Finite Group Databasebeta

← #29667614

Subgroups — #29667614

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457145C211yesmaximal, characteristic
2#21456947C211yesmaximal, characteristic, complemented
3#21454979C211yesmaximal, characteristic, complemented
4#21445389C211yesmaximal, characteristic, complemented
5#21445382C211yesmaximal, characteristic, complemented
6#21445323C211yesmaximal, characteristic, complemented
7#21445316C211yesmaximal, characteristic, complemented
8#21445265C211yesmaximal, characteristic, complemented
9#21445258C211yesmaximal, characteristic, complemented
10#21445199C211yesmaximal, characteristic, complemented
11#21445192C211yesmaximal, characteristic, complemented
12#21444605C211yesmaximal, characteristic, complemented
13#21444515C211yesmaximal, characteristic, complemented
14C2×#16839508C211yesmaximal, characteristic, complemented
15C61×#3218C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840158C2211yescharacteristic
18#16840158C2211yescharacteristic
19#16840110C2211yescharacteristic
20#16840110C2211yescharacteristic
21#16840080—21no—
22#16840080—21no—
23#16840059—21no—
24#16840057C2211yescharacteristic
25#16840052C2211yescharacteristic
26#16840049—21no—
27#16840049—21no—
28#16839996—21no—
29#16839993—21no—
30#16839974—21no—
31#16839962C2211yescharacteristic
32#16839957C2211yescharacteristic
33#16839893C2211yescharacteristic
34Q8×#92418C2211yescharacteristic
35#16839840C2211yescharacteristic
36#16839834—21no—
37D4×#92418—21no—
38D4×#92418C2211yescharacteristic
39#16839823—21no—
40#16839815C2211yescharacteristic
41#16839789—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C2×C4⋊Q8×C61C2211yescharacteristic
57C61×#529C2211yescharacteristic
58C61×#497—21no—
59C61×#491—21no—
60C61×#462C2211yescharacteristic
61C61×#462C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C61×#461C2211yescharacteristic
64C61×#451—21no—
65C61×#448—21no—
66C61×#432C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758201—21no—
69C2×#11758199—21no—
70C2×#11758194—21no—
71C22×#92418—21no—
72C22×#92418—21no—
73C22×#92418—21no—
74#14519777C2311yescharacteristic
75#14519774C2311yescharacteristic
76#14519765—21no—
77#14519751—21no—
78#14519751—21no—
79C4×D244—21no—
80C4×D244—21no—
81#14519710—21no—
82#14519708—21no—
83#14519708—21no—
84#14519708—21no—
85#14519708—21no—
86#14519708—21no—
87C4⋊#92418—21no—
88C4⋊#92418—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418D411yescharacteristic
92C4⋊#92418D411yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519698—21no—
99#14519697—21no—
100#14519697—21no—
101#14519697—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105C22⋊#92418—21no—
106C22⋊#92418—21no—
107C22⋊#92418D411yescharacteristic
108C22⋊#92418D411yescharacteristic
109#14519688—21no—
110C4×#92418—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C22×Q8×C61—21no—
114C2×Q16×C61—21no—
115C2×Q16×C61—21no—
116C2×SD16×C61—21no—
117C2×SD16×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#126×C61—21no—
124#125×C61D411yescharacteristic
125#124×C61D411yescharacteristic
126#123×C61—21no—
127C22⋊Q8×C61D411yescharacteristic
128#121×C61D411yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142C22⋊C8×C61—21no—
143#97×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—81no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—41no—
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61#4111yescharacteristic
157C2×C22⋊D61—41no—
158#11758222—82no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×C4×D61—41no—
163C2×Dic122—21no—
164Q16×C61—81no—
165Q16×C61—81no—
166SD16×C61—81no—
167SD16×C61—81no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
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—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61C2×D411yescharacteristic
181C4⋊C4×C61C2×D411yescharacteristic
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C42×C61—21no—
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61#4111yescharacteristic
191C42×C61C2411yescharacteristic
192#11758201—81no—
193#11758199—81no—
194#11758198—41no—
195#11758198—41no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198#11758194—81no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—81no—
204C2×#92418—81no—
205C2×#92418—81no—
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C23×C61—21no—
211C23×C61#12111yescharacteristic
212C22×D61—41no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—82no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—42no—
223C2×C4×C61—22no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—82no—
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C22⋊D61—82no—
243C2×Dic61—41no—
244D244—41no—
245D244—41no—
246D244—41no—
247D244—41no—
248D244—81no—
249C4×D61—82no—
250Dic122—81no—
251C8×C61—41no—
252C8×C61—41no—
253#92418—21no—
254#92418—21no—
255#92418—21no—
256#92418—21no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#19589—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61#47112yes—
268C22×C61C2×#12111yescharacteristic
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—81no—
280C4×C61—81no—
281C4×C61#57611yescharacteristic
282C4×C61#57711yescharacteristic
283C4×C61#57711yescharacteristic
284C4×C61#57811yescharacteristic
285Dic61—81no—
286#3247—611no—
287#3227—611no—
288#3218D6111yescharacteristic, complemented
289#2994—611no—
290#1702—611no—
291#1701—611no—
292#1692—611no—
293#1691—611no—
294#1682—611no—
295#1681—611no—
296#1672—611no—
297#1671—611no—
298#1573—611no—
299#1551—611no—
300C2×#332—611no—
301C2×C61—22no—
302C2×C61—81no—
303C2×C61#304611yescharacteristic
304C2×C61#306211yescharacteristic
305C2×C61C2×#47111yescharacteristic
306D61—161no—
307#532—611no—
308C2×C4⋊Q8C2×D6111yescharacteristic
309#529C2×D6111yescharacteristic
310#498—611no—
311#498—611no—
312#497—21no—
313#491—21no—
314#486—611no—
315#486—611no—
316#481—1221no—
317#481—1221no—
318#478—1221no—
319#477—611no—
320#476—611no—
321#476—1221no—
322#476—1221no—
323#466—1221no—
324#465—1221no—
325#463—1221no—
326#462C2×D6111yescharacteristic
327#462C2×D6111yescharacteristic
328#461C2×D6111yescharacteristic
329#461C2×D6111yescharacteristic
330#460—611no—
331#459—611no—
332#451—21no—
333#448—21no—
334#446—611no—
335C8×Q8—611no—
336#436—611no—
337#435—1221no—
338C8×D4—611no—
339C8×D4—1221no—
340#433—1221no—
341#432C2×D6111yescharacteristic
342#431—611no—
343#424—1221no—
344C2×C4⋊C8—611no—
345C2×C4⋊C8—611no—
346#335—611no—
347#335—611no—
348#334—611no—
349#334—611no—
350#333—611no—
351#333—611no—
352#332—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#331—611no—
357#331—611no—
358C61#1958911yescharacteristic, complemented, Sylow
359C2×#41—1221no—
360C22×Q8—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—1221no—
366C2×D8—1221no—
367C2×M16—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370C22×C8—1221no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—611no—
375C4⋊Q8C22×D6111yescharacteristic
376C4⋊Q8C22×D6111yescharacteristic
377#127—611no—
378#126—21no—
379#125C22⋊D6111yescharacteristic
380#124—1221no—
381#124C22⋊D6111yescharacteristic
382#123—21no—
383C22⋊Q8C22⋊D6111yescharacteristic
384#121—1221no—
385#121—1221no—
386#121C22⋊D6111yescharacteristic
387C4×Q8C22×D6111yescharacteristic
388C4×D4—21no—
389C4×D4—1221no—
390C4×D4—1221no—
391C4×D4C22×D6111yescharacteristic
392#117—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C42C22×D6111yescharacteristic
396#107—1221no—
397#106—1221no—
398#106—1221no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402C4⋊C8—611no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8C22×D6111yescharacteristic
413C4⋊C8C22×D6111yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426C22⋊C8—21no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431#97—21no—
432#97—1221no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—1221no—
436#41—4882no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—81no—
441C2×Q8—81no—
442C2×Q8—1221no—
443C2×Q8C2×C22⋊D6111yescharacteristic
444C2×D4—21no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—2441no—
449C2×D4C2×C22⋊D6111yescharacteristic
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—2441no—
453C22×C4D4×D6111yescharacteristic
454C22×C4#1175822411yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456Q16—81no—
457Q16—81no—
458SD16—81no—
459SD16—81no—
460SD16—4881no—
461D8—4881no—
462M16—4881no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—4881no—
474C2×C8—4881no—
475C2×C8—4881no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4C2×C22⋊D6111yescharacteristic
489C4⋊C4C2×C22⋊D6111yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—2441no—
496C22⋊C4—2441no—
497C42—21no—
498C42D4×D6111yescharacteristic
499C42#1175822411yescharacteristic
500C42C2×C22⋊D6111yescharacteristic
501C42C23×D6111yescharacteristic
502C23—21no—
503C23—2441no—
504C23#1451974911yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—82no—
512Q8—4881no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—4881no—
517D4—4882no—
518D4—2441no—
519D4—2441no—
520D4—2441no—
521D4—2441no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—4882no—
536C2×C4—2441no—
537C2×C4#1451974911yescharacteristic
538C2×C4#1451974911yescharacteristic
539C2×C4#1451974911yescharacteristic
540C2×C4C2×D4×D6111yescharacteristic
541C2×C4C22×C22⋊D6111yescharacteristic
542C2×C4C2×#1175822411yescharacteristic
543C8—41no—
544C8—41no—
545C8—1221no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C8—2441no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—4881no—
559C22—4881no—
560C22—4881no—
561C22#1684002712yes—
562C22C2×#1451974911yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—4881no—
573C4#1684056511yescharacteristic
574C4#1684057111yescharacteristic
575C4#1684057311yescharacteristic
576C4#1684057811yescharacteristic
577C2—22no—
578C2—81no—
579C2—9761no—
580C2#2145537311yescharacteristic
581C2#2145549511yescharacteristic
582C2C2×#1684002711yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3218C2
socleC22×C61C2×#121
prime radical#21457145C2
hypercenter#3218D61
hypocenterC61#19589
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3218

Complements

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

NH ≅ G/Ntype
2. #21456947C2semidirect
3. #21454979C2semidirect
4. #21445389C2semidirect
5. #21445382C2semidirect
6. #21445323C2semidirect
7. #21445316C2semidirect
8. #21445265C2semidirect
9. #21445258C2semidirect
10. #21445199C2semidirect
11. #21445192C2semidirect
12. #21444605C2semidirect
13. #21444515C2semidirect
14. C2×#16839508C2semidirect
15. C61×#3218C2semidirect
288. #3218D61semidirect
358. C61#19589semidirect

Maximal subgroups

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

subgroupindex
#214571452
#214569472
#214549792
#214453892
#214453822
#214453232
#214453162
#214452652
#214452582
#214451992
#214451922
#214446052
#214445152
C2×#168395082
C61×#32182
#1958961