Finite Group Databasebeta

← #30612647

Subgroups — #30612647

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462636C211yesmaximal, characteristic
2Q8×D61⋊C8C211yesmaximal, characteristic, complemented
3#21461447C211yesmaximal, characteristic, complemented
4#21461446C211yesmaximal, characteristic, complemented
5#21461443C211yesmaximal, characteristic, complemented
6#21461442C211yesmaximal, characteristic, complemented
7#21461407C211yesmaximal, characteristic, complemented
8#21461406C211yesmaximal, characteristic, complemented
9#21461404C211yesmaximal, characteristic, complemented
10#21461403C211yesmaximal, characteristic, complemented
11#21461393C211yesmaximal, characteristic, complemented
12#21461162C211yesmaximal, characteristic, complemented
13#21461137C211yesmaximal, characteristic
14#21461021C211yesmaximal, characteristic, complemented
15#21455904C211yesmaximal, characteristic
16#16840812C2211yescharacteristic
17#16840811—21no—
18#16840811—21no—
19#16840811C2211yescharacteristic
20#16840811C2211yescharacteristic
21#16840811C2211yescharacteristic
22Q8×#92420C2211yescharacteristic
23Q8×#92420C2211yescharacteristic
24#16840796C2211yescharacteristic
25#16840792—21no—
26#16840790—21no—
27#16840790C2211yescharacteristic
28#16840787—21no—
29#16840784C2211yescharacteristic
30D61⋊(C4⋊C8)—21no—
31D61⋊(C4⋊C8)C2211yescharacteristic
32#16840727—21no—
33C4×#11758213C2211yescharacteristic
34C4×D61⋊C8—21no—
35C4×D61⋊C8C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840297C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54#16840094C411yescharacteristic
55#16840077C411yescharacteristic
56#16840066C411yescharacteristic
57#16839985C411yescharacteristic
58#16839984C411yescharacteristic
59#16839919C411yescharacteristic
60#16839902C411yescharacteristic
61#16839856C2211yescharacteristic
62#16839854C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839847C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#479C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×D61⋊C8—21no—
70C2×D61⋊C8—21no—
71C2×D61⋊C8D411yescharacteristic
72C2×D61⋊C8D411yescharacteristic
73#14519844—21no—
74#14519844—21no—
75#14519844—21no—
76#14519844—21no—
77C4⋊#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87#14519832—21no—
88#14519832—21no—
89#14519832—21no—
90C4×#92420—21no—
91C4×#92420—21no—
92C4×#92420—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420D411yescharacteristic
96C4×#92420D411yescharacteristic
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×Q8×D61C2×C411yescharacteristic
102C2×Dic244C2×C411yescharacteristic
103C2×#11758202C2×C411yescharacteristic
104C2×#11758190C2×C411yescharacteristic
105C2×#11758201C2×C411yescharacteristic
106#14519772—21no—
107#14519765C2×C411yescharacteristic
108#14519762—21no—
109#14519757C2×C411yescharacteristic
110#14519752C2×C411yescharacteristic
111Q8×Dic61C2311yescharacteristic
112C4×Dic122—21no—
113C4×Dic122C2×C411yescharacteristic
114#14519742—21no—
115#14519742C2311yescharacteristic
116#14519742C2311yescharacteristic
117#14519739—21no—
118#14519739C2311yescharacteristic
119#14519735—21no—
120C4⋊C4×D61—21no—
121C4⋊C4×D61C2×C411yescharacteristic
122C42×D61—21no—
123C42×D61C2311yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519700C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519700C2×C411yescharacteristic
131#14519699C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137#125×C61C2×C411yescharacteristic
138C4×Q8×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145Q8×D61—22no—
146Q8×D61—22no—
147C2×D244—21no—
148C2×D244C22×C411yescharacteristic
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61C22×C411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61#4111yescharacteristic
155C2×Dic122—21no—
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420C2×D411yescharacteristic
165C2×#92420C2×D411yescharacteristic
166C2×#92420C2×D411yescharacteristic
167C2×#92420C2×D411yescharacteristic
168#11758213—24no—
169#11758213—42no—
170D61⋊C8—22no—
171D61⋊C8—41no—
172D61⋊C8—42no—
173D61⋊C8—42no—
174C2×C8×C61C22×C411yescharacteristic
175C2×C8×C61C22×C411yescharacteristic
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61C22×C411yescharacteristic
180C4⋊C4×C61C22×C411yescharacteristic
181C4⋊C4×C61C22×C411yescharacteristic
182C42×C61—21no—
183C42×C61C22×C411yescharacteristic
184#11758202—22no—
185#11758201—22no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C22×C411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204C4×Dic61C2411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207Dic244—22no—
208#11758190—22no—
209C22×D61—21no—
210C22×D61C4×D411yescharacteristic
211Q8×C61—21no—
212Q8×C61#13112yes—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61C4×D411yescharacteristic
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C23×C411yescharacteristic
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61C4×D411yescharacteristic
224C2×Dic61C22×D411yescharacteristic
225C2×Dic61C2×#4111yescharacteristic
226D244—21no—
227D244—21no—
228D244—42no—
229C4×D61—24no—
230C4×D61—22no—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61—21no—
235C4×D61—42no—
236C4×D61—41no—
237C4×D61—41no—
238Dic122—24no—
239Dic122—21no—
240Dic122—21no—
241Dic122—21no—
242Dic122#13112yes—
243#92420—22no—
244#92420—22no—
245#92420—21no—
246#92420—21no—
247#92420—21no—
248#92420—41no—
249#92420—41no—
250#92420—41no—
251#92420—41no—
252#92420#13712yes—
253C8×C61—21no—
254C8×C61—21no—
255#92418—21no—
256#92418—21no—
257#17911—611nomaximal, Sylow
258C22×C61C2×C4×D411yescharacteristic
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—41no—
262C2×D61—41no—
263C2×D61—41no—
264C2×D61#44312yes—
265C4×C61—22no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61C2×#13111yescharacteristic
272C4×C61C2×#13111yescharacteristic
273Dic61—21no—
274Dic61—22no—
275Dic61—21no—
276Dic61—41no—
277Dic61—41no—
278Dic61C2×#13711yescharacteristic
279Dic61#57511yescharacteristic
280#3108—611no—
281#2966—611no—
282C2×C8×Q8—611no—
283#1588—611no—
284#1588—611no—
285#1587—611no—
286#1587—611no—
287C8×Q16—611no—
288C8×Q16—611no—
289C8×SD16—611no—
290C8×SD16—611no—
291#1573—611no—
292#1491—611no—
293#1483—611no—
294C8×M16—611no—
295C2×C61#292911yescharacteristic
296C2×C61C4×#13711yescharacteristic
297C2×C61C2×#44311yescharacteristic
298D61—22no—
299D61—81no—
300#529—611no—
301C2×C4×Q8—611no—
302#483—611no—
303#480—611no—
304#479—611no—
305#479#692311yescharacteristic
306#464—611no—
307#464—611no—
308#451—611no—
309#448—611no—
310#446—611no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—611no—
315C8×Q8—611no—
316C8×Q8—1221no—
317C8×Q8—1221no—
318C4×Q16—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322#436—611no—
323#435—1221no—
324C8×D4—611no—
325C8×D4—1221no—
326#433—1221no—
327#432—611no—
328#431—611no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—1221no—
331#405—1221no—
332C4×M16—611no—
333C2×C4×C8—611no—
334C2×C4×C8—1221no—
335#335—611no—
336#335—611no—
337#334—611no—
338#334—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345D4⋊C8—611no—
346D4⋊C8—611no—
347#322—611no—
348#322—611no—
349C82—611no—
350C82—611no—
351C61#1791111yescharacteristic, complemented, Sylow
352C22×Q8—611no—
353C2×Q16—611no—
354C2×Q16—611no—
355C2×SD16—611no—
356C2×SD16—611no—
357C2×M16—1221no—
358C2×M16—1221no—
359C22×C8—611no—
360C22×C8—611no—
361C22×C8—1221no—
362C22×C8—1221no—
363#126—1221no—
364#125C2×#692311yescharacteristic
365#124—611no—
366#123—1221no—
367C22⋊Q8—611no—
368#121—611no—
369C4×Q8—611no—
370C4×Q8—611no—
371C4×Q8—611no—
372C4×Q8—611no—
373C4×Q8—1221no—
374C4×Q8—1221no—
375C4×Q8C2×#692311yescharacteristic
376C4×D4—611no—
377C4×D4—1221no—
378#117—1221no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—1221no—
381C2×C42—611no—
382C2×C42—1221no—
383#107—611no—
384#107C2×#692311yescharacteristic
385#106—611no—
386#106C2×#692311yescharacteristic
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8C2×#692311yescharacteristic
400#103—611no—
401#103—611no—
402#103—611no—
403#103—611no—
404#103C2×#692311yescharacteristic
405#103C2×#692311yescharacteristic
406#102—611no—
407#102—611no—
408C22⋊C8—611no—
409C22⋊C8—611no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—1221no—
414#97—1221no—
415#97—1221no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—1221no—
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8—1221no—
429C2×Q8—611no—
430C2×Q8—611no—
431C2×Q8—1221no—
432C2×Q8—1222no—
433C2×Q8—1222no—
434C2×Q8C22×#692311yescharacteristic
435C2×D4—611no—
436C2×D4—1221no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443Q16—1222no—
444Q16—1222no—
445SD16—1222no—
446SD16—1222no—
447M16—1224no—
448M16—2442no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—1222no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—2442no—
463C2×C8—2441no—
464C2×C8—2442no—
465C2×C8C22×#692311yescharacteristic
466C2×C8C22×#692311yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—611no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4C22×#692311yescharacteristic
478C4⋊C4C22×#692311yescharacteristic
479C4⋊C4C22×#692311yescharacteristic
480C22⋊C4—1221no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C42—21no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—1221no—
490C42—1221no—
491C42—1221no—
492C42—1221no—
493C42C22×#692311yescharacteristic
494C23—611no—
495C23—1221no—
496Q8—21no—
497Q8—612no—
498Q8—1224no—
499Q8—1221no—
500Q8—1221no—
501Q8—1221no—
502Q8#1451986512yes—
503D4—1221no—
504D4—1221no—
505D4—2442no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—611no—
511C2×C4—611no—
512C2×C4—611no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1222no—
516C2×C4—1224no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2442no—
525C2×C4D4×#692311yescharacteristic
526C2×C4D4×#692311yescharacteristic
527C2×C4C23×#692311yescharacteristic
528C8—21no—
529C8—21no—
530C8—612no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—1222no—
535C8—1222no—
536C8—1221no—
537C8—1221no—
538C8—2441no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C22—612no—
543C22—1221no—
544C22—1221no—
545C22—2441no—
546C22—2441no—
547C22—2441no—
548C22C2×D4×#692311yescharacteristic
549C4—22no—
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—611no—
556C4—611no—
557C4—1221no—
558C4—1222no—
559C4—1221no—
560C4—2441no—
561C4—2441no—
562C4D61⋊#13111yescharacteristic
563C4C2×#1451986511yescharacteristic
564C2—1222no—
565C2—4881no—
566C2#2146253511yescharacteristic
567C2#137×#692311yescharacteristic
568C2D61⋊#44311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#479C4
socleC22×C61C2×C4×D4
prime radical#14519752C2×C4
cosocleC4×Dic61C24
hypercenter#479#6923
hypocenterC61#17911
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. Q8×D61⋊C8C2semidirect
3. #21461447C2semidirect
4. #21461446C2semidirect
5. #21461443C2semidirect
6. #21461442C2semidirect
7. #21461407C2semidirect
8. #21461406C2semidirect
9. #21461404C2semidirect
10. #21461403C2semidirect
11. #21461393C2semidirect
12. #21461162C2semidirect
14. #21461021C2semidirect
351. C61#17911semidirect

Maximal subgroups

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

subgroupindex
#214626362
Q8×D61⋊C82
#214614472
#214614462
#214614432
#214614422
#214614072
#214614062
#214614042
#214614032
#214613932
#214611622
#214611372
#214610212
#214559042
#1791161