Finite Group Databasebeta

← #29849983

Subgroups — #29849983

Order 15616.

1994 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450252C212yesmaximal, complemented
2#21450241C212yesmaximal, complemented
3#21450230C212yesmaximal, complemented
4#21450219C212yesmaximal, complemented
5#21450204C214yesmaximal, complemented
6#21450059C214yesmaximal
7#21449119C214yesmaximal, complemented
8C4×#14519770C214yesmaximal, complemented
9#21448302C211yesmaximal, characteristic, complemented
10#21448302C211yesmaximal, characteristic, complemented
11#21448226C211yesmaximal, characteristic, complemented
12#21448202C211yesmaximal, characteristic
13#21448202C211yesmaximal, characteristic
14C4×#14519736C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
16C2×#14519770C2214yes—
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21C61⋊#401C2214yescomplemented
22#16839704C2214yescomplemented
23#16839703C2214yescomplemented
24#16839702C2214yescomplemented
25#16839690C2214yes—
26#16839690C2214yes—
27#16839687C2214yes—
28#16839685C2214yes—
29#16839660C2212yescomplemented
30#16839660C2212yescomplemented
31#16839660C2212yescomplemented
32#16839660C2212yescomplemented
33#16839656C2214yes—
34#16839655C2214yes—
35#16839650C2214yes—
36#16839649C2214yescomplemented
37#16839647C2214yescomplemented
38#16839644C2214yescomplemented
39#16839635C2214yes—
40#16839635C2214yes—
41#16839632C2211yescharacteristic, complemented
42#16839632C2211yescharacteristic, complemented
43#16839629C2214yescomplemented
44#16839628C2211yescharacteristic, complemented
45#16839628C2211yescharacteristic, complemented
46#16839625C2212yes—
47#16839625C2212yes—
48#16839622C2212yes—
49#16839622C2212yes—
50#16839622C2212yes—
51#16839622C2212yes—
52#16839622C2214yes—
53#16839618C2212yes—
54#16839618C2212yes—
55C4×#11758196C2212yescomplemented
56C4×#11758196C2214yescomplemented
57C4×#11758196C2212yescomplemented
58C4×C4⋊Dic61C2212yescomplemented
59C4×C4⋊Dic61C2212yescomplemented
60C4×C4⋊Dic61C2214yescomplemented
61C4×C22⋊Dic61C2214yes—
62C4×C22⋊Dic61C2214yes—
63C4×C22⋊Dic61C2214yes—
64#16839608C2212yescomplemented
65C42×Dic61C2212yescomplemented
66C24×C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2212yes—
68C22×C42×C61C2211yescharacteristic
69C22×C42×C61C2211yescharacteristic
70C4×C22⋊C4×C61C2212yes—
71C4×C22⋊C4×C61C2212yes—
72C4×C22⋊C4×C61C2212yes—
73C4×C22⋊C4×C61C2212yes—
74C2×#95×C61C2212yes—
75#14519770—216no—
76#14519736—24no—
77#14519736—24no—
78#14519736—24no—
79#14519736—24no—
80C2×C4⋊Dic61C2314yes—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2312yes—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2312yes—
87C2×C4⋊Dic61C2314yes—
88C2×#11758196C2314yes—
89C2×#11758196C2314yes—
90C2×#11758196C2314yes—
91C2×#11758196C2314yes—
92C2×C22⋊Dic61C2314yes—
93C2×C22⋊Dic61C2314yes—
94C2×C22⋊Dic61C2312yes—
95C2×C22⋊Dic61C2312yes—
96C2×C22⋊Dic61C2312yes—
97C2×C22⋊Dic61C2312yes—
98C2×C22⋊Dic61C2314yes—
99C2×C22⋊Dic61C2314yes—
100C2×C4×Dic61C2312yes—
101C2×C4×Dic61C2312yes—
102C2×C4×Dic61C2312yes—
103C2×C4×Dic61C2312yes—
104C2×C4×Dic61C2314yes—
105C2×C4×Dic61C2314yes—
106#14519684C2314yes—
107#14519684C2314yes—
108#14519684C2314yes—
109#14519684C2314yes—
110#14519684C2314yes—
111#14519684C2314yes—
112#14519684C2314yes—
113#14519684C2314yes—
114#14519684C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118C25×C61C2311yescharacteristic
119C23×C4×C61—24no—
120C23×C4×C61—24no—
121C23×C4×C61—24no—
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2312yes—
124C23×C4×C61C2312yes—
125C23×C4×C61C2312yes—
126C23×C4×C61C2312yes—
127C23×C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—28no—
129C2×C22⋊C4×C61C2312yes—
130C2×C22⋊C4×C61C2312yes—
131C2×C22⋊C4×C61C2312yes—
132C2×C22⋊C4×C61C2312yes—
133C2×C42×C61—24no—
134C2×C42×C61—24no—
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2312yes—
138C2×C42×C61C2312yes—
139C2×C42×C61C2311yescharacteristic
140C2×C42×C61C2311yescharacteristic
141#95×C61C2312yes—
142#95×C61C2312yes—
143#95×C61C2312yes—
144#95×C61C2312yes—
145C24×C61—24no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—42no—
150C24×C61C2412yes—
151C24×C61C2411yescharacteristic
152C22×C4×C61—24no—
153C22×C4×C61—24no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—24no—
158C22×C4×C61—24no—
159C22×C4×C61—24no—
160C22×C4×C61—24no—
161C22×C4×C61—24no—
162C22×C4×C61—24no—
163C22×C4×C61—24no—
164C22×C4×C61—24no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61—416no—
168C22×C4×C61#4114yes—
169C22×C4×C61#4114yes—
170C22×C4×C61#4114yes—
171C22×C4×C61C2412yes—
172C22×C4×C61C2412yes—
173C22×C4×C61C2412yes—
174C22×C4×C61C2412yes—
175C22×C4×C61C2412yes—
176C22×C4×C61C2411yescharacteristic
177C22×C4×C61C2411yescharacteristic
178C22×Dic61C2414yes—
179C22×Dic61C2412yes—
180C22×Dic61C2412yes—
181C22×Dic61C2414yes—
182C22×Dic61C2412yes—
183C22×Dic61C2412yes—
184C22⋊C4×C61—24no—
185C22⋊C4×C61—24no—
186C22⋊C4×C61—24no—
187C22⋊C4×C61#4118yes—
188C42×C61—22no—
189C42×C61—22no—
190C42×C61—24no—
191C42×C61—24no—
192C42×C61—22no—
193C42×C61—22no—
194C22⋊Dic61—24no—
195C22⋊Dic61—24no—
196C22⋊Dic61—24no—
197C22⋊Dic61—24no—
198C22⋊Dic61—28no—
199C22⋊Dic61—28no—
200C22⋊Dic61—44no—
201C22⋊Dic61—44no—
202C4⋊Dic61—24no—
203C4⋊Dic61—24no—
204C4⋊Dic61—22no—
205C4⋊Dic61—22no—
206C4⋊Dic61—22no—
207C4⋊Dic61—22no—
208C4⋊Dic61—28no—
209C4⋊Dic61—44no—
210#11758196—28no—
211#11758196—28no—
212#11758196—44no—
213#11758196—44no—
214C4×Dic61—24no—
215C4×Dic61—24no—
216C4×Dic61—24no—
217C4×Dic61—24no—
218C4×Dic61—28no—
219C4×Dic61—44no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—28no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61—22no—
229C23×C61—48no—
230C23×C61—48no—
231C23×C61—44no—
232C23×C61—44no—
233C23×C61C2×#4114yes—
234C23×C61C2×#4112yes—
235C23×C61C2×#4112yes—
236C23×C61C2×#4112yes—
237C23×C61C2511yescharacteristic
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—48no—
252C2×C4×C61—48no—
253C2×C4×C61—44no—
254C2×C4×C61—48no—
255C2×C4×C61—48no—
256C2×C4×C61#126116yescomplemented
257C2×C4×C61C2×#4114yes—
258C2×C4×C61C2×#4114yes—
259C2×C4×C61C2×#4112yes—
260C2×C4×C61C2×#4112yes—
261C2×C4×C61C2×#4112yes—
262C2×C4×C61C2×#4112yes—
263C2×C4×C61C2×#4112yes—
264C2×C4×C61C2×#4112yes—
265C2×Dic61—24no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—24no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—24no—
272C2×Dic61—24no—
273C2×Dic61—24no—
274C2×Dic61—24no—
275C2×Dic61—24no—
276C2×Dic61—24no—
277C2×Dic61—24no—
278C2×Dic61—24no—
279#34814—611nomaximal, Sylow
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—24no—
283C22×C61—24no—
284C22×C61—24no—
285C22×C61—24no—
286C22×C61—24no—
287C22×C61—416no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61C2×#12614yes—
293C22×C61C22×#4111yescharacteristic
294C22×C61C22×#4111yescharacteristic
295C22×C61C22×#4111yescharacteristic
296C22×C61C22×#4112yes—
297C22×C61#58512yes—
298C4×C61—24no—
299C4×C61—24no—
300C4×C61—42no—
301C4×C61—42no—
302C4×C61—42no—
303C4×C61C2×#12614yes—
304C4×C61C2×#12614yes—
305Dic61—42no—
306Dic61—42no—
307Dic61—42no—
308Dic61—42no—
309Dic61—44no—
310Dic61—44no—
311#2497—612no—
312#2496—612no—
313#2495—612no—
314#2494—612no—
315#2493—614no—
316#2480—614no—
317#2401—614no—
318C4×#126—614no—
319#2296—611no—
320#2296—611no—
321#2285—611no—
322#2280—611no—
323#2280—611no—
324C4×#117—611no—
325C2×C4×C22⋊C4D6111yescharacteristic
326C2×C61—24no—
327C2×C61—44no—
328C2×C61C22×#12611yescharacteristic
329C2×C61#344411yescharacteristic
330C2×C61#345511yescharacteristic
331C2×C61#347512yes—
332C2×C61#347512yes—
333C24×C4C2×D6111yescharacteristic
334C2×#126—614no—
335C2×#117—611no—
336C2×#117—611no—
337C2×#117—611no—
338C2×#117—611no—
339C22×C22⋊C4C2×D6112yes—
340C22×C42C2×D6111yescharacteristic
341C22×C42C2×D6111yescharacteristic
342#401—614no—
343#400—614no—
344#400—614no—
345#400—614no—
346#397—614no—
347#397—614no—
348#397—614no—
349#396—614no—
350#389—612no—
351#389—612no—
352#389—612no—
353#389—612no—
354#388—614no—
355#388—614no—
356#388—614no—
357#387—614no—
358#387—614no—
359#387—614no—
360#385—614no—
361#385—614no—
362#384—611no—
363#384—611no—
364#383—614no—
365#382—611no—
366#382—611no—
367#381—612no—
368#381—612no—
369#380—614no—
370#380—612no—
371#380—612no—
372#380—612no—
373#380—612no—
374#379—612no—
375#379—612no—
376C4×C4⋊C4—612no—
377C4×C4⋊C4—614no—
378C4×C4⋊C4—614no—
379C4×C4⋊C4—612no—
380C4×C4⋊C4—612no—
381C4×C4⋊C4—612no—
382C4×C22⋊C4—614no—
383C4×C22⋊C4—614no—
384C4×C22⋊C4—614no—
385C4×C22⋊C4C2×D6112yes—
386C4×C22⋊C4C2×D6112yes—
387C4×C22⋊C4C2×D6112yes—
388C4×C22⋊C4C2×D6112yes—
389#376—612no—
390C2×#95C2×D6112yes—
391C43—612no—
392C61#3481411yescharacteristic, complemented, Sylow
393C25C22×D6111yescharacteristic
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4C22×D6111yescharacteristic
398C23×C4C22×D6112yes—
399C23×C4C22×D6112yes—
400C23×C4C22×D6112yes—
401C23×C4C22×D6112yes—
402C23×C4C22×D6111yescharacteristic
403#126—12216no—
404#117—1224no—
405#117—1224no—
406#117—1224no—
407#117—1224no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—612no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—612no—
414C2×C4⋊C4—614no—
415C2×C4⋊C4—614no—
416C2×C4⋊C4—614no—
417C2×C4⋊C4—614no—
418C2×C4⋊C4—614no—
419C2×C4⋊C4—614no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—612no—
422C2×C22⋊C4—612no—
423C2×C22⋊C4—612no—
424C2×C22⋊C4—612no—
425C2×C22⋊C4—614no—
426C2×C22⋊C4—614no—
427C2×C22⋊C4—614no—
428C2×C22⋊C4—614no—
429C2×C22⋊C4C22×D6112yes—
430C2×C22⋊C4C22×D6112yes—
431C2×C22⋊C4C22×D6112yes—
432C2×C22⋊C4C22×D6112yes—
433C2×C42—24no—
434C2×C42—24no—
435C2×C42—614no—
436C2×C42—612no—
437C2×C42—612no—
438C2×C42—612no—
439C2×C42—612no—
440C2×C42—614no—
441C2×C42C22×D6112yes—
442C2×C42C22×D6111yescharacteristic
443C2×C42C22×D6111yescharacteristic
444C2×C42C22×D6111yescharacteristic
445C2×C42C22×D6111yescharacteristic
446C2×C42C22×D6112yes—
447#95—614no—
448#95—614no—
449#95—614no—
450#95—614no—
451#95—614no—
452#95—614no—
453#95—614no—
454#95—614no—
455#95—614no—
456#95—614no—
457#95—614no—
458#95—614no—
459#95C22×D6112yes—
460#95C22×D6112yes—
461#95C22×D6112yes—
462#95C22×D6112yes—
463C24—24no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—42no—
468C24C23×D6112yes—
469C24C23×D6111yescharacteristic
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—416no—
486C22×C4—614no—
487C22×C4—612no—
488C22×C4—612no—
489C22×C4—614no—
490C22×C4—612no—
491C22×C4—612no—
492C22×C4#1175822214yes—
493C22×C4#1175822414yes—
494C22×C4#1175822414yes—
495C22×C4C23×D6112yes—
496C22×C4C23×D6112yes—
497C22×C4C23×D6112yes—
498C22×C4C23×D6112yes—
499C22×C4C23×D6112yes—
500C22×C4C23×D6111yescharacteristic
501C22×C4C23×D6111yescharacteristic
502C4⋊C4—1224no—
503C4⋊C4—1224no—
504C4⋊C4—1228no—
505C4⋊C4—1228no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1228no—
511C4⋊C4—2444no—
512C4⋊C4—2444no—
513C4⋊C4—2444no—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—1224no—
518C22⋊C4—1224no—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C22⋊C4—1228no—
522C22⋊C4—1228no—
523C22⋊C4—2444no—
524C22⋊C4—2444no—
525C22⋊C4#1175822218yes—
526C42—22no—
527C42—22no—
528C42—24no—
529C42—24no—
530C42—22no—
531C42—22no—
532C42—1224no—
533C42—1224no—
534C42—1224no—
535C42—1224no—
536C42—1228no—
537C42—2444no—
538C23—22no—
539C23—22no—
540C23—28no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—48no—
548C23—48no—
549C23—44no—
550C23—44no—
551C23C2×#1175822412yes—
552C23C2×#1175822412yes—
553C23C2×#1175822214yes—
554C23C2×#1175822212yes—
555C23C24×D6111yescharacteristic
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—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—48no—
571C2×C4—44no—
572C2×C4—48no—
573C2×C4—48no—
574C2×C4—1224no—
575C2×C4—1224no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1224no—
581C2×C4—1224no—
582C2×C4—1224no—
583C2×C4—1224no—
584C2×C4—1224no—
585C2×C4—1224no—
586C2×C4—1224no—
587C2×C4—1224no—
588C2×C4#14519770116yescomplemented
589C2×C4C2×#1175822412yes—
590C2×C4C2×#1175822412yes—
591C2×C4C2×#1175822412yes—
592C2×C4C2×#1175822412yes—
593C2×C4C2×#1175822214yes—
594C2×C4C2×#1175822214yes—
595C2×C4C2×#1175822212yes—
596C2×C4C2×#1175822212yes—
597C22—22no—
598C22—22no—
599C22—24no—
600C22—24no—
601C22—24no—
602C22—24no—
603C22—24no—
604C22—416no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22C2×#1451977014yes—
610C22C22×#1175822411yescharacteristic
611C22C22×#1175822411yescharacteristic
612C22C22×#1175822211yescharacteristic
613C22C22×#1175822212yes—
614C22#1684059812yes—
615C4—24no—
616C4—24no—
617C4—42no—
618C4—42no—
619C4—42no—
620C4—2442no—
621C4—2442no—
622C4—2442no—
623C4—2442no—
624C4—2444no—
625C4—2444no—
626C4C2×#1451977014yes—
627C4C2×#1451977014yes—
628C2—24no—
629C2—44no—
630C2C22×#1451977011yescharacteristic
631C2#2145911511yescharacteristic
632C2#2145920911yescharacteristic
633C2#2145937712yes—
634C2#2145937712yes—
subgroupG/H
centerC22×C4C23×D61
commutator, socle, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C4×C22⋊C4×C61C2
prime radicalC25×C61C23
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#34814
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21450252C2semidirect
2. #21450241C2semidirect
3. #21450230C2semidirect
4. #21450219C2semidirect
5. #21450204C2semidirect
7. #21449119C2semidirect
8. C4×#14519770C2semidirect
9. #21448302C2semidirect
10. #21448302C2semidirect
11. #21448226C2semidirect
14. C4×#14519736C2semidirect
21. C61⋊#401C22semidirect
22. #16839704C22semidirect
23. #16839703C22semidirect
24. #16839702C22semidirect
29. #16839660C22semidirect
30. #16839660C22semidirect
31. #16839660C22semidirect
32. #16839660C22semidirect
36. #16839649C22semidirect
37. #16839647C22semidirect
38. #16839644C22semidirect
41. #16839632C22semidirect
42. #16839632C22semidirect
43. #16839629C22semidirect
44. #16839628C22semidirect
45. #16839628C22semidirect
55. C4×#11758196C22semidirect
56. C4×#11758196C22semidirect
57. C4×#11758196C22semidirect
58. C4×C4⋊Dic61C22semidirect
59. C4×C4⋊Dic61C22semidirect
60. C4×C4⋊Dic61C22semidirect
64. #16839608C22semidirect
65. C42×Dic61C22semidirect
256. C2×C4×C61#126semidirect
392. C61#34814semidirect
588. C2×C4#14519770semidirect

Maximal subgroups

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

subgroupindex
#214502522
#214502412
#214502302
#214502192
#214502042
#214500592
#214491192
C4×#145197702
#214483022
#214482262
#214482022
C4×#145197362
C2×C4×C22⋊C4×C612
#3481461