Finite Group Databasebeta

← #29671357

Subgroups — #29671357

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#21458176C211yesmaximal, characteristic, complemented
3D4×#11758200C211yesmaximal, characteristic, complemented
4#21445405C211yesmaximal, characteristic, complemented
5#21445318C211yesmaximal, characteristic, complemented
6#21445288C211yesmaximal, characteristic, complemented
7#21445192C211yesmaximal, characteristic, complemented
8#21445158C211yesmaximal, characteristic, complemented
9#21445103C211yesmaximal, characteristic, complemented
10#21445080C211yesmaximal, characteristic, complemented
11#21444935C211yesmaximal, characteristic, complemented
12#21444889C211yesmaximal, characteristic, complemented
13#21444707C211yesmaximal, characteristic, complemented
14D8×#92418C211yesmaximal, characteristic, complemented
15C61×#3272C211yesmaximal, characteristic
16C22×#11758200—21no—
17#16840469C2211yescharacteristic, complemented
18D4×Dic122C2211yescharacteristic
19#16840170—21no—
20#16840160C2211yescharacteristic, complemented
21#16840158C2211yescharacteristic, complemented
22#16840158C2211yescharacteristic, complemented
23#16840134C2211yescharacteristic
24#16840134C2211yescharacteristic
25#16840092—21no—
26#16840078—21no—
27#16840064—21no—
28#16840052C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840050—21no—
31#16840044C2211yescharacteristic, complemented
32#16840042C2211yescharacteristic, complemented
33#16839989—21no—
34#16839989—21no—
35#16839967C2211yescharacteristic
36#16839959C2211yescharacteristic
37#16839913—21no—
38#16839900—21no—
39#16839892C2211yescharacteristic, complemented
40#16839874—21no—
41C4×#11758200C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43D4×#92418C2211yescharacteristic, complemented
44C2×#14519708—21no—
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839506C2211yescharacteristic
51#16839492C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic, complemented
55C8×#92418C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C61—21no—
57C61×#547C2211yescharacteristic
58D42×C61C2211yescharacteristic
59C61×#492C2211yescharacteristic
60C61×#468—21no—
61C61×#461C2211yescharacteristic
62C61×#459C2211yescharacteristic
63C61×#450—21no—
64C61×#449—21no—
65C4×D8×C61C2211yescharacteristic
66C61×#436C2211yescharacteristic
67C22×Dic122—21no—
68C2×#11758200—21no—
69C2×#11758200—21no—
70C2×#11758200—21no—
71C2×#11758200—21no—
72C2×#11758200—41no—
73C2×#11758200—44no—
74C2×#11758200D411yescharacteristic
75C22×#92418—21no—
76C22×#92418—21no—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519776—21no—
80#14519768—21no—
81#14519756—21no—
82#14519756—21no—
83#14519754—41no—
84#14519754—41no—
85C4×Dic122C2311yescharacteristic
86D4×Dic61—21no—
87D4×Dic61—21no—
88C2×C4⋊Dic61—21no—
89#14519710—21no—
90#14519709—21no—
91#14519709—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96#14519708—21no—
97#14519708—41no—
98#14519708D411yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102#14519706—21no—
103#14519700—21no—
104#14519700—21no—
105#14519700D411yescharacteristic
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698—21no—
110#14519698D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519687—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119AGL(1,ℤ/8)×C61—44no—
120C2×SD16×C61—21no—
121C2×SD16×C61—21no—
122C2×SD16×C61—21no—
123C2×D8×C61—21no—
124C2×D8×C61D411yescharacteristic
125C2×M16×C61—21no—
126C4⋊Q8×C61C2311yescharacteristic
127#127×C61C2311yescharacteristic
128#123×C61—41no—
129C22⋊Q8×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—21no—
133#120×C61—41no—
134C4×D4×C61C2311yescharacteristic
135C4×D4×C61C2311yescharacteristic
136C4×D4×C61C2311yescharacteristic
137C2×C4⋊C4×C61—21no—
138#107×C61D411yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143#102×C61D411yescharacteristic
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C24×C61—41no—
147#41×C61—42no—
148#41×C61—81no—
149C2×Q8×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61—42no—
156C2×D4×C61—42no—
157C2×D4×C61—41no—
158C2×D4×C61—81no—
159C2×D4×C61—81no—
160C2×D4×C61C2×D411yescharacteristic
161C2×D4×C61C2×D411yescharacteristic
162C2×D4×C61C2×D411yescharacteristic
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—41no—
167C22×Dic61—41no—
168C22×Dic61—41no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—42no—
172C2×Dic122—41no—
173C2×Dic122—81no—
174C2×Dic122C2×D411yescharacteristic
175SD16×C61—42no—
176SD16×C61—42no—
177SD16×C61—81no—
178D8×C61—42no—
179D8×C61SD1614yescomplemented
180M16×C61—42no—
181C2×C8×C61—21no—
182C2×C8×C61C2×D411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—41no—
187C4⋊C4×C61C2×D411yescharacteristic
188C4⋊C4×C61C2×D411yescharacteristic
189C4⋊C4×C61C2×D411yescharacteristic
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C22⋊C4×C61—21no—
193C22⋊C4×C61—41no—
194C22⋊C4×C61—41no—
195C42×C61C2411yescharacteristic
196C22⋊Dic61—41no—
197C22⋊Dic61—41no—
198#11758200—22no—
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—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—42no—
219C2×#92418—42no—
220C2×#92418C2×D411yescharacteristic
221C2×#92418C2×D411yescharacteristic
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—41no—
226C23×C61—82no—
227C23×C61—82no—
228C23×C61—161no—
229Q8×C61—41no—
230Q8×C61—41no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61—21no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—81no—
240D4×C61—82no—
241D4×C61—82no—
242D4×C61—82no—
243D4×C61C2×SD1612yes—
244D4×C61C2×SD1612yescomplemented
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—82no—
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61H(5,𝔽2)11yescharacteristic
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—82no—
264C2×Dic61—161no—
265Dic122—21no—
266Dic122—21no—
267Dic122—41no—
268Dic122—41no—
269Dic122—82no—
270Dic122—81no—
271C8×C61—21no—
272C8×C61—41no—
273C8×C61C2×SD1612yescomplemented
274#92418—22no—
275#92418—21no—
276#92418—41no—
277#92418—41no—
278#92418—41no—
279#92418AGL(1,ℤ/8)12yescomplemented
280#19890—611nomaximal, Sylow
281C22×C61—22no—
282C22×C61—22no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61—81no—
293C22×C61—164no—
294C22×C61D4211yescharacteristic
295C4×C61—21no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61—81no—
300C4×C61C22×SD1611yescharacteristic
301C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C61#57711yescharacteristic
303C4×C61#57711yescharacteristic
304Dic61—41no—
305Dic61—41no—
306Dic61—81no—
307Dic61—81no—
308#3384—611no—
309#3335—611no—
310D4×SD16—611no—
311#3272D6111yescharacteristic
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×D8—611no—
323C2×C61—42no—
324C2×C61—42no—
325C2×C61—81no—
326C2×C61—161no—
327C2×C61#327211yescharacteristic
328C2×C61D4×SD1611yescharacteristic
329C2×C61#329111yescharacteristic
330C2×AGL(1,ℤ/8)—21no—
331C22×SD16—1221no—
332#554—611no—
333D4×Q8—611no—
334#547C2×D6111yescharacteristic
335D42C2×D6111yescharacteristic
336#501—1221no—
337#498—611no—
338#498—611no—
339#498—611no—
340#492—611no—
341#492—611no—
342#492C2×D6111yescharacteristic
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—21no—
352#465—1221no—
353#465—1221no—
354#461—611no—
355#461C2×D6111yescharacteristic
356#460—611no—
357#459C2×D6111yescharacteristic
358#450—21no—
359#450—1221no—
360#449—21no—
361#448—1221no—
362#446—611no—
363#442—1221no—
364C4×SD16—611no—
365C4×D8C2×D6111yescharacteristic
366#436C2×D6111yescharacteristic
367C8×D4—611no—
368C8×D4—611no—
369C2×#106—1221no—
370#335—611no—
371#334—611no—
372#333—611no—
373#332—611no—
374#332—611no—
375#331—611no—
376Q8⋊C8—611no—
377D4⋊C8—611no—
378D4⋊C8—611no—
379D4⋊C8—611no—
380C82—611no—
381C61#1989011yescharacteristic, complemented, Sylow
382C2×#41—21no—
383C22×Q8—1221no—
384C22×D4—21no—
385C22×D4—21no—
386AGL(1,ℤ/8)—44no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16—611no—
391C2×SD16—1221no—
392C2×SD16—1221no—
393C2×SD16—1221no—
394C2×SD16—1221no—
395C2×SD16—2441no—
396C2×SD16—2444no—
397C2×D8—21no—
398C2×D8C22⋊D6111yescharacteristic
399C2×M16—21no—
400C22×C8—1221no—
401C22×C8—1221no—
402C4⋊Q8—611no—
403C4⋊Q8—611no—
404C4⋊Q8—1221no—
405C4⋊Q8C22×D6111yescharacteristic
406#127C22×D6111yescharacteristic
407#125—1221no—
408#123—41no—
409C22⋊Q8—21no—
410C22⋊Q8—1221no—
411C22⋊Q8—1221no—
412C22⋊Q8—2441no—
413C22⋊Q8—2441no—
414#121—21no—
415#121—21no—
416#121—21no—
417#120—41no—
418C4×Q8—611no—
419C4×D4—1221no—
420C4×D4—1221no—
421C4×D4C22×D6111yescharacteristic
422C4×D4C22×D6111yescharacteristic
423C4×D4C22×D6111yescharacteristic
424C2×C4⋊C4—21no—
425C2×C4⋊C4—1221no—
426#107—1221no—
427#107C22⋊D6111yescharacteristic
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—611no—
440C4⋊C8—1221no—
441C4⋊C8C22×D6111yescharacteristic
442#103—21no—
443#103—611no—
444#103—1221no—
445#103—1221no—
446#102—21no—
447#102—611no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102C22⋊D6111yescharacteristic
453#102C22⋊D6111yescharacteristic
454C22⋊C8—21no—
455C22⋊C8—1221no—
456C22⋊C8—1221no—
457#97—1221no—
458C4×C8—611no—
459C4×C8—611no—
460C4×C8C22×D6111yescharacteristic
461C24—41no—
462#41—42no—
463#41—81no—
464C2×Q8—21no—
465C2×Q8—611no—
466C2×Q8—1221no—
467C2×Q8—1221no—
468C2×Q8—4881no—
469C2×Q8—2441no—
470C2×Q8—2442no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—41no—
479C2×D4—81no—
480C2×D4—81no—
481C2×D4D4×D6111yescharacteristic
482C2×D4C2×C22⋊D6111yescharacteristic
483C2×D4C2×C22⋊D6111yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—41no—
488C22×C4—2441no—
489C22×C4—2441no—
490SD16—42no—
491SD16—42no—
492SD16—81no—
493SD16—1222no—
494SD16—4881no—
495SD16—4882no—
496SD16—2442no—
497SD16—2442no—
498SD16—2442no—
499D8—42no—
500D8#1175820014yescomplemented
501M16—42no—
502C2×C8—21no—
503C2×C8—611no—
504C2×C8—611no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—2442no—
510C2×C8—2442no—
511C2×C8C2×C22⋊D6111yescharacteristic
512C2×C8C2×C22⋊D6111yescharacteristic
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—41no—
516C4⋊C4—611no—
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⋊C4D4×D6111yescharacteristic
526C4⋊C4C2×C22⋊D6111yescharacteristic
527C4⋊C4C2×C22⋊D6111yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—2441no—
534C22⋊C4—2441no—
535C42—1221no—
536C42C23×D6111yescharacteristic
537C23—21no—
538C23—21no—
539C23—21no—
540C23—41no—
541C23—82no—
542C23—82no—
543C23—161no—
544Q8—41no—
545Q8—41no—
546Q8—1221no—
547Q8—1221no—
548Q8—4881no—
549Q8—4882no—
550Q8—2441no—
551Q8—2441no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—81no—
561D4—82no—
562D4—82no—
563D4—82no—
564D4C2×#1175820012yes—
565D4C2×#1175820012yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—9761no—
580C2×C4—4882no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4C2×D4×D6111yescharacteristic
584C2×C4C22×C22⋊D6111yescharacteristic
585C2×C4#1451982211yescharacteristic
586C8—21no—
587C8—41no—
588C8—612no—
589C8—1222no—
590C8—1221no—
591C8—2441no—
592C8—2441no—
593C8—2441no—
594C8C2×#1175820012yescomplemented
595C22—22no—
596C22—22no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—164no—
608C22D4×C22⋊D6111yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—4881no—
615C4—4881no—
616C4—2441no—
617C4—2441no—
618C4C22×#1175820011yescharacteristic
619C4AGL(1,ℤ/8)×D6111yescharacteristic
620C4#1684057211yescharacteristic
621C4#1684057311yescharacteristic
622C2—42no—
623C2—42no—
624C2—81no—
625C2—161no—
626C2#2145741311yescharacteristic
627C2D4×#1175820011yescharacteristic
628C2#2145761011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3272C2
socleC22×C61D42
hypercenter#3272D61
hypocenterC61#19890
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3272

Complements

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

NH ≅ G/Ntype
1. #21458716C2semidirect
2. #21458176C2semidirect
3. D4×#11758200C2semidirect
4. #21445405C2semidirect
5. #21445318C2semidirect
6. #21445288C2semidirect
7. #21445192C2semidirect
8. #21445158C2semidirect
9. #21445103C2semidirect
10. #21445080C2semidirect
11. #21444935C2semidirect
12. #21444889C2semidirect
13. #21444707C2semidirect
14. D8×#92418C2semidirect
17. #16840469C22semidirect
20. #16840160C22semidirect
21. #16840158C22semidirect
22. #16840158C22semidirect
31. #16840044C22semidirect
32. #16840042C22semidirect
39. #16839892C22semidirect
43. D4×#92418C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839510C22semidirect
48. #16839508C22semidirect
49. #16839507C22semidirect
51. #16839492C22semidirect
54. D4⋊#92418C22semidirect
55. C8×#92418C22semidirect
179. D8×C61SD16semidirect
244. D4×C61C2×SD16semidirect
273. C8×C61C2×SD16semidirect
279. #92418AGL(1,ℤ/8)semidirect
381. C61#19890semidirect
500. D8#11758200semidirect
565. D4C2×#11758200semidirect
594. C8C2×#11758200semidirect

Maximal subgroups

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

subgroupindex
#214587162
#214581762
D4×#117582002
#214454052
#214453182
#214452882
#214451922
#214451582
#214451032
#214450802
#214449352
#214448892
#214447072
D8×#924182
C61×#32722
#1989061