Finite Group Databasebeta

← #29647587

Subgroups — #29647587

Order 15616.

882 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459907C211yesmaximal, characteristic
2#21454909C211yesmaximal, characteristic, complemented
3#21448471C211yesmaximal, characteristic, complemented
4#21444395C212yesmaximal
5#21444381C212yesmaximal, complemented
6#21444368C212yesmaximal, complemented
7#21444356C212yesmaximal
8#21444345C211yesmaximal, characteristic
9#21444318C211yesmaximal, characteristic, complemented
10#21444303C211yesmaximal, characteristic
11C61×#1506C211yesmaximal, characteristic, complemented
12#16840488C412yescomplemented
13#16840487C411yescharacteristic, complemented
14#16840487C411yescharacteristic, complemented
15#16840486C411yescharacteristic, complemented
16#16840484C412yescomplemented
17#16840454—21no—
18#16840445—22no—
19#16840427C411yescharacteristic, complemented
20#16840425—21no—
21#16840371—22no—
22#16840370—21no—
23#16840314C2212yes—
24#16840298C2212yes—
25#16840296C2211yescharacteristic
26#16840238—21no—
27C2×C4×Dic122C2211yescharacteristic
28#16839890—22no—
29#16839889—21no—
30#16839886—21no—
31#16839816C2212yes—
32#16839815C2211yescharacteristic
33#16839812C2212yes—
34#16839668—21no—
35#16839660—21no—
36#16839644—22no—
37#16839629C2212yes—
38#16839626C2212yes—
39C4×C4⋊Dic61C2211yescharacteristic
40#16839500C2212yes—
41#16839499C2212yes—
42#16839499C2212yes—
43#16839498C2211yescharacteristic
44#16839498C2211yescharacteristic
45#16839497C2212yes—
46#16839495C2211yescharacteristic
47#16839495C2211yescharacteristic
48C61×#533C2211yescharacteristic
49C61×#432C2211yescharacteristic
50C61×#376C2211yescharacteristic
51C61×#328C2212yes—
52C61×#328C2212yes—
53C22×Dic122D411yescharacteristic
54C2×Q8×D61—21no—
55#14519776—22no—
56#14519776C2×C412yes—
57#14519775—21no—
58#14519775C2×C412yes—
59#14519772—22no—
60#14519772—22no—
61#14519772—22no—
62#14519771—21no—
63#14519771—22no—
64#14519769—22no—
65#14519769C2×C411yescharacteristic
66#14519768—21no—
67#14519768—22no—
68#14519768C2×C412yes—
69#14519767—22no—
70#14519767—22no—
71#14519767—22no—
72#14519766C2×C412yes—
73#14519765C2×C411yescharacteristic
74#14519761—22no—
75#14519760—21no—
76#14519757—21no—
77#14519756C2311yescharacteristic
78#14519755—22no—
79#14519755—22no—
80#14519754—22no—
81#14519753—21no—
82#14519751C2311yescharacteristic
83Q8×Dic61—21no—
84Q8×Dic61C2×C412yes—
85Q8×Dic61C2×C412yes—
86C4×Dic122—22no—
87C4×Dic122C2×C411yescharacteristic
88C4×Dic122C2×C412yes—
89C4×Dic122C2×C411yescharacteristic
90C4×Dic122C2×C411yescharacteristic
91C4×Dic122D411yescharacteristic
92C4×Dic122D411yescharacteristic
93C4×Dic122D412yes—
94#14519742—21no—
95#14519742—22no—
96#14519742C2×C412yes—
97C4×D244C2×C411yescharacteristic
98#14519739C2×C412yes—
99C4×C22⋊D61—21no—
100#14519737—22no—
101#14519735—21no—
102#14519735—22no—
103#14519734—21no—
104#14519734—22no—
105#14519733—22no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61D411yescharacteristic
108C2×#11758196—22no—
109C2×#11758196D412yes—
110C2×C4×Dic61—21no—
111C2×C4×Dic61C2312yes—
112C4⋊#92418—21no—
113#14519706—22no—
114#14519706—22no—
115C22⋊#92418C2311yescharacteristic
116C22⋊#92418C2311yescharacteristic
117#14519687—22no—
118C4×#92418—21no—
119C8×Dic61—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684C2312yes—
124C4⋊Q8×C61C2×C411yescharacteristic
125C4⋊Q8×C61C2×C411yescharacteristic
126#125×C61—21no—
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61C2312yes—
129C4×Q8×C61—21no—
130C4×Q8×C61C2×C412yes—
131#117×C61—21no—
132C2×C42×C61—21no—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C22⋊C8×C61C2312yes—
136#97×C61—21no—
137#95×C61—21no—
138#95×C61C2311yescharacteristic
139#95×C61C2311yescharacteristic
140C2×Q8×C61—21no—
141C2×Q8×C61C22×C412yes—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—21no—
148C22×Dic61—22no—
149C22×Dic61C2×D412yes—
150C22×Dic61C2×D412yes—
151Q8×D61—44no—
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61—22no—
155C2×Dic122—22no—
156C2×Dic122—42no—
157C2×Dic122C22⋊C411yescharacteristic
158C2×Dic122C22⋊C411yescharacteristic
159C2×Dic122C22⋊C412yes—
160C2×Dic122C22×C411yescharacteristic
161C2×C8×C61—22no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61C22×C412yes—
168C22⋊C4×C61—22no—
169C42×C61—22no—
170C42×C61—42no—
171C42×C61C22×C411yescharacteristic
172C42×C61C22×C411yescharacteristic
173C42×C61C2×D411yescharacteristic
174C42×C61C2×D411yescharacteristic
175C22⋊Dic61—21no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198—22no—
181#11758198—22no—
182#11758198—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61—22no—
186C4⋊Dic61—42no—
187C4⋊Dic61C22⋊C411yescharacteristic
188C4⋊Dic61C22⋊C411yescharacteristic
189C4⋊Dic61C22⋊C412yes—
190C4⋊Dic61C22×C411yescharacteristic
191C4⋊Dic61C22×C411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—82no—
202#11758196C22⋊C412yes—
203#11758196C22⋊C412yes—
204#11758196C22⋊C412yes—
205#11758196C22⋊C412yes—
206C4×Dic61—21no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—81no—
211C4×Dic61C22×C412yes—
212C4×Dic61C22×C412yes—
213C4×Dic61C2×D412yes—
214C4×Dic61C2×D412yes—
215C2×#92418—21no—
216C2×#92418—21no—
217C23×C61C22×D411yescharacteristic
218C22×D61—21no—
219Q8×C61—42no—
220Q8×C61—42no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C23×C411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C22⋊D61—41no—
240C22⋊D61—41no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61C2×C22⋊C412yes—
251C2×Dic61C2×C22⋊C412yes—
252C2×Dic61C2×C22⋊C412yes—
253C2×Dic61C2×C22⋊C412yes—
254D244—41no—
255C4×D61—44no—
256C4×D61—42no—
257Dic122—22no—
258Dic122—22no—
259Dic122—42no—
260Dic122—44no—
261Dic122—41no—
262C8×C61—42no—
263#92418—41no—
264#92418—41no—
265#17601—611nomaximal, Sylow
266C22×C61—21no—
267C22×C61—21no—
268C22×C61C22×C22⋊C411yescharacteristic
269C22×C61#57711yescharacteristic
270C22×C61#57811yescharacteristic
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—42no—
280C4×C61—42no—
281C4×C61—81no—
282C4×C61—81no—
283C4×C61#42112yes—
284Dic61—22no—
285Dic61—22no—
286Dic61—22no—
287Dic61—22no—
288Dic61—41no—
289Dic61—41no—
290Dic61—41no—
291Dic61—82no—
292#3523—611no—
293#2984—611no—
294#2320—611no—
295#1521—612no—
296#1518—612no—
297#1515—612no—
298#1512—612no—
299#1509—611no—
300#1506D6111yescharacteristic, complemented
301#1503—611no—
302#1500—611no—
303C2×C61—21no—
304C2×C61—21no—
305C2×C61#288411yescharacteristic
306C2×C61#289811yescharacteristic
307C2×C61C2×#42111yescharacteristic
308D61—81no—
309#557—611no—
310#557—611no—
311#557—612no—
312#556—611no—
313#556—612no—
314#552—1222no—
315#552—1221no—
316D4×Q8—611no—
317D4×Q8—1221no—
318#541—1221no—
319#541—1222no—
320#533—612no—
321#533C2×D6111yescharacteristic
322#529—612no—
323#529—611no—
324#519—1221no—
325C2×C4×Q8—611no—
326#446—1222no—
327#446—1221no—
328C8×Q8—1221no—
329#432—612no—
330#432C2×D6111yescharacteristic
331#431—611no—
332#431—612no—
333#391—1221no—
334#389—1221no—
335#387—1222no—
336#383—612no—
337#382—612no—
338C4×C4⋊C4—611no—
339#376C2×D6111yescharacteristic
340#328—612no—
341#328—612no—
342#328—612no—
343#328—611no—
344#328—611no—
345#328C2×D6112yes—
346#328C2×D6112yes—
347#327—612no—
348#327—611no—
349#327—611no—
350C61#1760111yescharacteristic, complemented, Sylow
351C22×Q8—611no—
352C22×Q8—1221no—
353C4⋊Q8—612no—
354C4⋊Q8—612no—
355C4⋊Q8—1222no—
356C4⋊Q8—1221no—
357C4⋊Q8C4×D6111yescharacteristic
358C4⋊Q8C4×D6111yescharacteristic
359#126—1222no—
360#126—1222no—
361#126—1222no—
362#126—1222no—
363#126—1221no—
364#125—21no—
365#125—612no—
366#125—611no—
367#125—1222no—
368#125—1222no—
369#125—1222no—
370#125—1222no—
371#125—1222no—
372#125—1221no—
373#124—612no—
374#124—611no—
375#123—1222no—
376#123—1221no—
377C22⋊Q8—21no—
378C22⋊Q8—611no—
379C22⋊Q8—1222no—
380C22⋊Q8—1222no—
381C22⋊Q8—1222no—
382C22⋊Q8—1221no—
383C22⋊Q8—1221no—
384C22⋊Q8C22×D6112yes—
385#121—611no—
386C4×Q8—21no—
387C4×Q8—611no—
388C4×Q8—612no—
389C4×Q8—611no—
390C4×Q8—611no—
391C4×Q8—611no—
392C4×Q8—612no—
393C4×Q8—612no—
394C4×Q8—612no—
395C4×Q8—612no—
396C4×Q8—611no—
397C4×Q8—1222no—
398C4×Q8—1222no—
399C4×Q8—1221no—
400C4×Q8—1221no—
401C4×Q8C4×D6112yes—
402C4×D4—612no—
403C4×D4—611no—
404C4×D4—1222no—
405C4×D4—1221no—
406#117—21no—
407#117—1222no—
408#117—1222no—
409#117—1222no—
410#117—1221no—
411#117—1221no—
412C2×C4⋊C4—612no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—1222no—
415C2×C4⋊C4—1221no—
416C2×C42—21no—
417C2×C42—612no—
418C2×C42—1221no—
419C2×C42C22×D6111yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—1222no—
422C4⋊C8—1222no—
423C4⋊C8—1221no—
424C22⋊C8—611no—
425C22⋊C8—611no—
426C22⋊C8C22×D6112yes—
427#97—21no—
428#97—1222no—
429C4×C8—1222no—
430C4×C8—1221no—
431#95—21no—
432#95—612no—
433#95—1222no—
434#95—1222no—
435#95—1222no—
436#95C22×D6111yescharacteristic
437#95C22×D6111yescharacteristic
438C2×Q8—21no—
439C2×Q8—611no—
440C2×Q8—611no—
441C2×Q8—612no—
442C2×Q8—611no—
443C2×Q8—1222no—
444C2×Q8—2442no—
445C2×Q8—2444no—
446C2×Q8C2×C4×D6112yes—
447C2×D4—611no—
448C2×D4—1221no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—612no—
452C22×C4—612no—
453C22×C4—1222no—
454C22×C4—1221no—
455C22×C4—1222no—
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4C23×D6111yescharacteristic
459C2×C8—22no—
460C2×C8—1221no—
461C2×C8—1221no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—612no—
468C4⋊C4—612no—
469C4⋊C4—612no—
470C4⋊C4—612no—
471C4⋊C4—611no—
472C4⋊C4—611no—
473C4⋊C4—612no—
474C4⋊C4—611no—
475C4⋊C4—611no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1222no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—4882no—
489C4⋊C4—2442no—
490C4⋊C4C2×C4×D6112yes—
491C22⋊C4—22no—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C22⋊C4—1221no—
496C22⋊C4—1221no—
497C22⋊C4—1221no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C42—22no—
501C42—42no—
502C42—612no—
503C42—612no—
504C42—612no—
505C42—612no—
506C42—1222no—
507C42—1222no—
508C42—1222no—
509C42—1221no—
510C42—4881no—
511C42C2×C4×D6111yescharacteristic
512C42C2×C4×D6111yescharacteristic
513C42D4×D6111yescharacteristic
514C42D4×D6111yescharacteristic
515C23—1221no—
516C23C2×D4×D6111yescharacteristic
517Q8—42no—
518Q8—42no—
519Q8—1222no—
520Q8—1222no—
521Q8—2442no—
522Q8—2441no—
523Q8—2444no—
524D4—2441no—
525D4—2441no—
526D4—2441no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—612no—
540C2×C4—612no—
541C2×C4—612no—
542C2×C4—612no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—2444no—
549C2×C4—2442no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4C22⋊C4×D6111yescharacteristic
555C2×C4C22⋊C4×D6111yescharacteristic
556C2×C4C22⋊C4×D6111yescharacteristic
557C2×C4C22⋊C4×D6111yescharacteristic
558C2×C4C22×C4×D6111yescharacteristic
559C2×C4C2×D4×D6111yescharacteristic
560C8—42no—
561C8—2441no—
562C8—2441no—
563C22—21no—
564C22—21no—
565C22—2441no—
566C22—2441no—
567C22—2441no—
568C22C2×C22⋊C4×D6111yescharacteristic
569C22#1684057111yescharacteristic
570C22#1684057811yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—42no—
577C4—42no—
578C4—81no—
579C4—81no—
580C4—1222no—
581C4—1222no—
582C4—1222no—
583C4—1222no—
584C4—4882no—
585C4—2441no—
586C4—2441no—
587C4—2441no—
588C4#1683977712yes—
589C2—21no—
590C2—21no—
591C2—4881no—
592C2#2145428111yescharacteristic
593C2#2145435111yescharacteristic
594C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1506C2
socleC22×C61C22×C22⋊C4
prime radical#14519751C23
cosocleC22×C4×C61C24
hypercenter#1506D61
hypocenterC61#17601
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
2. #21454909C2semidirect
3. #21448471C2semidirect
5. #21444381C2semidirect
6. #21444368C2semidirect
9. #21444318C2semidirect
11. C61×#1506C2semidirect
12. #16840488C4semidirect
13. #16840487C4semidirect
14. #16840487C4semidirect
15. #16840486C4semidirect
16. #16840484C4semidirect
19. #16840427C4semidirect
300. #1506D61semidirect
350. C61#17601semidirect

Maximal subgroups

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

subgroupindex
#214599072
#214549092
#214484712
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