Finite Group Databasebeta

← #29646447

Subgroups — #29646447

Order 15616.

1332 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758226C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444266C211yesmaximal, characteristic, complemented
5#21444263C211yesmaximal, characteristic, complemented
6#21444261C211yesmaximal, characteristic, complemented
7#21444257C214yesmaximal, complemented
8#21444200C214yesmaximal, complemented
9C61×#1491C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic
11C2×M16×D61—21no—
12C4×#11758226—21no—
13C4×#11758226—21no—
14C4×#11758226—21no—
15C4×#11758226—21no—
16C4×#11758226C412yes—
17C4×#11758226C412yes—
18C4×#11758226C2212yes—
19C4×#11758226C2212yes—
20C2×Q8×Dic61C411yescharacteristic
21C2×C4×D244—21no—
22C2×C4×D244C2211yescharacteristic
23C2×#14519739—21no—
24C2×#14519739C411yescharacteristic
25C2×#14519735—21no—
26C2×#14519735C411yescharacteristic
27C2×C42×D61—21no—
28C2×C42×D61C2211yescharacteristic
29#16839819C2211yescharacteristic
30#16839817—21no—
31#16839814C2212yescomplemented
32#16839812—21no—
33#16839784C2212yescomplemented
34#16839724—21no—
35C4×#11758194C2211yescharacteristic
36#16839714—21no—
37#16839714—21no—
38M16×Dic61—21no—
39C4×#11758189C2212yescomplemented
40#97×D61—21no—
41C4×C8×D61C2212yescomplemented
42Q8⋊#92418C2214yescomplemented
43#16839491C2214yescomplemented
44#16839489C2214yescomplemented
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C2×#11758226—28no—
50C2×#11758226—21no—
51C2×#11758226—21no—
52C2×#11758226C2×C412yes—
53C2×#11758226C2×C412yes—
54C22×D244—21no—
55C22×D244C2×C411yescharacteristic
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C2×#11758194—21no—
63C2×#11758189—22no—
64C2×#11758189—22no—
65M16×D61—28no—
66C2×C8×D61—22no—
67Q8×Dic61—21no—
68Q8×Dic61—21no—
69Q8×Dic61C2×C412yes—
70Q8×Dic61C2×C412yes—
71C4×D244—22no—
72C4×D244—22no—
73C4×D244—22no—
74C4×D244—22no—
75C4×D244—21no—
76C4×D244—21no—
77C4×D244C2×C412yes—
78C4×D244C2312yes—
79#14519739—22no—
80#14519739—22no—
81#14519739—22no—
82#14519739—22no—
83#14519739—21no—
84#14519739—21no—
85#14519739C2×C412yes—
86#14519739C2×C412yes—
87#14519735—21no—
88#14519735—21no—
89#14519735—22no—
90#14519735—22no—
91#14519735—22no—
92#14519735—22no—
93#14519735C2×C412yes—
94#14519735C2×C412yes—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C42×D61—22no—
106C42×D61—22no—
107C42×D61—22no—
108C42×D61—22no—
109C42×D61C2×C411yescharacteristic
110C42×D61C2×C411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61C2311yescharacteristic
116C42×D61C2311yescharacteristic
117C4⋊#92418C2312yes—
118#14519706—22no—
119C22⋊#92418—21no—
120#14519689—22no—
121#14519688—21no—
122#14519688—21no—
123#14519687—22no—
124C4×#92418C2312yes—
125C8×Dic61—22no—
126C8×Dic61—22no—
127C22×Q8×C61C2×C411yescharacteristic
128C2×M16×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61—21no—
131C4×Q8×C61C2×C412yes—
132C4×Q8×C61C2312yes—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C42×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61C2312yes—
138C22⋊C8×C61—21no—
139#97×C61—21no—
140#97×C61—21no—
141C4×C8×C61C2312yes—
142C23×D61—21no—
143C23×D61C22⋊C411yescharacteristic
144C2×Q8×C61—24no—
145C2×Q8×C61—21no—
146C2×Q8×C61C22×C412yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×Dic61—21no—
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C22⋊C411yescharacteristic
155C22×Dic61C22⋊C411yescharacteristic
156#11758226—28no—
157#11758226—28no—
158#11758226—24no—
159#11758226—24no—
160#11758226—24no—
161#11758226M1618yescomplemented
162C2×D244—28no—
163C2×D244—22no—
164C2×D244—22no—
165C2×D244—21no—
166C2×D244—24no—
167C2×D244C22×C412yes—
168C2×C4×D61—28no—
169C2×C4×D61—24no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—24no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—42no—
178C2×C4×D61—44no—
179C2×C4×D61—44no—
180C2×C4×D61C22⋊C411yescharacteristic
181C2×C4×D61C22⋊C411yescharacteristic
182C2×C4×D61C22⋊C411yescharacteristic
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22×C411yescharacteristic
187C2×C4×D61C22×C411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192M16×C61—24no—
193C2×C8×C61—22no—
194C2×C8×C61—22no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61C22×C412yes—
199C42×C61—22no—
200C42×C61—22no—
201C42×C61C22×C411yescharacteristic
202C42×C61C2×D411yescharacteristic
203C42×C61C2×D411yescharacteristic
204C42×C61C2411yescharacteristic
205#11758198—22no—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210#11758198—22no—
211C4⋊Dic61—21no—
212C4⋊Dic61—22no—
213C4⋊Dic61—22no—
214C4⋊Dic61C22×C412yes—
215C4×Dic61—22no—
216C4×Dic61—22no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22×C411yescharacteristic
226C4×Dic61C22×C411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231#11758194—24no—
232C2×#92418—22no—
233C2×#92418—22no—
234#11758189—28no—
235#11758189—44no—
236C8×D61—28no—
237C23×C61C2×C22⋊C411yescharacteristic
238C22×D61—24no—
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—41no—
243C22×D61—42no—
244C22×D61—42no—
245C22×D61C2×C22⋊C411yescharacteristic
246C22×D61C2×C22⋊C411yescharacteristic
247Q8×C61—24no—
248Q8×C61—22no—
249Q8×C61C2×M1614yescomplemented
250C2×C4×C61—24no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—42no—
257C2×C4×C61C2×C22⋊C411yescharacteristic
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C23×C411yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—41no—
266C2×Dic61—42no—
267C2×Dic61#10414yes—
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274D244—28no—
275D244—24no—
276D244—28no—
277D244—22no—
278D244C2×M1614yescomplemented
279C4×D61—28no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—28no—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—41no—
291C4×D61—41no—
292C4×D61—44no—
293C4×D61—44no—
294C4×D61—44no—
295C4×D61—44no—
296C4×D61C2×M1614yes—
297C8×C61—24no—
298C8×C61—42no—
299#92418—24no—
300#92418—42no—
301#17447—611nomaximal, Sylow
302C22×C61—21no—
303C22×C61—21no—
304C22×C61C2×#10412yes—
305C22×C61C22×C22⋊C411yescharacteristic
306C2×D61—21no—
307C2×D61—21no—
308C2×D61—21no—
309C2×D61—24no—
310C2×D61—21no—
311C2×D61—21no—
312C2×D61—44no—
313C2×D61—48no—
314C2×D61—42no—
315C2×D61—42no—
316C2×D61#40712yes—
317C4×C61—24no—
318C4×C61—21no—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—42no—
323C4×C61C22×M1612yes—
324C4×C61#57512yes—
325Dic61—21no—
326Dic61—21no—
327Dic61—21no—
328Dic61—42no—
329Dic61#40712yes—
330Dic61C2×#10412yes—
331Dic61C2×#10412yes—
332C2×C4×#41—611no—
333#2920—611no—
334C2×C4×M16—611no—
335#1491—611no—
336#1491D6111yescharacteristic, complemented
337#1490—611no—
338#1490—611no—
339#1489—614no—
340#1476—614no—
341C2×C61—22no—
342C2×C61C2×#40711yescharacteristic
343C2×C61#289611yescharacteristic
344C2×C61C22×#10411yescharacteristic
345D61—22no—
346D61—41no—
347D61—44no—
348C22×#41—611no—
349C22×M16—1221no—
350C4×#41—612no—
351C4×#41—612no—
352C4×#41—612no—
353C4×#41—612no—
354C4×#41—1221no—
355C4×#41—1221no—
356C4×#41—1221no—
357C4×#41—1221no—
358C2×C4×Q8—611no—
359C2×C4×Q8C2×D6111yescharacteristic
360C2×C4×D4—611no—
361C2×C4×D4—611no—
362C2×C4×D4—1221no—
363C2×C4×D4—1221no—
364C2×#117—611no—
365C2×#117—1221no—
366C22×C42—611no—
367C22×C42—1221no—
368#432—611no—
369#432—1221no—
370#432C2×D6111yescharacteristic
371#431—612no—
372#431—1221no—
373#423—612no—
374#407—1221no—
375C4×M16—611no—
376C4×M16—612no—
377C4×M16—1221no—
378C4×M16—1221no—
379C4×M16—1221no—
380C4×M16C2×D6111yescharacteristic
381C2×#97—1221no—
382C2×C4×C8—612no—
383Q8⋊C8—614no—
384Q8⋊C8C2×D6114yescomplemented
385D4⋊C8—614no—
386D4⋊C8—614no—
387C61#1744711yescharacteristic, complemented, Sylow
388C2×#41—612no—
389C2×#41—612no—
390C2×#41—1221no—
391C2×#41—1221no—
392C2×#41—1228no—
393C22×Q8C4×D6111yescharacteristic
394C22×D4—611no—
395C22×D4—1221no—
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—611no—
399C23×C4—1221no—
400C23×C4—1221no—
401C23×C4—1221no—
402C2×M16—21no—
403C2×M16—1222no—
404C2×M16—1222no—
405C2×M16—1228no—
406C2×M16—1221no—
407C22×C8—1222no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—612no—
411C4×Q8—612no—
412C4×Q8—1221no—
413C4×Q8—1221no—
414C4×Q8C4×D6112yes—
415C4×Q8C22×D6112yes—
416C4×D4—612no—
417C4×D4—612no—
418C4×D4—612no—
419C4×D4—612no—
420C4×D4—1222no—
421C4×D4—1222no—
422C4×D4—1222no—
423C4×D4—1222no—
424C4×D4—1221no—
425C4×D4—1221no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1221no—
431C4×D4—1221no—
432#117—612no—
433#117—612no—
434#117—1222no—
435#117—1222no—
436#117—1222no—
437#117—1222no—
438#117—1221no—
439#117—1221no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4C4×D6111yescharacteristic
444C2×C22⋊C4—1221no—
445C2×C22⋊C4—1221no—
446C2×C22⋊C4—1221no—
447C2×C42—21no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—1222no—
460C2×C42—1222no—
461C2×C42—1222no—
462C2×C42—1222no—
463C2×C42—1221no—
464C2×C42—1221no—
465C2×C42C22×D6111yescharacteristic
466C4⋊C8—612no—
467C4⋊C8—1222no—
468C4⋊C8C22×D6112yes—
469C22⋊C8—21no—
470C22⋊C8—1222no—
471C22⋊C8—1221no—
472#97—21no—
473#97—21no—
474#97—1222no—
475#97—1221no—
476#97—1221no—
477C4×C8—612no—
478C4×C8—1222no—
479C4×C8—1222no—
480C4×C8C22×D6112yes—
481C24—611no—
482C24—1221no—
483#41—618no—
484#41—1224no—
485#41—1224no—
486#41—1228no—
487#41—1228no—
488#41—1224no—
489C2×Q8—24no—
490C2×Q8—21no—
491C2×Q8C2×C4×D6112yes—
492C2×D4—612no—
493C2×D4—1224no—
494C2×D4—1222no—
495C2×D4—1222no—
496C2×D4—1228no—
497C2×D4—1221no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1224no—
518C22×C4—1224no—
519C22×C4—1222no—
520C22×C4—1222no—
521C22×C4—1228no—
522C22×C4—1221no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—2442no—
526C22×C4—2444no—
527C22×C4—2444no—
528C22×C4C2×C4×D6111yescharacteristic
529C22×C4D4×D6111yescharacteristic
530C22×C4D4×D6111yescharacteristic
531M16—24no—
532M16—1228no—
533M16—1224no—
534M16—2444no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—1228no—
538C2×C8—1222no—
539C2×C8—1222no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—612no—
544C4⋊C4—1222no—
545C4⋊C4—1222no—
546C4⋊C4—1221no—
547C4⋊C4C2×C4×D6112yes—
548C22⋊C4—1222no—
549C22⋊C4—1222no—
550C22⋊C4—1222no—
551C22⋊C4—1222no—
552C22⋊C4—1222no—
553C22⋊C4—1222no—
554C42—22no—
555C42—22no—
556C42—611no—
557C42—611no—
558C42—611no—
559C42—611no—
560C42—611no—
561C42—611no—
562C42—611no—
563C42—611no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—1222no—
569C42—1222no—
570C42—1222no—
571C42—1222no—
572C42C2×C4×D6111yescharacteristic
573C42D4×D6111yescharacteristic
574C42D4×D6111yescharacteristic
575C42C23×D6111yescharacteristic
576C23—611no—
577C23—611no—
578C23—1222no—
579C23—1224no—
580C23—1222no—
581C23—1222no—
582C23—2441no—
583C23—2442no—
584C23—2442no—
585C23C22⋊C4×D6111yescharacteristic
586Q8—24no—
587Q8—22no—
588Q8M16×D6114yescomplemented
589D4—614no—
590D4—1228no—
591D4—1228no—
592D4—1224no—
593D4—1222no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—42no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
604C2×C4—614no—
605C2×C4—614no—
606C2×C4—611no—
607C2×C4—611no—
608C2×C4—611no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1228no—
615C2×C4—1222no—
616C2×C4—1228no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2444no—
625C2×C4—2444no—
626C2×C4—2444no—
627C2×C4—2441no—
628C2×C4—2442no—
629C2×C4—2444no—
630C2×C4C22⋊C4×D6111yescharacteristic
631C2×C4C22⋊C4×D6111yescharacteristic
632C2×C4C22⋊C4×D6111yescharacteristic
633C2×C4C22×C4×D6111yescharacteristic
634C2×C4C2×D4×D6111yescharacteristic
635C2×C4C2×D4×D6111yescharacteristic
636C8—24no—
637C8—42no—
638C8—1224no—
639C8—2442no—
640C22—21no—
641C22—21no—
642C22—612no—
643C22—1221no—
644C22—1221no—
645C22—1221no—
646C22—1221no—
647C22—1224no—
648C22—1221no—
649C22—2444no—
650C22—2448no—
651C22—2442no—
652C22—2442no—
653C22#104×D6112yes—
654C22C2×C22⋊C4×D6111yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—24no—
659C4—21no—
660C4—42no—
661C4—612no—
662C4—612no—
663C4—612no—
664C4—1221no—
665C4—1221no—
666C4—1221no—
667C4—2442no—
668C4C2×M16×D6112yes—
669C4#1684056112yes—
670C2—22no—
671C2—1222no—
672C2—2441no—
673C2—2444no—
674C2#407×D6111yescharacteristic
675C2#2145433711yescharacteristic
676C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1491C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758226C4
cosocleC42×C61C24
hypercenter#1491D61
hypocenterC61#17447
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. C4×M16×D61C2semidirect
4. #21444266C2semidirect
5. #21444263C2semidirect
6. #21444261C2semidirect
7. #21444257C2semidirect
8. #21444200C2semidirect
9. C61×#1491C2semidirect
31. #16839814C22semidirect
33. #16839784C22semidirect
39. C4×#11758189C22semidirect
41. C4×C8×D61C22semidirect
42. Q8⋊#92418C22semidirect
43. #16839491C22semidirect
44. #16839489C22semidirect
48. C61×Q8⋊C8C22semidirect
161. #11758226M16semidirect
249. Q8×C61C2×M16semidirect
278. D244C2×M16semidirect
336. #1491D61semidirect
384. Q8⋊C8C2×D61semidirect
387. C61#17447semidirect
588. Q8M16×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582262
#214544492
C4×M16×D612
#214442662
#214442632
#214442612
#214442572
#214442002
C61×#14912
#1744761