Finite Group Databasebeta

← #29601889

Subgroups — #29601889

Order 15616.

3686 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519733C211yesmaximal, characteristic, complemented
2C23×#11758198C211yesmaximal, characteristic
3C2×#16839623C211yesmaximal, characteristic, complemented
4C2×#16839617C211yesmaximal, characteristic
5C2×#16839617C211yesmaximal, characteristic
6#21444063C214yesmaximal, complemented
7#21444055C214yesmaximal, complemented
8#21444042C211yesmaximal, characteristic, complemented
9C61×C22⋊#95C211yesmaximal, characteristic, complemented
10C25×D61C2211yescharacteristic
11C24×Dic61C2211yescharacteristic
12C2×#14519733—24no—
13C2×#14519733—24no—
14C2×#14519733—24no—
15C22×#11758196C2212yescomplemented
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61C2211yescharacteristic
18C22×#11758198—24no—
19C22×#11758198—24no—
20C22×#11758198C418yescomplemented
21C22×#11758198C2214yes—
22C22×#11758198C2214yes—
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×C4×Dic61C2212yescomplemented
26#16839623—24no—
27#16839617—24no—
28#16839617—24no—
29C2×#14519684C2212yescomplemented
30C2×#14519684C2212yescomplemented
31C2×#14519684C2214yescomplemented
32C24×C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2211yescharacteristic
35C2×#95×C61C2214yescomplemented
36C24×D61—22no—
37C24×D61—22no—
38C24×D61—28no—
39C24×D61—22no—
40C24×D61—22no—
41C24×D61—22no—
42C24×D61—22no—
43C24×D61—44no—
44C24×D61C2×C414yes—
45C24×D61C2312yes—
46C23×Dic61—22no—
47C23×Dic61—22no—
48C23×Dic61—22no—
49C23×Dic61—22no—
50C23×Dic61C2×C414yes—
51C23×Dic61D414yes—
52C23×Dic61D414yes—
53C23×Dic61C2312yes—
54C23×Dic61C2312yes—
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57#14519733—232no—
58C2×#11758196—24no—
59C2×#11758196—24no—
60C2×#11758196—24no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—22no—
66C2×C22⋊Dic61D414yes—
67C2×#11758198—232no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—28no—
73C2×#11758198—28no—
74C2×#11758198—28no—
75C2×#11758198—28no—
76C2×#11758198—44no—
77C2×#11758198—44no—
78C2×#11758198C2×C418yes—
79C2×#11758198C2×C418yes—
80C2×C4×Dic61—24no—
81C2×C4×Dic61—24no—
82C2×C4×Dic61—24no—
83#14519684—24no—
84#14519684—24no—
85#14519684—44no—
86C25×C61C2311yescharacteristic
87C23×C4×C61—22no—
88C23×C4×C61—22no—
89C23×C4×C61—44no—
90C23×C4×C61C2×C414yes—
91C23×C4×C61C2312yes—
92C23×C4×C61C2312yes—
93C23×C4×C61C2312yes—
94C2×C22⋊C4×C61—22no—
95C2×C22⋊C4×C61—22no—
96C2×C22⋊C4×C61—22no—
97C2×C22⋊C4×C61—22no—
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61D414yes—
100#95×C61—44no—
101C24×C61—24no—
102C24×C61—24no—
103C24×C61C22×C412yes—
104C24×C61C2×D412yes—
105C24×C61C2×D412yes—
106C24×C61C2×D412yes—
107C24×C61C2×D412yes—
108C24×C61#4112yes—
109C24×C61#4112yes—
110C24×C61C2411yescharacteristic
111C23×D61—216no—
112C23×D61—216no—
113C23×D61—28no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—24no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—24no—
122C23×D61—24no—
123C23×D61—216no—
124C23×D61—28no—
125C23×D61—28no—
126C23×D61—48no—
127C23×D61—416no—
128C23×D61—416no—
129C23×D61—416no—
130C23×D61—416no—
131C23×D61—48no—
132C23×D61—48no—
133C23×D61—44no—
134C23×D61—44no—
135C23×D61—44no—
136C23×D61—44no—
137C23×D61C22×C414yes—
138C23×D61#4118yes—
139C22×C4×C61—28no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—24no—
145C22×C4×C61—24no—
146C22×C4×C61—24no—
147C22×C4×C61—24no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—24no—
152C22×C4×C61—24no—
153C22×C4×C61—48no—
154C22×C4×C61—48no—
155C22×C4×C61—48no—
156C22×C4×C61C22×C414yes—
157C22×C4×C61C2×D414yes—
158C22×Dic61—28no—
159C22×Dic61—28no—
160C22×Dic61—28no—
161C22×Dic61—28no—
162C22×Dic61—28no—
163C22×Dic61—28no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—24no—
175C22×Dic61—24no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—24no—
179C22×Dic61—22no—
180C22×Dic61—24no—
181C22×Dic61C22⋊C4116yescomplemented
182C22×Dic61C22×C412yes—
183C22×Dic61C22×C412yes—
184C22×Dic61C2×D414yes—
185C22×Dic61C2×D412yes—
186C22×Dic61C2×D412yes—
187C22×Dic61C2×D412yes—
188C22×Dic61C2×D412yes—
189C22⋊C4×C61—28no—
190C22⋊C4×C61—44no—
191C22⋊Dic61—28no—
192C22⋊Dic61—44no—
193#11758198—216no—
194#11758198—216no—
195#11758198—416no—
196#11758198—416no—
197#11758196—216no—
198C4×Dic61—216no—
199C23×C61—24no—
200C23×C61—24no—
201C23×C61—24no—
202C23×C61—24no—
203C23×C61—24no—
204C23×C61—24no—
205C23×C61—28no—
206C23×C61—28no—
207C23×C61—28no—
208C23×C61—28no—
209C23×C61C2×C22⋊C414yes—
210C23×C61C4×D414yes—
211C23×C61C4×D414yes—
212C23×C61#12014yes—
213C23×C61#12114yes—
214C23×C61#12114yes—
215C23×C61#12314yes—
216C23×C61C23×C411yescharacteristic
217C23×C61C22×D411yescharacteristic
218C23×C61C22×D411yescharacteristic
219C23×C61C22×D411yescharacteristic
220C23×C61C22×D411yescharacteristic
221C23×C61C2×#4114yes—
222C23×C61C2×#4111yescharacteristic
223C23×C61C2×#4111yescharacteristic
224C23×C61H(5,𝔽2)14yes—
225C22×D61—232no—
226C22×D61—24no—
227C22×D61—24no—
228C22×D61—24no—
229C22×D61—24no—
230C22×D61—24no—
231C22×D61—24no—
232C22×D61—28no—
233C22×D61—28no—
234C22×D61—28no—
235C22×D61—28no—
236C22×D61—28no—
237C22×D61—28no—
238C22×D61—432no—
239C22×D61—432no—
240C22×D61—416no—
241C22×D61—432no—
242C22×D61—432no—
243C22×D61—432no—
244C22×D61—432no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—44no—
250C22×D61—44no—
251C22×D61—44no—
252C22×D61—44no—
253C22×D61—44no—
254C22×D61—44no—
255C22×D61—416no—
256C22×D61#11718yescomplemented
257C2×C4×C61—24no—
258C2×C4×C61—24no—
259C2×C4×C61—24no—
260C2×C4×C61—24no—
261C2×C4×C61—28no—
262C2×C4×C61—416no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—44no—
266C2×C4×C61—44no—
267C2×C4×C61—44no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—44no—
272C2×C4×C61—44no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—232no—
286C2×Dic61—24no—
287C2×Dic61—28no—
288C2×Dic61—42no—
289C2×Dic61—42no—
290C2×Dic61—44no—
291C2×Dic61—42no—
292C2×Dic61—42no—
293C2×Dic61—42no—
294C2×Dic61—44no—
295C2×Dic61—44no—
296C2×Dic61C2×C22⋊C414yes—
297C2×Dic61C2×C22⋊C414yes—
298#13868—611nomaximal, Sylow
299C22×C61—24no—
300C22×C61—28no—
301C22×C61—28no—
302C22×C61—28no—
303C22×C61—28no—
304C22×C61—28no—
305C22×C61—28no—
306C22×C61—24no—
307C22×C61#38618yes—
308C22×C61C22×C22⋊C411yescharacteristic
309C22×C61C2×#11712yes—
310C22×C61C2×C4×D411yescharacteristic
311C22×C61C2×C4×D411yescharacteristic
312C22×C61#51812yes—
313C22×C61C2×#12011yescharacteristic
314C22×C61C2×#12111yescharacteristic
315C22×C61C2×#12111yescharacteristic
316C22×C61C2×#12311yescharacteristic
317C22×C61#52512yes—
318C22×C61#52512yes—
319C22×C61#53512yes—
320C22×C61#53512yes—
321C22×C61#54614yes—
322C22×C61#54614yes—
323C22×C61#55114yes—
324C22×C61#55114yes—
325C2×D61—28no—
326C2×D61—28no—
327C2×D61—28no—
328C2×D61—464no—
329C2×D61—44no—
330C2×D61—44no—
331C2×D61—44no—
332C2×D61—48no—
333C2×D61—48no—
334C2×D61—48no—
335C2×D61—48no—
336C2×D61—44no—
337C4×C61—44no—
338C4×C61—44no—
339C4×C61—82no—
340Dic61—24no—
341Dic61—24no—
342Dic61—44no—
343Dic61—82no—
344C22×#117—611no—
345C23×C22⋊C4—611no—
346C2×#381—611no—
347C2×#379—611no—
348C2×#379—611no—
349#1439—614no—
350#1437—614no—
351C22⋊#95—611no—
352C22⋊#95D6111yescharacteristic, complemented
353C2×C61—28no—
354C2×C61#228011yescharacteristic
355C2×C61C2×#38611yescharacteristic
356C2×C61#230911yescharacteristic
357C2×C61#234212yes—
358C2×C61#234212yes—
359C2×C61#240412yes—
360C2×C61#241112yes—
361C2×C61#241112yes—
362C2×C61#248212yes—
363D61—48no—
364C26—611no—
365C24×C4—611no—
366C24×C4C2×D6111yescharacteristic
367C2×#117—1224no—
368C2×#117—1224no—
369C2×#117—1224no—
370C22×C4⋊C4—612no—
371C22×C22⋊C4—611no—
372C22×C22⋊C4—618no—
373C22×C22⋊C4—612no—
374C22×C22⋊C4—612no—
375C22×C22⋊C4—611no—
376C22×C22⋊C4—614no—
377C22×C22⋊C4—614no—
378C22×C22⋊C4—1224no—
379C22×C22⋊C4—1224no—
380C22×C22⋊C4C2×D6111yescharacteristic
381C22×C22⋊C4C2×D6111yescharacteristic
382C22×C42—612no—
383#381—1224no—
384#379—1224no—
385#379—1224no—
386C2×#95—612no—
387C2×#95—612no—
388C2×#95—614no—
389C2×#95C2×D6114yescomplemented
390C61#1386811yescharacteristic, complemented, Sylow
391C25—612no—
392C25—614no—
393C25—1228no—
394C25—1222no—
395C25—1222no—
396C25—1222no—
397C25—1222no—
398C25—1222no—
399C25—1222no—
400C25—2444no—
401C25C22×D6111yescharacteristic
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—44no—
405C23×C4—614no—
406C23×C4—614no—
407C23×C4—614no—
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—612no—
411C23×C4—612no—
412C23×C4—1222no—
413C23×C4—1222no—
414C23×C4—1222no—
415C23×C4—1222no—
416C23×C4C4×D6114yes—
417C23×C4C22×D6112yes—
418C23×C4C22×D6112yes—
419C23×C4C22×D6112yes—
420#117—12232no—
421C2×C4⋊C4—1224no—
422C2×C4⋊C4—1224no—
423C2×C4⋊C4—1224no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—614no—
430C2×C22⋊C4—618no—
431C2×C22⋊C4—618no—
432C2×C22⋊C4—1224no—
433C2×C22⋊C4—1224no—
434C2×C22⋊C4—1224no—
435C2×C22⋊C4—1224no—
436C2×C22⋊C4—12232no—
437C2×C22⋊C4—1222no—
438C2×C22⋊C4—1222no—
439C2×C22⋊C4—1228no—
440C2×C22⋊C4—1228no—
441C2×C22⋊C4—1228no—
442C2×C22⋊C4—1222no—
443C2×C22⋊C4—1222no—
444C2×C22⋊C4—1222no—
445C2×C22⋊C4—1228no—
446C2×C22⋊C4—2444no—
447C2×C22⋊C4—2444no—
448C2×C22⋊C4D24414yes—
449C2×C42—1224no—
450C2×C42—1224no—
451C2×C42—1224no—
452#95—44no—
453#95—1224no—
454#95—1224no—
455#95—2444no—
456C24—24no—
457C24—24no—
458C24—614no—
459C24—618no—
460C24—12216no—
461C24—12216no—
462C24—12216no—
463C24—1222no—
464C24—1222no—
465C24—1222no—
466C24—1222no—
467C24—1224no—
468C24—1222no—
469C24—1222no—
470C24—1224no—
471C24—1224no—
472C24—1228no—
473C24—1228no—
474C24—1228no—
475C24—2448no—
476C24—24416no—
477C24—24416no—
478C24—24416no—
479C24—24416no—
480C24—2448no—
481C24—2448no—
482C24—2444no—
483C24—2444no—
484C24—2444no—
485C24—2444no—
486C24C2×C4×D6112yes—
487C24C2×D24412yes—
488C24#1175822212yes—
489C24D4×D6112yes—
490C24D4×D6112yes—
491C24D4×D6112yes—
492C24#1175822612yes—
493C24C23×D6111yescharacteristic
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—28no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—48no—
511C22×C4—612no—
512C22×C4—612no—
513C22×C4—612no—
514C22×C4—612no—
515C22×C4—612no—
516C22×C4—612no—
517C22×C4—6116no—
518C22×C4—614no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1228no—
528C22×C4—1228no—
529C22×C4—1228no—
530C22×C4—1228no—
531C22×C4—1228no—
532C22×C4—1228no—
533C22×C4—1222no—
534C22×C4—1222no—
535C22×C4—1224no—
536C22×C4—1224no—
537C22×C4—1222no—
538C22×C4—1222no—
539C22×C4—1224no—
540C22×C4—1222no—
541C22×C4—1224no—
542C22×C4C2×C4×D6114yes—
543C22×C4C2×D24414yes—
544C4⋊C4—12216no—
545C22⋊C4—28no—
546C22⋊C4—44no—
547C22⋊C4—12216no—
548C22⋊C4—12216no—
549C22⋊C4—1228no—
550C22⋊C4—24416no—
551C22⋊C4—24416no—
552C22⋊C4—2444no—
553C42—12216no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—28no—
561C23—28no—
562C23—28no—
563C23—28no—
564C23—618no—
565C23—12232no—
566C23—1224no—
567C23—1224no—
568C23—1224no—
569C23—1224no—
570C23—1224no—
571C23—1224no—
572C23—1228no—
573C23—1228no—
574C23—1228no—
575C23—1228no—
576C23—1228no—
577C23—1228no—
578C23—24432no—
579C23—24432no—
580C23—24432no—
581C23—24432no—
582C23—24416no—
583C23—24432no—
584C23—24432no—
585C23—2442no—
586C23—2442no—
587C23—2442no—
588C23—2442no—
589C23—2444no—
590C23—2444no—
591C23—2444no—
592C23—2444no—
593C23—24416no—
594C23—2444no—
595C23—2444no—
596C23C22⋊C4×D6114yes—
597C23#1451973914yes—
598C23C4×D24414yes—
599C23#1451974714yes—
600C23#1451975014yes—
601C23#1451975214yes—
602C23#1451976214yes—
603C23C22×C4×D6111yescharacteristic
604C23C2×D4×D6111yescharacteristic
605C23C2×D4×D6111yescharacteristic
606C23C2×D4×D6111yescharacteristic
607C23C22×D24411yescharacteristic
608C23#41×D6114yes—
609C23C2×#1175822211yescharacteristic
610C23C2×#1175822611yescharacteristic
611C23#1451982214yes—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—28no—
617C2×C4—416no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—614no—
629C2×C4—614no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—1222no—
635C2×C4—1222no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—12232no—
643C2×C4—1224no—
644C2×C4—1228no—
645C2×C4—2442no—
646C2×C4—2442no—
647C2×C4—2442no—
648C2×C4—2444no—
649C2×C4—2444no—
650C2×C4—2442no—
651C2×C4—2442no—
652C2×C4—2444no—
653C22—24no—
654C22—28no—
655C22—28no—
656C22—24no—
657C22—28no—
658C22—28no—
659C22—28no—
660C22—28no—
661C22—1228no—
662C22—1228no—
663C22—1228no—
664C22—24464no—
665C22—2444no—
666C22—2448no—
667C22—2448no—
668C22—2444no—
669C22—2444no—
670C22—2444no—
671C22—2448no—
672C22—2448no—
673C22#1683964018yes—
674C22C2×C22⋊C4×D6111yescharacteristic
675C22#117×D6112yes—
676C22C2×#1451973911yescharacteristic
677C22C2×C4×D24411yescharacteristic
678C22#1684023512yes—
679C22C2×#1451974711yescharacteristic
680C22C2×#1451975011yescharacteristic
681C22C2×#1451975211yescharacteristic
682C22C2×#1451976211yescharacteristic
683C22#1684027012yes—
684C22#1684027012yes—
685C22#1684032712yes—
686C22#1684032712yes—
687C22#1684040114yes—
688C22#1684040714yes—
689C22#1684043914yes—
690C22#1684044114yes—
691C4—44no—
692C4—44no—
693C4—82no—
694C4—1224no—
695C4—1224no—
696C4—4882no—
697C4—2444no—
698C2—28no—
699C2—2448no—
700C2#2144819911yescharacteristic
701C2C2×#1683964011yescharacteristic
702C2#2144840011yescharacteristic
703C2#2144866512yes—
704C2#2144867112yes—
705C2#2144913712yes—
706C2#2144920212yes—
707C2#2144920712yes—
708C2#2145009212yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenterC22⋊#95D61
hypocenterC61#13868
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#14519733C2semidirect
3. C2×#16839623C2semidirect
6. #21444063C2semidirect
7. #21444055C2semidirect
8. #21444042C2semidirect
9. C61×C22⋊#95C2semidirect
15. C22×#11758196C22semidirect
20. C22×#11758198C4semidirect
25. C22×C4×Dic61C22semidirect
29. C2×#14519684C22semidirect
30. C2×#14519684C22semidirect
31. C2×#14519684C22semidirect
35. C2×#95×C61C22semidirect
181. C22×Dic61C22⋊C4semidirect
256. C22×D61#117semidirect
352. C22⋊#95D61semidirect
389. C2×#95C2×D61semidirect
390. C61#13868semidirect

Maximal subgroups

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

subgroupindex
C22×#145197332
C23×#117581982
C2×#168396232
C2×#168396172
#214440632
#214440552
#214440422
C61×C22⋊#952
#1386861