Finite Group Databasebeta

← #29665363

Subgroups — #29665363

Order 15616.

676 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456936C211yesmaximal, characteristic
2#21455286C211yesmaximal, characteristic
3#462×D61C211yesmaximal, characteristic, complemented
4#21454898C211yesmaximal, characteristic, complemented
5#21445262C211yesmaximal, characteristic, complemented
6#21445261C211yesmaximal, characteristic, complemented
7#21445260C211yesmaximal, characteristic, complemented
8#21445214C211yesmaximal, characteristic, complemented
9#21445213C211yesmaximal, characteristic, complemented
10#21445212C211yesmaximal, characteristic, complemented
11#21445211C211yesmaximal, characteristic, complemented
12#21444592C211yesmaximal, characteristic, complemented
13#21444489C211yesmaximal, characteristic, complemented
14#21444465C211yesmaximal, characteristic
15C61×#1682C211yesmaximal, characteristic, complemented
16C2×#14519806—21no—
17C2×Q16×D61—21no—
18#16840310C2211yescharacteristic
19C4⋊Q8×D61C2211yescharacteristic
20C4×Q8×D61C2211yescharacteristic
21#16840167C2211yescharacteristic
22#16840165C2211yescharacteristic
23#16840108C2211yescharacteristic
24#16840074—21no—
25#16840074—21no—
26#16840040—21no—
27#16840040—21no—
28#16839983—21no—
29#16839982—21no—
30#16839973C2211yescharacteristic
31#16839973C2211yescharacteristic
32#16839972C2211yescharacteristic
33#16839972C2211yescharacteristic
34#16839971—21no—
35#16839970—21no—
36#16839969C2211yescharacteristic
37#16839959C2211yescharacteristic
38Q8×#92418C2211yescharacteristic
39C8×Dic122—21no—
40C8×Dic122C2211yescharacteristic
41#16839886—21no—
42#16839886C2211yescharacteristic
43#16839814—21no—
44#16839814C2211yescharacteristic
45#16839813—21no—
46#16839813C2211yescharacteristic
47#16839784C2211yescharacteristic
48C4⋊C8×D61C2211yescharacteristic
49#16839760—21no—
50#103×D61—21no—
51#16839515C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839508C2211yescharacteristic
57#16839507C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839506C2211yescharacteristic
60C61×#486C2211yescharacteristic
61C61×#462C2211yescharacteristic
62C61×#460C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#331C2211yescharacteristic
67C2×#11758224—21no—
68C2×Q8×D61—21no—
69C2×Q8×D61D411yescharacteristic
70#14519806—44no—
71C2×Dic244—21no—
72C2×Dic244—21no—
73C2×#11758202—21no—
74C2×#11758202—21no—
75C2×#11758202—21no—
76Q16×D61—44no—
77C2×#11758200—21no—
78C2×#11758189—21no—
79C2×C8×D61—21no—
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519776—21no—
83#14519776—21no—
84#14519775—21no—
85#14519764—21no—
86#14519748—21no—
87#14519748—21no—
88Q8×Dic61D411yescharacteristic
89C4×Dic122—21no—
90C4×Dic122C2311yescharacteristic
91#14519742—21no—
92#14519742D411yescharacteristic
93D4×Dic61—21no—
94D4×Dic61—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61D411yescharacteristic
99C42×D61—21no—
100C42×D61C2311yescharacteristic
101#14519711—21no—
102#14519711—21no—
103#14519710—21no—
104#14519710—21no—
105C4⋊#92418—21no—
106C4⋊#92418C2311yescharacteristic
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109#14519706—21no—
110#14519706—21no—
111#14519706—21no—
112#14519706—21no—
113#14519706D411yescharacteristic
114#14519706D411yescharacteristic
115#14519702—21no—
116#14519702—21no—
117#14519701—21no—
118#14519700—21no—
119#14519700—21no—
120#14519698—21no—
121#14519698—21no—
122#14519698—21no—
123#14519689—21no—
124#14519689D411yescharacteristic
125#14519689D411yescharacteristic
126C4×#92418—21no—
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C8×Dic61—21no—
130C8×Dic61—21no—
131C2×Q16×C61—21no—
132C2×SD16×C61—21no—
133C4⋊Q8×C61C2311yescharacteristic
134#127×C61C2311yescharacteristic
135C4×Q8×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#102×C61—21no—
142#102×C61—21no—
143#102×C61—21no—
144C4×C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×C22⋊D61—41no—
152C22×Dic61—41no—
153Q8×D61—22no—
154Q8×D61—42no—
155Q8×D61—42no—
156Q8×D61D814yes—
157#11758224—42no—
158#11758224—42no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—41no—
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61#4111yescharacteristic
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—41no—
169C2×Dic122C2×D411yescharacteristic
170Q16×C61—42no—
171SD16×C61—42no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61C2×D411yescharacteristic
181C42×C61—21no—
182C42×C61C2411yescharacteristic
183C22⋊Dic61—41no—
184C22⋊Dic61—41no—
185#11758202—42no—
186#11758202—42no—
187#11758202—42no—
188#11758200—42no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198#11758196—41no—
199#11758196—41no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61#4111yescharacteristic
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211Dic244—42no—
212Dic244—42no—
213#11758189—42no—
214C8×D61—42no—
215C23×C61—41no—
216C22×D61#12111yescharacteristic
217Q8×C61—21no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61C2×D812yes—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—81no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—41no—
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C22⋊D61—82no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—82no—
238C2×Dic61#12111yescharacteristic
239C2×Dic61#12111yescharacteristic
240C2×Dic61#12111yescharacteristic
241C4×D61—24no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—41no—
245C4×D61—81no—
246C4×D61—82no—
247C4×D61C2×D812yes—
248C4×D61#13512yes—
249Dic122—21no—
250Dic122—24no—
251Dic122—41no—
252Dic122—41no—
253Dic122—41no—
254Dic122—41no—
255Dic122—82no—
256Dic122C2×D812yes—
257C8×C61—21no—
258C8×C61—21no—
259C8×C61—41no—
260C8×C61—41no—
261C8×C61—41no—
262#92418—21no—
263#92418—21no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#19404—611nomaximal, Sylow
268C22×C61—81no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61C2×#12111yescharacteristic
272C2×D61—21no—
273C2×D61—21no—
274C2×D61#46612yes—
275C4×C61—22no—
276C4×C61—21no—
277C4×C61—41no—
278C4×C61—81no—
279C4×C61C22×D811yescharacteristic
280C4×C61C2×#13511yescharacteristic
281C4×C61#57811yescharacteristic
282C4×C61#57811yescharacteristic
283Dic61—21no—
284Dic61—22no—
285Dic61—21no—
286Dic61—41no—
287Dic61—81no—
288Dic61—81no—
289Dic61#46612yes—
290#3226—611no—
291#3037—611no—
292C2×#462—611no—
293#2982—611no—
294#1682—611no—
295#1682—611no—
296#1682—611no—
297#1682D6111yescharacteristic, complemented
298#1674—611no—
299#1674—611no—
300#1674—611no—
301#1674—611no—
302#1571—611no—
303#1546—611no—
304#1540—611no—
305C2×C61—161no—
306C2×C61#304411yescharacteristic
307C2×C61C2×#46611yescharacteristic
308C2×C61#306911yescharacteristic
309D61—22no—
310C2×#137—1221no—
311C22×Q16—1221no—
312#532—611no—
313C2×C4⋊Q8—611no—
314C2×C4×Q8—611no—
315#500—611no—
316#500—611no—
317#486—611no—
318#486C2×D6111yescharacteristic
319#480—1221no—
320#480—1221no—
321#474—1221no—
322#474—1221no—
323#464—1221no—
324#464—1221no—
325#462—611no—
326#462—611no—
327#462—611no—
328#462—611no—
329#462—611no—
330#462—1221no—
331#462—1221no—
332#462C2×D6111yescharacteristic
333#460—611no—
334#460C2×D6111yescharacteristic
335C8×Q8—611no—
336C8×Q8—611no—
337C8×Q8—611no—
338C8×Q8—1221no—
339C8×Q8—1221no—
340C8×Q8C2×D6111yescharacteristic
341#431—611no—
342#431—611no—
343#431—1221no—
344#431—1221no—
345#423—611no—
346C2×C4⋊C8—611no—
347#417—1221no—
348C2×#103—1221no—
349#335—611no—
350#335—611no—
351#335—611no—
352#335C2×D6111yescharacteristic
353#332—611no—
354#332—611no—
355#332—611no—
356#332—611no—
357#332—611no—
358#332C2×D6111yescharacteristic
359#331—611no—
360#331C2×D6111yescharacteristic
361C61#1940411yescharacteristic, complemented, Sylow
362C2×#41—1221no—
363C22×Q8—611no—
364C22×Q8—1221no—
365#137—2444no—
366C2×Q16—21no—
367C2×Q16—1221no—
368C2×Q16—1221no—
369C2×Q16—1221no—
370C2×Q16—1221no—
371C2×Q16—1221no—
372C2×Q16—2444no—
373C2×SD16—21no—
374C2×SD16—1221no—
375C2×M16—1221no—
376C22×C8—1221no—
377C4⋊Q8—611no—
378C4⋊Q8—611no—
379C4⋊Q8—1221no—
380C4⋊Q8—1221no—
381C4⋊Q8—1221no—
382C4⋊Q8C22×D6111yescharacteristic
383#127C22×D6111yescharacteristic
384#124—1221no—
385#121—1221no—
386#121—1221no—
387C4×Q8—611no—
388C4×Q8—611no—
389C4×Q8—611no—
390C4×Q8—1221no—
391C4×Q8—1221no—
392C4×Q8C22×D6111yescharacteristic
393C4×D4—1221no—
394C4×D4—1221no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C42—611no—
400C2×C42—1221no—
401#107—1221no—
402#107—1221no—
403#107—1221no—
404#107—1221no—
405C4⋊C8—21no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
418C4⋊C8C22×D6111yescharacteristic
419#103—21no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#103—1221no—
424#103—1221no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431C22⋊C8—611no—
432C22⋊C8—611no—
433C22⋊C8—1221no—
434C4×C8—21no—
435C4×C8—611no—
436C4×C8—1221no—
437C4×C8—1221no—
438C4×C8—1221no—
439C4×C8—1221no—
440C4×C8C22×D6111yescharacteristic
441#41—2442no—
442#41—2442no—
443C2×Q8—21no—
444C2×Q8—614no—
445C2×Q8—611no—
446C2×Q8—1221no—
447C2×Q8—1222no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×Q8—2441no—
451C2×Q8—2442no—
452C2×Q8—2442no—
453C2×Q8D4×D6111yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—2441no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—2441no—
464C22×C4—2441no—
465Q16—42no—
466Q16—2442no—
467Q16—2442no—
468Q16—2442no—
469Q16—2442no—
470Q16—2442no—
471SD16—42no—
472SD16—2442no—
473M16—2442no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—2442no—
483C2×C8D4×D6111yescharacteristic
484C2×C8D4×D6111yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—611no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—2441no—
498C4⋊C4—2441no—
499C4⋊C4D4×D6111yescharacteristic
500C22⋊C4—2441no—
501C22⋊C4—2441no—
502C42—21no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42C23×D6111yescharacteristic
510C23—41no—
511C23—611no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—612no—
516Q8—1224no—
517Q8—1221no—
518Q8—4882no—
519Q8—2441no—
520Q8—2441no—
521Q8—2441no—
522Q8—2441no—
523Q8D8×D6112yes—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—4882no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—611no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—611no—
537C2×C4—611no—
538C2×C4—1224no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—4881no—
544C2×C4—4882no—
545C2×C4—4882no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4C2×D4×D6111yescharacteristic
550C2×C4C2×D4×D6111yescharacteristic
551C2×C4#41×D6111yescharacteristic
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—1221no—
558C8—1221no—
559C8—2441no—
560C8—2441no—
561C8—2441no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—612no—
566C22—1221no—
567C22—1221no—
568C22#121×D6111yescharacteristic
569C4—22no—
570C4—21no—
571C4—41no—
572C4—81no—
573C4—612no—
574C4—1222no—
575C4—1221no—
576C4—1221no—
577C4—4881no—
578C4—4881no—
579C4—2441no—
580C4C2×D8×D6111yescharacteristic
581C4#135×D6111yescharacteristic
582C4#1684057611yescharacteristic
583C4#1684057811yescharacteristic
584C2—161no—
585C2—1222no—
586C2#2145534711yescharacteristic
587C2#466×D6111yescharacteristic
588C2#2145555111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1682C2
socleC22×C61C2×#121
prime radical#16840310C22
hypercenter#1682D61
hypocenterC61#19404
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1682

Complements

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

NH ≅ G/Ntype
3. #462×D61C2semidirect
4. #21454898C2semidirect
5. #21445262C2semidirect
6. #21445261C2semidirect
7. #21445260C2semidirect
8. #21445214C2semidirect
9. #21445213C2semidirect
10. #21445212C2semidirect
11. #21445211C2semidirect
12. #21444592C2semidirect
13. #21444489C2semidirect
15. C61×#1682C2semidirect
297. #1682D61semidirect
361. C61#19404semidirect

Maximal subgroups

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

subgroupindex
#214569362
#214552862
#462×D612
#214548982
#214452622
#214452612
#214452602
#214452142
#214452132
#214452122
#214452112
#214445922
#214444892
#214444652
C61×#16822
#1940461