Finite Group Databasebeta

← #30612743

Subgroups — #30612743

Order 15616.

620 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#21462761C211yesmaximal, characteristic, complemented
2#21462736C211yesmaximal, characteristic, complemented
3#21461443C211yesmaximal, characteristic, complemented
4#21461441C211yesmaximal, characteristic, complemented
5#21461429C211yesmaximal, characteristic, complemented
6#21461423C211yesmaximal, characteristic, complemented
7#21461416C211yesmaximal, characteristic, complemented
8#21461414C211yesmaximal, characteristic, complemented
9#21461404C211yesmaximal, characteristic, complemented
10#21461402C211yesmaximal, characteristic, complemented
11#21461386C211yesmaximal, characteristic, complemented
12#21461156C211yesmaximal, characteristic, complemented
13#21461134C211yesmaximal, characteristic, complemented
14#21461036C211yesmaximal, characteristic, complemented
15#21455832C211yesmaximal, characteristic
16#16840812C2211yescharacteristic
17#16840811C2211yescharacteristic
18#16840811C2211yescharacteristic
19#16840811C2211yescharacteristic
20#16840797—21no—
21#16840797C2211yescharacteristic
22#16840793—21no—
23#16840790C2211yescharacteristic
24#16840790C2211yescharacteristic
25#16840789—21no—
26#16840789—21no—
27D4×#92420C2211yescharacteristic
28#16840786—21no—
29#16840781—21no—
30#16840778C2211yescharacteristic
31#16840768—21no—
32#16840765C2211yescharacteristic
33D61⋊(C4⋊C8)—21no—
34C2×C4⋊#92420C2211yescharacteristic
35C4×#11758217C2211yescharacteristic
36#16840624C2211yescharacteristic
37#16840624C2211yescharacteristic
38#16840623C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840293C2211yescharacteristic
53#16840230C2211yescharacteristic
54#16840103C411yescharacteristic
55#16840072C411yescharacteristic
56#16840065C411yescharacteristic
57#16839983C411yescharacteristic
58#16839976C411yescharacteristic
59#16839926C411yescharacteristic
60#16839905C411yescharacteristic
61#16839856C2211yescharacteristic
62#16839853C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#482C411yescharacteristic
67C2×#11758217—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×D61⋊C8—21no—
71C2×D61⋊C8—21no—
72C22×#92420—21no—
73C22×#92420—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844—21no—
77#14519844—21no—
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420D411yescharacteristic
81C4⋊#92420D411yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86#14519834—21no—
87#14519834—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420D411yescharacteristic
91C22⋊#92420D411yescharacteristic
92#14519832—21no—
93#14519832—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758222C2×C411yescharacteristic
102C2×Dic244C2×C411yescharacteristic
103C2×#11758190C2×C411yescharacteristic
104C2×#11758200C2×C411yescharacteristic
105C2×#11758199C2×C411yescharacteristic
106#14519770—21no—
107#14519768C2×C411yescharacteristic
108#14519764C2×C411yescharacteristic
109#14519758—21no—
110#14519756C2×C411yescharacteristic
111#14519742C2×C411yescharacteristic
112#14519742C2311yescharacteristic
113#14519742C2311yescharacteristic
114D4×Dic61—21no—
115D4×Dic61C2311yescharacteristic
116#14519739C2×C411yescharacteristic
117#14519739C2311yescharacteristic
118#14519737—21no—
119#14519737—21no—
120#14519734—21no—
121#14519733—21no—
122C2×C4×Dic61C2311yescharacteristic
123C42×D61—21no—
124#14519710C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519700C2×C411yescharacteristic
131#14519700C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137#121×C61C2×C411yescharacteristic
138#117×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141#102×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C2×C22⋊D61—21no—
148C22×Dic61—21no—
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61#4111yescharacteristic
151#11758222—22no—
152#11758222—22no—
153C2×D244C22×C411yescharacteristic
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×Dic122C22×C411yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159#11758217—42no—
160#11758217—81no—
161#11758217—81no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—81no—
169C2×#92420—81no—
170C2×#92420C2×D411yescharacteristic
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173C2×#92420C2×D411yescharacteristic
174D61⋊C8—81no—
175D61⋊C8—81no—
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C22×C411yescharacteristic
178C4⋊C4×C61C22×C411yescharacteristic
179C4⋊C4×C61C22×C411yescharacteristic
180C4⋊C4×C61C22×C411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C42×C61—21no—
184C22⋊Dic61—21no—
185C22⋊Dic61—21no—
186C22⋊Dic61—21no—
187C22⋊Dic61—21no—
188#11758200—22no—
189#11758199—22no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C22×C411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61C22×C411yescharacteristic
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61#4111yescharacteristic
205C4×Dic61C2411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208Dic244—22no—
209#11758190—22no—
210C23×C61—21no—
211C23×C61C4×D411yescharacteristic
212C22×D61—21no—
213D4×C61—21no—
214D4×C61—21no—
215D4×C61—81no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61C4×D411yescharacteristic
222C2×C4×C61C23×C411yescharacteristic
223C22⋊D61—24no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61C4×D411yescharacteristic
233C2×Dic61C4×D411yescharacteristic
234C2×Dic61C22×D411yescharacteristic
235C2×Dic61C2×#4111yescharacteristic
236D244—21no—
237D244#13112yes—
238C4×D61—24no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—81no—
242Dic122—21no—
243Dic122—21no—
244Dic122—21no—
245Dic122#13112yes—
246#92420—22no—
247#92420—21no—
248#92420—21no—
249#92420—21no—
250#92420—21no—
251#92420—41no—
252#92420—41no—
253#92420—41no—
254#92420—41no—
255#92420—41no—
256C8×C61—21no—
257C8×C61—21no—
258#92418—21no—
259#92418—21no—
260#17927—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—22no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61C2×#13111yescharacteristic
276C4×C61C2×#13111yescharacteristic
277Dic61—22no—
278Dic61—21no—
279Dic61—21no—
280Dic61—21no—
281Dic61—41no—
282Dic61—41no—
283Dic61#57711yescharacteristic
284Dic61#57711yescharacteristic
285#3102—611no—
286#2993—611no—
287#2988—611no—
288#1587—611no—
289#1586—611no—
290#1583—611no—
291#1582—611no—
292#1580—611no—
293#1579—611no—
294C8×SD16—611no—
295C8×SD16—611no—
296#1570—611no—
297#1489—611no—
298#1483—611no—
299#1453—611no—
300C2×C61—41no—
301C2×C61—81no—
302C2×C61#292911yescharacteristic
303C2×C61#295211yescharacteristic
304C2×C61#295611yescharacteristic
305D61—42no—
306#529—611no—
307C4×#41—611no—
308#485—611no—
309#482#692311yescharacteristic
310#479—611no—
311#478—611no—
312#464—611no—
313#463—611no—
314#452—611no—
315#449—611no—
316#446—611no—
317C8×Q8—611no—
318C8×Q8—611no—
319C8×Q8—611no—
320C4×Q16—611no—
321C4×SD16—611no—
322C4×SD16—611no—
323C4×D8—611no—
324#436—611no—
325#436—1221no—
326#435—1221no—
327C8×D4—611no—
328C8×D4—611no—
329C8×D4—611no—
330C8×D4—1221no—
331C8×D4—1221no—
332#433—1221no—
333#431—611no—
334#431—611no—
335#431—1221no—
336#424—1221no—
337#423—611no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—1221no—
340C4×M16—611no—
341#334—611no—
342#334—611no—
343#334—611no—
344#334—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352D4⋊C8—611no—
353#322—611no—
354#322—611no—
355#322—611no—
356C82—611no—
357C61#1792711yescharacteristic, complemented, Sylow
358C2×#41—611no—
359C2×Q16—611no—
360C2×SD16—611no—
361C2×SD16—611no—
362C2×D8—611no—
363C2×M16—1221no—
364C2×M16—1221no—
365C2×M16—1221no—
366C22×C8—1221no—
367C22×C8—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370#126—1221no—
371#125—611no—
372#124—611no—
373#123—1221no—
374C22⋊Q8—611no—
375#121C2×#692311yescharacteristic
376C4×Q8—611no—
377C4×Q8—611no—
378C4×Q8—611no—
379C4×D4—611no—
380C4×D4—611no—
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4—1221no—
385#117—1221no—
386#117—1221no—
387#117C2×#692311yescharacteristic
388C2×C42—611no—
389C2×C42—1221no—
390#107—611no—
391#107C2×#692311yescharacteristic
392#106—611no—
393#106C2×#692311yescharacteristic
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408#103—611no—
409#103—611no—
410#103—611no—
411#103—611no—
412#102—611no—
413#102—611no—
414#102C2×#692311yescharacteristic
415#102C2×#692311yescharacteristic
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—611no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8C2×#692311yescharacteristic
424#97—1221no—
425#97—1221no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—1221no—
433C4×C8—1221no—
434C4×C8—1221no—
435#41—1222no—
436#41—1222no—
437C2×Q8—611no—
438C2×Q8—611no—
439C2×D4—21no—
440C2×D4—611no—
441C2×D4—1221no—
442C2×D4C22×#692311yescharacteristic
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4C22×#692311yescharacteristic
450Q16—1222no—
451SD16—1222no—
452SD16—1222no—
453D8—1222no—
454M16—4881no—
455M16—4881no—
456M16—2442no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—4881no—
470C2×C8—4881no—
471C2×C8—4881no—
472C2×C8—4881no—
473C2×C8C22×#692311yescharacteristic
474C2×C8C22×#692311yescharacteristic
475C4⋊C4—611no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4C22×#692311yescharacteristic
483C4⋊C4C22×#692311yescharacteristic
484C4⋊C4C22×#692311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—21no—
494C42—611no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42—1221no—
499C42—1221no—
500C42—1221no—
501C23—21no—
502C23—1221no—
503C23D4×#692311yescharacteristic
504Q8—612no—
505Q8—1221no—
506Q8—1221no—
507Q8—1221no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—612no—
512D4—1224no—
513D4—1221no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—611no—
523C2×C4—1224no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—4881no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4D4×#692311yescharacteristic
536C2×C4C23×#692311yescharacteristic
537C8—21no—
538C8—21no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—1222no—
544C8—1221no—
545C8—1221no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—1222no—
558C22—2441no—
559C22—2441no—
560C22C2×D4×#692311yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—611no—
566C4—611no—
567C4—1222no—
568C4—1221no—
569C4—1221no—
570C4—1221no—
571C4—2441no—
572C4—2441no—
573C4D61⋊#13111yescharacteristic
574C4D61⋊#13111yescharacteristic
575C2—41no—
576C2—81no—
577C2—2442no—
578C2#2146253611yescharacteristic
579C2#2146258211yescharacteristic
580C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#482C4
socleC22×C61C2×C4×D4
prime radical#16839905C4
cosocleC4×Dic61C24
hypercenter#482#6923
hypocenterC61#17927
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #21462761C2semidirect
2. #21462736C2semidirect
3. #21461443C2semidirect
4. #21461441C2semidirect
5. #21461429C2semidirect
6. #21461423C2semidirect
7. #21461416C2semidirect
8. #21461414C2semidirect
9. #21461404C2semidirect
10. #21461402C2semidirect
11. #21461386C2semidirect
12. #21461156C2semidirect
13. #21461134C2semidirect
14. #21461036C2semidirect
357. C61#17927semidirect

Maximal subgroups

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

subgroupindex
#214627612
#214627362
#214614432
#214614412
#214614292
#214614232
#214614162
#214614142
#214614042
#214614022
#214613862
#214611562
#214611342
#214610362
#214558322
#1792761