Finite Group Databasebeta

← #29601475

Subgroups — #29601475

Order 15616.

1790 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839624C211yesmaximal, characteristic
2C2×C4×#11758198C211yesmaximal, characteristic
3C2×#16839609C211yesmaximal, characteristic
4#21444055C212yesmaximal
5#21444055C212yesmaximal
6#21444044C211yesmaximal, characteristic, complemented
7#21444043C212yesmaximal, complemented
8C4×#14519684C211yesmaximal, characteristic, complemented
9#95×Dic61C211yesmaximal, characteristic, complemented
10#95×Dic61C212yesmaximal, complemented
11C61×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C22×#11758198C2212yes—
14C22×#11758198C2211yescharacteristic
15C22×#11758198C2211yescharacteristic
16C22×#11758198C2212yes—
17C22×C4×Dic61C2212yes—
18C22×C4×Dic61C2212yes—
19C22×C4×Dic61C2212yes—
20C22×C4×Dic61C2211yescharacteristic
21#16839624C418yescomplemented
22C4×#11758198C418yescomplemented
23#16839609C418yescomplemented
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2211yescharacteristic
33C22×C42×C61C2211yescharacteristic
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2211yescharacteristic
38C24×D61C2311yescharacteristic
39C23×Dic61C2312yes—
40C23×Dic61C2311yescharacteristic
41C23×Dic61C2311yescharacteristic
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2312yes—
44C22×C4×D61—42no—
45C22×C4×D61—42no—
46C22×C4×D61C2×C414yes—
47C22×C4×D61C2×C414yes—
48C22×C4×D61C2×C414yes—
49C2×#11758198—22no—
50C2×#11758198—22no—
51C2×#11758198—24no—
52C2×#11758198—22no—
53C2×#11758198—24no—
54C2×#11758198—22no—
55C2×#11758198—42no—
56C2×#11758198—42no—
57C2×#11758198C2×C418yes—
58C2×#11758198C2×C414yes—
59C2×#11758198C2×C414yes—
60C2×#11758198C2×C418yes—
61C2×C4×Dic61—24no—
62C2×C4×Dic61—24no—
63C2×C4×Dic61—24no—
64C2×C4×Dic61—24no—
65C2×C4×Dic61—42no—
66C2×C4×Dic61—42no—
67C2×C4×Dic61—42no—
68C2×C4×Dic61—42no—
69C2×C4×Dic61—42no—
70C2×C4×Dic61C2×C418yes—
71C2×C4×Dic61C2×C414yes—
72#14519684—24no—
73#14519684—24no—
74#14519684—24no—
75#14519684—42no—
76#14519684C2×C414yes—
77#14519684C2×C414yes—
78#14519684C2×C414yes—
79#14519684C2×C414yes—
80#14519684C2×C418yes—
81C23×C4×C61C2312yes—
82C23×C4×C61C2312yes—
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C2×C42×C61—42no—
87C2×C42×C61C2×C414yes—
88#95×C61—24no—
89#95×C61—42no—
90#95×C61C2×C414yes—
91#95×C61C2×C414yes—
92C24×C61C2411yescharacteristic
93C23×D61—22no—
94C23×D61—21no—
95C23×D61—21no—
96C23×D61—21no—
97C23×D61—22no—
98C23×D61—21no—
99C23×D61—22no—
100C23×D61—22no—
101C23×D61C22×C412yes—
102C23×D61C22×C412yes—
103C23×D61C22×C412yes—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
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—21no—
117C22×C4×C61—22no—
118C22×C4×C61—21no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61C22×C414yes—
125C22×C4×C61C22×C414yes—
126C22×C4×C61C22×C412yes—
127C22×C4×C61C22×C412yes—
128C22×C4×C61C22×C412yes—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C412yes—
131C22×C4×C61#4112yes—
132C22×C4×C61#4112yes—
133C22×Dic61—22no—
134C22×Dic61—22no—
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—21no—
147C22×Dic61—21no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61C22×C414yes—
152C22×Dic61C22×C412yes—
153C22×Dic61C22×C412yes—
154C22×Dic61C22×C412yes—
155C22×Dic61C22×C412yes—
156C22×Dic61C22×C414yes—
157C22×Dic61C22×C412yes—
158C22×Dic61#4114yes—
159C22×Dic61#4112yes—
160C22×Dic61#4112yes—
161C22×Dic61#4114yes—
162C2×C4×D61—48no—
163C2×C4×D61—44no—
164C2×C4×D61—44no—
165C2×C4×D61—48no—
166C2×C4×D61C42116yescomplemented
167C42×C61—44no—
168#11758198—28no—
169#11758198—216no—
170#11758198—28no—
171#11758198—48no—
172C4×Dic61—48no—
173C4×Dic61—44no—
174C4×Dic61—48no—
175C4×Dic61—48no—
176C23×C61C23×C411yescharacteristic
177C23×C61C23×C411yescharacteristic
178C23×C61C23×C411yescharacteristic
179C23×C61C2×#4111yescharacteristic
180C23×C61C2×#4112yes—
181C23×C61C2×#4111yescharacteristic
182C23×C61C2×#4111yescharacteristic
183C23×C61C2×#4112yes—
184C23×C61C2×#4111yescharacteristic
185C23×C61H(5,𝔽2)12yes—
186C23×C61H(5,𝔽2)12yes—
187C22×D61—24no—
188C22×D61—22no—
189C22×D61—22no—
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—22no—
193C22×D61—22no—
194C22×D61—22no—
195C22×D61—24no—
196C22×D61—22no—
197C22×D61—24no—
198C22×D61—24no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61C2×C4214yes—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—24no—
215C2×C4×C61—24no—
216C2×C4×C61—24no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—22no—
220C2×C4×C61—24no—
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—24no—
224C2×C4×C61—24no—
225C2×C4×C61—24no—
226C2×C4×C61—22no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61C2×C4214yes—
238C2×C4×C61#11714yes—
239C2×Dic61—22no—
240C2×Dic61—24no—
241C2×Dic61—24no—
242C2×Dic61—24no—
243C2×Dic61—22no—
244C2×Dic61—24no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—24no—
248C2×Dic61—24no—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—24no—
252C2×Dic61—24no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—22no—
258C2×Dic61—24no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61C2×C4214yes—
266C2×Dic61#11714yes—
267C2×Dic61#11718yes—
268C4×D61—416no—
269#13807—611nomaximal, Sylow
270C22×C61C22×C4211yescharacteristic
271C22×C61C2×#11711yescharacteristic
272C22×C61C2×#11712yes—
273C22×C61C2×#11711yescharacteristic
274C22×C61C4×#4111yescharacteristic
275C22×C61C4×#4111yescharacteristic
276C22×C61C4×#4111yescharacteristic
277C22×C61C4×#4111yescharacteristic
278C22×C61C4×#4112yes—
279C22×C61C4×#4111yescharacteristic
280C22×C61C4×#4111yescharacteristic
281C22×C61#51812yes—
282C22×C61#51812yes—
283C22×C61#51811yescharacteristic
284C22×C61#51811yescharacteristic
285C22×C61#55112yes—
286C22×C61#55112yes—
287C22×C61#55312yes—
288C22×C61#55312yes—
289C22×C61#55312yes—
290C22×C61#55312yes—
291C22×C61#55912yes—
292C22×C61#55912yes—
293C2×D61—24no—
294C2×D61—24no—
295C2×D61—24no—
296C2×D61—42no—
297C2×D61—44no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—44no—
301C2×D61—42no—
302C2×D61—44no—
303C2×D61—44no—
304C4×C61—24no—
305C4×C61—24no—
306C4×C61—42no—
307C4×C61—44no—
308C4×C61—44no—
309Dic61—24no—
310Dic61—28no—
311Dic61—24no—
312Dic61—42no—
313Dic61—44no—
314C2×#381—611no—
315C2×C4×C22⋊C4—611no—
316C2×C4×C22⋊C4—611no—
317#1437—612no—
318#1437—612no—
319#1434—612no—
320#1434—611no—
321#1434D6111yescharacteristic, complemented
322C4×#95—611no—
323C4×#95—612no—
324C4×#95—611no—
325C2×C61C4×#11711yescharacteristic
326C2×C61C4×#11711yescharacteristic
327C2×C61#227311yescharacteristic
328C2×C61#235311yescharacteristic
329C2×C61#235312yes—
330C2×C61#235311yescharacteristic
331C2×C61#235711yescharacteristic
332C2×C61#235712yes—
333C2×C61#235711yescharacteristic
334C2×C61#237412yes—
335C2×C61#237412yes—
336D61—44no—
337C24×C4—611no—
338C22×C22⋊C4—611no—
339C22×C22⋊C4—612no—
340C22×C22⋊C4—611no—
341C22×C22⋊C4—612no—
342C22×C42—612no—
343C22×C42—611no—
344C22×C42—612no—
345C22×C42—612no—
346C22×C42C2×D6111yescharacteristic
347#381—618no—
348C4×C22⋊C4—618no—
349C4×C22⋊C4—618no—
350C2×#95—611no—
351C2×#95—611no—
352C2×#95—612no—
353C2×#95—611no—
354C2×#95—611no—
355C2×#95—612no—
356C2×#95—612no—
357C2×#95—612no—
358C2×#95—612no—
359C2×#95C2×D6112yes—
360C2×#95C2×D6112yes—
361C2×#95C2×D6111yescharacteristic
362C2×#95C2×D6111yescharacteristic
363C61#1380711yescharacteristic, complemented, Sylow
364C25—611no—
365C23×C4—611no—
366C23×C4—612no—
367C23×C4—611no—
368C23×C4—614no—
369C23×C4—614no—
370C23×C4—614no—
371C23×C4—612no—
372C23×C4—611no—
373C23×C4—2442no—
374C23×C4—2442no—
375C23×C4C22×D6111yescharacteristic
376C23×C4C22×D6112yes—
377C23×C4C22×D6112yes—
378C23×C4C22×D6111yescharacteristic
379C23×C4C22×D6111yescharacteristic
380C2×C22⋊C4—614no—
381C2×C22⋊C4—618no—
382C2×C22⋊C4—614no—
383C2×C22⋊C4—618no—
384C2×C22⋊C4—1224no—
385C2×C22⋊C4—1222no—
386C2×C22⋊C4—1224no—
387C2×C22⋊C4—1222no—
388C2×C22⋊C4—1222no—
389C2×C22⋊C4—1222no—
390C2×C22⋊C4—2442no—
391C2×C22⋊C4—2442no—
392C2×C42—42no—
393C2×C42—618no—
394C2×C42—614no—
395C2×C42—1224no—
396C2×C42—1224no—
397C2×C42—1224no—
398C2×C42—1224no—
399C2×C42—2442no—
400C2×C42—2442no—
401C2×C42—2442no—
402C2×C42—2442no—
403C2×C42—2442no—
404C2×C42C4×D6114yes—
405#95—24no—
406#95—42no—
407#95—614no—
408#95—614no—
409#95—614no—
410#95—618no—
411#95—614no—
412#95—1224no—
413#95—1224no—
414#95—1224no—
415#95—2442no—
416#95C4×D6114yes—
417#95C4×D6114yes—
418C24—612no—
419C24—612no—
420C24—612no—
421C24—1221no—
422C24—1221no—
423C24—1222no—
424C24—1222no—
425C24—1221no—
426C24—1221no—
427C24—1222no—
428C24—1222no—
429C24C23×D6111yescharacteristic
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—612no—
451C22×C4—612no—
452C22×C4—612no—
453C22×C4—614no—
454C22×C4—612no—
455C22×C4—614no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—614no—
459C22×C4—6116no—
460C22×C4—614no—
461C22×C4—612no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1221no—
475C22×C4—1222no—
476C22×C4—1221no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—2448no—
481C22×C4—2448no—
482C22×C4—2444no—
483C22×C4—2444no—
484C22×C4C2×C4×D6114yes—
485C22×C4C2×C4×D6112yes—
486C22×C4C2×C4×D6114yes—
487C22×C4C2×C4×D6112yes—
488C22×C4C2×C4×D6112yes—
489C22×C4C2×C4×D6112yes—
490C22×C4C2×C4×D6112yes—
491C22×C4#1175822412yes—
492C22×C4#1175822612yes—
493C22⋊C4—1228no—
494C22⋊C4—12216no—
495C22⋊C4—1228no—
496C22⋊C4—2448no—
497C42—44no—
498C42—2444no—
499C42—2448no—
500C42—2448no—
501C42—2448no—
502C23—614no—
503C23—1224no—
504C23—1222no—
505C23—1222no—
506C23—1222no—
507C23—1222no—
508C23—1222no—
509C23—1222no—
510C23—1224no—
511C23—1222no—
512C23—1222no—
513C23—1224no—
514C23—1224no—
515C23—1222no—
516C23—1222no—
517C23—2442no—
518C23—2442no—
519C23—2442no—
520C23—2442no—
521C23—2442no—
522C23—2442no—
523C23—2442no—
524C23—2442no—
525C23C22×C4×D6111yescharacteristic
526C23C22×C4×D6111yescharacteristic
527C23C22×C4×D6111yescharacteristic
528C23#41×D6112yes—
529C23#41×D6111yescharacteristic
530C23#41×D6112yes—
531C23#41×D6111yescharacteristic
532C23C2×#1175822411yescharacteristic
533C23C2×#1175822611yescharacteristic
534C23#1451982212yes—
535C23#1451982312yes—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—614no—
564C2×C4—614no—
565C2×C4—618no—
566C2×C4—1224no—
567C2×C4—1224no—
568C2×C4—1224no—
569C2×C4—1222no—
570C2×C4—1224no—
571C2×C4—1224no—
572C2×C4—1224no—
573C2×C4—1224no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—1224no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1224no—
583C2×C4—1224no—
584C2×C4—1224no—
585C2×C4—1222no—
586C2×C4—24416no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4C42×D6114yes—
594C2×C4#1451973514yes—
595C22—1224no—
596C22—1224no—
597C22—1224no—
598C22—2442no—
599C22—2444no—
600C22—2442no—
601C22—2442no—
602C22—2444no—
603C22—2442no—
604C22—2444no—
605C22—2444no—
606C22C2×C42×D6111yescharacteristic
607C22#117×D6111yescharacteristic
608C22#117×D6112yes—
609C22C2×#1451973511yescharacteristic
610C22C4×#1175822411yescharacteristic
611C22C4×#1175822411yescharacteristic
612C22#1684023011yescharacteristic
613C22#1684023011yescharacteristic
614C22#1684023012yes—
615C22C4×#1175822611yescharacteristic
616C22C4×#1175822611yescharacteristic
617C22#1684023412yes—
618C22#1684023412yes—
619C22#1684023511yescharacteristic
620C22#1684023611yescharacteristic
621C22#1684043712yes—
622C22#1684043912yes—
623C22#1684045512yes—
624C22#1684045712yes—
625C22#1684046312yes—
626C22#1684046512yes—
627C22#1684049412yes—
628C22#1684049612yes—
629C4—24no—
630C4—24no—
631C4—42no—
632C4—44no—
633C4—44no—
634C4—1224no—
635C4—1228no—
636C4—1224no—
637C4—2442no—
638C4—2444no—
639C2—2444no—
640C2#2144815811yescharacteristic
641C2C4×#1451973511yescharacteristic
642C2#2144817111yescharacteristic
643C2#2144875211yescharacteristic
644C2#2144875812yes—
645C2#2144876111yescharacteristic
646C2#2144878711yescharacteristic
647C2#2144878912yes—
648C2#2144879411yescharacteristic
649C2#2144894712yes—
650C2#2144895112yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×#1434C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1434D61
hypocenterC61#13807
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
6. #21444044C2semidirect
7. #21444043C2semidirect
8. C4×#14519684C2semidirect
9. #95×Dic61C2semidirect
10. #95×Dic61C2semidirect
11. C61×#1434C2semidirect
21. #16839624C4semidirect
22. C4×#11758198C4semidirect
23. #16839609C4semidirect
166. C2×C4×D61C42semidirect
321. #1434D61semidirect
363. C61#13807semidirect

Maximal subgroups

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

subgroupindex
C2×#168396242
C2×C4×#117581982
C2×#168396092
#214440552
#214440442
#214440432
C4×#145196842
#95×Dic612
C61×#14342
#1380761