Finite Group Databasebeta

← D61×#2057 #29708030

Subgroups — D61×#2057 #29708030

Order 15616.

1454 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic
2C2×#107×D61C212yesmaximal
3#389×D61C211yesmaximal, characteristic
4#21447148C211yesmaximal, characteristic, complemented
5#21447147C211yesmaximal, characteristic, complemented
6#21447146C212yesmaximal, complemented
7#21447145C212yesmaximal, complemented
8#21447144C211yesmaximal, characteristic, complemented
9#340×D61C212yesmaximal
10#336×D61C211yesmaximal, characteristic
11C61×#2057C211yesmaximal, characteristic, complemented
12C22×Q8×D61—21no—
13C22×C8×D61C2212yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519776—21no—
16C2×#14519776C2212yes—
17C2×#14519775—21no—
18C4⋊Q8×D61—28no—
19C2×C4⋊C4×D61—21no—
20C2×C4⋊C4×D61—21no—
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2212yes—
23C2×C4⋊C4×D61C2211yescharacteristic
24C2×C42×D61C2211yescharacteristic
25C2×#14519711C2212yes—
26C2×#14519710C2212yes—
27C2×#14519710C2212yes—
28#107×D61—28no—
29#16839661C2211yescharacteristic
30#16839660C2211yescharacteristic
31#16839659—21no—
32#16839658C2211yescharacteristic
33#16839657—21no—
34#95×D61—21no—
35#16839525C2212yes—
36#16839524C2212yes—
37#16839524C2212yes—
38#16839517C2211yescharacteristic
39#16839516C2212yes—
40C2×C4⋊Q8×C61C2211yescharacteristic
41C2×#107×C61C2212yes—
42C61×#389C2211yescharacteristic
43C61×#340C2212yes—
44C61×#336C2211yescharacteristic
45C22×Dic122—21no—
46C22×Dic122—22no—
47C2×Q8×D61—28no—
48C2×Q8×D61—44no—
49C2×Q8×D61—44no—
50C22×C4×D61—22no—
51C22×C4×D61—21no—
52C22×C4×D61—21no—
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61C2311yescharacteristic
56C22×#92418C2312yes—
57C2×C8×D61—24no—
58C2×C8×D61—24no—
59C2×C8×D61Q818yescomplemented
60#14519777—24no—
61#14519776—28no—
62#14519776—24no—
63#14519776—24no—
64#14519775—28no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2312yes—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×#11758196—22no—
71C2×#11758196—22no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C4⋊C4×D61—28no—
77C4⋊C4×D61—24no—
78C4⋊C4×D61—22no—
79C4⋊C4×D61—24no—
80C4⋊C4×D61—44no—
81C4⋊C4×D61D418yes—
82C4⋊C4×D61Q814yescomplemented
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C42×D61—24no—
87#14519711—24no—
88#14519710—24no—
89#14519710—24no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93C22×Q8×C61—21no—
94C22×C8×C61C2312yes—
95C4⋊Q8×C61—24no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2312yes—
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C42×C61C2311yescharacteristic
102#107×C61—24no—
103#95×C61—21no—
104C23×D61C2×D411yescharacteristic
105C2×Q8×C61—24no—
106C2×Q8×C61—42no—
107C2×Q8×C61—42no—
108C22×C4×C61—22no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2411yescharacteristic
114C22×Dic61—22no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61C2×D411yescharacteristic
118C22×Dic61C2×D411yescharacteristic
119C22×Dic61C2×D411yescharacteristic
120Q8×D61—432no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C2×C4×D61—28no—
126C2×C4×D61—24no—
127C2×C4×D61—44no—
128C2×C4×D61—42no—
129C2×C4×D61—44no—
130C2×C4×D61—42no—
131C2×C4×D61—42no—
132C2×C4×D61—42no—
133C2×C4×D61—42no—
134C2×C4×D61D814yes—
135C2×C4×D61Q1614yes—
136C2×C4×D61C2×D414yes—
137C2×C4×D61C2×Q814yes—
138C2×C4×D61C2×Q812yes—
139C2×C4×D61#4112yes—
140C2×Dic122—24no—
141C2×Dic122—28no—
142C2×Dic122—44no—
143C2×Dic122—42no—
144C2×Dic122—42no—
145C2×Dic122—44no—
146C2×C8×C61—22no—
147C2×C8×C61—22no—
148C2×C8×C61C2×Q814yescomplemented
149C4⋊C4×C61—24no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—42no—
154C4⋊C4×C61C2×D414yes—
155C4⋊C4×C61C2×Q812yescomplemented
156C42×C61—22no—
157C4⋊Dic61—24no—
158C4⋊Dic61—22no—
159C4⋊Dic61—21no—
160C4⋊Dic61—22no—
161C4⋊Dic61—42no—
162C4⋊Dic61C2×D414yes—
163C4⋊Dic61C2×Q812yescomplemented
164#11758196—28no—
165#11758196—28no—
166#11758196—24no—
167#11758196—42no—
168#11758196—42no—
169#11758196—42no—
170C4×Dic61—22no—
171C4×Dic61—22no—
172C4×Dic61—22no—
173C2×#92418—22no—
174C2×#92418—22no—
175C2×#92418C2×Q814yescomplemented
176C8×D61—216no—
177C23×C61C22×D411yescharacteristic
178C22×D61#12012yes—
179C22×D61C22⋊Q812yes—
180C22×D61C4⋊Q812yes—
181C22×D61C2×D812yes—
182C22×D61C2×Q1612yes—
183C22×D61AGL(1,ℤ/8)12yes—
184C22×D61#13712yes—
185Q8×C61—48no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—24no—
191C2×C4×C61—22no—
192C2×C4×C61—41no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61C2×D812yes—
200C2×C4×C61C2×Q1612yes—
201C2×C4×C61C22×D412yes—
202C2×C4×C61C22×Q812yes—
203C2×C4×C61C22×Q811yescharacteristic
204C2×C4×C61C2×#4111yescharacteristic
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—24no—
210C2×Dic61—22no—
211C2×Dic61—41no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61#12012yes—
219C2×Dic61C22⋊Q812yes—
220C2×Dic61C4⋊Q812yes—
221C2×Dic61C2×D812yes—
222C2×Dic61C2×Q1612yes—
223C4×D61—28no—
224C4×D61—28no—
225C4×D61—416no—
226C4×D61—48no—
227C4×D61—84no—
228C4×D61C22⋊Q818yes—
229C4×D61C4⋊Q818yes—
230Dic122—416no—
231Dic122—48no—
232C8×C61—24no—
233#92418—24no—
234C2×#2057—611nomaximal, Sylow
235C22×C61C2×#12011yescharacteristic
236C22×C61C2×C22⋊Q811yescharacteristic
237C22×C61C2×C4⋊Q811yescharacteristic
238C22×C61C22×D811yescharacteristic
239C22×C61C22×Q1611yescharacteristic
240C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
241C22×C61C2×#13711yescharacteristic
242C2×D61#39514yes—
243C2×D61#44714yes—
244C2×D61#45114yes—
245C2×D61#47414yes—
246C2×D61#47714yes—
247C2×D61#50014yes—
248C2×D61#50114yes—
249C4×C61—22no—
250C4×C61—22no—
251C4×C61—44no—
252C4×C61—42no—
253C4×C61—81no—
254C4×C61C2×C22⋊Q812yes—
255C4×C61C2×C4⋊Q812yes—
256Dic61—22no—
257Dic61—22no—
258Dic61—44no—
259Dic61—42no—
260Dic61—81no—
261Dic61#39514yes—
262C22×C4⋊Q8—611no—
263C22×#107—612no—
264C2×#389—611no—
265#2057—612no—
266#2057—611no—
267#2057—612no—
268#2057—611no—
269#2057—611no—
270#2057D6111yescharacteristic, direct product factor
271C2×#340—612no—
272C2×#336—611no—
273C2×C61C2×#39511yescharacteristic
274C2×C61C2×#44711yescharacteristic
275C2×C61C2×#45111yescharacteristic
276C2×C61C2×#47411yescharacteristic
277C2×C61C2×#47711yescharacteristic
278C2×C61C2×#50011yescharacteristic
279C2×C61C2×#50111yescharacteristic
280D61#205718yesdirect product factor
281C23×Q8—1221no—
282C23×C8—612no—
283C2×C4⋊Q8—612no—
284C2×C4⋊Q8—611no—
285C2×C4⋊Q8—1221no—
286C2×C4⋊Q8—1221no—
287C2×C4⋊Q8—1228no—
288C2×C4⋊Q8C2×D6111yescharacteristic
289C22×C4⋊C4—612no—
290C22×C4⋊C4—611no—
291C22×C4⋊C4—611no—
292C22×C4⋊C4—1221no—
293C22×C4⋊C4—1221no—
294C22×C42—611no—
295C2×#107—612no—
296C2×#107—612no—
297C2×#107—612no—
298C2×#107—1228no—
299C2×#107C2×D6112yes—
300#389—611no—
301#389—611no—
302#389—611no—
303#389—1221no—
304#389—1221no—
305#389C2×D6111yescharacteristic
306C2×#95—1221no—
307#340—612no—
308#340—612no—
309#340—612no—
310#340C2×D6112yes—
311#336—612no—
312#336—611no—
313#336C2×D6111yescharacteristic
314C61C2×#205711yescharacteristic, complemented, Sylow
315C22×Q8—21no—
316C22×Q8—1222no—
317C22×Q8—1228no—
318C22×Q8—1221no—
319C22×Q8—2444no—
320C22×Q8—2444no—
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—1222no—
325C23×C4—1221no—
326C23×C4—1221no—
327C22×C8—612no—
328C22×C8—618no—
329C22×C8—1224no—
330C22×C8—1224no—
331C22×C8C22×D6112yes—
332C4⋊Q8—24no—
333C4⋊Q8—1224no—
334C4⋊Q8—1224no—
335C4⋊Q8—1228no—
336C4⋊Q8—1228no—
337C4⋊Q8—1224no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—612no—
341C2×C4⋊C4—611no—
342C2×C4⋊C4—618no—
343C2×C4⋊C4—614no—
344C2×C4⋊C4—611no—
345C2×C4⋊C4—1224no—
346C2×C4⋊C4—1222no—
347C2×C4⋊C4—1228no—
348C2×C4⋊C4—1224no—
349C2×C4⋊C4—1222no—
350C2×C4⋊C4—1221no—
351C2×C4⋊C4—1222no—
352C2×C4⋊C4—1221no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4—2444no—
358C2×C4⋊C4C22×D6111yescharacteristic
359C2×C4⋊C4C22×D6112yes—
360C2×C4⋊C4C22×D6111yescharacteristic
361C2×C42—611no—
362C2×C42—611no—
363C2×C42—611no—
364C2×C42—1224no—
365C2×C42C22×D6111yescharacteristic
366#107—24no—
367#107—1224no—
368#107—1224no—
369#107—1224no—
370#95—21no—
371#95—1221no—
372#95—1221no—
373#95—1221no—
374C24—611no—
375C2×Q8—24no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8—1224no—
379C2×Q8—1228no—
380C2×Q8—2442no—
381C2×Q8—2444no—
382C2×Q8—2444no—
383C2×Q8—24432no—
384C2×Q8—2442no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—611no—
389C22×C4—614no—
390C22×C4—612no—
391C22×C4—614no—
392C22×C4—612no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—614no—
396C22×C4—614no—
397C22×C4—1222no—
398C22×C4—1222no—
399C22×C4—1222no—
400C22×C4—1222no—
401C22×C4—1228no—
402C22×C4—1224no—
403C22×C4—1221no—
404C22×C4—1222no—
405C22×C4—1221no—
406C22×C4—2442no—
407C22×C4—2442no—
408C22×C4—2442no—
409C22×C4—2442no—
410C22×C4—2444no—
411C22×C4—2444no—
412C22×C4—2442no—
413C22×C4D4×D6111yescharacteristic
414C22×C4D4×D6111yescharacteristic
415C22×C4C23×D6111yescharacteristic
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—614no—
419C2×C8—12216no—
420C2×C8—1222no—
421C2×C8—1222no—
422C2×C8Q8×D6114yescomplemented
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—42no—
428C4⋊C4—614no—
429C4⋊C4—612no—
430C4⋊C4—1224no—
431C4⋊C4—1228no—
432C4⋊C4—1228no—
433C4⋊C4—1224no—
434C4⋊C4—1222no—
435C4⋊C4—1221no—
436C4⋊C4—1222no—
437C4⋊C4—2442no—
438C4⋊C4—2442no—
439C4⋊C4—2442no—
440C4⋊C4—2442no—
441C4⋊C4D4×D6114yes—
442C4⋊C4Q8×D6112yescomplemented
443C42—22no—
444C42—1222no—
445C42—1222no—
446C42—1222no—
447C23—612no—
448C23—612no—
449C23—612no—
450C23—612no—
451C23—612no—
452C23—612no—
453C23—612no—
454C23C2×D4×D6111yescharacteristic
455Q8—48no—
456Q8—2448no—
457Q8—24416no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—612no—
472C2×C4—612no—
473C2×C4—612no—
474C2×C4—618no—
475C2×C4—618no—
476C2×C4—612no—
477C2×C4—612no—
478C2×C4—1228no—
479C2×C4—1228no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—1224no—
485C2×C4—1222no—
486C2×C4—4884no—
487C2×C4—2448no—
488C2×C4—24416no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2442no—
494C2×C4—2442no—
495C2×C4—2441no—
496C2×C4D8×D6112yes—
497C2×C4Q16×D6112yes—
498C2×C4C2×D4×D6112yes—
499C2×C4C2×Q8×D6112yes—
500C2×C4C2×Q8×D6111yescharacteristic
501C2×C4#41×D6111yescharacteristic
502C8—24no—
503C8—1224no—
504C22—614no—
505C22—614no—
506C22—614no—
507C22—614no—
508C22—614no—
509C22—614no—
510C22—614no—
511C22#120×D6111yescharacteristic
512C22C22⋊Q8×D6111yescharacteristic
513C22C4⋊Q8×D6111yescharacteristic
514C22C2×D8×D6111yescharacteristic
515C22C2×Q16×D6111yescharacteristic
516C22AGL(1,ℤ/8)×D6111yescharacteristic
517C22#137×D6111yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—81no—
523C4—614no—
524C4—1222no—
525C4—1222no—
526C4—4881no—
527C4—2444no—
528C4—2442no—
529C4C22⋊Q8×D6112yes—
530C4C4⋊Q8×D6112yes—
531C2—618no—
532C2#395×D6111yescharacteristic
533C2#447×D6111yescharacteristic
534C2#451×D6111yescharacteristic
535C2#474×D6111yescharacteristic
536C2#477×D6111yescharacteristic
537C2#500×D6111yescharacteristic
538C2#501×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2057C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2057D61
hypocenterC61C2×#2057
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
4. #21447148C2semidirect
5. #21447147C2semidirect
6. #21447146C2semidirect
7. #21447145C2semidirect
8. #21447144C2semidirect
11. C61×#2057C2semidirect
59. C2×C8×D61Q8semidirect
82. C4⋊C4×D61Q8semidirect
148. C2×C8×C61C2×Q8semidirect
155. C4⋊C4×C61C2×Q8semidirect
163. C4⋊Dic61C2×Q8semidirect
175. C2×#92418C2×Q8semidirect
270. #2057D61direct (N × H)
280. D61#2057direct (N × H)
314. C61C2×#2057semidirect
422. C2×C8Q8×D61semidirect
442. C4⋊C4Q8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
C2×#107×D612
#389×D612
#214471482
#214471472
#214471462
#214471452
#214471442
#340×D612
#336×D612
C61×#20572
C2×#205761