Finite Group Databasebeta

← #30612746

Subgroups — #30612746

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#21462765C211yesmaximal, characteristic, complemented
2#21462737C211yesmaximal, characteristic, complemented
3#21461442C211yesmaximal, characteristic, complemented
4#21461439C211yesmaximal, characteristic, complemented
5#21461426C211yesmaximal, characteristic, complemented
6#21461423C211yesmaximal, characteristic, complemented
7#21461417C211yesmaximal, characteristic, complemented
8#21461413C211yesmaximal, characteristic, complemented
9#21461404C211yesmaximal, characteristic, complemented
10#21461403C211yesmaximal, characteristic, complemented
11#21461387C211yesmaximal, characteristic, complemented
12#21461157C211yesmaximal, characteristic, complemented
13#21461137C211yesmaximal, characteristic, complemented
14#21461037C211yesmaximal, characteristic, complemented
15#21455844C211yesmaximal, characteristic
16#16840812C2211yescharacteristic
17#16840811C2211yescharacteristic
18Q8×#92420C2211yescharacteristic
19Q8×#92420C2211yescharacteristic
20#16840796—21no—
21#16840796C2211yescharacteristic
22#16840792—21no—
23#16840790—21no—
24#16840790—21no—
25#16840790C2211yescharacteristic
26#16840790C2211yescharacteristic
27#16840790C2211yescharacteristic
28#16840787—21no—
29#16840780—21no—
30#16840780C2211yescharacteristic
31#16840769—21no—
32#16840766C2211yescharacteristic
33D61⋊(C4⋊C8)—21no—
34D61⋊(C4⋊C8)C2211yescharacteristic
35C4×#11758213C2211yescharacteristic
36#16840624C2211yescharacteristic
37#16840624C2211yescharacteristic
38#16840623C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840297C2211yescharacteristic
53C4×#11758226C2211yescharacteristic
54#16840105C411yescharacteristic
55#16840088C411yescharacteristic
56#16840059C411yescharacteristic
57#16839984C411yescharacteristic
58#16839978C411yescharacteristic
59#16839927C411yescharacteristic
60#16839910C411yescharacteristic
61#16839854C2211yescharacteristic
62#16839849C2211yescharacteristic
63#16839847C2211yescharacteristic
64#16839844C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#479C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×D61⋊C8—21no—
71C2×D61⋊C8—21no—
72C2×D61⋊C8—21no—
73C2×D61⋊C8—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844D411yescharacteristic
77#14519844D411yescharacteristic
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420—21no—
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834D411yescharacteristic
91#14519834D411yescharacteristic
92#14519832—21no—
93#14519832—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758226C2×C411yescharacteristic
102C2×#11758202C2×C411yescharacteristic
103C2×#11758190C2×C411yescharacteristic
104C2×#11758201C2×C411yescharacteristic
105C2×D488C2×C411yescharacteristic
106#14519772—21no—
107#14519765C2×C411yescharacteristic
108#14519762—21no—
109#14519757C2×C411yescharacteristic
110#14519752C2×C411yescharacteristic
111Q8×Dic61C2311yescharacteristic
112#14519742C2311yescharacteristic
113C4×D244—21no—
114C4×D244C2×C411yescharacteristic
115#14519739—21no—
116#14519739—21no—
117#14519739C2311yescharacteristic
118#14519739C2311yescharacteristic
119#14519735—21no—
120#14519735—21no—
121#14519735C2×C411yescharacteristic
122C42×D61—21no—
123C42×D61C2311yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519697C2×C411yescharacteristic
131#14519697C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137#125×C61C2×C411yescharacteristic
138C4×Q8×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145#11758226—22no—
146#11758226—22no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244C22×C411yescharacteristic
150C2×D244C22×C411yescharacteristic
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61C22×C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61#4111yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420C2×D411yescharacteristic
166C2×#92420C2×D411yescharacteristic
167C2×#92420C2×D411yescharacteristic
168C2×#92420C2×D411yescharacteristic
169#11758213—42no—
170#11758213—81no—
171#11758213—81no—
172D61⋊C8—81no—
173D61⋊C8—81no—
174D61⋊C8—81no—
175D61⋊C8—81no—
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C22×C411yescharacteristic
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61C22×C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C4⋊C4×C61C22×C411yescharacteristic
184C42×C61—21no—
185C42×C61C22×C411yescharacteristic
186#11758202—22no—
187#11758201—22no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61C22×C411yescharacteristic
199#11758196—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61#4111yescharacteristic
205C4×Dic61C2411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208D488—22no—
209#11758190—22no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61C4×D411yescharacteristic
213Q8×C61—21no—
214Q8×C61#13112yes—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C23×C411yescharacteristic
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61C4×D411yescharacteristic
225C2×Dic61C22×D411yescharacteristic
226C2×Dic61C2×#4111yescharacteristic
227D244—24no—
228D244—21no—
229D244—21no—
230D244—21no—
231D244—81no—
232D244#13112yes—
233C4×D61—24no—
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—41no—
242C4×D61—41no—
243C4×D61—81no—
244Dic122—21no—
245Dic122—21no—
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×C61C2×C4×D411yescharacteristic
262C2×D61—21no—
263C2×D61—22no—
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—22no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61C2×#13111yescharacteristic
278C4×C61C2×#13111yescharacteristic
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#292911yescharacteristic
301C2×C61#295211yescharacteristic
302C2×C61#295611yescharacteristic
303D61—41no—
304D61—42no—
305D61—81no—
306#529—611no—
307C4×#41—611no—
308#485—611no—
309#482—611no—
310#479#692311yescharacteristic
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#125C2×#692311yescharacteristic
372#124—611no—
373#123—1221no—
374C22⋊Q8—611no—
375#121—611no—
376C4×Q8—611no—
377C4×Q8—611no—
378C4×Q8C2×#692311yescharacteristic
379C4×D4—611no—
380C4×D4—611no—
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4—1221no—
385#117—611no—
386#117—1221no—
387#117—1221no—
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—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C4⋊C8C2×#692311yescharacteristic
408#103—611no—
409#103—611no—
410#103C2×#692311yescharacteristic
411#103C2×#692311yescharacteristic
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—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×Q8C22×#692311yescharacteristic
439C2×D4—611no—
440C2×D4—611no—
441C2×D4—1221no—
442C2×D4—1221no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
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—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—611no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4C22×#692311yescharacteristic
483C4⋊C4C22×#692311yescharacteristic
484C4⋊C4C22×#692311yescharacteristic
485C22⋊C4—1221no—
486C22⋊C4—1221no—
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—1221no—
498C42—1221no—
499C42—1221no—
500C42C22×#692311yescharacteristic
501C23—611no—
502C23—1221no—
503C23—1221no—
504Q8—21no—
505Q8—1221no—
506Q8—1221no—
507Q8#1451986512yes—
508D4—612no—
509D4—1224no—
510D4—1221no—
511D4—1221no—
512D4—1221no—
513D4—4881no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1224no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—4881no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4D4×#692311yescharacteristic
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—1222no—
552C22—1221no—
553C22—1221no—
554C22—1221no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22C2×D4×#692311yescharacteristic
561C4—22no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—611no—
568C4—611no—
569C4—1221no—
570C4—1221no—
571C4—2441no—
572C4—2441no—
573C4D61⋊#13111yescharacteristic
574C4C2×#1451986511yescharacteristic
575C2—4881no—
576C2—2441no—
577C2—2442no—
578C2#2146253511yescharacteristic
579C2#2146258211yescharacteristic
580C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#479C4
socleC22×C61C2×C4×D4
prime radical#16839910C4
cosocleC4×Dic61C24
hypercenter#479#6923
hypocenterC61#17927
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #21462765C2semidirect
2. #21462737C2semidirect
3. #21461442C2semidirect
4. #21461439C2semidirect
5. #21461426C2semidirect
6. #21461423C2semidirect
7. #21461417C2semidirect
8. #21461413C2semidirect
9. #21461404C2semidirect
10. #21461403C2semidirect
11. #21461387C2semidirect
12. #21461157C2semidirect
13. #21461137C2semidirect
14. #21461037C2semidirect
357. C61#17927semidirect

Maximal subgroups

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

subgroupindex
#214627652
#214627372
#214614422
#214614392
#214614262
#214614232
#214614172
#214614132
#214614042
#214614032
#214613872
#214611572
#214611372
#214610372
#214558442
#1792761