Finite Group Databasebeta

← #30612766

Subgroups — #30612766

Order 15616.

604 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462633C211yesmaximal, characteristic, complemented
2#21462631C211yesmaximal, characteristic, complemented
3#21461457C211yesmaximal, characteristic, complemented
4#21461456C211yesmaximal, characteristic, complemented
5#21461455C211yesmaximal, characteristic, complemented
6#21461452C211yesmaximal, characteristic, complemented
7#21461430C211yesmaximal, characteristic, complemented
8#21461428C211yesmaximal, characteristic, complemented
9#21461422C211yesmaximal, characteristic, complemented
10#21461420C211yesmaximal, characteristic, complemented
11#21461391C211yesmaximal, characteristic, complemented
12#21461151C211yesmaximal, characteristic, complemented
13#21461131C211yesmaximal, characteristic, complemented
14#21461025C211yesmaximal, characteristic, complemented
15#21455834C211yesmaximal, characteristic
16#16840813C2211yescharacteristic
17#16840812C2211yescharacteristic
18#16840812C2211yescharacteristic
19Q8×#92420C2211yescharacteristic
20#16840797C2211yescharacteristic
21#16840797C2211yescharacteristic
22#16840797C2211yescharacteristic
23#16840794—21no—
24#16840794—21no—
25#16840794—21no—
26#16840789—21no—
27D4×#92420C2211yescharacteristic
28#16840786—21no—
29#16840784C2211yescharacteristic
30#16840781C2211yescharacteristic
31#16840781C2211yescharacteristic
32#16840778—21no—
33#16840726—21no—
34C4×#11758217—21no—
35C4×D61⋊C8C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840291C2211yescharacteristic
53C4×#11758224C2211yescharacteristic
54#16840102C411yescharacteristic
55#16840085C411yescharacteristic
56#16840070C411yescharacteristic
57#16840062C411yescharacteristic
58#16839981C411yescharacteristic
59#16839921C411yescharacteristic
60#16839904C411yescharacteristic
61#16839854C2211yescharacteristic
62#16839853C2211yescharacteristic
63SD16×Dic61C2211yescharacteristic
64D8×Dic61C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#463C411yescharacteristic
67C2×#11758217—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×D61⋊C8D411yescharacteristic
71C2×D61⋊C8D411yescharacteristic
72C22×#92420—21no—
73#14519844—21no—
74C4⋊#92420—21no—
75C4⋊#92420—21no—
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84#14519834—21no—
85C22⋊#92420—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89#14519832—21no—
90#14519832—21no—
91#14519832—21no—
92#14519832—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420D411yescharacteristic
96C4×#92420D411yescharacteristic
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224C2×C411yescharacteristic
102C2×#11758202C2×C411yescharacteristic
103C2×#11758200C2×C411yescharacteristic
104#14519770—21no—
105#14519769C2×C411yescharacteristic
106#14519759—21no—
107#14519753C2×C411yescharacteristic
108#14519748C2×C411yescharacteristic
109Q8×Dic61C2311yescharacteristic
110C4×Dic122C2×C411yescharacteristic
111#14519742C2311yescharacteristic
112D4×Dic61C2311yescharacteristic
113D4×Dic61C2311yescharacteristic
114C4×C22⋊D61—21no—
115#14519737—21no—
116#14519737—21no—
117#14519735C2×C411yescharacteristic
118#14519733—21no—
119#14519733—21no—
120C2×C4×Dic61—21no—
121C42×D61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519710C2×C411yescharacteristic
124#14519709C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519698C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C2×D8×C61C2×C411yescharacteristic
139#124×C61C2×C411yescharacteristic
140C4×D4×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153#11758224—41no—
154#11758224—41no—
155C2×C4×D61C22×C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61#4111yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159#11758217—42no—
160#11758217—42no—
161#11758217—42no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—42no—
169C2×#92420C2×D411yescharacteristic
170C2×#92420C2×D411yescharacteristic
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173D61⋊C8—22no—
174D61⋊C8—22no—
175SD16×C61—41no—
176D8×C61—41no—
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C22×C411yescharacteristic
179C4⋊C4×C61C22×C411yescharacteristic
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C42×C61C22×C411yescharacteristic
184C22⋊Dic61—21no—
185C22⋊Dic61—21no—
186C22⋊Dic61—21no—
187#11758202—41no—
188#11758200—41no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61C22×C411yescharacteristic
193C4⋊Dic61C22×C411yescharacteristic
194C4⋊Dic61C22×C411yescharacteristic
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199#11758196—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61#4111yescharacteristic
206C4×Dic61C2411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C23×C61—21no—
210C23×C61—21no—
211C22×D61C4×D411yescharacteristic
212Q8×C61—21no—
213Q8×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—42no—
221C2×C4×C61C4×D411yescharacteristic
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C23×C411yescharacteristic
224C22⋊D61—42no—
225C22⋊D61—42no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—42no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C22×D411yescharacteristic
237C2×Dic61C2×#4111yescharacteristic
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—41no—
243Dic122—21no—
244Dic122—21no—
245#92420—21no—
246#92420—21no—
247#92420—41no—
248#92420—41no—
249#92420—41no—
250#92420—41no—
251#92420—41no—
252#92420—41no—
253#92420#13512yes—
254#92420#13512yes—
255C8×C61—21no—
256C8×C61—21no—
257#92418—21no—
258#92418—21no—
259#17932—611nomaximal, Sylow
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C2×C4×D411yescharacteristic
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—21no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61#56811yescharacteristic
275C4×C61#56811yescharacteristic
276Dic61—21no—
277Dic61—21no—
278Dic61—41no—
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282Dic61C2×#13511yescharacteristic
283Dic61C2×#13511yescharacteristic
284#3102—611no—
285#2966—611no—
286#2965—611no—
287#1591—611no—
288#1590—611no—
289#1590—611no—
290#1589—611no—
291#1584—611no—
292#1583—611no—
293#1582—611no—
294#1581—611no—
295#1572—611no—
296#1488—611no—
297#1482—611no—
298#1450—611no—
299C2×C61—81no—
300C2×C61—81no—
301C2×C61#293011yescharacteristic
302C2×C61C4×#13511yescharacteristic
303C2×C61#295511yescharacteristic
304D61—41no—
305#529—611no—
306C4×#41—611no—
307#485—611no—
308#482—611no—
309#479—611no—
310#478—611no—
311#464—611no—
312#463#692311yescharacteristic
313#452—611no—
314#449—611no—
315#446—611no—
316#446—611no—
317#446—611no—
318C8×Q8—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322C4×D8—611no—
323#436—611no—
324#436—611no—
325#436—611no—
326#435—1221no—
327#435—1221no—
328#435—1221no—
329C8×D4—611no—
330C8×D4—1221no—
331#433—1221no—
332#432—611no—
333#431—611no—
334#431—611no—
335#431—611no—
336#431—1221no—
337#405—1221no—
338C4×M16—1221no—
339C2×C4×C8—611no—
340#335—611no—
341#335—611no—
342#334—611no—
343#334—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352#322—611no—
353#322—611no—
354C82—611no—
355C82—611no—
356C61#1793211yescharacteristic, complemented, Sylow
357C2×#41—611no—
358C2×Q16—611no—
359C2×SD16—611no—
360C2×SD16C2×#692311yescharacteristic
361C2×D8C2×#692311yescharacteristic
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—1221no—
368#126—1221no—
369#125—611no—
370#124C2×#692311yescharacteristic
371#123—1221no—
372C22⋊Q8—611no—
373#121—611no—
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8—611no—
377C4×D4—611no—
378C4×D4—611no—
379C4×D4—1221no—
380C4×D4—1221no—
381C4×D4—1221no—
382C4×D4C2×#692311yescharacteristic
383#117—611no—
384#117—1221no—
385#117—1221no—
386C2×C42—611no—
387C2×C42—1221no—
388#107—611no—
389#107—611no—
390#106—611no—
391#106—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C2×#692311yescharacteristic
403#103—611no—
404#103—611no—
405#103—611no—
406#103C2×#692311yescharacteristic
407#102—611no—
408#102—611no—
409#102—611no—
410#102C2×#692311yescharacteristic
411C22⋊C8—611no—
412C22⋊C8—611no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—1221no—
421#97—1221no—
422#97—1221no—
423#97—1221no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—1221no—
433C4×C8—1221no—
434#41—2441no—
435#41—2441no—
436C2×Q8—611no—
437C2×Q8C22×#692311yescharacteristic
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4C22×#692311yescharacteristic
441C2×D4C22×#692311yescharacteristic
442C22×C4—21no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449Q16—2441no—
450SD16—41no—
451SD16—2441no—
452D8—41no—
453M16—2442no—
454M16—2442no—
455M16—2442no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—1222no—
463C2×C8—1222no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—2442no—
471C2×C8C22×#692311yescharacteristic
472C2×C8C22×#692311yescharacteristic
473C4⋊C4—611no—
474C4⋊C4—611no—
475C4⋊C4—611no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4C22×#692311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—1221no—
495C42—1221no—
496C42—1221no—
497C42—1221no—
498C42C22×#692311yescharacteristic
499C23—21no—
500C23—21no—
501C23—611no—
502Q8—21no—
503Q8—21no—
504Q8—1221no—
505Q8—1221no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—2442no—
511D4—2442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—42no—
515C2×C4—611no—
516C2×C4—611no—
517C2×C4—611no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2442no—
532C2×C4D4×#692311yescharacteristic
533C2×C4D4×#692311yescharacteristic
534C2×C4C23×#692311yescharacteristic
535C8—21no—
536C8—21no—
537C8—612no—
538C8—612no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—1221no—
556C22—1221no—
557C22—1221no—
558C22C2×D4×#692311yescharacteristic
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—611no—
564C4—611no—
565C4—1221no—
566C4—1221no—
567C4—2441no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4#1684084011yescharacteristic
572C4#1684084111yescharacteristic
573C2—81no—
574C2—81no—
575C2—2441no—
576C2#2146253711yescharacteristic
577C2#135×#692311yescharacteristic
578C2#2146259111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#463C4
socleC22×C61C2×C4×D4
prime radical#16839904C4
cosocleC4×Dic61C24
hypercenter#463#6923
hypocenterC61#17932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #21462633C2semidirect
2. #21462631C2semidirect
3. #21461457C2semidirect
4. #21461456C2semidirect
5. #21461455C2semidirect
6. #21461452C2semidirect
7. #21461430C2semidirect
8. #21461428C2semidirect
9. #21461422C2semidirect
10. #21461420C2semidirect
11. #21461391C2semidirect
12. #21461151C2semidirect
13. #21461131C2semidirect
14. #21461025C2semidirect
356. C61#17932semidirect

Maximal subgroups

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

subgroupindex
#214626332
#214626312
#214614572
#214614562
#214614552
#214614522
#214614302
#214614282
#214614222
#214614202
#214613912
#214611512
#214611312
#214610252
#214558342
#1793261