Finite Group Databasebeta

← #29609192

Subgroups — #29609192

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519758C211yesmaximal, characteristic
2C2×#16839656C212yesmaximal, complemented
3#21444085C212yesmaximal, complemented
4#21444062C212yesmaximal, complemented
5#21444060C211yesmaximal, characteristic
6#21444056C212yesmaximal, complemented
7#21444047C212yesmaximal, complemented
8#21444041C212yesmaximal, complemented
9C61×#1438C211yesmaximal, characteristic
10C24×Dic61C2211yescharacteristic
11C2×#14519758—28no—
12C2×#14519758C418yescomplemented
13C22×#11758196C2212yes—
14C22×#11758196C2212yes—
15C22×C22⋊Dic61C2212yes—
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61C2212yes—
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C4×Dic61C2212yes—
21#16839656—28no—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C23×D4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2212yes—
31C22×C22⋊C4×C61C2212yes—
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2211yescharacteristic
34C23×Dic61—24no—
35C23×Dic61—42no—
36C23×Dic61—41no—
37C23×Dic61—41no—
38C23×Dic61C2×C414yes—
39C23×Dic61C2312yes—
40C23×Dic61C2312yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43#14519758—232no—
44C2×#11758196—24no—
45C2×#11758196—24no—
46C2×#11758196—24no—
47C2×#11758196—24no—
48C2×#11758196—42no—
49C2×#11758196C2×C418yes—
50C2×C22⋊Dic61—24no—
51C2×C22⋊Dic61—24no—
52C2×C22⋊Dic61—24no—
53C2×C22⋊Dic61—24no—
54C2×C22⋊Dic61—24no—
55C2×C22⋊Dic61—41no—
56C2×C22⋊Dic61—42no—
57C2×C22⋊Dic61—41no—
58C2×C22⋊Dic61—42no—
59C2×C22⋊Dic61C2×C418yes—
60C2×C22⋊Dic61C2×C414yes—
61C2×C22⋊Dic61D418yes—
62C2×C4×Dic61—24no—
63C2×C4×Dic61—24no—
64C2×C4×Dic61—42no—
65#14519684—24no—
66#14519684—24no—
67#14519684—42no—
68#14519684—42no—
69#14519684—42no—
70#14519684—42no—
71#14519684—42no—
72C25×C61C2311yescharacteristic
73C25×C61C2311yescharacteristic
74C22×D4×C61—24no—
75C22×D4×C61—41no—
76C22×D4×C61—41no—
77C22×D4×C61—42no—
78C22×D4×C61C2×C414yes—
79C23×C4×C61C2312yes—
80C23×C4×C61C2311yescharacteristic
81C23×C4×C61C2312yes—
82C2×C22⋊C4×C61—24no—
83C2×C22⋊C4×C61—24no—
84C2×C22⋊C4×C61—24no—
85C2×C22⋊C4×C61—42no—
86C2×C22⋊C4×C61—42no—
87C2×C22⋊C4×C61—42no—
88#95×C61—41no—
89#95×C61—41no—
90C24×C61—22no—
91C24×C61—22no—
92C24×C61—22no—
93C24×C61—21no—
94C24×C61—21no—
95C24×C61—22no—
96C24×C61—22no—
97C24×C61—22no—
98C24×C61—22no—
99C24×C61—22no—
100C24×C61—22no—
101C24×C61—22no—
102C24×C61—21no—
103C24×C61—21no—
104C24×C61—22no—
105C24×C61C22×C412yes—
106C24×C61C22×C412yes—
107C24×C61C2×D414yes—
108C24×C61C2411yescharacteristic
109C2×D4×C61—28no—
110C2×D4×C61—44no—
111C2×D4×C61—44no—
112C2×D4×C61—48no—
113C2×D4×C61—48no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—21no—
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×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61C22×C412yes—
132C22×C4×C61#4114yes—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—28no—
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×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—44no—
158C22×Dic61—44no—
159C22×Dic61—48no—
160C22×Dic61—48no—
161C22×Dic61C22×C414yes—
162C22×Dic61C22×C414yes—
163C22×Dic61C2×D414yes—
164C22×Dic61C2×D414yes—
165C22×Dic61#4114yes—
166C22⋊C4×C61—48no—
167C22⋊C4×C61—48no—
168C22⋊Dic61—216no—
169C22⋊Dic61—44no—
170C22⋊Dic61—48no—
171C22⋊Dic61—44no—
172C22⋊Dic61C22⋊C4116yescomplemented
173#11758196—216no—
174#11758196—48no—
175C4×Dic61—48no—
176C23×C61—24no—
177C23×C61—22no—
178C23×C61—22no—
179C23×C61—24no—
180C23×C61—24no—
181C23×C61—24no—
182C23×C61—24no—
183C23×C61—24no—
184C23×C61—24no—
185C23×C61—24no—
186C23×C61—22no—
187C23×C61—24no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—24no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—41no—
196C23×C61—42no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61—42no—
200C23×C61—41no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61—42no—
211C23×C61—41no—
212C23×C61—42no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—42no—
216C23×C61—41no—
217C23×C61C2×C22⋊C414yes—
218C23×C61C23×C411yescharacteristic
219C23×C61C22×D412yes—
220C23×C61C2×#4112yes—
221C23×C61C2×#4112yes—
222C23×C61H(5,𝔽2)12yes—
223C23×C61H(5,𝔽2)11yescharacteristic
224C23×C61H(5,𝔽2)11yescharacteristic
225C23×C61H(5,𝔽2)12yes—
226C23×C612−1+412yes—
227D4×C61—416no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
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×Dic61—24no—
248C2×Dic61—24no—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—24no—
252C2×Dic61—24no—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—416no—
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—
275C2×Dic61C2×C22⋊C418yes—
276#14506—611nomaximal, Sylow
277C22×C61—24no—
278C22×C61—28no—
279C22×C61—44no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—44no—
283C22×C61—44no—
284C22×C61—44no—
285C22×C61—44no—
286C22×C61—42no—
287C22×C61—44no—
288C22×C61—44no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—82no—
292C22×C61—82no—
293C22×C61—82no—
294C22×C61—82no—
295C22×C61C22×C22⋊C411yescharacteristic
296C22×C61C4×#4112yes—
297C22×C61#51811yescharacteristic
298C22×C61#51811yescharacteristic
299C22×C61#52012yes—
300C22×C61#53512yes—
301C22×C61#53512yes—
302C22×C61#53812yes—
303C22×C61#53912yes—
304C22×C61#54012yes—
305C22×C61#54212yes—
306C22×C61#54612yes—
307C22×C61#54612yes—
308C22×C61#54712yes—
309C22×C61#54712yes—
310C22×C61#55111yescharacteristic
311C22×C61#55312yes—
312C22×C61#55911yescharacteristic
313C22×C61#56011yescharacteristic
314C22×C61#56212yes—
315C22×C61#56311yescharacteristic
316C4×C61—42no—
317C4×C61—44no—
318C4×C61—82no—
319Dic61—28no—
320Dic61—44no—
321Dic61—44no—
322Dic61—82no—
323C22×#123—611no—
324C2×#388—612no—
325#1445—612no—
326#1439—612no—
327#1438—611no—
328#1438D6111yescharacteristic
329#1437—612no—
330C4⋊#95—612no—
331C22⋊#95—612no—
332C2×C61—44no—
333C2×C61—82no—
334C2×C61#230911yescharacteristic
335C2×C61#233512yes—
336C2×C61#233912yes—
337C2×C61#237411yescharacteristic
338C2×C61#237611yescharacteristic
339C2×C61#270312yes—
340C2×C61#270612yes—
341C2×C61#271012yes—
342C2×C61#271812yes—
343C23×D4C2×D6111yescharacteristic
344C24×C4—611no—
345C2×#123—618no—
346C2×#123—1228no—
347C22×C4⋊C4—612no—
348C22×C4⋊C4—612no—
349C22×C22⋊C4—611no—
350C22×C22⋊C4—612no—
351C22×C22⋊C4—612no—
352C22×C22⋊C4—611no—
353C22×C22⋊C4—611no—
354C22×C22⋊C4C2×D6112yes—
355C22×C22⋊C4C2×D6112yes—
356C22×C42—612no—
357#388—1228no—
358C2×#95—612no—
359C2×#95—612no—
360C2×#95—612no—
361C2×#95—612no—
362C2×#95—612no—
363C2×#95—612no—
364C2×#95—612no—
365C2×#95C2×D6111yescharacteristic
366C2×#95C2×D6111yescharacteristic
367C61#1450611yescharacteristic, complemented, Sylow
368C25C22×D6111yescharacteristic
369C25C22×D6111yescharacteristic
370C22×D4—24no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4—42no—
374C22×D4C4×D6114yes—
375C23×C4—612no—
376C23×C4—612no—
377C23×C4—612no—
378C23×C4—614no—
379C23×C4—612no—
380C23×C4—1224no—
381C23×C4—2441no—
382C23×C4—2441no—
383C23×C4—2442no—
384C23×C4C22×D6112yes—
385C23×C4C22×D6111yescharacteristic
386C23×C4C22×D6112yes—
387#123—12232no—
388C2×C4⋊C4—618no—
389C2×C4⋊C4—1224no—
390C2×C4⋊C4—1224no—
391C2×C4⋊C4—1224no—
392C2×C4⋊C4—1224no—
393C2×C4⋊C4—2442no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—614no—
401C2×C22⋊C4—618no—
402C2×C22⋊C4—618no—
403C2×C22⋊C4—1224no—
404C2×C22⋊C4—1224no—
405C2×C22⋊C4—1224no—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1224no—
408C2×C22⋊C4—2441no—
409C2×C22⋊C4—2442no—
410C2×C22⋊C4—2441no—
411C2×C22⋊C4—2442no—
412C2×C42—1224no—
413C2×C42—1224no—
414C2×C42—2442no—
415#95—41no—
416#95—41no—
417#95—1224no—
418#95—1224no—
419#95—2442no—
420#95—2442no—
421#95—2442no—
422#95—2442no—
423#95—2442no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C2×C4×D6112yes—
440C24C2×C4×D6112yes—
441C24D4×D6114yes—
442C24C23×D6111yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—614no—
466C22×C4—614no—
467C22×C4—614no—
468C22×C4—614no—
469C22×C4—614no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1228no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—2444no—
495C22×C4—2444no—
496C22×C4—2448no—
497C22×C4—2448no—
498C22×C4C2×C4×D6112yes—
499C22×C4#1175822414yes—
500C4⋊C4—12216no—
501C4⋊C4—2448no—
502C22⋊C4—48no—
503C22⋊C4—48no—
504C22⋊C4—6116no—
505C22⋊C4—12216no—
506C22⋊C4—2444no—
507C22⋊C4—2448no—
508C22⋊C4—2444no—
509C42—2448no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—41no—
527C23—41no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—41no—
551C23C22⋊C4×D6114yes—
552C23C22×C4×D6111yescharacteristic
553C23C2×D4×D6112yes—
554C23#41×D6112yes—
555C23C2×#1175822412yes—
556C23#1451982211yescharacteristic
557C23#1451982211yescharacteristic
558C23#1451982212yes—
559C23#1451982212yes—
560C23#1451982412yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—618no—
582C2×C4—1224no—
583C2×C4—1224no—
584C2×C4—1224no—
585C2×C4—1224no—
586C2×C4—1224no—
587C2×C4—1224no—
588C2×C4—1224no—
589C2×C4—1224no—
590C2×C4—1224no—
591C2×C4—1224no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4—2442no—
600C2×C4—2442no—
601C2×C4—24416no—
602C2×C4—2442no—
603C2×C4—2442no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4—2442no—
610C22—28no—
611C22—24no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—42no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C2×C22⋊C4×D6111yescharacteristic
629C22C4×#1175822412yes—
630C22#1684023511yescharacteristic
631C22#1684023511yescharacteristic
632C22#1684024112yes—
633C22#1684032712yes—
634C22#1684032712yes—
635C22#1684034712yes—
636C22#1684035512yes—
637C22#1684036212yes—
638C22#1684037912yes—
639C22#1684039912yes—
640C22#1684040112yes—
641C22#1684041012yes—
642C22#1684041212yes—
643C22#1684044211yescharacteristic
644C22#1684045512yes—
645C22#1684049811yescharacteristic
646C22#1684049911yescharacteristic
647C22#1684050712yes—
648C22#1684051211yescharacteristic
649C4—44no—
650C4—42no—
651C4—82no—
652C4—1228no—
653C4—4882no—
654C4—2444no—
655C4—2444no—
656C2—44no—
657C2—82no—
658C2#2144840011yescharacteristic
659C2#2144861012yes—
660C2#2144864512yes—
661C2#2144895411yescharacteristic
662C2#2144896911yescharacteristic
663C2#2145246712yes—
664C2#2145251212yes—
665C2#2145256312yes—
666C2#2145267112yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1438C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenter#1438D61
hypocenterC61#14506
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#16839656C2semidirect
3. #21444085C2semidirect
4. #21444062C2semidirect
6. #21444056C2semidirect
7. #21444047C2semidirect
8. #21444041C2semidirect
12. C2×#14519758C4semidirect
172. C22⋊Dic61C22⋊C4semidirect
367. C61#14506semidirect

Maximal subgroups

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

subgroupindex
C22×#145197582
C2×#168396562
#214440852
#214440622
#214440602
#214440562
#214440472
#214440412
C61×#14382
#1450661