Finite Group Databasebeta

← #29671359

Subgroups — #29671359

Order 15616.

718 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458716C211yesmaximal, characteristic, complemented
2#21458177C211yesmaximal, characteristic, complemented
3D4×#11758190C211yesmaximal, characteristic, complemented
4#21457420C211yesmaximal, characteristic
5#21445406C211yesmaximal, characteristic, complemented
6#21445319C211yesmaximal, characteristic, complemented
7#21445292C211yesmaximal, characteristic, complemented
8#21445194C211yesmaximal, characteristic, complemented
9#21445160C211yesmaximal, characteristic, complemented
10#21445106C211yesmaximal, characteristic, complemented
11#21445084C211yesmaximal, characteristic, complemented
12#21444937C211yesmaximal, characteristic, complemented
13#21444893C211yesmaximal, characteristic, complemented
14#21444711C211yesmaximal, characteristic, complemented
15C8×D8×C61C211yesmaximal, characteristic, complemented
16C2×#14519801—21no—
17C22×#11758190—21no—
18#16840469C2211yescharacteristic, complemented
19D4×Dic122C2211yescharacteristic
20#16840416C2211yescharacteristic
21D4×D244C2211yescharacteristic
22#16840170—21no—
23#16840160C2211yescharacteristic, complemented
24#16840160C2211yescharacteristic, complemented
25#16840160C2211yescharacteristic, complemented
26#16840135C2211yescharacteristic
27#16840135C2211yescharacteristic
28#16840135C2211yescharacteristic
29#16840093—21no—
30#16840081—21no—
31#16840064—21no—
32#16840053C2211yescharacteristic
33#16840052C2211yescharacteristic
34#16840050—21no—
35#16840048C2211yescharacteristic, complemented
36#16840042C2211yescharacteristic, complemented
37#16840009—21no—
38#16839991—21no—
39#16839991—21no—
40#16839968C2211yescharacteristic
41#16839967C2211yescharacteristic
42#16839963C2211yescharacteristic
43#16839957C2211yescharacteristic
44#16839915—21no—
45#16839914—21no—
46#16839908—21no—
47#16839903—21no—
48#16839892C2211yescharacteristic, complemented
49#16839874—21no—
50C4×#11758190C2211yescharacteristic
51#16839841C2211yescharacteristic
52C2×#14519709—21no—
53#16839513C2211yescharacteristic, complemented
54#16839510C2211yescharacteristic, complemented
55#16839509C2211yescharacteristic, complemented
56#16839507C2211yescharacteristic, complemented
57#16839505C2211yescharacteristic
58#16839494C2211yescharacteristic, complemented
59#16839491C2211yescharacteristic
60C4×D8×C61C2211yescharacteristic
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic, complemented
63C61×#335C2211yescharacteristic, complemented
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic, complemented
66C82×C61C2211yescharacteristic, complemented
67C2×#11758224—21no—
68C22×Dic122—21no—
69C22×D244—21no—
70C2×D4×D61—21no—
71#14519801—44no—
72C2×#11758190—21no—
73C2×#11758190—21no—
74C2×#11758190—21no—
75C2×#11758190—21no—
76C2×#11758190—21no—
77C2×#11758190—21no—
78C2×#11758190—44no—
79C2×#11758190—41no—
80C2×#11758190D411yescharacteristic
81C2×#11758200—21no—
82C2×#11758199—21no—
83C2×#11758189—21no—
84#14519777C2311yescharacteristic
85#14519777C2311yescharacteristic
86#14519777C2311yescharacteristic
87#14519776—21no—
88#14519774C2311yescharacteristic
89#14519768—21no—
90#14519761—41no—
91#14519757—21no—
92#14519756—21no—
93#14519756—21no—
94#14519754—41no—
95#14519754—41no—
96#14519752—21no—
97#14519751—21no—
98#14519751—21no—
99#14519747—41no—
100C4×Dic122C2311yescharacteristic
101C4×D244C2311yescharacteristic
102D4×Dic61—21no—
103D4×Dic61—21no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—21no—
106#14519710—21no—
107#14519709—21no—
108#14519709—21no—
109#14519709—21no—
110#14519709—21no—
111#14519709—21no—
112#14519709—21no—
113#14519709—41no—
114#14519709D411yescharacteristic
115#14519708—21no—
116C4⋊#92418C2311yescharacteristic
117C4⋊#92418C2311yescharacteristic
118#14519706—21no—
119#14519702—21no—
120#14519702—21no—
121#14519702D411yescharacteristic
122#14519700—21no—
123#14519699—21no—
124#14519699—21no—
125#14519699D411yescharacteristic
126#14519698—21no—
127#14519698—21no—
128#14519697—21no—
129#14519689—21no—
130#14519687—21no—
131C2×D8×C61D411yescharacteristic
132C22×C8×C61—21no—
133C22×C8×C61—21no—
134C4×D4×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136#107×C61D411yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#102×C61D411yescharacteristic
140#102×C61D411yescharacteristic
141C22⋊C8×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C4×C8×C61C2311yescharacteristic
146C23×D61—41no—
147C2×D4×C61C2×D411yescharacteristic
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C2×C22⋊D61—41no—
152C2×C22⋊D61—41no—
153C22×Dic61—41no—
154C22×Dic61—41no—
155C22×Dic61—41no—
156#11758224—42no—
157#11758224—81no—
158D4×D61—42no—
159D4×D61—81no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—42no—
164C2×D244—41no—
165C2×D244—81no—
166C2×D244C2×D411yescharacteristic
167C2×C4×D61—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—42no—
172C2×Dic122—41no—
173C2×Dic122—81no—
174C2×Dic122C2×D411yescharacteristic
175D8×C61SD1614yescomplemented
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—42no—
180C2×C8×C61—42no—
181C2×C8×C61C2×D411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
184C2×C8×C61C2×D411yescharacteristic
185C4⋊C4×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C42×C61C2411yescharacteristic
190C22⋊Dic61—41no—
191C22⋊Dic61—41no—
192#11758200—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—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—41no—
204C4⋊Dic61—41no—
205C4⋊Dic61C2×D411yescharacteristic
206C4⋊Dic61C2×D411yescharacteristic
207#11758196—21no—
208#11758196—41no—
209#11758196—41no—
210C4×Dic61—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213#11758190—22no—
214#11758190—42no—
215#11758190—42no—
216#11758190—42no—
217#11758190—42no—
218#11758190—81no—
219#11758190—81no—
220#11758190—82no—
221#11758189—42no—
222C23×C61—21no—
223C23×C61—21no—
224C22×D61—21no—
225C22×D61—41no—
226C22×D61—82no—
227C22×D61—82no—
228C22×D61—161no—
229D4×C61—21no—
230D4×C61—21no—
231D4×C61C2×SD1612yes—
232D4×C61C2×SD1612yescomplemented
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61H(5,𝔽2)11yescharacteristic
242C22⋊D61—82no—
243C22⋊D61—82no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—82no—
251C2×Dic61—82no—
252C2×Dic61—161no—
253D244—21no—
254D244—21no—
255D244—41no—
256D244—41no—
257D244—41no—
258D244—41no—
259D244—81no—
260D244—82no—
261C4×D61—41no—
262C4×D61—41no—
263Dic122—21no—
264Dic122—21no—
265Dic122—41no—
266Dic122—41no—
267Dic122—41no—
268Dic122—41no—
269Dic122—82no—
270Dic122—81no—
271C8×C61—22no—
272C8×C61—21no—
273C8×C61—21no—
274C8×C61—41no—
275C8×C61—41no—
276C8×C61C2×SD1612yescomplemented
277C8×C61AGL(1,ℤ/8)12yescomplemented
278#92418—41no—
279#92418—41no—
280#19890—611nomaximal, Sylow
281C22×C61—22no—
282C22×C61—22no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61D4211yescharacteristic
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—81no—
294C2×D61—164no—
295C4×C61—21no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61C22×SD1611yescharacteristic
299C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C61#57711yescharacteristic
301C4×C61#57711yescharacteristic
302Dic61—41no—
303Dic61—41no—
304Dic61—41no—
305Dic61—81no—
306Dic61—81no—
307Dic61—81no—
308#3384—611no—
309#3335—611no—
310D4×SD16—611no—
311#3272—611no—
312#1705—611no—
313#1691—611no—
314#1686—611no—
315#1671—611no—
316#1665—611no—
317#1654—611no—
318#1651—611no—
319#1629—611no—
320#1622—611no—
321#1590—611no—
322C8×D8D6111yescharacteristic, complemented
323C2×C61—42no—
324C2×C61—42no—
325C2×C61#327211yescharacteristic
326C2×C61D4×SD1611yescharacteristic
327C2×C61#329111yescharacteristic
328D61—81no—
329D61—161no—
330C2×AGL(1,ℤ/8)—1221no—
331C22×SD16—1221no—
332#554—611no—
333D4×Q8—611no—
334#547—611no—
335D42—611no—
336#501—1221no—
337#498—611no—
338#498—611no—
339#498—611no—
340#492—611no—
341#492—611no—
342#492—611no—
343#483—1221no—
344#481—1221no—
345#478—1221no—
346#476—611no—
347#476—611no—
348#476—1221no—
349#475—611no—
350#474—611no—
351#468—1221no—
352#465—1221no—
353#465—1221no—
354#461—611no—
355#461—611no—
356#460—611no—
357#459—611no—
358#450—1221no—
359#450—1221no—
360#449—1221no—
361#448—1221no—
362#446—611no—
363#442—1221no—
364C4×SD16—611no—
365C4×D8C2×D6111yescharacteristic
366#436—611no—
367C8×D4C2×D6111yescharacteristic
368C8×D4C2×D6111yescharacteristic, complemented
369C2×#106—1221no—
370#335C2×D6111yescharacteristic, complemented
371#334—611no—
372#333—611no—
373#332—611no—
374#332—611no—
375#331—611no—
376Q8⋊C8—611no—
377D4⋊C8—611no—
378D4⋊C8C2×D6111yescharacteristic
379D4⋊C8C2×D6111yescharacteristic, complemented
380C82C2×D6111yescharacteristic, complemented
381C61#1989011yescharacteristic, complemented, Sylow
382C2×#41—1221no—
383C22×Q8—1221no—
384C22×D4—1221no—
385C22×D4—1221no—
386AGL(1,ℤ/8)—2444no—
387C2×SD16—611no—
388C2×SD16—1221no—
389C2×SD16—1221no—
390C2×SD16—1221no—
391C2×SD16—1221no—
392C2×SD16—1221no—
393C2×SD16—1221no—
394C2×SD16—1221no—
395C2×SD16—2441no—
396C2×SD16—2444no—
397C2×D8—1221no—
398C2×D8D24411yescharacteristic
399C2×M16—1221no—
400C22×C8—21no—
401C22×C8—21no—
402C4⋊Q8—611no—
403C4⋊Q8—611no—
404C4⋊Q8—611no—
405C4⋊Q8—1221no—
406#127—611no—
407#125—1221no—
408#123—2441no—
409C22⋊Q8—1221no—
410C22⋊Q8—1221no—
411C22⋊Q8—1221no—
412C22⋊Q8—2441no—
413C22⋊Q8—2441no—
414#121—1221no—
415#121—1221no—
416#121—1221no—
417#120—2441no—
418C4×Q8—611no—
419C4×D4—611no—
420C4×D4—1221no—
421C4×D4—1221no—
422C4×D4C22×D6111yescharacteristic
423C4×D4C22×D6111yescharacteristic
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426#107—1221no—
427#107D24411yescharacteristic
428#106—611no—
429#106—1221no—
430#106—1221no—
431#106—1221no—
432#106—1221no—
433#106—1221no—
434#106—1221no—
435#106—1221no—
436#106—2441no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—1221no—
440C4⋊C8C22×D6111yescharacteristic
441C4⋊C8C22×D6111yescharacteristic
442#103—611no—
443#103—1221no—
444#103—1221no—
445#103—1221no—
446#102—611no—
447#102—1221no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102D24411yescharacteristic
453#102D24411yescharacteristic
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8—1221no—
457#97—1221no—
458C4×C8C22×D6111yescharacteristic
459C4×C8C22×D6111yescharacteristic
460C4×C8C22×D6111yescharacteristic
461C24—2441no—
462#41—4881no—
463#41—2442no—
464C2×Q8—611no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×Q8—1221no—
468C2×Q8—4881no—
469C2×Q8—2441no—
470C2×Q8—2442no—
471C2×D4—611no—
472C2×D4—1221no—
473C2×D4—1221no—
474C2×D4—1221no—
475C2×D4—4881no—
476C2×D4—4881no—
477C2×D4—2441no—
478C2×D4—2442no—
479C2×D4—2441no—
480C2×D4—2441no—
481C2×D4—2442no—
482C2×D4C2×D24411yescharacteristic
483C2×D4C2×D24411yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—1221no—
487C22×C4—2441no—
488C22×C4—2441no—
489C22×C4—2441no—
490SD16—1222no—
491SD16—4882no—
492SD16—4881no—
493SD16—4881no—
494SD16—2442no—
495SD16—2442no—
496SD16—2442no—
497SD16—2442no—
498SD16—2442no—
499D8—2442no—
500D8#1175819014yescomplemented
501M16—2442no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—42no—
506C2×C8—42no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8C2×D24411yescharacteristic
510C2×C8C2×D24411yescharacteristic
511C2×C8D4×D6111yescharacteristic
512C2×C8D4×D6111yescharacteristic
513C4⋊C4—611no—
514C4⋊C4—611no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—2441no—
523C4⋊C4—2441no—
524C4⋊C4—2441no—
525C4⋊C4—2441no—
526C4⋊C4C2×D24411yescharacteristic
527C4⋊C4C2×D24411yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—1221no—
531C22⋊C4—2441no—
532C22⋊C4—2441no—
533C22⋊C4—2441no—
534C22⋊C4—2441no—
535C42—1221no—
536C42C23×D6111yescharacteristic
537C23—21no—
538C23—21no—
539C23—1221no—
540C23—9761no—
541C23—4882no—
542C23—4882no—
543C23—2441no—
544Q8—1221no—
545Q8—1221no—
546Q8—4881no—
547Q8—4882no—
548Q8—2441no—
549Q8—2441no—
550Q8—2441no—
551Q8—2441no—
552D4—21no—
553D4—21no—
554D4—1221no—
555D4—1221no—
556D4—4881no—
557D4—4882no—
558D4—4882no—
559D4—4882no—
560D4—2441no—
561D4—2441no—
562D4—2441no—
563D4—2441no—
564D4C2×#1175819012yes—
565D4C2×#1175819012yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—9761no—
576C2×C4—4882no—
577C2×C4—4882no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4C2×D4×D6111yescharacteristic
584C2×C4C22×D24411yescharacteristic
585C2×C4#1451982311yescharacteristic
586C8—22no—
587C8—21no—
588C8—21no—
589C8—41no—
590C8—41no—
591C8—2441no—
592C8—2441no—
593C8C2×#1175819012yescomplemented
594C8#1451980112yescomplemented
595C22—22no—
596C22—22no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—9764no—
602C22—4881no—
603C22—4881no—
604C22—4881no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22D4×D24411yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—4881no—
613C4—4881no—
614C4—4881no—
615C4—2441no—
616C4—2441no—
617C4—2441no—
618C4C22×#1175819011yescharacteristic
619C4C2×#1451980111yescharacteristic
620C4#1684056911yescharacteristic
621C4#1684057411yescharacteristic
622C2—42no—
623C2—42no—
624C2—9761no—
625C2—4881no—
626C2#2145742011yescharacteristic
627C2D4×#1175819011yescharacteristic
628C2#2145761311yescharacteristic
subgroupG/H
centerC22D4×D244
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC8×D8×C61C2
socleC22×C61D42
prime radical#21457420C2
hypercenterC8×D8D61
hypocenterC61#19890
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
1. #21458716C2semidirect
2. #21458177C2semidirect
3. D4×#11758190C2semidirect
5. #21445406C2semidirect
6. #21445319C2semidirect
7. #21445292C2semidirect
8. #21445194C2semidirect
9. #21445160C2semidirect
10. #21445106C2semidirect
11. #21445084C2semidirect
12. #21444937C2semidirect
13. #21444893C2semidirect
14. #21444711C2semidirect
15. C8×D8×C61C2semidirect
18. #16840469C22semidirect
23. #16840160C22semidirect
24. #16840160C22semidirect
25. #16840160C22semidirect
35. #16840048C22semidirect
36. #16840042C22semidirect
48. #16839892C22semidirect
53. #16839513C22semidirect
54. #16839510C22semidirect
55. #16839509C22semidirect
56. #16839507C22semidirect
58. #16839494C22semidirect
62. C8×D4×C61C22semidirect
63. C61×#335C22semidirect
65. C61×D4⋊C8C22semidirect
66. C82×C61C22semidirect
175. D8×C61SD16semidirect
232. D4×C61C2×SD16semidirect
276. C8×C61C2×SD16semidirect
277. C8×C61AGL(1,ℤ/8)semidirect
322. C8×D8D61semidirect
368. C8×D4C2×D61semidirect
370. #335C2×D61semidirect
379. D4⋊C8C2×D61semidirect
380. C82C2×D61semidirect
381. C61#19890semidirect
500. D8#11758190semidirect
565. D4C2×#11758190semidirect
593. C8C2×#11758190semidirect
594. C8#14519801semidirect

Maximal subgroups

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

subgroupindex
#214587162
#214581772
D4×#117581902
#214574202
#214454062
#214453192
#214452922
#214451942
#214451602
#214451062
#214450842
#214449372
#214448932
#214447112
C8×D8×C612
#1989061