Finite Group Databasebeta

← #30610258

Subgroups — #30610258

Order 15616.

1424 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462408C212yesmaximal, complemented
2#21461094C212yesmaximal, complemented
3#21461085C214yesmaximal, complemented
4#21461076C211yesmaximal, characteristic, complemented
5#21461065C212yesmaximal, complemented
6#21461056C211yesmaximal, characteristic, complemented
7D61⋊#323C212yesmaximal, complemented
8C2×#16840405C211yesmaximal, characteristic
9C2×#14519865—22no—
10#16840737—24no—
11#16840737—22no—
12#16840733C2214yescomplemented
13#16840733C2212yescomplemented
14D61⋊(C22⋊C8)C2214yescomplemented
15D61⋊(C22⋊C8)C2212yescomplemented
16#16840607C2212yescomplemented
17#16840607C2212yescomplemented
18#16840606C2211yescharacteristic
19#16840606C2212yes—
20#16840606C2211yescharacteristic
21#16840605C2214yescomplemented
22#16840605C2214yescomplemented
23C22×#11758226C2211yescharacteristic
24C22×D4×D61C411yescharacteristic
25#16840405—22no—
26#16840405—24no—
27#16840405—22no—
28C2×#14519759C2212yes—
29C2×#14519753C411yescharacteristic
30C2×#14519750C412yes—
31C2×#14519748C2211yescharacteristic
32C2×#14519747C412yes—
33C2×C4×D244C411yescharacteristic
34C2×C4×D244C2211yescharacteristic
35C2×C22⋊C4×D61C2212yes—
36C2×#124×C61C411yescharacteristic
37#14519865—48no—
38C2×#11758213—24no—
39C2×#11758213—22no—
40C2×D61⋊C8—24no—
41C2×D61⋊C8—22no—
42#14519834—24no—
43#14519834—22no—
44#14519834—24no—
45#14519834—22no—
46C22⋊#92420C2312yes—
47C22⋊#92420C2314yes—
48C22⋊#92420C2312yes—
49C24×D61C2×C412yes—
50C2×#11758226—44no—
51C2×#11758226D412yes—
52C2×#11758226D414yes—
53C2×#11758226D412yes—
54C22×D244C2×C411yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×D244C2×C412yes—
57C22×C22⋊D61C2×C412yes—
58C22×C22⋊D61C2×C412yes—
59C2×D4×D61—22no—
60C2×D4×D61—21no—
61C2×D4×D61—21no—
62C2×D4×D61—44no—
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C412yes—
65C22×C4×D61C2312yes—
66C22×C4×D61C2311yescharacteristic
67#14519759—24no—
68#14519759—24no—
69#14519753—22no—
70#14519753—22no—
71#14519750—24no—
72#14519750—24no—
73#14519748—22no—
74#14519748—22no—
75#14519747—24no—
76#14519747—24no—
77C4×D244—22no—
78C4×D244—21no—
79C4×D244—21no—
80C4×D244—22no—
81C4×D244—22no—
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196C2×C412yes—
85C2×C22⋊Dic61C2312yes—
86C2×#11758198C2×C412yes—
87C2×#11758198C2×C412yes—
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2311yescharacteristic
90C22⋊C4×D61—24no—
91C22⋊C4×D61—24no—
92C22×Q8×C61C2×C411yescharacteristic
93C22×D4×C61C2×C411yescharacteristic
94#124×C61—22no—
95#124×C61—22no—
96C2×C22⋊C4×C61C2×C412yes—
97C2×C22⋊C4×C61C2×C412yes—
98C2×C42×C61C2×C411yescharacteristic
99C24×C61C22×C412yes—
100C23×D61—22no—
101C23×D61—22no—
102C23×D61—24no—
103C23×D61—42no—
104C23×D61—44no—
105C23×D61—82no—
106C23×D61C22×C412yes—
107C23×D61C22×C411yescharacteristic
108C23×D61C22×C411yescharacteristic
109C2×Q8×C61—42no—
110C2×Q8×C61C22⋊C412yes—
111C2×Q8×C61C22⋊C412yes—
112C2×D4×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—42no—
115C22×C4×C61C22×C411yescharacteristic
116C22×C4×C61C22×C411yescharacteristic
117C22×C4×C61C22×C411yescharacteristic
118C22×C4×C61C22×C412yes—
119C2×C22⋊D61—22no—
120C2×C22⋊D61—22no—
121C2×C22⋊D61—24no—
122C2×C22⋊D61—44no—
123C2×C22⋊D61—82no—
124C22×Dic61C22×C411yescharacteristic
125C22×Dic61C22×C412yes—
126C22×Dic61C2411yescharacteristic
127#11758226—28no—
128#11758226—48no—
129#11758226—44no—
130D4×D61—48no—
131D4×D61—44no—
132D4×D61—44no—
133C2×D244—24no—
134C2×D244—22no—
135C2×D244—22no—
136C2×D244—44no—
137C2×D244—41no—
138C2×D244C22⋊C412yes—
139C2×D244C22⋊C411yescharacteristic
140C2×D244C22⋊C414yes—
141C2×D244C22⋊C414yes—
142C2×D244C22⋊C411yescharacteristic
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—42no—
148C2×C4×D61—44no—
149C2×C4×D61—42no—
150C2×C4×D61—82no—
151C2×C4×D61C2×D414yes—
152C2×C4×D61C2×D412yes—
153C2×C4×D61C2×D414yes—
154C2×C4×D61C2×D412yes—
155C2×#92420—22no—
156C2×#92420—24no—
157C2×#92420—22no—
158#11758213—48no—
159#11758213—44no—
160D61⋊C8—48no—
161D61⋊C8—44no—
162C22⋊C4×C61—24no—
163C22⋊C4×C61—24no—
164C42×C61—21no—
165C42×C61—21no—
166C22⋊Dic61—24no—
167#11758198—22no—
168#11758198—22no—
169#11758198—22no—
170#11758198—24no—
171#11758198—22no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—22no—
175#11758196—24no—
176C23×C61—22no—
177C23×C61—22no—
178C23×C61—22no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61C23×C411yescharacteristic
182C22×D61—21no—
183C22×D61—22no—
184C22×D61—21no—
185C22×D61—22no—
186C22×D61—21no—
187C22×D61—21no—
188C22×D61—24no—
189C22×D61—42no—
190C22×D61—41no—
191C22×D61—41no—
192C22×D61—44no—
193C22×D61—44no—
194C22×D61—44no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—44no—
198C22×D61—82no—
199C22×D61—82no—
200C22×D61—88no—
201C22×D61—88no—
202C22×D61C2×C22⋊C412yes—
203C22×D61C2×C22⋊C412yes—
204C22×D61C2×C22⋊C412yes—
205C22×D61#13112yescomplemented
206Q8×C61—24no—
207Q8×C61—42no—
208D4×C61—42no—
209D4×C61—42no—
210C2×C4×C61—22no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—42no—
216C2×C4×C61—41no—
217C2×C4×C61C2×C22⋊C414yes—
218C2×C4×C61C2×C22⋊C411yescharacteristic
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C22⋊D61—44no—
221C22⋊D61—44no—
222C22⋊D61—84no—
223C2×Dic61—21no—
224C2×Dic61—22no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—42no—
228C2×Dic61C22×D412yes—
229D244—24no—
230D244—28no—
231D244—22no—
232D244—44no—
233D244—44no—
234D244#9914yes—
235C4×D61—28no—
236C4×D61—24no—
237C4×D61—44no—
238C4×D61—42no—
239C4×D61—42no—
240C4×D61—42no—
241C4×D61—82no—
242C4×D61—82no—
243#92420—42no—
244#92420—44no—
245#92420—42no—
246#17411—611nomaximal, Sylow
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—42no—
250C22×C61—42no—
251C22×C61—42no—
252C22×C61—82no—
253C22×C61—82no—
254C22×C61C22×C22⋊C411yescharacteristic
255C22×C61C2×#13111yescharacteristic
256C22×C61#56811yescharacteristic
257C2×D61—22no—
258C2×D61—22no—
259C2×D61—22no—
260C2×D61—22no—
261C2×D61—22no—
262C2×D61—22no—
263C2×D61—22no—
264C2×D61—22no—
265C2×D61—22no—
266C2×D61—44no—
267C2×D61—44no—
268C2×D61—42no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—42no—
272C2×D61—88no—
273C2×D61—81no—
274C2×D61—81no—
275C2×D61—88no—
276C2×D61C2×#9914yes—
277C4×C61—24no—
278C4×C61—21no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61C2×#9912yes—
282Dic61—22no—
283Dic61—41no—
284Dic61—42no—
285C2×#546—611no—
286#2880—612no—
287#1471—612no—
288#1468—614no—
289#1465—611no—
290#1462—612no—
291#1459—611no—
292C2×#323—612no—
293C2×C61—21no—
294C2×C61—21no—
295C2×C61—82no—
296C2×C61#288011yescharacteristic
297C2×C61C22×#9911yescharacteristic
298C2×C61#288811yescharacteristic
299D61—24no—
300D61—42no—
301D61—42no—
302D61—42no—
303C22×#41—611no—
304C23×D4—611no—
305C2×#131—1222no—
306#546—1222no—
307#546—1224no—
308#546—1222no—
309C2×#124#692311yescharacteristic
310C2×#123—612no—
311C2×C22⋊Q8—611no—
312C2×#121—611no—
313C2×#121—612no—
314C2×#120—612no—
315C2×C4×D4—611no—
316C2×C4×D4—611no—
317C22×C22⋊C4—612no—
318#408—1222no—
319#408—1224no—
320#407—614no—
321#407—612no—
322C2×C22⋊C8—614no—
323C2×C22⋊C8—612no—
324#324—612no—
325#324—612no—
326#323—614no—
327#323—614no—
328#323—611no—
329#323—612no—
330#323—611no—
331C61#1741111yescharacteristic, complemented, Sylow
332C25—612no—
333C2×#41—612no—
334C2×#41—614no—
335C2×#41—612no—
336C2×#41—2444no—
337C22×Q8C2×#692311yescharacteristic
338C22×D4—612no—
339C22×D4—612no—
340C22×D4—611no—
341C22×D4—612no—
342C22×D4—611no—
343C22×D4—1221no—
344C22×D4—1222no—
345C22×D4—1221no—
346C22×D4—2444no—
347C22×D4C2×#692311yescharacteristic
348C23×C4—612no—
349C23×C4—611no—
350C23×C4—612no—
351C23×C4—611no—
352#131—2448no—
353C2×M16—1224no—
354C2×M16—1222no—
355C22×C8—1224no—
356C22×C8—1222no—
357#124—22no—
358#124—22no—
359#123—1224no—
360#123—1224no—
361C22⋊Q8—1222no—
362C22⋊Q8—1222no—
363#121—1224no—
364#121—1224no—
365#121—1222no—
366#121—1222no—
367#120—1224no—
368#120—1224no—
369C4×D4—1222no—
370C4×D4—1222no—
371C4×D4—1221no—
372C4×D4—1222no—
373C4×D4—1221no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—612no—
377C2×C22⋊C4—612no—
378C2×C22⋊C4—611no—
379C2×C22⋊C4—612no—
380C2×C22⋊C4—612no—
381C2×C22⋊C4—611no—
382C2×C22⋊C4—1224no—
383C2×C22⋊C4—1224no—
384C2×C22⋊C4C2×#692312yes—
385C2×C22⋊C4C2×#692312yes—
386C2×C42C2×#692311yescharacteristic
387C22⋊C8—612no—
388C22⋊C8—614no—
389C22⋊C8—612no—
390C22⋊C8—1224no—
391C22⋊C8—1222no—
392C22⋊C8—1224no—
393C22⋊C8—1222no—
394C24—612no—
395C24—611no—
396C24—611no—
397C24—1224no—
398C24—1222no—
399C24—1222no—
400C24—4882no—
401C24—2442no—
402C24—2444no—
403C24C22×#692312yes—
404#41—1228no—
405#41—2448no—
406#41—2444no—
407C2×Q8—42no—
408C2×Q8C22⋊#692312yes—
409C2×Q8C22⋊#692312yes—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—42no—
413C2×D4—611no—
414C2×D4—612no—
415C2×D4—611no—
416C2×D4—614no—
417C2×D4—614no—
418C2×D4—1224no—
419C2×D4—1222no—
420C2×D4—1222no—
421C2×D4—1224no—
422C2×D4—1222no—
423C2×D4—1222no—
424C2×D4—4882no—
425C2×D4—2441no—
426C2×D4—2444no—
427C2×D4—2444no—
428C2×D4—2448no—
429C2×D4—2444no—
430C2×D4—2444no—
431C22×C4—611no—
432C22×C4—614no—
433C22×C4—612no—
434C22×C4—614no—
435C22×C4—612no—
436C22×C4—612no—
437C22×C4—611no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—4882no—
443C22×C4—2442no—
444C22×C4—2442no—
445C22×C4—2444no—
446C22×C4C22×#692311yescharacteristic
447C22×C4C22×#692311yescharacteristic
448C22×C4C22×#692311yescharacteristic
449C22×C4C22×#692312yes—
450M16—2448no—
451M16—2444no—
452C2×C8—1222no—
453C2×C8—1224no—
454C2×C8—1222no—
455C2×C8—2448no—
456C2×C8—2444no—
457C4⋊C4—1222no—
458C4⋊C4—1224no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—1222no—
464C22⋊C4—1222no—
465C22⋊C4—1222no—
466C22⋊C4—1222no—
467C22⋊C4—1224no—
468C22⋊C4—1224no—
469C42—21no—
470C42—21no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—42no—
475C23—42no—
476C23—612no—
477C23—612no—
478C23—612no—
479C23—612no—
480C23—1224no—
481C23—1221no—
482C23—1221no—
483C23—1221no—
484C23—1222no—
485C23—1221no—
486C23—1222no—
487C23—4882no—
488C23—4882no—
489C23—4888no—
490C23—4888no—
491C23—2441no—
492C23—2441no—
493C23—2442no—
494C23—2441no—
495C23—2441no—
496C23—2444no—
497C23—2444no—
498C23—2444no—
499C23—2444no—
500C23C23×#692311yescharacteristic
501Q8—24no—
502Q8—42no—
503D4—42no—
504D4—42no—
505D4—614no—
506D4—1224no—
507D4—1228no—
508D4—1222no—
509D4—4884no—
510D4—2444no—
511D4—2444no—
512D4—2444no—
513D4—2444no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—612no—
522C2×C4—1228no—
523C2×C4—1224no—
524C2×C4—1222no—
525C2×C4—1221no—
526C2×C4—4882no—
527C2×C4—4882no—
528C2×C4—2442no—
529C2×C4—2444no—
530C2×C4—2442no—
531C2×C4—2441no—
532C2×C4—2442no—
533C2×C4—2442no—
534C2×C4—2441no—
535C2×C4C2×C22⋊#692311yescharacteristic
536C2×C4C2×C22⋊#692314yes—
537C2×C4C2×C22⋊#692311yescharacteristic
538C8—2442no—
539C8—2444no—
540C8—2442no—
541C22—21no—
542C22—21no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—82no—
547C22—82no—
548C22—614no—
549C22—1222no—
550C22—1222no—
551C22—1222no—
552C22—1222no—
553C22—1222no—
554C22—1222no—
555C22—1222no—
556C22—1222no—
557C22—1222no—
558C22—4881no—
559C22—4881no—
560C22—4888no—
561C22—4888no—
562C22—2444no—
563C22—2444no—
564C22—2442no—
565C22—2442no—
566C22—2441no—
567C22—2441no—
568C22C22×C22⋊#692311yescharacteristic
569C22D61⋊#13111yescharacteristic
570C22#1684084111yescharacteristic
571C4—21no—
572C4—24no—
573C4—41no—
574C4—41no—
575C4—1222no—
576C4—2441no—
577C4—2442no—
578C4D61⋊#9912yes—
579C2—21no—
580C2—21no—
581C2—82no—
582C2—1224no—
583C2—2442no—
584C2—2442no—
585C2—2442no—
586C2#2146241011yescharacteristic
587C2C2×D61⋊#9911yescharacteristic
588C2#2146243011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#124×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840405C2
cosocleC22×Dic61C24
hypercenterC2×#124#6923
hypocenterC61#17411
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×Q8 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21462408C2semidirect
2. #21461094C2semidirect
3. #21461085C2semidirect
4. #21461076C2semidirect
5. #21461065C2semidirect
6. #21461056C2semidirect
7. D61⋊#323C2semidirect
12. #16840733C22semidirect
13. #16840733C22semidirect
14. D61⋊(C22⋊C8)C22semidirect
15. D61⋊(C22⋊C8)C22semidirect
16. #16840607C22semidirect
17. #16840607C22semidirect
21. #16840605C22semidirect
22. #16840605C22semidirect
205. C22×D61#131semidirect
331. C61#17411semidirect

Maximal subgroups

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

subgroupindex
#214624082
#214610942
#214610852
#214610762
#214610652
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