Finite Group Databasebeta

← #29671497

Subgroups — #29671497

Order 15616.

710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458803C211yesmaximal, characteristic, complemented
2#21458052C211yesmaximal, characteristic, complemented
3D4×#11758199C211yesmaximal, characteristic
4#21445423C211yesmaximal, characteristic, complemented
5#21445380C211yesmaximal, characteristic, complemented
6#21445377C211yesmaximal, characteristic, complemented
7#21445182C211yesmaximal, characteristic, complemented
8#21445177C211yesmaximal, characteristic, complemented
9#21444998C211yesmaximal, characteristic, complemented
10#21444997C211yesmaximal, characteristic, complemented
11#21444929C211yesmaximal, characteristic, complemented
12#21444928C211yesmaximal, characteristic, complemented
13#21444702C211yesmaximal, characteristic, complemented
14SD16×#92418C211yesmaximal, characteristic, complemented
15C61×#3324C211yesmaximal, characteristic, complemented
16C22×#11758199—21no—
17#16840485C2211yescharacteristic, complemented
18D4×D244C2211yescharacteristic
19#16840144—21no—
20#16840141C2211yescharacteristic, complemented
21#16840138C2211yescharacteristic
22#16840110C2211yescharacteristic, complemented
23#16840109C2211yescharacteristic, complemented
24#16840108C2211yescharacteristic, complemented
25#16840088—21no—
26#16840042C2211yescharacteristic
27#16840011—21no—
28#16839996—21no—
29#16839984—21no—
30#16839981—21no—
31#16839967C2211yescharacteristic, complemented
32#16839964C2211yescharacteristic, complemented
33#16839962C2211yescharacteristic, complemented
34#16839957C2211yescharacteristic
35#16839954C2211yescharacteristic
36#16839911—21no—
37#16839896—21no—
38#16839895—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C4×#11758202—21no—
41C4×#11758199C2211yescharacteristic
42#16839841C2211yescharacteristic, complemented
43D4×#92418C2211yescharacteristic
44#16839765—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839508C2211yescharacteristic, complemented
48#16839507C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic, complemented
55C8×#92418C2211yescharacteristic, complemented
56C61×#556C2211yescharacteristic, complemented
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic, complemented
59C61×#482—21no—
60C61×#474C2211yescharacteristic
61C61×#468—21no—
62C61×#460C2211yescharacteristic, complemented
63C61×#450—21no—
64C4×SD16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic, complemented
66C61×#418—21no—
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—21no—
77C2×#11758199—21no—
78C2×#11758199—44no—
79C2×#11758199D411yescharacteristic
80C2×#11758189—21no—
81C22×#92418—21no—
82#14519777C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519772—41no—
85#14519765—21no—
86#14519753—21no—
87#14519752—21no—
88#14519751—21no—
89#14519747—41no—
90C4×Dic122—21no—
91C4×D244C2311yescharacteristic
92#14519735—21no—
93#14519710—21no—
94#14519710D411yescharacteristic
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701—21no—
100#14519700—21no—
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—41no—
106#14519698D411yescharacteristic
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61D411yescharacteristic
120C2×M16×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#126×C61—41no—
124#124×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#120×C61—41no—
129C4×Q8×C61—21no—
130C4×Q8×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#117×C61—21no—
134#107×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61D411yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C24×C61—41no—
146C23×D61—41no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
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—81no—
157C2×D4×C61—81no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C2×C22⋊D61—41no—
163D4×D61—42no—
164D4×D61—81no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—42no—
169C2×D244—41no—
170C2×D244—81no—
171C2×D244C2×D411yescharacteristic
172C2×C4×D61—21no—
173C2×Dic122—21no—
174SD16×C61—22no—
175SD16×C61—81no—
176M16×C61—81no—
177C2×C8×C61—21no—
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—41no—
184C4⋊C4×C61C2×D411yescharacteristic
185C4⋊C4×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—41no—
190C22⋊C4×C61—41no—
191C22⋊C4×C61—41no—
192C42×C61—21no—
193C42×C61—41no—
194C42×C61C2411yescharacteristic
195#11758202—42no—
196#11758202—81no—
197#11758201—81no—
198#11758201—81no—
199#11758200—81no—
200#11758199—22no—
201#11758199—42no—
202#11758199—42no—
203#11758199—42no—
204#11758199—81no—
205#11758198—21no—
206#11758198—41no—
207#11758198—41no—
208#11758198—41no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61C2×D411yescharacteristic
212#11758196—41no—
213C4×Dic61—41no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—42no—
219C2×#92418C2×D411yescharacteristic
220C2×#92418C2×D411yescharacteristic
221#11758189—81no—
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—21no—
234Q8×C61—21no—
235Q8×C61—41no—
236Q8×C61—41no—
237D4×C61—21no—
238D4×C61—21no—
239D4×C61—21no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—41no—
244D4×C61—81no—
245D4×C61—82no—
246D4×C61—82no—
247D4×C61#13512yes—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C22×D411yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C22⋊D61—82no—
261C2×Dic61—21no—
262C2×Dic61—41no—
263D244—21no—
264D244—21no—
265D244—41no—
266D244—41no—
267D244—41no—
268D244—41no—
269D244—81no—
270D244—82no—
271C4×D61—41no—
272C4×D61—41no—
273Dic122—41no—
274Dic122—41no—
275C8×C61—21no—
276C8×C61—21no—
277C8×C61—41no—
278#92418—21no—
279#92418—41no—
280#92418—41no—
281#92418—41no—
282#92418—41no—
283#92418AGL(1,ℤ/8)12yes—
284#19900—611nomaximal, Sylow
285C22×C61—22no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—81no—
292C22×C61—81no—
293C22×C61—81no—
294C22×C61—164no—
295C22×C61D4211yescharacteristic
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—81no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—164no—
303C4×C61—21no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—41no—
307C4×C61—41no—
308C4×C61—81no—
309C4×C61C2×#13511yescharacteristic
310C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
311C4×C61#57611yescharacteristic
312C4×C61#57611yescharacteristic
313Dic61—41no—
314Dic61—81no—
315#3393—611no—
316#3324—611no—
317#3324D6111yescharacteristic, complemented
318D4×D8—611no—
319#1709—611no—
320#1701—611no—
321#1701—611no—
322#1669—611no—
323#1668—611no—
324#1639—611no—
325#1639—611no—
326#1628—611no—
327#1628—611no—
328#1589—611no—
329C8×SD16—611no—
330C2×C61—42no—
331C2×C61—81no—
332C2×C61—161no—
333C2×C61#327411yescharacteristic
334C2×C61#328011yescharacteristic
335C2×C61#329011yescharacteristic
336D61—81no—
337D61—161no—
338C22×D8—1221no—
339#556—611no—
340#556C2×D6111yescharacteristic, complemented
341D42—611no—
342D42C2×D6111yescharacteristic
343#495—1221no—
344#494—611no—
345#493—611no—
346#486—611no—
347#486—611no—
348#486—611no—
349#486C2×D6111yescharacteristic, complemented
350#482—21no—
351#482—1221no—
352#474—611no—
353#474C2×D6111yescharacteristic
354#468—21no—
355#468—1221no—
356#466—1221no—
357#464—1221no—
358#464—1221no—
359#461—611no—
360#461—611no—
361#460—611no—
362#460C2×D6111yescharacteristic, complemented
363#459—611no—
364#459—611no—
365#450—21no—
366#450—1221no—
367#447—1221no—
368#447—1221no—
369C8×Q8—611no—
370C4×Q16—1221no—
371C4×SD16C2×D6111yescharacteristic
372C4×D8—611no—
373#436—611no—
374#436C2×D6111yescharacteristic, complemented
375C8×D4—611no—
376#418—21no—
377#418—1221no—
378#335—611no—
379#334—611no—
380#332—611no—
381#332—611no—
382#331—611no—
383#331—611no—
384Q8⋊C8—611no—
385D4⋊C8—611no—
386D4⋊C8—611no—
387D4⋊C8—611no—
388C82—611no—
389C61#1990011yescharacteristic, complemented, Sylow
390C22×D4—21no—
391C22×D4—21no—
392C22×D4—1221no—
393C22×D4—1221no—
394C2×Q16—1221no—
395C2×Q16—1221no—
396C2×SD16—21no—
397C2×SD16—1221no—
398C2×SD16—1221no—
399C2×SD16—1221no—
400C2×SD16C22⋊D6111yescharacteristic
401C2×D8—611no—
402C2×D8—1221no—
403C2×D8—1221no—
404C2×D8—1221no—
405C2×D8—1221no—
406C2×D8—2444no—
407C2×M16—21no—
408C2×M16—1221no—
409C22×C8—1221no—
410C4⋊Q8—611no—
411C4⋊Q8C22×D6111yescharacteristic
412#127—611no—
413#127C22×D6111yescharacteristic
414#126—41no—
415#126—2441no—
416#124—21no—
417#124—1221no—
418C22⋊Q8—21no—
419C22⋊Q8—1221no—
420#121—21no—
421#121—21no—
422#121—1221no—
423#121—1221no—
424#120—41no—
425#120—2441no—
426C4×Q8—21no—
427C4×Q8—1221no—
428C4×Q8C22×D6111yescharacteristic
429C4×D4—611no—
430C4×D4C22×D6111yescharacteristic
431C4×D4C22×D6111yescharacteristic
432#117—21no—
433#117—1221no—
434#107—21no—
435#107—611no—
436#107—1221no—
437#106C22⋊D6111yescharacteristic
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8—1221no—
442C4⋊C8C22×D6111yescharacteristic
443#103—1221no—
444#103—1221no—
445#103C22⋊D6111yescharacteristic
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—1221no—
458#102—2441no—
459#102—2441no—
460#102C22⋊D6111yescharacteristic
461C22⋊C8—21no—
462C22⋊C8—1221no—
463C22⋊C8—1221no—
464C4×C8—611no—
465C4×C8—611no—
466C4×C8—1221no—
467C4×C8C22×D6111yescharacteristic
468C24—41no—
469C24—2441no—
470C2×Q8—21no—
471C2×Q8—1221no—
472C2×Q8C2×C22⋊D6111yescharacteristic
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—81no—
481C2×D4—81no—
482C2×D4—611no—
483C2×D4—1221no—
484C2×D4—1221no—
485C2×D4—1221no—
486C2×D4—4881no—
487C2×D4—4881no—
488C2×D4—2441no—
489C2×D4—2442no—
490C2×D4—2441no—
491C2×D4—2442no—
492C2×D4D4×D6111yescharacteristic
493C2×D4C2×C22⋊D6111yescharacteristic
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—1221no—
497Q16—4881no—
498Q16—2442no—
499SD16—22no—
500SD16—81no—
501SD16—4881no—
502SD16—4881no—
503SD16—4881no—
504D8—1222no—
505D8—4881no—
506D8—2442no—
507D8—2442no—
508D8—2442no—
509M16—81no—
510M16—4881no—
511C2×C8—21no—
512C2×C8—611no—
513C2×C8—611no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—2442no—
519C2×C8C2×C22⋊D6111yescharacteristic
520C2×C8C2×C22⋊D6111yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—611no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—2441no—
529C4⋊C4D4×D6111yescharacteristic
530C4⋊C4C2×C22⋊D6111yescharacteristic
531C4⋊C4C2×C22⋊D6111yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—1221no—
538C22⋊C4—2441no—
539C22⋊C4—2441no—
540C22⋊C4—2441no—
541C42—21no—
542C42—41no—
543C42—2441no—
544C42C23×D6111yescharacteristic
545C23—21no—
546C23—21no—
547C23—41no—
548C23—82no—
549C23—82no—
550C23—161no—
551C23—1221no—
552C23—9761no—
553C23—4882no—
554C23—4882no—
555C23—2441no—
556Q8—21no—
557Q8—21no—
558Q8—41no—
559Q8—41no—
560Q8—2441no—
561Q8—2441no—
562D4—21no—
563D4—21no—
564D4—21no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—81no—
570D4—82no—
571D4—82no—
572D4—1221no—
573D4—1221no—
574D4—4881no—
575D4—4882no—
576D4—4882no—
577D4—2441no—
578D4—2441no—
579D4—2441no—
580D4—2441no—
581D4#1451979712yes—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—1221no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4C2×D4×D6111yescharacteristic
596C2×C4C22×C22⋊D6111yescharacteristic
597C2×C4#1451982211yescharacteristic
598C8—21no—
599C8—21no—
600C8—41no—
601C8—612no—
602C8—1221no—
603C8—2441no—
604C8—2441no—
605C8—2441no—
606C8—2441no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—164no—
617C22—9764no—
618C22—4881no—
619C22—4881no—
620C22—4881no—
621C22—2441no—
622C22—2441no—
623C22—2441no—
624C22D4×C22⋊D6111yescharacteristic
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4—4881no—
632C4—2441no—
633C4C2×#1451979711yescharacteristic
634C4AGL(1,ℤ/8)×D6111yescharacteristic
635C4#1684056511yescharacteristic
636C4#1684056611yescharacteristic
637C2—42no—
638C2—81no—
639C2—161no—
640C2—9761no—
641C2—4881no—
642C2#2145743311yescharacteristic
643C2#2145750011yescharacteristic
644C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3324C2
socleC22×C61D42
prime radicalD4×#11758199C2
hypercenter#3324D61
hypocenterC61#19900
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3324

Complements

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

NH ≅ G/Ntype
1. #21458803C2semidirect
2. #21458052C2semidirect
4. #21445423C2semidirect
5. #21445380C2semidirect
6. #21445377C2semidirect
7. #21445182C2semidirect
8. #21445177C2semidirect
9. #21444998C2semidirect
10. #21444997C2semidirect
11. #21444929C2semidirect
12. #21444928C2semidirect
13. #21444702C2semidirect
14. SD16×#92418C2semidirect
15. C61×#3324C2semidirect
17. #16840485C22semidirect
20. #16840141C22semidirect
22. #16840110C22semidirect
23. #16840109C22semidirect
24. #16840108C22semidirect
31. #16839967C22semidirect
32. #16839964C22semidirect
33. #16839962C22semidirect
39. Q8×#92418C22semidirect
42. #16839841C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839508C22semidirect
48. #16839507C22semidirect
49. #16839506C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
54. #16839489C22semidirect
55. C8×#92418C22semidirect
56. C61×#556C22semidirect
58. C61×#486C22semidirect
62. C61×#460C22semidirect
65. C61×#436C22semidirect
317. #3324D61semidirect
340. #556C2×D61semidirect
349. #486C2×D61semidirect
362. #460C2×D61semidirect
374. #436C2×D61semidirect
389. C61#19900semidirect

Maximal subgroups

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

subgroupindex
#214588032
#214580522
D4×#117581992
#214454232
#214453802
#214453772
#214451822
#214451772
#214449982
#214449972
#214449292
#214449282
#214447022
SD16×#924182
C61×#33242
#1990061