Finite Group Databasebeta

← #30613244

Subgroups — #30613244

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462664C211yesmaximal, characteristic, complemented
2#21462562C211yesmaximal, characteristic, complemented
3#21461469C211yesmaximal, characteristic, complemented
4#21461452C211yesmaximal, characteristic, complemented
5#21461449C211yesmaximal, characteristic, complemented
6#21461440C211yesmaximal, characteristic, complemented
7#21461429C211yesmaximal, characteristic, complemented
8#21461420C211yesmaximal, characteristic, complemented
9#21461410C211yesmaximal, characteristic, complemented
10#21461402C211yesmaximal, characteristic, complemented
11#21461393C211yesmaximal, characteristic, complemented
12#21461179C211yesmaximal, characteristic, complemented
13#21461115C211yesmaximal, characteristic, complemented
14#21461037C211yesmaximal, characteristic, complemented
15#21455876C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840811C2211yescharacteristic
18#16840811C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840797C2211yescharacteristic
21#16840797C2211yescharacteristic
22#16840797C2211yescharacteristic
23#16840795—21no—
24#16840795—21no—
25#16840793—21no—
26#16840793—21no—
27D4×#92420C2211yescharacteristic
28D4×#92420C2211yescharacteristic
29#16840784C2211yescharacteristic
30#16840782—21no—
31#16840780C2211yescharacteristic
32D61⋊(C4⋊C8)C2211yescharacteristic
33#16840736—21no—
34C4×#11758213C2211yescharacteristic
35C4×#11758217—21no—
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42D4⋊#92420C2211yescharacteristic
43D4⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840310C2211yescharacteristic
53C4×#11758224C2211yescharacteristic
54#16840084C411yescharacteristic
55#16840084C411yescharacteristic
56#16840058C411yescharacteristic
57#16840052C411yescharacteristic
58#16839959C411yescharacteristic
59#16839904C411yescharacteristic
60#16839904C411yescharacteristic
61#16839853C2211yescharacteristic
62#16839853C2211yescharacteristic
63D8×Dic61C2211yescharacteristic
64D8×Dic61C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#459C411yescharacteristic
67#14519864—44no—
68C2×#11758213D411yescharacteristic
69C2×#11758213D411yescharacteristic
70C2×#11758217—21no—
71C2×#11758217—21no—
72C2×#11758217—21no—
73C2×#11758217—21no—
74C2×D61⋊C8—21no—
75C22×#92420—21no—
76C22×#92420—21no—
77#14519844—21no—
78#14519844—21no—
79#14519844—21no—
80#14519844—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86#14519834—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832D411yescharacteristic
95#14519832D411yescharacteristic
96C4×#92420—21no—
97C4×#92420—21no—
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C2×#11758224—21no—
103C2×#11758224C2×C411yescharacteristic
104C2×#11758200C2×C411yescharacteristic
105C2×#11758200C2×C411yescharacteristic
106#14519777C2×C411yescharacteristic
107#14519764—21no—
108#14519748—21no—
109#14519748C2×C411yescharacteristic
110#14519748C2×C411yescharacteristic
111C4×Dic122C2×C411yescharacteristic
112#14519742C2311yescharacteristic
113D4×Dic61—21no—
114D4×Dic61C2311yescharacteristic
115D4×Dic61C2311yescharacteristic
116D4×Dic61C2311yescharacteristic
117C4×C22⋊D61—21no—
118#14519737—21no—
119#14519735C2×C411yescharacteristic
120#14519733—21no—
121C2×C4×Dic61—21no—
122C42×D61C2311yescharacteristic
123#14519711C2×C411yescharacteristic
124#14519711C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519708C2×C411yescharacteristic
127C4⋊#92418C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519702C2×C411yescharacteristic
130#14519698C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135#14519689C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C2×D8×C61C2×C411yescharacteristic
139C2×D8×C61C2×C411yescharacteristic
140#127×C61C2×C411yescharacteristic
141C4×D4×C61C2×C411yescharacteristic
142C4⋊C8×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C2×D4×C61C22×C411yescharacteristic
150C22×C4×C61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C2×C22⋊D61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158#11758224—22no—
159#11758224—41no—
160#11758224—42no—
161#11758224—42no—
162C2×C4×D61C22×C411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61#4111yescharacteristic
165C2×Dic122—21no—
166C2×Dic122C22×C411yescharacteristic
167#11758217—42no—
168#11758217—42no—
169#11758217—42no—
170#11758217—42no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—42no—
178C2×#92420—42no—
179C2×#92420C2×D411yescharacteristic
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182C2×#92420C2×D411yescharacteristic
183#11758213—22no—
184#11758213—41no—
185D61⋊C8—42no—
186D8×C61—41no—
187D8×C61—41no—
188C2×C8×C61C22×C411yescharacteristic
189C2×C8×C61C22×C411yescharacteristic
190C4⋊C4×C61C22×C411yescharacteristic
191C22⋊C4×C61—21no—
192C42×C61C22×C411yescharacteristic
193C22⋊Dic61—21no—
194C22⋊Dic61—21no—
195C22⋊Dic61—21no—
196C22⋊Dic61—21no—
197C22⋊Dic61—21no—
198#11758200—22no—
199#11758200—22no—
200#11758198—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61C22×C411yescharacteristic
203C4⋊Dic61C22×C411yescharacteristic
204C4⋊Dic61C22×C411yescharacteristic
205#11758196—21no—
206#11758196—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61#4111yescharacteristic
212C4×Dic61C2411yescharacteristic
213C2×#92418C22×C411yescharacteristic
214C2×#92418C22×C411yescharacteristic
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C22×D61C4×D411yescharacteristic
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—42no—
226D4×C61—81no—
227C2×C4×C61—21no—
228C2×C4×C61—81no—
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C22⋊D61—42no—
233C22⋊D61—42no—
234C22⋊D61—42no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—42no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61C4×D411yescharacteristic
247C2×Dic61C22×D411yescharacteristic
248C2×Dic61C2×#4111yescharacteristic
249C4×D61—21no—
250C4×D61—21no—
251C4×D61—21no—
252C4×D61—21no—
253C4×D61—41no—
254Dic122—21no—
255Dic122—42no—
256Dic122#13112yescomplemented
257#92420—21no—
258#92420—21no—
259#92420—21no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265#92420—41no—
266#92420AGL(1,ℤ/8)12yes—
267C8×C61—21no—
268C8×C61—21no—
269#92418—21no—
270#92418—21no—
271#18011—611nomaximal, Sylow
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61C2×C4×D411yescharacteristic
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—41no—
288C4×C61C2×#13111yescharacteristic
289C4×C61#56811yescharacteristic
290Dic61—22no—
291Dic61—21no—
292Dic61—21no—
293Dic61—41no—
294Dic61—41no—
295Dic61—41no—
296Dic61C2×AGL(1,ℤ/8)11yescharacteristic
297Dic61#57511yescharacteristic
298#3106—611no—
299#2971—611no—
300#2935—611no—
301#1594—611no—
302#1589—611no—
303#1588—611no—
304#1586—611no—
305#1583—611no—
306#1581—611no—
307SD16⋊C8—611no—
308C8×SD16—611no—
309#1573—611no—
310#1496—611no—
311#1477—611no—
312#1453—611no—
313C2×C61—81no—
314C2×C61—81no—
315C2×C61—81no—
316C2×C61#293311yescharacteristic
317C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
318C2×C61#295711yescharacteristic
319D61—41no—
320C2×#131—1221no—
321#532—611no—
322C4×#41—611no—
323#482—611no—
324#482—611no—
325#477—611no—
326#476—611no—
327#460—611no—
328#459#692311yescharacteristic
329#449—611no—
330#449—611no—
331C8×Q8—611no—
332C8×Q8—611no—
333C4×SD16—611no—
334C4×SD16—611no—
335C4×D8—611no—
336C4×D8—611no—
337#436—611no—
338#436—611no—
339#436—611no—
340#436—611no—
341#436—1221no—
342#436—1221no—
343#435—1221no—
344#435—1221no—
345C8×D4—611no—
346C8×D4—611no—
347#432—611no—
348#432—1221no—
349#431—611no—
350#431—611no—
351C2×C4⋊C8—611no—
352#408—1221no—
353C4×M16—611no—
354C4×M16—1221no—
355#335—611no—
356#335—611no—
357#334—611no—
358#334—611no—
359Q8⋊C8—611no—
360Q8⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367#322—611no—
368#322—611no—
369#322—611no—
370C82—611no—
371C61#1801111yescharacteristic, complemented, Sylow
372C2×#41—611no—
373C2×#41—1221no—
374C2×SD16—611no—
375C2×SD16—611no—
376C2×D8C2×#692311yescharacteristic
377C2×D8C2×#692311yescharacteristic
378#131—2444no—
379C2×M16—611no—
380C2×M16—611no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C22×C8—1221no—
386C22×C8—1221no—
387C22×C8—1221no—
388C4⋊Q8—611no—
389#127C2×#692311yescharacteristic
390#124—1221no—
391#121—611no—
392#121—611no—
393#121—1221no—
394C4×Q8—611no—
395C4×Q8—611no—
396C4×D4—611no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—1221no—
400C4×D4—1221no—
401C4×D4—1221no—
402C4×D4C2×#692311yescharacteristic
403#117—611no—
404#117—1221no—
405C2×C42—611no—
406C2×C42—1221no—
407#107—611no—
408#107—611no—
409#106—611no—
410#106—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420C4⋊C8C2×#692311yescharacteristic
421#103—611no—
422#103—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427#102C2×#692311yescharacteristic
428#102C2×#692311yescharacteristic
429C22⋊C8—611no—
430C22⋊C8—611no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439#97—611no—
440#97—611no—
441#97—1221no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—611no—
448C4×C8—1221no—
449C4×C8—1221no—
450#41—1222no—
451#41—2441no—
452#41—2442no—
453#41—2442no—
454C2×Q8—611no—
455C2×Q8—1221no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4C22×#692311yescharacteristic
462C2×D4C22×#692311yescharacteristic
463C2×D4C22×#692311yescharacteristic
464C22×C4—21no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472SD16—1222no—
473SD16—1222no—
474D8—41no—
475D8—41no—
476M16—1222no—
477M16—2442no—
478M16—2442no—
479M16—2441no—
480M16—2442no—
481M16—2442no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—2442no—
495C2×C8—2442no—
496C2×C8—2442no—
497C2×C8C22×#692311yescharacteristic
498C2×C8C22×#692311yescharacteristic
499C4⋊C4—611no—
500C4⋊C4—611no—
501C4⋊C4—611no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4C22×#692311yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—1221no—
517C42—1221no—
518C42—1221no—
519C42C22×#692311yescharacteristic
520C23—21no—
521C23—21no—
522C23—21no—
523C23—611no—
524Q8—612no—
525Q8—1221no—
526Q8—2442no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—81no—
535D4—2442no—
536D4—2442no—
537D4—2442no—
538C2×C4—21no—
539C2×C4—81no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2442no—
559C2×C4D4×#692311yescharacteristic
560C2×C4D4×#692311yescharacteristic
561C2×C4C23×#692311yescharacteristic
562C8—21no—
563C8—21no—
564C8—612no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—1221no—
569C8—1221no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C8—2441no—
574C8—2441no—
575C8—2441no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—1221no—
586C22—1221no—
587C22—1221no—
588C22C2×D4×#692311yescharacteristic
589C4—21no—
590C4—21no—
591C4—41no—
592C4—611no—
593C4—611no—
594C4—1221no—
595C4—1222no—
596C4—1221no—
597C4—2441no—
598C4—2441no—
599C4—2441no—
600C4D61⋊#13111yescharacteristic
601C4#1684084011yescharacteristic
602C2—81no—
603C2—81no—
604C2—81no—
605C2—2441no—
606C2#2146255011yescharacteristic
607C2AGL(1,ℤ/8)×#692311yescharacteristic
608C2#2146259511yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#459C4
socleC22×C61C2×C4×D4
prime radical#21455876C2
cosocleC4×Dic61C24
hypercenter#459#6923
hypocenterC61#18011
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #21462664C2semidirect
2. #21462562C2semidirect
3. #21461469C2semidirect
4. #21461452C2semidirect
5. #21461449C2semidirect
6. #21461440C2semidirect
7. #21461429C2semidirect
8. #21461420C2semidirect
9. #21461410C2semidirect
10. #21461402C2semidirect
11. #21461393C2semidirect
12. #21461179C2semidirect
13. #21461115C2semidirect
14. #21461037C2semidirect
256. Dic122#131semidirect
371. C61#18011semidirect

Maximal subgroups

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

subgroupindex
#214626642
#214625622
#214614692
#214614522
#214614492
#214614402
#214614292
#214614202
#214614102
#214614022
#214613932
#214611792
#214611152
#214610372
#214558762
#1801161