Finite Group Databasebeta

← #30610486

Subgroups — #30610486

Order 15616.

1138 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462738C211yesmaximal, characteristic, complemented
2#21462628C211yesmaximal, characteristic, complemented
3#21461163C212yesmaximal, complemented
4#21461156C212yesmaximal, complemented
5#21461152C212yesmaximal, complemented
6#21461149C212yesmaximal, complemented
7#21461123C211yesmaximal, characteristic, complemented
8#21461116C211yesmaximal, characteristic, complemented
9#21461112C211yesmaximal, characteristic, complemented
10C2×#16840612C211yesmaximal, characteristic, complemented
11#21459030C211yesmaximal, characteristic
12#16840813—21no—
13#16840813—21no—
14#16840797—21no—
15#16840797—21no—
16#16840793—22no—
17#16840793—22no—
18#16840783C2212yes—
19#16840779C2212yes—
20#16840778C2211yescharacteristic
21#16840778C2211yescharacteristic
22#16840765C2212yes—
23C2×C4⋊#92420C2211yescharacteristic
24C4×#11758217C2212yes—
25C2×C4×#92420C2211yescharacteristic
26#16840612C2212yes—
27#16840612C2212yes—
28#16840612C2211yescharacteristic
29#16840612C2211yescharacteristic
30#16840612C2212yes—
31#16840612C2212yes—
32#16840612C2212yes—
33#16840610C2211yescharacteristic
34#16840610C2211yescharacteristic
35#16840610C2212yes—
36C2×#14519824C411yescharacteristic
37#16840243C412yes—
38#16840243C411yescharacteristic
39#16840241—22no—
40#16840241—21no—
41#16840239C412yes—
42#16840239C411yescharacteristic
43#16840238—21no—
44#41×Dic61C2211yescharacteristic
45#16840230C2211yescharacteristic
46#16840230C2212yes—
47C4×#11758224—22no—
48C4×#11758224—21no—
49C2×#14519742C2211yescharacteristic
50C2×#14519742C2212yes—
51C4×Q8×D61—21no—
52C61×#520C411yescharacteristic
53C2×#11758217—22no—
54C2×#11758217—22no—
55C22×#92420—21no—
56C22×#92420—21no—
57#14519844—22no—
58#14519844—22no—
59C4⋊#92420—21no—
60C4⋊#92420—21no—
61C4⋊#92420C2312yes—
62C4⋊#92420C2311yescharacteristic
63C4⋊#92420C2311yescharacteristic
64C22⋊#92420—21no—
65C22⋊#92420—21no—
66C22⋊#92420—22no—
67C22⋊#92420—22no—
68#14519832—22no—
69#14519832—22no—
70C4×#92420—21no—
71C4×#92420—21no—
72C4×#92420C2311yescharacteristic
73C4×#92420C2311yescharacteristic
74C4×#92420C2312yes—
75#14519824—24no—
76#14519824—24no—
77C2×#11758222C2×C412yes—
78C2×#11758222C2×C411yescharacteristic
79C2×#11758224—22no—
80C2×#11758224—21no—
81C22×Dic122C2×C412yes—
82C22×Dic122C2×C411yescharacteristic
83C2×Q8×D61—21no—
84Q8×Dic61D411yescharacteristic
85Q8×Dic61D411yescharacteristic
86C4×Dic122—22no—
87C4×Dic122—21no—
88C4×Dic122—22no—
89C4×Dic122—21no—
90#14519742—21no—
91#14519742—22no—
92#14519742—21no—
93#14519742—22no—
94#14519742C2×C412yes—
95#14519742C2×C412yes—
96#14519742C2×C412yes—
97#14519742C2×C411yescharacteristic
98#14519742C2×C412yes—
99#14519742C2312yes—
100#14519742C2311yescharacteristic
101D4×Dic61D412yes—
102D4×Dic61D411yescharacteristic
103D4×Dic61D412yes—
104D4×Dic61D411yescharacteristic
105#14519739C2×C411yescharacteristic
106#14519739C2×C412yes—
107#14519739C2311yescharacteristic
108C4×C22⋊D61—22no—
109C4×C22⋊D61—22no—
110C4×C22⋊D61—22no—
111#14519737—21no—
112#14519737—22no—
113#14519737—21no—
114#14519737—22no—
115#14519736C2×C412yes—
116#14519736C2×C411yescharacteristic
117#14519735—22no—
118#14519735—21no—
119#14519734—21no—
120#14519734—22no—
121#14519733—22no—
122#14519733—22no—
123#14519733—22no—
124C2×#11758196—21no—
125C2×#11758196—22no—
126C4⋊C4×D61—22no—
127C4⋊C4×D61—21no—
128C2×C4×Dic61—21no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61C2311yescharacteristic
131C2×C4×Dic61C2312yes—
132C42×D61—21no—
133C42×D61—22no—
134C2×#41×C61C2×C411yescharacteristic
135C4×Q8×C61—21no—
136C4×D4×C61—22no—
137C4×D4×C61—21no—
138#117×C61C2×C412yes—
139#117×C61C2×C411yescharacteristic
140C2×C4⋊C4×C61C2×C412yes—
141C2×C4⋊C4×C61C2×C411yescharacteristic
142#41×C61—22no—
143#41×C61—22no—
144C2×Q8×C61C22⋊C411yescharacteristic
145C2×D4×C61C22⋊C412yes—
146C2×D4×C61C22⋊C411yescharacteristic
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C22×C411yescharacteristic
151C2×C22⋊D61—22no—
152C2×C22⋊D61—21no—
153C22×Dic61—22no—
154C22×Dic61—21no—
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D412yes—
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D412yes—
159Q8×D61—28no—
160#11758224—216no—
161#11758224—28no—
162#11758222—22no—
163#11758222—24no—
164#11758222—24no—
165#11758222M1614yescomplemented
166C2×D244C22×C411yescharacteristic
167C2×C4×D61—22no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—22no—
172C2×Dic122—22no—
173C2×Dic122—21no—
174C2×Dic122—22no—
175C2×Dic122—24no—
176C2×Dic122—24no—
177C2×Dic122M1614yescomplemented
178C2×Dic122C22×C411yescharacteristic
179C2×Dic122C22×C412yes—
180#11758217—44no—
181#11758217—82no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—21no—
185C2×#92420—21no—
186C2×#92420—22no—
187C2×#92420—22no—
188C2×#92420—42no—
189C2×#92420—81no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61C22×C411yescharacteristic
193C4⋊C4×C61C22×C412yes—
194C4⋊C4×C61C22×C411yescharacteristic
195C22⋊C4×C61—22no—
196C22⋊C4×C61—21no—
197C42×C61—22no—
198C42×C61—21no—
199C22⋊Dic61C22⋊C412yes—
200C22⋊Dic61C22⋊C412yes—
201C22⋊Dic61C22⋊C412yes—
202#11758198—21no—
203#11758198—22no—
204#11758198—21no—
205C4⋊Dic61C22⋊C412yes—
206C4⋊Dic61C22⋊C411yescharacteristic
207C4⋊Dic61C22⋊C412yes—
208C4⋊Dic61C22⋊C411yescharacteristic
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—21no—
213#11758196—22no—
214#11758196—22no—
215#11758196—21no—
216C4×Dic61—21no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—22no—
220C4×Dic61—22no—
221C4×Dic61—21no—
222C4×Dic61—22no—
223C4×Dic61C22×C411yescharacteristic
224C4×Dic61C22×C412yes—
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D412yes—
228C4×Dic61C2×D412yes—
229C4×Dic61C2411yescharacteristic
230C23×C61C2×C22⋊C412yes—
231C23×C61C2×C22⋊C411yescharacteristic
232C22×D61—21no—
233Q8×C61—22no—
234D4×C61—24no—
235D4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—21no—
239C2×C4×C61—22no—
240C2×C4×C61—21no—
241C2×C4×C61—81no—
242C2×C4×C61—82no—
243C2×C4×C61C2×C22⋊C412yes—
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×M1612yes—
246C2×C4×C61C2×M1612yes—
247C2×C4×C61C23×C411yescharacteristic
248C22⋊D61—28no—
249C22⋊D61—24no—
250C2×Dic61—28no—
251C2×Dic61—21no—
252C2×Dic61—22no—
253C2×Dic61—24no—
254C2×Dic61—21no—
255C2×Dic61—22no—
256C2×Dic61—21no—
257C2×Dic61—22no—
258C2×Dic61—41no—
259C2×Dic61—42no—
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C412yes—
264C2×Dic61C22×D411yescharacteristic
265C2×Dic61C22×D411yescharacteristic
266D244—21no—
267D244C2×M1612yes—
268C4×D61—28no—
269C4×D61—24no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—81no—
273C4×D61—82no—
274Dic122—28no—
275Dic122—22no—
276Dic122—21no—
277Dic122—24no—
278Dic122C2×M1612yes—
279Dic122C2×M1614yes—
280#92420—22no—
281#92420—41no—
282#92420—42no—
283#92420—42no—
284#92420—41no—
285#92420—41no—
286#17454—611nomaximal, Sylow
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—22no—
292C22×C61#40712yes—
293C22×C61C22×C22⋊C411yescharacteristic
294C2×D61—22no—
295C2×D61—41no—
296C2×D61—41no—
297C4×C61—22no—
298C4×C61—41no—
299C4×C61—42no—
300C4×C61—41no—
301C4×C61#40712yes—
302C4×C61C22×M1611yescharacteristic
303C4×C61C22×M1611yescharacteristic
304Dic61—22no—
305Dic61—24no—
306Dic61—21no—
307Dic61—22no—
308Dic61—21no—
309Dic61—21no—
310Dic61—22no—
311Dic61#57711yescharacteristic
312Dic61#57811yescharacteristic
313C4×2−1+4—611no—
314#2989—611no—
315#2965—611no—
316#1491—612no—
317#1489—612no—
318#1488—612no—
319#1487—612no—
320#1479—611no—
321#1477—611no—
322#1476—611no—
323C2×Q8⋊C8—611no—
324C2×C61—22no—
325C2×C61—42no—
326C2×C61C2×#40711yescharacteristic
327C2×C61#289811yescharacteristic
328C2×C61#290111yescharacteristic
329D61—42no—
330C2×2−1+4—611no—
331#520—611no—
332#520—612no—
333#520—1222no—
334#520—1221no—
335#520#692311yescharacteristic
336#519—611no—
337#519—612no—
338#519—1221no—
339C4×#41—611no—
340C4×#41—611no—
341C4×#41—612no—
342C4×#41—1222no—
343C4×#41—1221no—
344C2×C4×Q8—611no—
345C2×C4×Q8—612no—
346C2×C4×Q8—1221no—
347#446—1221no—
348#446—1221no—
349#436—1221no—
350#436—1221no—
351#435—1222no—
352#435—1222no—
353#432—612no—
354#431—611no—
355#431—612no—
356#431—611no—
357#423—612no—
358C2×C4⋊C8—611no—
359C4×M16—612no—
360C2×C4×C8—611no—
361Q8⋊C8—612no—
362Q8⋊C8—612no—
363Q8⋊C8—611no—
364Q8⋊C8—611no—
365Q8⋊C8—612no—
366Q8⋊C8—612no—
367Q8⋊C8—612no—
368D4⋊C8—611no—
369D4⋊C8—611no—
370D4⋊C8—612no—
371C61#1745411yescharacteristic, complemented, Sylow
3722−1+4—1224no—
3732−1+4—1224no—
374C2×#41—611no—
375C2×#41—612no—
376C2×#41—1221no—
377C2×#41—1222no—
378C2×#41C2×#692311yescharacteristic
379C22×Q8—611no—
380C22×Q8—612no—
381C22×Q8—1221no—
382C2×M16—1222no—
383C2×M16—1222no—
384C22×C8—1221no—
385C22×C8—1221no—
386C4×Q8—21no—
387C4×Q8—611no—
388C4×Q8—611no—
389C4×Q8—612no—
390C4×Q8—611no—
391C4×Q8—612no—
392C4×Q8—612no—
393C4×Q8—612no—
394C4×Q8—611no—
395C4×Q8—612no—
396C4×Q8—1222no—
397C4×Q8—1221no—
398C4×Q8—1222no—
399C4×Q8—1221no—
400C4×Q8—1221no—
401C4×Q8—1222no—
402C4×Q8—1221no—
403C4×Q8—1222no—
404C4×D4—22no—
405C4×D4—21no—
406C4×D4—612no—
407C4×D4—611no—
408C4×D4—612no—
409C4×D4—611no—
410C4×D4—611no—
411C4×D4—611no—
412C4×D4—612no—
413C4×D4—1221no—
414C4×D4—1222no—
415C4×D4—1221no—
416C4×D4—1222no—
417C4×D4—1222no—
418C4×D4—1222no—
419C4×D4—1222no—
420#117—612no—
421#117—611no—
422#117—1221no—
423#117—1222no—
424#117—1222no—
425#117—1222no—
426#117—1222no—
427#117—1222no—
428#117—1221no—
429#117C2×#692312yes—
430#117C2×#692311yescharacteristic
431C2×C4⋊C4—1222no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1222no—
435C2×C4⋊C4C2×#692312yes—
436C2×C4⋊C4C2×#692311yescharacteristic
437C2×C42—611no—
438C2×C42—612no—
439C2×C42—1221no—
440C2×C42—1222no—
441C2×C42—1221no—
442C2×C42—1222no—
443C4⋊C8—612no—
444C4⋊C8—611no—
445C4⋊C8—611no—
446C4⋊C8—1221no—
447C4⋊C8—1221no—
448C4⋊C8—1222no—
449C4⋊C8—1222no—
450C22⋊C8—1221no—
451C22⋊C8—1221no—
452C22⋊C8—1222no—
453C22⋊C8—1222no—
454#97—1222no—
455#97—1222no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—612no—
459C4×C8—1221no—
460C4×C8—1221no—
461#41—22no—
462#41—22no—
463#41—614no—
464#41—1224no—
465#41—1224no—
466#41—12216no—
467#41—1228no—
468#41—1222no—
469C2×Q8—614no—
470C2×Q8—612no—
471C2×Q8—611no—
472C2×Q8—1224no—
473C2×Q8—1224no—
474C2×Q8—1228no—
475C2×Q8—1222no—
476C2×Q8—1221no—
477C2×Q8—1222no—
478C2×Q8C22⋊#692311yescharacteristic
479C2×D4—611no—
480C2×D4—1222no—
481C2×D4—1221no—
482C2×D4C22⋊#692312yes—
483C2×D4C22⋊#692311yescharacteristic
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—611no—
487C22×C4—612no—
488C22×C4—611no—
489C22×C4—612no—
490C22×C4—1221no—
491C22×C4—1222no—
492C22×C4—1221no—
493C22×C4—1222no—
494C22×C4—1221no—
495C22×C4—1222no—
496C22×C4—1221no—
497C22×C4C22×#692312yes—
498C22×C4C22×#692311yescharacteristic
499M16—4882no—
500M16—2444no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1222no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1222no—
507C2×C8—4881no—
508C2×C8—2442no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—612no—
512C4⋊C4—611no—
513C4⋊C4—612no—
514C4⋊C4—611no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1222no—
522C4⋊C4C22×#692311yescharacteristic
523C4⋊C4C22×#692312yes—
524C4⋊C4C22×#692311yescharacteristic
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—612no—
528C22⋊C4—612no—
529C22⋊C4—612no—
530C22⋊C4—1221no—
531C22⋊C4—1221no—
532C22⋊C4—1222no—
533C42—22no—
534C42—21no—
535C42—611no—
536C42—611no—
537C42—612no—
538C42—612no—
539C42—611no—
540C42—611no—
541C42—612no—
542C42—1221no—
543C42—1222no—
544C42—1221no—
545C42—1222no—
546C42—1222no—
547C42—1222no—
548C42—1222no—
549C23—1221no—
550C23C2×C22⋊#692312yes—
551C23C2×C22⋊#692311yescharacteristic
552Q8—22no—
553Q8—614no—
554Q8—612no—
555Q8—1228no—
556Q8—1224no—
557Q8—1222no—
558Q8—1221no—
559D4—24no—
560D4—22no—
561D4—612no—
562D4—1228no—
563D4—1224no—
564D4—1221no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—81no—
571C2×C4—82no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—612no—
575C2×C4—611no—
576C2×C4—612no—
577C2×C4—611no—
578C2×C4—1228no—
579C2×C4—1221no—
580C2×C4—1222no—
581C2×C4—1221no—
582C2×C4—1222no—
583C2×C4—1228no—
584C2×C4—1224no—
585C2×C4—1222no—
586C2×C4—1221no—
587C2×C4—1224no—
588C2×C4—4881no—
589C2×C4—4882no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2442no—
594C2×C4C2×C22⋊#692312yes—
595C2×C4C2×C22⋊#692311yescharacteristic
596C2×C4D61⋊M1612yes—
597C2×C4D61⋊M1612yes—
598C2×C4C23×#692311yescharacteristic
599C8—1222no—
600C8—2441no—
601C8—2442no—
602C8—2441no—
603C8—2441no—
604C8—2442no—
605C22—21no—
606C22—21no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—1222no—
611C22—2441no—
612C22—2441no—
613C22#1684073412yes—
614C22C22×C22⋊#692311yescharacteristic
615C4—22no—
616C4—41no—
617C4—42no—
618C4—41no—
619C4—611no—
620C4—611no—
621C4—1224no—
622C4—1222no—
623C4—1221no—
624C4—1222no—
625C4—1221no—
626C4—1221no—
627C4—1222no—
628C4#1684073412yes—
629C4C2×D61⋊M1611yescharacteristic
630C4C2×D61⋊M1611yescharacteristic
631C2—22no—
632C2—42no—
633C2—2442no—
634C2C2×#1684073411yescharacteristic
635C2#2146244111yescharacteristic
636C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#520C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519824C4
cosocleC4×Dic61C24
hypercenter#520#6923
hypocenterC61#17454
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #21462738C2semidirect
2. #21462628C2semidirect
3. #21461163C2semidirect
4. #21461156C2semidirect
5. #21461152C2semidirect
6. #21461149C2semidirect
7. #21461123C2semidirect
8. #21461116C2semidirect
9. #21461112C2semidirect
10. C2×#16840612C2semidirect
165. #11758222M16semidirect
177. C2×Dic122M16semidirect
371. C61#17454semidirect

Maximal subgroups

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

subgroupindex
#214627382
#214626282
#214611632
#214611562
#214611522
#214611492
#214611232
#214611162
#214611122
C2×#168406122
#214590302
#1745461