Finite Group Databasebeta

← #29665164

Subgroups — #29665164

Order 15616.

606 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#21457181C211yesmaximal, characteristic
2#21456215C211yesmaximal, characteristic, complemented
3#21454824C211yesmaximal, characteristic, complemented
4#21445389C211yesmaximal, characteristic, complemented
5#21445382C211yesmaximal, characteristic, complemented
6#21445375C211yesmaximal, characteristic, complemented
7#21445368C211yesmaximal, characteristic, complemented
8#21445265C211yesmaximal, characteristic, complemented
9#21445258C211yesmaximal, characteristic, complemented
10#21445251C211yesmaximal, characteristic, complemented
11#21445244C211yesmaximal, characteristic, complemented
12#21444587C211yesmaximal, characteristic, complemented
13#21444525C211yesmaximal, characteristic, complemented
14#21444491C211yesmaximal, characteristic, complemented
15C61×#3218C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840124—21no—
18#16840124—21no—
19#16840114C2211yescharacteristic
20#16840114C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840059—21no—
24#16840047C2211yescharacteristic
25#16840042C2211yescharacteristic
26#16840013—21no—
27#16840010—21no—
28#16839974—21no—
29#16839962C2211yescharacteristic
30#16839957C2211yescharacteristic
31#16839893C2211yescharacteristic
32Q8×#92418C2211yescharacteristic
33#16839840—21no—
34#16839840C2211yescharacteristic
35#16839834—21no—
36D4×#92418C2211yescharacteristic
37#16839823—21no—
38#16839815C2211yescharacteristic
39#16839786C2211yescharacteristic
40#16839761—21no—
41#16839761—21no—
42#16839718—21no—
43C4×#11758194C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
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—
71C2×#11758194—21no—
72C2×#11758194D411yescharacteristic
73C2×#11758194D411yescharacteristic
74C22×#92418—21no—
75#14519777C2311yescharacteristic
76#14519774C2311yescharacteristic
77#14519765—21no—
78#14519751—21no—
79#14519751—21no—
80C4×D244—21no—
81C4×D244—21no—
82#14519710—21no—
83#14519708—21no—
84C4⋊#92418—21no—
85C4⋊#92418—21no—
86C4⋊#92418—21no—
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91#14519701—21no—
92#14519700—21no—
93#14519700—21no—
94#14519700—21no—
95#14519700—21no—
96#14519698—21no—
97#14519697—21no—
98#14519697—21no—
99#14519697—21no—
100#14519697—21no—
101#14519697—21no—
102#14519697—21no—
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105C22⋊#92418—21no—
106#14519688—21no—
107#14519688D411yescharacteristic
108#14519688D411yescharacteristic
109C4×#92418—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—42no—
159#11758222—42no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×C4×D61—41no—
164C2×Dic122—21no—
165Q16×C61—81no—
166Q16×C61—81no—
167SD16×C61—81no—
168SD16×C61—81no—
169C2×C8×C61—21no—
170C2×C8×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—21no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61—41no—
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C42×C61—21no—
189C42×C61C2×D411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61#4111yescharacteristic
192C42×C61C2411yescharacteristic
193#11758201—81no—
194#11758199—81no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199#11758194—41no—
200#11758194—41no—
201#11758194—42no—
202#11758194—81no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—42no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C23×C61—21no—
213C23×C61#12111yescharacteristic
214C22×D61—41no—
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—82no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—81no—
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—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—82no—
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C22⋊D61—82no—
245C2×Dic61—41no—
246D244—41no—
247D244—41no—
248D244—41no—
249D244—41no—
250D244—81no—
251C4×D61—82no—
252Dic122—41no—
253Dic122—41no—
254C8×C61—41no—
255C8×C61—41no—
256#92418—21no—
257#92418—21no—
258#92418—21no—
259#92418—21no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#19383—611nomaximal, Sylow
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61C2×#12111yescharacteristic
272C2×D61—81no—
273C2×D61—81no—
274C2×D61—81no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61#57511yescharacteristic
285C4×C61#57511yescharacteristic
286C4×C61#57611yescharacteristic
287C4×C61#57711yescharacteristic
288Dic61—81no—
289#3251—611no—
290#3218D6111yescharacteristic, complemented
291#3141—611no—
292#2969—611no—
293#1702—611no—
294#1701—611no—
295#1700—611no—
296#1699—611no—
297#1682—611no—
298#1681—611no—
299#1680—611no—
300#1679—611no—
301#1569—611no—
302#1553—611no—
303#1546—611no—
304C2×C61—41no—
305C2×C61—81no—
306C2×C61#304011yescharacteristic
307C2×C61#306211yescharacteristic
308C2×C61#306911yescharacteristic
309D61—161no—
310#532—611no—
311C2×C4⋊Q8C2×D6111yescharacteristic
312#529C2×D6111yescharacteristic
313#497—21no—
314#491—21no—
315#489—1221no—
316#489—1221no—
317#487—611no—
318#487—611no—
319#486—611no—
320#486—611no—
321#478—1221no—
322#475—611no—
323#474—611no—
324#469—1221no—
325#468—1221no—
326#463—1221no—
327#462C2×D6111yescharacteristic
328#462C2×D6111yescharacteristic
329#461C2×D6111yescharacteristic
330#461C2×D6111yescharacteristic
331#460—611no—
332#459—611no—
333#451—21no—
334#448—21no—
335#446—611no—
336C8×Q8—611no—
337#436—611no—
338#436—1221no—
339#435—1221no—
340C8×D4—611no—
341#433—1221no—
342#432C2×D6111yescharacteristic
343#431—611no—
344#423—611no—
345#417—1221no—
346#417—1221no—
347#405—1221no—
348C4×M16—611no—
349#335—611no—
350#335—611no—
351#334—611no—
352#334—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#332—611no—
357#332—611no—
358#332—611no—
359#331—611no—
360#331—611no—
361C61#1938311yescharacteristic, complemented, Sylow
362C2×#41—1221no—
363C22×Q8—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—1221no—
369C2×D8—1221no—
370C2×M16—611no—
371C2×M16—611no—
372C2×M16—1221no—
373C2×M16—1221no—
374C22×C8—1221no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—611no—
379C4⋊Q8C22×D6111yescharacteristic
380C4⋊Q8C22×D6111yescharacteristic
381#127—611no—
382#126—21no—
383#125C22⋊D6111yescharacteristic
384#124—1221no—
385#124C22⋊D6111yescharacteristic
386#123—21no—
387C22⋊Q8C22⋊D6111yescharacteristic
388#121—1221no—
389#121—1221no—
390#121C22⋊D6111yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—21no—
393C4×D4—1221no—
394C4×D4—1221no—
395C4×D4C22×D6111yescharacteristic
396#117—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C42C22×D6111yescharacteristic
400#107—1221no—
401#106—1221no—
402C4⋊C8—611no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8C22×D6111yescharacteristic
410C4⋊C8C22×D6111yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427C22⋊C8—21no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431#97—21no—
432#97—611no—
433#97—611no—
434#97—1221no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—1221no—
438C4×C8—1221no—
439#41—2442no—
440#41—2442no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—81no—
445C2×Q8—81no—
446C2×Q8—1221no—
447C2×Q8C2×C22⋊D6111yescharacteristic
448C2×D4—21no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—2441no—
453C2×D4C2×C22⋊D6111yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—2441no—
457C22×C4D4×D6111yescharacteristic
458C22×C4#1175822411yescharacteristic
459C22×C4C2×C22⋊D6111yescharacteristic
460Q16—81no—
461Q16—81no—
462SD16—81no—
463SD16—81no—
464SD16—4881no—
465D8—4881no—
466M16—4881no—
467M16—2441no—
468M16—2441no—
469M16—2442no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—2442no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4C2×C22⋊D6111yescharacteristic
494C4⋊C4C2×C22⋊D6111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—2441no—
501C22⋊C4—2441no—
502C42—21no—
503C42D4×D6111yescharacteristic
504C42#1175822411yescharacteristic
505C42C2×C22⋊D6111yescharacteristic
506C42C23×D6111yescharacteristic
507C23—21no—
508C23—2441no—
509C23#1451974911yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—82no—
517Q8—2441no—
518Q8—2441no—
519D4—21no—
520D4—21no—
521D4—81no—
522D4—4881no—
523D4—4882no—
524D4—2441no—
525D4—2441no—
526D4—2441no—
527D4—2441no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—4882no—
542C2×C4—2441no—
543C2×C4#1451974911yescharacteristic
544C2×C4#1451974911yescharacteristic
545C2×C4#1451974911yescharacteristic
546C2×C4C2×D4×D6111yescharacteristic
547C2×C4C22×C22⋊D6111yescharacteristic
548C2×C4C2×#1175822411yescharacteristic
549C8—41no—
550C8—41no—
551C8—1221no—
552C8—1221no—
553C8—1221no—
554C8—1221no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—4881no—
566C22—4881no—
567C22—4881no—
568C22C2×#1451974911yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—4881no—
579C4#1684056111yescharacteristic
580C4#1684056111yescharacteristic
581C4#1684056511yescharacteristic
582C4#1684057311yescharacteristic
583C2—41no—
584C2—81no—
585C2—9761no—
586C2#2145531511yescharacteristic
587C2#2145549511yescharacteristic
588C2#2145555311yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3218C2
socleC22×C61C2×#121
prime radical#21457181C2
hypercenter#3218D61
hypocenterC61#19383
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. #21456215C2semidirect
3. #21454824C2semidirect
4. #21445389C2semidirect
5. #21445382C2semidirect
6. #21445375C2semidirect
7. #21445368C2semidirect
8. #21445265C2semidirect
9. #21445258C2semidirect
10. #21445251C2semidirect
11. #21445244C2semidirect
12. #21444587C2semidirect
13. #21444525C2semidirect
14. #21444491C2semidirect
15. C61×#3218C2semidirect
290. #3218D61semidirect
361. C61#19383semidirect

Maximal subgroups

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

subgroupindex
#214571812
#214562152
#214548242
#214453892
#214453822
#214453752
#214453682
#214452652
#214452582
#214452512
#214452442
#214445872
#214445252
#214444912
C61×#32182
#1938361