Finite Group Databasebeta

← #29650522

Subgroups — #29650522

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455831C211yesmaximal, characteristic
2#21454968C211yesmaximal, characteristic, complemented
3#21454937C211yesmaximal, characteristic, complemented
4#21444730C211yesmaximal, characteristic, complemented
5#21444725C211yesmaximal, characteristic, complemented
6#21444712C211yesmaximal, characteristic, complemented
7#21444706C211yesmaximal, characteristic, complemented
8#21444687C211yesmaximal, characteristic, complemented
9#21444680C211yesmaximal, characteristic, complemented
10#21444659C211yesmaximal, characteristic, complemented
11#21444652C211yesmaximal, characteristic, complemented
12#21444589C211yesmaximal, characteristic, complemented
13#21444259C211yesmaximal, characteristic, complemented
14#21444116C211yesmaximal, characteristic, complemented
15C61×#1483C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840100C411yescharacteristic
18#16840083C411yescharacteristic
19#16840066C411yescharacteristic
20#16840059C411yescharacteristic
21#16839981C411yescharacteristic
22#16839974C411yescharacteristic
23#16839922C411yescharacteristic
24#16839905C411yescharacteristic
25#16839893C2211yescharacteristic
26#16839889C2211yescharacteristic
27#16839889C2211yescharacteristic
28Q8×#92418C2211yescharacteristic
29C4×#11758202C2211yescharacteristic
30C4×#11758201C2211yescharacteristic
31C4×#11758200C2211yescharacteristic
32C4×#11758199C2211yescharacteristic
33#16839840—21no—
34#16839840C2211yescharacteristic
35#16839839C2211yescharacteristic
36#16839839C2211yescharacteristic
37#16839834—21no—
38#16839833—21no—
39#16839833—21no—
40D4×#92418C2211yescharacteristic
41#16839823—21no—
42#16839818—21no—
43#16839815C2211yescharacteristic
44#16839815C2211yescharacteristic
45#16839789—21no—
46#16839786C2211yescharacteristic
47#16839784—21no—
48#16839512C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#529C2211yescharacteristic
61C2×C4⋊C8×C61C2211yescharacteristic
62C4×M16×C61C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758200C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758194—21no—
73C2×#11758194—21no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C22×#92418—21no—
77C4×Dic122C2×C411yescharacteristic
78C4×Dic122C2311yescharacteristic
79C4×D244C2×C411yescharacteristic
80C4×D244C2311yescharacteristic
81C4×C22⋊D61—21no—
82C4×C22⋊D61—21no—
83#14519736C2×C411yescharacteristic
84#14519734—21no—
85C42×D61—21no—
86#14519710C2×C411yescharacteristic
87#14519710C2×C411yescharacteristic
88#14519708C2×C411yescharacteristic
89#14519708C2×C411yescharacteristic
90C4⋊#92418—21no—
91C4⋊#92418—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2×C411yescharacteristic
94C4⋊#92418C2×C411yescharacteristic
95C4⋊#92418D411yescharacteristic
96C4⋊#92418D411yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519706—21no—
101#14519701C2×C411yescharacteristic
102#14519701C2×C411yescharacteristic
103#14519700C2×C411yescharacteristic
104#14519700C2×C411yescharacteristic
105#14519698C2×C411yescharacteristic
106#14519698C2×C411yescharacteristic
107#14519697C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418C2×C411yescharacteristic
112C22⋊#92418C2×C411yescharacteristic
113C22⋊#92418D411yescharacteristic
114C22⋊#92418D411yescharacteristic
115#14519689—21no—
116#14519689—21no—
117#14519688—21no—
118#14519687—21no—
119#14519687—21no—
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C2×M16×C61—21no—
126C22×C8×C61—21no—
127#126×C61—21no—
128#125×C61C2×C411yescharacteristic
129#124×C61C2×C411yescharacteristic
130#123×C61—21no—
131C22⋊Q8×C61C2×C411yescharacteristic
132#121×C61C2×C411yescharacteristic
133C4×Q8×C61C2311yescharacteristic
134C4×D4×C61—21no—
135C4×D4×C61C2311yescharacteristic
136#117×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×C22⋊D61—21no—
152#11758222—41no—
153#11758222—41no—
154C2×D244C22×C411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×Dic122C22×C411yescharacteristic
159M16×C61—42no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—81no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61C22×C411yescharacteristic
170C4⋊C4×C61C22×C411yescharacteristic
171C22⋊C4×C61—21no—
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C42×C61—21no—
177C42×C61C22×C411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C42×C61#4111yescharacteristic
180C42×C61C2411yescharacteristic
181C22⋊Dic61—21no—
182#11758202—41no—
183#11758201—41no—
184#11758200—41no—
185#11758199—41no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195#11758194—81no—
196#11758194—81no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208#11758189—81no—
209#11758189—81no—
210C23×C61—21no—
211C23×C61C4×D411yescharacteristic
212C22×D61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—81no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C22⋊D61—42no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238D244—21no—
239D244—21no—
240C4×D61—42no—
241C4×D61—41no—
242C4×D61—41no—
243C4×D61—81no—
244Dic122—21no—
245Dic122—21no—
246C8×C61—22no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—21no—
254#92418—21no—
255#92418—21no—
256#92418—21no—
257#92418—21no—
258#92418—41no—
259#92418—41no—
260#17955—611nomaximal, Sylow
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61C2×C4×D411yescharacteristic
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61#56811yescharacteristic
279C4×C61#56811yescharacteristic
280C4×C61#57711yescharacteristic
281C4×C61#57711yescharacteristic
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285#3102—611no—
286#2993—611no—
287#2989—611no—
288#1594—611no—
289#1593—611no—
290#1590—611no—
291#1590—611no—
292#1587—611no—
293#1586—611no—
294#1583—611no—
295#1582—611no—
296#1570—611no—
297#1489—611no—
298#1483D6111yescharacteristic, complemented
299#1453—611no—
300C2×C61—41no—
301C2×C61—81no—
302C2×C61#293011yescharacteristic
303C2×C61#295211yescharacteristic
304C2×C61#295611yescharacteristic
305D61—81no—
306#529C2×D6111yescharacteristic
307C4×#41—611no—
308#485—611no—
309#482—611no—
310#479—611no—
311#478—611no—
312#464—611no—
313#463—611no—
314#452—611no—
315#449—611no—
316#446—611no—
317#446—611no—
318#446—611no—
319C8×Q8—611no—
320C4×Q16—611no—
321C4×SD16—611no—
322C4×SD16—611no—
323C4×D8—611no—
324#436—611no—
325#436—611no—
326#436—611no—
327#436—1221no—
328#435—1221no—
329#435—1221no—
330#435—1221no—
331C8×D4—611no—
332#433—1221no—
333#432—1221no—
334#431—611no—
335#431—611no—
336#424—1221no—
337#423—611no—
338#423—1221no—
339C2×C4⋊C8C2×D6111yescharacteristic
340C4×M16C2×D6111yescharacteristic
341#334—611no—
342#334—611no—
343#334—611no—
344#334—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8C2×D6111yescharacteristic
348Q8⋊C8C2×D6111yescharacteristic
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8C2×D6111yescharacteristic
352D4⋊C8C2×D6111yescharacteristic
353#322—611no—
354#322—611no—
355#322—611no—
356C82—611no—
357C61#1795511yescharacteristic, complemented, Sylow
358C2×#41—611no—
359C2×Q16—611no—
360C2×SD16—611no—
361C2×SD16—611no—
362C2×D8—611no—
363C2×M16—21no—
364C2×M16—1221no—
365C2×M16—1221no—
366C2×M16—1221no—
367C2×M16—1221no—
368C22×C8—21no—
369C22×C8—1221no—
370#126—21no—
371#125C4×D6111yescharacteristic
372#124C4×D6111yescharacteristic
373#123—21no—
374C22⋊Q8C4×D6111yescharacteristic
375#121C4×D6111yescharacteristic
376C4×Q8—611no—
377C4×Q8—611no—
378C4×Q8C22×D6111yescharacteristic
379C4×D4—21no—
380C4×D4—611no—
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4C22×D6111yescharacteristic
385#117—21no—
386#117—611no—
387#117—1221no—
388C2×C42—1221no—
389C2×C42C22×D6111yescharacteristic
390#107—611no—
391#107—611no—
392#106—611no—
393#106—611no—
394C4⋊C8—21no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8C22×D6111yescharacteristic
407C4⋊C8C22×D6111yescharacteristic
408#103—611no—
409#103—611no—
410#103—611no—
411#103—611no—
412#102—611no—
413#102—611no—
414#102—611no—
415#102—611no—
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—611no—
419C22⋊C8—611no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424#97—21no—
425#97—1221no—
426#97—1221no—
427#97—1221no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—1221no—
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435#41—2441no—
436#41—2441no—
437C2×Q8—611no—
438C2×Q8C2×C4×D6111yescharacteristic
439C2×D4—21no—
440C2×D4—611no—
441C2×D4—1221no—
442C2×D4C2×C4×D6111yescharacteristic
443C22×C4—21no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4C2×C4×D6111yescharacteristic
448C22×C4D4×D6111yescharacteristic
449C22×C4#1175822411yescharacteristic
450Q16—2441no—
451SD16—2441no—
452SD16—2441no—
453D8—2441no—
454M16—42no—
455M16—4881no—
456M16—4881no—
457M16—4881no—
458M16—4881no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—81no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—4881no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—611no—
480C4⋊C4—611no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4C2×C4×D6111yescharacteristic
484C4⋊C4C2×C4×D6111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—21no—
494C42—1221no—
495C42—1221no—
496C42—1221no—
497C42C2×C4×D6111yescharacteristic
498C42D4×D6111yescharacteristic
499C42#1175822411yescharacteristic
500C42C23×D6111yescharacteristic
501C23—21no—
502C23—1221no—
503C23#1451973711yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—1221no—
507Q8—1221no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—1221no—
512D4—1221no—
513D4—2442no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—4881no—
528C2×C4—2442no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4#1451973711yescharacteristic
532C2×C4#1451973711yescharacteristic
533C2×C4#1451973711yescharacteristic
534C2×C4C22×C4×D6111yescharacteristic
535C2×C4C2×D4×D6111yescharacteristic
536C2×C4C2×#1175822411yescharacteristic
537C8—22no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—1221no—
542C8—1221no—
543C8—1221no—
544C8—1221no—
545C8—1221no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—2441no—
550C8—2441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22C2×#1451973711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4#1684052711yescharacteristic
572C4#1684052711yescharacteristic
573C4#1684057111yescharacteristic
574C4#1684057211yescharacteristic
575C2—41no—
576C2—81no—
577C2—4881no—
578C2#2145452511yescharacteristic
579C2#2145469811yescharacteristic
580C2#2145472511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1483C2
socleC22×C61C2×C4×D4
prime radical#16839905C4
cosocleC42×C61C24
hypercenter#1483D61
hypocenterC61#17955
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
2. #21454968C2semidirect
3. #21454937C2semidirect
4. #21444730C2semidirect
5. #21444725C2semidirect
6. #21444712C2semidirect
7. #21444706C2semidirect
8. #21444687C2semidirect
9. #21444680C2semidirect
10. #21444659C2semidirect
11. #21444652C2semidirect
12. #21444589C2semidirect
13. #21444259C2semidirect
14. #21444116C2semidirect
15. C61×#1483C2semidirect
298. #1483D61semidirect
357. C61#17955semidirect

Maximal subgroups

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

subgroupindex
#214558312
#214549682
#214549372
#214447302
#214447252
#214447122
#214447062
#214446872
#214446802
#214446592
#214446522
#214445892
#214442592
#214441162
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