Finite Group Databasebeta

← #29667569

Subgroups — #29667569

Order 15616.

584 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456955C211yesmaximal, characteristic, complemented
2#21456791C211yesmaximal, characteristic
3#21454979C211yesmaximal, characteristic, complemented
4#21445382C211yesmaximal, characteristic, complemented
5#21445361C211yesmaximal, characteristic, complemented
6#21445335C211yesmaximal, characteristic, complemented
7#21445320C211yesmaximal, characteristic, complemented
8#21445265C211yesmaximal, characteristic, complemented
9#21445230C211yesmaximal, characteristic, complemented
10#21445206C211yesmaximal, characteristic, complemented
11#21445203C211yesmaximal, characteristic, complemented
12#21444610C211yesmaximal, characteristic, complemented
13#21444497C211yesmaximal, characteristic, complemented
14#21444476C211yesmaximal, characteristic, complemented
15C61×#3252C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840165C2211yescharacteristic
18#16840158C2211yescharacteristic
19#16840144—21no—
20#16840119—21no—
21#16840110C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840086—21no—
24#16840086—21no—
25#16840059—21no—
26#16840059—21no—
27#16839972C2211yescharacteristic
28#16839967C2211yescharacteristic
29#16839962C2211yescharacteristic
30#16839957C2211yescharacteristic
31#16839922—21no—
32#16839905—21no—
33#16839893C2211yescharacteristic
34Q8×#92418C2211yescharacteristic
35#16839840C2211yescharacteristic
36#16839834—21no—
37D4×#92418—21no—
38D4×#92418C2211yescharacteristic
39#16839823—21no—
40#16839815C2211yescharacteristic
41#16839815C2211yescharacteristic
42#16839789—21no—
43C2×C4⋊#92418C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#529C2211yescharacteristic
58C61×#479—21no—
59C61×#477C2211yescharacteristic
60C61×#476C2211yescharacteristic
61C61×#470—21no—
62C61×#468—21no—
63C61×#464—21no—
64C61×#462C2211yescharacteristic
65C61×#461C2211yescharacteristic
66C61×#423C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758199—21no—
72C2×#11758194—21no—
73C22×#92418—21no—
74C22×#92418—21no—
75#14519777C2311yescharacteristic
76#14519774C2311yescharacteristic
77#14519765—21no—
78#14519751—21no—
79#14519751—21no—
80C4×D244—21no—
81C4×D244—21no—
82#14519710—21no—
83#14519710—21no—
84#14519708—21no—
85#14519708—21no—
86C4⋊#92418—21no—
87C4⋊#92418—21no—
88C4⋊#92418—21no—
89C4⋊#92418D411yescharacteristic
90C4⋊#92418D411yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519700—21no—
96#14519700—21no—
97#14519697—21no—
98#14519697—21no—
99#14519697—21no—
100#14519697—21no—
101#14519697—21no—
102#14519697—21no—
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105C22⋊#92418—21no—
106C22⋊#92418D411yescharacteristic
107C22⋊#92418D411yescharacteristic
108#14519688—21no—
109C4×#92418—21no—
110C4×#92418—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C2×Q16×C61—21no—
114C2×SD16×C61—21no—
115C2×M16×C61—21no—
116C4⋊Q8×C61C2311yescharacteristic
117C4⋊Q8×C61C2311yescharacteristic
118#126×C61—21no—
119#125×C61—21no—
120#125×C61D411yescharacteristic
121#124×C61D411yescharacteristic
122#123×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61D411yescharacteristic
126#121×C61D411yescharacteristic
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#117×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×C61—21no—
142#103×C61—21no—
143#102×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C2×C22⋊D61—41no—
154#11758222—81no—
155#11758222—81no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×C4×D61—41no—
160C2×Dic122—21no—
161Q16×C61—81no—
162SD16×C61—81no—
163M16×C61—81no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—41no—
184C42×C61—21no—
185C42×C61—41no—
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61#4111yescharacteristic
189C42×C61C2411yescharacteristic
190#11758202—81no—
191#11758201—81no—
192#11758200—81no—
193#11758199—81no—
194#11758198—41no—
195#11758198—41no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198#11758194—81no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—81no—
204C2×#92418—81no—
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C23×C61—21no—
210C23×C61#12111yescharacteristic
211C22×D61—41no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—81no—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—42no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C22⋊D61—82no—
239C2×Dic61—41no—
240D244—41no—
241D244—41no—
242D244—41no—
243D244—41no—
244D244—81no—
245C4×D61—82no—
246Dic122—41no—
247Dic122—41no—
248C8×C61—41no—
249C8×C61—41no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—21no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#19586—611nomaximal, Sylow
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61C2×#12111yescharacteristic
266C2×D61—81no—
267C2×D61—81no—
268C2×D61—81no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61#57611yescharacteristic
279C4×C61#57711yescharacteristic
280C4×C61#57711yescharacteristic
281C4×C61#57811yescharacteristic
282Dic61—81no—
283#3252D6111yescharacteristic, complemented
284#3228—611no—
285#3212—611no—
286#2994—611no—
287#1701—611no—
288#1698—611no—
289#1694—611no—
290#1691—611no—
291#1682—611no—
292#1677—611no—
293#1673—611no—
294#1672—611no—
295#1574—611no—
296#1547—611no—
297#1542—611no—
298C2×C61—41no—
299C2×C61—81no—
300C2×C61#304611yescharacteristic
301C2×C61#306211yescharacteristic
302C2×C61#306711yescharacteristic
303D61—161no—
304#533C2×D6111yescharacteristic
305#532—611no—
306#529C2×D6111yescharacteristic
307#500—611no—
308#498—611no—
309#495—1221no—
310#488—1221no—
311#486—611no—
312#486—611no—
313#482—1221no—
314#482—1221no—
315#479—21no—
316#478—1221no—
317#478—1221no—
318#477C2×D6111yescharacteristic
319#476C2×D6111yescharacteristic
320#470—21no—
321#468—21no—
322#464—21no—
323#462—611no—
324#462C2×D6111yescharacteristic
325#461—611no—
326#461C2×D6111yescharacteristic
327#460—611no—
328#459—611no—
329#452—1221no—
330#449—1221no—
331#446—611no—
332C8×Q8—611no—
333#436—611no—
334#435—1221no—
335C8×D4—611no—
336C8×D4—1221no—
337#433—1221no—
338#431—611no—
339#431—611no—
340#424—1221no—
341#423C2×D6111yescharacteristic
342C2×C4⋊C8—611no—
343#335—611no—
344#335—611no—
345#334—611no—
346#334—611no—
347#333—611no—
348#333—611no—
349#332—611no—
350#332—611no—
351#332—611no—
352#332—611no—
353#331—611no—
354#331—611no—
355C61#1958611yescharacteristic, complemented, Sylow
356C2×#41—1221no—
357C2×Q16—21no—
358C2×Q16—1221no—
359C2×SD16—21no—
360C2×SD16—1221no—
361C2×SD16—1221no—
362C2×D8—1221no—
363C2×M16—21no—
364C2×M16—1221no—
365C22×C8—1221no—
366C22×C8—1221no—
367C4⋊Q8—611no—
368C4⋊Q8C22×D6111yescharacteristic
369C4⋊Q8C22×D6111yescharacteristic
370#127—611no—
371#126—21no—
372#125—21no—
373#125C22⋊D6111yescharacteristic
374#124—1221no—
375#124C22⋊D6111yescharacteristic
376#123—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8C22⋊D6111yescharacteristic
380#121—1221no—
381#121—1221no—
382#121C22⋊D6111yescharacteristic
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C22×D6111yescharacteristic
386C4×D4—21no—
387C4×D4—1221no—
388C4×D4—1221no—
389C4×D4C22×D6111yescharacteristic
390#117—21no—
391#117—21no—
392C2×C42C22×D6111yescharacteristic
393#107—21no—
394#107—1221no—
395#107—1221no—
396#106—21no—
397#106—1221no—
398#106—1221no—
399C4⋊C8—21no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8C22×D6111yescharacteristic
410C4⋊C8C22×D6111yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—1221no—
415#103—1221no—
416#102—21no—
417#102—1221no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423C22⋊C8—611no—
424C22⋊C8—611no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428#97—1221no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—1221no—
432C4×C8—1221no—
433#41—4881no—
434#41—4881no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—1221no—
438C2×Q8C2×C22⋊D6111yescharacteristic
439C2×D4—21no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—2441no—
444C2×D4C2×C22⋊D6111yescharacteristic
445C22×C4—21no—
446C22×C4—2441no—
447C22×C4D4×D6111yescharacteristic
448C22×C4#1175822411yescharacteristic
449C22×C4C2×C22⋊D6111yescharacteristic
450Q16—81no—
451Q16—4881no—
452SD16—81no—
453SD16—4881no—
454SD16—4881no—
455D8—4881no—
456M16—81no—
457M16—4881no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—4881no—
469C2×C8—4881no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4C2×C22⋊D6111yescharacteristic
483C4⋊C4C2×C22⋊D6111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—2441no—
491C22⋊C4—2441no—
492C42—21no—
493C42—41no—
494C42D4×D6111yescharacteristic
495C42#1175822411yescharacteristic
496C42C2×C22⋊D6111yescharacteristic
497C42C23×D6111yescharacteristic
498C23—21no—
499C23—2441no—
500C23#1451974911yescharacteristic
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—2441no—
507Q8—2441no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—4881no—
512D4—4882no—
513D4—2441no—
514D4—2441no—
515D4—2441no—
516D4—2441no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—4882no—
530C2×C4—2441no—
531C2×C4#1451974911yescharacteristic
532C2×C4#1451974911yescharacteristic
533C2×C4#1451974911yescharacteristic
534C2×C4C2×D4×D6111yescharacteristic
535C2×C4C22×C22⋊D6111yescharacteristic
536C2×C4C2×#1175822411yescharacteristic
537C8—41no—
538C8—41no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—4881no—
554C22—4881no—
555C22—4881no—
556C22C2×#1451974911yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—4881no—
567C4#1684056511yescharacteristic
568C4#1684057011yescharacteristic
569C4#1684057111yescharacteristic
570C4#1684057811yescharacteristic
571C2—41no—
572C2—81no—
573C2—9761no—
574C2#2145537311yescharacteristic
575C2#2145550111yescharacteristic
576C2#2145553611yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3252C2
socleC22×C61C2×#121
prime radical#21456791C2
hypercenter#3252D61
hypocenterC61#19586
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3252

Complements

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

NH ≅ G/Ntype
1. #21456955C2semidirect
3. #21454979C2semidirect
4. #21445382C2semidirect
5. #21445361C2semidirect
6. #21445335C2semidirect
7. #21445320C2semidirect
8. #21445265C2semidirect
9. #21445230C2semidirect
10. #21445206C2semidirect
11. #21445203C2semidirect
12. #21444610C2semidirect
13. #21444497C2semidirect
14. #21444476C2semidirect
15. C61×#3252C2semidirect
283. #3252D61semidirect
355. C61#19586semidirect

Maximal subgroups

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

subgroupindex
#214569552
#214567912
#214549792
#214453822
#214453612
#214453352
#214453202
#214452652
#214452302
#214452062
#214452032
#214446102
#214444972
#214444762
C61×#32522
#1958661