Finite Group Databasebeta

← #30612978

Subgroups — #30612978

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462765C211yesmaximal, characteristic, complemented
2#21462711C211yesmaximal, characteristic, complemented
3#21461468C211yesmaximal, characteristic, complemented
4#21461461C211yesmaximal, characteristic, complemented
5#21461454C211yesmaximal, characteristic, complemented
6#21461451C211yesmaximal, characteristic, complemented
7#21461417C211yesmaximal, characteristic, complemented
8#21461411C211yesmaximal, characteristic, complemented
9#21461404C211yesmaximal, characteristic, complemented
10#21461400C211yesmaximal, characteristic, complemented
11#21461384C211yesmaximal, characteristic, complemented
12#21461173C211yesmaximal, characteristic, complemented
13#21461166C211yesmaximal, characteristic, complemented
14#21461017C211yesmaximal, characteristic, complemented
15#21456416C211yesmaximal, characteristic
16#16840812C2211yescharacteristic
17#16840811C2211yescharacteristic
18#16840796—21no—
19#16840796C2211yescharacteristic
20#16840796C2211yescharacteristic
21#16840796C2211yescharacteristic
22#16840792—21no—
23#16840792—21no—
24#16840792—21no—
25#16840790C2211yescharacteristic
26#16840790C2211yescharacteristic
27#16840790C2211yescharacteristic
28#16840787—21no—
29#16840784C2211yescharacteristic
30#16840780C2211yescharacteristic
31#16840769—21no—
32#16840766C2211yescharacteristic
33#16840737—21no—
34#16840737—21no—
35C4×D61⋊C8C2211yescharacteristic
36#16840625C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840623C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#16840603C2211yescharacteristic
49#16840603C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840313C2211yescharacteristic
53#16840297C2211yescharacteristic
54#16840151C411yescharacteristic
55#16840128C411yescharacteristic
56#16840124C411yescharacteristic
57#16840016C411yescharacteristic
58#16840016C411yescharacteristic
59#16840009C411yescharacteristic
60#16840009C411yescharacteristic
61#16839849C2211yescharacteristic
62#16839849C2211yescharacteristic
63#16839844C2211yescharacteristic
64#16839844C2211yescharacteristic
65#16839714C2211yescharacteristic
66C61×#501C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758213—21no—
71C2×D61⋊C8—21no—
72C2×D61⋊C8—21no—
73C2×D61⋊C8—21no—
74C2×D61⋊C8—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—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834—21no—
91#14519834D411yescharacteristic
92#14519834D411yescharacteristic
93#14519832—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758226—21no—
102C2×#11758190C2×C411yescharacteristic
103C2×#11758190C2×C411yescharacteristic
104C2×D488C2×C411yescharacteristic
105C2×D488C2×C411yescharacteristic
106C2×#11758189C2×C411yescharacteristic
107C2×#11758189C2×C411yescharacteristic
108#14519774C2×C411yescharacteristic
109#14519772—21no—
110#14519766—21no—
111#14519765C2×C411yescharacteristic
112#14519762—21no—
113#14519757C2×C411yescharacteristic
114#14519752—21no—
115#14519752C2×C411yescharacteristic
116#14519752C2×C411yescharacteristic
117#14519752C2×C411yescharacteristic
118#14519742C2311yescharacteristic
119#14519739—21no—
120#14519739—21no—
121#14519739C2311yescharacteristic
122#14519739C2311yescharacteristic
123#14519739C2311yescharacteristic
124#14519735—21no—
125C42×D61C2311yescharacteristic
126#14519700C2×C411yescharacteristic
127#14519700C2×C411yescharacteristic
128#14519697C2×C411yescharacteristic
129#14519697C2×C411yescharacteristic
130#14519697C2×C411yescharacteristic
131#14519697C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519688C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C4⋊Q8×C61C2×C411yescharacteristic
138#125×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#107×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142#106×C61C2×C411yescharacteristic
143#97×C61C2×C411yescharacteristic
144C2×Q8×C61—21no—
145#11758226—81no—
146#11758226—81no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244C22×C411yescharacteristic
153C2×D244C22×C411yescharacteristic
154C2×D244C22×C411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61C22×C411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61#4111yescharacteristic
161C2×Dic122C22×C411yescharacteristic
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420C2×D411yescharacteristic
169C2×#92420C2×D411yescharacteristic
170C2×#92420C2×D411yescharacteristic
171C2×#92420C2×D411yescharacteristic
172#11758213—81no—
173#11758213—81no—
174#11758213—81no—
175#11758213—81no—
176D61⋊C8—42no—
177D61⋊C8—81no—
178D61⋊C8—81no—
179D61⋊C8—81no—
180C2×C8×C61C22×C411yescharacteristic
181C2×C8×C61C22×C411yescharacteristic
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61C22×C411yescharacteristic
186C4⋊C4×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C42×C61C22×C411yescharacteristic
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196#11758198—21no—
197#11758198—21no—
198#11758198—21no—
199C4⋊Dic61—21no—
200#11758196—21no—
201C4×Dic61—21no—
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204C4×Dic61C2411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207D488—22no—
208D488—22no—
209#11758190—22no—
210#11758190—22no—
211#11758189—22no—
212#11758189—22no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61C4×D411yescharacteristic
217Q8×C61—81no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C23×C411yescharacteristic
225C2×Dic61—21no—
226C2×Dic61C4×D411yescharacteristic
227C2×Dic61C22×D411yescharacteristic
228C2×Dic61C2×#4111yescharacteristic
229D244—21no—
230D244—21no—
231D244—21no—
232D244—21no—
233D244—21no—
234D244—21no—
235D244—81no—
236D244—81no—
237D244—81no—
238D244—81no—
239D244—81no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251Dic122—21no—
252Dic122—21no—
253#92420—22no—
254#92420—21no—
255#92420—21no—
256#92420—21no—
257#92420—21no—
258#92420—41no—
259#92420—41no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263C8×C61#13112yes—
264C8×C61#13112yes—
265#92418—21no—
266#92418—21no—
267#17968—611nomaximal, Sylow
268C22×C61C2×C4×D411yescharacteristic
269C2×D61—21no—
270C2×D61—21no—
271C2×D61—21no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—41no—
284C4×C61—41no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61C2×#13111yescharacteristic
288C4×C61C2×#13111yescharacteristic
289Dic61—21no—
290Dic61—21no—
291Dic61—41no—
292Dic61#57611yescharacteristic
293Dic61#57711yescharacteristic
294#3171—611no—
295#2993—611no—
296#2981—611no—
297#1594—611no—
298#1592—611no—
299#1590—611no—
300#1589—611no—
301#1580—611no—
302SD16⋊C8—611no—
303C8×SD16—611no—
304C8×D8—611no—
305#1569—611no—
306#1494—611no—
307#1492—611no—
308C8×M16—611no—
309C2×C61#293111yescharacteristic
310C2×C61#294611yescharacteristic
311C2×C61#295611yescharacteristic
312D61—41no—
313D61—81no—
314D61—81no—
315D61—81no—
316#532—611no—
317#529—611no—
318#501#692311yescharacteristic
319#496—611no—
320#490—611no—
321#489—611no—
322#469—611no—
323#469—611no—
324#468—611no—
325#468—611no—
326#446—611no—
327C8×Q8—611no—
328C4×SD16—611no—
329C4×SD16—611no—
330C4×D8—611no—
331C4×D8—611no—
332#436—611no—
333#436—611no—
334#436—611no—
335#436—1221no—
336#435—1221no—
337#435—1221no—
338#435—1221no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—611no—
342#433—1221no—
343#432—611no—
344#431—611no—
345#424—1221no—
346#423—611no—
347#408—1221no—
348#408—1221no—
349C4×M16—611no—
350C2×C4×C8—611no—
351#335—611no—
352#335—611no—
353#334—611no—
354#334—611no—
355Q8⋊C8—611no—
356Q8⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363#322—611no—
364#322—611no—
365C82—611no—
366C82—611no—
367C61#1796811yescharacteristic, complemented, Sylow
368C2×#41—1221no—
369C2×SD16—611no—
370C2×SD16—611no—
371C2×D8—611no—
372C2×D8—611no—
373C2×M16—611no—
374C2×M16—611no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383C4⋊Q8C2×#692311yescharacteristic
384#127—611no—
385#126—1221no—
386#125C2×#692311yescharacteristic
387#124—611no—
388#124—1221no—
389#123—1221no—
390C22⋊Q8—611no—
391#121—611no—
392#121—611no—
393#121—611no—
394#121—1221no—
395C4×Q8—611no—
396C4×D4—611no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—1221no—
400C4×D4—1221no—
401#117—1221no—
402C2×C42—611no—
403#107C2×#692311yescharacteristic
404#107C2×#692311yescharacteristic
405#106C2×#692311yescharacteristic
406#106C2×#692311yescharacteristic
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416#103—611no—
417#103—611no—
418#102—611no—
419#102—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424C22⋊C8—611no—
425C22⋊C8—611no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433#97—611no—
434#97—1221no—
435#97—1221no—
436#97C2×#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—
445#41—4881no—
446#41—4881no—
447C2×Q8—21no—
448C2×Q8—611no—
449C2×D4—611no—
450C2×D4—611no—
451C2×D4—611no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463SD16—1222no—
464SD16—1222no—
465D8—1222no—
466D8—1222no—
467M16—1222no—
468M16—1222no—
469M16—4881no—
470M16—4881no—
471M16—4881no—
472M16—4881no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—4881no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8—2442no—
489C2×C8C22×#692311yescharacteristic
490C2×C8C22×#692311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4C22×#692311yescharacteristic
497C4⋊C4C22×#692311yescharacteristic
498C4⋊C4C22×#692311yescharacteristic
499C4⋊C4C22×#692311yescharacteristic
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
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—1221no—
513C42C22×#692311yescharacteristic
514C23—611no—
515C23—1221no—
516C23—1221no—
517C23—1221no—
518Q8—81no—
519Q8—1221no—
520Q8—1221no—
521D4—1221no—
522D4—1221no—
523D4—1221no—
524D4—1221no—
525D4—1221no—
526D4—1221no—
527D4—4881no—
528D4—4881no—
529D4—4881no—
530D4—4881no—
531D4—4881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—611no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4D4×#692311yescharacteristic
552C2×C4D4×#692311yescharacteristic
553C2×C4C23×#692311yescharacteristic
554C8—1221no—
555C8—1221no—
556C8—1221no—
557C8—1221no—
558C8—1222no—
559C8—1221no—
560C8—1221no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C8—2441no—
565C8—2441no—
566C8#1451986512yes—
567C8#1451986512yes—
568C22—1221no—
569C22—1221no—
570C22—1221no—
571C22—2441no—
572C22—2441no—
573C22—2441no—
574C22—2441no—
575C22—2441no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22C2×D4×#692311yescharacteristic
581C4—21no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—611no—
588C4—611no—
589C4—1221no—
590C4—1221no—
591C4—2441no—
592C4C2×#1451986511yescharacteristic
593C4C2×#1451986511yescharacteristic
594C2—4881no—
595C2—4881no—
596C2—4881no—
597C2—2441no—
598C2#2146254411yescharacteristic
599C2#2146257611yescharacteristic
600C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#501C4
socleC22×C61C2×C4×D4
prime radical#21456416C2
cosocleC4×Dic61C24
hypercenter#501#6923
hypocenterC61#17968
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #21462765C2semidirect
2. #21462711C2semidirect
3. #21461468C2semidirect
4. #21461461C2semidirect
5. #21461454C2semidirect
6. #21461451C2semidirect
7. #21461417C2semidirect
8. #21461411C2semidirect
9. #21461404C2semidirect
10. #21461400C2semidirect
11. #21461384C2semidirect
12. #21461173C2semidirect
13. #21461166C2semidirect
14. #21461017C2semidirect
367. C61#17968semidirect

Maximal subgroups

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

subgroupindex
#214627652
#214627112
#214614682
#214614612
#214614542
#214614512
#214614172
#214614112
#214614042
#214614002
#214613842
#214611732
#214611662
#214610172
#214564162
#1796861