Finite Group Databasebeta

← #29646466

Subgroups — #29646466

Order 15616.

1246 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758226C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3#21454447C211yesmaximal, characteristic, complemented
4#21444257C214yesmaximal, complemented
5#21444252C214yesmaximal, complemented
6#21444214C211yesmaximal, characteristic, complemented
7#21444211C211yesmaximal, characteristic, complemented
8#21444209C211yesmaximal, characteristic, complemented
9C61×#1479C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic
11C4×#11758226—21no—
12C4×#11758226—21no—
13C4×#11758226—21no—
14C4×#11758226—21no—
15C4×#11758226C412yes—
16C4×#11758226C412yes—
17C4×#11758226C2212yes—
18C4×#11758226C2212yes—
19C2×Q8×Dic61C411yescharacteristic
20C2×C4×D244—21no—
21C2×C4×D244C2211yescharacteristic
22C2×#14519739—21no—
23C2×#14519739C411yescharacteristic
24C2×#14519735—21no—
25C2×#14519735C411yescharacteristic
26C2×C42×D61—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839818C2212yescomplemented
30#16839816—21no—
31#16839816—21no—
32#16839815C2211yescharacteristic
33#16839815C2211yescharacteristic
34#16839813—21no—
35#16839813C2212yescomplemented
36#16839784—21no—
37#16839784C2212yescomplemented
38#16839724—21no—
39#16839724—21no—
40C4×#11758189—21no—
41C4×#11758189C2212yescomplemented
42Q8⋊#92418C2214yescomplemented
43#16839491C2214yescomplemented
44#16839489C2214yescomplemented
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C2×#11758226—24no—
50C2×#11758226—24no—
51C2×#11758226—21no—
52C2×#11758226—21no—
53C2×#11758226C2×C412yes—
54C2×#11758226C2×C412yes—
55C22×D244—21no—
56C22×D244C2×C411yescharacteristic
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C2×#11758189—22no—
64C2×#11758189—22no—
65Q8×Dic61—21no—
66Q8×Dic61—21no—
67Q8×Dic61C2×C412yes—
68Q8×Dic61C2×C412yes—
69C4×D244—22no—
70C4×D244—22no—
71C4×D244—22no—
72C4×D244—22no—
73C4×D244—21no—
74C4×D244—21no—
75C4×D244C2×C412yes—
76C4×D244C2312yes—
77#14519739—22no—
78#14519739—22no—
79#14519739—22no—
80#14519739—22no—
81#14519739—21no—
82#14519739—21no—
83#14519739C2×C412yes—
84#14519739C2×C412yes—
85#14519735—21no—
86#14519735—21no—
87#14519735—22no—
88#14519735—22no—
89#14519735—22no—
90#14519735—22no—
91#14519735C2×C412yes—
92#14519735C2×C412yes—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61C2×C411yescharacteristic
101C2×C4×Dic61D411yescharacteristic
102C2×C4×Dic61D411yescharacteristic
103C42×D61—22no—
104C42×D61—22no—
105C42×D61—22no—
106C42×D61—22no—
107C42×D61C2×C411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61C2311yescharacteristic
114C42×D61C2311yescharacteristic
115C4⋊#92418—21no—
116C4⋊#92418C2312yes—
117#14519706—22no—
118#14519706—22no—
119C22⋊#92418—21no—
120C22⋊#92418—21no—
121#14519689—22no—
122#14519689—22no—
123#14519687—22no—
124#14519687—22no—
125C4×#92418—21no—
126C4×#92418C2312yes—
127C22×Q8×C61C2×C411yescharacteristic
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61C2×C412yes—
131C4×Q8×C61C2312yes—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2312yes—
138C22⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2312yes—
142C23×D61—21no—
143C23×D61C22⋊C411yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—22no—
146C2×Q8×C61M1614yescomplemented
147C2×Q8×C61C22×C412yes—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×Dic61—21no—
154C22×Dic61C22⋊C411yescharacteristic
155C22×Dic61C22⋊C411yescharacteristic
156C22×Dic61C22⋊C411yescharacteristic
157#11758226—28no—
158#11758226—28no—
159#11758226—24no—
160#11758226—24no—
161#11758226—24no—
162#11758226—24no—
163C2×D244—28no—
164C2×D244—22no—
165C2×D244—22no—
166C2×D244—21no—
167C2×D244—22no—
168C2×D244M1614yescomplemented
169C2×D244C22×C412yes—
170C2×C4×D61—28no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61—44no—
182C2×C4×D61—44no—
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22×C411yescharacteristic
190C2×C4×D61C22×C411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×C8×C61—22no—
196C2×C8×C61—22no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—22no—
200C4⋊C4×C61C22×C412yes—
201C42×C61—22no—
202C42×C61—22no—
203C42×C61C22×C411yescharacteristic
204C42×C61C2×D411yescharacteristic
205C42×C61C2×D411yescharacteristic
206C42×C61C2411yescharacteristic
207#11758198—22no—
208#11758198—22no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213C4⋊Dic61—21no—
214C4⋊Dic61—22no—
215C4⋊Dic61—22no—
216C4⋊Dic61C22×C412yes—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—22no—
220C4×Dic61—22no—
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22×C411yescharacteristic
228C4×Dic61C22×C411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C4×Dic61C2×D411yescharacteristic
232C4×Dic61C2×D411yescharacteristic
233C2×#92418—22no—
234C2×#92418—22no—
235#11758189—44no—
236#11758189—44no—
237C23×C61C2×C22⋊C411yescharacteristic
238C22×D61—22no—
239C22×D61—22no—
240C22×D61—24no—
241C22×D61—41no—
242C22×D61—41no—
243C22×D61—42no—
244C22×D61—42no—
245C22×D61C2×C22⋊C411yescharacteristic
246C22×D61C2×C22⋊C411yescharacteristic
247Q8×C61—22no—
248Q8×C61—24no—
249Q8×C61C2×M1614yes—
250C2×C4×C61—22no—
251C2×C4×C61—24no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—41no—
255C2×C4×C61—42no—
256C2×C4×C61C2×C22⋊C411yescharacteristic
257C2×C4×C61C2×C22⋊C411yescharacteristic
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C2×M1612yes—
260C2×C4×C61C2×M1612yes—
261C2×C4×C61C23×C411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—41no—
268C2×Dic61—42no—
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C2×C22⋊C411yescharacteristic
275D244—28no—
276D244—28no—
277D244—22no—
278D244—24no—
279D244C2×M1614yes—
280C4×D61—28no—
281C4×D61—28no—
282C4×D61—21no—
283C4×D61—21no—
284C4×D61—21no—
285C4×D61—21no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—22no—
291C4×D61—22no—
292C4×D61—41no—
293C4×D61—41no—
294C4×D61—41no—
295C4×D61—41no—
296C4×D61—44no—
297C4×D61—44no—
298C4×D61—44no—
299C4×D61—44no—
300C8×C61—42no—
301C8×C61—42no—
302#92418—42no—
303#92418—42no—
304#17450—611nomaximal, Sylow
305C22×C61—21no—
306C22×C61—21no—
307C22×C61#40712yes—
308C22×C61C22×C22⋊C411yescharacteristic
309C2×D61—21no—
310C2×D61—21no—
311C2×D61—24no—
312C2×D61—21no—
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—44no—
317C2×D61—48no—
318C2×D61—42no—
319C2×D61—42no—
320C4×C61—24no—
321C4×C61—21no—
322C4×C61—21no—
323C4×C61—21no—
324C4×C61—42no—
325C4×C61#40712yes—
326C4×C61C22×M1611yescharacteristic
327C4×C61C22×M1611yescharacteristic
328C4×C61#57512yes—
329Dic61—21no—
330Dic61—21no—
331Dic61—21no—
332Dic61—21no—
333Dic61—21no—
334Dic61—42no—
335Dic61#42112yes—
336C2×C4×#41—611no—
337#2920—611no—
338#2920—611no—
339#1489—614no—
340#1488—614no—
341#1479—611no—
342#1479D6111yescharacteristic, complemented
343#1478—611no—
344#1478—611no—
345C2×C61—22no—
346C2×C61C2×#40711yescharacteristic
347C2×C61#289611yescharacteristic
348C2×C61C2×#42111yescharacteristic
349D61—41no—
350D61—41no—
351D61—44no—
352C22×#41—611no—
353C4×#41—612no—
354C4×#41—612no—
355C4×#41—612no—
356C4×#41—612no—
357C4×#41—1221no—
358C4×#41—1221no—
359C4×#41—1221no—
360C4×#41—1221no—
361C2×C4×Q8—611no—
362C2×C4×Q8C2×D6111yescharacteristic
363C2×C4×D4—611no—
364C2×C4×D4—611no—
365C2×C4×D4—1221no—
366C2×C4×D4—1221no—
367C2×#117—611no—
368C2×#117—1221no—
369C22×C42—611no—
370C22×C42—1221no—
371#432—612no—
372#432—1221no—
373#432—1221no—
374#432—1221no—
375#431—611no—
376#431—612no—
377#431—611no—
378#431—1221no—
379#431C2×D6111yescharacteristic
380#431C2×D6111yescharacteristic
381#423—612no—
382#423—1221no—
383#407—1221no—
384#407—1221no—
385C4×M16—612no—
386C4×M16—1221no—
387Q8⋊C8—614no—
388Q8⋊C8C2×D6114yescomplemented
389D4⋊C8—614no—
390D4⋊C8—614no—
391C61#1745011yescharacteristic, complemented, Sylow
392C2×#41—612no—
393C2×#41—612no—
394C2×#41—1221no—
395C2×#41—1221no—
396C2×#41—1224no—
397C2×#41—1224no—
398C22×Q8C4×D6111yescharacteristic
399C22×D4—611no—
400C22×D4—1221no—
401C23×C4—611no—
402C23×C4—611no—
403C23×C4—611no—
404C23×C4—1221no—
405C23×C4—1221no—
406C23×C4—1221no—
407C2×M16—1222no—
408C2×M16—1222no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—612no—
412C4×Q8—612no—
413C4×Q8—1221no—
414C4×Q8—1221no—
415C4×Q8C4×D6112yes—
416C4×Q8C22×D6112yes—
417C4×D4—612no—
418C4×D4—612no—
419C4×D4—612no—
420C4×D4—612no—
421C4×D4—1222no—
422C4×D4—1222no—
423C4×D4—1222no—
424C4×D4—1222no—
425C4×D4—1221no—
426C4×D4—1221no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1221no—
432C4×D4—1221no—
433#117—612no—
434#117—612no—
435#117—1222no—
436#117—1222no—
437#117—1222no—
438#117—1222no—
439#117—1221no—
440#117—1221no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4C4×D6111yescharacteristic
445C2×C22⋊C4—1221no—
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C42—21no—
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—611no—
460C2×C42—1222no—
461C2×C42—1222no—
462C2×C42—1222no—
463C2×C42—1222no—
464C2×C42—1221no—
465C2×C42—1221no—
466C2×C42C22×D6111yescharacteristic
467C4⋊C8—21no—
468C4⋊C8—612no—
469C4⋊C8—1222no—
470C4⋊C8—1222no—
471C4⋊C8—1221no—
472C4⋊C8C22×D6112yes—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—1222no—
476C22⋊C8—1222no—
477C22⋊C8—1221no—
478C22⋊C8—1221no—
479#97—1222no—
480#97—1222no—
481C4×C8—21no—
482C4×C8—612no—
483C4×C8—1221no—
484C4×C8C22×D6112yes—
485C24—611no—
486C24—1221no—
487#41—1224no—
488#41—1224no—
489#41—1228no—
490#41—1228no—
491#41—1224no—
492#41—1224no—
493C2×Q8—21no—
494C2×Q8—22no—
495C2×Q8#1175818914yescomplemented
496C2×Q8C2×C4×D6112yes—
497C2×D4—612no—
498C2×D4—614no—
499C2×D4—1222no—
500C2×D4—1222no—
501C2×D4—1228no—
502C2×D4—1221no—
503C2×D4—1222no—
504C22×C4—21no—
505C22×C4—21no—
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—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—1222no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—1228no—
526C22×C4—1222no—
527C22×C4—1222no—
528C22×C4—1221no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4—2442no—
532C22×C4—2444no—
533C22×C4—2442no—
534C22×C4—2444no—
535C22×C4C2×C4×D6111yescharacteristic
536C22×C4D4×D6111yescharacteristic
537C22×C4D4×D6111yescharacteristic
538M16—2444no—
539M16—2444no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—1222no—
543C2×C8—1222no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—612no—
548C4⋊C4—1222no—
549C4⋊C4—1222no—
550C4⋊C4—1221no—
551C4⋊C4C2×C4×D6112yes—
552C22⋊C4—1222no—
553C22⋊C4—1222no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C22⋊C4—1222no—
558C42—22no—
559C42—22no—
560C42—611no—
561C42—611no—
562C42—611no—
563C42—611no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—611no—
572C42—1222no—
573C42—1222no—
574C42—1222no—
575C42—1222no—
576C42C2×C4×D6111yescharacteristic
577C42D4×D6111yescharacteristic
578C42D4×D6111yescharacteristic
579C42C23×D6111yescharacteristic
580C23—611no—
581C23—611no—
582C23—1222no—
583C23—1224no—
584C23—1222no—
585C23—2441no—
586C23—2441no—
587C23—2442no—
588C23—2442no—
589C23C22⋊C4×D6111yescharacteristic
590Q8—24no—
591Q8—22no—
592Q8C2×#1175818914yes—
593D4—614no—
594D4—1228no—
595D4—1228no—
596D4—1224no—
597D4—1222no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—611no—
605C2×C4—611no—
606C2×C4—611no—
607C2×C4—611no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1228no—
613C2×C4—1228no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4—2444no—
630C2×C4—2444no—
631C2×C4—2444no—
632C2×C4—2441no—
633C2×C4—2442no—
634C2×C4—2444no—
635C2×C4C22⋊C4×D6111yescharacteristic
636C2×C4C22⋊C4×D6111yescharacteristic
637C2×C4C22⋊C4×D6111yescharacteristic
638C2×C4M16×D6112yes—
639C2×C4C2×#1175818912yes—
640C2×C4C22×C4×D6111yescharacteristic
641C2×C4C2×D4×D6111yescharacteristic
642C2×C4C2×D4×D6111yescharacteristic
643C8—42no—
644C8—42no—
645C8—2442no—
646C8—2442no—
647C22—21no—
648C22—21no—
649C22—1221no—
650C22—1221no—
651C22—1221no—
652C22—1221no—
653C22—1224no—
654C22—1221no—
655C22—1221no—
656C22—2444no—
657C22—2448no—
658C22—2442no—
659C22—2442no—
660C22#1683972412yes—
661C22C2×C22⋊C4×D6111yescharacteristic
662C4—21no—
663C4—21no—
664C4—21no—
665C4—24no—
666C4—42no—
667C4—612no—
668C4—1221no—
669C4—1221no—
670C4—1221no—
671C4—1221no—
672C4—1221no—
673C4—2442no—
674C4#1683972412yes—
675C4C2×M16×D6111yescharacteristic
676C4C22×#1175818911yescharacteristic
677C4#1684056112yes—
678C2—22no—
679C2—2441no—
680C2—2441no—
681C2—2444no—
682C2C2×#1683972411yescharacteristic
683C2#2145433711yescharacteristic
684C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1479C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758226C4
cosocleC42×C61C24
hypercenter#1479D61
hypocenterC61#17450
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #21454447C2semidirect
4. #21444257C2semidirect
5. #21444252C2semidirect
6. #21444214C2semidirect
7. #21444211C2semidirect
8. #21444209C2semidirect
9. C61×#1479C2semidirect
29. #16839818C22semidirect
35. #16839813C22semidirect
37. #16839784C22semidirect
41. C4×#11758189C22semidirect
42. Q8⋊#92418C22semidirect
43. #16839491C22semidirect
44. #16839489C22semidirect
48. C61×Q8⋊C8C22semidirect
146. C2×Q8×C61M16semidirect
168. C2×D244M16semidirect
342. #1479D61semidirect
388. Q8⋊C8C2×D61semidirect
391. C61#17450semidirect
495. C2×Q8#11758189semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582262
#214544472
#214442572
#214442522
#214442142
#214442112
#214442092
C61×#14792
#1745061