Finite Group Databasebeta

← #29665139

Subgroups — #29665139

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457175C211yesmaximal, characteristic
2#21457040C211yesmaximal, characteristic, complemented
3#21454823C211yesmaximal, characteristic, complemented
4#21445398C211yesmaximal, characteristic, complemented
5#21445391C211yesmaximal, characteristic, complemented
6#21445356C211yesmaximal, characteristic, complemented
7#21445349C211yesmaximal, characteristic, complemented
8#21445274C211yesmaximal, characteristic, complemented
9#21445267C211yesmaximal, characteristic, complemented
10#21445232C211yesmaximal, characteristic, complemented
11#21445225C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444524C211yesmaximal, characteristic, complemented
14#21444500C211yesmaximal, characteristic, complemented
15C61×#3141C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840168—21no—
18#16840124—21no—
19#16840092—21no—
20#16840075—21no—
21#16840062—21no—
22#16840054C2211yescharacteristic
23#16840054C2211yescharacteristic
24#16840049C2211yescharacteristic
25#16840049C2211yescharacteristic
26#16840044C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840013—21no—
29#16840006—21no—
30#16839977—21no—
31#16839959C2211yescharacteristic
32#16839954C2211yescharacteristic
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#16839511C2211yescharacteristic
51#16839511C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839506C2211yescharacteristic
55#16839506C2211yescharacteristic
56C61×#532C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C61×#489—21no—
59C61×#489—21no—
60C61×#487C2211yescharacteristic
61C61×#487C2211yescharacteristic
62C61×#486C2211yescharacteristic
63C61×#486C2211yescharacteristic
64C61×#417—21no—
65C61×#417—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758200—21no—
68C2×#11758199—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#14519700—21no—
98#14519700—21no—
99#14519700—21no—
100#14519698—21no—
101#14519698—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—
113C2×#41×C61—21no—
114C22×Q8×C61—21no—
115C2×M16×C61D411yescharacteristic
116C2×M16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#127×C61C2311yescharacteristic
124#124×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127C4×D4×C61—21no—
128C4×D4×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#102×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#97×C61D411yescharacteristic
141#97×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—42no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—41no—
150C2×Q8×C61—82no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—41no—
155C22×C4×C61—41no—
156C22×C4×C61—41no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C2×C22⋊D61—21no—
161C2×D244C2×D411yescharacteristic
162C2×C4×D61—21no—
163C2×Dic122C2×D411yescharacteristic
164M16×C61—41no—
165M16×C61—41no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C22⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C42×C61C2×D411yescharacteristic
181C42×C61C2×D411yescharacteristic
182C42×C61#4111yescharacteristic
183C42×C61C2411yescharacteristic
184C22⋊Dic61—21no—
185#11758200—81no—
186#11758199—81no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61C2×D411yescharacteristic
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197C4×Dic61—21no—
198#11758194—81no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205#11758189—42no—
206C8×D61—42no—
207C23×C61—41no—
208C23×C61#12111yescharacteristic
209C22×D61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—82no—
213Q8×C61—81no—
214Q8×C61—81no—
215D4×C61—41no—
216D4×C61—41no—
217D4×C61—41no—
218D4×C61—41no—
219D4×C61—81no—
220D4×C61—82no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—82no—
230C2×C4×C61—82no—
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C22⋊D61—81no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241D244—21no—
242D244—21no—
243C4×D61—41no—
244C4×D61—41no—
245Dic122—21no—
246Dic122—21no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—21no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#19382—611nomaximal, Sylow
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61C2×#12111yescharacteristic
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61—81no—
275C4×C61#57511yescharacteristic
276C4×C61#57511yescharacteristic
277C4×C61#57711yescharacteristic
278C4×C61#57811yescharacteristic
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282#3251—611no—
283#3238—611no—
284#3141D6111yescharacteristic, complemented
285#2969—611no—
286#1704—611no—
287#1703—611no—
288#1698—611no—
289#1697—611no—
290#1684—611no—
291#1683—611no—
292#1678—611no—
293#1677—611no—
294#1569—611no—
295#1553—611no—
296#1548—611no—
297C2×C61—41no—
298C2×C61—161no—
299C2×C61#304011yescharacteristic
300C2×C61#306311yescharacteristic
301C2×C61#306811yescharacteristic
302D61—81no—
303#532C2×D6111yescharacteristic
304C2×C4⋊Q8C2×D6111yescharacteristic
305#529—611no—
306#501—1221no—
307#489—21no—
308#489—21no—
309#489—1221no—
310#487C2×D6111yescharacteristic
311#487C2×D6111yescharacteristic
312#486C2×D6111yescharacteristic
313#486C2×D6111yescharacteristic
314#483—1221no—
315#480—1221no—
316#478—1221no—
317#477—611no—
318#477—611no—
319#476—611no—
320#476—611no—
321#475—611no—
322#474—611no—
323#469—1221no—
324#468—1221no—
325#463—1221no—
326#460—611no—
327#459—611no—
328#446—611no—
329C8×Q8—611no—
330#436—611no—
331#436—1221no—
332#435—1221no—
333C8×D4—611no—
334#433—1221no—
335#432—611no—
336#431—611no—
337#423—611no—
338#417—21no—
339#417—21no—
340#405—1221no—
341C4×M16C2×D6111yescharacteristic
342#335—611no—
343#335—611no—
344#334—611no—
345#334—611no—
346#333—611no—
347#333—611no—
348#333—611no—
349#333—611no—
350#332—611no—
351#332—611no—
352#331—611no—
353#331—611no—
354C61#1938211yescharacteristic, complemented, Sylow
355C2×#41—21no—
356C22×Q8—21no—
357C2×SD16—1221no—
358C2×D8—1221no—
359C2×M16—1221no—
360C2×M16—1221no—
361C2×M16C22⋊D6111yescharacteristic
362C2×M16C22⋊D6111yescharacteristic
363C22×C8—1221no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8C22×D6111yescharacteristic
368C4⋊Q8C22×D6111yescharacteristic
369C4⋊Q8C22×D6111yescharacteristic
370#127C22×D6111yescharacteristic
371#126—1221no—
372#125—611no—
373#124—21no—
374#124—611no—
375#123—1221no—
376C22⋊Q8—611no—
377#121—21no—
378#121—21no—
379#121—611no—
380C4×Q8—611no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—611no—
384C4×D4—1221no—
385#117—1221no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C42C22×D6111yescharacteristic
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419#102—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424#97—1221no—
425#97—1221no—
426#97C22⋊D6111yescharacteristic
427#97C22⋊D6111yescharacteristic
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8C22×D6111yescharacteristic
431C4×C8C22×D6111yescharacteristic
432#41—42no—
433#41—42no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—41no—
438C2×Q8—82no—
439C2×Q8—611no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—611no—
445C2×D4—1221no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—1221no—
449C22×C4D4×D6111yescharacteristic
450C22×C4#1175822411yescharacteristic
451C22×C4C2×C22⋊D6111yescharacteristic
452SD16—4881no—
453D8—4881no—
454M16—41no—
455M16—41no—
456M16—4881no—
457M16—2442no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—2442no—
465C2×C8C2×C22⋊D6111yescharacteristic
466C2×C8C2×C22⋊D6111yescharacteristic
467C2×C8C2×C22⋊D6111yescharacteristic
468C2×C8C2×C22⋊D6111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—611no—
478C4⋊C4—611no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C42—1221no—
491C42D4×D6111yescharacteristic
492C42#1175822411yescharacteristic
493C42C2×C22⋊D6111yescharacteristic
494C42C23×D6111yescharacteristic
495C23—41no—
496C23—1221no—
497C23#1451974811yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502Q8—82no—
503Q8—1221no—
504Q8—1221no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4—82no—
511D4—1221no—
512D4—1221no—
513D4—4881no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4#1451974811yescharacteristic
530C2×C4#1451974811yescharacteristic
531C2×C4#1451974811yescharacteristic
532C2×C4C2×D4×D6111yescharacteristic
533C2×C4C22×C22⋊D6111yescharacteristic
534C2×C4C2×#1175822411yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C8—2441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—2441no—
552C22—2441no—
553C22—2441no—
554C22C2×#1451974811yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—2441no—
563C4—2441no—
564C4—2441no—
565C4#1684056011yescharacteristic
566C4#1684056011yescharacteristic
567C4#1684057111yescharacteristic
568C4#1684057811yescharacteristic
569C2—41no—
570C2—161no—
571C2—4881no—
572C2#2145530911yescharacteristic
573C2#2145550411yescharacteristic
574C2#2145554311yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3141C2
socleC22×C61C2×#121
prime radical#21457175C2
hypercenter#3141D61
hypocenterC61#19382
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #21457040C2semidirect
3. #21454823C2semidirect
4. #21445398C2semidirect
5. #21445391C2semidirect
6. #21445356C2semidirect
7. #21445349C2semidirect
8. #21445274C2semidirect
9. #21445267C2semidirect
10. #21445232C2semidirect
11. #21445225C2semidirect
12. #21444586C2semidirect
13. #21444524C2semidirect
14. #21444500C2semidirect
15. C61×#3141C2semidirect
284. #3141D61semidirect
354. C61#19382semidirect

Maximal subgroups

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

subgroupindex
#214571752
#214570402
#214548232
#214453982
#214453912
#214453562
#214453492
#214452742
#214452672
#214452322
#214452252
#214445862
#214445242
#214445002
C61×#31412
#1938261