Finite Group Databasebeta

← #29608797

Subgroups — #29608797

Order 15616.

2134 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519765C211yesmaximal, characteristic
2C2×#16839640C212yesmaximal
3#21444089C212yesmaximal, complemented
4#21444067C212yesmaximal, complemented
5#21444067C212yesmaximal, complemented
6#21444046C211yesmaximal, characteristic, complemented
7#21444040C212yesmaximal, complemented
8#21444040C212yesmaximal, complemented
9C61×#1434C211yesmaximal, characteristic, complemented
10C23×Dic122C2211yescharacteristic
11C23×D244C2211yescharacteristic
12C23×C4×D61C2212yes—
13C2×#14519765—28no—
14C2×#14519765C418yescomplemented
15C22×#11758198C2212yes—
16C22×#11758198C2212yes—
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20#16839640—28no—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2212yes—
29C22×C42×C61C2211yescharacteristic
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2211yescharacteristic
34C24×D61C2312yes—
35C22×Dic122—24no—
36C22×Dic122—42no—
37C22×Dic122—41no—
38C22×Dic122—41no—
39C22×Dic122C2×C414yescomplemented
40C22×D244—41no—
41C22×D244—42no—
42C22×D244—41no—
43C22×D244C2×C414yes—
44C22×D244D418yes—
45C23×Dic61C2312yes—
46C23×Dic61C2312yes—
47C23×Dic61C2312yes—
48C22×C4×D61—24no—
49C22×C4×D61—24no—
50C22×C4×D61—24no—
51C22×C4×D61—42no—
52C22×C4×D61—42no—
53C22×C4×D61—42no—
54C22×C4×D61—42no—
55#14519765—232no—
56C2×#11758198—24no—
57C2×#11758198—24no—
58C2×#11758198—24no—
59C2×#11758198—24no—
60C2×#11758198—24no—
61C2×#11758198—24no—
62C2×#11758198—24no—
63C2×#11758198—24no—
64C2×#11758198—24no—
65C2×#11758198—42no—
66C2×#11758198—42no—
67C2×#11758198—42no—
68C2×#11758198—42no—
69C2×#11758198C2×C418yescomplemented
70C2×#11758198C2×C418yescomplemented
71#14519684—24no—
72#14519684—24no—
73#14519684—41no—
74#14519684—42no—
75#14519684—42no—
76#14519684—42no—
77#14519684—42no—
78#14519684—41no—
79C23×C4×C61C2312yes—
80C23×C4×C61C2311yescharacteristic
81C23×C4×C61C2311yescharacteristic
82C23×C4×C61C2312yes—
83C23×C4×C61C2311yescharacteristic
84C2×C42×C61—24no—
85C2×C42×C61C2×C414yescomplemented
86#95×C61—24no—
87#95×C61—24no—
88#95×C61—41no—
89#95×C61—41no—
90C24×C61C2411yescharacteristic
91C23×D61—22no—
92C23×D61—22no—
93C23×D61—22no—
94C23×D61—22no—
95C23×D61—22no—
96C23×D61—22no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—22no—
100C23×D61—22no—
101C23×D61—22no—
102C23×D61—22no—
103C23×D61C22×C414yes—
104C23×D61C2×D414yes—
105C23×D61C2×D414yes—
106C22×C4×C61—22no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61C22×C412yes—
131C22×C4×C61C22×C412yes—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C2×D414yes—
134C22×C4×C61#4114yes—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61C22×C414yes—
155C22×Dic61#4114yes—
156C2×D244—44no—
157C2×D244—44no—
158C2×D244—48no—
159C2×D244—48no—
160C2×D244C22⋊C4116yes—
161C2×C4×D61—48no—
162C2×C4×D61—48no—
163C2×C4×D61—48no—
164C2×C4×D61—48no—
165C2×C4×D61—48no—
166C2×C4×D61—48no—
167C2×C4×D61—48no—
168C2×Dic122—28no—
169C2×Dic122—44no—
170C2×Dic122—44no—
171C2×Dic122—48no—
172C2×Dic122—48no—
173C42×C61—28no—
174#11758198—216no—
175#11758198—216no—
176#11758198—48no—
177#11758198—48no—
178#11758198—48no—
179C23×C61C23×C411yescharacteristic
180C23×C61C22×D412yes—
181C23×C61C2×#4112yes—
182C23×C61C2×#4112yes—
183C23×C61H(5,𝔽2)12yes—
184C23×C61H(5,𝔽2)11yescharacteristic
185C23×C61H(5,𝔽2)11yescharacteristic
186C23×C61H(5,𝔽2)11yescharacteristic
187C23×C61H(5,𝔽2)11yescharacteristic
188C23×C612−1+411yescharacteristic
189C23×C612−1+411yescharacteristic
190C22×D61—24no—
191C22×D61—24no—
192C22×D61—24no—
193C22×D61—24no—
194C22×D61—24no—
195C22×D61—24no—
196C22×D61—24no—
197C22×D61—24no—
198C22×D61—24no—
199C22×D61—24no—
200C22×D61—24no—
201C22×D61—24no—
202C22×D61—24no—
203C22×D61—24no—
204C22×D61—24no—
205C22×D61—24no—
206C22×D61—24no—
207C22×D61—24no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—42no—
223C22×D61—42no—
224C22×D61C2×C22⋊C418yes—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—24no—
228C2×C4×C61—24no—
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—24no—
236C2×C4×C61—24no—
237C2×C4×C61—24no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61C2×C22⋊C414yes—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—24no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61—42no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275D244—416no—
276C4×D61—432no—
277Dic122—416no—
278#14473—611nomaximal, Sylow
279C22×C61C22×C22⋊C411yescharacteristic
280C22×C61C4×#4111yescharacteristic
281C22×C61C4×#4111yescharacteristic
282C22×C61#51811yescharacteristic
283C22×C61#51811yescharacteristic
284C22×C61#52011yescharacteristic
285C22×C61#52011yescharacteristic
286C22×C61#53412yes—
287C22×C61#53412yes—
288C22×C61#53812yes—
289C22×C61#53812yes—
290C22×C61#54212yes—
291C22×C61#54212yes—
292C22×C61#54612yes—
293C22×C61#54612yes—
294C22×C61#54712yes—
295C22×C61#54712yes—
296C22×C61#55112yes—
297C22×C61#55512yes—
298C22×C61H(3,𝔽4)11yescharacteristic
299C22×C61#56211yescharacteristic
300C22×C61#56211yescharacteristic
301C22×C61#56311yescharacteristic
302C2×D61—28no—
303C2×D61—28no—
304C2×D61—28no—
305C2×D61—44no—
306C2×D61—44no—
307C2×D61—44no—
308C2×D61—44no—
309C2×D61—44no—
310C2×D61—44no—
311C2×D61—44no—
312C2×D61—44no—
313C2×D61—44no—
314C2×D61—44no—
315C2×D61—44no—
316C2×D61—44no—
317C4×C61—24no—
318C4×C61—42no—
319C4×C61—42no—
320C4×C61—44no—
321C4×C61—82no—
322Dic61—44no—
323Dic61—44no—
324Dic61—82no—
325C22×#124—611no—
326C2×#386—612no—
327#1446—612no—
328#1440—612no—
329#1440—612no—
330#1434—611no—
331#1434D6111yescharacteristic, complemented
332C22⋊#95—612no—
333C22⋊#95—612no—
334C2×C61#230811yescharacteristic
335C2×C61#233711yescharacteristic
336C2×C61#233711yescharacteristic
337C2×C61#233911yescharacteristic
338C2×C61#233911yescharacteristic
339C2×C61#237211yescharacteristic
340C2×C61#237911yescharacteristic
341C2×C61#268412yes—
342C2×C61#268612yes—
343C2×C61#268612yes—
344C2×C61#271712yes—
345D61—48no—
346C23×Q8—611no—
347C23×D4—611no—
348C24×C4—612no—
349C2×#124—618no—
350C2×#124—1228no—
351C22×C22⋊C4—612no—
352C22×C22⋊C4—612no—
353C22×C22⋊C4—612no—
354C22×C22⋊C4—612no—
355C22×C22⋊C4—612no—
356C22×C42C2×D6111yescharacteristic
357#386—1228no—
358C2×#95—612no—
359C2×#95—612no—
360C2×#95—611no—
361C2×#95—612no—
362C2×#95—612no—
363C2×#95—612no—
364C2×#95—611no—
365C2×#95—612no—
366C2×#95C2×D6112yes—
367C2×#95C2×D6112yes—
368C2×#95C2×D6111yescharacteristic
369C2×#95C2×D6111yescharacteristic
370C61#1447311yescharacteristic, complemented, Sylow
371C25—612no—
372C22×Q8—614no—
373C22×Q8—1224no—
374C22×Q8—2441no—
375C22×Q8—2441no—
376C22×Q8—2442no—
377C22×D4—614no—
378C22×D4—618no—
379C22×D4—2441no—
380C22×D4—2442no—
381C22×D4—2441no—
382C23×C4—612no—
383C23×C4—612no—
384C23×C4—612no—
385C23×C4—1224no—
386C23×C4—1224no—
387C23×C4—1224no—
388C23×C4—2442no—
389C23×C4—2442no—
390C23×C4—2442no—
391C23×C4—2442no—
392C23×C4C22×D6112yes—
393C23×C4C22×D6111yescharacteristic
394C23×C4C22×D6111yescharacteristic
395C23×C4C22×D6112yes—
396C23×C4C22×D6111yescharacteristic
397#124—12232no—
398C2×C22⋊C4—618no—
399C2×C22⋊C4—618no—
400C2×C22⋊C4—1224no—
401C2×C22⋊C4—1224no—
402C2×C22⋊C4—1224no—
403C2×C22⋊C4—1224no—
404C2×C22⋊C4—1224no—
405C2×C22⋊C4—1224no—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1224no—
408C2×C22⋊C4—1224no—
409C2×C22⋊C4—2442no—
410C2×C22⋊C4—2442no—
411C2×C22⋊C4—2442no—
412C2×C22⋊C4—2442no—
413C2×C42—24no—
414C2×C42C4×D6114yescomplemented
415#95—24no—
416#95—24no—
417#95—41no—
418#95—41no—
419#95—1224no—
420#95—1224no—
421#95—2441no—
422#95—2441no—
423#95—2442no—
424#95—2442no—
425#95—2442no—
426#95—2442no—
427C24—614no—
428C24—614no—
429C24—614no—
430C24—1222no—
431C24—1222no—
432C24—1222no—
433C24—1222no—
434C24—1222no—
435C24—1222no—
436C24—1222no—
437C24—1222no—
438C24—1222no—
439C24—1222no—
440C24—1222no—
441C24—1222no—
442C24C23×D6111yescharacteristic
443C2×Q8—1228no—
444C2×Q8—2444no—
445C2×Q8—2444no—
446C2×Q8—2448no—
447C2×Q8—2448no—
448C2×D4—6116no—
449C2×D4—2444no—
450C2×D4—2444no—
451C2×D4—2448no—
452C2×D4—2448no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—614no—
478C22×C4—614no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—2448no—
499C22×C4—2448no—
500C22×C4—2448no—
501C22×C4—2448no—
502C22×C4—2448no—
503C22×C4—2448no—
504C22×C4—2448no—
505C22×C4C2×C4×D6112yes—
506C22×C4C2×C4×D6112yes—
507C22×C4C2×C4×D6112yes—
508C22×C4#1175822214yes—
509C22×C4D4×D6114yes—
510C22⋊C4—12216no—
511C22⋊C4—12216no—
512C22⋊C4—2448no—
513C22⋊C4—2448no—
514C22⋊C4—2448no—
515C42—28no—
516C23—618no—
517C23—1224no—
518C23—1224no—
519C23—1224no—
520C23—1224no—
521C23—1224no—
522C23—1224no—
523C23—1224no—
524C23—1224no—
525C23—1224no—
526C23—1224no—
527C23—1224no—
528C23—1224no—
529C23—1224no—
530C23—1224no—
531C23—1224no—
532C23—1224no—
533C23—1224no—
534C23—1224no—
535C23—2442no—
536C23—2442no—
537C23—2442no—
538C23—2442no—
539C23—2442no—
540C23—2442no—
541C23—2442no—
542C23—2442no—
543C23—2442no—
544C23—2442no—
545C23—2442no—
546C23—2442no—
547C23—2442no—
548C23—2442no—
549C23—2442no—
550C23—2442no—
551C23C22×C4×D6111yescharacteristic
552C23C2×D4×D6112yes—
553C23#41×D6112yes—
554C23C2×#1175822212yes—
555C23#1451982211yescharacteristic
556C23#1451982311yescharacteristic
557C23#1451982311yescharacteristic
558C23#1451982312yes—
559C23#1451982311yescharacteristic
560C23#1451982411yescharacteristic
561C23#1451982511yescharacteristic
562Q8—24416no—
563D4—24416no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1224no—
598C2×C4—24432no—
599C2×C4—2442no—
600C2×C4—2442no—
601C2×C4—2442no—
602C2×C4—2442no—
603C2×C4—2442no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4—2442no—
610C2×C4—2442no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4C22⋊C4×D6114yes—
615C22—1228no—
616C22—1228no—
617C22—1228no—
618C22—2444no—
619C22—2444no—
620C22—2444no—
621C22—2444no—
622C22—2444no—
623C22—2444no—
624C22—2444no—
625C22—2444no—
626C22—2444no—
627C22—2444no—
628C22—2444no—
629C22—2444no—
630C22C2×C22⋊C4×D6111yescharacteristic
631C22#1684023011yescharacteristic
632C22C4×#1175822211yescharacteristic
633C22#1684023611yescharacteristic
634C22#1684023611yescharacteristic
635C22#1684024211yescharacteristic
636C22#1684024311yescharacteristic
637C22#1684032312yes—
638C22#1684032312yes—
639C22#1684034512yes—
640C22#1684035112yes—
641C22#1684037812yes—
642C22#1684038412yes—
643C22#1684040812yes—
644C22#1684040912yes—
645C22#1684041412yes—
646C22#1684041712yes—
647C22#1684043612yes—
648C22#1684047512yes—
649C22#1684050411yescharacteristic
650C22#1684050611yescharacteristic
651C22#1684051011yescharacteristic
652C22#1684051611yescharacteristic
653C4—24no—
654C4—44no—
655C4—42no—
656C4—42no—
657C4—82no—
658C4—4882no—
659C4—2444no—
660C4—2444no—
661C2—2448no—
662C2#2144839611yescharacteristic
663C2#2144862911yescharacteristic
664C2#2144863211yescharacteristic
665C2#2144864711yescharacteristic
666C2#2144865011yescharacteristic
667C2#2144892911yescharacteristic
668C2#2144899011yescharacteristic
669C2#2145220012yes—
670C2#2145222612yes—
671C2#2145222812yes—
672C2#2145265912yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1434D61
hypocenterC61#14473
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. #21444089C2semidirect
4. #21444067C2semidirect
5. #21444067C2semidirect
6. #21444046C2semidirect
7. #21444040C2semidirect
8. #21444040C2semidirect
9. C61×#1434C2semidirect
14. C2×#14519765C4semidirect
39. C22×Dic122C2×C4semidirect
69. C2×#11758198C2×C4semidirect
70. C2×#11758198C2×C4semidirect
85. C2×C42×C61C2×C4semidirect
331. #1434D61semidirect
370. C61#14473semidirect
414. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197652
C2×#168396402
#214440892
#214440672
#214440462
#214440402
C61×#14342
#1447361