Finite Group Databasebeta

← #29680756

Subgroups — #29680756

Order 15616.

1630 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519735C211yesmaximal, characteristic
2C2×#16839803C212yesmaximal, complemented
3C2×#16839724C211yesmaximal, characteristic
4#380×D61C211yesmaximal, characteristic
5#21446019C212yesmaximal, complemented
6#21446015C212yesmaximal, complemented
7#21446014C211yesmaximal, characteristic, complemented
8#21446011C211yesmaximal, characteristic, complemented
9#21446007C211yesmaximal, characteristic, complemented
10#21445537C212yesmaximal, complemented
11C61×#1852C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C22×#11758189C2212yes—
14C2×#14519735—28no—
15C2×#14519735—21no—
16C2×#14519735—21no—
17C2×#14519735C2212yes—
18C2×#14519735C2212yes—
19C22×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C22×#11758198—21no—
23C2×C22⋊C4×D61—21no—
24C22×C4×Dic61—21no—
25#16839803—28no—
26C2×#14519710C2212yescomplemented
27C2×#14519709C2212yescomplemented
28C2×#14519708C2212yescomplemented
29#16839724C418yescomplemented
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519689C2212yes—
32#16839622C2211yescharacteristic
33#16839621—21no—
34#16839620—21no—
35#16839619C2211yescharacteristic
36#16839619C2211yescharacteristic
37#95×D61—21no—
38#16839525C2212yescomplemented
39#16839524C2212yescomplemented
40#16839524C2212yescomplemented
41C22×C4⋊C4×C61C2211yescharacteristic
42C2×#107×C61C2212yescomplemented
43C2×C22⋊C8×C61C2211yescharacteristic
44C61×#380C2211yescharacteristic
45C61×#340C2212yescomplemented
46C24×D61D411yescharacteristic
47C23×Dic61—21no—
48C23×Dic61D411yescharacteristic
49C22×C4×D61—24no—
50C22×C4×D61—24no—
51C22×C4×D61—21no—
52C22×C4×D61—21no—
53C22×C4×D61C2×C414yes—
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61Q814yes—
57C22×C4×D61C2311yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C2×#11758189—24no—
60C2×#11758189—24no—
61C2×#11758189C2×C418yescomplemented
62C22×#92418C2312yes—
63#14519735—28no—
64#14519735—28no—
65#14519735—24no—
66#14519735—24no—
67#14519735—24no—
68#14519735D418yes—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—24no—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2312yes—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C4⋊C4×D61—24no—
77C4⋊C4×D61—24no—
78C2×C22⋊Dic61—21no—
79C2×#11758198—28no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C22⋊C4×D61—44no—
85C2×C4×Dic61—28no—
86C2×C4×Dic61—22no—
87C2×C4×Dic61—22no—
88#14519710—24no—
89#14519709—24no—
90#14519708—24no—
91C22⋊#92418C2×C414yescomplemented
92#14519689C2×C418yescomplemented
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96C23×C4×C61—21no—
97C23×C4×C61C2311yescharacteristic
98C22×C8×C61C2312yes—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—24no—
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2312yes—
104C2×C22⋊C4×C61—21no—
105#107×C61—24no—
106C22⋊C8×C61C2×C414yescomplemented
107#95×C61—21no—
108C24×C61C2×D411yescharacteristic
109C23×D61—22no—
110C23×D61—22no—
111C23×D61—22no—
112C23×D61—22no—
113C23×D61—41no—
114C23×D61—41no—
115C23×D61C4⋊C414yes—
116C23×D61C2×D411yescharacteristic
117C23×D61C2×D411yescharacteristic
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—24no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—42no—
125C22×C4×C61—42no—
126C22×C4×C61C22×C412yes—
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×Q812yes—
129C22×C4×C61C2411yescharacteristic
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61—24no—
133C22×Dic61—22no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—42no—
137C22×Dic61—42no—
138C22×Dic61C4⋊C414yes—
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—216no—
148C2×C4×D61—216no—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61C4⋊C414yes—
156C2×C4×D61C4⋊C414yes—
157C2×C4×D61C22×C412yes—
158C2×C4×D61C22×C412yes—
159C2×C4×D61C2×D414yes—
160C2×C4×D61C2×Q812yes—
161C2×C4×D61C2×Q812yes—
162C2×C4×D61#4114yes—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C2×C8×C61C22×C414yes—
166C4⋊C4×C61—24no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61C2×D414yes—
171C22⋊C4×C61—42no—
172C22⋊Dic61—42no—
173#11758198—28no—
174#11758198—28no—
175#11758198—42no—
176#11758198—42no—
177C4⋊Dic61—24no—
178C4⋊Dic61—22no—
179C4⋊Dic61—22no—
180C4⋊Dic61—22no—
181C4⋊Dic61C2×D414yes—
182#11758196—42no—
183#11758196—42no—
184C4×Dic61—28no—
185C4×Dic61—28no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418C22×C414yes—
189#11758189—216no—
190C23×C61—21no—
191C23×C61—21no—
192C23×C61—21no—
193C23×C61—21no—
194C23×C61C2×C4⋊C412yes—
195C23×C61AGL(1,ℤ/8)12yes—
196C23×C61#13712yes—
197C23×C61C22×D411yescharacteristic
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—21no—
201C22×D61—21no—
202C22×D61—21no—
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—28no—
209C22×D61—28no—
210C22×D61—44no—
211C22×D61—44no—
212C22×D61—44no—
213C22×D61—44no—
214C22×D61—44no—
215C22×D61C2×C4⋊C412yes—
216C22×D61C2×C4⋊C412yes—
217C22×D61#12012yes—
218C22×D61#12312yes—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—24no—
222C2×C4×C61—24no—
223C2×C4×C61—24no—
224C2×C4×C61—48no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61C2×C4⋊C412yes—
234C2×C4×C61C23×C411yescharacteristic
235C2×C4×C61C22×D412yes—
236C2×C4×C61C22×Q811yescharacteristic
237C2×C4×C61C2×#4112yes—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—28no—
241C2×Dic61—24no—
242C2×Dic61—48no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61C2×C4⋊C412yes—
252C2×Dic61C2×C4⋊C412yes—
253C2×Dic61#12012yes—
254C2×Dic61#12312yes—
255C4×D61—28no—
256C4×D61—24no—
257C4×D61—24no—
258C4×D61—28no—
259C4×D61—84no—
260C4×D61—84no—
261C4×D61C4×D418yes—
262C4×D61C22⋊Q818yes—
263C8×C61—24no—
264#92418—24no—
265#20846—611nomaximal, Sylow
266C22×C61—22no—
267C22×C61—22no—
268C22×C61—22no—
269C22×C61—22no—
270C22×C61—22no—
271C22×C61—22no—
272C22×C61#42814yescomplemented
273C22×C61C22×C4⋊C411yescharacteristic
274C22×C61C2×#12011yescharacteristic
275C22×C61C2×#12311yescharacteristic
276C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C61C2×#13711yescharacteristic
278C22×C61#57511yescharacteristic
279C22×C61#57511yescharacteristic
280C2×D61—22no—
281C2×D61—22no—
282C2×D61—22no—
283C2×D61—22no—
284C2×D61—22no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—416no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61#38514yes—
295C4×C61—22no—
296C4×C61—44no—
297C4×C61—81no—
298C4×C61—81no—
299C4×C61C2×C4×D412yes—
300C4×C61C2×C22⋊Q812yes—
301Dic61—22no—
302Dic61—44no—
303Dic61—81no—
304Dic61—81no—
305Dic61#38514yes—
306C22×#117—611no—
307C2×#428—612no—
308C2×#407—611no—
309C2×#380—611no—
310#1854—612no—
311#1854—612no—
312#1853—611no—
313#1853—611no—
314#1852—611no—
315#1852D6111yescharacteristic, complemented
316#1736—612no—
317C2×C61—24no—
318C2×C61C2×#38511yescharacteristic
319C2×C61C2×#42811yescharacteristic
320C2×C61#291111yescharacteristic
321C2×C61#300611yescharacteristic
322C2×C61#300711yescharacteristic
323C2×C61#309411yescharacteristic
324C2×C61#309511yescharacteristic
325D61—24no—
326D61—42no—
327C24×C4—611no—
328C22×M16—612no—
329C2×#117—612no—
330C2×#117—612no—
331C2×#117—1228no—
332C2×#117—1221no—
333C2×#117—1221no—
334C22×C4⋊C4—611no—
335C22×C4⋊C4—611no—
336C22×C4⋊C4—611no—
337C22×C4⋊C4C2×D6111yescharacteristic
338C22×C22⋊C4—1221no—
339C22×C22⋊C4—1221no—
340C22×C42—1221no—
341#428—1228no—
342C2×#107—612no—
343C2×#107C2×D6112yescomplemented
344C2×#106—612no—
345C2×#106—612no—
346#407—618no—
347C2×C22⋊C8—611no—
348C2×C22⋊C8—612no—
349C2×C22⋊C8C2×D6111yescharacteristic
350#380—611no—
351#380—611no—
352#380—611no—
353#380—1221no—
354#380—1221no—
355#380C2×D6111yescharacteristic
356C2×#95—1221no—
357#340—612no—
358#340—612no—
359#340—612no—
360#340C2×D6112yescomplemented
361C61#2084611yescharacteristic, complemented, Sylow
362C25—611no—
363C23×C4—21no—
364C23×C4—611no—
365C23×C4—611no—
366C23×C4—614no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—614no—
370C23×C4—611no—
371C23×C4—1224no—
372C23×C4—1224no—
373C23×C4—1221no—
374C23×C4—1221no—
375C23×C4—1221no—
376C23×C4C22×D6111yescharacteristic
377C2×M16—618no—
378C2×M16—1224no—
379C2×M16—1224no—
380C22×C8—612no—
381C22×C8C22×D6112yes—
382#117—618no—
383#117—1224no—
384#117—1224no—
385#117—1228no—
386#117—1228no—
387#117—1224no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—612no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—1224no—
394C2×C4⋊C4—1224no—
395C2×C4⋊C4—1224no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4C22×D6111yescharacteristic
400C2×C4⋊C4C22×D6111yescharacteristic
401C2×C4⋊C4C22×D6112yes—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—1222no—
404C2×C22⋊C4—1222no—
405C2×C22⋊C4—1228no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—2444no—
410C2×C42—1222no—
411C2×C42—1222no—
412C2×C42—1228no—
413#107—24no—
414#107—1224no—
415#106—1224no—
416#106—1224no—
417C22⋊C8—614no—
418C22⋊C8—618no—
419C22⋊C8C4×D6114yescomplemented
420#95—21no—
421#95—1221no—
422#95—1221no—
423#95—1221no—
424C24—611no—
425C24—611no—
426C24—614no—
427C24—1222no—
428C24—1222no—
429C24—1222no—
430C24—1222no—
431C24—2441no—
432C24—2441no—
433C24D4×D6111yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—611no—
443C22×C4—612no—
444C22×C4—614no—
445C22×C4—612no—
446C22×C4—614no—
447C22×C4—611no—
448C22×C4—614no—
449C22×C4—612no—
450C22×C4—612no—
451C22×C4—614no—
452C22×C4—614no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—12216no—
456C22×C4—12216no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1224no—
464C22×C4—1222no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—2442no—
468C22×C4—2442no—
469C22×C4—2442no—
470C22×C4—2442no—
471C22×C4—2442no—
472C22×C4—2442no—
473C22×C4—2442no—
474C22×C4—2442no—
475C22×C4C2×C4×D6112yes—
476C22×C4D4×D6111yescharacteristic
477C22×C4Q8×D6112yes—
478C22×C4C23×D6111yescharacteristic
479M16—12216no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—614no—
483C2×C8—1222no—
484C2×C8—1222no—
485C2×C8C2×C4×D6114yes—
486C4⋊C4—24no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—614no—
491C4⋊C4—1224no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—2442no—
496C4⋊C4—2442no—
497C4⋊C4D4×D6114yes—
498C22⋊C4—42no—
499C22⋊C4—1228no—
500C22⋊C4—1228no—
501C22⋊C4—2442no—
502C22⋊C4—2442no—
503C22⋊C4—2442no—
504C42—1228no—
505C42—1228no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—612no—
511C23—612no—
512C23—612no—
513C23—612no—
514C23—1228no—
515C23—1221no—
516C23—1221no—
517C23—1221no—
518C23—1221no—
519C23—1221no—
520C23—1221no—
521C23—1221no—
522C23—1221no—
523C23—1221no—
524C23—1221no—
525C23—1228no—
526C23—2444no—
527C23—2444no—
528C23—2444no—
529C23—2444no—
530C23—2444no—
531C23C4⋊C4×D6112yes—
532C23#1451980112yes—
533C23#1451980912yes—
534C23C2×D4×D6111yescharacteristic
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—48no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—618no—
553C2×C4—618no—
554C2×C4—612no—
555C2×C4—1228no—
556C2×C4—1228no—
557C2×C4—1228no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1224no—
561C2×C4—1224no—
562C2×C4—1224no—
563C2×C4—4884no—
564C2×C4—4884no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2448no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4C4⋊C4×D6112yes—
575C2×C4C22×C4×D6111yescharacteristic
576C2×C4C2×D4×D6112yes—
577C2×C4C2×Q8×D6111yescharacteristic
578C2×C4#41×D6112yes—
579C8—24no—
580C8—1224no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—614no—
588C22—1222no—
589C22—1222no—
590C22—1222no—
591C22—1222no—
592C22—1222no—
593C22—1222no—
594C22—1222no—
595C22—1222no—
596C22—1222no—
597C22—24416no—
598C22—2441no—
599C22—2441no—
600C22—2441no—
601C22—2441no—
602C22#1683980314yescomplemented
603C22C2×C4⋊C4×D6111yescharacteristic
604C22#120×D6111yescharacteristic
605C22#123×D6111yescharacteristic
606C22C2×#1451980111yescharacteristic
607C22C2×#1451980911yescharacteristic
608C22#1684055811yescharacteristic
609C22#1684056111yescharacteristic
610C4—22no—
611C4—44no—
612C4—81no—
613C4—81no—
614C4—614no—
615C4—1222no—
616C4—4881no—
617C4—4881no—
618C4—2444no—
619C4C4×D4×D6112yes—
620C4C22⋊Q8×D6112yes—
621C2—24no—
622C2—1224no—
623C2—2442no—
624C2#385×D6111yescharacteristic
625C2C2×#1683980311yescharacteristic
626C2#2145440611yescharacteristic
627C2#2145506611yescharacteristic
628C2#2145507811yescharacteristic
629C2#2145575411yescharacteristic
630C2#2145576411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1852C2
socleC23×C61C22×D4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1852D61
hypocenterC61#20846
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#16839803C2semidirect
5. #21446019C2semidirect
6. #21446015C2semidirect
7. #21446014C2semidirect
8. #21446011C2semidirect
9. #21446007C2semidirect
10. #21445537C2semidirect
11. C61×#1852C2semidirect
26. C2×#14519710C22semidirect
27. C2×#14519709C22semidirect
28. C2×#14519708C22semidirect
29. #16839724C4semidirect
38. #16839525C22semidirect
39. #16839524C22semidirect
40. #16839524C22semidirect
42. C2×#107×C61C22semidirect
45. C61×#340C22semidirect
61. C2×#11758189C2×C4semidirect
91. C22⋊#92418C2×C4semidirect
92. #14519689C2×C4semidirect
106. C22⋊C8×C61C2×C4semidirect
272. C22×C61#428semidirect
315. #1852D61semidirect
343. C2×#107C2×D61semidirect
360. #340C2×D61semidirect
361. C61#20846semidirect
419. C22⋊C8C4×D61semidirect
602. C22#16839803semidirect

Maximal subgroups

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

subgroupindex
C22×#145197352
C2×#168398032
C2×#168397242
#380×D612
#214460192
#214460152
#214460142
#214460112
#214460072
#214455372
C61×#18522
#2084661