Finite Group Databasebeta

← #29667600

Subgroups — #29667600

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457158C211yesmaximal, characteristic
2#21457039C211yesmaximal, characteristic
3#21456959C211yesmaximal, characteristic, complemented
4#21454980C211yesmaximal, characteristic
5#21445400C211yesmaximal, characteristic, complemented
6#21445328C211yesmaximal, characteristic, complemented
7#21445318C211yesmaximal, characteristic, complemented
8#21445274C211yesmaximal, characteristic, complemented
9#21445268C211yesmaximal, characteristic, complemented
10#21445202C211yesmaximal, characteristic, complemented
11#21445196C211yesmaximal, characteristic, complemented
12#21444601C211yesmaximal, characteristic, complemented
13#21444518C211yesmaximal, characteristic, complemented
14#333×D61C211yesmaximal, characteristic, complemented
15C61×#1703C211yesmaximal, characteristic, complemented
16#16840317C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18#16840294C2211yescharacteristic
19#16840169—21no—
20#16840160C2211yescharacteristic
21#16840158C2211yescharacteristic
22#16840120—21no—
23#16840112C2211yescharacteristic
24#16840094—21no—
25#16840091—21no—
26#16840091—21no—
27#16840074—21no—
28#16840068—21no—
29#16840058C2211yescharacteristic
30#16840054C2211yescharacteristic
31#16840052C2211yescharacteristic
32#16840045—21no—
33#16840045—21no—
34#16840044C2211yescharacteristic
35#16840004—21no—
36#16839990—21no—
37#16839983—21no—
38#16839973C2211yescharacteristic
39#16839967C2211yescharacteristic
40#16839889C2211yescharacteristic
41C8×Dic122C2211yescharacteristic
42#16839831—21no—
43D4×#92418C2211yescharacteristic
44#16839825—21no—
45#16839820—21no—
46#16839818C2211yescharacteristic
47#16839813C2211yescharacteristic
48#16839790—21no—
49C4⋊C8×D61C2211yescharacteristic
50C4⋊C8×D61C2211yescharacteristic
51#16839515C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839508C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#476C2211yescharacteristic
62C61×#474C2211yescharacteristic
63C61×#436C2211yescharacteristic
64C61×#334C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Dic244—21no—
69C2×#11758200—21no—
70C22×#92418—21no—
71C2×C8×D61—21no—
72C2×C8×D61—21no—
73#14519777C2311yescharacteristic
74#14519777C2311yescharacteristic
75#14519776—21no—
76#14519776—21no—
77#14519775—21no—
78#14519770—21no—
79#14519768—21no—
80#14519768D411yescharacteristic
81#14519764D411yescharacteristic
82#14519759—21no—
83#14519757—21no—
84#14519757D411yescharacteristic
85#14519753—21no—
86#14519748D411yescharacteristic
87Q8×Dic61—21no—
88C4×Dic122C2311yescharacteristic
89#14519742—21no—
90C4×C22⋊D61—21no—
91#14519736—21no—
92#14519735—21no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61—21no—
95C42×D61C2311yescharacteristic
96#14519711—21no—
97#14519710—21no—
98#14519709—21no—
99#14519709—21no—
100#14519708—21no—
101#14519708—21no—
102#14519708—21no—
103#14519708—21no—
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519706D411yescharacteristic
112#14519706D411yescharacteristic
113#14519702—21no—
114#14519702—21no—
115#14519701—21no—
116#14519701—21no—
117#14519700—21no—
118#14519700—21no—
119#14519700—21no—
120#14519698—21no—
121C22⋊#92418—21no—
122#14519689—21no—
123#14519689D411yescharacteristic
124#14519689D411yescharacteristic
125#14519687—21no—
126#14519687—21no—
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×M16×C61—21no—
130C4⋊Q8×C61C2311yescharacteristic
131C4⋊Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#107×C61—21no—
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×D4×C61C2×D411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149Q8×D61—82no—
150C2×C4×D61—41no—
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61#4111yescharacteristic
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—41no—
157C2×Dic122C2×D411yescharacteristic
158M16×C61—81no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61C2×D411yescharacteristic
169C22⋊C4×C61—21no—
170C42×C61C2411yescharacteristic
171C22⋊Dic61—21no—
172C22⋊Dic61—21no—
173C22⋊Dic61—21no—
174#11758200—81no—
175#11758198—21no—
176#11758198—41no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—41no—
184C4⋊Dic61C2×D411yescharacteristic
185#11758196—21no—
186#11758196—21no—
187#11758196—41no—
188#11758196—41no—
189#11758196—41no—
190C4×Dic61—21no—
191C4×Dic61—41no—
192C4×Dic61C2×D411yescharacteristic
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61#4111yescharacteristic
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—81no—
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201Dic244—81no—
202C8×D61—81no—
203C8×D61—81no—
204C23×C61—21no—
205C22×D61#12111yescharacteristic
206Q8×C61—41no—
207Q8×C61—41no—
208Q8×C61—81no—
209D4×C61—21no—
210D4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C22⋊D61—42no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61#12111yescharacteristic
225C2×Dic61#12111yescharacteristic
226C2×Dic61#12111yescharacteristic
227C4×D61—22no—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—82no—
233Dic122—21no—
234Dic122—21no—
235Dic122—41no—
236Dic122—41no—
237Dic122—82no—
238Dic122—81no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—41no—
242C8×C61—41no—
243C8×C61—41no—
244#92418—21no—
245#92418—21no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#19588—611nomaximal, Sylow
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61C2×#12111yescharacteristic
254C2×D61—21no—
255C2×D61—21no—
256C2×D61#47112yes—
257C4×C61—21no—
258C4×C61—41no—
259C4×C61—81no—
260C4×C61—81no—
261C4×C61#57711yescharacteristic
262C4×C61#57711yescharacteristic
263C4×C61#57811yescharacteristic
264C4×C61#57811yescharacteristic
265Dic61—21no—
266Dic61—21no—
267Dic61—21no—
268Dic61—41no—
269Dic61—41no—
270Dic61—81no—
271Dic61—81no—
272#3248—611no—
273#3238—611no—
274#3229—611no—
275#2994—611no—
276#1704—611no—
277#1703D6111yescharacteristic, complemented
278#1692—611no—
279#1691—611no—
280#1684—611no—
281#1683—611no—
282#1672—611no—
283#1671—611no—
284#1573—611no—
285#1552—611no—
286C2×#333—611no—
287C2×C61—81no—
288C2×C61#304611yescharacteristic
289C2×C61#306311yescharacteristic
290C2×C61C2×#47111yescharacteristic
291D61—22no—
292#533—611no—
293C2×C4⋊Q8—611no—
294#529—611no—
295#501—1221no—
296#498—611no—
297#498—611no—
298#489—1221no—
299#487—611no—
300#487C2×D6111yescharacteristic
301#483—1221no—
302#483—1221no—
303#483—1221no—
304#480—1221no—
305#479—1221no—
306#477—611no—
307#477—611no—
308#476—611no—
309#476C2×D6111yescharacteristic
310#475—611no—
311#475—1221no—
312#475—1221no—
313#474C2×D6111yescharacteristic
314#467—1221no—
315#465—1221no—
316#464—1221no—
317#462—611no—
318#461—611no—
319#446—611no—
320C8×Q8—611no—
321#436C2×D6111yescharacteristic
322#435—1221no—
323C8×D4—611no—
324C8×D4—1221no—
325#433—1221no—
326#432—611no—
327#431—611no—
328#424—1221no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—611no—
331#335—611no—
332#335—611no—
333#334—611no—
334#334C2×D6111yescharacteristic
335#333—611no—
336#333—611no—
337#333—611no—
338#333C2×D6111yescharacteristic
339#332—611no—
340#332—611no—
341#332—611no—
342#332C2×D6111yescharacteristic
343C61#1958811yescharacteristic, complemented, Sylow
344C22×Q8—1221no—
345C2×Q16—1221no—
346C2×SD16—1221no—
347C2×M16—21no—
348C22×C8—1221no—
349C22×C8—1221no—
350C22×C8—1221no—
351C4⋊Q8—611no—
352C4⋊Q8—611no—
353C4⋊Q8—1221no—
354C4⋊Q8—1221no—
355C4⋊Q8—1221no—
356C4⋊Q8C22×D6111yescharacteristic
357C4⋊Q8C22×D6111yescharacteristic
358#126—1221no—
359#125—611no—
360#125—1221no—
361#124—611no—
362#123—1221no—
363C22⋊Q8—611no—
364C22⋊Q8—1221no—
365C22⋊Q8—1221no—
366#121—611no—
367C4×Q8—611no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×D4—1221no—
371C4×D4C22×D6111yescharacteristic
372#117—1221no—
373#117—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C42—611no—
377#107—21no—
378#107—1221no—
379#107—1221no—
380#106—21no—
381#106—1221no—
382#106—1221no—
383#106—1221no—
384#106—1221no—
385#106—1221no—
386#106—1221no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398C4⋊C8C22×D6111yescharacteristic
399#103—21no—
400#103—21no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#102—21no—
409#102—21no—
410#102—1221no—
411C22⋊C8—21no—
412C22⋊C8—611no—
413C22⋊C8—611no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416#97—1221no—
417#97—1221no—
418C4×C8—611no—
419C4×C8—1221no—
420C4×C8C22×D6111yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—611no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—4882no—
427C2×Q8—2441no—
428C2×D4—1221no—
429C2×D4D4×D6111yescharacteristic
430C22×C4—21no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—2441no—
435Q16—4881no—
436SD16—4881no—
437M16—81no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—611no—
442C2×C8—611no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8—4881no—
447C2×C8—4881no—
448C2×C8—4881no—
449C2×C8D4×D6111yescharacteristic
450C2×C8D4×D6111yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—611no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—2441no—
465C4⋊C4—2441no—
466C4⋊C4—2441no—
467C4⋊C4—2441no—
468C4⋊C4D4×D6111yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—1221no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—2441no—
475C42—611no—
476C42—611no—
477C42—611no—
478C42—1221no—
479C42—2441no—
480C42C23×D6111yescharacteristic
481C23—21no—
482C23—611no—
483Q8—41no—
484Q8—41no—
485Q8—81no—
486Q8—1221no—
487Q8—1221no—
488Q8—4881no—
489Q8—4882no—
490Q8—2441no—
491Q8—2441no—
492D4—21no—
493D4—21no—
494D4—2442no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—611no—
501C2×C4—611no—
502C2×C4—611no—
503C2×C4—1222no—
504C2×C4—1221no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—4882no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4C2×D4×D6111yescharacteristic
515C2×C4#41×D6111yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—1221no—
522C8—1221no—
523C8—2441no—
524C8—2441no—
525C8—2441no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—612no—
530C22—1221no—
531C22—1221no—
532C22#121×D6111yescharacteristic
533C4—21no—
534C4—41no—
535C4—81no—
536C4—81no—
537C4—1221no—
538C4—1221no—
539C4—1221no—
540C4—4881no—
541C4—4881no—
542C4—2441no—
543C4—2441no—
544C4#1684057111yescharacteristic
545C4#1684057211yescharacteristic
546C4#1684057611yescharacteristic
547C4#1684057811yescharacteristic
548C2—81no—
549C2—1222no—
550C2#2145537011yescharacteristic
551C2#2145550711yescharacteristic
552C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1703C2
socleC22×C61C2×#121
prime radical#14519748D4
hypercenter#1703D61
hypocenterC61#19588
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1703

Complements

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

NH ≅ G/Ntype
3. #21456959C2semidirect
5. #21445400C2semidirect
6. #21445328C2semidirect
7. #21445318C2semidirect
8. #21445274C2semidirect
9. #21445268C2semidirect
10. #21445202C2semidirect
11. #21445196C2semidirect
12. #21444601C2semidirect
13. #21444518C2semidirect
14. #333×D61C2semidirect
15. C61×#1703C2semidirect
277. #1703D61semidirect
343. C61#19588semidirect

Maximal subgroups

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

subgroupindex
#214571582
#214570392
#214569592
#214549802
#214454002
#214453282
#214453182
#214452742
#214452682
#214452022
#214451962
#214446012
#214445182
#333×D612
C61×#17032
#1958861