Finite Group Databasebeta

← #29670591

Subgroups — #29670591

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458607C211yesmaximal, characteristic
2#21458457C211yesmaximal, characteristic, complemented
3Q16×D244C211yesmaximal, characteristic, complemented
4#21445478C211yesmaximal, characteristic, complemented
5#21445371C211yesmaximal, characteristic, complemented
6#21445261C211yesmaximal, characteristic, complemented
7#21445253C211yesmaximal, characteristic
8#21445189C211yesmaximal, characteristic, complemented
9#21445096C211yesmaximal, characteristic, complemented
10#21445081C211yesmaximal, characteristic, complemented
11#21445005C211yesmaximal, characteristic, complemented
12#21444920C211yesmaximal, characteristic
13#21444670C211yesmaximal, characteristic, complemented
14#21444629C211yesmaximal, characteristic, complemented
15C61×#3365C211yesmaximal, characteristic, complemented
16C2×Q16×D61—21no—
17Q8×D244C2211yescharacteristic
18Q8×D244C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840142C2211yescharacteristic
21#16840121—21no—
22#16840112—21no—
23#16840112C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840108C2211yescharacteristic
26#16840052—21no—
27#16840047—21no—
28#16840047C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840004—21no—
31#16839974—21no—
32#16839972C2211yescharacteristic
33#16839972C2211yescharacteristic
34#16839964—21no—
35#16839964C2211yescharacteristic
36#16839954C2211yescharacteristic
37#16839919—21no—
38#16839919—21no—
39#16839893C2211yescharacteristic
40Q8×#92418C2211yescharacteristic
41#16839872—21no—
42C4×#11758201—21no—
43C4×#11758201C2211yescharacteristic
44C8×D244C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839509C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#559C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#488—21no—
59C61×#486C2211yescharacteristic
60C61×#478—21no—
61C61×#475C2211yescharacteristic
62C61×#464—21no—
63C61×#460C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×Q16×C61C2211yescharacteristic
66C4×SD16×C61—21no—
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×Dic244—21no—
70C2×Dic244—21no—
71C2×#11758202—21no—
72C2×#11758202—21no—
73Q16×D61—44no—
74C2×#11758201—21no—
75C2×#11758201D411yescharacteristic
76C2×#11758199—21no—
77C2×C8×D61—21no—
78#14519777—21no—
79#14519777—21no—
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519757—21no—
83#14519757—21no—
84#14519757—41no—
85#14519757—41no—
86C4×D244—21no—
87C4×D244—21no—
88C4×D244C2311yescharacteristic
89#14519708—21no—
90#14519708—21no—
91#14519708—41no—
92#14519708D411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701D411yescharacteristic
104#14519700—21no—
105#14519700—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698—41no—
110#14519697D411yescharacteristic
111#14519689—21no—
112#14519688—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×Q16×C61D411yescharacteristic
117C2×SD16×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120#127×C61C2311yescharacteristic
121#125×C61—21no—
122#125×C61—41no—
123#124×C61—21no—
124#124×C61—21no—
125#123×C61—41no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×D4×C61—21no—
132C4×D4×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137#103×C61—21no—
138#103×C61D411yescharacteristic
139#103×C61D411yescharacteristic
140#102×C61—21no—
141#102×C61—21no—
142#102×C61—21no—
143C4×C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C22×C4×C61—41no—
153Q8×D61—42no—
154Q8×D61—42no—
155Q8×D61—81no—
156Q8×D61—81no—
157C2×D244C2×D411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—41no—
164C2×Dic122—41no—
165Q16×C61—22no—
166SD16×C61—42no—
167C2×C8×C61—21no—
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—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C4⋊C4×C61C2×D411yescharacteristic
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—41no—
188C42×C61C2411yescharacteristic
189#11758202—42no—
190#11758202—42no—
191#11758201—22no—
192#11758201—42no—
193#11758199—42no—
194#11758198—21no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—41no—
202C4⋊Dic61—41no—
203C4⋊Dic61C2×D411yescharacteristic
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210Dic244—42no—
211Dic244—81no—
212C8×D61—42no—
213C23×C61—41no—
214C22×D61—21no—
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—21no—
219Q8×C61—21no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61AGL(1,ℤ/8)12yes—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—81no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—41no—
235C2×C4×C61—161no—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C2×Dic61—21no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242D244—21no—
243D244#13512yes—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—82no—
247C4×D61—82no—
248Dic122—41no—
249Dic122—41no—
250Dic122—41no—
251Dic122—41no—
252Dic122—82no—
253Dic122—82no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—41no—
257#92418—21no—
258#92418—21no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#19837—611nomaximal, Sylow
264C22×C61—81no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61D4211yescharacteristic
268C2×D61—22no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—22no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—81no—
279C4×C61C2×#13511yescharacteristic
280C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C61#57711yescharacteristic
282C4×C61#57811yescharacteristic
283Dic61—41no—
284Dic61—81no—
285Dic61—81no—
286#3373—611no—
287#3365D6111yescharacteristic, complemented
288#3359—611no—
289D4×Q16—611no—
290#1720—611no—
291#1700—611no—
292#1682—611no—
293#1681—611no—
294#1670—611no—
295#1653—611no—
296#1651—611no—
297#1640—611no—
298#1627—611no—
299#1584—611no—
300SD16⋊C8—611no—
301C2×C61—161no—
302C2×C61#326511yescharacteristic
303C2×C61#328511yescharacteristic
304C2×C61#328911yescharacteristic
305D61—42no—
306C22×Q16—1221no—
307#559C2×D6111yescharacteristic
308#557C2×D6111yescharacteristic
309D4×Q8—611no—
310D4×Q8—611no—
311#498—611no—
312#494—611no—
313#489—1221no—
314#488—21no—
315#487—611no—
316#487—1221no—
317#486—611no—
318#486—611no—
319#486C2×D6111yescharacteristic
320#478—21no—
321#476—1221no—
322#475—611no—
323#475—611no—
324#475—1221no—
325#475C2×D6111yescharacteristic
326#467—1221no—
327#464—21no—
328#463—1221no—
329#462—611no—
330#462—611no—
331#461—611no—
332#461—1221no—
333#460C2×D6111yescharacteristic
334#459—611no—
335#451—1221no—
336#451—1221no—
337#446—611no—
338C8×Q8—611no—
339C8×Q8C2×D6111yescharacteristic
340#442—1221no—
341C4×Q16C2×D6111yescharacteristic
342C4×SD16—21no—
343C4×SD16—611no—
344C4×SD16—1221no—
345C8×D4—611no—
346#335—611no—
347#335—611no—
348#332—611no—
349#332—611no—
350#332—611no—
351#331—611no—
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354Q8⋊C8—611no—
355D4⋊C8—611no—
356#322—611no—
357C61#1983711yescharacteristic, complemented, Sylow
358C22×Q8—1221no—
359C22×Q8—1221no—
360C2×Q16—1221no—
361C2×Q16—1221no—
362C2×Q16—1221no—
363C2×Q16—1221no—
364C2×Q16—2444no—
365C2×Q16C22⋊D6111yescharacteristic
366C2×SD16—21no—
367C2×SD16—611no—
368C2×SD16—1221no—
369C2×D8—1221no—
370C22×C8—1221no—
371C4⋊Q8—21no—
372C4⋊Q8—611no—
373C4⋊Q8—611no—
374C4⋊Q8—1221no—
375C4⋊Q8—1221no—
376C4⋊Q8C22×D6111yescharacteristic
377#127C22×D6111yescharacteristic
378#125—21no—
379#125—41no—
380#124—21no—
381#124—21no—
382#123—41no—
383C22⋊Q8—1221no—
384C22⋊Q8—1221no—
385C22⋊Q8—2441no—
386C22⋊Q8—2441no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C22×D6111yescharacteristic
390C4×Q8C22×D6111yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—611no—
395C4×D4—1221no—
396C4×D4—1221no—
397#107C22⋊D6111yescharacteristic
398#106—21no—
399#106—611no—
400#106—1221no—
401#106—1221no—
402#106—2441no—
403C4⋊C8—21no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8C22×D6111yescharacteristic
410#103—21no—
411#103—611no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103C22⋊D6111yescharacteristic
420#103C22⋊D6111yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—611no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—2441no—
429C22⋊C8—1221no—
430#97—1221no—
431C4×C8—21no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—1221no—
435C4×C8C22×D6111yescharacteristic
436C2×Q8—21no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×Q8—4881no—
440C2×Q8—4881no—
441C2×Q8—2441no—
442C2×Q8—2441no—
443C2×Q8—2442no—
444C2×Q8—2442no—
445C2×Q8D4×D6111yescharacteristic
446C2×Q8C2×C22⋊D6111yescharacteristic
447C2×Q8C2×C22⋊D6111yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—611no—
452C22×C4—41no—
453C22×C4—1221no—
454C22×C4—2441no—
455C22×C4—2441no—
456Q16—22no—
457Q16—4881no—
458Q16—2442no—
459Q16—2442no—
460Q16—2442no—
461SD16—42no—
462SD16—1222no—
463SD16—2442no—
464D8—2442no—
465C2×C8—21no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—2442no—
473C2×C8C2×C22⋊D6111yescharacteristic
474C2×C8C2×C22⋊D6111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—611no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—2441no—
489C4⋊C4—2441no—
490C4⋊C4D4×D6111yescharacteristic
491C4⋊C4C2×C22⋊D6111yescharacteristic
492C4⋊C4C2×C22⋊D6111yescharacteristic
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—1221no—
497C22⋊C4—2441no—
498C22⋊C4—2441no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C23×D6111yescharacteristic
504C23—41no—
505C23—1221no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—4882no—
514Q8—4882no—
515Q8—2441no—
516Q8—2441no—
517Q8—2441no—
518Q8—2441no—
519Q8#1451980212yes—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—612no—
526D4—1221no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—161no—
535C2×C4—1221no—
536C2×C4—4882no—
537C2×C4—4882no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4C2×D4×D6111yescharacteristic
543C2×C4C22×C22⋊D6111yescharacteristic
544C2×C4#1451982211yescharacteristic
545C8—21no—
546C8—21no—
547C8—41no—
548C8—1221no—
549C8—1221no—
550C8—2441no—
551C8—2441no—
552C8—2441no—
553C8—2441no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—1222no—
558C22—2441no—
559C22—2441no—
560C22D4×C22⋊D6111yescharacteristic
561C4—22no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—4881no—
570C4—4881no—
571C4—2441no—
572C4#135×D6111yescharacteristic
573C4C2×#1451980211yescharacteristic
574C4#1684057011yescharacteristic
575C4#1684057611yescharacteristic
576C2—161no—
577C2—2442no—
578C2#2145731511yescharacteristic
579C2#2145755411yescharacteristic
580C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3365C2
socleC22×C61D42
prime radical#16839954C22
hypercenter#3365D61
hypocenterC61#19837
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3365

Complements

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

NH ≅ G/Ntype
2. #21458457C2semidirect
3. Q16×D244C2semidirect
4. #21445478C2semidirect
5. #21445371C2semidirect
6. #21445261C2semidirect
8. #21445189C2semidirect
9. #21445096C2semidirect
10. #21445081C2semidirect
11. #21445005C2semidirect
13. #21444670C2semidirect
14. #21444629C2semidirect
15. C61×#3365C2semidirect
287. #3365D61semidirect
357. C61#19837semidirect

Maximal subgroups

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

subgroupindex
#214586072
#214584572
Q16×D2442
#214454782
#214453712
#214452612
#214452532
#214451892
#214450962
#214450812
#214450052
#214449202
#214446702
#214446292
C61×#33652
#1983761