Finite Group Databasebeta

← #29646497

Subgroups — #29646497

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
1C4×#14519824C211yesmaximal, characteristic
2#21454786C211yesmaximal, characteristic, complemented
3#21444265C212yesmaximal, complemented
4#21444256C212yesmaximal, complemented
5#21444251C212yesmaximal, complemented
6#21444247C212yesmaximal, complemented
7#21444213C211yesmaximal, characteristic, complemented
8#21444204C211yesmaximal, characteristic, complemented
9#21444199C211yesmaximal, characteristic, complemented
10C2×#16839492C211yesmaximal, characteristic, complemented
11C61×#2989C211yesmaximal, characteristic, complemented
12C2×#14519824C411yescharacteristic
13#16840245C411yescharacteristic
14#16840242C412yes—
15#16840242C411yescharacteristic
16#16840241—22no—
17#16840241—21no—
18#16840239C412yes—
19#16840239C411yescharacteristic
20#16840238—21no—
21C4×#11758222C2211yescharacteristic
22C4×#11758222C2212yes—
23C4×#11758224—22no—
24C4×#11758224—21no—
25C2×C4×Dic122C2211yescharacteristic
26C2×C4×Dic122C2212yes—
27C4×Q8×D61—21no—
28#16839893—21no—
29#16839840—21no—
30#16839834—22no—
31#16839815C2211yescharacteristic
32#16839815C2212yes—
33C4×#11758194C2212yes—
34C2×C4×#92418C2211yescharacteristic
35#16839492C2212yes—
36#16839492C2212yes—
37#16839492C2211yescharacteristic
38#16839492C2211yescharacteristic
39#16839492C2212yes—
40#16839492C2212yes—
41#16839492C2212yes—
42#16839489C2211yescharacteristic
43#16839489C2211yescharacteristic
44#16839489C2212yes—
45C4×#41×C61C2211yescharacteristic
46C61×#446—21no—
47C61×#436—21no—
48C61×#435—22no—
49C61×#432C2212yes—
50C61×#431C2211yescharacteristic
51C61×#423C2212yes—
52C2×C4⋊C8×C61C2211yescharacteristic
53#14519824—24no—
54#14519824—24no—
55C2×#11758222C2×C412yes—
56C2×#11758222C2×C411yescharacteristic
57C2×#11758224—22no—
58C2×#11758224—21no—
59C22×Dic122C2×C412yes—
60C22×Dic122C2×C411yescharacteristic
61C2×Q8×D61—21no—
62C2×#11758194—22no—
63C22×#92418—21no—
64Q8×Dic61—21no—
65C4×Dic122—21no—
66C4×Dic122—22no—
67C4×Dic122—21no—
68C4×Dic122—22no—
69C4×Dic122C2×C412yes—
70C4×Dic122C2×C412yes—
71C4×Dic122C2×C412yes—
72C4×Dic122C2×C411yescharacteristic
73C4×Dic122C2×C412yes—
74C4×Dic122C2312yes—
75C4×Dic122C2311yescharacteristic
76#14519742—22no—
77#14519742—21no—
78#14519742—22no—
79#14519742—21no—
80C4×D244C2×C411yescharacteristic
81C4×D244C2×C412yes—
82C4×D244C2311yescharacteristic
83D4×Dic61—22no—
84D4×Dic61—21no—
85C4×C22⋊D61—21no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—21no—
88C4×C22⋊D61—22no—
89#14519737—22no—
90#14519737—22no—
91#14519737—22no—
92#14519736C2×C412yes—
93#14519736C2×C411yescharacteristic
94#14519735—22no—
95#14519735—21no—
96#14519734—21no—
97#14519734—22no—
98#14519733—22no—
99#14519733—22no—
100#14519733—22no—
101C2×C4⋊Dic61C2×C412yes—
102C2×C4⋊Dic61C2×C411yescharacteristic
103C2×#11758196—21no—
104C2×#11758196—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—22no—
109C42×D61—21no—
110C42×D61—22no—
111C4⋊#92418—22no—
112C4⋊#92418—21no—
113C22⋊#92418—21no—
114C22⋊#92418—22no—
115#14519688—22no—
116C4×#92418—21no—
117C4×#92418C2311yescharacteristic
118C4×#92418C2311yescharacteristic
119C4×#92418C2312yes—
120C2×#41×C61C2×C411yescharacteristic
121C2×M16×C61—22no—
122C22×C8×C61—21no—
123C4×Q8×C61D411yescharacteristic
124C4×Q8×C61D411yescharacteristic
125C4×D4×C61D412yes—
126C4×D4×C61D411yescharacteristic
127C4×D4×C61D412yes—
128C4×D4×C61D411yescharacteristic
129#117×C61C2×C412yes—
130#117×C61C2×C411yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2312yes—
133C4⋊C8×C61—21no—
134C4⋊C8×C61—22no—
135C4⋊C8×C61C2312yes—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61—22no—
140#97×C61—22no—
141C4×C8×C61—21no—
142#41×C61—22no—
143#41×C61—22no—
144C2×Q8×C61C22⋊C411yescharacteristic
145C2×D4×C61C22⋊C412yes—
146C2×D4×C61C22⋊C411yescharacteristic
147C22×C4×C61C22×C412yes—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D412yes—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—21no—
155C22×Dic61—22no—
156C22×Dic61—21no—
157C22×Dic61—22no—
158C22×Dic61—21no—
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—
180M16×C61—82no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—22no—
184C2×C8×C61—81no—
185C4⋊C4×C61C22⋊C412yes—
186C4⋊C4×C61C22⋊C411yescharacteristic
187C4⋊C4×C61C22⋊C412yes—
188C4⋊C4×C61C22⋊C411yescharacteristic
189C22⋊C4×C61C22⋊C412yes—
190C22⋊C4×C61C22⋊C412yes—
191C22⋊C4×C61C22⋊C412yes—
192C42×C61C22×C411yescharacteristic
193C42×C61C22×C412yes—
194C42×C61C2×D411yescharacteristic
195C42×C61C2×D412yes—
196C42×C61C2×D411yescharacteristic
197C42×C61C2×D412yes—
198C42×C61C2411yescharacteristic
199C22⋊Dic61—22no—
200C22⋊Dic61—21no—
201#11758198—21no—
202#11758198—22no—
203#11758198—21no—
204C4⋊Dic61—22no—
205C4⋊Dic61—21no—
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—21no—
220C4×Dic61—22no—
221C4×Dic61—22no—
222C4×Dic61—22no—
223C4×Dic61—21no—
224C4×Dic61—22no—
225#11758194—44no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—22no—
229C2×#92418—42no—
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—22no—
242C2×C4×C61—41no—
243C2×C4×C61—42no—
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C412yes—
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C412yes—
248C2×C4×C61C2×C22⋊C412yes—
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×M1612yes—
251C2×C4×C61C2×M1612yes—
252C2×C4×C61C23×C411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C22⋊D61—28no—
256C22⋊D61—24no—
257C2×Dic61—28no—
258C2×Dic61—21no—
259C2×Dic61—22no—
260C2×Dic61—24no—
261C2×Dic61—21no—
262C2×Dic61—22no—
263C2×Dic61—21no—
264C2×Dic61—81no—
265C2×Dic61—82no—
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—
280C8×C61—42no—
281C8×C61—41no—
282C8×C61—41no—
283#92418—22no—
284#92418—41no—
285#92418—42no—
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—21no—
299C4×C61—22no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—22no—
303C4×C61#40712yes—
304C4×C61C22×M1611yescharacteristic
305C4×C61C22×M1611yescharacteristic
306C4×C61#57711yescharacteristic
307C4×C61#57811yescharacteristic
308Dic61—22no—
309Dic61—24no—
310Dic61—41no—
311Dic61—42no—
312Dic61—41no—
313C4×2−1+4—611no—
314#2989D6111yescharacteristic, complemented
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—611no—
333#520—612no—
334#520—1222no—
335#520—1221no—
336#519—611no—
337#519—612no—
338#519—1221no—
339C4×#41—611no—
340C4×#41—612no—
341C4×#41—1222no—
342C4×#41—1221no—
343C4×#41C2×D6111yescharacteristic
344C2×C4×Q8—611no—
345C2×C4×Q8—612no—
346C2×C4×Q8—1221no—
347#446—21no—
348#446—1221no—
349#436—21no—
350#436—1221no—
351#435—22no—
352#435—1222no—
353#432C2×D6112yes—
354#431—611no—
355#431—612no—
356#431C2×D6111yescharacteristic
357#423C2×D6112yes—
358C2×C4⋊C8C2×D6111yescharacteristic
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×#41C4×D6111yescharacteristic
379C22×Q8—611no—
380C22×Q8—612no—
381C22×Q8—1221no—
382C2×M16—22no—
383C2×M16—1222no—
384C22×C8—21no—
385C22×C8—1221no—
386C4×Q8—612no—
387C4×Q8—612no—
388C4×Q8—612no—
389C4×Q8—611no—
390C4×Q8—612no—
391C4×Q8—612no—
392C4×Q8—611no—
393C4×Q8—1221no—
394C4×Q8—1222no—
395C4×Q8—1221no—
396C4×Q8—1222no—
397C4×Q8—1221no—
398C4×Q8—1221no—
399C4×Q8—1222no—
400C4×Q8—1221no—
401C4×Q8—1222no—
402C4×Q8D24411yescharacteristic
403C4×Q8C22⋊D6111yescharacteristic
404C4×D4—611no—
405C4×D4—612no—
406C4×D4—611no—
407C4×D4—1222no—
408C4×D4—1221no—
409C4×D4—1221no—
410C4×D4—1222no—
411C4×D4—1221no—
412C4×D4—1222no—
413C4×D4—1222no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4D24412yes—
417C4×D4D24411yescharacteristic
418C4×D4C22⋊D6112yes—
419C4×D4C22⋊D6111yescharacteristic
420#117—612no—
421#117—611no—
422#117—1222no—
423#117—1221no—
424#117—1222no—
425#117—1222no—
426#117—1222no—
427#117—1221no—
428#117—1222no—
429#117C4×D6112yes—
430#117C4×D6111yescharacteristic
431C2×C4⋊C4—612no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—1221no—
434C2×C4⋊C4—1222no—
435C2×C4⋊C4—1222no—
436C2×C4⋊C4—1221no—
437C2×C42—1221no—
438C2×C42—1222no—
439C2×C42—1221no—
440C2×C42—1222no—
441C2×C42C22×D6111yescharacteristic
442C2×C42C22×D6112yes—
443C4⋊C8—21no—
444C4⋊C8—22no—
445C4⋊C8—1222no—
446C4⋊C8—1221no—
447C4⋊C8C22×D6112yes—
448C4⋊C8C22×D6111yescharacteristic
449C4⋊C8C22×D6111yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—22no—
452C22⋊C8—1221no—
453C22⋊C8—1222no—
454#97—22no—
455#97—1222no—
456C4×C8—21no—
457C4×C8—611no—
458C4×C8—611no—
459C4×C8—612no—
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—612no—
470C2×Q8—611no—
471C2×Q8—614no—
472C2×Q8—1224no—
473C2×Q8—1224no—
474C2×Q8—1228no—
475C2×Q8—1222no—
476C2×Q8—1221no—
477C2×Q8—1222no—
478C2×Q8#1175819811yescharacteristic
479C2×D4—611no—
480C2×D4—1222no—
481C2×D4—1221no—
482C2×D4#1175819812yes—
483C2×D4#1175819811yescharacteristic
484C22×C4—1222no—
485C22×C4—1221no—
486C22×C4—1222no—
487C22×C4—1221no—
488C22×C4—1222no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1222no—
492C22×C4—1221no—
493C22×C4C2×C4×D6112yes—
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C2×D24411yescharacteristic
496C22×C4C2×D24412yes—
497C22×C4C2×C22⋊D6111yescharacteristic
498C22×C4C2×C22⋊D6112yes—
499M16—82no—
500M16—2444no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—22no—
504C2×C8—81no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1222no—
508C2×C8—2442no—
509C4⋊C4—611no—
510C4⋊C4—612no—
511C4⋊C4—611no—
512C4⋊C4—1222no—
513C4⋊C4—1221no—
514C4⋊C4—1222no—
515C4⋊C4—1221no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1221no—
520C4⋊C4—1222no—
521C4⋊C4#1175819812yes—
522C4⋊C4#1175819811yescharacteristic
523C4⋊C4#1175819812yes—
524C4⋊C4#1175819811yescharacteristic
525C22⋊C4—1222no—
526C22⋊C4—1221no—
527C22⋊C4—1221no—
528C22⋊C4—1221no—
529C22⋊C4—1222no—
530C22⋊C4#1175819812yes—
531C22⋊C4#1175819812yes—
532C22⋊C4#1175819812yes—
533C42—1222no—
534C42—1221no—
535C42—1222no—
536C42—1221no—
537C42—1221no—
538C42—1222no—
539C42—1222no—
540C42—1222no—
541C42—1222no—
542C42C2×C4×D6111yescharacteristic
543C42C2×C4×D6112yes—
544C42C2×D24411yescharacteristic
545C42C2×D24412yes—
546C42C2×C22⋊D6111yescharacteristic
547C42C2×C22⋊D6112yes—
548C42C23×D6111yescharacteristic
549C23—1221no—
550C23C2×#1175819812yes—
551C23C2×#1175819811yescharacteristic
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—22no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—1228no—
574C2×C4—1228no—
575C2×C4—1222no—
576C2×C4—1221no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—1221no—
580C2×C4—1222no—
581C2×C4—1221no—
582C2×C4—4881no—
583C2×C4—4882no—
584C2×C4—4881no—
585C2×C4—4882no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4C2×#1175819811yescharacteristic
589C2×C4C2×#1175819812yes—
590C2×C4C2×#1175819811yescharacteristic
591C2×C4C2×#1175819812yes—
592C2×C4C2×#1175819812yes—
593C2×C4C2×#1175819811yescharacteristic
594C2×C4M16×D6112yes—
595C2×C4M16×D6112yes—
596C2×C4C22×C4×D6111yescharacteristic
597C2×C4C22×C22⋊D6111yescharacteristic
598C2×C4C22×D24411yescharacteristic
599C8—42no—
600C8—41no—
601C8—41no—
602C8—1222no—
603C8—2441no—
604C8—2442no—
605C22—21no—
606C22—21no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—1222no—
611C22—2441no—
612C22—2441no—
613C22#1683972512yes—
614C22C22×#1175819811yescharacteristic
615C4—21no—
616C4—22no—
617C4—21no—
618C4—21no—
619C4—22no—
620C4—22no—
621C4—1224no—
622C4—1222no—
623C4—2441no—
624C4—2442no—
625C4—2441no—
626C4#1683972512yes—
627C4C2×M16×D6111yescharacteristic
628C4C2×M16×D6111yescharacteristic
629C4#1684057311yescharacteristic
630C4#1684057711yescharacteristic
631C2—22no—
632C2—42no—
633C2—2442no—
634C2C2×#1683972511yescharacteristic
635C2#2145434911yescharacteristic
636C2#2145436411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2989C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519824C4
cosocleC42×C61C24
hypercenter#2989D61
hypocenterC61#17454
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
2. #21454786C2semidirect
3. #21444265C2semidirect
4. #21444256C2semidirect
5. #21444251C2semidirect
6. #21444247C2semidirect
7. #21444213C2semidirect
8. #21444204C2semidirect
9. #21444199C2semidirect
10. C2×#16839492C2semidirect
11. C61×#2989C2semidirect
165. #11758222M16semidirect
177. C2×Dic122M16semidirect
314. #2989D61semidirect
371. C61#17454semidirect

Maximal subgroups

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

subgroupindex
C4×#145198242
#214547862
#214442652
#214442562
#214442512
#214442472
#214442132
#214442042
#214441992
C2×#168394922
C61×#29892
#1745461