Finite Group Databasebeta

← #29671351

Subgroups — #29671351

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#21458170C211yesmaximal, characteristic, complemented
2D4×#11758201C211yesmaximal, characteristic, complemented
3#21457420C211yesmaximal, characteristic
4#21445407C211yesmaximal, characteristic, complemented
5#21445315C211yesmaximal, characteristic, complemented
6#21445291C211yesmaximal, characteristic, complemented
7#21445196C211yesmaximal, characteristic, complemented
8#21445162C211yesmaximal, characteristic, complemented
9#21445102C211yesmaximal, characteristic, complemented
10#21445082C211yesmaximal, characteristic, complemented
11#21444934C211yesmaximal, characteristic, complemented
12#21444891C211yesmaximal, characteristic, complemented
13#21444709C211yesmaximal, characteristic, complemented
14D8×#92418C211yesmaximal, characteristic, complemented
15C61×#3384C211yesmaximal, characteristic, complemented
16C2×#14519801—21no—
17C22×#11758201—21no—
18#16840416C2211yescharacteristic
19D4×D244C2211yescharacteristic
20#16840158C2211yescharacteristic, complemented
21#16840158C2211yescharacteristic, complemented
22#16840136C2211yescharacteristic
23#16840136C2211yescharacteristic
24#16840135C2211yescharacteristic
25#16840090—21no—
26#16840080—21no—
27#16840049C2211yescharacteristic
28#16840047C2211yescharacteristic, complemented
29#16840009—21no—
30#16839993—21no—
31#16839993—21no—
32#16839967C2211yescharacteristic
33#16839964C2211yescharacteristic
34#16839962C2211yescharacteristic
35#16839957C2211yescharacteristic
36#16839914—21no—
37#16839912—21no—
38#16839908—21no—
39#16839901—21no—
40C4×#11758201C2211yescharacteristic
41#16839841C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43D4×#92418C2211yescharacteristic, complemented
44C2×#14519708—21no—
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839509C2211yescharacteristic, complemented
49#16839508C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic, complemented
56C61×#554C2211yescharacteristic, complemented
57D4×Q8×C61C2211yescharacteristic
58C61×#501—21no—
59C61×#498C2211yescharacteristic, complemented
60C61×#478—21no—
61C61×#476—21no—
62C61×#476C2211yescharacteristic
63C61×#474C2211yescharacteristic, complemented
64C61×#446C2211yescharacteristic, complemented
65C61×#442—21no—
66C4×D8×C61C2211yescharacteristic
67C2×#11758224—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70#14519801—44no—
71C2×#11758190—21no—
72C2×#11758190—21no—
73C2×#11758200—21no—
74C2×#11758201—21no—
75C2×#11758201—21no—
76C2×#11758201—21no—
77C2×#11758201—21no—
78C2×#11758201—41no—
79C2×#11758201—44no—
80C2×#11758201D411yescharacteristic
81C2×#11758199—21no—
82C2×#11758189—21no—
83C22×#92418—21no—
84C22×#92418—21no—
85#14519777C2311yescharacteristic
86#14519774C2311yescharacteristic
87#14519761—41no—
88#14519757—21no—
89#14519752—21no—
90#14519751—21no—
91#14519751—21no—
92#14519747—41no—
93C4×D244C2311yescharacteristic
94C2×C4⋊Dic61—21no—
95#14519708—21no—
96#14519708—21no—
97#14519708—21no—
98#14519708—21no—
99#14519708—41no—
100#14519708D411yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104#14519701—21no—
105#14519701—21no—
106#14519701D411yescharacteristic
107#14519700—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697—21no—
111#14519697D411yescharacteristic
112C22⋊#92418—21no—
113C22⋊#92418—21no—
114#14519689—21no—
115C4×#92418C2311yescharacteristic
116C4×#92418C2311yescharacteristic
117C22×Q8×C61—21no—
118C2×D8×C61D411yescharacteristic
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#125×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126C22⋊Q8×C61—41no—
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C2×C4⋊C4×C61—21no—
133#107×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136#106×C61—21no—
137#106×C61—21no—
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143#102×C61D411yescharacteristic
144#97×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C23×D61—41no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—41no—
150C2×Q8×C61—42no—
151C2×Q8×C61—81no—
152C2×Q8×C61C2×D411yescharacteristic
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—41no—
158C22×C4×C61—41no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161C22×Dic61—41no—
162#11758224—42no—
163#11758224—81no—
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—
175D8×C61SD1614yescomplemented
176C2×C8×C61—21no—
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—41no—
185C4⋊C4×C61—41no—
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—41no—
193C22⋊C4×C61—41no—
194C42×C61—21no—
195C42×C61C2411yescharacteristic
196#11758201—22no—
197#11758201—42no—
198#11758201—42no—
199#11758201—42no—
200#11758201—81no—
201#11758201—82no—
202#11758200—42no—
203#11758199—42no—
204#11758198—21no—
205#11758198—41no—
206#11758198—41no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—41no—
210C4⋊Dic61C2×D411yescharacteristic
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—42no—
216C2×#92418—42no—
217C2×#92418C2×D411yescharacteristic
218C2×#92418C2×D411yescharacteristic
219#11758190—42no—
220#11758190—81no—
221#11758189—42no—
222C23×C61—21no—
223C23×C61—21no—
224C22×D61—21no—
225C22×D61—41no—
226C22×D61—82no—
227C22×D61—82no—
228C22×D61—161no—
229Q8×C61—21no—
230Q8×C61—21no—
231Q8×C61—41no—
232Q8×C61—41no—
233Q8×C61—81no—
234Q8×C61—82no—
235D4×C61—21no—
236D4×C61—21no—
237D4×C61C2×SD1612yes—
238D4×C61C2×SD1612yescomplemented
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—82no—
250C2×C4×C61—161no—
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61H(5,𝔽2)11yescharacteristic
254C22⋊D61—82no—
255C22⋊D61—82no—
256C2×Dic61—21no—
257C2×Dic61—41no—
258C2×Dic61—82no—
259D244—21no—
260D244—21no—
261D244—41no—
262D244—41no—
263D244—41no—
264D244—41no—
265D244—81no—
266D244—82no—
267C4×D61—41no—
268C4×D61—41no—
269Dic122—41no—
270Dic122—41no—
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×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×C61—41no—
299C4×C61—41no—
300C4×C61—81no—
301C4×C61—81no—
302C4×C61C22×SD1611yescharacteristic
303C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C61#57711yescharacteristic
305C4×C61#57711yescharacteristic
306Dic61—41no—
307Dic61—81no—
308#3384D6111yescharacteristic, complemented
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×D8—611no—
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#554C2×D6111yescharacteristic, complemented
333D4×Q8C2×D6111yescharacteristic
334#547—611no—
335D42—611no—
336#501—21no—
337#498—611no—
338#498—611no—
339#498C2×D6111yescharacteristic, complemented
340#492—611no—
341#492—611no—
342#492—611no—
343#483—1221no—
344#481—1221no—
345#478—21no—
346#476—21no—
347#476—611no—
348#476C2×D6111yescharacteristic
349#475—611no—
350#474C2×D6111yescharacteristic, complemented
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#446C2×D6111yescharacteristic, complemented
363#442—21no—
364C4×SD16—611no—
365C4×D8C2×D6111yescharacteristic
366#436—611no—
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—1221no—
383C22×Q8—21no—
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×D8C22⋊D6111yescharacteristic
399C2×M16—1221no—
400C22×C8—1221no—
401C22×C8—1221no—
402C4⋊Q8—21no—
403C4⋊Q8—611no—
404C4⋊Q8C22×D6111yescharacteristic
405C4⋊Q8C22×D6111yescharacteristic
406#127—611no—
407#125—21no—
408#123—2441no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—41no—
412C22⋊Q8—41no—
413C22⋊Q8—1221no—
414#121—1221no—
415#121—1221no—
416#121—1221no—
417#120—2441no—
418C4×Q8C22×D6111yescharacteristic
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—611no—
422C4×D4C22×D6111yescharacteristic
423C4×D4C22×D6111yescharacteristic
424C2×C4⋊C4—21no—
425C2×C4⋊C4—1221no—
426#107—21no—
427#107C22⋊D6111yescharacteristic
428#106—21no—
429#106—21no—
430#106—21no—
431#106—611no—
432#106—1221no—
433#106—1221no—
434#106—1221no—
435#106—1221no—
436#106—2441no—
437C4⋊C8—21no—
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8C22×D6111yescharacteristic
442#103—611no—
443#103—1221no—
444#103—1221no—
445#103—1221no—
446#102—21no—
447#102—21no—
448#102—611no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102C22⋊D6111yescharacteristic
453#102C22⋊D6111yescharacteristic
454C22⋊C8—1221no—
455C22⋊C8—1221no—
456C22⋊C8—1221no—
457#97—21no—
458C4×C8—611no—
459C4×C8—611no—
460C4×C8C22×D6111yescharacteristic
461C24—2441no—
462#41—4881no—
463#41—2442no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—41no—
467C2×Q8—42no—
468C2×Q8—81no—
469C2×Q8—1221no—
470C2×Q8D4×D6111yescharacteristic
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×C22⋊D6111yescharacteristic
483C2×D4C2×C22⋊D6111yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—1221no—
489C22×C4—2441no—
490SD16—1222no—
491SD16—4881no—
492SD16—4882no—
493SD16—4881no—
494SD16—2442no—
495SD16—2442no—
496SD16—2442no—
497SD16—2442no—
498SD16—2442no—
499D8—2442no—
500D8#1175820114yescomplemented
501M16—2442no—
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—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—611no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—2441no—
525C4⋊C4D4×D6111yescharacteristic
526C4⋊C4C2×C22⋊D6111yescharacteristic
527C4⋊C4C2×C22⋊D6111yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—1221no—
533C22⋊C4—2441no—
534C22⋊C4—2441no—
535C42—21no—
536C42C23×D6111yescharacteristic
537C23—21no—
538C23—21no—
539C23—1221no—
540C23—9761no—
541C23—4882no—
542C23—4882no—
543C23—2441no—
544Q8—21no—
545Q8—21no—
546Q8—41no—
547Q8—41no—
548Q8—81no—
549Q8—82no—
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×#1175820112yes—
565D4C2×#1175820112yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—161no—
578C2×C4—1221no—
579C2×C4—4882no—
580C2×C4—2441no—
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×#1175820112yescomplemented
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×C22⋊D6111yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—4881no—
617C4—2441no—
618C4C22×#1175820111yescharacteristic
619C4AGL(1,ℤ/8)×D6111yescharacteristic
620C4#1684057011yescharacteristic
621C4#1684057211yescharacteristic
622C2—42no—
623C2—42no—
624C2—9761no—
625C2—4881no—
626C2#2145741311yescharacteristic
627C2D4×#1175820111yescharacteristic
628C2#2145761011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3384C2
socleC22×C61D42
prime radical#21457420C2
hypercenter#3384D61
hypocenterC61#19890
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3384

Complements

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

NH ≅ G/Ntype
1. #21458170C2semidirect
2. D4×#11758201C2semidirect
4. #21445407C2semidirect
5. #21445315C2semidirect
6. #21445291C2semidirect
7. #21445196C2semidirect
8. #21445162C2semidirect
9. #21445102C2semidirect
10. #21445082C2semidirect
11. #21444934C2semidirect
12. #21444891C2semidirect
13. #21444709C2semidirect
14. D8×#92418C2semidirect
15. C61×#3384C2semidirect
20. #16840158C22semidirect
21. #16840158C22semidirect
28. #16840047C22semidirect
43. D4×#92418C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839509C22semidirect
49. #16839508C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. C8×#92418C22semidirect
56. C61×#554C22semidirect
59. C61×#498C22semidirect
63. C61×#474C22semidirect
64. C61×#446C22semidirect
175. D8×C61SD16semidirect
238. D4×C61C2×SD16semidirect
273. C8×C61C2×SD16semidirect
279. #92418AGL(1,ℤ/8)semidirect
308. #3384D61semidirect
332. #554C2×D61semidirect
339. #498C2×D61semidirect
350. #474C2×D61semidirect
362. #446C2×D61semidirect
381. C61#19890semidirect
500. D8#11758201semidirect
565. D4C2×#11758201semidirect
594. C8C2×#11758201semidirect

Maximal subgroups

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

subgroupindex
#214581702
D4×#117582012
#214574202
#214454072
#214453152
#214452912
#214451962
#214451622
#214451022
#214450822
#214449342
#214448912
#214447092
D8×#924182
C61×#33842
#1989061