Finite Group Databasebeta

← #30612941

Subgroups — #30612941

Order 15616.

614 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462635C211yesmaximal, characteristic, complemented
2#21462632C211yesmaximal, characteristic, complemented
3#21461467C211yesmaximal, characteristic, complemented
4#21461464C211yesmaximal, characteristic, complemented
5#21461462C211yesmaximal, characteristic, complemented
6#21461461C211yesmaximal, characteristic, complemented
7#21461416C211yesmaximal, characteristic, complemented
8#21461413C211yesmaximal, characteristic, complemented
9#21461411C211yesmaximal, characteristic, complemented
10SD16⋊#92420C211yesmaximal, characteristic, complemented
11#21461381C211yesmaximal, characteristic, complemented
12#21461172C211yesmaximal, characteristic, complemented
13#21461170C211yesmaximal, characteristic, complemented
14C2×#16840603C211yesmaximal, characteristic, complemented
15#21456382C211yesmaximal, characteristic
16#16840813C2211yescharacteristic
17#16840812C2211yescharacteristic
18#16840811C2211yescharacteristic
19Q8×#92420C2211yescharacteristic
20#16840797C2211yescharacteristic
21#16840796C2211yescharacteristic
22#16840793—21no—
23#16840791—21no—
24#16840790C2211yescharacteristic
25#16840789—21no—
26D4×#92420—21no—
27D4×#92420C2211yescharacteristic
28#16840787—21no—
29#16840786—21no—
30#16840783C2211yescharacteristic
31#16840783C2211yescharacteristic
32#16840727—21no—
33#16840726—21no—
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840625C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840624C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#16840603C2211yescharacteristic
49#16840603C2211yescharacteristic
50#16840603C2211yescharacteristic
51#16840603C2211yescharacteristic
52#16840298C2211yescharacteristic
53#16840293C2211yescharacteristic
54#16840162C411yescharacteristic
55#16840143C411yescharacteristic
56#16840118C411yescharacteristic
57#16840115C411yescharacteristic
58#16840001C411yescharacteristic
59#16839996C411yescharacteristic
60#16839991C411yescharacteristic
61#16839854C2211yescharacteristic
62SD16×Dic61C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839842C2211yescharacteristic
65C2×C8×Dic61C2211yescharacteristic
66C61×#465C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758217—21no—
69C2×D61⋊C8—21no—
70C22×#92420—21no—
71C22×#92420—21no—
72C22×#92420D411yescharacteristic
73C22×#92420D411yescharacteristic
74#14519844—21no—
75#14519844—21no—
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84C22⋊#92420—21no—
85C22⋊#92420—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88#14519832—21no—
89#14519832—21no—
90#14519832—21no—
91#14519832—21no—
92C4×#92420—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420D411yescharacteristic
96C4×#92420D411yescharacteristic
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758202C2×C411yescharacteristic
102C2×#11758190C2×C411yescharacteristic
103C2×#11758199C2×C411yescharacteristic
104C22×#92418C2×C411yescharacteristic
105#14519772—21no—
106#14519770—21no—
107#14519768C2×C411yescharacteristic
108#14519768C2×C411yescharacteristic
109#14519766C2×C411yescharacteristic
110#14519764C2×C411yescharacteristic
111#14519761—21no—
112#14519758—21no—
113#14519756C2×C411yescharacteristic
114#14519751C2×C411yescharacteristic
115Q8×Dic61C2311yescharacteristic
116#14519742C2311yescharacteristic
117D4×Dic61—21no—
118D4×Dic61C2311yescharacteristic
119#14519739C2311yescharacteristic
120#14519737—21no—
121#14519735—21no—
122#14519733—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519709C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519701C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133C8×Dic61C2×C411yescharacteristic
134C8×Dic61C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C22×C8×C61C2×C411yescharacteristic
139C22⋊Q8×C61C2×C411yescharacteristic
140#121×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61#4111yescharacteristic
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×Dic122C22×C411yescharacteristic
155#11758217—42no—
156C2×#92420—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—41no—
163C2×#92420—41no—
164C2×#92420—42no—
165C2×#92420—42no—
166C2×#92420C2×D411yescharacteristic
167C2×#92420C2×D411yescharacteristic
168C2×#92420C2×D411yescharacteristic
169C2×#92420C2×D411yescharacteristic
170#11758213—42no—
171D61⋊C8—42no—
172SD16×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61C22×C411yescharacteristic
175C2×C8×C61C22×C411yescharacteristic
176C4⋊C4×C61—21no—
177C4⋊C4×C61C22×C411yescharacteristic
178C4⋊C4×C61C22×C411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊Dic61—21no—
182C22⋊Dic61—21no—
183C22⋊Dic61—21no—
184C22⋊Dic61—21no—
185#11758202—22no—
186#11758199—22no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61C22×C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199#11758196—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61C22×C411yescharacteristic
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61#4111yescharacteristic
205C4×Dic61C2411yescharacteristic
206C2×#92418—22no—
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209#11758190—22no—
210C23×C61—21no—
211C23×C61C4×D411yescharacteristic
212C22×D61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—42no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C23×C411yescharacteristic
225C22⋊D61—42no—
226C2×Dic61—22no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61C4×D411yescharacteristic
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C22×D411yescharacteristic
237C2×Dic61C2×#4111yescharacteristic
238D244—21no—
239D244—21no—
240C4×D61—41no—
241C4×D61—41no—
242Dic122—21no—
243Dic122—21no—
244#92420—21no—
245#92420—21no—
246#92420—21no—
247#92420—21no—
248#92420—41no—
249#92420—41no—
250#92420—41no—
251#92420—41no—
252#92420—41no—
253#92420—41no—
254C8×C61—21no—
255C8×C61#13112yes—
256#92418—21no—
257#92418#13112yes—
258#17963—611nomaximal, Sylow
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61#44412yes—
265C22×C61C2×C4×D411yescharacteristic
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C4×C61—21no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61C2×#13111yescharacteristic
274C4×C61C2×#13111yescharacteristic
275Dic61—21no—
276Dic61—21no—
277Dic61—21no—
278Dic61—41no—
279Dic61—41no—
280Dic61—41no—
281Dic61#57511yescharacteristic
282Dic61#57511yescharacteristic
283#3168—611no—
284#2966—611no—
285#2966—611no—
286#1594—611no—
287#1593—611no—
288#1592—611no—
289#1592—611no—
290#1580—611no—
291#1579—611no—
292SD16⋊C8—611no—
293SD16⋊C8—611no—
294#1568—611no—
295#1494—611no—
296#1494—611no—
297C2×#322—611no—
298C2×C61—22no—
299C2×C61—81no—
300C2×C61#293111yescharacteristic
301C2×C61#294311yescharacteristic
302C2×C61C2×#44411yescharacteristic
303D61—81no—
304#529—611no—
305#529—611no—
306#499—611no—
307#495—611no—
308#488—611no—
309#488—611no—
310#467—611no—
311#466—611no—
312#465—611no—
313#465#692311yescharacteristic
314#446—611no—
315#446—611no—
316C8×Q8—611no—
317C8×Q8—611no—
318C4×Q16—611no—
319C4×SD16—611no—
320C4×SD16—611no—
321C4×D8—611no—
322#436—611no—
323#436—611no—
324#435—1221no—
325#435—1221no—
326C8×D4—611no—
327C8×D4—611no—
328C8×D4—1221no—
329C8×D4—1221no—
330#433—1221no—
331#433—1221no—
332#432—611no—
333#432—611no—
334#405—1221no—
335#405—1221no—
336C2×C4×C8—611no—
337C2×C4×C8—611no—
338C2×C4×C8—611no—
339#335—611no—
340#335—611no—
341#334—611no—
342#334—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347D4⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351#322—611no—
352#322—611no—
353#322—611no—
354#322—611no—
355C61#1796311yescharacteristic, complemented, Sylow
356C2×Q16—611no—
357C2×SD16—611no—
358C2×SD16C2×#692311yescharacteristic
359C2×D8—611no—
360C2×M16—1221no—
361C2×M16—1221no—
362C22×C8—611no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—1221no—
366C22×C8—1221no—
367C22×C8—1221no—
368C22×C8C2×#692311yescharacteristic
369#126—1221no—
370#126—1221no—
371#125—611no—
372#125—611no—
373#124—611no—
374#124—611no—
375#123—1221no—
376#123—1221no—
377C22⋊Q8—611no—
378C22⋊Q8C2×#692311yescharacteristic
379#121—611no—
380#121C2×#692311yescharacteristic
381C4×Q8—611no—
382C4×Q8—611no—
383C4×D4—611no—
384C4×D4—611no—
385C4×D4—1221no—
386C4×D4—1221no—
387#117—1221no—
388#117—1221no—
389C2×C42—611no—
390#107—611no—
391#107—611no—
392#106—611no—
393#106C2×#692311yescharacteristic
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402#103—611no—
403#103—611no—
404#103—611no—
405#103C2×#692311yescharacteristic
406#102—611no—
407#102—611no—
408#102—611no—
409#102C2×#692311yescharacteristic
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416#97—1221no—
417#97—1221no—
418#97—1221no—
419#97—1221no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8—1221no—
433C2×Q8—611no—
434C2×Q8C22×#692311yescharacteristic
435C2×D4—21no—
436C2×D4—611no—
437C2×D4—1221no—
438C2×D4C22×#692311yescharacteristic
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4C22×#692311yescharacteristic
444Q16—1222no—
445SD16—22no—
446SD16—1222no—
447D8—1222no—
448M16—2442no—
449M16—2442no—
450C2×C8—22no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—1222no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—2441no—
465C2×C8—2441no—
466C2×C8—2442no—
467C2×C8—2442no—
468C2×C8—2442no—
469C2×C8C22×#692311yescharacteristic
470C2×C8C22×#692311yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—611no—
473C4⋊C4—611no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4C22×#692311yescharacteristic
482C4⋊C4C22×#692311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—611no—
494C42—611no—
495C42—611no—
496C42—611no—
497C42—1221no—
498C42—1221no—
499C23—21no—
500C23—1221no—
501C23D4×#692311yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—1221no—
505Q8—1221no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—1221no—
510D4—1221no—
511D4—2442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—611no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1222no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4D4×#692311yescharacteristic
532C2×C4C23×#692311yescharacteristic
533C8—21no—
534C8—612no—
535C8—1221no—
536C8—1221no—
537C8—1221no—
538C8—1221no—
539C8—1221no—
540C8—2441no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8#1451986412yes—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—2441no—
553C22—2441no—
554C22—2441no—
555C22#1684080712yes—
556C22C2×D4×#692311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—611no—
562C4—611no—
563C4—1221no—
564C4—1221no—
565C4—1221no—
566C4—2441no—
567C4—2441no—
568C4—2441no—
569C4C2×#1451986411yescharacteristic
570C4D61⋊#13111yescharacteristic
571C2—22no—
572C2—81no—
573C2—4881no—
574C2#2146254211yescharacteristic
575C2#2146257311yescharacteristic
576C2C2×#1684080711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#465C4
socleC22×C61C2×C4×D4
prime radical#16839996C4
cosocleC4×Dic61C24
hypercenter#465#6923
hypocenterC61#17963
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #21462635C2semidirect
2. #21462632C2semidirect
3. #21461467C2semidirect
4. #21461464C2semidirect
5. #21461462C2semidirect
6. #21461461C2semidirect
7. #21461416C2semidirect
8. #21461413C2semidirect
9. #21461411C2semidirect
10. SD16⋊#92420C2semidirect
11. #21461381C2semidirect
12. #21461172C2semidirect
13. #21461170C2semidirect
14. C2×#16840603C2semidirect
355. C61#17963semidirect

Maximal subgroups

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

subgroupindex
#214626352
#214626322
#214614672
#214614642
#214614622
#214614612
#214614162
#214614132
#214614112
SD16⋊#924202
#214613812
#214611722
#214611702
C2×#168406032
#214563822
#1796361