Finite Group Databasebeta

← #29670539

Subgroups — #29670539

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458815C211yesmaximal, characteristic
2#21458513C211yesmaximal, characteristic, complemented
3#21458461C211yesmaximal, characteristic, complemented
4#21445473C211yesmaximal, characteristic, complemented
5#21445380C211yesmaximal, characteristic
6#21445251C211yesmaximal, characteristic, complemented
7#21445246C211yesmaximal, characteristic, complemented
8#21445169C211yesmaximal, characteristic, complemented
9#21445075C211yesmaximal, characteristic, complemented
10#21445060C211yesmaximal, characteristic, complemented
11#21445003C211yesmaximal, characteristic, complemented
12#21444922C211yesmaximal, characteristic
13#21444660C211yesmaximal, characteristic, complemented
14#21444638C211yesmaximal, characteristic, complemented
15C61×#3328C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic
17#16840491C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840144—21no—
20#16840136C2211yescharacteristic
21#16840118—21no—
22#16840114—21no—
23#16840114C2211yescharacteristic
24#16840110C2211yescharacteristic
25#16840109C2211yescharacteristic
26#16840065—21no—
27#16840047C2211yescharacteristic
28#16840044—21no—
29#16840044C2211yescharacteristic
30#16839986—21no—
31#16839984—21no—
32#16839974—21no—
33#16839969C2211yescharacteristic
34#16839967—21no—
35#16839967C2211yescharacteristic
36#16839962C2211yescharacteristic
37#16839957C2211yescharacteristic
38Q8×#92418C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40C8×Dic122C2211yescharacteristic
41C4×#11758201—21no—
42C4×#11758200—21no—
43C4×#11758200C2211yescharacteristic
44#16839847—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839508C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#556C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#485—21no—
60C61×#475C2211yescharacteristic
61C61×#470—21no—
62C61×#462C2211yescharacteristic
63C61×#451—21no—
64C4×Q16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#419—21no—
67C2×#11758202—21no—
68C2×#11758200—21no—
69C2×#11758200D411yescharacteristic
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758199—21no—
74#14519777—21no—
75#14519777C2311yescharacteristic
76#14519774C2311yescharacteristic
77#14519768—21no—
78#14519768—41no—
79#14519766—21no—
80#14519765—21no—
81#14519762—41no—
82Q8×Dic61—21no—
83C4×Dic122—21no—
84C4×Dic122C2311yescharacteristic
85C4×D244—21no—
86#14519739—21no—
87#14519710—41no—
88#14519708—21no—
89#14519708—21no—
90#14519708D411yescharacteristic
91C4⋊#92418—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519701—21no—
98#14519701—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700D411yescharacteristic
104#14519699—21no—
105#14519699—21no—
106#14519698D411yescharacteristic
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110C4×#92418—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C22×Q8×C61—21no—
116C2×Q16×C61—21no—
117C2×Q16×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#126×C61—41no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—41no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—42no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×Q8×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—41no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×C4×D61—41no—
158C2×Dic122—21no—
159C2×Dic122C2×D411yescharacteristic
160Q16×C61—22no—
161Q16×C61—81no—
162M16×C61—81no—
163C2×C8×C61—21no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
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—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C4⋊C4×C61C2×D411yescharacteristic
177C22⋊C4×C61—21no—
178C22⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—41no—
184C42×C61C2411yescharacteristic
185#11758202—81no—
186#11758201—42no—
187#11758201—42no—
188#11758201—81no—
189#11758200—41no—
190#11758200—42no—
191#11758199—81no—
192#11758198—41no—
193#11758198—41no—
194#11758198—41no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—41no—
198C4⋊Dic61—41no—
199C4⋊Dic61C2×D411yescharacteristic
200#11758196—21no—
201#11758196—41no—
202C4×Dic61—21no—
203C4×Dic61—41no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C23×C61—21no—
211C22×D61—41no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—82no—
220Q8×C61#13512yes—
221D4×C61—21no—
222D4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—82no—
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—41no—
239D244—41no—
240D244—41no—
241D244—41no—
242D244—41no—
243D244—81no—
244C4×D61—161no—
245Dic122—21no—
246Dic122—21no—
247Dic122—41no—
248Dic122—41no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252#92418—21no—
253#92418—21no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#19834—611nomaximal, Sylow
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61D4211yescharacteristic
263C2×D61—81no—
264C2×D61—81no—
265C2×D61—81no—
266C4×C61—22no—
267C4×C61—21no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61C2×#13511yescharacteristic
275C4×C61#57511yescharacteristic
276C4×C61#57711yescharacteristic
277C4×C61#57711yescharacteristic
278Dic61—41no—
279Dic61—41no—
280Dic61—81no—
281#3394—611no—
282#3365—611no—
283#3359—611no—
284#3328D6111yescharacteristic, complemented
285#1719—611no—
286#1701—611no—
287#1680—611no—
288#1680—611no—
289#1666—611no—
290#1650—611no—
291#1648—611no—
292#1640—611no—
293#1627—611no—
294#1583—611no—
295#1579—611no—
296C2×C61—81no—
297C2×C61#327111yescharacteristic
298C2×C61#328211yescharacteristic
299C2×C61#328911yescharacteristic
300D61—161no—
301#559—611no—
302#557—611no—
303#556C2×D6111yescharacteristic
304D4×Q8C2×D6111yescharacteristic
305#500—611no—
306#495—1221no—
307#492—611no—
308#488—1221no—
309#487—611no—
310#487—1221no—
311#487C2×D6111yescharacteristic
312#486—611no—
313#486—611no—
314#485—21no—
315#478—1221no—
316#475—611no—
317#475—611no—
318#475—1221no—
319#475C2×D6111yescharacteristic
320#470—21no—
321#464—1221no—
322#464—1221no—
323#463—1221no—
324#462—611no—
325#462C2×D6111yescharacteristic
326#461—611no—
327#461—1221no—
328#460—611no—
329#459—611no—
330#451—21no—
331C8×Q8—611no—
332C8×Q8—611no—
333C8×Q8—611no—
334C4×Q16C2×D6111yescharacteristic
335C4×SD16—611no—
336C4×SD16—1221no—
337C4×SD16—1221no—
338C4×SD16—1221no—
339#436C2×D6111yescharacteristic
340#419—21no—
341#334—611no—
342#334—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#331—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349Q8⋊C8—611no—
350D4⋊C8—611no—
351#322—611no—
352C61#1983411yescharacteristic, complemented, Sylow
353C22×Q8—21no—
354C2×Q16—21no—
355C2×Q16—1221no—
356C2×Q16C22⋊D6111yescharacteristic
357C2×SD16—611no—
358C2×SD16—1221no—
359C2×SD16—1221no—
360C2×SD16—1221no—
361C2×SD16—1221no—
362C2×D8—1221no—
363C2×M16—21no—
364C4⋊Q8—21no—
365C4⋊Q8—611no—
366C4⋊Q8—1221no—
367C4⋊Q8C22×D6111yescharacteristic
368C4⋊Q8C22×D6111yescharacteristic
369#127—611no—
370#126—41no—
371#125—1221no—
372#125—2441no—
373#124—21no—
374#124—1221no—
375#124—1221no—
376#123—2441no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
380C4×Q8—21no—
381C4×Q8—611no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×Q8C22×D6111yescharacteristic
385C4×Q8C22×D6111yescharacteristic
386C4×D4—21no—
387C4×D4—1221no—
388C4×D4—1221no—
389C4×D4C22×D6111yescharacteristic
390#117—21no—
391#107—2441no—
392#107C22⋊D6111yescharacteristic
393#106—21no—
394#106—611no—
395#106—1221no—
396#106—1221no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8C22×D6111yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—611no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103C22⋊D6111yescharacteristic
416#103C22⋊D6111yescharacteristic
417#102—611no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—2441no—
423C22⋊C8—21no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8C22×D6111yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—42no—
434C2×Q8—81no—
435C2×Q8—611no—
436C2×Q8—1221no—
437C2×Q8C2×C22⋊D6111yescharacteristic
438C2×Q8C2×C22⋊D6111yescharacteristic
439C2×D4—1221no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4D4×D6111yescharacteristic
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—2441no—
446Q16—22no—
447Q16—81no—
448Q16—4881no—
449SD16—4881no—
450SD16—2441no—
451SD16—2442no—
452SD16—2442no—
453SD16—2442no—
454D8—4881no—
455M16—81no—
456C2×C8—21no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8C2×C22⋊D6111yescharacteristic
464C2×C8C2×C22⋊D6111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—611no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—2441no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C4⋊C4D4×D6111yescharacteristic
481C4⋊C4C2×C22⋊D6111yescharacteristic
482C4⋊C4C2×C22⋊D6111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—2441no—
488C22⋊C4—2441no—
489C22⋊C4—2441no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42—1221no—
494C42—2441no—
495C42C23×D6111yescharacteristic
496C23—21no—
497C23—2441no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—82no—
506Q8—1221no—
507Q8—1221no—
508Q8—2441no—
509Q8—2441no—
510Q8#1451979712yes—
511D4—21no—
512D4—21no—
513D4—4881no—
514D4—2441no—
515D4—2441no—
516D4—2441no—
517D4—2441no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—9761no—
531C2×C4—2441no—
532C2×C4C2×D4×D6111yescharacteristic
533C2×C4C22×C22⋊D6111yescharacteristic
534C2×C4#1451982211yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—1221no—
539C8—1221no—
540C8—2441no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—4881no—
548C22—4881no—
549C22—4881no—
550C22D4×C22⋊D6111yescharacteristic
551C4—22no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—4881no—
560C4—2441no—
561C4—2441no—
562C4C2×#1451979711yescharacteristic
563C4#1684056111yescharacteristic
564C4#1684057111yescharacteristic
565C4#1684057311yescharacteristic
566C2—81no—
567C2—9761no—
568C2#2145739811yescharacteristic
569C2#2145752211yescharacteristic
570C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3328C2
socleC22×C61D42
prime radical#16839957C22
hypercenter#3328D61
hypocenterC61#19834
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3328

Complements

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

NH ≅ G/Ntype
2. #21458513C2semidirect
3. #21458461C2semidirect
4. #21445473C2semidirect
6. #21445251C2semidirect
7. #21445246C2semidirect
8. #21445169C2semidirect
9. #21445075C2semidirect
10. #21445060C2semidirect
11. #21445003C2semidirect
13. #21444660C2semidirect
14. #21444638C2semidirect
15. C61×#3328C2semidirect
284. #3328D61semidirect
352. C61#19834semidirect

Maximal subgroups

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

subgroupindex
#214588152
#214585132
#214584612
#214454732
#214453802
#214452512
#214452462
#214451692
#214450752
#214450602
#214450032
#214449222
#214446602
#214446382
C61×#33282
#1983461