Finite Group Databasebeta

← #29646504

Subgroups — #29646504

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#21454932C211yesmaximal, characteristic, complemented
3#21454785C211yesmaximal, characteristic, complemented
4#21444264C212yesmaximal, complemented
5#21444255C212yesmaximal, complemented
6#21444250C212yesmaximal, complemented
7#21444246C212yesmaximal, complemented
8#21444213C211yesmaximal, characteristic, complemented
9#21444206C211yesmaximal, characteristic, complemented
10C2×#16839494C211yesmaximal, characteristic, complemented
11C61×#1476C211yesmaximal, characteristic, complemented
12C2×#14519824C411yescharacteristic
13#16840245C411yescharacteristic
14#16840242—21no—
15#16840242C411yescharacteristic
16#16840241—22no—
17#16840241C412yes—
18#16840239—21no—
19#16840239C411yescharacteristic
20#16840238C412yes—
21C4×#11758222—21no—
22C4×#11758222C2211yescharacteristic
23C4×#11758224—22no—
24C4×#11758224C2212yes—
25C2×C4×Dic122—21no—
26C2×C4×Dic122C2211yescharacteristic
27C4×Q8×D61C2212yes—
28#16839892—21no—
29#16839892—21no—
30#16839841—21no—
31#16839841—21no—
32#16839833—22no—
33#16839830—22no—
34#16839818C2212yes—
35#16839815C2211yescharacteristic
36#16839813C2212yes—
37#16839784C2212yes—
38C2×C4⋊#92418C2211yescharacteristic
39C4×#11758189C2212yes—
40#16839494C2212yes—
41#16839494C2212yes—
42Q8⋊#92418C2212yes—
43#16839492C2212yes—
44#16839492C2212yes—
45D4⋊#92418C2212yes—
46C4×#41×C61C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C2×C4×C8×C61C2211yescharacteristic
49C61×Q8⋊C8C2211yescharacteristic
50C61×Q8⋊C8C2211yescharacteristic
51C61×D4⋊C8C2211yescharacteristic
52C61×D4⋊C8C2211yescharacteristic
53#14519824—24no—
54#14519824—24no—
55C2×#11758222—21no—
56C2×#11758222C2×C411yescharacteristic
57C2×#11758224—22no—
58C2×#11758224C2×C412yes—
59C22×Dic122—21no—
60C22×Dic122C2×C411yescharacteristic
61C2×Q8×D61C2×C412yes—
62C2×#11758189—22no—
63C2×#11758189—22no—
64C22×#92418—21no—
65Q8×Dic61C2×C412yes—
66C4×Dic122—21no—
67C4×Dic122—21no—
68C4×Dic122—21no—
69C4×Dic122—21no—
70C4×Dic122—21no—
71C4×Dic122—22no—
72C4×Dic122—22no—
73C4×Dic122C2×C412yes—
74C4×Dic122D411yescharacteristic
75C4×Dic122D411yescharacteristic
76C4×Dic122C2312yes—
77#14519742—22no—
78#14519742—22no—
79#14519742C2×C412yes—
80#14519742C2×C412yes—
81C4×D244—21no—
82C4×D244D411yescharacteristic
83C4×D244D411yescharacteristic
84D4×Dic61—22no—
85D4×Dic61C2×C412yes—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61D412yes—
89C4×C22⋊D61D412yes—
90#14519737—22no—
91#14519737—22no—
92#14519737—22no—
93#14519736—21no—
94#14519736C2×C411yescharacteristic
95#14519735—22no—
96#14519735C2×C412yes—
97#14519734—22no—
98#14519734C2×C412yes—
99#14519733—22no—
100#14519733—22no—
101#14519733—22no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61C2×C411yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—22no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61C2×C412yes—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—22no—
110C42×D61—22no—
111C42×D61C2312yes—
112C4⋊#92418—21no—
113C4⋊#92418—21no—
114C4⋊#92418C2312yes—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118#14519689—22no—
119#14519689—22no—
120#14519687—22no—
121#14519687—22no—
122C4×#92418C2312yes—
123C2×#41×C61C2×C411yescharacteristic
124C22×C8×C61—21no—
125C4×Q8×C61C2×C411yescharacteristic
126C4×Q8×C61C2311yescharacteristic
127C4×D4×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61C2×C411yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132#117×C61C2×C411yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C22⋊C8×C61—21no—
138C4×C8×C61—21no—
139C4×C8×C61—21no—
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142#41×C61—22no—
143#41×C61M1614yescomplemented
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61C22⋊C412yes—
155C22×Dic61—21no—
156C22×Dic61—22no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159Q8×D61—24no—
160Q8×D61—24no—
161#11758224—216no—
162#11758224—24no—
163#11758224—24no—
164#11758222—28no—
165#11758222—22no—
166#11758222—22no—
167C2×D244C22⋊C411yescharacteristic
168C2×C4×D61—22no—
169C2×C4×D61—22no—
170C2×C4×D61C22×C412yes—
171C2×C4×D61C2×D412yes—
172C2×C4×D61C2×D412yes—
173C2×Dic122—28no—
174C2×Dic122—21no—
175C2×Dic122—22no—
176C2×Dic122—22no—
177C2×Dic122C22⋊C411yescharacteristic
178C2×Dic122M1614yescomplemented
179C2×Dic122C22×C412yes—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—42no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61C22×C411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61—21no—
195C42×C61C22×C411yescharacteristic
196C42×C61C2×D411yescharacteristic
197C42×C61C2×D411yescharacteristic
198C42×C61C2411yescharacteristic
199C22⋊Dic61—22no—
200C22⋊Dic61C22⋊C412yes—
201#11758198—22no—
202#11758198C22⋊C412yes—
203#11758198C22⋊C412yes—
204C4⋊Dic61—21no—
205C4⋊Dic61—22no—
206C4⋊Dic61C22⋊C411yescharacteristic
207C4⋊Dic61C22⋊C411yescharacteristic
208C4⋊Dic61C22×C412yes—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—22no—
214#11758196C22⋊C412yes—
215#11758196C22⋊C412yes—
216C4×Dic61—22no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—22no—
220C4×Dic61—22no—
221C4×Dic61—22no—
222C4×Dic61C22×C412yes—
223C4×Dic61C2×D412yes—
224C4×Dic61C2×D412yes—
225C2×#92418—22no—
226C2×#92418—22no—
227C2×#92418—81no—
228#11758189—44no—
229#11758189—82no—
230C23×C61—21no—
231C23×C61C2×C22⋊C411yescharacteristic
232C22×D61C2×C22⋊C412yes—
233Q8×C61—21no—
234Q8×C61C2×M1612yes—
235D4×C61—24no—
236D4×C61—21no—
237D4×C61C2×M1612yes—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—24no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—81no—
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×M1612yes—
252C2×C4×C61C2×M1612yes—
253C2×C4×C61C23×C411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C2×C4×C61C22×D411yescharacteristic
256C22⋊D61—28no—
257C22⋊D61—24no—
258C2×Dic61—28no—
259C2×Dic61—22no—
260C2×Dic61—24no—
261C2×Dic61—22no—
262C2×Dic61—82no—
263C2×Dic61—81no—
264C2×Dic61C2×C22⋊C412yes—
265C2×Dic61C2×C22⋊C412yes—
266C2×Dic61C2×C22⋊C412yes—
267D244—22no—
268C4×D61—28no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—42no—
274C4×D61—82no—
275Dic122—28no—
276Dic122—22no—
277Dic122—22no—
278Dic122—24no—
279Dic122C2×M1614yes—
280C8×C61—22no—
281C8×C61—41no—
282C8×C61—41no—
283C8×C61—41no—
284#92418—42no—
285#92418—42no—
286#17454—611nomaximal, Sylow
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—22no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61#40712yes—
293C22×C61C22×C22⋊C411yescharacteristic
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C4×C61—22no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61#40712yes—
304C4×C61C22×M1611yescharacteristic
305C4×C61C22×M1611yescharacteristic
306C4×C61#57711yescharacteristic
307C4×C61#57811yescharacteristic
308Dic61—22no—
309Dic61—24no—
310Dic61—22no—
311Dic61—22no—
312Dic61—42no—
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#1476D6111yescharacteristic, complemented
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—1221no—
335#520—1222no—
336#519—612no—
337#519—611no—
338#519—1221no—
339C4×#41—611no—
340C4×#41—612no—
341C4×#41—1221no—
342C4×#41—1222no—
343C4×#41C2×D6111yescharacteristic
344C2×C4×Q8—612no—
345C2×C4×Q8—611no—
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#431C2×D6111yescharacteristic
357#423—612no—
358C2×C4⋊C8—611no—
359C4×M16—612no—
360C2×C4×C8C2×D6111yescharacteristic
361Q8⋊C8—612no—
362Q8⋊C8—612no—
363Q8⋊C8—612no—
364Q8⋊C8—612no—
365Q8⋊C8—612no—
366Q8⋊C8C2×D6111yescharacteristic
367Q8⋊C8C2×D6111yescharacteristic
368D4⋊C8—612no—
369D4⋊C8C2×D6111yescharacteristic
370D4⋊C8C2×D6111yescharacteristic
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—612no—
380C22×Q8—611no—
381C22×Q8—1221no—
382C2×M16—1222no—
383C2×M16—1222no—
384C22×C8—21no—
385C22×C8—1221no—
386C4×Q8—611no—
387C4×Q8—611no—
388C4×Q8—612no—
389C4×Q8—612no—
390C4×Q8—612no—
391C4×Q8—612no—
392C4×Q8—612no—
393C4×Q8—1222no—
394C4×Q8—1221no—
395C4×Q8—1222no—
396C4×Q8—1221no—
397C4×Q8—1221no—
398C4×Q8—1222no—
399C4×Q8—1222no—
400C4×Q8—1221no—
401C4×Q8—1221no—
402C4×Q8C4×D6111yescharacteristic
403C4×Q8C22×D6111yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—612no—
407C4×D4—612no—
408C4×D4—612no—
409C4×D4—611no—
410C4×D4—611no—
411C4×D4—1221no—
412C4×D4—1222no—
413C4×D4—1222no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—1222no—
418C4×D4C4×D6111yescharacteristic
419C4×D4C22×D6111yescharacteristic
420#117—21no—
421#117—611no—
422#117—612no—
423#117—612no—
424#117—1222no—
425#117—1222no—
426#117—1222no—
427#117—1222no—
428#117—1222no—
429#117—1221no—
430#117C4×D6111yescharacteristic
431C2×C4⋊C4—611no—
432C2×C4⋊C4—612no—
433C2×C4⋊C4—1222no—
434C2×C4⋊C4—1222no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C42—21no—
438C2×C42—612no—
439C2×C42—1222no—
440C2×C42—1222no—
441C2×C42—1221no—
442C2×C42C22×D6111yescharacteristic
443C4⋊C8—612no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C4⋊C8—1221no—
447C4⋊C8—1221no—
448C4⋊C8C22×D6111yescharacteristic
449C4⋊C8C22×D6111yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—1222no—
452C22⋊C8—1222no—
453C22⋊C8—1221no—
454#97—1222no—
455#97—1222no—
456C4×C8—21no—
457C4×C8—21no—
458C4×C8—612no—
459C4×C8C22×D6111yescharacteristic
460C4×C8C22×D6111yescharacteristic
461#41—22no—
462#41—1228no—
463#41—1224no—
464#41—12216no—
465#41—1224no—
466#41—1222no—
467#41—1222no—
468#41#1175818914yescomplemented
469C2×Q8—611no—
470C2×Q8—612no—
471C2×Q8—614no—
472C2×Q8—1222no—
473C2×Q8—1228no—
474C2×Q8—1224no—
475C2×Q8—1224no—
476C2×Q8—1221no—
477C2×Q8—1222no—
478C2×Q8C2×C4×D6111yescharacteristic
479C2×D4—21no—
480C2×D4—612no—
481C2×D4—611no—
482C2×D4—1222no—
483C2×D4C2×C4×D6111yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—612no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4C2×C4×D6111yescharacteristic
497C22×C4D4×D6111yescharacteristic
498C22×C4D4×D6111yescharacteristic
499M16—4882no—
500M16—2444no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—42no—
506C2×C8—1222no—
507C2×C8—1222no—
508C2×C8—4881no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—612no—
512C4⋊C4—611no—
513C4⋊C4—612no—
514C4⋊C4—611no—
515C4⋊C4—612no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1221no—
522C4⋊C4—1222no—
523C4⋊C4C2×C4×D6111yescharacteristic
524C4⋊C4C2×C4×D6111yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—612no—
529C22⋊C4—612no—
530C22⋊C4—612no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—612no—
537C42—612no—
538C42—612no—
539C42—1222no—
540C42—1222no—
541C42—1222no—
542C42—1222no—
543C42—1222no—
544C42—1222no—
545C42C2×C4×D6111yescharacteristic
546C42D4×D6111yescharacteristic
547C42D4×D6111yescharacteristic
548C42C23×D6111yescharacteristic
549C23—21no—
550C23—612no—
551C23C22⋊C4×D6111yescharacteristic
552Q8—21no—
553Q8—614no—
554Q8—1228no—
555Q8—1222no—
556Q8—1224no—
557Q8—1222no—
558Q8C2×#1175818912yes—
559D4—24no—
560D4—21no—
561D4—1228no—
562D4—1224no—
563D4—1222no—
564D4C2×#1175818912yes—
565C2×C4—21no—
566C2×C4—24no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—612no—
576C2×C4—612no—
577C2×C4—612no—
578C2×C4—1228no—
579C2×C4—1228no—
580C2×C4—1222no—
581C2×C4—1224no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—4882no—
588C2×C4—4882no—
589C2×C4—4881no—
590C2×C4—2442no—
591C2×C4C22⋊C4×D6111yescharacteristic
592C2×C4C22⋊C4×D6111yescharacteristic
593C2×C4C22⋊C4×D6111yescharacteristic
594C2×C4M16×D6112yes—
595C2×C4C2×#1175818912yes—
596C2×C4C22×C4×D6111yescharacteristic
597C2×C4C2×D4×D6111yescharacteristic
598C2×C4C2×D4×D6111yescharacteristic
599C8—22no—
600C8—41no—
601C8—41no—
602C8—41no—
603C8—2442no—
604C8—2442no—
605C22—21no—
606C22—21no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—1222no—
611C22—1222no—
612C22—1222no—
613C22#1683972412yes—
614C22C2×C22⋊C4×D6111yescharacteristic
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—1222no—
622C4—1222no—
623C4—1222no—
624C4—1224no—
625C4—2442no—
626C4#1683972412yes—
627C4C2×M16×D6111yescharacteristic
628C4C22×#1175818911yescharacteristic
629C4#1684056911yescharacteristic
630C4#1684057611yescharacteristic
631C2—22no—
632C2—42no—
633C2—2442no—
634C2C2×#1683972411yescharacteristic
635C2#2145434811yescharacteristic
636C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1476C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519824C4
cosocleC42×C61C24
hypercenter#1476D61
hypocenterC61#17454
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #21454932C2semidirect
3. #21454785C2semidirect
4. #21444264C2semidirect
5. #21444255C2semidirect
6. #21444250C2semidirect
7. #21444246C2semidirect
8. #21444213C2semidirect
9. #21444206C2semidirect
10. C2×#16839494C2semidirect
11. C61×#1476C2semidirect
143. #41×C61M16semidirect
178. C2×Dic122M16semidirect
322. #1476D61semidirect
371. C61#17454semidirect
468. #41#11758189semidirect

Maximal subgroups

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

subgroupindex
C4×#145198242
#214549322
#214547852
#214442642
#214442552
#214442502
#214442462
#214442132
#214442062
C2×#168394942
C61×#14762
#1745461