Finite Group Databasebeta

← #29670089

Subgroups — #29670089

Order 15616.

720 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1SD16×Dic122C211yesmaximal, characteristic, complemented
2#21458486C211yesmaximal, characteristic, complemented
3D4×#11758200C211yesmaximal, characteristic, complemented
4#21445445C211yesmaximal, characteristic, complemented
5#21445318C211yesmaximal, characteristic, complemented
6#21445226C211yesmaximal, characteristic, complemented
7#21445176C211yesmaximal, characteristic, complemented
8#21445165C211yesmaximal, characteristic, complemented
9#21445019C211yesmaximal, characteristic, complemented
10#21444935C211yesmaximal, characteristic, complemented
11#21444921C211yesmaximal, characteristic, complemented
12#21444896C211yesmaximal, characteristic, complemented
13#21444660C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3274C211yesmaximal, characteristic
16C22×#11758200—21no—
17Q8×Dic122C2211yescharacteristic, complemented
18D4×Dic122C2211yescharacteristic
19#16840160C2211yescharacteristic, complemented
20#16840159—21no—
21#16840134C2211yescharacteristic
22#16840134C2211yescharacteristic
23#16840108—21no—
24#16840108C2211yescharacteristic, complemented
25#16840108C2211yescharacteristic, complemented
26#16840052—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic
29#16840050—21no—
30#16840047C2211yescharacteristic, complemented
31#16840045—21no—
32#16839989—21no—
33#16839967C2211yescharacteristic
34#16839959—21no—
35#16839959C2211yescharacteristic
36#16839959C2211yescharacteristic, complemented
37#16839913—21no—
38#16839900—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C8×Dic122C2211yescharacteristic, complemented
41SD16×Dic61—21no—
42C4×#11758200—21no—
43C4×#11758200C2211yescharacteristic
44D4×#92418C2211yescharacteristic
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839507C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic
50#16839506C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52#16839492C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C61—21no—
57C61×#550C2211yescharacteristic
58D42×C61C2211yescharacteristic
59C61×#493C2211yescharacteristic
60C61×#469—21no—
61C61×#460C2211yescharacteristic
62C61×#459C2211yescharacteristic
63C61×#449—21no—
64C61×#447—21no—
65C4×SD16×C61C2211yescharacteristic
66C61×#436C2211yescharacteristic
67C22×Dic122—21no—
68C2×#11758200—21no—
69C2×#11758200—21no—
70C2×#11758200—21no—
71C2×#11758200—21no—
72C2×#11758200—21no—
73C2×#11758200—41no—
74C2×#11758200—44no—
75C2×#11758200D411yescharacteristic
76C22×#92418—21no—
77#14519777—21no—
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519776—21no—
81#14519776—21no—
82#14519776—41no—
83#14519756—21no—
84#14519754—41no—
85Q8×Dic61—21no—
86C4×Dic122—21no—
87C4×Dic122C2311yescharacteristic
88D4×Dic61—21no—
89#14519709—21no—
90#14519709—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708D411yescharacteristic
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519701—21no—
101#14519700—21no—
102#14519700D411yescharacteristic
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698—41no—
110#14519698D411yescharacteristic
111C22⋊#92418—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C8×Dic61—21no—
116C2×#41×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119AGL(1,ℤ/8)×C61—44no—
120C2×SD16×C61—21no—
121C2×SD16×C61D411yescharacteristic
122C2×D8×C61—21no—
123C2×D8×C61—21no—
124C2×D8×C61—21no—
125C2×M16×C61—21no—
126#127×C61—21no—
127#127×C61C2311yescharacteristic
128#127×C61C2311yescharacteristic
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—41no—
133#120×C61—41no—
134C4×Q8×C61C2311yescharacteristic
135C4×D4×C61—21no—
136C4×D4×C61C2311yescharacteristic
137C4×D4×C61C2311yescharacteristic
138#106×C61D411yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61D411yescharacteristic
141#102×C61—21no—
142#102×C61—21no—
143#102×C61D411yescharacteristic
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C24×C61—41no—
147#41×C61—42no—
148#41×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61—41no—
159C2×D4×C61—41no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—81no—
163C2×D4×C61—81no—
164C2×D4×C61C2×D411yescharacteristic
165C2×D4×C61C2×D411yescharacteristic
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—41no—
169C22×Dic61—41no—
170C2×Dic122—21no—
171C2×Dic122—21no—
172C2×Dic122—42no—
173C2×Dic122—41no—
174C2×Dic122—41no—
175C2×Dic122—81no—
176C2×Dic122C2×D411yescharacteristic
177SD16×C61—42no—
178SD16×C61SD1614yescomplemented
179D8×C61—42no—
180D8×C61—42no—
181D8×C61—81no—
182M16×C61—42no—
183C2×C8×C61—21no—
184C2×C8×C61C2×D411yescharacteristic
185C2×C8×C61C2×D411yescharacteristic
186C4⋊C4×C61—21no—
187C4⋊C4×C61C2×D411yescharacteristic
188C4⋊C4×C61C2×D411yescharacteristic
189C4⋊C4×C61C2×D411yescharacteristic
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C22⋊C4×C61—41no—
193C22⋊C4×C61—41no—
194C42×C61—21no—
195C42×C61C2411yescharacteristic
196C22⋊Dic61—41no—
197#11758200—22no—
198#11758200—42no—
199#11758200—42no—
200#11758200—42no—
201#11758200—42no—
202#11758200—81no—
203#11758200—82no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—41no—
209C4⋊Dic61C2×D411yescharacteristic
210#11758196—21no—
211#11758196—41no—
212#11758196—41no—
213C4×Dic61—21no—
214C4×Dic61—41no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—42no—
220C2×#92418C2×D411yescharacteristic
221C2×#92418C2×D411yescharacteristic
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—82no—
227C23×C61—82no—
228C23×C61—161no—
229Q8×C61—21no—
230Q8×C61C2×SD1612yescomplemented
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—82no—
243D4×C61—81no—
244D4×C61—81no—
245D4×C61—82no—
246D4×C61—82no—
247D4×C61—161no—
248D4×C61C2×SD1612yes—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—82no—
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61H(5,𝔽2)11yescharacteristic
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—82no—
266Dic122—21no—
267Dic122—41no—
268Dic122—41no—
269Dic122—82no—
270Dic122—81no—
271Dic122—161no—
272Dic122AGL(1,ℤ/8)12yescomplemented
273C8×C61—21no—
274C8×C61—41no—
275C8×C61C2×SD1612yescomplemented
276#92418—21no—
277#92418—21no—
278#92418—41no—
279#92418—41no—
280#92418—41no—
281#92418—41no—
282#19804—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—81no—
293C22×C61—81no—
294C22×C61—81no—
295C22×C61—164no—
296C22×C61D4211yescharacteristic
297C4×C61—22no—
298C4×C61—21no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61C22×SD1611yescharacteristic
303C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C61#57711yescharacteristic
305C4×C61#57711yescharacteristic
306Dic61—22no—
307Dic61—41no—
308Dic61—81no—
309Dic61—81no—
310Q8×SD16—611no—
311#3362—611no—
312D4×SD16—611no—
313#3274D6111yescharacteristic
314#1715—611no—
315#1691—611no—
316#1677—611no—
317#1668—611no—
318#1666—611no—
319#1642—611no—
320#1629—611no—
321#1627—611no—
322#1623—611no—
323#1583—611no—
324SD16⋊C8—611no—
325C2×C61—42no—
326C2×C61—81no—
327C2×C61—161no—
328C2×C61—161no—
329C2×C61#326511yescharacteristic
330C2×C61D4×SD1611yescharacteristic
331C2×C61#328811yescharacteristic
332C2×AGL(1,ℤ/8)—21no—
333C22×SD16—1221no—
334Q82—611no—
335#550C2×D6111yescharacteristic
336D4×Q8—611no—
337D42C2×D6111yescharacteristic
338#498—611no—
339#498—1221no—
340#493C2×D6111yescharacteristic
341#492—611no—
342#492—611no—
343#486—611no—
344#486—611no—
345#486—1221no—
346#476—611no—
347#476—611no—
348#476—1221no—
349#476—1221no—
350#475—611no—
351#475—1221no—
352#469—21no—
353#465—1221no—
354#461—611no—
355#460—611no—
356#460—611no—
357#460—1221no—
358#460C2×D6111yescharacteristic
359#459C2×D6111yescharacteristic
360#450—1221no—
361#449—21no—
362#448—1221no—
363#447—21no—
364C8×Q8—611no—
365C8×Q8—611no—
366C4×SD16—611no—
367C4×SD16—1221no—
368C4×SD16—1221no—
369C4×SD16C2×D6111yescharacteristic
370#436C2×D6111yescharacteristic
371C8×D4—611no—
372#335—611no—
373#334—611no—
374#333—611no—
375#332—611no—
376#331—611no—
377#331—611no—
378Q8⋊C8—611no—
379Q8⋊C8—611no—
380D4⋊C8—611no—
381D4⋊C8—611no—
382#322—611no—
383C61#1980411yescharacteristic, complemented, Sylow
384C2×#41—21no—
385C22×Q8—1221no—
386C22×D4—21no—
387C22×D4—21no—
388AGL(1,ℤ/8)—44no—
389C2×SD16—21no—
390C2×SD16—611no—
391C2×SD16—1221no—
392C2×SD16—1221no—
393C2×SD16—1221no—
394C2×SD16—1221no—
395C2×SD16—1221no—
396C2×SD16—2441no—
397C2×SD16—2444no—
398C2×SD16C22⋊D6111yescharacteristic
399C2×D8—21no—
400C2×D8—21no—
401C2×D8—21no—
402C2×M16—21no—
403C22×C8—1221no—
404C4⋊Q8—611no—
405C4⋊Q8—611no—
406C4⋊Q8—1221no—
407C4⋊Q8—1221no—
408C4⋊Q8—1221no—
409C4⋊Q8—2441no—
410#127—21no—
411#127C22×D6111yescharacteristic
412#127C22×D6111yescharacteristic
413C22⋊Q8—1221no—
414C22⋊Q8—2441no—
415#121—21no—
416#121—21no—
417#121—21no—
418#121—41no—
419#120—41no—
420C4×Q8—611no—
421C4×Q8—1221no—
422C4×Q8—1221no—
423C4×Q8C22×D6111yescharacteristic
424C4×D4—21no—
425C4×D4—1221no—
426C4×D4C22×D6111yescharacteristic
427C4×D4C22×D6111yescharacteristic
428#106—611no—
429#106—1221no—
430#106—1221no—
431#106—1221no—
432#106—1221no—
433#106—1221no—
434#106C22⋊D6111yescharacteristic
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—611no—
438C4⋊C8—1221no—
439C4⋊C8—1221no—
440C4⋊C8C22×D6111yescharacteristic
441#103—611no—
442#103—1221no—
443#103—1221no—
444#103C22⋊D6111yescharacteristic
445#102—21no—
446#102—21no—
447#102—611no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102—1221no—
453#102—1221no—
454#102—2441no—
455#102C22⋊D6111yescharacteristic
456C22⋊C8—21no—
457C22⋊C8—1221no—
458C4×C8—611no—
459C4×C8—611no—
460C4×C8—1221no—
461C4×C8—1221no—
462C4×C8C22×D6111yescharacteristic
463C24—41no—
464#41—42no—
465#41—81no—
466C2×Q8—611no—
467C2×Q8—1221no—
468C2×Q8—1221no—
469C2×Q8—4881no—
470C2×Q8—2441no—
471C2×Q8—2441no—
472C2×Q8—2442no—
473C2×Q8C2×C22⋊D6111yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4D4×D6111yescharacteristic
489C2×D4C2×C22⋊D6111yescharacteristic
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—41no—
493C22×C4—2441no—
494SD16—42no—
495SD16—1222no—
496SD16—4881no—
497SD16—4882no—
498SD16—2442no—
499SD16—2442no—
500SD16—2442no—
501SD16—2442no—
502SD16#1175820014yescomplemented
503D8—42no—
504D8—42no—
505D8—81no—
506M16—42no—
507C2×C8—21no—
508C2×C8—611no—
509C2×C8—611no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—2442no—
515C2×C8C2×C22⋊D6111yescharacteristic
516C2×C8C2×C22⋊D6111yescharacteristic
517C4⋊C4—21no—
518C4⋊C4—611no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—2441no—
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—2441no—
535C42—21no—
536C42—1221no—
537C42—2441no—
538C42C23×D6111yescharacteristic
539C23—21no—
540C23—21no—
541C23—41no—
542C23—41no—
543C23—82no—
544C23—82no—
545C23—161no—
546Q8—21no—
547Q8—612no—
548Q8—1221no—
549Q8—9761no—
550Q8—4881no—
551Q8—4882no—
552Q8—2441no—
553Q8—2441no—
554Q8C2×#1175820012yescomplemented
555D4—21no—
556D4—21no—
557D4—21no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—82no—
567D4—81no—
568D4—81no—
569D4—82no—
570D4—82no—
571D4—161no—
572D4C2×#1175820012yes—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—82no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—4882no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C22×C22⋊D6111yescharacteristic
589C2×C4#1451982211yescharacteristic
590C8—21no—
591C8—41no—
592C8—1221no—
593C8—1221no—
594C8—2441no—
595C8—2441no—
596C8—2441no—
597C8—2441no—
598C8C2×#1175820012yescomplemented
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—164no—
612C22D4×C22⋊D6111yescharacteristic
613C4—22no—
614C4—21no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—1222no—
619C4—4881no—
620C4—4881no—
621C4—2441no—
622C4C22×#1175820011yescharacteristic
623C4AGL(1,ℤ/8)×D6111yescharacteristic
624C4#1684057211yescharacteristic
625C4#1684057311yescharacteristic
626C2—42no—
627C2—81no—
628C2—161no—
629C2—161no—
630C2#2145730811yescharacteristic
631C2D4×#1175820011yescharacteristic
632C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3274C2
socleC22×C61D42
hypercenter#3274D61
hypocenterC61#19804
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3274

Complements

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

NH ≅ G/Ntype
1. SD16×Dic122C2semidirect
2. #21458486C2semidirect
3. D4×#11758200C2semidirect
4. #21445445C2semidirect
5. #21445318C2semidirect
6. #21445226C2semidirect
7. #21445176C2semidirect
8. #21445165C2semidirect
9. #21445019C2semidirect
10. #21444935C2semidirect
11. #21444921C2semidirect
12. #21444896C2semidirect
13. #21444660C2semidirect
14. SD16⋊#92418C2semidirect
17. Q8×Dic122C22semidirect
19. #16840160C22semidirect
24. #16840108C22semidirect
25. #16840108C22semidirect
30. #16840047C22semidirect
36. #16839959C22semidirect
39. Q8×#92418C22semidirect
40. C8×Dic122C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839510C22semidirect
48. #16839507C22semidirect
50. #16839506C22semidirect
51. Q8⋊#92418C22semidirect
52. #16839492C22semidirect
55. #16839483C22semidirect
178. SD16×C61SD16semidirect
230. Q8×C61C2×SD16semidirect
272. Dic122AGL(1,ℤ/8)semidirect
275. C8×C61C2×SD16semidirect
383. C61#19804semidirect
502. SD16#11758200semidirect
554. Q8C2×#11758200semidirect
598. C8C2×#11758200semidirect

Maximal subgroups

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

subgroupindex
SD16×Dic1222
#214584862
D4×#117582002
#214454452
#214453182
#214452262
#214451762
#214451652
#214450192
#214449352
#214449212
#214448962
#214446602
SD16⋊#924182
C61×#32742
#1980461