Finite Group Databasebeta

← #30613295

Subgroups — #30613295

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462751C211yesmaximal, characteristic, complemented
2#21462699C211yesmaximal, characteristic, complemented
3#21461452C211yesmaximal, characteristic, complemented
4#21461450C211yesmaximal, characteristic, complemented
5#21461448C211yesmaximal, characteristic, complemented
6#21461446C211yesmaximal, characteristic, complemented
7#21461441C211yesmaximal, characteristic, complemented
8#21461440C211yesmaximal, characteristic, complemented
9#21461403C211yesmaximal, characteristic, complemented
10SD16×#92420C211yesmaximal, characteristic, complemented
11#21461395C211yesmaximal, characteristic, complemented
12#21461164C211yesmaximal, characteristic, complemented
13#21461110C211yesmaximal, characteristic, complemented
14#21461024C211yesmaximal, characteristic, complemented
15#21455872C211yesmaximal, characteristic
16Q8×#92420C2211yescharacteristic
17Q8×#92420C2211yescharacteristic
18#16840797—21no—
19#16840797—21no—
20#16840797C2211yescharacteristic
21#16840797C2211yescharacteristic
22#16840797C2211yescharacteristic
23#16840796C2211yescharacteristic
24#16840795—21no—
25#16840790C2211yescharacteristic
26#16840789—21no—
27D4×#92420C2211yescharacteristic
28#16840779—21no—
29#16840779C2211yescharacteristic
30#16840778C2211yescharacteristic
31#16840765—21no—
32#16840765C2211yescharacteristic
33#16840736—21no—
34#16840735—21no—
35C2×C4×#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840307C2211yescharacteristic
53#41×Dic61C2211yescharacteristic
54#16840087C411yescharacteristic
55#16840083C411yescharacteristic
56#16840055C411yescharacteristic
57#16840050C411yescharacteristic
58#16839960C411yescharacteristic
59#16839955C411yescharacteristic
60#16839907C411yescharacteristic
61SD16×Dic61C2211yescharacteristic
62#16839847C2211yescharacteristic
63D8×Dic61C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#449C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C2×#11758217—21no—
72C2×D61⋊C8—21no—
73C22×#92420—21no—
74C22×#92420—21no—
75#14519844—21no—
76#14519844D411yescharacteristic
77#14519844D411yescharacteristic
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420D411yescharacteristic
92C22⋊#92420D411yescharacteristic
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758224—21no—
102C2×#11758201C2×C411yescharacteristic
103C2×#11758199C2×C411yescharacteristic
104#14519776C2×C411yescharacteristic
105#14519773C2×C411yescharacteristic
106#14519763—21no—
107#14519751C2×C411yescharacteristic
108#14519749—21no—
109Q8×Dic61C2×C411yescharacteristic
110Q8×Dic61C2311yescharacteristic
111D4×Dic61—21no—
112D4×Dic61—21no—
113D4×Dic61C2×C411yescharacteristic
114D4×Dic61C2311yescharacteristic
115D4×Dic61C2311yescharacteristic
116#14519739C2311yescharacteristic
117#14519737—21no—
118#14519736—21no—
119#14519736C2×C411yescharacteristic
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519710C2×C411yescharacteristic
124#14519709C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519701C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×#41×C61C2×C411yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139C2×D8×C61C2×C411yescharacteristic
140#121×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144#41×C61—22no—
145#41×C61—41no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61C22×C411yescharacteristic
150C2×D4×C61C22×C411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61#4111yescharacteristic
161#11758224—81no—
162#11758224—81no—
163C2×D244C22×C411yescharacteristic
164C2×C4×D61—21no—
165C2×Dic122—21no—
166#11758217—81no—
167#11758217—81no—
168#11758217—81no—
169#11758217—81no—
170C2×#92420—24no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—81no—
178C2×#92420C2×D411yescharacteristic
179C2×#92420C2×D411yescharacteristic
180C2×#92420C2×D411yescharacteristic
181C2×#92420C2×D411yescharacteristic
182#11758213—81no—
183D61⋊C8—81no—
184SD16×C61—22no—
185D8×C61—41no—
186C2×C8×C61C22×C411yescharacteristic
187C2×C8×C61C22×C411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊Dic61—21no—
191C22⋊Dic61—21no—
192C22⋊Dic61—21no—
193C22⋊Dic61—21no—
194#11758201—22no—
195#11758199—41no—
196#11758198—21no—
197#11758198—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61C22×C411yescharacteristic
201C4⋊Dic61C22×C411yescharacteristic
202C4⋊Dic61C22×C411yescharacteristic
203#11758196—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61C22×C411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61#4111yescharacteristic
210C4×Dic61C2411yescharacteristic
211C2×#92418C22×C411yescharacteristic
212C2×#92418C22×C411yescharacteristic
213C23×C61—21no—
214C23×C61—21no—
215C23×C61C4×D411yescharacteristic
216C22×D61—21no—
217Q8×C61—21no—
218Q8×C61#13112yes—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—42no—
224D4×C61—81no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—42no—
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C22⋊D61—42no—
233C22⋊D61—81no—
234C22⋊D61—81no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—22no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—42no—
246C2×Dic61C4×D411yescharacteristic
247C2×Dic61C4×D411yescharacteristic
248C2×Dic61C22×D411yescharacteristic
249C2×Dic61C2×#4111yescharacteristic
250D244—21no—
251D244—21no—
252C4×D61—41no—
253C4×D61—41no—
254Dic122—81no—
255#92420—22no—
256#92420—22no—
257#92420—21no—
258#92420—21no—
259#92420—21no—
260#92420—21no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265C8×C61—21no—
266C8×C61—21no—
267#92418—21no—
268#92418—21no—
269#18018—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61C2×C4×D411yescharacteristic
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C4×C61—21no—
284C4×C61—22no—
285C4×C61—41no—
286C4×C61C2×#13111yescharacteristic
287C4×C61#56811yescharacteristic
288Dic61—21no—
289Dic61—21no—
290Dic61—41no—
291Dic61—41no—
292Dic61—41no—
293Dic61#44312yes—
294Dic61#57611yescharacteristic
295Dic61#57711yescharacteristic
296#3106—611no—
297#2991—611no—
298#2979—611no—
299#1589—611no—
300#1589—611no—
301#1588—611no—
302#1588—611no—
303#1586—611no—
304#1586—611no—
305C8×SD16—611no—
306C8×SD16—611no—
307#1574—611no—
308#1492—611no—
309#1476—611no—
310#1450—611no—
311C2×C61—41no—
312C2×C61—81no—
313C2×C61—81no—
314C2×C61#293311yescharacteristic
315C2×C61#294611yescharacteristic
316C2×C61C2×#44311yescharacteristic
317D61—81no—
318#532—611no—
319C4×#41—611no—
320#482—611no—
321#482—611no—
322#477—611no—
323#476—611no—
324#460—611no—
325#459—611no—
326#449—611no—
327#449#692311yescharacteristic
328C8×Q8—611no—
329C8×Q8—611no—
330C4×SD16—611no—
331C4×SD16—611no—
332C4×D8—611no—
333C4×D8—611no—
334#436—611no—
335#436—611no—
336#436—611no—
337#436—611no—
338#436—1221no—
339#436—1221no—
340#436—1221no—
341C8×D4—611no—
342C8×D4—611no—
343C8×D4—1221no—
344#431—611no—
345#431—611no—
346#431—611no—
347#431—1221no—
348#423—611no—
349#423—1221no—
350#408—1221no—
351#408—1221no—
352C2×C4×C8—611no—
353#335—611no—
354#335—611no—
355#334—611no—
356#334—611no—
357Q8⋊C8—611no—
358Q8⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365#322—611no—
366#322—611no—
367C82—611no—
368C82—611no—
369C61#1801811yescharacteristic, complemented, Sylow
370C2×#41—1221no—
371C2×#41C2×#692311yescharacteristic
372C2×SD16—611no—
373C2×SD16C2×#692311yescharacteristic
374C2×D8—611no—
375C2×D8C2×#692311yescharacteristic
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C4⋊Q8—611no—
385#127—611no—
386#124—1221no—
387#121—611no—
388#121—1221no—
389#121C2×#692311yescharacteristic
390C4×Q8—611no—
391C4×Q8—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—1221no—
397C4×D4—1221no—
398C4×D4—1221no—
399#117—611no—
400#117—1221no—
401C2×C42—611no—
402C2×C42—1221no—
403#107—611no—
404#107—611no—
405#106—611no—
406#106—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418#103—611no—
419#103C2×#692311yescharacteristic
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102C2×#692311yescharacteristic
426C22⋊C8—611no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8C2×#692311yescharacteristic
437C4×C8—611no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—1221no—
444C4×C8—1221no—
445C4×C8—1221no—
446C4×C8—1221no—
447#41—22no—
448#41—41no—
449#41—4881no—
450#41—4881no—
451C2×Q8—1221no—
452C2×Q8C22×#692311yescharacteristic
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—611no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4C22×#692311yescharacteristic
460C2×D4C22×#692311yescharacteristic
461C22×C4—21no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4C22×#692311yescharacteristic
469SD16—22no—
470SD16—1222no—
471D8—41no—
472D8—2441no—
473M16—4881no—
474M16—4881no—
475M16—4881no—
476M16—4881no—
477M16—4881no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1224no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—4881no—
492C2×C8—4881no—
493C2×C8C22×#692311yescharacteristic
494C2×C8C22×#692311yescharacteristic
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—611no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4C22×#692311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—1221no—
514C42—1221no—
515C42—1221no—
516C23—21no—
517C23—21no—
518C23—1221no—
519C23D4×#692311yescharacteristic
520Q8—21no—
521Q8—4881no—
522Q8#1451986412yes—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—42no—
528D4—81no—
529D4—1221no—
530D4—1221no—
531D4—4881no—
532D4—4881no—
533D4—2442no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—42no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1222no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2442no—
556C2×C4D4×#692311yescharacteristic
557C2×C4C23×#692311yescharacteristic
558C8—21no—
559C8—21no—
560C8—1221no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—1222no—
565C8—1222no—
566C8—1221no—
567C8—1221no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22C2×D4×#692311yescharacteristic
585C4—21no—
586C4—22no—
587C4—41no—
588C4—611no—
589C4—611no—
590C4—612no—
591C4—1221no—
592C4—1221no—
593C4—2441no—
594C4—2441no—
595C4—2441no—
596C4C2×#1451986411yescharacteristic
597C4#1684084011yescharacteristic
598C2—41no—
599C2—81no—
600C2—81no—
601C2—4881no—
602C2#2146255111yescharacteristic
603C2#2146257611yescharacteristic
604C2D61⋊#44311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#449C4
socleC22×C61C2×C4×D4
prime radical#21455872C2
cosocleC4×Dic61C24
hypercenter#449#6923
hypocenterC61#18018
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #21462751C2semidirect
2. #21462699C2semidirect
3. #21461452C2semidirect
4. #21461450C2semidirect
5. #21461448C2semidirect
6. #21461446C2semidirect
7. #21461441C2semidirect
8. #21461440C2semidirect
9. #21461403C2semidirect
10. SD16×#92420C2semidirect
11. #21461395C2semidirect
12. #21461164C2semidirect
13. #21461110C2semidirect
14. #21461024C2semidirect
369. C61#18018semidirect

Maximal subgroups

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

subgroupindex
#214627512
#214626992
#214614522
#214614502
#214614482
#214614462
#214614412
#214614402
#214614032
SD16×#924202
#214613952
#214611642
#214611102
#214610242
#214558722
#1801861