Finite Group Databasebeta

← #30610986

Subgroups — #30610986

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462497C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊#6923C211yesmaximal, characteristic, complemented
3#21461220C214yesmaximal, complemented
4#21461205C214yesmaximal, complemented
5#21461203C212yesmaximal, complemented
6#21461199C212yesmaximal, complemented
7#21459114C211yesmaximal, characteristic
8C22×C4⋊#6923—21no—
9C22×C4×#6923—21no—
10#16840785C2212yes—
11#16840784—21no—
12#16840781C2212yes—
13#16840780—21no—
14#16840765—21no—
15#16840734C2212yes—
16C4×#11758217—21no—
17C4×C4⋊#6923—21no—
18C4×C4⋊#6923—21no—
19C4×C4⋊#6923C2212yes—
20C4×C4⋊#6923C2212yes—
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—
48C2×C4×#6923—22no—
49C2×C4×#6923—22no—
50C2×C4×#6923—44no—
51#14519844—22no—
52C4⋊#92420—22no—
53#14519834—22no—
54#14519834C2314yes—
55#14519832—22no—
56C4×#92420—22no—
57(C2×#6923)⋊C4—22no—
58(C2×#6923)⋊C4C2314yes—
59C2×#11758224—21no—
60C2×#11758224—21no—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64#14519777C2×C411yescharacteristic, complemented
65#14519777C2×C411yescharacteristic, complemented
66#14519770—22no—
67#14519770—22no—
68#14519769C2×C412yescomplemented
69#14519768—21no—
70#14519768—21no—
71#14519764—21no—
72#14519764—21no—
73#14519759—22no—
74#14519759—22no—
75#14519758—22no—
76#14519757—21no—
77#14519757—21no—
78#14519756—21no—
79#14519756—21no—
80#14519753C2×C412yes—
81#14519753C2312yes—
82#14519748—21no—
83#14519748—21no—
84#14519748C2×C412yes—
85#14519748C2312yes—
86#14519745—22no—
87Q8×Dic61C2×C412yescomplemented
88Q8×Dic61C2×C412yescomplemented
89C4×Dic122—21no—
90C4×Dic122—21no—
91#14519742—21no—
92#14519742—21no—
93D4×Dic61—22no—
94D4×Dic61—22no—
95D4×Dic61—21no—
96D4×Dic61—21no—
97D4×Dic61C2×C412yescomplemented
98D4×Dic61C2×C412yescomplemented
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101#14519737—22no—
102#14519737—22no—
103#14519736—22no—
104#14519736C2×C412yes—
105#14519735—21no—
106#14519735—21no—
107#14519733—22no—
108#14519733—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61C2311yescharacteristic
120C42×D61C2311yescharacteristic
121C2×#41×C61C2×C412yes—
122C4⋊Q8×C61C2×C411yescharacteristic, complemented
123#127×C61C2×C411yescharacteristic, complemented
124#124×C61C2×C412yescomplemented
125#121×C61—21no—
126#121×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61—21no—
129C2×C42×C61C2×C411yescharacteristic
130C23×D61C2×D411yescharacteristic
131C22×#6923—28no—
132C22×#6923—24no—
133C22×#6923—44no—
134C22×#6923—44no—
135#41×C61—44no—
136C2×Q8×C61C22×C412yes—
137C2×D4×C61—22no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61C22×C412yes—
141C22×C4×C61—22no—
142C22×C4×C61C22⋊C411yescharacteristic
143C22×C4×C61C22⋊C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61C22⋊C411yescharacteristic
150C22×Dic61C22⋊C411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152#11758224—44no—
153#11758224—42no—
154#11758224—42no—
155C2×C4×D61—24no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—42no—
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22×C411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2411yescharacteristic
171C2×Dic122—21no—
172C2×Dic122—21no—
173#11758217—44no—
174C2×#92420—24no—
175C4⋊#6923—28no—
176C4⋊#6923—28no—
177C4×#6923—44no—
178C4×#6923—44no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C42×C61C22⋊C411yescharacteristic
184C42×C61C22⋊C411yescharacteristic
185C42×C61C22×C411yescharacteristic
186C42×C61C22×C411yescharacteristic
187C22⋊Dic61—22no—
188C22⋊Dic61—22no—
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192#11758198—22no—
193#11758198—22no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61C22×C412yes—
199C4⋊Dic61C22×C412yes—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22×C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C23×C61—22no—
220C23×C61C2×C22⋊C411yescharacteristic
221C22×D61—22no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—22no—
225C22×D61C2×C22⋊C411yescharacteristic
226C22×D61C22×D411yescharacteristic
227C2×#6923—28no—
228C2×#6923—416no—
229C2×#6923—44no—
230C2×#6923—44no—
231Q8×C61—42no—
232D4×C61—42no—
233D4×C61—44no—
234D4×C61—42no—
235D4×C61—42no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—44no—
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C23×C411yescharacteristic
247C22⋊D61—42no—
248C22⋊D61—42no—
249C22⋊D61—44no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—44no—
256C2×Dic61—44no—
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61C2×C22⋊C411yescharacteristic
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C22×D411yescharacteristic
263C4×D61—21no—
264C4×D61—21no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61#10414yes—
275C4×D61AGL(1,ℤ/8)12yes—
276C4×D61#13712yes—
277Dic122—42no—
278Dic122—42no—
279#92420—44no—
280#17546—611nomaximal, Sylow
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—42no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61#41012yes—
287C22×C61C22×C22⋊C411yescharacteristic
288C2×D61—24no—
289C2×D61—24no—
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—21no—
294C2×D61C2×#10412yes—
295C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
296C2×D61C2×#13711yescharacteristic
297#6923—48no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—42no—
303C4×C61#41712yes—
304C4×C61C2×#10412yes—
305Dic61—21no—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—42no—
310Dic61—42no—
311Dic61#41712yes—
312Dic61C2×#10412yes—
313#3444—611no—
314#2920—611no—
315C2×C4×C4⋊C4—611no—
316#1509—614no—
317#1504—614no—
318#1503—612no—
319#1502—612no—
320C2×C61—22no—
321C2×C61—82no—
322C2×C61C2×#41011yescharacteristic
323C2×C61C2×#41711yescharacteristic
324C2×C61C22×#10411yescharacteristic
325D61—21no—
326D61—21no—
327D61—22no—
328#533—611no—
329#533—611no—
330#533—611no—
331#532—611no—
332#532—611no—
333#532#692311yescharacteristic, complemented
334#529—612no—
335#529—612no—
336#529—1221no—
337#529—1221no—
338#529—1221no—
339#529—1221no—
340#525—612no—
341#525—1221no—
342#525—1221no—
343C4×#41—612no—
344C4×#41—1221no—
345C4×#41—1221no—
346C22×C4⋊C4—1221no—
347C22×C42—611no—
348C22×C42—1221no—
349#432—612no—
350#432—1221no—
351#431—612no—
352#431—1221no—
353#423—1221no—
354#407—612no—
355C4×M16—1221no—
356C4×C4⋊C4—612no—
357C4×C4⋊C4—612no—
358C4×C4⋊C4—1221no—
359C4×C4⋊C4—1221no—
360C2×#95—612no—
361#328—618no—
362#327—618no—
363C61#1754611yescharacteristic, complemented, Sylow
364C2×#41—1221no—
365C2×#41—1221no—
366C2×#41C2×#692312yes—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—1222no—
371C2×M16—1222no—
372C4⋊Q8—611no—
373C4⋊Q8—611no—
374C4⋊Q8C2×#692311yescharacteristic, complemented
375#127C2×#692311yescharacteristic, complemented
376#126—1222no—
377#126—1222no—
378#125—612no—
379#125—1221no—
380#125—1221no—
381#124—1221no—
382#124—1221no—
383#124C2×#692312yescomplemented
384#123—1222no—
385#123—1222no—
386#123—1222no—
387C22⋊Q8—612no—
388C22⋊Q8—612no—
389C22⋊Q8—1221no—
390C22⋊Q8—1221no—
391C22⋊Q8—1221no—
392C22⋊Q8—1221no—
393#121—21no—
394#121—21no—
395#121—612no—
396#121—612no—
397#121—1221no—
398#121—1221no—
399#120—1222no—
400C4×Q8—612no—
401C4×Q8—612no—
402C4×Q8—1221no—
403C4×Q8—1221no—
404C4×Q8—1221no—
405C4×Q8—1221no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—612no—
409C4×D4—612no—
410C4×D4—1221no—
411C4×D4—1221no—
412C4×D4—1222no—
413C4×D4—1222no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—1222no—
418#117—612no—
419#117—1222no—
420#117—1222no—
421#117—1222no—
422#117—1221no—
423#117—1221no—
424C2×C4⋊C4—1222no—
425C2×C4⋊C4—1222no—
426C2×C4⋊C4—1228no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—1222no—
439C2×C42—1222no—
440C2×C42—1222no—
441C2×C42—2444no—
442C2×C42C2×#692311yescharacteristic
443C4⋊C8—1222no—
444C4⋊C8—1222no—
445C22⋊C8—614no—
446C22⋊C8—1222no—
447#97—1222no—
448C4×C8—1222no—
449#95—614no—
450#95—1222no—
451C24—611no—
452#41—44no—
453#41—2442no—
454#41—2442no—
455#41—2444no—
456C2×Q8—1221no—
457C2×Q8—1221no—
458C2×Q8C22×#692312yes—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4C22×#692312yes—
465C22×C4—22no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—1222no—
482C22×C4—1224no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1224no—
487C22×C4—1228no—
488C22×C4—2442no—
489C22×C4—2444no—
490C22×C4—2444no—
491C22×C4C22⋊#692311yescharacteristic
492C22×C4C22⋊#692311yescharacteristic
493C22×C4C22×#692311yescharacteristic
494M16—2444no—
495C2×C8—1224no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—612no—
499C4⋊C4—612no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1228no—
505C4⋊C4—1228no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C22⋊C4—1222no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—1222no—
532C42—1222no—
533C42—1222no—
534C42—2444no—
535C42—2444no—
536C42C22⋊#692311yescharacteristic
537C42C22⋊#692311yescharacteristic
538C42C22×#692311yescharacteristic
539C42C22×#692311yescharacteristic
540C23—22no—
541C23—611no—
542C23—611no—
543C23—1222no—
544C23—1221no—
545C23—1221no—
546C23—1222no—
547C23C2×C22⋊#692311yescharacteristic
548Q8—42no—
549Q8—2442no—
550Q8—2442no—
551D4—42no—
552D4—44no—
553D4—42no—
554D4—42no—
555D4—2442no—
556D4—2442no—
557D4—2444no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—44no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—612no—
566C2×C4—612no—
567C2×C4—614no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1228no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2444no—
590C2×C4—2444no—
591C2×C4—2444no—
592C2×C4—24416no—
593C2×C4—2444no—
594C2×C4C2×C22⋊#692311yescharacteristic
595C2×C4C2×C22⋊#692311yescharacteristic
596C2×C4C2×C22⋊#692311yescharacteristic
597C2×C4C2×C22⋊#692311yescharacteristic
598C2×C4C2×C22⋊#692311yescharacteristic
599C2×C4C23×#692311yescharacteristic
600C8—2444no—
601C22—21no—
602C22—21no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—611no—
607C22—611no—
608C22—612no—
609C22—1224no—
610C22—1224no—
611C22—1221no—
612C22—1221no—
613C22—1221no—
614C22—1221no—
615C22#1684074212yes—
616C22C22×C22⋊#692311yescharacteristic
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—42no—
622C4—612no—
623C4—612no—
624C4—1221no—
625C4—1221no—
626C4—1221no—
627C4—1221no—
628C4—2448no—
629C4—2442no—
630C4—2442no—
631C4#1684075312yes—
632C4D61⋊#10412yes—
633C2—22no—
634C2—82no—
635C2—1221no—
636C2—1221no—
637C2—1222no—
638C2C2×#1684074211yescharacteristic
639C2C2×#1684075311yescharacteristic
640C2C2×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#17546
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×C4×C4⋊#6923C2semidirect
3. #21461220C2semidirect
4. #21461205C2semidirect
5. #21461203C2semidirect
6. #21461199C2semidirect
24. #16840319C4semidirect
25. #16840317C4semidirect
27. #16840310C4semidirect
33. #16840291C4semidirect
38. #41×Dic61C4semidirect
42. C61×#532C4semidirect
64. #14519777C2×C4semidirect
65. #14519777C2×C4semidirect
68. #14519769C2×C4semidirect
87. Q8×Dic61C2×C4semidirect
88. Q8×Dic61C2×C4semidirect
97. D4×Dic61C2×C4semidirect
98. D4×Dic61C2×C4semidirect
122. C4⋊Q8×C61C2×C4semidirect
123. #127×C61C2×C4semidirect
124. #124×C61C2×C4semidirect
333. #532#6923semidirect
363. C61#17546semidirect
374. C4⋊Q8C2×#6923semidirect
375. #127C2×#6923semidirect
383. #124C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624972
C2×C4×C4⋊#69232
#214612202
#214612052
#214612032
#214611992
#214591142
#1754661