Finite Group Databasebeta

← #29665124

Subgroups — #29665124

Order 15616.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457186C211yesmaximal, characteristic
2#21457049C211yesmaximal, characteristic
3#21454823C211yesmaximal, characteristic
4#21445398C211yesmaximal, characteristic, complemented
5#21445391C211yesmaximal, characteristic, complemented
6#21445370C211yesmaximal, characteristic, complemented
7#21445363C211yesmaximal, characteristic, complemented
8#21445274C211yesmaximal, characteristic, complemented
9#21445267C211yesmaximal, characteristic, complemented
10#21445246C211yesmaximal, characteristic, complemented
11#21445239C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444529C211yesmaximal, characteristic, complemented
14#21444504C211yesmaximal, characteristic, complemented
15C61×#3139C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840168—21no—
18#16840124—21no—
19#16840097—21no—
20#16840080—21no—
21#16840069—21no—
22#16840054C2211yescharacteristic
23#16840049C2211yescharacteristic
24#16840044C2211yescharacteristic
25#16840044C2211yescharacteristic
26#16840039C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840018—21no—
29#16840010—21no—
30#16839984—21no—
31#16839969C2211yescharacteristic
32#16839964C2211yescharacteristic
33#16839892C2211yescharacteristic
34C8×Dic122C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839838—21no—
37#16839831—21no—
38C8×D244C2211yescharacteristic
39#16839824—21no—
40#16839819C2211yescharacteristic
41#16839815C2211yescharacteristic
42#16839786C2211yescharacteristic
43#16839719—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839508C2211yescharacteristic
55#16839508C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C61×#491—21no—
59C61×#491—21no—
60C61×#487C2211yescharacteristic
61C61×#487C2211yescharacteristic
62C61×#487C2211yescharacteristic
63C61×#487C2211yescharacteristic
64C61×#419—21no—
65C61×#419—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758201—21no—
69C2×#11758194—21no—
70C2×#11758189—21no—
71C2×C8×D61—21no—
72#14519771—21no—
73#14519769D411yescharacteristic
74#14519765D411yescharacteristic
75#14519760—21no—
76#14519756D411yescharacteristic
77#14519751D411yescharacteristic
78C4×Dic122C2311yescharacteristic
79C4×D244C2311yescharacteristic
80C4×C22⋊D61—21no—
81#14519734—21no—
82#14519710—21no—
83#14519710—21no—
84#14519710—21no—
85#14519708—21no—
86#14519708—21no—
87#14519708—21no—
88C4⋊#92418—21no—
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519706—21no—
97#14519701—21no—
98#14519701—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105C22⋊#92418—21no—
106C22⋊#92418—21no—
107#14519689—21no—
108#14519689—21no—
109#14519688—21no—
110#14519687—21no—
111C4×#92418—21no—
112C8×Dic61—21no—
113C22×Q8×C61—21no—
114C2×M16×C61D411yescharacteristic
115C2×M16×C61D411yescharacteristic
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#125×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128#117×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#103×C61—21no—
133#103×C61—21no—
134#103×C61—21no—
135#103×C61—21no—
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#97×C61D411yescharacteristic
141#97×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—42no—
149C2×Q8×C61—42no—
150C2×Q8×C61—41no—
151C22×C4×C61—41no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—21no—
156C2×D244C2×D411yescharacteristic
157C2×C4×D61—21no—
158C2×Dic122C2×D411yescharacteristic
159M16×C61—41no—
160M16×C61—41no—
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C22⋊C4×C61—41no—
178C42×C61—41no—
179C42×C61C2×D411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61#4111yescharacteristic
182C42×C61C2411yescharacteristic
183C22⋊Dic61—21no—
184#11758202—81no—
185#11758201—81no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190C4⋊Dic61C2×D411yescharacteristic
191C4⋊Dic61C2×D411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196C4×Dic61—21no—
197#11758194—81no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204#11758189—42no—
205C8×D61—42no—
206C23×C61#12111yescharacteristic
207C22×D61—21no—
208Q8×C61—41no—
209Q8×C61—41no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—82no—
215Q8×C61—81no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—82no—
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C22⋊D61—81no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236D244—21no—
237D244—21no—
238C4×D61—41no—
239C4×D61—41no—
240Dic122—21no—
241Dic122—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#19381—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61C2×#12111yescharacteristic
257C2×D61—41no—
258C2×D61—41no—
259C2×D61—41no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—81no—
265C4×C61—81no—
266C4×C61—81no—
267C4×C61—81no—
268C4×C61#57511yescharacteristic
269C4×C61#57511yescharacteristic
270C4×C61#57711yescharacteristic
271C4×C61#57811yescharacteristic
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275#3252—611no—
276#3239—611no—
277#3139D6111yescharacteristic, complemented
278#2969—611no—
279#1704—611no—
280#1703—611no—
281#1700—611no—
282#1699—611no—
283#1684—611no—
284#1683—611no—
285#1680—611no—
286#1679—611no—
287#1569—611no—
288#1554—611no—
289#1549—611no—
290C2×C61—41no—
291C2×C61#304011yescharacteristic
292C2×C61#306311yescharacteristic
293C2×C61#306911yescharacteristic
294D61—81no—
295#533C2×D6111yescharacteristic
296C2×C4⋊Q8C2×D6111yescharacteristic
297#529—611no—
298#501—1221no—
299#491—21no—
300#491—21no—
301#489—1221no—
302#487C2×D6111yescharacteristic
303#487C2×D6111yescharacteristic
304#487C2×D6111yescharacteristic
305#487C2×D6111yescharacteristic
306#484—1221no—
307#481—1221no—
308#479—1221no—
309#477—611no—
310#476—611no—
311#475—611no—
312#475—611no—
313#474—611no—
314#474—611no—
315#470—1221no—
316#468—1221no—
317#464—1221no—
318#462—611no—
319#461—611no—
320#446—611no—
321C8×Q8—611no—
322#436—611no—
323#436—1221no—
324#435—1221no—
325C8×D4—611no—
326#433—1221no—
327#432—611no—
328#431—611no—
329#423—611no—
330#419—21no—
331#419—21no—
332#405—1221no—
333C4×M16C2×D6111yescharacteristic
334#335—611no—
335#335—611no—
336#334—611no—
337#334—611no—
338#333—611no—
339#333—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346C61#1938111yescharacteristic, complemented, Sylow
347C22×Q8—21no—
348C2×Q16—1221no—
349C2×SD16—1221no—
350C2×M16—1221no—
351C2×M16—1221no—
352C2×M16C22⋊D6111yescharacteristic
353C2×M16C22⋊D6111yescharacteristic
354C22×C8—1221no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C22×D6111yescharacteristic
359C4⋊Q8C22×D6111yescharacteristic
360C4⋊Q8C22×D6111yescharacteristic
361C4⋊Q8C22×D6111yescharacteristic
362#126—1221no—
363#125—21no—
364#125—611no—
365#124—611no—
366#123—1221no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—611no—
370#121—611no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—611no—
374C4×D4—611no—
375C4×D4—1221no—
376#117—21no—
377#117—1221no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C42C22×D6111yescharacteristic
381#107—1221no—
382#107—1221no—
383#107—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—611no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#102—1221no—
410#102—1221no—
411#102—1221no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416#97—1221no—
417#97—1221no—
418#97C22⋊D6111yescharacteristic
419#97C22⋊D6111yescharacteristic
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8C22×D6111yescharacteristic
423C4×C8C22×D6111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—41no—
431C2×Q8—611no—
432C2×D4—611no—
433C2×D4—1221no—
434C22×C4—41no—
435C22×C4—1221no—
436C22×C4D4×D6111yescharacteristic
437C22×C4#1175822411yescharacteristic
438C22×C4C2×C22⋊D6111yescharacteristic
439Q16—4881no—
440SD16—4881no—
441M16—41no—
442M16—41no—
443M16—4881no—
444M16—2442no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—2442no—
452C2×C8C2×C22⋊D6111yescharacteristic
453C2×C8C2×C22⋊D6111yescharacteristic
454C2×C8C2×C22⋊D6111yescharacteristic
455C2×C8C2×C22⋊D6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—611no—
469C4⋊C4—611no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C22⋊C4—41no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C42—41no—
481C42—1221no—
482C42D4×D6111yescharacteristic
483C42#1175822411yescharacteristic
484C42C2×C22⋊D6111yescharacteristic
485C42C23×D6111yescharacteristic
486C23—1221no—
487C23#1451974811yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—82no—
496Q8—1221no—
497Q8—1221no—
498D4—1221no—
499D4—1221no—
500D4—4881no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—82no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4#1451974811yescharacteristic
517C2×C4#1451974811yescharacteristic
518C2×C4#1451974811yescharacteristic
519C2×C4C2×D4×D6111yescharacteristic
520C2×C4C22×C22⋊D6111yescharacteristic
521C2×C4C2×#1175822411yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—2441no—
527C8—2441no—
528C8—2441no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—2441no—
536C22—2441no—
537C22—2441no—
538C22C2×#1451974811yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—2441no—
548C4—2441no—
549C4—2441no—
550C4#1684056011yescharacteristic
551C4#1684056011yescharacteristic
552C4#1684057111yescharacteristic
553C4#1684057811yescharacteristic
554C2—41no—
555C2—4881no—
556C2#2145530911yescharacteristic
557C2#2145550411yescharacteristic
558C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3139C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#3139D61
hypocenterC61#19381
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
4. #21445398C2semidirect
5. #21445391C2semidirect
6. #21445370C2semidirect
7. #21445363C2semidirect
8. #21445274C2semidirect
9. #21445267C2semidirect
10. #21445246C2semidirect
11. #21445239C2semidirect
12. #21444586C2semidirect
13. #21444529C2semidirect
14. #21444504C2semidirect
15. C61×#3139C2semidirect
277. #3139D61semidirect
346. C61#19381semidirect

Maximal subgroups

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

subgroupindex
#214571862
#214570492
#214548232
#214453982
#214453912
#214453702
#214453632
#214452742
#214452672
#214452462
#214452392
#214445862
#214445292
#214445042
C61×#31392
#1938161