Finite Group Databasebeta

← #29685361

Subgroups — #29685361

Order 15616.

1222 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840296C211yesmaximal, characteristic
2C4×#14519736C211yesmaximal, characteristic, complemented
3#21446803C212yesmaximal, complemented
4#21446654C212yesmaximal
5#21446275C214yesmaximal, complemented
6C4×#14519691C214yesmaximal, complemented
7C61×#2283C211yesmaximal, characteristic, complemented
8#16840296—21no—
9#16840296—21no—
10#16840296—21no—
11#16840296—21no—
12#16840296—21no—
13#16840296—21no—
14#16840296—21no—
15#16840296—21no—
16C2×#14519771C412yescomplemented
17C2×#14519769C411yescharacteristic, complemented
18C2×#14519765C411yescharacteristic, complemented
19C2×#14519760C2212yes—
20C2×#14519756C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×C4×Dic122C411yescharacteristic, complemented
23C2×C4×D244C411yescharacteristic, complemented
24C2×C4×C22⋊D61C2212yes—
25C2×#14519736C2212yes—
26C2×#14519734C412yescomplemented
27C2×#14519691C2218yes—
28C4×C4⋊Dic61—21no—
29C4×C4⋊Dic61—21no—
30C4×C22⋊Dic61C2212yes—
31C4×C22⋊Dic61C2212yes—
32#16839608—21no—
33C42×Dic61—21no—
34#16839528C2218yes—
35C22×C42×C61C2211yescharacteristic
36C61×#383—21no—
37C61×#382—21no—
38C61×#381C2212yes—
39C61×#380C2212yes—
40C4×C4⋊C4×C61—21no—
41C4×C22⋊C4×C61C2212yes—
42C61×#376—21no—
43C22×Dic122C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61C2312yes—
46C22×C4×D61C2×C412yes—
47#14519771—22no—
48#14519771—22no—
49#14519771—22no—
50#14519771—22no—
51#14519769—21no—
52#14519769—21no—
53#14519769—21no—
54#14519769—21no—
55#14519765—21no—
56#14519765—21no—
57#14519765—21no—
58#14519765—21no—
59#14519760—22no—
60#14519760—22no—
61#14519760—22no—
62#14519760—22no—
63#14519756—21no—
64#14519756—21no—
65#14519756—21no—
66#14519756—21no—
67#14519751—21no—
68#14519751—21no—
69#14519751—21no—
70#14519751—21no—
71C4×Dic122—21no—
72C4×Dic122—21no—
73C4×Dic122—21no—
74C4×Dic122—21no—
75C4×D244—21no—
76C4×D244—21no—
77C4×D244—21no—
78C4×D244—21no—
79C4×C22⋊D61—22no—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83#14519736—28no—
84#14519734—22no—
85#14519734—22no—
86#14519734—22no—
87#14519734—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×#11758196C2×C412yes—
92C2×#11758196C2×C412yes—
93C2×#11758196C2×C412yes—
94C2×#11758196C2×C412yes—
95C2×C22⋊Dic61C2312yes—
96C2×C22⋊Dic61C2314yes—
97C2×#11758198C2×C412yes—
98C2×#11758198C2×C412yes—
99C2×#11758198C2×C412yes—
100C2×#11758198C2×C412yes—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61C2×C412yes—
105#14519691—216no—
106#14519684—22no—
107#14519684—22no—
108C23×C4×C61C2311yescharacteristic
109C23×C4×C61C2311yescharacteristic
110C23×C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61—22no—
112C2×C22⋊C4×C61C2314yes—
113C2×C42×C61—22no—
114C2×C42×C61C2×C411yescharacteristic
115C2×C42×C61C2×C411yescharacteristic
116C2×C42×C61C2×C411yescharacteristic
117C2×C42×C61C2×C411yescharacteristic
118C2×C42×C61D411yescharacteristic
119C2×C42×C61D411yescharacteristic
120C2×C42×C61D411yescharacteristic
121C2×C42×C61D411yescharacteristic
122C2×C42×C61D411yescharacteristic
123C2×C42×C61D411yescharacteristic
124C2×C42×C61D411yescharacteristic
125C2×C42×C61D411yescharacteristic
126#95×C61—22no—
127#95×C61—22no—
128#95×C61—22no—
129#95×C61—22no—
130C24×C61C2411yescharacteristic
131C23×D61C22×C412yes—
132C22×C4×C61—24no—
133C22×C4×C61—24no—
134C22×C4×C61—42no—
135C22×C4×C61—42no—
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—28no—
157C22×Dic61—24no—
158C22×Dic61C22×C412yes—
159C22×Dic61C22×C412yes—
160C22×Dic61C22×C412yes—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—42no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—44no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—42no—
170C4⋊C4×C61—44no—
171C22⋊C4×C61—28no—
172C42×C61—44no—
173C42×C61C22⋊C411yescharacteristic
174C42×C61C22⋊C411yescharacteristic
175C42×C61C22⋊C411yescharacteristic
176C42×C61C22⋊C411yescharacteristic
177C42×C61C22⋊C411yescharacteristic
178C42×C61C22⋊C411yescharacteristic
179C42×C61C22⋊C411yescharacteristic
180C42×C61C22⋊C411yescharacteristic
181C42×C61C22⋊C411yescharacteristic
182C42×C61C22⋊C411yescharacteristic
183C42×C61C22⋊C411yescharacteristic
184C42×C61C22⋊C411yescharacteristic
185C42×C61C22⋊C411yescharacteristic
186C42×C61C22⋊C411yescharacteristic
187C42×C61C22⋊C411yescharacteristic
188C42×C61C22⋊C411yescharacteristic
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191C22⋊Dic61—24no—
192C22⋊Dic61#4118yes—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201C4⋊Dic61—28no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—22no—
214C4×Dic61—28no—
215C4×Dic61—22no—
216C4×Dic61—22no—
217C4×Dic61—44no—
218C4×Dic61—44no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61C23×C411yescharacteristic
222C23×C61C22×D411yescharacteristic
223C23×C61C22×D411yescharacteristic
224C23×C61C2×#4114yes—
225C22×D61—22no—
226C22×D61—24no—
227C22×D61—42no—
228C22×D61—42no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—44no—
248C2×C4×C61—44no—
249C2×C4×C61—44no—
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C2×C22⋊C411yescharacteristic
256C2×C4×C61C2×C22⋊C411yescharacteristic
257C2×C4×C61C2×C22⋊C411yescharacteristic
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C22⋊D61—44no—
263C22⋊D61—44no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—24no—
268C2×Dic61—28no—
269C2×Dic61—44no—
270C2×Dic61—44no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273D244—42no—
274D244—42no—
275C4×D61—44no—
276C4×D61—44no—
277Dic122—42no—
278Dic122—42no—
279#21421—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—44no—
287C22×C61C22×C22⋊C411yescharacteristic
288C22×C61C4×#4112yes—
289C22×C61#52512yes—
290C22×C61#53212yes—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—84no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—84no—
306C4×C61#41012yes—
307C4×C61#41012yes—
308Dic61—48no—
309Dic61—42no—
310Dic61—42no—
311Dic61—42no—
312C2×#529—611no—
313#2283D6111yescharacteristic, complemented
314C4×#117—611no—
315#1996—612no—
316#1964—612no—
317#1899—614no—
318C4×#99—614no—
319C2×C61—22no—
320C2×C61—22no—
321C2×C61—22no—
322C2×C61#229711yescharacteristic
323C2×C61C2×#41011yescharacteristic
324C2×C61C2×#41011yescharacteristic
325D61—82no—
326#529—1221no—
327#529—1221no—
328#529—1221no—
329#529—1221no—
330#529—1221no—
331#529—1221no—
332#529—1221no—
333#529—1221no—
334C2×#126—612no—
335C2×#125—611no—
336C2×#124—611no—
337C2×#123—612no—
338C2×C22⋊Q8—611no—
339C2×#121—611no—
340C2×C4×Q8—611no—
341C2×C4×D4—612no—
342C2×C4×D4—611no—
343C2×#117—612no—
344C2×#117—612no—
345C22×C42C2×D6111yescharacteristic
346C2×#99—618no—
347#383—21no—
348#382—21no—
349#381C2×D6112yes—
350#380C2×D6112yes—
351C4×C4⋊C4—21no—
352C4×C4⋊C4—1221no—
353C4×C4⋊C4—1221no—
354C4×C22⋊C4—612no—
355C4×C22⋊C4—612no—
356C4×C22⋊C4C2×D6112yes—
357#376—21no—
358#376—1221no—
359C43—1221no—
360#342—618no—
361C61#2142111yescharacteristic, complemented, Sylow
362C22×Q8—611no—
363C22×D4—612no—
364C22×D4—611no—
365C23×C4—612no—
366C23×C4C22×D6111yescharacteristic
367C23×C4C22×D6111yescharacteristic
368C23×C4C22×D6111yescharacteristic
369#126—1222no—
370#126—1222no—
371#126—1222no—
372#126—1222no—
373#125—1221no—
374#125—1221no—
375#125—1221no—
376#125—1221no—
377#124—1221no—
378#124—1221no—
379#124—1221no—
380#124—1221no—
381#123—1222no—
382#123—1222no—
383#123—1222no—
384#123—1222no—
385C22⋊Q8—1221no—
386C22⋊Q8—1221no—
387C22⋊Q8—1221no—
388C22⋊Q8—1221no—
389#121—1221no—
390#121—1221no—
391#121—1221no—
392#121—1221no—
393C4×Q8—1221no—
394C4×Q8—1221no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×D4—1222no—
398C4×D4—1222no—
399C4×D4—1222no—
400C4×D4—1222no—
401C4×D4—1221no—
402C4×D4—1221no—
403C4×D4—1221no—
404C4×D4—1221no—
405#117—1228no—
406#117—1222no—
407#117—1222no—
408#117—1222no—
409#117—1222no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—612no—
412C2×C4⋊C4—612no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—612no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—612no—
417C2×C4⋊C4—1222no—
418C2×C22⋊C4—614no—
419C2×C22⋊C4—612no—
420C2×C22⋊C4—612no—
421C2×C22⋊C4—612no—
422C2×C22⋊C4—612no—
423C2×C22⋊C4—612no—
424C2×C22⋊C4C22×D6114yes—
425C2×C42—22no—
426C2×C42—612no—
427C2×C42—1222no—
428C2×C42—1222no—
429C2×C42—1222no—
430C2×C42C4×D6111yescharacteristic
431C2×C42C4×D6111yescharacteristic
432C2×C42C4×D6111yescharacteristic
433C2×C42C4×D6111yescharacteristic
434C2×C42D24411yescharacteristic
435C2×C42D24411yescharacteristic
436C2×C42D24411yescharacteristic
437C2×C42D24411yescharacteristic
438C2×C42C22⋊D6111yescharacteristic
439C2×C42C22⋊D6111yescharacteristic
440C2×C42C22⋊D6111yescharacteristic
441C2×C42C22⋊D6111yescharacteristic
442#99—12216no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—1222no—
448#95—1222no—
449C24—612no—
450C24C23×D6111yescharacteristic
451C2×Q8—1221no—
452C2×Q8—1221no—
453C2×Q8—2442no—
454C2×D4—1222no—
455C2×D4—1222no—
456C2×D4—1228no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—2442no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—612no—
465C22×C4—612no—
466C22×C4—612no—
467C22×C4—1224no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—2444no—
471C22×C4C2×C4×D6111yescharacteristic
472C22×C4C2×C4×D6111yescharacteristic
473C22×C4C2×C4×D6111yescharacteristic
474C22×C4C2×C4×D6111yescharacteristic
475C22×C4C2×C4×D6111yescharacteristic
476C22×C4C2×C4×D6111yescharacteristic
477C22×C4C2×D24411yescharacteristic
478C22×C4C2×D24411yescharacteristic
479C22×C4C2×D24411yescharacteristic
480C22×C4C2×D24411yescharacteristic
481C22×C4C2×D24411yescharacteristic
482C22×C4C2×D24411yescharacteristic
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C2×C22⋊D6111yescharacteristic
485C22×C4C2×C22⋊D6111yescharacteristic
486C22×C4C2×C22⋊D6111yescharacteristic
487C22×C4C2×C22⋊D6111yescharacteristic
488C22×C4C2×C22⋊D6111yescharacteristic
489C4⋊C4—44no—
490C4⋊C4—1228no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C22⋊C4—28no—
504C22⋊C4—618no—
505C22⋊C4—1222no—
506C22⋊C4—1222no—
507C22⋊C4—1224no—
508C22⋊C4—1222no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C42—44no—
517C42—1228no—
518C42—1222no—
519C42—1222no—
520C42—2444no—
521C42—2444no—
522C42#1175819811yescharacteristic
523C42#1175819811yescharacteristic
524C42#1175819811yescharacteristic
525C42#1175819811yescharacteristic
526C42#1175819811yescharacteristic
527C42#1175819811yescharacteristic
528C42#1175819811yescharacteristic
529C42#1175819811yescharacteristic
530C42#1175819811yescharacteristic
531C42#1175819811yescharacteristic
532C42#1175819811yescharacteristic
533C42#1175819811yescharacteristic
534C42#1175819811yescharacteristic
535C42#1175819811yescharacteristic
536C42#1175819811yescharacteristic
537C42#1175819811yescharacteristic
538C23—41no—
539C23—41no—
540C23—1224no—
541C23—1222no—
542C23—2442no—
543C23—2442no—
544C23C22×C4×D6111yescharacteristic
545C23C22×C22⋊D6111yescharacteristic
546C23C22×D24411yescharacteristic
547C23#41×D6114yes—
548Q8—2442no—
549Q8—2442no—
550D4—2442no—
551D4—2444no—
552D4—2444no—
553D4—2442no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1224no—
579C2×C4—1228no—
580C2×C4—2444no—
581C2×C4—2444no—
582C2×C4—2444no—
583C2×C4—2444no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4C2×#1175819811yescharacteristic
587C2×C4C2×#1175819811yescharacteristic
588C2×C4C2×#1175819811yescharacteristic
589C2×C4C2×#1175819811yescharacteristic
590C2×C4C2×#1175819811yescharacteristic
591C2×C4C2×#1175819811yescharacteristic
592C2×C4C2×#1175819811yescharacteristic
593C2×C4C2×#1175819811yescharacteristic
594C2×C4C2×#1175819811yescharacteristic
595C2×C4C2×#1175819811yescharacteristic
596C2×C4C2×#1175819811yescharacteristic
597C2×C4C2×#1175819811yescharacteristic
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—44no—
605C22—4884no—
606C22—2442no—
607C22—2442no—
608C22—2442no—
609C22C22×#1175819811yescharacteristic
610C22#1684023012yes—
611C22#1684027412yes—
612C22#1684030812yes—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—84no—
624C4—2448no—
625C4—2442no—
626C4—2442no—
627C4—2442no—
628C4#1683973512yes—
629C4#1683973512yes—
630C2—22no—
631C2—22no—
632C2—22no—
633C2—4882no—
634C2#2144830711yescharacteristic
635C2C2×#1683973511yescharacteristic
636C2C2×#1683973511yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2283C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519751C22
cosocleC24×C61C24
hypercenter#2283D61
hypocenterC61#21421
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
2. C4×#14519736C2semidirect
3. #21446803C2semidirect
5. #21446275C2semidirect
6. C4×#14519691C2semidirect
7. C61×#2283C2semidirect
16. C2×#14519771C4semidirect
17. C2×#14519769C4semidirect
18. C2×#14519765C4semidirect
22. C2×C4×Dic122C4semidirect
23. C2×C4×D244C4semidirect
26. C2×#14519734C4semidirect
313. #2283D61semidirect
361. C61#21421semidirect

Maximal subgroups

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

subgroupindex
C2×#168402962
C4×#145197362
#214468032
#214466542
#214462752
C4×#145196912
C61×#22832
#2142161