Finite Group Databasebeta

← #29648262

Subgroups — #29648262

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459643C211yesmaximal, characteristic
2#21454834C211yesmaximal, characteristic
3#21454831C211yesmaximal, characteristic
4#21444456C211yesmaximal, characteristic, complemented
5#21444444C212yesmaximal, complemented
6#21444432C212yesmaximal, complemented
7#21444432C212yesmaximal, complemented
8#21444421C211yesmaximal, characteristic, complemented
9#21444413C211yesmaximal, characteristic, complemented
10#330×D61C212yesmaximal, complemented
11C61×#1528C211yesmaximal, characteristic, complemented
12#16840489—21no—
13#16840489—21no—
14#16840468—21no—
15#16840468—21no—
16#16840467—22no—
17#16840467—22no—
18#16840393C411yescharacteristic
19#16840393C411yescharacteristic
20#16840392C412yes—
21#16840392C412yes—
22#16840319C2211yescharacteristic
23#16840318C2212yes—
24#125×D61C2212yes—
25#16840243C411yescharacteristic
26#16840243C411yescharacteristic
27C4×#11758222C2211yescharacteristic
28#16839892—21no—
29#16839889—21no—
30#16839836—22no—
31#16839831—22no—
32C8×D244—21no—
33#16839827—21no—
34#16839819C2211yescharacteristic
35#16839817C2212yes—
36#16839817C2212yes—
37C4×#11758194C2211yescharacteristic
38#97×D61C2212yes—
39#97×D61C2212yes—
40#16839504C2212yes—
41#16839504C2212yes—
42#16839503C2211yescharacteristic
43#16839503C2212yes—
44#16839503C2211yescharacteristic
45#16839503C2211yescharacteristic
46#16839503C2211yescharacteristic
47#16839503C2212yes—
48C2×#125×C61C2211yescharacteristic
49C61×#432C2211yescharacteristic
50C4×M16×C61C2211yescharacteristic
51C61×#330C2212yes—
52C61×#330C2212yes—
53C2×#11758222C2×C411yescharacteristic
54C2×#11758194—21no—
55C2×C8×D61—22no—
56C2×C8×D61—22no—
57#14519777C2×C411yescharacteristic
58#14519777C2×C411yescharacteristic
59#14519776—21no—
60#14519776—21no—
61#14519776—22no—
62#14519776—22no—
63#14519776C2×C412yes—
64#14519776C2×C412yes—
65#14519769C2311yescharacteristic
66#14519769C2311yescharacteristic
67#14519768—21no—
68#14519768—21no—
69#14519768C2×C412yes—
70#14519768C2×C412yes—
71#14519767—22no—
72#14519767—22no—
73#14519767—22no—
74#14519767—22no—
75#14519757—22no—
76#14519757—22no—
77#14519756—21no—
78#14519756—21no—
79#14519756—22no—
80#14519756—22no—
81#14519755—22no—
82#14519755—22no—
83#14519755—22no—
84#14519755—22no—
85C4×Dic122—21no—
86C4×Dic122—21no—
87C4×Dic122D411yescharacteristic
88C4×Dic122D411yescharacteristic
89#14519742—21no—
90#14519742—21no—
91#14519742—22no—
92#14519742—22no—
93C4×D244D411yescharacteristic
94C4×D244D411yescharacteristic
95#14519739—21no—
96#14519739—21no—
97C4×C22⋊D61—22no—
98C4×C22⋊D61—22no—
99C4×C22⋊D61D412yes—
100C4×C22⋊D61D412yes—
101#14519736C2×C411yescharacteristic
102#14519736C2×C411yescharacteristic
103#14519736C2×C411yescharacteristic
104#14519735C2×C412yes—
105#14519735C2×C412yes—
106#14519734C2×C412yes—
107C4⋊C4×D61—22no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61C2×C412yes—
110C4⋊C4×D61C2×C412yes—
111C42×D61C2312yes—
112C4⋊#92418—21no—
113#14519706—22no—
114#14519706—22no—
115C22⋊#92418—21no—
116#14519689—22no—
117#14519689—22no—
118#14519688C2311yescharacteristic
119#14519688C2312yes—
120#14519688C2311yescharacteristic
121#14519687—22no—
122#14519687—22no—
123C4×#92418—21no—
124C2×M16×C61—21no—
125#125×C61—21no—
126#125×C61—21no—
127#125×C61C2×C412yes—
128#125×C61C2312yes—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136#97×C61C2311yescharacteristic
137#97×C61C2312yes—
138#97×C61C2311yescharacteristic
139C4×C8×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C2×C22⋊D61C22⋊C412yes—
146#11758222—24no—
147C2×D244C22⋊C411yescharacteristic
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61C22×C412yes—
151C2×C4×D61C2×D412yes—
152C2×C4×D61C2×D412yes—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—22no—
156C2×Dic122—22no—
157C2×Dic122C22⋊C411yescharacteristic
158M16×C61—42no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61C22×C412yes—
169C4⋊C4×C61C22×C412yes—
170C42×C61C22×C411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C42×C61C2×D411yescharacteristic
173C42×C61C2411yescharacteristic
174C22⋊Dic61—21no—
175C22⋊Dic61—21no—
176C22⋊Dic61C22⋊C412yes—
177#11758198—22no—
178#11758198—22no—
179#11758198C22⋊C412yes—
180#11758198C22⋊C412yes—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61C22⋊C411yescharacteristic
186C4⋊Dic61C22⋊C411yescharacteristic
187C4⋊Dic61C22×C411yescharacteristic
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190C4⋊Dic61C22×C411yescharacteristic
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196C22⋊C412yes—
202#11758196C22⋊C412yes—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61C22×C412yes—
208C4×Dic61C2×D412yes—
209C4×Dic61C2×D412yes—
210#11758194—42no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—22no—
214C8×D61—44no—
215C8×D61—44no—
216C23×C61C2×C22⋊C411yescharacteristic
217C22×D61C2×C22⋊C412yes—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—81no—
224C2×C4×C61—81no—
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C22⋊D61—24no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61C2×C22⋊C412yes—
237C2×Dic61C2×C22⋊C412yes—
238C2×Dic61C2×C22⋊C412yes—
239D244#10114yes—
240C4×D61—24no—
241C4×D61—42no—
242C4×D61—42no—
243C4×D61—82no—
244C4×D61—82no—
245Dic122—22no—
246Dic122—82no—
247Dic122—82no—
248Dic122—81no—
249Dic122—81no—
250C8×C61—22no—
251C8×C61—42no—
252C8×C61—41no—
253#92418—22no—
254#92418—42no—
255#92418—41no—
256#17689—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61C22×C22⋊C411yescharacteristic
261C2×D61—22no—
262C2×D61—22no—
263C2×D61C2×#10114yes—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—42no—
270C4×C61—42no—
271C4×C61C2×#10112yes—
272Dic61—22no—
273Dic61—22no—
274Dic61—22no—
275Dic61—41no—
276Dic61—41no—
277Dic61—41no—
278Dic61—41no—
279#3504—611no—
280#2970—611no—
281#2970—611no—
282#1537—611no—
283#1534—612no—
284#1531—612no—
285#1531—612no—
286#1528—611no—
287#1528D6111yescharacteristic, complemented
288#1526—611no—
289C2×#330—612no—
290C2×C61—41no—
291C2×C61C22×#10111yescharacteristic
292C2×C61#290111yescharacteristic
293C2×C61#290111yescharacteristic
294D61—24no—
295#557—1221no—
296#557—1221no—
297#554—1222no—
298#554—1222no—
299#554—1221no—
300#554—1221no—
301#544—612no—
302#544—612no—
303#544—611no—
304#544—611no—
305#533—612no—
306#533—611no—
307C2×#125—612no—
308C2×#125C2×D6111yescharacteristic
309#520—611no—
310#520—611no—
311C4×#41—611no—
312#446—1221no—
313#446—1221no—
314#435—1222no—
315#435—1222no—
316C8×D4—1221no—
317C8×D4—1221no—
318#432—611no—
319#432—612no—
320#432—612no—
321#432C2×D6111yescharacteristic
322C4×M16—611no—
323C4×M16C2×D6111yescharacteristic
324C2×#97—612no—
325C2×#97—612no—
326#330—612no—
327#330—612no—
328#330—612no—
329#330—612no—
330#330—611no—
331#330—611no—
332#330—611no—
333#330—611no—
334#330C2×D6112yes—
335#330C2×D6112yes—
336C61#1768911yescharacteristic, complemented, Sylow
337C2×#41—611no—
338C2×M16—21no—
339C2×M16—1221no—
340C22×C8—1222no—
341C22×C8—1222no—
342C4⋊Q8—612no—
343C4⋊Q8—612no—
344C4⋊Q8—611no—
345C4⋊Q8—611no—
346C4⋊Q8—1222no—
347C4⋊Q8—1222no—
348C4⋊Q8—1221no—
349C4⋊Q8—1221no—
350#125—21no—
351#125—21no—
352#125—612no—
353#125—612no—
354#125—611no—
355#125—611no—
356#125—1222no—
357#125—1222no—
358#125—1222no—
359#125—1222no—
360#125—1221no—
361#125—1221no—
362#125C4×D6112yes—
363#125C22×D6112yes—
364C22⋊Q8—1222no—
365C22⋊Q8—1222no—
366C22⋊Q8—1222no—
367C22⋊Q8—1222no—
368C22⋊Q8—1222no—
369C22⋊Q8—1222no—
370C22⋊Q8—1222no—
371C22⋊Q8—1222no—
372C22⋊Q8—1221no—
373C22⋊Q8—1221no—
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8—1222no—
377C4×Q8—1222no—
378C4×Q8—1221no—
379C4×Q8—1221no—
380C4×Q8—1221no—
381C4×Q8—1221no—
382C4×D4—612no—
383C4×D4—612no—
384C4×D4—611no—
385C4×D4—611no—
386C4×D4—1221no—
387C4×D4—1221no—
388C4×D4—1222no—
389C4×D4—1222no—
390#117—611no—
391#117—612no—
392#117—611no—
393#117—611no—
394#117—612no—
395#117—612no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1222no—
402C2×C4⋊C4C4×D6111yescharacteristic
403C2×C4⋊C4C4×D6111yescharacteristic
404C2×C42—612no—
405C2×C42C22×D6111yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—1222no—
408C4⋊C8—1222no—
409C4⋊C8—1221no—
410C22⋊C8—21no—
411C22⋊C8—1222no—
412C22⋊C8—1222no—
413C22⋊C8—1221no—
414#97—611no—
415#97—612no—
416#97—611no—
417#97—1222no—
418#97—1222no—
419#97C22×D6111yescharacteristic
420#97C22×D6112yes—
421#97C22×D6111yescharacteristic
422C4×C8—21no—
423C4×C8—1221no—
424#41—1224no—
425C2×Q8—611no—
426C2×Q8—1222no—
427C2×Q8—1222no—
428C2×Q8—1221no—
429C2×Q8—1221no—
430C2×D4—612no—
431C2×D4—611no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—612no—
435C22×C4—612no—
436C22×C4—612no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4C2×C4×D6111yescharacteristic
440C22×C4D4×D6111yescharacteristic
441C22×C4D4×D6111yescharacteristic
442M16—42no—
443M16—2442no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—22no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1222no—
450C2×C8—2444no—
451C2×C8—2444no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—612no—
459C4⋊C4—612no—
460C4⋊C4—611no—
461C4⋊C4—611no—
462C4⋊C4—611no—
463C4⋊C4—611no—
464C4⋊C4—611no—
465C4⋊C4—611no—
466C4⋊C4—1222no—
467C4⋊C4—1222no—
468C4⋊C4—1222no—
469C4⋊C4—1222no—
470C4⋊C4—1222no—
471C4⋊C4—1222no—
472C4⋊C4—1222no—
473C4⋊C4—1222no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4C2×C4×D6112yes—
481C4⋊C4C2×C4×D6112yes—
482C22⋊C4—612no—
483C22⋊C4—612no—
484C22⋊C4—612no—
485C22⋊C4—1222no—
486C22⋊C4—1222no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C42—612no—
490C42—612no—
491C42—612no—
492C42—1222no—
493C42—1222no—
494C42—1221no—
495C42—1221no—
496C42C2×C4×D6111yescharacteristic
497C42D4×D6111yescharacteristic
498C42D4×D6111yescharacteristic
499C42C23×D6111yescharacteristic
500C23—612no—
501C23C22⋊C4×D6111yescharacteristic
502Q8—1222no—
503Q8—4881no—
504Q8—4881no—
505Q8—4882no—
506Q8—4882no—
507D4—614no—
508D4—1224no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—81no—
515C2×C4—81no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—1224no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—4882no—
525C2×C4—4882no—
526C2×C4—2442no—
527C2×C4—2442no—
528C2×C4C22⋊C4×D6111yescharacteristic
529C2×C4C22⋊C4×D6111yescharacteristic
530C2×C4C22⋊C4×D6111yescharacteristic
531C2×C4C22×C4×D6111yescharacteristic
532C2×C4C2×D4×D6111yescharacteristic
533C2×C4C2×D4×D6111yescharacteristic
534C8—22no—
535C8—42no—
536C8—41no—
537C8—1222no—
538C8—2442no—
539C8—2441no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—614no—
544C22—1222no—
545C22—1222no—
546C22C2×C22⋊C4×D6111yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—42no—
554C4—1222no—
555C4—1222no—
556C4—1222no—
557C4—2441no—
558C4—2441no—
559C4—2441no—
560C4—2441no—
561C4#101×D6112yes—
562C2—41no—
563C2—1224no—
564C2C2×#101×D6111yescharacteristic
565C2#2145436311yescharacteristic
566C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1528C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenter#1528D61
hypocenterC61#17689
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
4. #21444456C2semidirect
5. #21444444C2semidirect
6. #21444432C2semidirect
7. #21444432C2semidirect
8. #21444421C2semidirect
9. #21444413C2semidirect
10. #330×D61C2semidirect
11. C61×#1528C2semidirect
287. #1528D61semidirect
336. C61#17689semidirect

Maximal subgroups

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

subgroupindex
#214596432
#214548342
#214548312
#214444562
#214444442
#214444322
#214444212
#214444132
#330×D612
C61×#15282
#1768961