Finite Group Databasebeta

← #29669630

Subgroups — #29669630

Order 15616.

712 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458468C211yesmaximal, characteristic, complemented
2#21458052C211yesmaximal, characteristic, complemented
3D4×#11758199C211yesmaximal, characteristic
4#21445459C211yesmaximal, characteristic, complemented
5#21445349C211yesmaximal, characteristic, complemented
6#21445272C211yesmaximal, characteristic, complemented
7#21445256C211yesmaximal, characteristic, complemented
8#21445177C211yesmaximal, characteristic, complemented
9#21444998C211yesmaximal, characteristic, complemented
10#21444934C211yesmaximal, characteristic, complemented
11#21444928C211yesmaximal, characteristic, complemented
12#21444891C211yesmaximal, characteristic, complemented
13#21444648C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3295C211yesmaximal, characteristic, complemented
16C22×#11758199—21no—
17#16840485C2211yescharacteristic, complemented
18D4×D244C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840136C2211yescharacteristic, complemented
21#16840119—21no—
22#16840114C2211yescharacteristic, complemented
23#16840109C2211yescharacteristic, complemented
24#16840108C2211yescharacteristic, complemented
25#16840088—21no—
26#16840066—21no—
27#16840049C2211yescharacteristic, complemented
28#16840042C2211yescharacteristic
29#16840011—21no—
30#16839996—21no—
31#16839977—21no—
32#16839967C2211yescharacteristic, complemented
33#16839962C2211yescharacteristic, complemented
34#16839957C2211yescharacteristic
35#16839954C2211yescharacteristic
36#16839911—21no—
37#16839896—21no—
38#16839895—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C4×#11758200—21no—
41C4×#11758199C2211yescharacteristic
42#16839841C2211yescharacteristic, complemented
43D4×#92418C2211yescharacteristic
44#16839765—21no—
45#16839515C2211yescharacteristic, complemented
46#16839514C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839507C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C61×#554C2211yescharacteristic, complemented
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic, complemented
59C61×#481—21no—
60C61×#476C2211yescharacteristic
61C61×#465—21no—
62C61×#460C2211yescharacteristic, complemented
63C61×#450—21no—
64C4×SD16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic, complemented
66C2×#102×C61—21no—
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758201—41no—
72C2×#11758199—21no—
73C2×#11758199—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—44no—
77C2×#11758199D411yescharacteristic
78C2×#11758189—21no—
79C22×#92418—21no—
80#14519777C2311yescharacteristic
81#14519774C2311yescharacteristic
82#14519772—41no—
83#14519765—21no—
84#14519753—21no—
85#14519752—21no—
86#14519751—21no—
87#14519747—41no—
88C4×Dic122—21no—
89C4×D244C2311yescharacteristic
90#14519735—21no—
91#14519710—21no—
92#14519710D411yescharacteristic
93#14519708—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519700—21no—
99#14519700—21no—
100#14519700—21no—
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—41no—
106#14519698D411yescharacteristic
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61D411yescharacteristic
120C22×C8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#125×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126#121×C61—21no—
127#121×C61—21no—
128#120×C61—41no—
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133C2×C4⋊C4×C61—21no—
134#106×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61D411yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C24×C61—41no—
146C23×D61—41no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61—42no—
155C2×D4×C61—42no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—41no—
163C2×C22⋊D61—41no—
164D4×D61—42no—
165D4×D61—81no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—42no—
170C2×D244—41no—
171C2×D244—81no—
172C2×D244C2×D411yescharacteristic
173C2×C4×D61—21no—
174C2×Dic122—21no—
175SD16×C61—22no—
176SD16×C61—81no—
177C2×C8×C61—21no—
178C2×C8×C61—81no—
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—41no—
185C4⋊C4×C61—41no—
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C4⋊C4×C61C2×D411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—41no—
192C22⋊C4×C61—41no—
193C42×C61—21no—
194C42×C61C2411yescharacteristic
195#11758201—81no—
196#11758201—82no—
197#11758200—42no—
198#11758199—22no—
199#11758199—42no—
200#11758199—42no—
201#11758199—42no—
202#11758199—81no—
203#11758198—21no—
204#11758198—41no—
205#11758198—41no—
206#11758198—41no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61C2×D411yescharacteristic
210#11758196—41no—
211C4×Dic61—41no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—42no—
217C2×#92418C2×D411yescharacteristic
218C2×#92418C2×D411yescharacteristic
219#11758189—81no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—41no—
223C23×C61—82no—
224C23×C61—82no—
225C23×C61—161no—
226C22×D61—21no—
227C22×D61—41no—
228C22×D61—82no—
229C22×D61—82no—
230C22×D61—161no—
231Q8×C61—21no—
232Q8×C61—21no—
233Q8×C61—81no—
234D4×C61—21no—
235D4×C61—21no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—81no—
241D4×C61—82no—
242D4×C61—82no—
243D4×C61#13512yes—
244D4×C61AGL(1,ℤ/8)12yes—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—161no—
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61H(5,𝔽2)11yescharacteristic
258C22⋊D61—82no—
259C2×Dic61—21no—
260C2×Dic61—41no—
261D244—21no—
262D244—21no—
263D244—41no—
264D244—41no—
265D244—41no—
266D244—41no—
267D244—81no—
268D244—82no—
269C4×D61—41no—
270C4×D61—41no—
271Dic122—41no—
272Dic122—41no—
273C8×C61—21no—
274C8×C61—21no—
275C8×C61—41no—
276#92418—21no—
277#92418—21no—
278#92418—41no—
279#92418—41no—
280#92418—41no—
281#92418—41no—
282#19773—611nomaximal, Sylow
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—81no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61—164no—
293C22×C61D4211yescharacteristic
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—81no—
300C2×D61—164no—
301C4×C61—21no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—81no—
307C4×C61C2×#13511yescharacteristic
308C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
309C4×C61#57611yescharacteristic
310C4×C61#57711yescharacteristic
311Dic61—41no—
312Dic61—81no—
313#3360—611no—
314#3324—611no—
315#3295D6111yescharacteristic, complemented
316D4×D8—611no—
317#1717—611no—
318#1697—611no—
319#1683—611no—
320#1681—611no—
321#1668—611no—
322#1639—611no—
323#1629—611no—
324#1628—611no—
325#1622—611no—
326#1581—611no—
327SD16⋊C8—611no—
328C2×C61—42no—
329C2×C61—42no—
330C2×C61—161no—
331C2×C61#326511yescharacteristic
332C2×C61#328011yescharacteristic
333C2×C61#328811yescharacteristic
334D61—81no—
335D61—161no—
336C22×D8—1221no—
337#556—611no—
338#554C2×D6111yescharacteristic, complemented
339D42—611no—
340D42C2×D6111yescharacteristic
341#493—611no—
342#492—611no—
343#488—1221no—
344#487—611no—
345#486—611no—
346#486—611no—
347#486C2×D6111yescharacteristic, complemented
348#482—1221no—
349#481—21no—
350#479—1221no—
351#476—611no—
352#476C2×D6111yescharacteristic
353#474—611no—
354#468—1221no—
355#466—1221no—
356#465—21no—
357#463—1221no—
358#461—611no—
359#460—611no—
360#460C2×D6111yescharacteristic, complemented
361#459—611no—
362#459—611no—
363#450—21no—
364#450—1221no—
365#447—1221no—
366#447—1221no—
367C8×Q8—611no—
368C4×SD16—1221no—
369C4×SD16C2×D6111yescharacteristic
370C4×D8—611no—
371#436—611no—
372C8×D4—611no—
373C8×D4C2×D6111yescharacteristic, complemented
374#418—1221no—
375C2×#102—21no—
376#335—611no—
377#335—611no—
378#333—611no—
379#332—611no—
380#331—611no—
381#331—611no—
382Q8⋊C8—611no—
383D4⋊C8—611no—
384D4⋊C8—611no—
385D4⋊C8—611no—
386#322—611no—
387C61#1977311yescharacteristic, complemented, Sylow
388C22×D4—21no—
389C22×D4—21no—
390C22×D4—1221no—
391C22×D4—1221no—
392C2×SD16—21no—
393C2×SD16—1221no—
394C2×SD16—1221no—
395C2×SD16—2441no—
396C2×SD16C22⋊D6111yescharacteristic
397C2×D8—611no—
398C2×D8—1221no—
399C2×D8—1221no—
400C2×D8—1221no—
401C2×D8—1221no—
402C2×D8—2444no—
403C2×M16—1221no—
404C22×C8—21no—
405C22×C8—1221no—
406C4⋊Q8—611no—
407C4⋊Q8C22×D6111yescharacteristic
408#127—611no—
409#127C22×D6111yescharacteristic
410#126—2441no—
411#125—21no—
412#124—1221no—
413C22⋊Q8—21no—
414C22⋊Q8—41no—
415C22⋊Q8—1221no—
416#121—21no—
417#121—21no—
418#121—1221no—
419#121—1221no—
420#120—41no—
421#120—2441no—
422C4×Q8—1221no—
423C4×Q8C22×D6111yescharacteristic
424C4×D4—21no—
425C4×D4—611no—
426C4×D4C22×D6111yescharacteristic
427C4×D4C22×D6111yescharacteristic
428#117—1221no—
429C2×C4⋊C4—21no—
430#107—611no—
431#107—1221no—
432#106—21no—
433#106—1221no—
434#106C22⋊D6111yescharacteristic
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—611no—
438C4⋊C8—1221no—
439C4⋊C8C22×D6111yescharacteristic
440#103—1221no—
441#103—1221no—
442#103—1221no—
443#103C22⋊D6111yescharacteristic
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—611no—
449#102—611no—
450#102—1221no—
451#102—1221no—
452#102—1221no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456#102—1221no—
457#102—2441no—
458#102C22⋊D6111yescharacteristic
459C22⋊C8—21no—
460C22⋊C8—1221no—
461C22⋊C8—1221no—
462C4×C8—611no—
463C4×C8—611no—
464C4×C8—1221no—
465C4×C8C22×D6111yescharacteristic
466C24—41no—
467C24—2441no—
468C2×Q8—21no—
469C2×Q8—1221no—
470C2×Q8C2×C22⋊D6111yescharacteristic
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—81no—
479C2×D4—81no—
480C2×D4—611no—
481C2×D4—1221no—
482C2×D4—1221no—
483C2×D4—1221no—
484C2×D4—4881no—
485C2×D4—4881no—
486C2×D4—2441no—
487C2×D4—2442no—
488C2×D4—2441no—
489C2×D4—2442no—
490C2×D4D4×D6111yescharacteristic
491C2×D4C2×C22⋊D6111yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—1221no—
496SD16—22no—
497SD16—81no—
498SD16—4882no—
499SD16—4881no—
500SD16—2442no—
501D8—1222no—
502D8—4881no—
503D8—2442no—
504D8—2442no—
505D8—2442no—
506M16—4881no—
507C2×C8—21no—
508C2×C8—81no—
509C2×C8—611no—
510C2×C8—611no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—2442no—
516C2×C8C2×C22⋊D6111yescharacteristic
517C2×C8C2×C22⋊D6111yescharacteristic
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—611no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—2441no—
527C4⋊C4D4×D6111yescharacteristic
528C4⋊C4C2×C22⋊D6111yescharacteristic
529C4⋊C4C2×C22⋊D6111yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—1221no—
535C22⋊C4—2441no—
536C22⋊C4—2441no—
537C22⋊C4—2441no—
538C42—21no—
539C42—2441no—
540C42C23×D6111yescharacteristic
541C23—21no—
542C23—21no—
543C23—41no—
544C23—82no—
545C23—82no—
546C23—161no—
547C23—1221no—
548C23—9761no—
549C23—4882no—
550C23—4882no—
551C23—2441no—
552Q8—21no—
553Q8—21no—
554Q8—81no—
555Q8—2441no—
556Q8—2441no—
557D4—21no—
558D4—21no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—81no—
564D4—82no—
565D4—82no—
566D4—1221no—
567D4—1221no—
568D4—4881no—
569D4—4882no—
570D4—4882no—
571D4—2441no—
572D4—2441no—
573D4—2441no—
574D4—2441no—
575D4#1451979712yes—
576D4#1451980412yes—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—161no—
587C2×C4—1221no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4C2×D4×D6111yescharacteristic
592C2×C4C22×C22⋊D6111yescharacteristic
593C2×C4#1451982211yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—1221no—
598C8—1221no—
599C8—2441no—
600C8—2441no—
601C8—2441no—
602C8—2441no—
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—164no—
613C22—9764no—
614C22—4881no—
615C22—4881no—
616C22—4881no—
617C22—2441no—
618C22—2441no—
619C22—2441no—
620C22D4×C22⋊D6111yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—81no—
627C4—4881no—
628C4—2441no—
629C4C2×#1451979711yescharacteristic
630C4C2×#1451980411yescharacteristic
631C4#1684056511yescharacteristic
632C4#1684056811yescharacteristic
633C2—42no—
634C2—42no—
635C2—161no—
636C2—9761no—
637C2—4881no—
638C2#2145731411yescharacteristic
639C2#2145750011yescharacteristic
640C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3295C2
socleC22×C61D42
prime radicalD4×#11758199C2
hypercenter#3295D61
hypocenterC61#19773
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3295

Complements

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

NH ≅ G/Ntype
1. #21458468C2semidirect
2. #21458052C2semidirect
4. #21445459C2semidirect
5. #21445349C2semidirect
6. #21445272C2semidirect
7. #21445256C2semidirect
8. #21445177C2semidirect
9. #21444998C2semidirect
10. #21444934C2semidirect
11. #21444928C2semidirect
12. #21444891C2semidirect
13. #21444648C2semidirect
14. SD16⋊#92418C2semidirect
15. C61×#3295C2semidirect
17. #16840485C22semidirect
20. #16840136C22semidirect
22. #16840114C22semidirect
23. #16840109C22semidirect
24. #16840108C22semidirect
27. #16840049C22semidirect
32. #16839967C22semidirect
33. #16839962C22semidirect
39. Q8×#92418C22semidirect
42. #16839841C22semidirect
45. #16839515C22semidirect
46. #16839514C22semidirect
47. #16839511C22semidirect
48. #16839507C22semidirect
49. #16839506C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
54. #16839489C22semidirect
55. #16839483C22semidirect
56. C61×#554C22semidirect
58. C61×#486C22semidirect
62. C61×#460C22semidirect
65. C8×D4×C61C22semidirect
315. #3295D61semidirect
338. #554C2×D61semidirect
347. #486C2×D61semidirect
360. #460C2×D61semidirect
373. C8×D4C2×D61semidirect
387. C61#19773semidirect

Maximal subgroups

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

subgroupindex
#214584682
#214580522
D4×#117581992
#214454592
#214453492
#214452722
#214452562
#214451772
#214449982
#214449342
#214449282
#214448912
#214446482
SD16⋊#924182
C61×#32952
#1977361