Finite Group Databasebeta

← #29647427

Subgroups — #29647427

Order 15616.

1070 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×#16840293C211yesmaximal, characteristic
2C2×#16839816C211yesmaximal, characteristic, complemented
3#21448221C211yesmaximal, characteristic, complemented
4#21444392C211yesmaximal, characteristic, complemented
5#21444390C211yesmaximal, characteristic, complemented
6#21444387C211yesmaximal, characteristic
7#21444354C214yesmaximal, complemented
8#21444341C214yesmaximal, complemented
9C61×#1519C211yesmaximal, characteristic
10#16840293—21no—
11#16840293—21no—
12#16840293—21no—
13#16840293—21no—
14#16840293C412yescomplemented
15#16840293C412yescomplemented
16#16840293C2212yes—
17#16840293C2212yes—
18C2×#14519770—21no—
19C2×#14519768C411yescharacteristic, complemented
20C2×#14519764C411yescharacteristic, complemented
21C2×#14519758—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519742C411yescharacteristic, complemented
24C2×D4×Dic61—21no—
25C2×D4×Dic61C411yescharacteristic, complemented
26C2×#14519733—21no—
27C2×#14519733—21no—
28C22×C4×Dic61C2211yescharacteristic
29#16839816—21no—
30#16839816—21no—
31#16839816C2212yescomplemented
32#16839816C2212yescomplemented
33C2×#14519706—21no—
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519687—21no—
36#16839631—21no—
37#16839626C2212yescomplemented
38#16839622C2211yescharacteristic
39#16839620—21no—
40C4⋊C4×Dic61—21no—
41#16839613C2212yescomplemented
42#16839500C2214yescomplemented
43#16839498C2214yescomplemented
44#16839496C2214yes—
45C2×#121×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C61×#327C2214yes—
49C22×Dic122C2×C411yescharacteristic
50C23×Dic61—21no—
51C23×Dic61D411yescharacteristic
52C23×Dic61D411yescharacteristic
53C22×#92418—21no—
54#14519770—22no—
55#14519770—22no—
56#14519770—22no—
57#14519770—22no—
58#14519768—21no—
59#14519768—21no—
60#14519768C2×C412yes—
61#14519768C2×C412yes—
62#14519764—21no—
63#14519764—21no—
64#14519764C2×C412yes—
65#14519764C2×C412yes—
66#14519758—22no—
67#14519758—22no—
68#14519758—22no—
69#14519758—22no—
70#14519756—21no—
71#14519756—21no—
72#14519756C2×C412yes—
73#14519756C2312yes—
74#14519742—21no—
75#14519742—21no—
76#14519742C2×C412yes—
77#14519742C2×C412yes—
78D4×Dic61—22no—
79D4×Dic61—22no—
80D4×Dic61—22no—
81D4×Dic61—22no—
82D4×Dic61—21no—
83D4×Dic61—21no—
84D4×Dic61C2×C412yes—
85D4×Dic61C2×C412yes—
86#14519733—22no—
87#14519733—22no—
88#14519733—22no—
89#14519733—22no—
90#14519733—44no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118#14519706—22no—
119#14519706—22no—
120C22⋊#92418—21no—
121C22⋊#92418C2312yes—
122#14519687—22no—
123#14519687—22no—
124#14519684—22no—
125#14519684C2312yes—
126C22×D4×C61—21no—
127C22×D4×C61C2×C411yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C22×C8×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61C2×C412yes—
133#121×C61C2312yes—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61C2312yes—
140#95×C61C2312yes—
141C24×C61—21no—
142C24×C61C2×D411yescharacteristic
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—21no—
146C2×D4×C61—42no—
147C2×D4×C61—42no—
148C2×D4×C61—42no—
149C2×D4×C61C22×C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—22no—
152C22×C4×C61—42no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—42no—
167C22×Dic61—44no—
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22⋊C411yescharacteristic
172C22×Dic61C22⋊C411yescharacteristic
173C22×Dic61C22⋊C411yescharacteristic
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C2×Dic122—21no—
181C2×Dic122—42no—
182C2×Dic122C22×C412yes—
183C2×C8×C61—22no—
184C2×C8×C61—42no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—42no—
187C4⋊C4×C61C22×C412yes—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—42no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—22no—
197C22⋊Dic61—22no—
198C22⋊Dic61—22no—
199C22⋊Dic61—42no—
200C4⋊Dic61—21no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61—42no—
204C4⋊Dic61C22×C412yes—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—44no—
212#11758196—44no—
213C4×Dic61—22no—
214C4×Dic61—22no—
215C4×Dic61—44no—
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
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×Dic61C22×C411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C4×Dic61C2×D411yescharacteristic
232C2×#92418—22no—
233C2×#92418—42no—
234C23×C61—22no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61C2×C22⋊C411yescharacteristic
241C23×C61C2×C22⋊C411yescharacteristic
242C23×C61AGL(1,ℤ/8)12yes—
243C23×C61#13712yes—
244C23×C61C22×D411yescharacteristic
245D4×C61—42no—
246D4×C61—42no—
247D4×C61—42no—
248D4×C61—44no—
249D4×C61—42no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—22no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61—42no—
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C23×C411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—44no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—44no—
285C2×Dic61—42no—
286C2×Dic61—42no—
287C2×Dic61—42no—
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C2×Dic61C2×C22⋊C411yescharacteristic
293C2×Dic61C2×C22⋊C411yescharacteristic
294C2×Dic61C2×C22⋊C411yescharacteristic
295C2×Dic61C2×C22⋊C411yescharacteristic
296Dic122—42no—
297Dic122—42no—
298C8×C61—42no—
299#92418—42no—
300#17581—611nomaximal, Sylow
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—21no—
307C22×C61—42no—
308C22×C61—42no—
309C22×C61—42no—
310C22×C61—42no—
311C22×C61—42no—
312C22×C61—84no—
313C22×C61#41712yes—
314C22×C61#41712yes—
315C22×C61C22×C22⋊C411yescharacteristic
316C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
317C22×C61C2×#13711yescharacteristic
318C4×C61—21no—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61—42no—
322C4×C61—82no—
323C4×C61#41012yes—
324Dic61—21no—
325Dic61—21no—
326Dic61—21no—
327Dic61—21no—
328Dic61—21no—
329Dic61—21no—
330Dic61—21no—
331Dic61—42no—
332Dic61—42no—
333Dic61—82no—
334Dic61#42112yes—
335C2×#529—611no—
336C2×#432—611no—
337#2285—611no—
338#1520—611no—
339#1520—611no—
340#1519—611no—
341#1519D6111yescharacteristic
342#1512—614no—
343#1509—614no—
344C2×C61—21no—
345C2×C61—22no—
346C2×C61—21no—
347C2×C61—22no—
348C2×C61—82no—
349C2×C61C2×#41011yescharacteristic
350C2×C61C2×#41711yescharacteristic
351C2×C61C2×#42111yescharacteristic
352#529—612no—
353#529—612no—
354#529—612no—
355#529—612no—
356#529—1221no—
357#529—1221no—
358#529—1221no—
359#529—1221no—
360C2×#126—1221no—
361C2×#125—611no—
362C2×#124—611no—
363C2×#123—1221no—
364C2×C22⋊Q8—611no—
365C2×#121C2×D6111yescharacteristic
366C2×C4×Q8—611no—
367C2×C4×D4—611no—
368C2×C4×D4—1221no—
369C2×#117—1221no—
370C2×#117—1221no—
371C22×C42—611no—
372#432—612no—
373#432—612no—
374#432—1221no—
375#432—1221no—
376C2×C4⋊C8—1221no—
377C2×C22⋊C8—611no—
378C2×C22⋊C8C2×D6111yescharacteristic
379C2×#97—1221no—
380#384—1221no—
381#382—612no—
382#380—611no—
383#380—1221no—
384#380C2×D6111yescharacteristic
385C4×C4⋊C4—612no—
386C4×C4⋊C4—1221no—
387#328—614no—
388#328—614no—
389#327—614no—
390#327C2×D6114yes—
391C61#1758111yescharacteristic, complemented, Sylow
392C22×Q8—611no—
393C22×D4—21no—
394C22×D4C4×D6111yescharacteristic
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—1221no—
398C23×C4C22×D6111yescharacteristic
399C22×C8—21no—
400C22×C8—1221no—
401#126—1222no—
402#126—1222no—
403#126—1222no—
404#126—1222no—
405#125—612no—
406#125—612no—
407#125—1221no—
408#125—1221no—
409#124—612no—
410#124—612no—
411#124—1221no—
412#124—1221no—
413#123—1222no—
414#123—1222no—
415#123—1222no—
416#123—1222no—
417C22⋊Q8—612no—
418C22⋊Q8—612no—
419C22⋊Q8—1221no—
420C22⋊Q8—1221no—
421#121—21no—
422#121—21no—
423#121C4×D6112yes—
424#121C22×D6112yes—
425C4×Q8—612no—
426C4×Q8—612no—
427C4×Q8—1221no—
428C4×Q8—1221no—
429C4×D4—612no—
430C4×D4—612no—
431C4×D4—1221no—
432C4×D4—1221no—
433C4×D4—1222no—
434C4×D4—1222no—
435C4×D4—1222no—
436C4×D4—1222no—
437#117—1222no—
438#117—1222no—
439#117—1222no—
440#117—1222no—
441#117—2444no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4—1221no—
448C2×C4⋊C4—1222no—
449C2×C4⋊C4—1222no—
450C2×C4⋊C4—1221no—
451C2×C4⋊C4C4×D6111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42—611no—
466C2×C42—611no—
467C2×C42—611no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—1221no—
472C2×C42—1222no—
473C4⋊C8—1222no—
474C4⋊C8—1222no—
475C22⋊C8—21no—
476C22⋊C8—612no—
477C22⋊C8—1221no—
478C22⋊C8C22×D6112yes—
479#97—1222no—
480#97—1222no—
481#95—612no—
482#95—1222no—
483#95C22×D6112yes—
484C24—21no—
485C24D4×D6111yescharacteristic
486C2×Q8—612no—
487C2×Q8—1221no—
488C2×Q8—2442no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4C2×C4×D6112yes—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—42no—
499C22×C4—611no—
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—1222no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1222no—
518C22×C4—2442no—
519C22×C4—2444no—
520C22×C4C2×C4×D6111yescharacteristic
521C22×C4C2×C4×D6111yescharacteristic
522C22×C4D4×D6111yescharacteristic
523C22×C4D4×D6111yescharacteristic
524C22×C4D4×D6111yescharacteristic
525C22×C4C23×D6111yescharacteristic
526C2×C8—22no—
527C2×C8—42no—
528C2×C8—1222no—
529C2×C8—2442no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—612no—
533C4⋊C4—1222no—
534C4⋊C4—1222no—
535C4⋊C4—1222no—
536C4⋊C4—1222no—
537C4⋊C4—1222no—
538C4⋊C4—1222no—
539C4⋊C4—1222no—
540C4⋊C4—1221no—
541C4⋊C4—1222no—
542C4⋊C4—2442no—
543C4⋊C4—2444no—
544C4⋊C4—2444no—
545C4⋊C4C2×C4×D6112yes—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—42no—
549C22⋊C4—1222no—
550C22⋊C4—1222no—
551C22⋊C4—1222no—
552C22⋊C4—1222no—
553C22⋊C4—1222no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C22⋊C4—2442no—
558C42—611no—
559C42—611no—
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—611no—
573C42—611no—
574C42—1222no—
575C42—1222no—
576C42—2444no—
577C23—22no—
578C23—41no—
579C23—41no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23C22⋊C4×D6111yescharacteristic
584C23C22⋊C4×D6111yescharacteristic
585C23#1451980112yes—
586C23#1451980612yes—
587C23C2×D4×D6111yescharacteristic
588Q8—2442no—
589Q8—2442no—
590D4—42no—
591D4—44no—
592D4—42no—
593D4—42no—
594D4—42no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—611no—
607C2×C4—611no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—611no—
613C2×C4—611no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—2444no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2444no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4C22⋊C4×D6111yescharacteristic
638C2×C4C22⋊C4×D6111yescharacteristic
639C2×C4C22×C4×D6111yescharacteristic
640C2×C4C2×D4×D6111yescharacteristic
641C8—42no—
642C8—2442no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—84no—
655C22#1683976012yes—
656C22#1683976012yes—
657C22C2×C22⋊C4×D6111yescharacteristic
658C22C2×#1451980111yescharacteristic
659C22C2×#1451980611yescharacteristic
660C4—21no—
661C4—21no—
662C4—21no—
663C4—42no—
664C4—82no—
665C4—612no—
666C4—1221no—
667C4—1221no—
668C4—1221no—
669C4—1221no—
670C4—1221no—
671C4—1221no—
672C4—1221no—
673C4—4882no—
674C4—2442no—
675C4—2442no—
676C4#1683973412yes—
677C2—21no—
678C2—22no—
679C2—22no—
680C2—21no—
681C2—82no—
682C2C2×#1683973411yescharacteristic
683C2C2×#1683976011yescharacteristic
684C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1519C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#121×C61C22
cosocleC22×C4×C61C24
hypercenter#1519D61
hypocenterC61#17581
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. C2×#16839816C2semidirect
3. #21448221C2semidirect
4. #21444392C2semidirect
5. #21444390C2semidirect
7. #21444354C2semidirect
8. #21444341C2semidirect
14. #16840293C4semidirect
15. #16840293C4semidirect
19. C2×#14519768C4semidirect
20. C2×#14519764C4semidirect
23. C2×#14519742C4semidirect
25. C2×D4×Dic61C4semidirect
31. #16839816C22semidirect
32. #16839816C22semidirect
37. #16839626C22semidirect
41. #16839613C22semidirect
42. #16839500C22semidirect
43. #16839498C22semidirect
391. C61#17581semidirect

Maximal subgroups

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

subgroupindex
C2×#168402932
C2×#168398162
#214482212
#214443922
#214443902
#214443872
#214443542
#214443412
C61×#15192
#1758161