Finite Group Databasebeta

← #29849984

Subgroups — #29849984

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#21450254C212yesmaximal, complemented
2#21450243C212yesmaximal, complemented
3#21450232C212yesmaximal, complemented
4#21450221C212yesmaximal, complemented
5#21450208C214yesmaximal, complemented
6#21450062C214yesmaximal
7#21449119C214yesmaximal, complemented
8C4×#14519770C214yesmaximal, complemented
9#21448303C211yesmaximal, characteristic, complemented
10#21448301C211yesmaximal, characteristic, complemented
11#21448222C211yesmaximal, characteristic, complemented
12#21448202C211yesmaximal, characteristic
13#117×Dic61C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic61C211yesmaximal, characteristic
15C61×#2280C211yesmaximal, characteristic
16C2×#14519770C2214yes—
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C22×C22⋊Dic61C2212yes—
20C22×C4×Dic61C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22C61⋊#401C2214yescomplemented
23#16839704C2214yescomplemented
24#16839703C2214yescomplemented
25#16839702C2214yescomplemented
26#16839690C2214yes—
27#16839690C2214yes—
28#16839687C2214yes—
29#16839685C2214yes—
30#16839661C2212yescomplemented
31#16839661C2212yescomplemented
32#16839658C2212yescomplemented
33#16839658C2212yescomplemented
34#16839656C2214yes—
35#16839655C2214yes—
36#16839650C2214yes—
37#16839649C2214yescomplemented
38#16839647C2214yescomplemented
39#16839644C2214yescomplemented
40#16839637C2214yes—
41#16839634C2214yes—
42#16839631C2211yescharacteristic, complemented
43#16839631C2211yescharacteristic, complemented
44#16839629C2214yescomplemented
45#16839627C2211yescharacteristic, complemented
46#16839627C2211yescharacteristic, complemented
47#16839625C2212yes—
48#16839622C2212yes—
49#16839622C2212yes—
50#16839620C2214yes—
51#16839618C2212yes—
52C4⋊C4×Dic61C2212yescomplemented
53C4⋊C4×Dic61C2212yescomplemented
54C4×#11758196C2214yescomplemented
55C4×#11758196C2212yescomplemented
56C4×#11758196C2212yescomplemented
57C4×C4⋊Dic61C2214yescomplemented
58C22⋊C4×Dic61C2214yes—
59C4×C22⋊Dic61C2212yes—
60C4×C22⋊Dic61C2214yes—
61C4×C22⋊Dic61C2212yes—
62C4×C22⋊Dic61C2212yes—
63C4×C22⋊Dic61C2212yes—
64#16839608C2212yescomplemented
65C2×#14519684C2212yes—
66C42×Dic61C2212yescomplemented
67C24×C4×C61C2211yescharacteristic
68C2×#117×C61C2211yescharacteristic
69C2×#117×C61C2211yescharacteristic
70C61×#381C2212yes—
71C61×#380C2212yes—
72C61×#380C2212yes—
73C61×#379C2212yes—
74C4×C22⋊C4×C61C2214yes—
75C23×Dic61C2312yes—
76C23×Dic61C2312yes—
77#14519770—216no—
78#14519736—24no—
79#14519736—24no—
80C2×C4⋊Dic61C2314yes—
81C2×C4⋊Dic61C2312yes—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2314yes—
85C2×#11758196C2314yes—
86C2×#11758196C2314yes—
87C2×#11758196C2314yes—
88C2×#11758196C2314yes—
89C2×C22⋊Dic61—28no—
90C2×C22⋊Dic61C2312yes—
91C2×C22⋊Dic61C2312yes—
92C2×C22⋊Dic61C2314yes—
93C2×C22⋊Dic61C2312yes—
94C2×C22⋊Dic61C2312yes—
95C2×C22⋊Dic61C2312yes—
96C2×C22⋊Dic61C2314yes—
97C2×C22⋊Dic61C2312yes—
98C2×C4×Dic61—24no—
99C2×C4×Dic61—24no—
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2312yes—
103C2×C4×Dic61C2312yes—
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C2×C4×Dic61C2312yes—
107C2×C4×Dic61C2312yes—
108C2×C4×Dic61C2314yes—
109C2×C4×Dic61C2314yes—
110#14519684C2314yes—
111#14519684C2314yes—
112#14519684C2314yes—
113#14519684C2314yes—
114#14519684C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2312yes—
118#14519684C2314yes—
119#14519684C2312yes—
120#14519684C2314yes—
121#14519684C2312yes—
122#14519684C2312yes—
123#14519684C2314yes—
124C25×C61C2311yescharacteristic
125C23×C4×C61—24no—
126C23×C4×C61—24no—
127C23×C4×C61—24no—
128C23×C4×C61C2312yes—
129C23×C4×C61C2312yes—
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132#117×C61—24no—
133#117×C61—24no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2312yes—
137C2×C22⋊C4×C61C2314yes—
138C2×C22⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2312yes—
140C2×C22⋊C4×C61C2314yes—
141C2×C42×C61C2312yes—
142C2×C42×C61C2312yes—
143#95×C61C2314yes—
144#95×C61C2314yes—
145C24×C61—22no—
146C24×C61—24no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—42no—
150C24×C61C2412yes—
151C24×C61C2411yescharacteristic
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—24no—
156C22×C4×C61—24no—
157C22×C4×C61—24no—
158C22×C4×C61—24no—
159C22×C4×C61—24no—
160C22×C4×C61—24no—
161C22×C4×C61—416no—
162C22×C4×C61#4114yes—
163C22×C4×C61#4114yes—
164C22×C4×C61#4114yes—
165C22×C4×C61C2412yes—
166C22×C4×C61C2412yes—
167C22×C4×C61C2412yes—
168C22×C4×C61C2414yes—
169C22×C4×C61C2411yescharacteristic
170C22×C4×C61C2411yescharacteristic
171C22×Dic61—24no—
172C22×Dic61—24no—
173C22×Dic61—24no—
174C22×Dic61—24no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C22×Dic61C2412yes—
178C22×Dic61C2412yes—
179C22×Dic61C2414yes—
180C22×Dic61C2412yes—
181C22×Dic61C2412yes—
182C22×Dic61C2412yes—
183C22×Dic61C2412yes—
184C4⋊C4×C61—24no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C22⋊C4×C61—24no—
188C22⋊C4×C61—24no—
189C22⋊C4×C61—28no—
190C22⋊C4×C61—44no—
191C42×C61—24no—
192C42×C61—24no—
193C22⋊Dic61—24no—
194C22⋊Dic61—24no—
195C22⋊Dic61—24no—
196C22⋊Dic61—28no—
197C22⋊Dic61—24no—
198C22⋊Dic61—24no—
199C22⋊Dic61—44no—
200C22⋊Dic61#4118yes—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61—24no—
204C4⋊Dic61—28no—
205C4⋊Dic61—44no—
206#11758196—28no—
207#11758196—28no—
208#11758196—44no—
209#11758196—44no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—24no—
213C4×Dic61—24no—
214C4×Dic61—22no—
215C4×Dic61—22no—
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—24no—
239C2×C4×C61—24no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—24no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—24no—
247C2×C4×C61—24no—
248C2×C4×C61—44no—
249C2×C4×C61—48no—
250C2×C4×C61—48no—
251C2×C4×C61#126116yescomplemented
252C2×C4×C61C2×#4112yes—
253C2×C4×C61C2×#4112yes—
254C2×C4×C61C2×#4112yes—
255C2×C4×C61C2×#4112yes—
256C2×C4×C61C2×#4112yes—
257C2×C4×C61C2×#4112yes—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—24no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—24no—
272C2×Dic61—24no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—48no—
276C2×Dic61—48no—
277C2×Dic61C2×#4114yes—
278C2×Dic61C2×#4114yes—
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×#4112yes—
294C22×C61C22×#4111yescharacteristic
295C22×C61C22×#4111yescharacteristic
296C22×C61C22×#4111yescharacteristic
297C22×C61#58512yes—
298C4×C61—42no—
299C4×C61—42no—
300C4×C61—42no—
301C4×C61—44no—
302C4×C61C2×#12614yes—
303C4×C61C2×#12614yes—
304Dic61—24no—
305Dic61—24no—
306Dic61—42no—
307Dic61—42no—
308Dic61—44no—
309Dic61—42no—
310Dic61—42no—
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#2280D6111yescharacteristic
324C4×#117—611no—
325C2×C4×C22⋊C4—611no—
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×#117C2×D6111yescharacteristic
338C2×#117C2×D6111yescharacteristic
339C22×C22⋊C4—612no—
340C22×C42—611no—
341C22×C42—611no—
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#381C2×D6112yes—
369#380—612no—
370#380—612no—
371#380—614no—
372#380C2×D6112yes—
373#380C2×D6112yes—
374#379—612no—
375#379C2×D6112yes—
376C4×C4⋊C4—612no—
377C4×C4⋊C4—612no—
378C4×C4⋊C4—612no—
379C4×C4⋊C4—614no—
380C4×C4⋊C4—614no—
381C4×C4⋊C4—612no—
382C4×C22⋊C4—612no—
383C4×C22⋊C4—614no—
384C4×C22⋊C4—612no—
385C4×C22⋊C4—612no—
386C4×C22⋊C4—612no—
387C4×C22⋊C4—614no—
388C4×C22⋊C4C2×D6114yes—
389#376—612no—
390C2×#95—612no—
391C43—612no—
392C61#3481411yescharacteristic, complemented, Sylow
393C25C22×D6111yescharacteristic
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—612no—
398C23×C4—612no—
399C23×C4C22×D6111yescharacteristic
400C23×C4C22×D6112yes—
401C23×C4C22×D6112yes—
402C23×C4C22×D6111yescharacteristic
403#126—12216no—
404#117—24no—
405#117—24no—
406#117—1224no—
407#117—1224no—
408C2×C4⋊C4—612no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—614no—
412C2×C4⋊C4—614no—
413C2×C4⋊C4—614no—
414C2×C4⋊C4—614no—
415C2×C4⋊C4—614no—
416C2×C4⋊C4—614no—
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6112yes—
420C2×C22⋊C4—612no—
421C2×C22⋊C4—612no—
422C2×C22⋊C4—612no—
423C2×C22⋊C4—612no—
424C2×C22⋊C4—612no—
425C2×C22⋊C4—612no—
426C2×C22⋊C4—614no—
427C2×C22⋊C4—614no—
428C2×C22⋊C4—1228no—
429C2×C22⋊C4C22×D6112yes—
430C2×C22⋊C4C22×D6112yes—
431C2×C22⋊C4C22×D6114yes—
432C2×C22⋊C4C22×D6114yes—
433C2×C42—614no—
434C2×C42—612no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—612no—
438C2×C42—612no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—612no—
442C2×C42—614no—
443C2×C42—1224no—
444C2×C42—1224no—
445C2×C42C22×D6112yes—
446C2×C42C22×D6112yes—
447#95—612no—
448#95—612no—
449#95—612no—
450#95—612no—
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#95—614no—
460#95—614no—
461#95C22×D6114yes—
462#95C22×D6114yes—
463C24—24no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—42no—
468C24C23×D6112yes—
469C24C23×D6111yescharacteristic
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—416no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—612no—
484C22×C4—614no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—1224no—
488C22×C4—1224no—
489C22×C4—1224no—
490C22×C4—1224no—
491C22×C4—2442no—
492C22×C4—2442no—
493C22×C4#1175822214yes—
494C22×C4#1175822414yes—
495C22×C4#1175822414yes—
496C22×C4C23×D6112yes—
497C22×C4C23×D6112yes—
498C22×C4C23×D6112yes—
499C22×C4C23×D6114yes—
500C22×C4C23×D6111yescharacteristic
501C22×C4C23×D6111yescharacteristic
502C4⋊C4—24no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—1228no—
506C4⋊C4—1228no—
507C4⋊C4—1228no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1224no—
511C4⋊C4—2444no—
512C4⋊C4—2444no—
513C4⋊C4—2444no—
514C22⋊C4—28no—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—44no—
518C22⋊C4—618no—
519C22⋊C4—1224no—
520C22⋊C4—1224no—
521C22⋊C4—1224no—
522C22⋊C4—1228no—
523C22⋊C4—1224no—
524C22⋊C4—1224no—
525C22⋊C4—2444no—
526C42—24no—
527C42—24no—
528C42—1228no—
529C42—1222no—
530C42—1224no—
531C42—1222no—
532C42—1224no—
533C42—1222no—
534C42—1224no—
535C42—1222no—
536C42—1224no—
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—
551C23#41×D6114yes—
552C23C2×#1175822412yes—
553C23C2×#1175822412yes—
554C23C2×#1175822212yes—
555C23C24×D6111yescharacteristic
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—44no—
567C2×C4—48no—
568C2×C4—48no—
569C2×C4—614no—
570C2×C4—614no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1224no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1224no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1224no—
584C2×C4—1224no—
585C2×C4—1224no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—2448no—
589C2×C4—2448no—
590C2×C4#14519770116yescomplemented
591C2×C4C2×#1175822412yes—
592C2×C4C2×#1175822412yes—
593C2×C4C2×#1175822412yes—
594C2×C4C2×#1175822412yes—
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—
610C22C2×#41×D6112yes—
611C22C22×#1175822411yescharacteristic
612C22C22×#1175822411yescharacteristic
613C22C22×#1175822211yescharacteristic
614C22#1684059812yes—
615C4—42no—
616C4—42no—
617C4—42no—
618C4—44no—
619C4—1224no—
620C4—1224no—
621C4—2442no—
622C4—2442no—
623C4—2444no—
624C4—2442no—
625C4—2442no—
626C4C2×#1451977014yes—
627C4C2×#1451977014yes—
628C2—24no—
629C2—44no—
630C2C22×#1451977011yescharacteristic
631C2#2145911111yescharacteristic
632C2#2145920711yescharacteristic
633C2#2145937312yes—
634C2#2145937912yes—
subgroupG/H
centerC22×C4C23×D61
commutator, socle, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC61×#2280C2
prime radicalC25×C61C23
hypercenter#2280D61
hypocenterC61#34814
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. #21450254C2semidirect
2. #21450243C2semidirect
3. #21450232C2semidirect
4. #21450221C2semidirect
5. #21450208C2semidirect
7. #21449119C2semidirect
8. C4×#14519770C2semidirect
9. #21448303C2semidirect
10. #21448301C2semidirect
11. #21448222C2semidirect
13. #117×Dic61C2semidirect
22. C61⋊#401C22semidirect
23. #16839704C22semidirect
24. #16839703C22semidirect
25. #16839702C22semidirect
30. #16839661C22semidirect
31. #16839661C22semidirect
32. #16839658C22semidirect
33. #16839658C22semidirect
37. #16839649C22semidirect
38. #16839647C22semidirect
39. #16839644C22semidirect
42. #16839631C22semidirect
43. #16839631C22semidirect
44. #16839629C22semidirect
45. #16839627C22semidirect
46. #16839627C22semidirect
52. C4⋊C4×Dic61C22semidirect
53. C4⋊C4×Dic61C22semidirect
54. C4×#11758196C22semidirect
55. C4×#11758196C22semidirect
56. C4×#11758196C22semidirect
57. C4×C4⋊Dic61C22semidirect
64. #16839608C22semidirect
66. C42×Dic61C22semidirect
251. C2×C4×C61#126semidirect
392. C61#34814semidirect
590. C2×C4#14519770semidirect

Maximal subgroups

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

subgroupindex
#214502542
#214502432
#214502322
#214502212
#214502082
#214500622
#214491192
C4×#145197702
#214483032
#214483012
#214482222
#214482022
#117×Dic612
C2×C4×C22⋊Dic612
C61×#22802
#3481461