Finite Group Databasebeta

← #30613248

Subgroups — #30613248

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#21462565C211yesmaximal, characteristic, complemented
3#21461467C211yesmaximal, characteristic, complemented
4#21461450C211yesmaximal, characteristic, complemented
5#21461447C211yesmaximal, characteristic, complemented
6#21461441C211yesmaximal, characteristic, complemented
7#21461427C211yesmaximal, characteristic, complemented
8#21461421C211yesmaximal, characteristic, complemented
9#21461411C211yesmaximal, characteristic, complemented
10#21461404C211yesmaximal, characteristic, complemented
11#21461393C211yesmaximal, characteristic, complemented
12#21461180C211yesmaximal, characteristic, complemented
13#21461115C211yesmaximal, characteristic, complemented
14#21461037C211yesmaximal, characteristic, complemented
15#21455881C211yesmaximal, characteristic
16C2×#14519865—21no—
17#16840811C2211yescharacteristic
18#16840811C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840797C2211yescharacteristic
21#16840796C2211yescharacteristic
22#16840796C2211yescharacteristic
23#16840795—21no—
24#16840795—21no—
25#16840792—21no—
26#16840792—21no—
27#16840790C2211yescharacteristic
28#16840790C2211yescharacteristic
29#16840784C2211yescharacteristic
30#16840782—21no—
31#16840780C2211yescharacteristic
32D61⋊(C4⋊C8)C2211yescharacteristic
33#16840737—21no—
34C4×#11758213C2211yescharacteristic
35C4×#11758217—21no—
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840313C2211yescharacteristic
53C4×#11758224C2211yescharacteristic
54#16840088C411yescharacteristic
55#16840088C411yescharacteristic
56#16840054C411yescharacteristic
57#16839963C411yescharacteristic
58#16839957C411yescharacteristic
59#16839908C411yescharacteristic
60#16839908C411yescharacteristic
61#16839849C2211yescharacteristic
62#16839849C2211yescharacteristic
63#16839842C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#476C411yescharacteristic
67#14519865—44no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758213D411yescharacteristic
71C2×#11758213D411yescharacteristic
72C2×#11758217—21no—
73C2×#11758217—21no—
74C2×D61⋊C8—21no—
75C2×D61⋊C8—21no—
76C2×D61⋊C8—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—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834—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×#11758226—21no—
103C2×#11758224C2×C411yescharacteristic
104C2×#11758190C2×C411yescharacteristic
105C2×#11758190C2×C411yescharacteristic
106C2×#11758199C2×C411yescharacteristic
107C2×#11758199C2×C411yescharacteristic
108#14519774C2×C411yescharacteristic
109#14519766—21no—
110#14519752—21no—
111#14519752C2×C411yescharacteristic
112#14519752C2×C411yescharacteristic
113C4×Dic122C2×C411yescharacteristic
114#14519742C2311yescharacteristic
115D4×Dic61C2311yescharacteristic
116#14519739—21no—
117#14519739C2311yescharacteristic
118#14519739C2311yescharacteristic
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519735C2×C411yescharacteristic
122#14519733—21no—
123C2×C4×Dic61—21no—
124C42×D61C2311yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519710C2×C411yescharacteristic
127C4⋊#92418C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135#14519689C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C4⋊Q8×C61C2×C411yescharacteristic
139C4×D4×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142C4⋊C8×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145C2×Q8×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151#11758226—42no—
152#11758226—42no—
153#11758224—22no—
154#11758224—41no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244C22×C411yescharacteristic
160C2×D244C22×C411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61C22×C411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61#4111yescharacteristic
166C2×Dic122C22×C411yescharacteristic
167#11758217—42no—
168#11758217—42no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178C2×#92420C2×D411yescharacteristic
179#11758213—22no—
180#11758213—41no—
181#11758213—42no—
182#11758213—42no—
183D61⋊C8—42no—
184D61⋊C8—42no—
185D61⋊C8—42no—
186C2×C8×C61C22×C411yescharacteristic
187C2×C8×C61C22×C411yescharacteristic
188C4⋊C4×C61—21no—
189C4⋊C4×C61C22×C411yescharacteristic
190C4⋊C4×C61C22×C411yescharacteristic
191C4⋊C4×C61C22×C411yescharacteristic
192C22⋊C4×C61—21no—
193C42×C61C22×C411yescharacteristic
194C22⋊Dic61—21no—
195#11758199—41no—
196#11758199—41no—
197#11758198—21no—
198#11758198—21no—
199#11758198—21no—
200#11758198—21no—
201#11758198—21no—
202C4⋊Dic61C22×C411yescharacteristic
203#11758196—21no—
204#11758196—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61#4111yescharacteristic
210C4×Dic61C2411yescharacteristic
211C2×#92418C22×C411yescharacteristic
212C2×#92418C22×C411yescharacteristic
213#11758190—22no—
214#11758190—22no—
215C23×C61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61C4×D411yescharacteristic
219Q8×C61—42no—
220D4×C61—21no—
221D4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—81no—
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C23×C411yescharacteristic
229C22⋊D61—42no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—42no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C22×D411yescharacteristic
237C2×Dic61C2×#4111yescharacteristic
238D244—21no—
239D244—21no—
240D244—21no—
241D244—21no—
242D244—42no—
243D244—42no—
244D244—42no—
245D244—81no—
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255Dic122—21no—
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×C61C2×C4×D411yescharacteristic
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—41no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61C2×#13111yescharacteristic
291C4×C61#56811yescharacteristic
292Dic61—22no—
293Dic61—21no—
294Dic61—21no—
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#293311yescharacteristic
315C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
316C2×C61#295711yescharacteristic
317D61—41no—
318D61—81no—
319D61—81no—
320C2×#131—1221no—
321#532—611no—
322C4×#41—611no—
323#482—611no—
324#482—611no—
325#477—611no—
326#476#692311yescharacteristic
327#460—611no—
328#459—611no—
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×D8—611no—
377C2×D8—611no—
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⋊Q8C2×#692311yescharacteristic
389#127—611no—
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#106C2×#692311yescharacteristic
410#106C2×#692311yescharacteristic
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—21no—
455C2×Q8—611no—
456C2×D4—611no—
457C2×D4—611no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—1221no—
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—2441no—
475D8—2441no—
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—21no—
500C4⋊C4—611no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4C22×#692311yescharacteristic
504C4⋊C4C22×#692311yescharacteristic
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—611no—
522C23—1221no—
523C23—1221no—
524Q8—42no—
525Q8—612no—
526Q8—1221no—
527D4—21no—
528D4—21no—
529D4—1221no—
530D4—1221no—
531D4—1221no—
532D4—1221no—
533D4—4881no—
534D4—2442no—
535D4—2442no—
536D4—2442no—
537D4—2442no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—81no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
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—1221no—
580C22—1221no—
581C22—1221no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22—2441no—
587C22—2441no—
588C22C2×D4×#692311yescharacteristic
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—611no—
595C4—611no—
596C4—1221no—
597C4—1222no—
598C4—1221no—
599C4—2441no—
600C4D61⋊#13111yescharacteristic
601C4#1684084211yescharacteristic
602C2—81no—
603C2—4881no—
604C2—4881no—
605C2—2441no—
606C2#2146255411yescharacteristic
607C2AGL(1,ℤ/8)×#692311yescharacteristic
608C2#2146259711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#476C4
socleC22×C61C2×C4×D4
prime radical#21455881C2
cosocleC4×Dic61C24
hypercenter#476#6923
hypocenterC61#18011
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #21462664C2semidirect
2. #21462565C2semidirect
3. #21461467C2semidirect
4. #21461450C2semidirect
5. #21461447C2semidirect
6. #21461441C2semidirect
7. #21461427C2semidirect
8. #21461421C2semidirect
9. #21461411C2semidirect
10. #21461404C2semidirect
11. #21461393C2semidirect
12. #21461180C2semidirect
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
#214625652
#214614672
#214614502
#214614472
#214614412
#214614272
#214614212
#214614112
#214614042
#214613932
#214611802
#214611152
#214610372
#214558812
#1801161