Finite Group Databasebeta

← #29669615

Subgroups — #29669615

Order 15616.

710 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458126C211yesmaximal, characteristic, complemented
2#21457632C211yesmaximal, characteristic, complemented
3#21457537C211yesmaximal, characteristic, complemented
4#21445480C211yesmaximal, characteristic, complemented
5#21445377C211yesmaximal, characteristic, complemented
6#21445254C211yesmaximal, characteristic, complemented
7#21445242C211yesmaximal, characteristic, complemented
8#21445182C211yesmaximal, characteristic, complemented
9#21445103C211yesmaximal, characteristic, complemented
10#21445102C211yesmaximal, characteristic, complemented
11#21444998C211yesmaximal, characteristic, complemented
12#21444907C211yesmaximal, characteristic, complemented
13#21444648C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3294C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17#16840417C2211yescharacteristic, complemented
18#16840416C2211yescharacteristic
19#16840158C2211yescharacteristic, complemented
20#16840141C2211yescharacteristic, complemented
21#16840113C2211yescharacteristic, complemented
22#16840108C2211yescharacteristic
23#16840108C2211yescharacteristic
24#16840099—21no—
25#16840073—21no—
26#16840042C2211yescharacteristic
27#16840042C2211yescharacteristic
28#16840007—21no—
29#16840001—21no—
30#16839996—21no—
31#16839967C2211yescharacteristic
32#16839967C2211yescharacteristic, complemented
33#16839964C2211yescharacteristic, complemented
34#16839954C2211yescharacteristic
35#16839924—21no—
36#16839922—21no—
37#16839904—21no—
38#16839896—21no—
39C4×#11758199C2211yescharacteristic
40#16839841C2211yescharacteristic, complemented
41D4×#92418C2211yescharacteristic
42D4×#92418C2211yescharacteristic, complemented
43#16839760—21no—
44C2×#14519698—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839509C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839506C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C61×#547C2211yescharacteristic
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#480—21no—
60C61×#474C2211yescharacteristic
61C61×#466—21no—
62C61×#459C2211yescharacteristic
63C61×#447—21no—
64C4×D8×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#102×C61—21no—
67C2×#11758222—21no—
68C2×#11758224—21no—
69#14519797—44no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758201—21no—
75C2×#11758199—21no—
76C2×#11758199D411yescharacteristic
77C2×#11758189—21no—
78C22×#92418—21no—
79C22×#92418—21no—
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519761—41no—
83#14519759—41no—
84#14519757—21no—
85#14519756—21no—
86#14519751—21no—
87#14519748—21no—
88C4×D244C2311yescharacteristic
89C2×C4⋊Dic61—21no—
90C4⋊C4×D61—21no—
91#14519710—21no—
92#14519710—21no—
93#14519710D411yescharacteristic
94#14519708—41no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519702—21no—
99#14519702—21no—
100#14519701—21no—
101#14519700—21no—
102#14519700—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—41no—
109#14519698D411yescharacteristic
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119C2×D8×C61—21no—
120C2×D8×C61D411yescharacteristic
121C22×C8×C61—21no—
122C4⋊Q8×C61C2311yescharacteristic
123#127×C61C2311yescharacteristic
124#123×C61—41no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#121×C61—21no—
129#120×C61—41no—
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133C2×C4⋊C4×C61—21no—
134#107×C61—21no—
135#107×C61D411yescharacteristic
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—
146#41×C61—42no—
147#41×C61—81no—
148C2×Q8×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61—42no—
155C2×D4×C61—42no—
156C2×D4×C61—41no—
157C2×D4×C61—81no—
158C2×D4×C61—81no—
159C2×D4×C61C2×D411yescharacteristic
160C2×D4×C61C2×D411yescharacteristic
161C2×D4×C61C2×D411yescharacteristic
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—41no—
166C2×C22⋊D61—41no—
167C2×C22⋊D61—41no—
168C22×Dic61—41no—
169#11758224—42no—
170#11758224—81no—
171#11758222—42no—
172#11758222—81no—
173C2×D244C2×D411yescharacteristic
174C2×C4×D61—21no—
175C2×C4×D61—41no—
176C2×Dic122—21no—
177C2×Dic122—21no—
178D8×C61—22no—
179D8×C61—81no—
180C2×C8×C61—21no—
181C2×C8×C61—81no—
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—
197#11758202—42no—
198#11758202—81no—
199#11758201—42no—
200#11758200—42no—
201#11758200—81no—
202#11758199—22no—
203#11758199—81no—
204#11758198—21no—
205#11758198—41no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—41no—
211C4⋊Dic61C2×D411yescharacteristic
212#11758196—41no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—42no—
218C2×#92418—81no—
219C2×#92418C2×D411yescharacteristic
220C2×#92418C2×D411yescharacteristic
221#11758189—81no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—41no—
226C23×C61—82no—
227C23×C61—82no—
228C23×C61—161no—
229C22×D61—21no—
230Q8×C61—41no—
231Q8×C61—41no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61—21no—
235D4×C61—21no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—81no—
241D4×C61—82no—
242D4×C61—82no—
243D4×C61—82no—
244D4×C61#13512yescomplemented
245D4×C61AGL(1,ℤ/8)12yes—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
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—41no—
256C2×C4×C61—82no—
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C22⋊D61—82no—
261C22⋊D61—82no—
262C2×Dic61—21no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—82no—
266D244—21no—
267D244—21no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—82no—
271Dic122—41no—
272Dic122—41no—
273Dic122—41no—
274Dic122—41no—
275C8×C61—21no—
276C8×C61—21no—
277C8×C61—41no—
278#92418—21no—
279#92418—21no—
280#92418—41no—
281#92418—41no—
282#92418—41no—
283#92418—41no—
284#19772—611nomaximal, Sylow
285C22×C61—22no—
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—81no—
295C22×C61—81no—
296C22×C61—81no—
297C22×C61—164no—
298C22×C61D4211yescharacteristic
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—41no—
302C4×C61—21no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—81no—
307C4×C61C2×#13511yescharacteristic
308C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
309C4×C61#57611yescharacteristic
310C4×C61#57611yescharacteristic
311Dic61—41no—
312Dic61—81no—
313Dic61—81no—
314#3330—611no—
315#3294—611no—
316#3294D6111yescharacteristic, complemented
317#3283—611no—
318#1720—611no—
319#1701—611no—
320#1681—611no—
321#1679—611no—
322#1669—611no—
323#1654—611no—
324#1654—611no—
325#1639—611no—
326#1625—611no—
327#1581—611no—
328#1580—611no—
329C2×C61—42no—
330C2×C61—42no—
331C2×C61—81no—
332C2×C61—161no—
333C2×C61#326411yescharacteristic
334C2×C61#328011yescharacteristic
335C2×C61#328911yescharacteristic
336D61—81no—
337C2×#135—1221no—
338#547—611no—
339#547—611no—
340#547C2×D6111yescharacteristic
341D42C2×D6111yescharacteristic
342#498—611no—
343#494—611no—
344#487—611no—
345#486—611no—
346#486—611no—
347#486C2×D6111yescharacteristic
348#484—1221no—
349#480—21no—
350#480—1221no—
351#474—611no—
352#474—611no—
353#474C2×D6111yescharacteristic
354#468—1221no—
355#467—1221no—
356#466—21no—
357#466—1221no—
358#461—611no—
359#461—611no—
360#461—611no—
361#459—611no—
362#459C2×D6111yescharacteristic
363#452—1221no—
364#452—1221no—
365#449—1221no—
366#447—21no—
367#447—1221no—
368C4×D8—611no—
369C4×D8C2×D6111yescharacteristic
370#436—611no—
371C8×D4—611no—
372C8×D4—611no—
373C8×D4C2×D6111yescharacteristic
374#417—1221no—
375C2×#102—21no—
376C2×#102—1221no—
377#335—611no—
378#334—611no—
379#332—611no—
380#332—611no—
381#332—611no—
382#331—611no—
383D4⋊C8—611no—
384D4⋊C8—611no—
385D4⋊C8—611no—
386D4⋊C8—611no—
387#322—611no—
388C61#1977211yescharacteristic, complemented, Sylow
389C2×#41—21no—
390C2×#41—1221no—
391C2×#41—1221no—
392C22×D4—21no—
393C22×D4—21no—
394#135—2444no—
395C2×Q16—1221no—
396C2×Q16—1221no—
397C2×SD16—1221no—
398C2×SD16—1221no—
399C2×SD16—1221no—
400C2×D8—21no—
401C2×D8—611no—
402C2×D8—1221no—
403C2×D8C22⋊D6111yescharacteristic
404C2×M16—1221no—
405C22×C8—21no—
406C22×C8—1221no—
407C22×C8—1221no—
408C4⋊Q8—611no—
409C4⋊Q8—611no—
410C4⋊Q8C22×D6111yescharacteristic
411#127C22×D6111yescharacteristic
412#123—41no—
413#123—2441no—
414#123—2441no—
415C22⋊Q8—21no—
416C22⋊Q8—1221no—
417C22⋊Q8—1221no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121—1221no—
422#121—1221no—
423#120—41no—
424C4×D4—611no—
425C4×D4C22×D6111yescharacteristic
426C4×D4C22×D6111yescharacteristic
427C4×D4C22×D6111yescharacteristic
428C2×C4⋊C4—21no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431#107—21no—
432#107—611no—
433#107—1221no—
434#107—1221no—
435#107C22⋊D6111yescharacteristic
436#106—2441no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8C22×D6111yescharacteristic
441#103—1221no—
442#103—1221no—
443#103—1221no—
444#103—1221no—
445#103—1221no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102—21no—
450#102—611no—
451#102—611no—
452#102—1221no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456#102—1221no—
457#102—2441no—
458#102C22⋊D6111yescharacteristic
459#102C22⋊D6111yescharacteristic
460C22⋊C8—21no—
461C22⋊C8—1221no—
462C22⋊C8—1221no—
463C22⋊C8—1221no—
464C4×C8—611no—
465C4×C8—611no—
466C4×C8C22×D6111yescharacteristic
467C24—41no—
468#41—42no—
469#41—81no—
470#41—4881no—
471#41—4881no—
472#41—2442no—
473#41—2442no—
474C2×Q8—21no—
475C2×Q8—1221no—
476C2×Q8—1221no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—41no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4—611no—
488C2×D4—2441no—
489C2×D4—2441no—
490C2×D4D4×D6111yescharacteristic
491C2×D4C2×C22⋊D6111yescharacteristic
492C2×D4C2×C22⋊D6111yescharacteristic
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—41no—
497C22×C4—1221no—
498C22×C4—2441no—
499C22×C4—2441no—
500Q16—4881no—
501Q16—2442no—
502SD16—4881no—
503SD16—2442no—
504SD16—2442no—
505D8—22no—
506D8—81no—
507D8—1222no—
508D8—4881no—
509M16—4881no—
510C2×C8—21no—
511C2×C8—81no—
512C2×C8—611no—
513C2×C8—611no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—4881no—
519C2×C8—2442no—
520C2×C8C2×C22⋊D6111yescharacteristic
521C2×C8C2×C22⋊D6111yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—611no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—2441no—
531C4⋊C4—2441no—
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—1221no—
541C22⋊C4—2441no—
542C22⋊C4—2441no—
543C42C23×D6111yescharacteristic
544C23—21no—
545C23—21no—
546C23—21no—
547C23—41no—
548C23—82no—
549C23—82no—
550C23—161no—
551C23—1221no—
552Q8—41no—
553Q8—41no—
554Q8—2441no—
555Q8—2441no—
556Q8—2441no—
557Q8—2441no—
558D4—21no—
559D4—21no—
560D4—21no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—82no—
570D4—1221no—
571D4—1221no—
572D4—4882no—
573D4—4882no—
574D4#1451979712yescomplemented
575D4#1451980112yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—82no—
587C2×C4—1221no—
588C2×C4—4882no—
589C2×C4—4882no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4C2×D4×D6111yescharacteristic
595C2×C4C22×C22⋊D6111yescharacteristic
596C2×C4#1451982211yescharacteristic
597C8—21no—
598C8—21no—
599C8—41no—
600C8—1221no—
601C8—1221no—
602C8—2441no—
603C8—2441no—
604C8—2441no—
605C8—2441no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—164no—
619C22—2441no—
620C22—2441no—
621C22—2441no—
622C22D4×C22⋊D6111yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—4881no—
629C4—4881no—
630C4—2441no—
631C4C2×#1451979711yescharacteristic
632C4C2×#1451980111yescharacteristic
633C4#1684056311yescharacteristic
634C4#1684056511yescharacteristic
635C2—42no—
636C2—42no—
637C2—81no—
638C2—161no—
639C2—4881no—
640C2#2145729911yescharacteristic
641C2#2145750011yescharacteristic
642C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3294C2
socleC22×C61D42
hypercenter#3294D61
hypocenterC61#19772
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. #21458126C2semidirect
2. #21457632C2semidirect
3. #21457537C2semidirect
4. #21445480C2semidirect
5. #21445377C2semidirect
6. #21445254C2semidirect
7. #21445242C2semidirect
8. #21445182C2semidirect
9. #21445103C2semidirect
10. #21445102C2semidirect
11. #21444998C2semidirect
12. #21444907C2semidirect
13. #21444648C2semidirect
14. #21444643C2semidirect
15. C61×#3294C2semidirect
17. #16840417C22semidirect
19. #16840158C22semidirect
20. #16840141C22semidirect
21. #16840113C22semidirect
32. #16839967C22semidirect
33. #16839964C22semidirect
40. #16839841C22semidirect
42. D4×#92418C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839509C22semidirect
48. #16839508C22semidirect
49. #16839507C22semidirect
53. D4⋊#92418C22semidirect
54. #16839489C22semidirect
55. #16839483C22semidirect
244. D4×C61#135semidirect
316. #3294D61semidirect
388. C61#19772semidirect
574. D4#14519797semidirect

Maximal subgroups

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

subgroupindex
#214581262
#214576322
#214575372
#214454802
#214453772
#214452542
#214452422
#214451822
#214451032
#214451022
#214449982
#214449072
#214446482
#214446432
C61×#32942
#1977261