986 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#407×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic
3#380×D61C211yesmaximal, characteristic
4#21443726C211yesmaximal, characteristic, complemented
5#21443725C211yesmaximal, characteristic, complemented
6#21443724C211yesmaximal, characteristic, complemented
7C61×#1305C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C2×M16×D61—21no—
10C2×M16×D61C412yescomplemented
11C2×C4⋊C4×D61—21no—
12C2×C22⋊C4×D61C412yes—
13#16839726C2211yescharacteristic
14#16839726C2211yescharacteristic
15#16839725—21no—
16#16839725C412yescomplemented
17#16839724—21no—
18#16839724—21no—
19#16839724—21no—
20#16839724C412yescomplemented
21C22⋊C8×D61—21no—
22C22⋊C8×D61—21no—
23C22⋊C8×D61—21no—
24C22⋊C8×D61C412yescomplemented
25#16839622C2211yescharacteristic
26#16839621—21no—
27#16839620C412yes—
28#16839619—21no—
29#95×D61—21no—
30C61×#407C2211yescharacteristic
31C61×#407C2211yescharacteristic
32C61×#380C2211yescharacteristic
33C24×D61C2×C411yescharacteristic
34C23×Dic61C2×C411yescharacteristic
35C22×C4×D61—22no—
36C22×C4×D61—44no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61C2×C411yescharacteristic
39C22×C4×D61C2×C411yescharacteristic
40C22×C4×D61C2×C411yescharacteristic
41C22×C4×D61D411yescharacteristic
42C22×C4×D61D411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×C4×D61D411yescharacteristic
46C22×C4×D61D411yescharacteristic
47C22×C4×D61Q811yescharacteristic
48C22×C4×D61Q811yescharacteristic
49C2×#11758194—21no—
50C2×#11758194C2×C412yescomplemented
51C2×#11758189—22no—
52C2×#11758189—22no—
53M16×D61—44no—
54M16×D61—44no—
55C2×C8×D61—22no—
56C2×C8×D61—22no—
57C2×C4⋊Dic61—21no—
58C2×#11758196—22no—
59C4⋊C4×D61—44no—
60C2×C22⋊Dic61C2×C412yes—
61C2×#11758198—22no—
62C22⋊C4×D61—44no—
63C22⋊#92418—21no—
64C22⋊#92418—21no—
65C22⋊#92418—21no—
66C22⋊#92418C2×C412yescomplemented
67#14519689—22no—
68#14519689—22no—
69#14519689—22no—
70#14519689—22no—
71#14519684—21no—
72#14519684—22no—
73C23×C4×C61C2311yescharacteristic
74C2×M16×C61—21no—
75C2×M16×C61C2×C412yescomplemented
76C2×C4⋊C4×C61—21no—
77C2×C22⋊C4×C61C2×C412yes—
78C22⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61C2×C412yescomplemented
82#95×C61—21no—
83C24×C61C22×C411yescharacteristic
84C23×D61—22no—
85C23×D61—22no—
86C23×D61—42no—
87C23×D61—42no—
88C23×D61C4211yescharacteristic
89C23×D61C4211yescharacteristic
90C23×D61C22⋊C411yescharacteristic
91C23×D61C22⋊C411yescharacteristic
92C23×D61C4⋊C411yescharacteristic
93C23×D61C4⋊C411yescharacteristic
94C22×C4×C61—22no—
95C22×C4×C61—42no—
96C22×C4×C61C22×C411yescharacteristic
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×Q811yescharacteristic
102C22×Dic61—22no—
103C22×Dic61—42no—
104C22×Dic61C4211yescharacteristic
105C22×Dic61C4211yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C4⋊C411yescharacteristic
109C22×Dic61C4⋊C411yescharacteristic
110C2×C4×D61—24no—
111C2×C4×D61—24no—
112C2×C4×D61—24no—
113C2×C4×D61—42no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61—42no—
117C2×C4×D61—42no—
118C2×C4×D61—42no—
119C2×C4×D61—42no—
120C2×C4×D61—42no—
121C2×C4×D61—42no—
122C2×C4×D61—44no—
123C2×C4×D61—44no—
124C2×C4×D61—44no—
125C2×C4×D61C22⋊C411yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C22⋊C411yescharacteristic
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C22⋊C411yescharacteristic
132C2×C4×D61C22⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C4⋊C411yescharacteristic
136C2×C4×D61C4⋊C411yescharacteristic
137C2×C4×D61C4⋊C411yescharacteristic
138C2×C4×D61C4⋊C411yescharacteristic
139C2×C4×D61C4⋊C411yescharacteristic
140C2×C4×D61C4⋊C411yescharacteristic
141M16×C61—42no—
142M16×C61—42no—
143C2×C8×C61—22no—
144C2×C8×C61—22no—
145C4⋊C4×C61—42no—
146C22⋊C4×C61—42no—
147C22⋊Dic61—42no—
148#11758198—44no—
149C4⋊Dic61—42no—
150#11758196—44no—
151#11758194—42no—
152#11758194—42no—
153C2×#92418—22no—
154C2×#92418—22no—
155#11758189—44no—
156#11758189—44no—
157C8×D61—44no—
158C8×D61—44no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—41no—
162C23×C61—41no—
163C23×C61C2×C4211yescharacteristic
164C23×C61C2×C22⋊C411yescharacteristic
165C23×C61C2×C4⋊C411yescharacteristic
166C22×D61—22no—
167C22×D61—22no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—22no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—41no—
184C22×D61—48no—
185C22×D61—48no—
186C22×D61#9511yescharacteristic
187C22×D61#9511yescharacteristic
188C22×D61#9511yescharacteristic
189C22×D61#9511yescharacteristic
190C22×D61#10012yes—
191C22×D61#10112yes—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—22no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61C2×C22⋊C411yescharacteristic
202C2×C4×C61C2×C22⋊C411yescharacteristic
203C2×C4×C61C2×C4⋊C411yescharacteristic
204C2×C4×C61C2×C4⋊C411yescharacteristic
205C2×Dic61—22no—
206C2×Dic61—22no—
207C2×Dic61—22no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61#9511yescharacteristic
215C2×Dic61#9511yescharacteristic
216C2×Dic61#9511yescharacteristic
217C2×Dic61#9511yescharacteristic
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—22no—
223C4×D61—22no—
224C4×D61—22no—
225C4×D61—22no—
226C4×D61—22no—
227C4×D61—41no—
228C4×D61—41no—
229C4×D61—41no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—88no—
234C4×D61#9914yes—
235C8×C61—42no—
236C8×C61—42no—
237#92418—42no—
238#92418—42no—
239C2×#1305—611nomaximal, Sylow
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—42no—
249C22×C61—42no—
250C22×C61C2×#9511yescharacteristic
251C22×C61C2×#10011yescharacteristic
252C22×C61C2×#10111yescharacteristic
253C2×D61—21no—
254C2×D61—21no—
255C2×D61—24no—
256C2×D61—24no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—44no—
264C2×D61—44no—
265C2×D61—42no—
266C2×D61—42no—
267C2×D61—44no—
268C2×D61—44no—
269C2×D61#34212yes—
270C2×D61#34312yes—
271C2×D61#34312yes—
272C2×D61#34412yes—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—82no—
277C4×C61C2×#9912yes—
278Dic61—21no—
279Dic61—21no—
280Dic61—21no—
281Dic61—82no—
282Dic61#34212yes—
283C2×#407—611no—
284C2×#407—611no—
285C2×#380—611no—
286#1305—611no—
287#1305—611no—
288#1305—611no—
289#1305D6111yescharacteristic, direct product factor
290C2×C61—21no—
291C2×C61—21no—
292C2×C61—41no—
293C2×C61—41no—
294C2×C61C2×#34211yescharacteristic
295C2×C61C2×#34311yescharacteristic
296C2×C61C2×#34411yescharacteristic
297D61—22no—
298D61—41no—
299D61—41no—
300D61#130514yesdirect product factor
301C24×C4—611no—
302C22×M16—612no—
303C22×M16—1221no—
304C22×C4⋊C4—1221no—
305C22×C22⋊C4—612no—
306#407—611no—
307#407—612no—
308#407—611no—
309#407—612no—
310#407—1221no—
311#407—1221no—
312#407—1221no—
313#407—1221no—
314#407C2×D6111yescharacteristic
315#407C2×D6111yescharacteristic
316C2×C22⋊C8—612no—
317C2×C22⋊C8—1221no—
318C2×C22⋊C8—1221no—
319C2×C22⋊C8—1221no—
320#380—611no—
321#380—612no—
322#380—1221no—
323#380—1221no—
324#380C2×D6111yescharacteristic
325C2×#95—1221no—
326C61C2×#130511yescharacteristic, complemented, Sylow
327C25—611no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—611no—
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—611no—
337C23×C4—611no—
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—1222no—
342C23×C4—2444no—
343C23×C4C22×D6111yescharacteristic
344C2×M16—21no—
345C2×M16—612no—
346C2×M16—1222no—
347C2×M16—1222no—
348C2×M16—1221no—
349C2×M16—2444no—
350C2×M16—2444no—
351C2×M16C4×D6112yescomplemented
352C22×C8—1222no—
353C22×C8—1222no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4—2444no—
358C2×C22⋊C4—612no—
359C2×C22⋊C4—1222no—
360C2×C22⋊C4—2444no—
361C2×C22⋊C4C4×D6112yes—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—612no—
366C22⋊C8—1222no—
367C22⋊C8—1222no—
368C22⋊C8—1222no—
369C22⋊C8—1222no—
370C22⋊C8—1221no—
371C22⋊C8—1221no—
372C22⋊C8—1221no—
373C22⋊C8C4×D6112yescomplemented
374#95—21no—
375#95—1222no—
376#95—1221no—
377C24—611no—
378C24—611no—
379C24—611no—
380C24—611no—
381C24—611no—
382C24—611no—
383C24—1222no—
384C24—1222no—
385C24—2442no—
386C24—2442no—
387C24C2×C4×D6111yescharacteristic
388C22×C4—22no—
389C22×C4—42no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—1224no—
413C22×C4—1224no—
414C22×C4—1224no—
415C22×C4—1222no—
416C22×C4—2442no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4—2442no—
420C22×C4—2442no—
421C22×C4—2442no—
422C22×C4—2442no—
423C22×C4—2442no—
424C22×C4—2442no—
425C22×C4—2444no—
426C22×C4—2444no—
427C22×C4—2444no—
428C22×C4—2442no—
429C22×C4C2×C4×D6111yescharacteristic
430C22×C4C2×C4×D6111yescharacteristic
431C22×C4D4×D6111yescharacteristic
432C22×C4D4×D6111yescharacteristic
433C22×C4D4×D6111yescharacteristic
434C22×C4Q8×D6111yescharacteristic
435M16—42no—
436M16—42no—
437M16—2444no—
438M16—2444no—
439M16—2442no—
440M16—2442no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—1222no—
444C2×C8—1222no—
445C2×C8—2444no—
446C2×C8—2444no—
447C4⋊C4—42no—
448C4⋊C4—2442no—
449C4⋊C4—2444no—
450C22⋊C4—42no—
451C22⋊C4—2444no—
452C22⋊C4—2442no—
453C23—21no—
454C23—21no—
455C23—41no—
456C23—41no—
457C23—611no—
458C23—612no—
459C23—612no—
460C23—611no—
461C23—611no—
462C23—611no—
463C23—1222no—
464C23—1222no—
465C23—1222no—
466C23—1222no—
467C23—1222no—
468C23—1222no—
469C23—1222no—
470C23—1222no—
471C23—1222no—
472C23—1222no—
473C23—1221no—
474C23—1221no—
475C23—2441no—
476C23—2441no—
477C23—2441no—
478C23—2441no—
479C23—2441no—
480C23—2441no—
481C23—2448no—
482C23—2448no—
483C23C42×D6111yescharacteristic
484C23C22⋊C4×D6111yescharacteristic
485C23C4⋊C4×D6111yescharacteristic
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—611no—
496C2×C4—614no—
497C2×C4—611no—
498C2×C4—611no—
499C2×C4—611no—
500C2×C4—1222no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1222no—
504C2×C4—1222no—
505C2×C4—1222no—
506C2×C4—1222no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1222no—
512C2×C4—4888no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2442no—
523C2×C4—2442no—
524C2×C4—2442no—
525C2×C4C22⋊C4×D6111yescharacteristic
526C2×C4C22⋊C4×D6111yescharacteristic
527C2×C4C4⋊C4×D6111yescharacteristic
528C2×C4C4⋊C4×D6111yescharacteristic
529C8—42no—
530C8—42no—
531C8—2442no—
532C8—2442no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—42no—
542C22—42no—
543C22—612no—
544C22—612no—
545C22—612no—
546C22—612no—
547C22—1224no—
548C22—1224no—
549C22—1221no—
550C22—1221no—
551C22—1221no—
552C22—1221no—
553C22—1221no—
554C22—1221no—
555C22—1221no—
556C22—1221no—
557C22—2442no—
558C22—2442no—
559C22—2444no—
560C22—2444no—
561C22—2444no—
562C22—2444no—
563C22#95×D6111yescharacteristic
564C22#100×D6111yescharacteristic
565C22#101×D6111yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—82no—
570C4—612no—
571C4—1221no—
572C4—1221no—
573C4—1221no—
574C4—4882no—
575C4#99×D6112yes—
576C2—21no—
577C2—21no—
578C2—41no—
579C2—41no—
580C2—614no—
581C2—1222no—
582C2—2441no—
583C2—2441no—
584C2#342×D6111yescharacteristic
585C2#343×D6111yescharacteristic
586C2#344×D6111yescharacteristic
subgroupG/H
centerC22#95×D61
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1305C2
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1305D61
hypocenterC61C2×#1305
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
4. #21443726C2semidirect
5. #21443725C2semidirect
6. #21443724C2semidirect
7. C61×#1305C2semidirect
10. C2×M16×D61C4semidirect
16. #16839725C4semidirect
20. #16839724C4semidirect
24. C22⋊C8×D61C4semidirect
50. C2×#11758194C2×C4semidirect
66. C22⋊#92418C2×C4semidirect
75. C2×M16×C61C2×C4semidirect
81. C22⋊C8×C61C2×C4semidirect
289. #1305D61direct (N × H)
300. D61#1305direct (N × H)
326. C61C2×#1305semidirect
351. C2×M16C4×D61semidirect
373. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#407×D612
#380×D612
#214437262
#214437252
#214437242
C61×#13052
C2×#130561