Finite Group Databasebeta

← #29647599

Subgroups — #29647599

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454908C211yesmaximal, characteristic, complemented
2#21448470C211yesmaximal, characteristic, complemented
3#21444396C212yesmaximal, complemented
4#21444379C212yesmaximal, complemented
5#21444366C212yesmaximal, complemented
6#21444357C212yesmaximal, complemented
7#21444344C211yesmaximal, characteristic, complemented
8#21444327C211yesmaximal, characteristic, complemented
9#21444314C211yesmaximal, characteristic, complemented
10#21444305C211yesmaximal, characteristic, complemented
11C61×#3522C211yesmaximal, characteristic
12#16839893—22no—
13#16839893—21no—
14Q8×#92418—21no—
15#16839819C2212yes—
16#16839819C2211yescharacteristic
17#16839815C2212yes—
18#16839815C2211yescharacteristic
19#16839669—21no—
20#16839661—21no—
21#16839648—22no—
22#16839630C2212yes—
23#16839628C2212yes—
24C4×C4⋊Dic61C2211yescharacteristic
25#16839608C2211yescharacteristic
26#16839499C2211yescharacteristic
27#16839499C2212yes—
28#16839499C2211yescharacteristic
29#16839496C2212yes—
30#16839496C2212yes—
31#16839496C2211yescharacteristic
32#16839496C2212yes—
33#16839496C2212yes—
34#16839496C2211yescharacteristic
35#16839496C2212yes—
36C61×#559C411yescharacteristic, complemented
37C61×#559C412yescomplemented
38Q82×C61C411yescharacteristic, complemented
39C61×#554C411yescharacteristic, complemented
40C61×#554C412yescomplemented
41C61×#550C411yescharacteristic, complemented
42C61×#548—21no—
43C61×#547—22no—
44C61×#547—21no—
45C61×#542—21no—
46C61×#542—22no—
47C61×#532C2212yes—
48C61×#532C2211yescharacteristic
49C61×#529C2212yes—
50C61×#529C2211yescharacteristic
51C61×#520—21no—
52C2×C4×Q8×C61C2211yescharacteristic
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—22no—
55C2×C4×Dic61—21no—
56C2×C4×Dic61—21no—
57C4⋊#92418—22no—
58C4⋊#92418—21no—
59C4⋊#92418—21no—
60C4⋊#92418—22no—
61C22⋊#92418C2311yescharacteristic
62C22⋊#92418C2311yescharacteristic
63C22⋊#92418C2312yes—
64#14519688—22no—
65#14519688—21no—
66C4×#92418—21no—
67C4×#92418—22no—
68#14519684—21no—
69#14519684—22no—
70#14519684—22no—
71#14519684—22no—
72#14519684C2311yescharacteristic
73#14519684C2311yescharacteristic
74#14519684C2312yes—
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61—22no—
78C22×Q8×C61D411yescharacteristic
79C4⋊Q8×C61—22no—
80C4⋊Q8×C61—21no—
81C4⋊Q8×C61C2×C412yes—
82C4⋊Q8×C61C2×C411yescharacteristic
83#127×C61C2×C412yes—
84#127×C61C2×C411yescharacteristic
85#126×C61—22no—
86#126×C61—21no—
87#125×C61C2×C412yes—
88#125×C61C2×C411yescharacteristic
89#124×C61—21no—
90#124×C61—22no—
91#124×C61—22no—
92#124×C61—21no—
93#124×C61C2×C412yes—
94#124×C61C2×C411yescharacteristic
95#123×C61—21no—
96#123×C61—22no—
97#123×C61—22no—
98#123×C61—22no—
99#123×C61—22no—
100C22⋊Q8×C61—21no—
101C22⋊Q8×C61—22no—
102C22⋊Q8×C61—22no—
103C22⋊Q8×C61—22no—
104C22⋊Q8×C61—22no—
105C22⋊Q8×C61C2311yescharacteristic
106#121×C61—21no—
107#121×C61—22no—
108#121×C61—22no—
109#121×C61—21no—
110#121×C61C2311yescharacteristic
111#121×C61C2312yes—
112C4×Q8×C61—21no—
113C4×Q8×C61C2×C412yes—
114C4×Q8×C61C2×C411yescharacteristic
115C4×Q8×C61C2×C411yescharacteristic
116C4×Q8×C61C2×C411yescharacteristic
117C4×Q8×C61C2×C412yes—
118C4×Q8×C61D411yescharacteristic
119C4×Q8×C61D412yes—
120C4×Q8×C61D411yescharacteristic
121C4×D4×C61—21no—
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C4×D4×C61—21no—
125C4×D4×C61—21no—
126C4×D4×C61—22no—
127C4×D4×C61C2×C412yes—
128C4×D4×C61C2×C412yes—
129C4×D4×C61C2×C412yes—
130C4×D4×C61C2×C412yes—
131C4×D4×C61C2×C411yescharacteristic
132#117×C61—21no—
133#117×C61—22no—
134C2×C4⋊C4×C61—22no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61D412yes—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C2×C42×C61C2312yes—
140#41×C61—44no—
141#41×C61—81no—
142#41×C61—82no—
143#41×C61—81no—
144#41×C61—82no—
145C2×Q8×C61—22no—
146C2×Q8×C61—21no—
147C2×Q8×C61—42no—
148C2×Q8×C61C22⋊C411yescharacteristic
149C2×Q8×C61C22⋊C411yescharacteristic
150C2×Q8×C61C22⋊C412yes—
151C2×Q8×C61C22×C411yescharacteristic
152C2×D4×C61—21no—
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C2×D4×C61—21no—
156C2×D4×C61—22no—
157C2×D4×C61—21no—
158C2×D4×C61C22×C411yescharacteristic
159C2×D4×C61C22×C412yes—
160C22×C4×C61—22no—
161C22×C4×C61—21no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2411yescharacteristic
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61C22⋊C412yes—
183C4⋊C4×C61C22⋊C411yescharacteristic
184C4⋊C4×C61C22⋊C412yes—
185C4⋊C4×C61C22⋊C411yescharacteristic
186C4⋊C4×C61C22⋊C412yes—
187C4⋊C4×C61C22⋊C412yes—
188C4⋊C4×C61C22⋊C412yes—
189C4⋊C4×C61C22×C411yescharacteristic
190C4⋊C4×C61C22×C411yescharacteristic
191C4⋊C4×C61C22×C412yes—
192C22⋊C4×C61—21no—
193C22⋊C4×C61—21no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—22no—
197C22⋊C4×C61—22no—
198C22⋊C4×C61—21no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—21no—
203C22⋊C4×C61—22no—
204C42×C61—22no—
205C42×C61—21no—
206C42×C61C22×C411yescharacteristic
207C42×C61C22×C412yes—
208C42×C61C22×C412yes—
209C42×C61C22×C411yescharacteristic
210C42×C61C2×D411yescharacteristic
211C42×C61C2×D412yes—
212C42×C61C2×D412yes—
213C42×C61C2×D411yescharacteristic
214C4⋊Dic61—42no—
215C4⋊Dic61—82no—
216C4×Dic61—42no—
217C4×Dic61—81no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—22no—
221C23×C61—22no—
222C23×C61—21no—
223C23×C61C22×D411yescharacteristic
224Q8×C61—22no—
225Q8×C61—22no—
226Q8×C61—42no—
227Q8×C61—41no—
228Q8×C61—81no—
229Q8×C61—82no—
230D4×C61—41no—
231D4×C61—42no—
232D4×C61—44no—
233D4×C61—42no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—42no—
237D4×C61—42no—
238D4×C61—81no—
239D4×C61—82no—
240C2×C4×C61—21no—
241C2×C4×C61—22no—
242C2×C4×C61—21no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—21no—
246C2×C4×C61—22no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—42no—
250C2×C4×C61—41no—
251C2×C4×C61—44no—
252C2×C4×C61—42no—
253C2×C4×C61—82no—
254C2×C4×C61—82no—
255C2×C4×C61—82no—
256C2×C4×C61C2×C22⋊C412yes—
257C2×C4×C61C2×C22⋊C411yescharacteristic
258C2×C4×C61C2×C22⋊C412yes—
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C412yes—
261C2×C4×C61C2×C22⋊C412yes—
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C23×C411yescharacteristic
265C2×C4×C61C22×D411yescharacteristic
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—42no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275#92418—41no—
276#92418—41no—
277#92418—42no—
278#17602—611nomaximal, Sylow
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—42no—
282C22×C61—41no—
283C22×C61—42no—
284C22×C61—41no—
285C22×C61—42no—
286C22×C61—41no—
287C22×C61C22×C22⋊C411yescharacteristic
288C22×C61#57611yescharacteristic
289C22×C61#57711yescharacteristic
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—22no—
294C4×C61—21no—
295C4×C61—22no—
296C4×C61—21no—
297C4×C61—22no—
298C4×C61—22no—
299C4×C61—41no—
300C4×C61—42no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61#42112yes—
304Dic61—81no—
305Dic61—82no—
306Dic61—81no—
307#3522D6111yescharacteristic
308#2984—611no—
309#2320—611no—
310#1521—612no—
311#1517—612no—
312#1514—612no—
313#1512—612no—
314#1509—611no—
315#1505—611no—
316#1502—611no—
317#1500—611no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—82no—
321C2×C61—81no—
322C2×C61#288411yescharacteristic
323C2×C61#289711yescharacteristic
324C2×C61C2×#42111yescharacteristic
325#559Dic6112yescomplemented
326#559Dic6111yescharacteristic, complemented
327Q82Dic6111yescharacteristic, complemented
328#554Dic6111yescharacteristic, complemented
329#554Dic6112yescomplemented
330#550Dic6111yescharacteristic, complemented
331#548—21no—
332#547—22no—
333#547—21no—
334#542—21no—
335#542—22no—
336#532C2×D6111yescharacteristic
337#532C2×D6112yes—
338#529C2×D6111yescharacteristic
339#529C2×D6112yes—
340#520—21no—
341C2×C4×Q8C2×D6111yescharacteristic
342#446—1221no—
343#446—1222no—
344C8×Q8—1221no—
345#432—611no—
346#432—612no—
347#431—611no—
348#431—612no—
349#391—1221no—
350#389—1221no—
351#387—1222no—
352#383—612no—
353#382—612no—
354C4×C4⋊C4—611no—
355#376—611no—
356#328—611no—
357#328—611no—
358#328—612no—
359#327—611no—
360#327—611no—
361#327—612no—
362#327—612no—
363#327—612no—
364#327—612no—
365#327—612no—
366C61#1760211yescharacteristic, complemented, Sylow
367C2×#41—21no—
368C2×#41—21no—
369C2×#41—22no—
370C22×Q8C22⋊D6111yescharacteristic
371C4⋊Q8—22no—
372C4⋊Q8—21no—
373C4⋊Q8C2×Dic6111yescharacteristic
374C4⋊Q8C2×Dic6112yes—
375#127C2×Dic6111yescharacteristic
376#127C2×Dic6112yes—
377#126—22no—
378#126—21no—
379#125C2×Dic6111yescharacteristic
380#125C2×Dic6112yes—
381#124—21no—
382#124—22no—
383#124—22no—
384#124—21no—
385#124C2×Dic6111yescharacteristic
386#124C2×Dic6112yes—
387#123—21no—
388#123—22no—
389#123—22no—
390#123—22no—
391#123—22no—
392C22⋊Q8—21no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8C22×D6111yescharacteristic
398#121—21no—
399#121—22no—
400#121—22no—
401#121—21no—
402#121C22×D6111yescharacteristic
403#121C22×D6112yes—
404C4×Q8—21no—
405C4×Q8C2×Dic6111yescharacteristic
406C4×Q8C2×Dic6112yes—
407C4×Q8C2×Dic6111yescharacteristic
408C4×Q8C2×Dic6111yescharacteristic
409C4×Q8C2×Dic6112yes—
410C4×Q8C22⋊D6111yescharacteristic
411C4×Q8C22⋊D6111yescharacteristic
412C4×Q8C22⋊D6112yes—
413C4×D4—21no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—22no—
419C4×D4C2×Dic6111yescharacteristic
420C4×D4C2×Dic6112yes—
421C4×D4C2×Dic6112yes—
422C4×D4C2×Dic6112yes—
423C4×D4C2×Dic6112yes—
424#117—21no—
425#117—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—1222no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4C22⋊D6112yes—
431C2×C4⋊C4C22⋊D6111yescharacteristic
432C2×C42—1221no—
433C2×C42—1221no—
434C2×C42C22×D6111yescharacteristic
435C2×C42C22×D6112yes—
436C4⋊C8—1222no—
437C4⋊C8—1221no—
438C4⋊C8—1221no—
439C4⋊C8—1222no—
440C22⋊C8—611no—
441C22⋊C8—611no—
442C22⋊C8—612no—
443#97—1222no—
444#97—1221no—
445C4×C8—1221no—
446C4×C8—1222no—
447#95—611no—
448#95—611no—
449#95—612no—
450#95—1221no—
451#95—1222no—
452#95—1222no—
453#95—1222no—
454#41—44no—
455#41—81no—
456#41—82no—
457#41—81no—
458#41—82no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—42no—
462C2×Q8C22⋊Dic6111yescharacteristic
463C2×Q8C22⋊Dic6111yescharacteristic
464C2×Q8C22⋊Dic6112yes—
465C2×Q8C22×Dic6111yescharacteristic
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4C22×Dic6111yescharacteristic
473C2×D4C22×Dic6112yes—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1222no—
482C22×C4C2×C22⋊D6111yescharacteristic
483C22×C4C2×C22⋊D6112yes—
484C22×C4C2×C22⋊D6111yescharacteristic
485C22×C4C2×C22⋊D6112yes—
486C22×C4C23×D6111yescharacteristic
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1222no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—4882no—
500C4⋊C4—2442no—
501C4⋊C4C22⋊Dic6112yes—
502C4⋊C4C22⋊Dic6111yescharacteristic
503C4⋊C4C22⋊Dic6112yes—
504C4⋊C4C22⋊Dic6111yescharacteristic
505C4⋊C4C22⋊Dic6112yes—
506C4⋊C4C22⋊Dic6112yes—
507C4⋊C4C22⋊Dic6112yes—
508C4⋊C4C22×Dic6111yescharacteristic
509C4⋊C4C22×Dic6112yes—
510C4⋊C4C22×Dic6111yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—22no—
516C22⋊C4—21no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—21no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C42—22no—
524C42—21no—
525C42—4881no—
526C42—2442no—
527C42C22×Dic6111yescharacteristic
528C42C22×Dic6112yes—
529C42C22×Dic6112yes—
530C42C22×Dic6111yescharacteristic
531C42C2×C22⋊D6111yescharacteristic
532C42C2×C22⋊D6112yes—
533C42C2×C22⋊D6112yes—
534C42C2×C22⋊D6111yescharacteristic
535C23—22no—
536C23—21no—
537C23C22×C22⋊D6111yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—42no—
541Q8—41no—
542Q8—81no—
543Q8—82no—
544D4—41no—
545D4—42no—
546D4—44no—
547D4—42no—
548D4—41no—
549D4—41no—
550D4—42no—
551D4—42no—
552D4—81no—
553D4—82no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—44no—
566C2×C4—42no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2442no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4C2×C22⋊Dic6112yes—
580C2×C4C2×C22⋊Dic6111yescharacteristic
581C2×C4C2×C22⋊Dic6112yes—
582C2×C4C2×C22⋊Dic6111yescharacteristic
583C2×C4C2×C22⋊Dic6112yes—
584C2×C4C2×C22⋊Dic6112yes—
585C2×C4C2×C22⋊Dic6111yescharacteristic
586C2×C4C2×C22⋊Dic6111yescharacteristic
587C2×C4C23×Dic6111yescharacteristic
588C2×C4C22×C22⋊D6111yescharacteristic
589C8—2441no—
590C8—2441no—
591C8—2442no—
592C22—21no—
593C22—21no—
594C22—42no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—42no—
599C22—41no—
600C22C22×C22⋊Dic6111yescharacteristic
601C22#1684056511yescharacteristic
602C22#1684057311yescharacteristic
603C4—21no—
604C4—22no—
605C4—21no—
606C4—22no—
607C4—21no—
608C4—22no—
609C4—22no—
610C4—21no—
611C4—21no—
612C4—42no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—4881no—
617C4—4882no—
618C4—4881no—
619C4#1683977912yes—
620C2—21no—
621C2—21no—
622C2—82no—
623C2—81no—
624C2#2145428311yescharacteristic
625C2#2145434511yescharacteristic
626C2C2×#1683977911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3522C2
socleC22×C61C22×C22⋊C4
cosocleC22×C4×C61C24
hypercenter#3522D61
hypocenterC61#17602
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #3522

Complements

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

NH ≅ G/Ntype
1. #21454908C2semidirect
2. #21448470C2semidirect
3. #21444396C2semidirect
4. #21444379C2semidirect
5. #21444366C2semidirect
6. #21444357C2semidirect
7. #21444344C2semidirect
8. #21444327C2semidirect
9. #21444314C2semidirect
10. #21444305C2semidirect
36. C61×#559C4semidirect
37. C61×#559C4semidirect
38. Q82×C61C4semidirect
39. C61×#554C4semidirect
40. C61×#554C4semidirect
41. C61×#550C4semidirect
325. #559Dic61semidirect
326. #559Dic61semidirect
327. Q82Dic61semidirect
328. #554Dic61semidirect
329. #554Dic61semidirect
330. #550Dic61semidirect
366. C61#17602semidirect

Maximal subgroups

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

subgroupindex
#214549082
#214484702
#214443962
#214443792
#214443662
#214443572
#214443442
#214443272
#214443142
#214443052
C61×#35222
#1760261