Finite Group Databasebeta

← #29646473

Subgroups — #29646473

Order 15616.

1292 conjugacy classes of subgroups.

The subgroup lattice has 692 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#423×D61C211yesmaximal, characteristic, complemented
4#21444257C214yesmaximal, complemented
5#21444248C211yesmaximal, characteristic, complemented
6#21444245C211yesmaximal, characteristic, complemented
7#21444243C211yesmaximal, characteristic, complemented
8#21444205C214yesmaximal, complemented
9C61×#1487C211yesmaximal, 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#16839818—21no—
30#16839816—21no—
31#16839815C2211yescharacteristic
32#16839813C2212yescomplemented
33#16839786C2211yescharacteristic
34#16839785—21no—
35#16839784—21no—
36#16839784—21no—
37#16839784C2212yescomplemented
38C4⋊C8×D61—21no—
39C4⋊C8×D61C2212yescomplemented
40#16839724—21no—
41C4×#11758189C2212yescomplemented
42Q8⋊#92418C2214yescomplemented
43#16839491C2214yescomplemented
44#16839489C2214yescomplemented
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#423C2211yescharacteristic
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—44no—
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⋊#92418—21no—
118C4⋊#92418—21no—
119C4⋊#92418C2312yes—
120#14519706—22no—
121#14519706—22no—
122#14519706—22no—
123C22⋊#92418—21no—
124#14519689—22no—
125#14519687—22no—
126C4×#92418C2312yes—
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×C61—21no—
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2312yes—
140C22⋊C8×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—22no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—24no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—42no—
179C2×C4×D61—44no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
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×D61C22×C411yescharacteristic
189C2×C4×D61C22×C411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194M16×C61—42no—
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
233#11758194—42no—
234C2×#92418—22no—
235C2×#92418—22no—
236#11758189—44no—
237#11758189—44no—
238C8×D61—44no—
239C23×C61C2×C22⋊C411yescharacteristic
240C22×D61—24no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—41no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61C2×C22⋊C411yescharacteristic
248C22×D61C2×C22⋊C411yescharacteristic
249Q8×C61—24no—
250Q8×C61—22no—
251Q8×C61C2×M1614yescomplemented
252C2×C4×C61—24no—
253C2×C4×C61—22no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—41no—
257C2×C4×C61—42no—
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61AGL(1,ℤ/8)12yes—
262C2×C4×C61#13712yes—
263C2×C4×C61C23×C411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C22×D411yescharacteristic
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—42no—
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61C2×C22⋊C411yescharacteristic
276C2×Dic61C2×C22⋊C411yescharacteristic
277D244—28no—
278D244—24no—
279D244—28no—
280D244—22no—
281D244C2×M1614yescomplemented
282C4×D61—28no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—21no—
286C4×D61—21no—
287C4×D61—21no—
288C4×D61—21no—
289C4×D61—22no—
290C4×D61—22no—
291C4×D61—28no—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—41no—
296C4×D61—41no—
297C4×D61—44no—
298C4×D61—42no—
299C4×D61—42no—
300C4×D61—44no—
301C4×D61—44no—
302C4×D61C2×M1614yes—
303C8×C61—42no—
304C8×C61—42no—
305#92418—42no—
306#92418—42no—
307#17451—611nomaximal, Sylow
308C22×C61—21no—
309C22×C61—21no—
310C22×C61#41712yes—
311C22×C61C22×C22⋊C411yescharacteristic
312C2×D61—21no—
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—24no—
316C2×D61—21no—
317C2×D61—21no—
318C2×D61—44no—
319C2×D61—48no—
320C2×D61—42no—
321C2×D61—42no—
322C2×D61#40712yes—
323C4×C61—24no—
324C4×C61—21no—
325C4×C61—21no—
326C4×C61—21no—
327C4×C61—42no—
328C4×C61#41712yes—
329C4×C61C22×M1612yes—
330C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
331C4×C61C2×#13711yescharacteristic
332Dic61—21no—
333Dic61—21no—
334Dic61—21no—
335Dic61—21no—
336Dic61—42no—
337Dic61#40712yes—
338Dic61#42112yes—
339C2×C4×#41—611no—
340#2920—611no—
341C2×#423—611no—
342#1489—614no—
343#1487—611no—
344#1487D6111yescharacteristic, complemented
345#1486—611no—
346#1486—611no—
347#1477—614no—
348C2×C61—22no—
349C2×C61C2×#40711yescharacteristic
350C2×C61C2×#41711yescharacteristic
351C2×C61C2×#42111yescharacteristic
352D61—22no—
353D61—41no—
354D61—44no—
355C22×#41—611no—
356C22×M16—1221no—
357C4×#41—612no—
358C4×#41—612no—
359C4×#41—612no—
360C4×#41—612no—
361C4×#41—1221no—
362C4×#41—1221no—
363C4×#41—1221no—
364C4×#41—1221no—
365C2×C4×Q8—611no—
366C2×C4×Q8C2×D6111yescharacteristic
367C2×C4×D4—611no—
368C2×C4×D4—611no—
369C2×C4×D4—1221no—
370C2×C4×D4—1221no—
371C2×#117—611no—
372C2×#117—1221no—
373C22×C42—611no—
374C22×C42—1221no—
375#432—1221no—
376#432—1221no—
377#431—611no—
378#431—612no—
379#431C2×D6111yescharacteristic
380#423—611no—
381#423—612no—
382#423—1221no—
383#423—1221no—
384#423—1221no—
385#423C2×D6111yescharacteristic
386C2×C4⋊C8—612no—
387C2×C4⋊C8—1221no—
388#407—1221no—
389C4×M16—612no—
390Q8⋊C8—614no—
391Q8⋊C8C2×D6114yescomplemented
392D4⋊C8—614no—
393D4⋊C8—614no—
394C61#1745111yescharacteristic, complemented, Sylow
395C2×#41—612no—
396C2×#41—612no—
397C2×#41—1221no—
398C2×#41—1221no—
399C2×#41—1228no—
400C22×Q8C4×D6111yescharacteristic
401C22×D4—611no—
402C22×D4—1221no—
403C23×C4—611no—
404C23×C4—611no—
405C23×C4—611no—
406C23×C4—1221no—
407C23×C4—1221no—
408C23×C4—1221no—
409C2×M16—21no—
410C2×M16—1222no—
411C2×M16—1222no—
412C2×M16—1221no—
413C2×M16—2444no—
414C22×C8—1222no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—612no—
418C4×Q8—612no—
419C4×Q8—1221no—
420C4×Q8—1221no—
421C4×Q8C4×D6112yes—
422C4×Q8C22×D6112yes—
423C4×D4—612no—
424C4×D4—612no—
425C4×D4—612no—
426C4×D4—612no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1221no—
432C4×D4—1221no—
433C4×D4—1222no—
434C4×D4—1222no—
435C4×D4—1222no—
436C4×D4—1222no—
437C4×D4—1221no—
438C4×D4—1221no—
439#117—612no—
440#117—612no—
441#117—1222no—
442#117—1222no—
443#117—1222no—
444#117—1222no—
445#117—1221no—
446#117—1221no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—1221no—
450C2×C4⋊C4C4×D6111yescharacteristic
451C2×C22⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C22⋊C4—1221no—
454C2×C42—21no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42—611no—
466C2×C42—1222no—
467C2×C42—1222no—
468C2×C42—1222no—
469C2×C42—1222no—
470C2×C42—1221no—
471C2×C42—1221no—
472C2×C42C22×D6111yescharacteristic
473C4⋊C8—21no—
474C4⋊C8—21no—
475C4⋊C8—612no—
476C4⋊C8—1222no—
477C4⋊C8—1222no—
478C4⋊C8—1222no—
479C4⋊C8—1221no—
480C4⋊C8—1221no—
481C4⋊C8C22×D6112yes—
482C22⋊C8—21no—
483C22⋊C8—1222no—
484C22⋊C8—1221no—
485#97—1222no—
486C4×C8—612no—
487C4×C8C22×D6112yes—
488C24—611no—
489C24—1221no—
490#41—618no—
491#41—1224no—
492#41—1224no—
493#41—1228no—
494#41—1228no—
495#41—1224no—
496C2×Q8—24no—
497C2×Q8—21no—
498C2×Q8C2×C4×D6112yes—
499C2×D4—612no—
500C2×D4—1224no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1228no—
504C2×D4—1221no—
505C22×C4—21no—
506C22×C4—21no—
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—611no—
522C22×C4—1222no—
523C22×C4—1222no—
524C22×C4—1224no—
525C22×C4—1222no—
526C22×C4—1222no—
527C22×C4—1228no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1221no—
531C22×C4—1222no—
532C22×C4—1222no—
533C22×C4—2442no—
534C22×C4—2444no—
535C22×C4—2442no—
536C22×C4—2442no—
537C22×C4C2×C4×D6111yescharacteristic
538C22×C4D4×D6111yescharacteristic
539C22×C4D4×D6111yescharacteristic
540M16—42no—
541M16—2444no—
542M16—2444no—
543M16—2442no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—1222no—
547C2×C8—1222no—
548C2×C8—2444no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—612no—
553C4⋊C4—1222no—
554C4⋊C4—1222no—
555C4⋊C4—1221no—
556C4⋊C4C2×C4×D6112yes—
557C22⋊C4—1222no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C22⋊C4—1222no—
561C22⋊C4—1222no—
562C22⋊C4—1222no—
563C42—22no—
564C42—22no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42—611no—
574C42—611no—
575C42—611no—
576C42—611no—
577C42—1222no—
578C42—1222no—
579C42—1222no—
580C42—1222no—
581C42C2×C4×D6111yescharacteristic
582C42D4×D6111yescharacteristic
583C42D4×D6111yescharacteristic
584C42C23×D6111yescharacteristic
585C23—611no—
586C23—611no—
587C23—1222no—
588C23—1224no—
589C23—1222no—
590C23—1222no—
591C23—2441no—
592C23—2442no—
593C23—2442no—
594C23C22⋊C4×D6111yescharacteristic
595Q8—24no—
596Q8—22no—
597Q8M16×D6114yescomplemented
598D4—614no—
599D4—1228no—
600D4—1228no—
601D4—1224no—
602D4—1222no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—614no—
612C2×C4—611no—
613C2×C4—611no—
614C2×C4—611no—
615C2×C4—611no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1228no—
620C2×C4—1222no—
621C2×C4—1228no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1222no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2444no—
636C2×C4—2444no—
637C2×C4—2442no—
638C2×C4—2444no—
639C2×C4—2442no—
640C2×C4—2442no—
641C2×C4C22⋊C4×D6111yescharacteristic
642C2×C4C22⋊C4×D6111yescharacteristic
643C2×C4C22⋊C4×D6111yescharacteristic
644C2×C4#1451980412yes—
645C2×C4#1451980912yes—
646C2×C4C22×C4×D6111yescharacteristic
647C2×C4C2×D4×D6111yescharacteristic
648C2×C4C2×D4×D6111yescharacteristic
649C8—42no—
650C8—42no—
651C8—2442no—
652C8—2442no—
653C22—21no—
654C22—21no—
655C22—612no—
656C22—1221no—
657C22—1221no—
658C22—1221no—
659C22—1224no—
660C22—1221no—
661C22—1221no—
662C22—2444no—
663C22—2448no—
664C22—2442no—
665C22—2442no—
666C22#1683976212yes—
667C22C2×C22⋊C4×D6111yescharacteristic
668C4—21no—
669C4—21no—
670C4—24no—
671C4—21no—
672C4—42no—
673C4—612no—
674C4—612no—
675C4—1221no—
676C4—1221no—
677C4—1221no—
678C4—1221no—
679C4—2442no—
680C4#1683976212yes—
681C4C2×M16×D6112yes—
682C4C2×#1451980411yescharacteristic
683C4C2×#1451980911yescharacteristic
684C2—22no—
685C2—1222no—
686C2—2441no—
687C2—2444no—
688C2#407×D6111yescharacteristic
689C2C2×#1683976211yescharacteristic
690C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1487C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758226C4
cosocleC42×C61C24
hypercenter#1487D61
hypocenterC61#17451
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #423×D61C2semidirect
4. #21444257C2semidirect
5. #21444248C2semidirect
6. #21444245C2semidirect
7. #21444243C2semidirect
8. #21444205C2semidirect
9. C61×#1487C2semidirect
32. #16839813C22semidirect
37. #16839784C22semidirect
39. C4⋊C8×D61C22semidirect
41. C4×#11758189C22semidirect
42. Q8⋊#92418C22semidirect
43. #16839491C22semidirect
44. #16839489C22semidirect
48. C61×Q8⋊C8C22semidirect
161. #11758226M16semidirect
251. Q8×C61C2×M16semidirect
281. D244C2×M16semidirect
344. #1487D61semidirect
391. Q8⋊C8C2×D61semidirect
394. C61#17451semidirect
597. 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
#214544472
#423×D612
#214442572
#214442482
#214442452
#214442432
#214442052
C61×#14872
#1745161