Finite Group Databasebeta

← #29669624

Subgroups — #29669624

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#21458464C211yesmaximal, characteristic, complemented
2#21457645C211yesmaximal, characteristic, complemented
3D4×#11758199C211yesmaximal, characteristic
4#21445455C211yesmaximal, characteristic, complemented
5#21445352C211yesmaximal, characteristic, complemented
6#21445268C211yesmaximal, characteristic, complemented
7#21445253C211yesmaximal, characteristic, complemented
8#21445177C211yesmaximal, characteristic, complemented
9#21444997C211yesmaximal, characteristic, complemented
10#21444935C211yesmaximal, characteristic, complemented
11#21444929C211yesmaximal, characteristic, complemented
12#21444890C211yesmaximal, characteristic, complemented
13#21444646C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3324C211yesmaximal, characteristic, complemented
16C22×#11758199—21no—
17#16840472C2211yescharacteristic, complemented
18D4×D244C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840134C2211yescharacteristic, complemented
21#16840116—21no—
22#16840112C2211yescharacteristic, complemented
23#16840110C2211yescharacteristic, complemented
24#16840109C2211yescharacteristic, complemented
25#16840082—21no—
26#16840069—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic, complemented
29#16839996—21no—
30#16839994—21no—
31#16839974—21no—
32#16839964C2211yescharacteristic, complemented
33#16839962C2211yescharacteristic, complemented
34#16839957C2211yescharacteristic
35#16839954C2211yescharacteristic
36#16839911—21no—
37#16839896—21no—
38#16839895—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C4×#11758201—21no—
41C4×#11758199C2211yescharacteristic
42C8×D244C2211yescharacteristic, complemented
43D4×#92418C2211yescharacteristic
44#102×D61—21no—
45#16839515C2211yescharacteristic, complemented
46#16839514C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C61×#556C2211yescharacteristic, complemented
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic, complemented
59C61×#482—21no—
60C61×#474C2211yescharacteristic
61C61×#468—21no—
62C61×#460C2211yescharacteristic, complemented
63C61×#450—21no—
64C4×SD16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic, complemented
66C61×#418—21no—
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758200—41no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758199—21no—
73C2×#11758199—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—44no—
77C2×#11758199D411yescharacteristic
78C22×#92418—21no—
79C2×C8×D61—21no—
80#14519777C2311yescharacteristic
81#14519774C2311yescharacteristic
82#14519769—21no—
83#14519755—41no—
84#14519753—21no—
85#14519752—21no—
86#14519751—21no—
87#14519747—41no—
88C4×D244—21no—
89C4×D244C2311yescharacteristic
90C4⋊C4×D61—21no—
91#14519710D411yescharacteristic
92#14519708—21no—
93#14519708—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698D411yescharacteristic
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
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
120C2×M16×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#126×C61—41no—
124#124×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#120×C61—41no—
129C4×Q8×C61—21no—
130C4×Q8×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#117×C61—21no—
134#107×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—
162C2×C22⋊D61—41no—
163D4×D61—42no—
164D4×D61—81no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—42no—
169C2×D244—41no—
170C2×D244—81no—
171C2×D244C2×D411yescharacteristic
172C2×C4×D61—21no—
173C2×C4×D61—41no—
174C2×Dic122—21no—
175SD16×C61—22no—
176SD16×C61—81no—
177M16×C61—81no—
178C2×C8×C61—21no—
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×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—41no—
191C22⋊C4×C61—41no—
192C22⋊C4×C61—41no—
193C42×C61—21no—
194C42×C61—41no—
195C42×C61C2411yescharacteristic
196#11758201—42no—
197#11758201—81no—
198#11758200—82no—
199#11758199—22no—
200#11758199—42no—
201#11758199—42no—
202#11758199—42no—
203#11758199—81no—
204#11758198—21no—
205#11758198—41no—
206#11758198—41no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61C2×D411yescharacteristic
210#11758196—41no—
211#11758196—41no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—42no—
217C2×#92418C2×D411yescharacteristic
218C2×#92418C2×D411yescharacteristic
219C8×D61—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—41no—
234Q8×C61—41no—
235D4×C61—21no—
236D4×C61—21no—
237D4×C61—21no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—81no—
243D4×C61—82no—
244D4×C61—82no—
245D4×C61#13512yes—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
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—41no—
263D244—41no—
264D244—41no—
265D244—41no—
266D244—81no—
267D244—82no—
268D244AGL(1,ℤ/8)12yes—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—161no—
272Dic122—81no—
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—41no—
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—22no—
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#3324D6111yescharacteristic, complemented
315#3295—611no—
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—81no—
330C2×C61—161no—
331C2×C61#326511yescharacteristic
332C2×C61#328011yescharacteristic
333C2×C61#328811yescharacteristic
334D61—42no—
335D61—161no—
336C22×D8—1221no—
337#556C2×D6111yescharacteristic, complemented
338#554—611no—
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—21no—
349#481—1221no—
350#479—1221no—
351#476—611no—
352#476—611no—
353#474C2×D6111yescharacteristic
354#468—21no—
355#466—1221no—
356#465—1221no—
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#436C2×D6111yescharacteristic, complemented
372C8×D4—611no—
373C8×D4—611no—
374#418—21no—
375C2×#102—1221no—
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—21no—
404C22×C8—1221no—
405C22×C8—1221no—
406C4⋊Q8—611no—
407C4⋊Q8C22×D6111yescharacteristic
408#127—611no—
409#127C22×D6111yescharacteristic
410#126—41no—
411#125—1221no—
412#124—21no—
413C22⋊Q8—21no—
414C22⋊Q8—1221no—
415C22⋊Q8—2441no—
416#121—21no—
417#121—21no—
418#121—1221no—
419#121—1221no—
420#120—41no—
421#120—2441no—
422C4×Q8—21no—
423C4×Q8C22×D6111yescharacteristic
424C4×D4—611no—
425C4×D4—1221no—
426C4×D4C22×D6111yescharacteristic
427C4×D4C22×D6111yescharacteristic
428#117—21no—
429C2×C4⋊C4—1221no—
430#107—21no—
431#107—611no—
432#106—1221no—
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—1221no—
495C22×C4—2441no—
496SD16—22no—
497SD16—81no—
498SD16—4882no—
499SD16—4881no—
500SD16—2442no—
501D8—1222no—
502D8—4881no—
503D8—2442no—
504D8—2442no—
505D8—2442no—
506M16—81no—
507C2×C8—21no—
508C2×C8—611no—
509C2×C8—611no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—4881no—
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—611no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—2441no—
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—41no—
535C22⋊C4—1221no—
536C22⋊C4—2441no—
537C22⋊C4—2441no—
538C42—21no—
539C42—41no—
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—41no—
555Q8—41no—
556Q8—4881no—
557D4—21no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—81no—
565D4—82no—
566D4—82no—
567D4—612no—
568D4—1221no—
569D4—4881no—
570D4—4882no—
571D4—4882no—
572D4—2441no—
573D4—2441no—
574D4—2441no—
575D4—2441no—
576D4#1451979712yes—
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—1221no—
587C2×C4—9761no—
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—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—164no—
613C22—1222no—
614C22—9764no—
615C22—4881no—
616C22—4881no—
617C22—4881no—
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
630C4AGL(1,ℤ/8)×D6111yescharacteristic
631C4#1684056511yescharacteristic
632C4#1684057211yescharacteristic
633C2—42no—
634C2—81no—
635C2—161no—
636C2—9761no—
637C2—2442no—
638C2#2145730811yescharacteristic
639C2#2145750011yescharacteristic
640C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3324C2
socleC22×C61D42
prime radicalD4×#11758199C2
hypercenter#3324D61
hypocenterC61#19773
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3324

Complements

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

NH ≅ G/Ntype
1. #21458464C2semidirect
2. #21457645C2semidirect
4. #21445455C2semidirect
5. #21445352C2semidirect
6. #21445268C2semidirect
7. #21445253C2semidirect
8. #21445177C2semidirect
9. #21444997C2semidirect
10. #21444935C2semidirect
11. #21444929C2semidirect
12. #21444890C2semidirect
13. #21444646C2semidirect
14. SD16⋊#92418C2semidirect
15. C61×#3324C2semidirect
17. #16840472C22semidirect
20. #16840134C22semidirect
22. #16840112C22semidirect
23. #16840110C22semidirect
24. #16840109C22semidirect
28. #16840052C22semidirect
32. #16839964C22semidirect
33. #16839962C22semidirect
39. Q8×#92418C22semidirect
42. C8×D244C22semidirect
45. #16839515C22semidirect
46. #16839514C22semidirect
47. #16839510C22semidirect
48. #16839508C22semidirect
49. #16839506C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
54. #16839489C22semidirect
55. #16839483C22semidirect
56. C61×#556C22semidirect
58. C61×#486C22semidirect
62. C61×#460C22semidirect
65. C61×#436C22semidirect
314. #3324D61semidirect
337. #556C2×D61semidirect
347. #486C2×D61semidirect
360. #460C2×D61semidirect
371. #436C2×D61semidirect
387. C61#19773semidirect

Maximal subgroups

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

subgroupindex
#214584642
#214576452
D4×#117581992
#214454552
#214453522
#214452682
#214452532
#214451772
#214449972
#214449352
#214449292
#214448902
#214446462
SD16⋊#924182
C61×#33242
#1977361