Finite Group Databasebeta

← #30610216

Subgroups — #30610216

Order 15616.

1048 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462684C211yesmaximal, characteristic, complemented
2#21462674C211yesmaximal, characteristic, complemented
3#21461103C212yesmaximal, complemented
4#21461096C212yesmaximal, complemented
5#21461088C212yesmaximal, complemented
6#21461085C212yesmaximal, complemented
7#21461076C212yesmaximal, complemented
8#21461065C212yesmaximal, complemented
9C2×#16840351C211yesmaximal, characteristic
10#16840796—24no—
11#16840792—24no—
12#16840782C2212yescomplemented
13#16840778C2212yescomplemented
14#16840733C2212yes—
15#16840733C2212yes—
16#16840733C2212yescomplemented
17D61⋊(C22⋊C8)C2212yescomplemented
18#16840607C2214yescomplemented
19#16840606C2214yes—
20#16840606C2214yescomplemented
21#16840605C2214yes—
22#16840351—24no—
23#16840351—24no—
24C2×#14519772C2211yescharacteristic
25C2×#14519765C411yescharacteristic
26C2×#14519763C2211yescharacteristic
27C2×#14519762C411yescharacteristic
28C2×#14519759C2211yescharacteristic
29C2×#14519755C411yescharacteristic
30C2×#14519752C411yescharacteristic
31C2×#14519752C2211yescharacteristic
32C2×#14519750C411yescharacteristic
33C2×#14519747C411yescharacteristic
34C2×#14519747C411yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×C22⋊C4×D61C2211yescharacteristic
38C2×#126×C61C411yescharacteristic
39C2×#11758213—22no—
40C2×#11758213—22no—
41C2×#11758213—22no—
42C2×D61⋊C8—22no—
43#14519844—22no—
44C4⋊#92420—22no—
45#14519834—22no—
46#14519834—22no—
47#14519834—22no—
48#14519834—22no—
49C22⋊#92420C2314yes—
50C22⋊#92420C2314yes—
51#14519832—22no—
52C4×#92420—22no—
53C24×D61C2×C411yescharacteristic
54C22×Dic122C2×C411yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×D244C2×C411yescharacteristic
57C22×D244C2×C411yescharacteristic
58C22×D244C2×C411yescharacteristic
59C22×D244C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×C4×D61C2311yescharacteristic
66#14519772—22no—
67#14519772—22no—
68#14519765—24no—
69#14519763—22no—
70#14519763—22no—
71#14519762—24no—
72#14519759—22no—
73#14519759—22no—
74#14519755—24no—
75#14519752—24no—
76#14519752—22no—
77#14519752—22no—
78#14519750—24no—
79#14519747—24no—
80#14519747—24no—
81C4×D244—22no—
82C4×D244—22no—
83#14519739D414yes—
84#14519739D414yes—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196C2×C411yescharacteristic
87C2×#11758196C2×C411yescharacteristic
88C2×C22⋊Dic61C2311yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2311yescharacteristic
98C2×#11758198C2311yescharacteristic
99C22⋊C4×D61—22no—
100C22⋊C4×D61—22no—
101C2×C4×Dic61C2311yescharacteristic
102#126×C61—24no—
103C2×C4⋊C4×C61C2×C411yescharacteristic
104C2×C4⋊C4×C61C2×C411yescharacteristic
105C2×C4⋊C4×C61C2×C411yescharacteristic
106C2×C22⋊C4×C61C2×C411yescharacteristic
107C2×C22⋊C4×C61C2×C411yescharacteristic
108C2×C22⋊C4×C61C2×C411yescharacteristic
109C2×C42×C61C2×C411yescharacteristic
110C24×C61C22×C411yescharacteristic
111C23×D61—22no—
112C23×D61—42no—
113C23×D61—81no—
114C23×D61—81no—
115C23×D61C22×C411yescharacteristic
116C23×D61C22×C411yescharacteristic
117C23×D61C22×C411yescharacteristic
118C23×D61C22×C411yescharacteristic
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61—81no—
128C2×C22⋊D61—81no—
129C22×Dic61C22×C411yescharacteristic
130C22×Dic61C22×C411yescharacteristic
131C22×Dic61C22×C411yescharacteristic
132C22×Dic61C2411yescharacteristic
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—22no—
136C2×D244—22no—
137C2×D244—42no—
138C2×D244—42no—
139C2×D244—81no—
140C2×D244—81no—
141C2×D244—81no—
142C2×D244C22⋊C414yes—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—81no—
146C2×C4×D61—81no—
147C2×C4×D61—81no—
148C2×C4×D61—81no—
149C2×C4×D61C2×D412yes—
150C2×C4×D61C2×D412yes—
151C2×C4×D61C2×D412yes—
152C2×C4×D61C2×D412yes—
153C2×Dic122—22no—
154C2×Dic122—81no—
155C2×#92420—24no—
156C2×#92420—24no—
157#11758213—82no—
158#11758213—82no—
159#11758213—82no—
160D61⋊C8—82no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61C22⋊C414yes—
164C22⋊C4×C61—22no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C42×C61—22no—
168C22⋊Dic61—21no—
169C22⋊Dic61—21no—
170#11758198—22no—
171#11758198—22no—
172#11758198—22no—
173#11758198—22no—
174#11758198—22no—
175#11758198—22no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198C22⋊C414yes—
181#11758198C22⋊C414yes—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184#11758196—22no—
185#11758196—22no—
186C4×Dic61C2×D412yes—
187C4×Dic61C2×D412yes—
188C23×C61—21no—
189C23×C61—22no—
190C23×C61—41no—
191C23×C61—41no—
192C23×C61C23×C411yescharacteristic
193C22×D61—22no—
194C22×D61—22no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—22no—
198C22×D61—22no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—44no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—82no—
209C22×D61—82no—
210C22×D61—88no—
211C22×D61C2×C22⋊C412yes—
212C22×D61C2×C22⋊C412yes—
213C2×C4×C61—22no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—22no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C2×C22⋊C412yes—
223C2×C4×C61C2×C22⋊C412yes—
224C2×C4×C61C2×C22⋊C412yes—
225C22⋊D61—82no—
226C22⋊D61—82no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61C2×C22⋊C412yes—
234C2×Dic61C22×D411yescharacteristic
235C2×Dic61C22×D411yescharacteristic
236D244—44no—
237D244—44no—
238D244—82no—
239D244—82no—
240D244—82no—
241C4×D61—42no—
242C4×D61—42no—
243C4×D61—42no—
244C4×D61—42no—
245C4×D61—82no—
246C4×D61—82no—
247Dic122—82no—
248#92420—44no—
249#92420—44no—
250#17405—611nomaximal, Sylow
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61—41no—
256C22×C61—82no—
257C22×C61C22×C22⋊C411yescharacteristic
258C22×C61#56812yes—
259C2×D61—22no—
260C2×D61—22no—
261C2×D61—22no—
262C2×D61—22no—
263C2×D61—22no—
264C2×D61—22no—
265C2×D61—44no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—82no—
273C2×D61—88no—
274C2×D61—82no—
275C2×D61—82no—
276C4×C61—22no—
277C4×C61—22no—
278C4×C61—22no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61—41no—
282Dic61—21no—
283Dic61—21no—
284Dic61—22no—
285Dic61—41no—
286Dic61—41no—
287C2×#538—611no—
288#2975—611no—
289#2973—611no—
290#1473—612no—
291#1471—612no—
292#1469—612no—
293#1468—612no—
294#1465—612no—
295#1462—612no—
296C2×C61—22no—
297C2×C61—81no—
298C2×C61#287911yescharacteristic
299C2×C61#288311yescharacteristic
300C2×C61#288811yescharacteristic
301D61—42no—
302D61—42no—
303D61—81no—
304D61—81no—
305#538—1224no—
306#538—1224no—
307C2×#126—611no—
308C2×#126#692311yescharacteristic
309C2×#124—611no—
310C2×#124—611no—
311C2×#123—611no—
312C2×#123—611no—
313C2×C22⋊Q8—611no—
314C2×#121—611no—
315C2×#121—611no—
316C2×#121—611no—
317C2×#120—611no—
318C2×#120—611no—
319C2×C4×D4—611no—
320C2×C4×D4—611no—
321C22×C22⋊C4—611no—
322#436—1224no—
323#435—1224no—
324#432—612no—
325#431—612no—
326#407—612no—
327#407—612no—
328#407—612no—
329C2×C22⋊C8—612no—
330#324—614no—
331#323—614no—
332#323—614no—
333#323—614no—
334C61#1740511yescharacteristic, complemented, Sylow
335C25—611no—
336C22×Q8—611no—
337C22×D4—611no—
338C22×D4—611no—
339C22×D4—611no—
340C22×D4—611no—
341C22×D4—611no—
342C22×D4—611no—
343C22×D4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—611no—
348C2×M16—1222no—
349C2×M16—1222no—
350C2×M16—1222no—
351C22×C8—1222no—
352#126—24no—
353#126—1222no—
354#126—1222no—
355#124—1224no—
356#124—1222no—
357#124—1222no—
358#123—1222no—
359#123—1222no—
360#123—1224no—
361C22⋊Q8—1224no—
362#121—1224no—
363#121—1222no—
364#121—1222no—
365#121—1224no—
366#120—1224no—
367#120—1224no—
368C4×D4—614no—
369C4×D4—614no—
370C4×D4—1222no—
371C4×D4—1222no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4C2×#692311yescharacteristic
376C2×C4⋊C4C2×#692311yescharacteristic
377C2×C4⋊C4C2×#692311yescharacteristic
378C2×C22⋊C4—611no—
379C2×C22⋊C4—611no—
380C2×C22⋊C4—611no—
381C2×C22⋊C4—611no—
382C2×C22⋊C4—611no—
383C2×C22⋊C4—611no—
384C2×C22⋊C4—611no—
385C2×C22⋊C4—611no—
386C2×C22⋊C4—611no—
387C2×C22⋊C4—611no—
388C2×C22⋊C4—611no—
389C2×C22⋊C4—1222no—
390C2×C22⋊C4—1222no—
391C2×C22⋊C4C2×#692311yescharacteristic
392C2×C22⋊C4C2×#692311yescharacteristic
393C2×C22⋊C4C2×#692311yescharacteristic
394C2×C42—611no—
395C2×C42C2×#692311yescharacteristic
396C4⋊C8—1222no—
397C4⋊C8—1222no—
398C22⋊C8—614no—
399C22⋊C8—614no—
400C22⋊C8—1222no—
401C22⋊C8—1222no—
402C22⋊C8—1222no—
403C22⋊C8—1222no—
404#97—1222no—
405C4×C8—1222no—
406C24—611no—
407C24—611no—
408C24—611no—
409C24—611no—
410C24—1222no—
411C24—4881no—
412C24—4881no—
413C24—2442no—
414C24C22×#692311yescharacteristic
415C2×Q8—1222no—
416C2×Q8—4881no—
417C2×D4—614no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1222no—
423C2×D4—1222no—
424C2×D4—4881no—
425C2×D4—4881no—
426C2×D4—4881no—
427C2×D4—4881no—
428C2×D4—4881no—
429C2×D4—2442no—
430C2×D4—2442no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—612no—
434C22×C4—612no—
435C22×C4—612no—
436C22×C4—612no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—4881no—
442C22×C4—4881no—
443C22×C4—4881no—
444C22×C4—4881no—
445C22×C4C22×#692311yescharacteristic
446C22×C4C22×#692311yescharacteristic
447C22×C4C22×#692311yescharacteristic
448C22×C4C22×#692311yescharacteristic
449C22×C4C22×#692311yescharacteristic
450C22×C4C22×#692311yescharacteristic
451M16—4882no—
452M16—4882no—
453M16—4882no—
454C2×C8—1224no—
455C2×C8—1224no—
456C2×C8—4882no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—1222no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1222no—
463C4⋊C4C22⋊#692314yes—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—614no—
468C22⋊C4—614no—
469C22⋊C4—1221no—
470C22⋊C4—1221no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1222no—
474C22⋊C4—1222no—
475C22⋊C4—1222no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1222no—
479C22⋊C4—1222no—
480C22⋊C4—1222no—
481C42—22no—
482C42—612no—
483C42—612no—
484C23—21no—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—612no—
489C23—612no—
490C23—1222no—
491C23—1222no—
492C23—1222no—
493C23—1222no—
494C23—1221no—
495C23—1221no—
496C23—4882no—
497C23—4882no—
498C23—4888no—
499C23—2441no—
500C23—2441no—
501C23—2441no—
502C23—2441no—
503C23—2441no—
504C23—2441no—
505C23—2441no—
506C23—2441no—
507C23—2444no—
508C23C23×#692311yescharacteristic
509Q8—4882no—
510D4—4882no—
511D4—4882no—
512D4—4882no—
513D4—4882no—
514D4—4882no—
515D4—2444no—
516D4—2444no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—612no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—4882no—
532C2×C4—4882no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4C2×C22⋊#692312yes—
542C2×C4C2×C22⋊#692312yes—
543C2×C4C2×C22⋊#692312yes—
544C8—2444no—
545C8—2444no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—82no—
552C22—1222no—
553C22—1222no—
554C22—1222no—
555C22—1222no—
556C22—1222no—
557C22—1222no—
558C22—4882no—
559C22—4882no—
560C22—4882no—
561C22—4888no—
562C22—2444no—
563C22—2441no—
564C22—2441no—
565C22—2441no—
566C22—2441no—
567C22—2441no—
568C22—2441no—
569C22C22×C22⋊#692311yescharacteristic
570C22#1684084112yes—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—1221no—
578C4—1221no—
579C4—1222no—
580C4—2441no—
581C4—2441no—
582C2—22no—
583C2—81no—
584C2—4881no—
585C2—4881no—
586C2—2442no—
587C2—2442no—
588C2#2146240411yescharacteristic
589C2#2146241911yescharacteristic
590C2#2146243011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#126×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840351C2
cosocleC22×Dic61C24
hypercenterC2×#126#6923
hypocenterC61#17405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #21462684C2semidirect
2. #21462674C2semidirect
3. #21461103C2semidirect
4. #21461096C2semidirect
5. #21461088C2semidirect
6. #21461085C2semidirect
7. #21461076C2semidirect
8. #21461065C2semidirect
12. #16840782C22semidirect
13. #16840778C22semidirect
16. #16840733C22semidirect
17. D61⋊(C22⋊C8)C22semidirect
18. #16840607C22semidirect
20. #16840606C22semidirect
334. C61#17405semidirect

Maximal subgroups

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

subgroupindex
#214626842
#214626742
#214611032
#214610962
#214610882
#214610852
#214610762
#214610652
C2×#168403512
#1740561