Finite Group Databasebeta

← #29648012

Subgroups — #29648012

Order 15616.

964 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459792C211yesmaximal, characteristic
2#21454834C211yesmaximal, characteristic, complemented
3#21454248C211yesmaximal, characteristic, complemented
4#21444438C212yesmaximal, complemented
5#21444434C211yesmaximal, characteristic, complemented
6#21444424C211yesmaximal, characteristic, complemented
7#21444419C212yesmaximal, complemented
8#21444408C211yesmaximal, characteristic, complemented
9#21444406C212yesmaximal, complemented
10#330×D61C212yesmaximal, complemented
11C61×#1526C211yesmaximal, characteristic, complemented
12C2×#14519785—21no—
13#16840487C411yescharacteristic
14#16840473C411yescharacteristic
15#16840473C411yescharacteristic
16#16840456C412yes—
17#16840453—22no—
18#16840451C412yes—
19#16840446—21no—
20#16840415C411yescharacteristic
21#16840414—21no—
22#16840370—21no—
23#16840358—22no—
24#16840297C2212yes—
25#16840296C2211yescharacteristic
26#125×D61C2212yes—
27#16840244—21no—
28C4×#11758222C2211yescharacteristic
29#16839892—21no—
30#16839831—22no—
31C8×D244—21no—
32#16839819C2211yescharacteristic
33#16839817C2212yes—
34#16839720—21no—
35#16839716—22no—
36#16839714C2212yes—
37C2×#14519688C2211yescharacteristic
38#97×D61C2212yes—
39#97×D61C2212yes—
40#16839504C2212yes—
41#16839504C2212yes—
42#16839503C2211yescharacteristic
43#16839503C2212yes—
44#16839503C2211yescharacteristic
45#16839501C2211yescharacteristic
46#16839501C2212yes—
47#16839501C2211yescharacteristic
48C61×#533C2211yescharacteristic
49C4×M16×C61C2211yescharacteristic
50C4×M16×C61C2211yescharacteristic
51C61×#330C2212yes—
52C61×#330C2212yes—
53C2×#11758226—21no—
54C2×#11758222D411yescharacteristic
55#14519785—28no—
56C2×#11758189—22no—
57C22×#92418—21no—
58C2×C8×D61—22no—
59C2×C8×D61—22no—
60#14519775—21no—
61#14519772—22no—
62#14519771—21no—
63#14519771—22no—
64#14519770—22no—
65#14519769—22no—
66#14519769C2311yescharacteristic
67#14519768—21no—
68#14519768C2×C412yes—
69#14519768C2×C412yes—
70#14519767—22no—
71#14519767—22no—
72#14519767—22no—
73#14519765C2311yescharacteristic
74#14519762—22no—
75#14519762—22no—
76#14519760—21no—
77#14519759—22no—
78#14519759—22no—
79#14519757—21no—
80#14519757C2×C412yes—
81#14519756C2×C411yescharacteristic
82#14519753—22no—
83#14519753—21no—
84#14519753—22no—
85#14519752C2×C412yes—
86#14519751C2×C411yescharacteristic
87#14519750—22no—
88Q8×Dic61—21no—
89C4×Dic122C2×C411yescharacteristic
90C4×Dic122C2×C411yescharacteristic
91C4×Dic122D411yescharacteristic
92#14519742C2×C412yes—
93C4×D244—22no—
94C4×D244C2×C411yescharacteristic
95C4×D244C2×C411yescharacteristic
96C4×D244D411yescharacteristic
97#14519739—21no—
98#14519739—22no—
99#14519739C2×C412yes—
100C4×C22⋊D61—21no—
101C4×C22⋊D61C2×C412yes—
102C4×C22⋊D61D412yes—
103#14519736D411yescharacteristic
104#14519735—22no—
105#14519734—21no—
106#14519734—22no—
107#14519734D412yes—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—21no—
111C4⋊C4×D61C2×C412yes—
112C4⋊C4×D61C2×C412yes—
113C42×D61C2312yes—
114C4⋊#92418—21no—
115#14519706—22no—
116C22⋊#92418—21no—
117#14519689—22no—
118#14519688—21no—
119#14519688C2311yescharacteristic
120#14519688C2312yes—
121#14519688C2311yescharacteristic
122#14519687—22no—
123#14519687—22no—
124C8×Dic61—22no—
125C2×M16×C61—21no—
126C2×M16×C61—21no—
127C4⋊Q8×C61C2×C411yescharacteristic
128C4⋊Q8×C61C2×C411yescharacteristic
129#125×C61C2312yes—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C4×Q8×C61—21no—
133C4×Q8×C61—21no—
134#117×C61C2×C412yes—
135C2×C42×C61C2311yescharacteristic
136#97×C61C2311yescharacteristic
137#97×C61C2312yes—
138#97×C61C2311yescharacteristic
139C4×C8×C61—21no—
140C4×C8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C2×C22⋊D61—21no—
147C2×C22⋊D61C22⋊C412yes—
148#11758226—44no—
149#11758222—24no—
150C2×D244—22no—
151C2×D244C22⋊C411yescharacteristic
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—22no—
154C2×C4×D61—21no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61C22×C412yes—
158C2×C4×D61C2×D412yes—
159C2×C4×D61C2×D412yes—
160C2×Dic122C22⋊C411yescharacteristic
161C2×Dic122C22×C411yescharacteristic
162M16×C61—24no—
163M16×C61—42no—
164C2×C8×C61—22no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61C22×C412yes—
172C4⋊C4×C61C22×C412yes—
173C22⋊C4×C61—22no—
174C42×C61—22no—
175C42×C61C22×C411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180C22⋊Dic61C22⋊C412yes—
181#11758198—22no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—22no—
187#11758198—22no—
188#11758198C22⋊C412yes—
189#11758198C22⋊C412yes—
190C4⋊Dic61—22no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61C22⋊C411yescharacteristic
194C4⋊Dic61C22⋊C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196C4⋊Dic61C22×C411yescharacteristic
197#11758196—21no—
198#11758196—21no—
199#11758196—21no—
200#11758196—21no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196C22⋊C412yes—
207#11758196C22⋊C412yes—
208C4×Dic61—21no—
209C4×Dic61—22no—
210C4×Dic61C22×C412yes—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D412yes—
213C2×#92418—24no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—22no—
217#11758189—28no—
218C8×D61—28no—
219C8×D61—44no—
220C23×C61C2×C22⋊C411yescharacteristic
221C22×D61—21no—
222C22×D61C2×C22⋊C412yes—
223Q8×C61—42no—
224Q8×C61—81no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C23×C411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C22⋊D61—24no—
237C22⋊D61—81no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61C2×C22⋊C412yes—
242C2×Dic61C2×C22⋊C412yes—
243C2×Dic61C2×C22⋊C412yes—
244D244—41no—
245D244—44no—
246D244#10414yes—
247C4×D61—24no—
248C4×D61—42no—
249C4×D61—42no—
250C4×D61—44no—
251C4×D61—42no—
252C4×D61—82no—
253C4×D61—82no—
254Dic122—22no—
255Dic122—41no—
256C8×C61—24no—
257C8×C61—22no—
258C8×C61—41no—
259#92418—22no—
260#92418—22no—
261#92418—42no—
262#17653—611nomaximal, Sylow
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61C22×C22⋊C411yescharacteristic
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61C2×#10414yes—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—42no—
279C4×C61—42no—
280C4×C61C2×#10412yes—
281Dic61—22no—
282Dic61—22no—
283Dic61—22no—
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287#3515—611no—
288#2970—611no—
289#2875—611no—
290#1532—612no—
291#1531—611no—
292#1529—611no—
293#1528—612no—
294#1526D6111yescharacteristic, complemented
295#1524—611no—
296#1524—612no—
297C2×#330—612no—
298C2×C61—41no—
299C2×C61#288911yescharacteristic
300C2×C61C22×#10411yescharacteristic
301C2×C61#290111yescharacteristic
302D61—24no—
303D61—81no—
304C2×#131—1221no—
305#557—611no—
306#554—611no—
307#554—611no—
308#553—612no—
309#552—612no—
310#552—1222no—
311#552—1221no—
312#547—611no—
313#547—1221no—
314#541—1221no—
315#539—1222no—
316#533C2×D6111yescharacteristic
317#529—612no—
318#529—611no—
319C2×#125—612no—
320#520—1221no—
321C4×#41—611no—
322#446—1221no—
323#435—1222no—
324C8×D4—1221no—
325#432—611no—
326#432—612no—
327#405—1222no—
328#405—1221no—
329C4×M16—612no—
330C4×M16C2×D6111yescharacteristic
331C4×M16C2×D6111yescharacteristic
332C2×#97—611no—
333C2×#97—612no—
334C2×#97—612no—
335#330—612no—
336#330—612no—
337#330—611no—
338#330—612no—
339#330—611no—
340#330C2×D6112yes—
341#330C2×D6112yes—
342#329—611no—
343#329—612no—
344#329—611no—
345C61#1765311yescharacteristic, complemented, Sylow
346C2×#41—611no—
347C2×#41—1221no—
348#131—1228no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—1222no—
352C22×C8—1222no—
353C22×C8—1222no—
354C22×C8—1221no—
355C4⋊Q8—1221no—
356C4⋊Q8C4×D6111yescharacteristic
357C4⋊Q8C4×D6111yescharacteristic
358#126—1222no—
359#126—1222no—
360#126—1222no—
361#126—1221no—
362#125—612no—
363#125—612no—
364#125—611no—
365#125—1222no—
366#125—1222no—
367#125—1222no—
368#125—1222no—
369#125—1221no—
370#125C22×D6112yes—
371#124—611no—
372#123—1222no—
373#123—1222no—
374#123—1222no—
375#123—1222no—
376#123—1221no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—611no—
380C22⋊Q8—612no—
381C22⋊Q8—1222no—
382C22⋊Q8—1221no—
383C22⋊Q8—1222no—
384C22⋊Q8—1221no—
385#121—611no—
386#121—612no—
387#121—1222no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—611no—
391C4×Q8—611no—
392C4×Q8—612no—
393C4×Q8—611no—
394C4×Q8—1221no—
395C4×D4—612no—
396C4×D4—612no—
397C4×D4—612no—
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—611no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4—1221no—
404C4×D4—1221no—
405#117—611no—
406#117—612no—
407#117—1222no—
408#117—1222no—
409#117—1221no—
410#117C4×D6112yes—
411C2×C4⋊C4—612no—
412C2×C4⋊C4—612no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1222no—
415C2×C4⋊C4—1222no—
416C2×C42—612no—
417C2×C42C22×D6111yescharacteristic
418C4⋊C8—1222no—
419C4⋊C8—1221no—
420C22⋊C8—1222no—
421C22⋊C8—1221no—
422#97—611no—
423#97—611no—
424#97—612no—
425#97—1222no—
426#97—1222no—
427#97—1221no—
428#97C22×D6111yescharacteristic
429#97C22×D6112yes—
430#97C22×D6111yescharacteristic
431C4×C8—21no—
432C4×C8—21no—
433C4×C8—1222no—
434#41—1224no—
435#41—2444no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—611no—
439C2×Q8—611no—
440C2×D4—612no—
441C2×D4—611no—
442C2×D4—611no—
443C2×D4—1222no—
444C2×D4—1221no—
445C22×C4—612no—
446C22×C4—612no—
447C22×C4—612no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1221no—
452C22×C4C2×C4×D6111yescharacteristic
453C22×C4D4×D6111yescharacteristic
454C22×C4D4×D6111yescharacteristic
455M16—24no—
456M16—42no—
457M16—1228no—
458C2×C8—22no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—1228no—
462C2×C8—1224no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1222no—
466C2×C8—2444no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—611no—
472C4⋊C4—612no—
473C4⋊C4—612no—
474C4⋊C4—611no—
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1222no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4C2×C4×D6112yes—
490C4⋊C4C2×C4×D6112yes—
491C22⋊C4—22no—
492C22⋊C4—612no—
493C22⋊C4—612no—
494C22⋊C4—612no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C42—22no—
504C42—612no—
505C42—612no—
506C42—612no—
507C42—1222no—
508C42—1221no—
509C42C2×C4×D6111yescharacteristic
510C42D4×D6111yescharacteristic
511C42D4×D6111yescharacteristic
512C42C23×D6111yescharacteristic
513C23—612no—
514C23—1221no—
515C23C22⋊C4×D6111yescharacteristic
516Q8—42no—
517Q8—81no—
518Q8—1222no—
519Q8—2441no—
520D4—614no—
521D4—1224no—
522D4—4881no—
523D4—2441no—
524D4—2444no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—1224no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—4882no—
538C2×C4—4882no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2444no—
542C2×C4—2442no—
543C2×C4C22⋊C4×D6111yescharacteristic
544C2×C4C22⋊C4×D6111yescharacteristic
545C2×C4C22⋊C4×D6111yescharacteristic
546C2×C4C22×C4×D6111yescharacteristic
547C2×C4C2×D4×D6111yescharacteristic
548C2×C4C2×D4×D6111yescharacteristic
549C8—24no—
550C8—22no—
551C8—41no—
552C8—1222no—
553C8—1222no—
554C8—2442no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—614no—
559C22—1222no—
560C22—1222no—
561C22—2441no—
562C22—2441no—
563C22—2441no—
564C22C2×C22⋊C4×D6111yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—42no—
571C4—42no—
572C4—1222no—
573C4—1222no—
574C4—1222no—
575C4—2441no—
576C4—2441no—
577C4—2441no—
578C4#104×D6112yes—
579C2—41no—
580C2—1224no—
581C2—4881no—
582C2#2145429911yescharacteristic
583C2C2×#104×D6111yescharacteristic
584C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1526C2
socleC22×C61C22×C22⋊C4
prime radical#21459792C2
cosocleC42×C61C24
hypercenter#1526D61
hypocenterC61#17653
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
2. #21454834C2semidirect
3. #21454248C2semidirect
4. #21444438C2semidirect
5. #21444434C2semidirect
6. #21444424C2semidirect
7. #21444419C2semidirect
8. #21444408C2semidirect
9. #21444406C2semidirect
10. #330×D61C2semidirect
11. C61×#1526C2semidirect
294. #1526D61semidirect
345. C61#17653semidirect

Maximal subgroups

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

subgroupindex
#214597922
#214548342
#214542482
#214444382
#214444342
#214444242
#214444192
#214444082
#214444062
#330×D612
C61×#15262
#1765361