Finite Group Databasebeta

← #30610956

Subgroups — #30610956

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462497C211yesmaximal, characteristic, complemented
2C2×#16840698C211yesmaximal, characteristic, complemented
3#21461213C212yesmaximal, complemented
4#21461208C212yesmaximal, complemented
5#21461205C214yesmaximal, complemented
6#21461191C214yesmaximal, complemented
7#21459114C211yesmaximal, characteristic
8C22×C4×#6923—21no—
9#16840785—21no—
10#16840784C2212yes—
11#16840781—21no—
12#16840780C2212yes—
13#16840765—21no—
14#16840734C2212yes—
15C4×#11758217—21no—
16#16840698—21no—
17#16840698—21no—
18#16840698C2212yes—
19#16840698C2212yes—
20C2×(C2×#6923)⋊C4—21no—
21C2×(C2×#6923)⋊C4C2212yes—
22#16840616C2218yes—
23#16840613C2218yes—
24#16840319C411yescharacteristic, complemented
25#16840317C411yescharacteristic, complemented
26#16840317C2211yescharacteristic
27#16840310C411yescharacteristic, complemented
28#16840310C2211yescharacteristic
29#16840294—21no—
30#16840294—21no—
31#16840293—21no—
32#16840293—21no—
33#16840291C412yescomplemented
34#16840291C2212yes—
35#16840272—21no—
36#16840272—21no—
37#16840269C2212yes—
38#41×Dic61C412yescomplemented
39C4×#11758224—21no—
40C4×#11758224—21no—
41C2×C42×D61C2211yescharacteristic
42C61×#532C411yescharacteristic, complemented
43C23×#6923—22no—
44C2×#11758217—22no—
45C2×C4×#6923—28no—
46C2×C4×#6923—22no—
47C2×C4×#6923—22no—
48#14519844—22no—
49C4⋊#92420—22no—
50#14519834—22no—
51#14519834C2314yes—
52#14519832—22no—
53C4×#92420—22no—
54(C2×#6923)⋊C4—22no—
55(C2×#6923)⋊C4—22no—
56(C2×#6923)⋊C4—22no—
57(C2×#6923)⋊C4C2314yes—
58C2×#11758224—21no—
59C2×#11758224—21no—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63#14519777C2×C411yescharacteristic, complemented
64#14519777C2×C411yescharacteristic, complemented
65#14519770—22no—
66#14519770—22no—
67#14519769C2×C412yescomplemented
68#14519768—21no—
69#14519768—21no—
70#14519764—21no—
71#14519764—21no—
72#14519759—22no—
73#14519759—22no—
74#14519758—22no—
75#14519757—21no—
76#14519757—21no—
77#14519756—21no—
78#14519756—21no—
79#14519753C2×C412yes—
80#14519753C2312yes—
81#14519748—21no—
82#14519748—21no—
83#14519748C2×C412yes—
84#14519748C2312yes—
85#14519745—22no—
86Q8×Dic61C2×C412yescomplemented
87Q8×Dic61C2×C412yescomplemented
88C4×Dic122—21no—
89C4×Dic122—21no—
90#14519742—21no—
91#14519742—21no—
92D4×Dic61—22no—
93D4×Dic61—22no—
94D4×Dic61—21no—
95D4×Dic61—21no—
96D4×Dic61C2×C412yescomplemented
97D4×Dic61C2×C412yescomplemented
98C4×C22⋊D61—22no—
99C4×C22⋊D61—22no—
100#14519737—22no—
101#14519737—22no—
102#14519736—22no—
103#14519736C2×C412yes—
104#14519735—21no—
105#14519735—21no—
106#14519733—22no—
107#14519733—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120C2×#41×C61C2×C412yes—
121C4⋊Q8×C61C2×C411yescharacteristic, complemented
122#127×C61C2×C411yescharacteristic, complemented
123#124×C61C2×C412yescomplemented
124#121×C61—21no—
125#121×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C2×C42×C61C2×C411yescharacteristic
129C23×D61C2×D411yescharacteristic
130C22×#6923—28no—
131C22×#6923—24no—
132C22×#6923—44no—
133C22×#6923—44no—
134#41×C61—44no—
135C2×Q8×C61C22×C412yes—
136C2×D4×C61—22no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61C22×C412yes—
140C22×C4×C61—22no—
141C22×C4×C61C22⋊C411yescharacteristic
142C22×C4×C61C22⋊C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151#11758224—44no—
152#11758224—44no—
153C2×C4×D61—24no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61C22⋊C411yescharacteristic
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22×C411yescharacteristic
161C2×C4×D61C2×D411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61C2×D411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2411yescharacteristic
168C2×Dic122—21no—
169C2×Dic122—21no—
170#11758217—44no—
171C2×#92420—24no—
172C4×#6923—28no—
173C4×#6923—28no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—22no—
178C42×C61C22⋊C411yescharacteristic
179C42×C61C22⋊C411yescharacteristic
180C42×C61C22×C411yescharacteristic
181C42×C61C22×C411yescharacteristic
182C22⋊Dic61—22no—
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187#11758198—22no—
188#11758198—22no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61C22×C412yes—
194C4⋊Dic61C22×C412yes—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61C22⋊C411yescharacteristic
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22⋊C411yescharacteristic
206C4×Dic61C22⋊C411yescharacteristic
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22×C411yescharacteristic
209C4×Dic61C22×C411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C23×C61—22no—
215C23×C61C2×C22⋊C411yescharacteristic
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—22no—
219C22×D61C2×C22⋊C411yescharacteristic
220C22×D61C22×D411yescharacteristic
221C2×#6923—28no—
222C2×#6923—416no—
223C2×#6923—44no—
224C2×#6923—44no—
225Q8×C61—42no—
226D4×C61—42no—
227D4×C61—42no—
228D4×C61—44no—
229D4×C61—42no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—41no—
234C2×C4×C61—44no—
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C23×C411yescharacteristic
241C22⋊D61—44no—
242C22⋊D61—44no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—41no—
248C2×Dic61—44no—
249C2×Dic61—44no—
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C22×D411yescharacteristic
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—41no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—41no—
267C4×D61#10414yes—
268Dic122—42no—
269Dic122—42no—
270#92420—44no—
271#17541—611nomaximal, Sylow
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—42no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61#41012yes—
278C22×C61C22×C22⋊C411yescharacteristic
279C2×D61—28no—
280C2×D61—21no—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61C2×#10412yes—
285C2×D61#57512yes—
286#6923—48no—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—42no—
293C4×C61C2×#10412yes—
294Dic61—21no—
295Dic61—21no—
296Dic61—21no—
297Dic61—21no—
298Dic61—21no—
299Dic61—42no—
300Dic61—42no—
301Dic61C2×#10412yes—
302#3444—611no—
303#2920—611no—
304C2×#376—611no—
305#1506—612no—
306#1505—612no—
307#1504—614no—
308#1500—614no—
309C2×C61—22no—
310C2×C61—82no—
311C2×C61C2×#41011yescharacteristic
312C2×C61#289611yescharacteristic
313C2×C61C22×#10411yescharacteristic
314D61—22no—
315D61—22no—
316#533—611no—
317#533—611no—
318#533—611no—
319#532—611no—
320#532—611no—
321#532#692311yescharacteristic, complemented
322#529—612no—
323#529—612no—
324#529—1221no—
325#529—1221no—
326#529—1221no—
327#529—1221no—
328#525—612no—
329#525—1221no—
330#525—1221no—
331C4×#41—612no—
332C4×#41—1221no—
333C4×#41—1221no—
334C22×C42—611no—
335C22×C42—1221no—
336#432—612no—
337#432—1221no—
338#431—612no—
339#431—1221no—
340#423—1221no—
341#407—612no—
342C4×M16—1221no—
343#376—612no—
344#376—612no—
345#376—1221no—
346#376—1221no—
347C2×#95—612no—
348C2×#95—1221no—
349#328—618no—
350#327—618no—
351C61#1754111yescharacteristic, complemented, Sylow
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41C2×#692312yes—
355C23×C4—611no—
356C23×C4—611no—
357C23×C4—611no—
358C23×C4—1222no—
359C2×M16—1222no—
360C4⋊Q8—611no—
361C4⋊Q8—611no—
362C4⋊Q8C2×#692311yescharacteristic, complemented
363#127C2×#692311yescharacteristic, complemented
364#126—1222no—
365#126—1222no—
366#125—612no—
367#125—1221no—
368#125—1221no—
369#124—1221no—
370#124—1221no—
371#124C2×#692312yescomplemented
372#123—1222no—
373#123—1222no—
374#123—1222no—
375C22⋊Q8—612no—
376C22⋊Q8—612no—
377C22⋊Q8—1221no—
378C22⋊Q8—1221no—
379C22⋊Q8—1221no—
380C22⋊Q8—1221no—
381#121—21no—
382#121—21no—
383#121—612no—
384#121—612no—
385#121—1221no—
386#121—1221no—
387#120—1222no—
388C4×Q8—612no—
389C4×Q8—612no—
390C4×Q8—1221no—
391C4×Q8—1221no—
392C4×Q8—1221no—
393C4×Q8—1221no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—612no—
397C4×D4—612no—
398C4×D4—1221no—
399C4×D4—1221no—
400C4×D4—1222no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4—1222no—
404C4×D4—1222no—
405C4×D4—1222no—
406#117—612no—
407#117—1222no—
408#117—1222no—
409#117—1222no—
410#117—1221no—
411#117—1221no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—1222no—
424C2×C42—1222no—
425C2×C42—1222no—
426C2×C42—1228no—
427C2×C42C2×#692311yescharacteristic
428C4⋊C8—1222no—
429C4⋊C8—1222no—
430C22⋊C8—614no—
431C22⋊C8—1222no—
432#97—1222no—
433C4×C8—1222no—
434#95—614no—
435#95—1222no—
436#95—1222no—
437#95—1222no—
438C24—611no—
439#41—44no—
440#41—2444no—
441#41—2444no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C2×Q8C22×#692312yes—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4C22×#692312yes—
451C22×C4—22no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—1224no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1224no—
471C22×C4—1228no—
472C22×C4—2442no—
473C22×C4—2442no—
474C22×C4—2444no—
475C22×C4—2444no—
476C22×C4C22⋊#692311yescharacteristic
477C22×C4C22⋊#692311yescharacteristic
478C22×C4C22×#692311yescharacteristic
479M16—2444no—
480C2×C8—1224no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—612no—
484C4⋊C4—612no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C42—611no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—1222no—
515C42—1222no—
516C42—1228no—
517C42—1228no—
518C42—1222no—
519C42C22⋊#692311yescharacteristic
520C42C22⋊#692311yescharacteristic
521C42C22×#692311yescharacteristic
522C42C22×#692311yescharacteristic
523C23—22no—
524C23—611no—
525C23—611no—
526C23—1222no—
527C23—1222no—
528C23—1222no—
529C23C2×C22⋊#692311yescharacteristic
530Q8—42no—
531Q8—2442no—
532Q8—2442no—
533D4—42no—
534D4—42no—
535D4—44no—
536D4—42no—
537D4—2444no—
538D4—2444no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—44no—
544C2×C4—611no—
545C2×C4—614no—
546C2×C4—611no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1228no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2444no—
568C2×C4—2441no—
569C2×C4—2444no—
570C2×C4—2444no—
571C2×C4—24416no—
572C2×C4—2444no—
573C2×C4C2×C22⋊#692311yescharacteristic
574C2×C4C2×C22⋊#692311yescharacteristic
575C2×C4C2×C22⋊#692311yescharacteristic
576C2×C4C2×C22⋊#692311yescharacteristic
577C2×C4C2×C22⋊#692311yescharacteristic
578C2×C4C23×#692311yescharacteristic
579C8—2444no—
580C22—21no—
581C22—21no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—612no—
586C22—612no—
587C22—1228no—
588C22—1221no—
589C22—1221no—
590C22—1221no—
591C22—1221no—
592C22#1684074212yes—
593C22C22×C22⋊#692311yescharacteristic
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—42no—
600C4—612no—
601C4—1221no—
602C4—1221no—
603C4—1221no—
604C4—1221no—
605C4—1221no—
606C4—2448no—
607C4—2442no—
608C4—2442no—
609C4D61⋊#10412yes—
610C2—22no—
611C2—82no—
612C2—1222no—
613C2—1222no—
614C2C2×#1684074211yescharacteristic
615C2#2146243911yescharacteristic
616C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#532C4
socleC22×C61C22×C22⋊C4
prime radical#21459114C2
cosocleC2×C4×D61C24
hypercenter#532#6923
hypocenterC61#17541
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #21462497C2semidirect
2. C2×#16840698C2semidirect
3. #21461213C2semidirect
4. #21461208C2semidirect
5. #21461205C2semidirect
6. #21461191C2semidirect
24. #16840319C4semidirect
25. #16840317C4semidirect
27. #16840310C4semidirect
33. #16840291C4semidirect
38. #41×Dic61C4semidirect
42. C61×#532C4semidirect
63. #14519777C2×C4semidirect
64. #14519777C2×C4semidirect
67. #14519769C2×C4semidirect
86. Q8×Dic61C2×C4semidirect
87. Q8×Dic61C2×C4semidirect
96. D4×Dic61C2×C4semidirect
97. D4×Dic61C2×C4semidirect
121. C4⋊Q8×C61C2×C4semidirect
122. #127×C61C2×C4semidirect
123. #124×C61C2×C4semidirect
321. #532#6923semidirect
351. C61#17541semidirect
362. C4⋊Q8C2×#6923semidirect
363. #127C2×#6923semidirect
371. #124C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624972
C2×#168406982
#214612132
#214612082
#214612052
#214611912
#214591142
#1754161