Finite Group Databasebeta

← #29671471

Subgroups — #29671471

Order 15616.

724 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458237C211yesmaximal, characteristic, complemented
2#21458063C211yesmaximal, characteristic, complemented
3D4×#11758199C211yesmaximal, characteristic, complemented
4#21445410C211yesmaximal, characteristic, complemented
5#21445352C211yesmaximal, characteristic, complemented
6#21445349C211yesmaximal, characteristic, complemented
7#21445216C211yesmaximal, characteristic, complemented
8#21445172C211yesmaximal, characteristic, complemented
9#21444935C211yesmaximal, characteristic, complemented
10#21444934C211yesmaximal, characteristic, complemented
11#21444902C211yesmaximal, characteristic, complemented
12#21444901C211yesmaximal, characteristic, complemented
13#21444702C211yesmaximal, characteristic, complemented
14D8×#92418C211yesmaximal, characteristic, complemented
15C61×#3325C211yesmaximal, characteristic, complemented
16C22×#11758199—21no—
17#16840477C2211yescharacteristic, complemented
18D4×D244C2211yescharacteristic
19#16840165C2211yescharacteristic, complemented
20#16840138C2211yescharacteristic
21#16840136C2211yescharacteristic, complemented
22#16840134C2211yescharacteristic, complemented
23#16840109C2211yescharacteristic, complemented
24#16840089—21no—
25#16840086—21no—
26#16840083—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic, complemented
29#16840049C2211yescharacteristic, complemented
30#16840014—21no—
31#16839996—21no—
32#16839996—21no—
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic, complemented
35#16839954C2211yescharacteristic
36#16839896—21no—
37#16839895—21no—
38#16839894—21no—
39C4×#11758199C2211yescharacteristic
40#16839841C2211yescharacteristic, complemented
41D4×#92418C2211yescharacteristic
42D4×#92418C2211yescharacteristic, complemented
43#16839798—21no—
44#16839765—21no—
45#16839515C2211yescharacteristic, complemented
46#16839514C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839510C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic, complemented
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic, complemented
55C8×#92418C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic, complemented
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic, complemented
59C61×#482—21no—
60C61×#476C2211yescharacteristic
61C61×#469—21no—
62C61×#459C2211yescharacteristic, complemented
63C61×#447—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic, complemented
66C61×#418—21no—
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758200—41no—
70C2×#11758201—41no—
71C2×#11758199—21no—
72C2×#11758199—21no—
73C2×#11758199—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—44no—
77C2×#11758199D411yescharacteristic
78C2×#11758189—21no—
79C22×#92418—21no—
80C22×#92418—21no—
81#14519777C2311yescharacteristic
82#14519774C2311yescharacteristic
83#14519763—41no—
84#14519752—21no—
85#14519751—21no—
86#14519751—21no—
87#14519748—21no—
88#14519747—41no—
89C4×D244C2311yescharacteristic
90#14519736—21no—
91#14519735—21no—
92#14519710—21no—
93#14519710—21no—
94#14519710D411yescharacteristic
95#14519708—21no—
96#14519708—21no—
97#14519708—21no—
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
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—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C2×D8×C61—21no—
119C2×D8×C61D411yescharacteristic
120C2×M16×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#124×C61—41no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#120×C61—41no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#117×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C24×C61—41no—
146C23×D61—41no—
147C2×Q8×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61—42no—
154C2×D4×C61—42no—
155C2×D4×C61—41no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C2×D4×C61C2×D411yescharacteristic
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166D4×D61—42no—
167D4×D61—81no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—42no—
172C2×D244—41no—
173C2×D244—81no—
174C2×D244C2×D411yescharacteristic
175C2×C4×D61—21no—
176C2×Dic122—21no—
177D8×C61—22no—
178D8×C61—81no—
179M16×C61—81no—
180C2×C8×C61—21no—
181C2×C8×C61C2×D411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—41no—
192C22⋊C4×C61—41no—
193C22⋊C4×C61—41no—
194C42×C61—41no—
195C42×C61C2411yescharacteristic
196C22⋊Dic61—41no—
197#11758201—82no—
198#11758200—82no—
199#11758199—22no—
200#11758199—42no—
201#11758199—42no—
202#11758199—42no—
203#11758199—81no—
204#11758199—81no—
205#11758198—21no—
206#11758198—41no—
207#11758198—41no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61C2×D411yescharacteristic
211C4×Dic61—41no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—42no—
217C2×#92418—42no—
218C2×#92418C2×D411yescharacteristic
219C2×#92418C2×D411yescharacteristic
220#11758189—81no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—41no—
225C23×C61—82no—
226C23×C61—82no—
227C23×C61—161no—
228C22×D61—21no—
229C22×D61—41no—
230C22×D61—82no—
231C22×D61—82no—
232C22×D61—161no—
233Q8×C61—81no—
234D4×C61—21no—
235D4×C61—21no—
236D4×C61—21no—
237D4×C61—21no—
238D4×C61—21no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—81no—
244D4×C61—82no—
245D4×C61—82no—
246D4×C61—161no—
247D4×C61#13512yes—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61H(5,𝔽2)11yescharacteristic
261C22⋊D61—82no—
262C22⋊D61—161no—
263C2×Dic61—21no—
264C2×Dic61—41no—
265D244—21no—
266D244—21no—
267D244—41no—
268D244—41no—
269D244—41no—
270D244—41no—
271D244—81no—
272D244—82no—
273C4×D61—41no—
274C4×D61—41no—
275Dic122—81no—
276C8×C61—21no—
277C8×C61—21no—
278C8×C61—41no—
279#92418—22no—
280#92418—21no—
281#92418—41no—
282#92418—41no—
283#92418—41no—
284#92418AGL(1,ℤ/8)12yes—
285#19898—611nomaximal, Sylow
286C22×C61—22no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—81no—
296C22×C61—81no—
297C22×C61—81no—
298C22×C61—164no—
299C22×C61D4211yescharacteristic
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—41no—
303C2×D61—81no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—164no—
307C4×C61—21no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—81no—
312C4×C61C2×#13511yescharacteristic
313C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
314C4×C61#57611yescharacteristic
315C4×C61#57711yescharacteristic
316Dic61—41no—
317Dic61—81no—
318#3341—611no—
319#3325—611no—
320#3325D6111yescharacteristic, complemented
321D4×D8—611no—
322#1706—611no—
323#1697—611no—
324#1697—611no—
325#1675—611no—
326#1667—611no—
327#1629—611no—
328#1629—611no—
329#1624—611no—
330#1624—611no—
331#1589—611no—
332C8×D8—611no—
333C2×C61—42no—
334C2×C61—81no—
335C2×C61—81no—
336C2×C61—161no—
337C2×C61#327211yescharacteristic
338C2×C61#328011yescharacteristic
339C2×C61#329211yescharacteristic
340D61—81no—
341D61—161no—
342C22×D8—1221no—
343#555—611no—
344#555C2×D6111yescharacteristic, complemented
345D42—611no—
346D42C2×D6111yescharacteristic
347#500—611no—
348#493—611no—
349#492—611no—
350#492—611no—
351#486—611no—
352#486C2×D6111yescharacteristic, complemented
353#482—21no—
354#482—1221no—
355#482—1221no—
356#482—1221no—
357#476—611no—
358#476—611no—
359#476—611no—
360#476C2×D6111yescharacteristic
361#469—21no—
362#469—1221no—
363#466—1221no—
364#466—1221no—
365#459—611no—
366#459—611no—
367#459—611no—
368#459C2×D6111yescharacteristic, complemented
369#447—21no—
370#447—1221no—
371#447—1221no—
372#447—1221no—
373C4×D8—611no—
374C4×D8C2×D6111yescharacteristic
375#436—611no—
376#436C2×D6111yescharacteristic, complemented
377C8×D4—611no—
378C8×D4—611no—
379#427—1221no—
380#418—21no—
381#418—1221no—
382#335—611no—
383#335—611no—
384#333—611no—
385#333—611no—
386#331—611no—
387#331—611no—
388D4⋊C8—611no—
389D4⋊C8—611no—
390D4⋊C8—611no—
391D4⋊C8—611no—
392C82—611no—
393C61#1989811yescharacteristic, complemented, Sylow
394C22×D4—21no—
395C22×D4—21no—
396C22×D4—1221no—
397C22×D4—1221no—
398C2×SD16—2441no—
399C2×SD16—2441no—
400C2×D8—21no—
401C2×D8—611no—
402C2×D8—1221no—
403C2×D8—1221no—
404C2×D8—1221no—
405C2×D8—1221no—
406C2×D8—1221no—
407C2×D8—2444no—
408C2×D8C22⋊D6111yescharacteristic
409C2×M16—21no—
410C2×M16—1221no—
411C22×C8—1221no—
412C22×C8—1221no—
413C4⋊Q8—611no—
414C4⋊Q8C22×D6111yescharacteristic
415#127—611no—
416#127C22×D6111yescharacteristic
417#124—41no—
418#124—2441no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121—21no—
423#121—1221no—
424#121—1221no—
425#121—1221no—
426#121—1221no—
427#120—41no—
428#120—2441no—
429C4×D4—611no—
430C4×D4C22×D6111yescharacteristic
431C4×D4C22×D6111yescharacteristic
432C4×D4C22×D6111yescharacteristic
433#117—21no—
434#117—21no—
435#117—1221no—
436#117—1221no—
437#107—611no—
438#107—1221no—
439#107—1221no—
440#107C22⋊D6111yescharacteristic
441#106—21no—
442#106—1221no—
443#106—1221no—
444#106—1221no—
445C4⋊C8—611no—
446C4⋊C8—611no—
447C4⋊C8—611no—
448C4⋊C8C22×D6111yescharacteristic
449#102—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—611no—
454#102—611no—
455#102—1221no—
456#102—1221no—
457#102—1221no—
458#102—1221no—
459#102—1221no—
460#102—1221no—
461#102—1221no—
462#102—1221no—
463#102C22⋊D6111yescharacteristic
464#102C22⋊D6111yescharacteristic
465C22⋊C8—21no—
466C22⋊C8—1221no—
467C22⋊C8—1221no—
468C22⋊C8—1221no—
469C4×C8—611no—
470C4×C8—611no—
471C4×C8C22×D6111yescharacteristic
472C24—41no—
473C24—2441no—
474C2×Q8—21no—
475C2×Q8—1221no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—41no—
484C2×D4—81no—
485C2×D4—81no—
486C2×D4—611no—
487C2×D4—1221no—
488C2×D4—1221no—
489C2×D4—1221no—
490C2×D4—4881no—
491C2×D4—4881no—
492C2×D4—2441no—
493C2×D4—2442no—
494C2×D4—2441no—
495C2×D4—2441no—
496C2×D4—2442no—
497C2×D4D4×D6111yescharacteristic
498C2×D4C2×C22⋊D6111yescharacteristic
499C2×D4C2×C22⋊D6111yescharacteristic
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—1221no—
504SD16—4882no—
505SD16—4882no—
506D8—22no—
507D8—81no—
508D8—1222no—
509D8—4881no—
510D8—4881no—
511D8—2442no—
512D8—2442no—
513D8—2442no—
514M16—81no—
515M16—4881no—
516C2×C8—21no—
517C2×C8—611no—
518C2×C8—611no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—2442no—
524C2×C8—2442no—
525C2×C8C2×C22⋊D6111yescharacteristic
526C2×C8C2×C22⋊D6111yescharacteristic
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—611no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4D4×D6111yescharacteristic
533C4⋊C4C2×C22⋊D6111yescharacteristic
534C4⋊C4C2×C22⋊D6111yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—1221no—
542C22⋊C4—2441no—
543C22⋊C4—2441no—
544C22⋊C4—2441no—
545C42—41no—
546C42—2441no—
547C42C23×D6111yescharacteristic
548C23—21no—
549C23—21no—
550C23—21no—
551C23—41no—
552C23—82no—
553C23—82no—
554C23—161no—
555C23—1221no—
556C23—9761no—
557C23—4882no—
558C23—4882no—
559C23—2441no—
560Q8—81no—
561Q8—4881no—
562D4—21no—
563D4—21no—
564D4—21no—
565D4—21no—
566D4—21no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—81no—
572D4—82no—
573D4—82no—
574D4—161no—
575D4—1221no—
576D4—1221no—
577D4—9761no—
578D4—4881no—
579D4—4882no—
580D4—4882no—
581D4—2441no—
582D4—2441no—
583D4—2441no—
584D4—2441no—
585D4#1451979712yes—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—1221no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4C2×D4×D6111yescharacteristic
601C2×C4C22×C22⋊D6111yescharacteristic
602C2×C4#1451982211yescharacteristic
603C8—21no—
604C8—21no—
605C8—41no—
606C8—612no—
607C8—1222no—
608C8—1221no—
609C8—2441no—
610C8—2441no—
611C8—2441no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—164no—
625C22—9764no—
626C22—4881no—
627C22—4881no—
628C22—4881no—
629C22—2441no—
630C22—2441no—
631C22—2441no—
632C22D4×C22⋊D6111yescharacteristic
633C4—21no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—4881no—
639C4—2441no—
640C4C2×#1451979711yescharacteristic
641C4AGL(1,ℤ/8)×D6111yescharacteristic
642C4#1684056511yescharacteristic
643C4#1684057211yescharacteristic
644C2—42no—
645C2—81no—
646C2—81no—
647C2—161no—
648C2—9761no—
649C2—4881no—
650C2#2145741311yescharacteristic
651C2#2145750011yescharacteristic
652C2#2145761611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3325C2
socleC22×C61D42
hypercenter#3325D61
hypocenterC61#19898
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #21458237C2semidirect
2. #21458063C2semidirect
3. D4×#11758199C2semidirect
4. #21445410C2semidirect
5. #21445352C2semidirect
6. #21445349C2semidirect
7. #21445216C2semidirect
8. #21445172C2semidirect
9. #21444935C2semidirect
10. #21444934C2semidirect
11. #21444902C2semidirect
12. #21444901C2semidirect
13. #21444702C2semidirect
14. D8×#92418C2semidirect
15. C61×#3325C2semidirect
17. #16840477C22semidirect
19. #16840165C22semidirect
21. #16840136C22semidirect
22. #16840134C22semidirect
23. #16840109C22semidirect
28. #16840052C22semidirect
29. #16840049C22semidirect
34. #16839957C22semidirect
40. #16839841C22semidirect
42. D4×#92418C22semidirect
45. #16839515C22semidirect
46. #16839514C22semidirect
47. #16839511C22semidirect
48. #16839510C22semidirect
49. #16839506C22semidirect
50. #16839505C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
54. #16839489C22semidirect
55. C8×#92418C22semidirect
56. C61×#555C22semidirect
58. C61×#486C22semidirect
62. C61×#459C22semidirect
65. C61×#436C22semidirect
320. #3325D61semidirect
344. #555C2×D61semidirect
352. #486C2×D61semidirect
368. #459C2×D61semidirect
376. #436C2×D61semidirect
393. C61#19898semidirect

Maximal subgroups

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

subgroupindex
#214582372
#214580632
D4×#117581992
#214454102
#214453522
#214453492
#214452162
#214451722
#214449352
#214449342
#214449022
#214449012
#214447022
D8×#924182
C61×#33252
#1989861