Finite Group Databasebeta

← #29663311

Subgroups — #29663311

Order 15616.

582 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456969C211yesmaximal, characteristic
2#21456962C211yesmaximal, characteristic
3#487×D61C211yesmaximal, characteristic
4#21454748C211yesmaximal, characteristic
5#21445404C211yesmaximal, characteristic, complemented
6#21445403C211yesmaximal, characteristic, complemented
7#21445400C211yesmaximal, characteristic, complemented
8#21445399C211yesmaximal, characteristic, complemented
9#21445278C211yesmaximal, characteristic, complemented
10#21445277C211yesmaximal, characteristic, complemented
11#21445274C211yesmaximal, characteristic, complemented
12#21444566C211yesmaximal, characteristic
13#21444498C211yesmaximal, characteristic
14#21444489C211yesmaximal, characteristic
15C61×#1684C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19#16840166—21no—
20#16840159—21no—
21#16840114C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840111—21no—
25#16840111—21no—
26#16840111—21no—
27#16840111—21no—
28#16840099—21no—
29#16840096—21no—
30#16840094—21no—
31#16840091—21no—
32#16840058C2211yescharacteristic
33#16840057C2211yescharacteristic
34#16840054C2211yescharacteristic
35#16840048C2211yescharacteristic
36#16840047C2211yescharacteristic
37#16840044C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839891—21no—
40#16839889C2211yescharacteristic
41C8×Dic122—21no—
42C8×Dic122C2211yescharacteristic
43#16839814C2211yescharacteristic
44#16839814C2211yescharacteristic
45#16839787—21no—
46#16839784C2211yescharacteristic
47#103×D61—21no—
48#103×D61—21no—
49#16839716—21no—
50C4×C8×D61C2211yescharacteristic
51#16839515C2211yescharacteristic
52#16839512C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839508C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#477C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×#11758189—21no—
70C2×C8×D61D411yescharacteristic
71C2×C8×D61D411yescharacteristic
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519776—21no—
75#14519776—21no—
76#14519776—21no—
77#14519776—21no—
78#14519776D411yescharacteristic
79#14519775—21no—
80#14519775—21no—
81#14519775D411yescharacteristic
82#14519767—21no—
83#14519757D411yescharacteristic
84#14519755—21no—
85#14519753D411yescharacteristic
86C4×Dic122—21no—
87C4×Dic122C2311yescharacteristic
88#14519734—21no—
89C4⋊C4×D61—21no—
90C4⋊C4×D61—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C42×D61C2311yescharacteristic
94#14519711—21no—
95#14519710—21no—
96#14519710—21no—
97#14519709—21no—
98#14519708—21no—
99#14519708—21no—
100C4⋊#92418—21no—
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519702—21no—
108#14519702—21no—
109#14519702—21no—
110#14519702—21no—
111#14519701—21no—
112#14519701—21no—
113#14519701—21no—
114#14519701—21no—
115#14519700—21no—
116#14519700—21no—
117#14519700—21no—
118#14519700—21no—
119#14519689—21no—
120#14519689—21no—
121#14519688—21no—
122#14519687—21no—
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C4⋊Q8×C61C2311yescharacteristic
130C4⋊Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61—21no—
133#106×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147Q8×D61—42no—
148Q8×D61—42no—
149Q8×D61—82no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61#4111yescharacteristic
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—41no—
159C2×Dic122—41no—
160C2×Dic122C2×D411yescharacteristic
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61C2×D411yescharacteristic
172C42×C61—21no—
173C42×C61C2411yescharacteristic
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61C2×D411yescharacteristic
182#11758196—21no—
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—41no—
188#11758196—41no—
189#11758196—41no—
190#11758196—41no—
191C4×Dic61—21no—
192C4×Dic61C2×D411yescharacteristic
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61#4111yescharacteristic
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200#11758189—42no—
201C8×D61—22no—
202C8×D61—22no—
203C22×D61#12111yescharacteristic
204Q8×C61—21no—
205Q8×C61—21no—
206Q8×C61—41no—
207Q8×C61—41no—
208Q8×C61—81no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61C22×D411yescharacteristic
214C2×C4×C61C22×D411yescharacteristic
215C2×C4×C61C2×#4111yescharacteristic
216C2×Dic61—21no—
217C2×Dic61—21no—
218C2×Dic61—41no—
219C2×Dic61—41no—
220C2×Dic61#12111yescharacteristic
221C2×Dic61#12111yescharacteristic
222C2×Dic61#12111yescharacteristic
223C4×D61—21no—
224C4×D61—21no—
225C4×D61—22no—
226C4×D61—82no—
227C4×D61—82no—
228C4×D61#13512yes—
229C4×D61#13712yes—
230Dic122—21no—
231Dic122—21no—
232Dic122—42no—
233Dic122—41no—
234Dic122—41no—
235Dic122—82no—
236Dic122—82no—
237Dic122—81no—
238C8×C61—21no—
239C8×C61—21no—
240C8×C61—41no—
241C8×C61—41no—
242C8×C61—41no—
243#92418—21no—
244#92418—21no—
245#92418—41no—
246#92418—41no—
247#92418—41no—
248#19215—611nomaximal, Sylow
249C22×C61C2×#12111yescharacteristic
250C2×D61—21no—
251C2×D61—21no—
252C2×D61#46412yes—
253C4×C61—21no—
254C4×C61—41no—
255C4×C61—41no—
256C4×C61—81no—
257C4×C61—81no—
258C4×C61C2×#13511yescharacteristic
259C4×C61C2×#13711yescharacteristic
260C4×C61#57811yescharacteristic
261C4×C61#57811yescharacteristic
262Dic61—21no—
263Dic61—41no—
264Dic61—41no—
265Dic61—81no—
266Dic61—81no—
267Dic61#46412yes—
268Dic61#47112yes—
269#3230—611no—
270#3229—611no—
271C2×#487—611no—
272#2960—611no—
273#1704—611no—
274#1704—611no—
275#1704—611no—
276#1704—611no—
277#1684—611no—
278#1684—611no—
279#1684—611no—
280#1684D6111yescharacteristic, complemented
281#1564—611no—
282#1548—611no—
283#1546—611no—
284C2×C61C2×#46411yescharacteristic
285C2×C61#305911yescharacteristic
286C2×C61C2×#47111yescharacteristic
287D61—22no—
288#533—611no—
289C2×C4⋊Q8—611no—
290C2×C4⋊Q8—611no—
291#500—1221no—
292#498—1221no—
293#487—611no—
294#487—611no—
295#487—611no—
296#487—1221no—
297#487—1221no—
298#487—1221no—
299#487—1221no—
300#487C2×D6111yescharacteristic
301#484—1221no—
302#484—1221no—
303#483—1221no—
304#483—1221no—
305#477—611no—
306#477—611no—
307#477—611no—
308#477C2×D6111yescharacteristic
309#475—611no—
310#475—611no—
311#475—611no—
312#475C2×D6111yescharacteristic
313#446—611no—
314#446—611no—
315#446—1221no—
316C8×Q8—611no—
317C8×Q8—1221no—
318C8×Q8C2×D6111yescharacteristic
319#431—611no—
320#431—611no—
321#424—1221no—
322#423—611no—
323C2×#103—1221no—
324C2×#103—1221no—
325#405—1221no—
326C2×C4×C8—611no—
327#335—611no—
328#335C2×D6111yescharacteristic
329#334—611no—
330#334—611no—
331#333—611no—
332#333—611no—
333#333—611no—
334#333C2×D6111yescharacteristic
335#332—611no—
336#332—611no—
337#332—611no—
338#332C2×D6111yescharacteristic
339C61#1921511yescharacteristic, complemented, Sylow
340C22×Q8—1221no—
341C22×Q8—1221no—
342C2×M16—1221no—
343C22×C8—611no—
344C22×C8—611no—
345C4⋊Q8—611no—
346C4⋊Q8—611no—
347C4⋊Q8—611no—
348C4⋊Q8—611no—
349C4⋊Q8—1221no—
350C4⋊Q8—1221no—
351C4⋊Q8—1221no—
352C4⋊Q8—1221no—
353C4⋊Q8—1221no—
354C4⋊Q8—1221no—
355C4⋊Q8C22×D6111yescharacteristic
356C4⋊Q8C22×D6111yescharacteristic
357#125—1221no—
358C22⋊Q8—611no—
359C22⋊Q8—611no—
360C22⋊Q8—1221no—
361C4×Q8—611no—
362C4×Q8—1221no—
363C4×Q8C22×D6111yescharacteristic
364#117—1221no—
365C2×C4⋊C4—1221no—
366C2×C4⋊C4—1221no—
367C2×C4⋊C4—1221no—
368C2×C4⋊C4—1221no—
369C2×C42—611no—
370#107—21no—
371#107—1221no—
372#107—1221no—
373#107—1221no—
374#106—21no—
375#106—1221no—
376#106—1221no—
377#106—1221no—
378C4⋊C8—21no—
379C4⋊C8—611no—
380C4⋊C8—611no—
381C4⋊C8—611no—
382C4⋊C8—1221no—
383C4⋊C8—1221no—
384C4⋊C8—1221no—
385C4⋊C8—1221no—
386C4⋊C8C22×D6111yescharacteristic
387C4⋊C8C22×D6111yescharacteristic
388C4⋊C8C22×D6111yescharacteristic
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—1221no—
394#103—1221no—
395#103—1221no—
396#103—1221no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407#97—1221no—
408#97—1221no—
409C4×C8—21no—
410C4×C8—611no—
411C4×C8—611no—
412C4×C8—611no—
413C4×C8—1221no—
414C4×C8—1221no—
415C4×C8—1221no—
416C4×C8C22×D6111yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—611no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—4882no—
424C2×Q8—2441no—
425C2×Q8—2441no—
426C2×Q8—2442no—
427C2×Q8—2442no—
428C2×Q8D4×D6111yescharacteristic
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—2441no—
433C22×C4—2441no—
434M16—2442no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—611no—
439C2×C8—611no—
440C2×C8—1222no—
441C2×C8—1222no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8D4×D6111yescharacteristic
446C2×C8D4×D6111yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—2441no—
464C4⋊C4—2441no—
465C4⋊C4—2441no—
466C4⋊C4—2441no—
467C4⋊C4D4×D6111yescharacteristic
468C22⋊C4—1221no—
469C22⋊C4—1221no—
470C42—21no—
471C42—611no—
472C42—611no—
473C42—611no—
474C42—1221no—
475C42C23×D6111yescharacteristic
476C23—611no—
477Q8—21no—
478Q8—21no—
479Q8—41no—
480Q8—41no—
481Q8—81no—
482Q8—1221no—
483Q8—1221no—
484Q8—4881no—
485Q8—4882no—
486Q8—4882no—
487Q8—2442no—
488Q8—2441no—
489Q8—2441no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—611no—
495C2×C4—611no—
496C2×C4—612no—
497C2×C4—612no—
498C2×C4—611no—
499C2×C4—1222no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—4882no—
505C2×C4—4882no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4C2×D4×D6111yescharacteristic
509C2×C4C2×D4×D6111yescharacteristic
510C2×C4#41×D6111yescharacteristic
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—1221no—
517C8—1221no—
518C8—2441no—
519C8—2441no—
520C8—2441no—
521C22—612no—
522C22—1221no—
523C22—1221no—
524C22#121×D6111yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—81no—
529C4—81no—
530C4—612no—
531C4—612no—
532C4—1221no—
533C4—4881no—
534C4—4881no—
535C4—2441no—
536C4—2441no—
537C4#135×D6111yescharacteristic
538C4#137×D6111yescharacteristic
539C4#1684057511yescharacteristic
540C4#1684057611yescharacteristic
541C2—1222no—
542C2#464×D6111yescharacteristic
543C2#2145546911yescharacteristic
544C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1684C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1684D61
hypocenterC61#19215
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1684

Complements

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

NH ≅ G/Ntype
5. #21445404C2semidirect
6. #21445403C2semidirect
7. #21445400C2semidirect
8. #21445399C2semidirect
9. #21445278C2semidirect
10. #21445277C2semidirect
11. #21445274C2semidirect
15. C61×#1684C2semidirect
280. #1684D61semidirect
339. C61#19215semidirect

Maximal subgroups

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

subgroupindex
#214569692
#214569622
#487×D612
#214547482
#214454042
#214454032
#214454002
#214453992
#214452782
#214452772
#214452742
#214445662
#214444982
#214444892
C61×#16842
#1921561