Finite Group Databasebeta

← #30615143

Subgroups — #30615143

Order 15616.

1418 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840786C212yesmaximal, complemented
2#21461712C212yesmaximal, complemented
3#21461677C212yesmaximal, complemented
4#21461675C211yesmaximal, characteristic, complemented
5#21461673C211yesmaximal, characteristic, complemented
6#21461641C211yesmaximal, characteristic
7#21461641C211yesmaximal, characteristic
8#21461549C212yesmaximal, complemented
9#21461545C211yesmaximal, characteristic, complemented
10C4×C22⋊#92420C211yesmaximal, characteristic, complemented
11C22×#14519733C211yesmaximal, characteristic
12#16840786—28no—
13C2×#14519844C2212yescomplemented
14C2×C4⋊#92420C2212yescomplemented
15C2×C22⋊#92420C2211yescharacteristic
16C2×C22⋊#92420C2211yescharacteristic
17C2×C22⋊#92420C2211yescharacteristic
18C2×C22⋊#92420C2211yescharacteristic
19C2×C22⋊#92420C2212yes—
20C2×C22⋊#92420C2212yes—
21C2×C22⋊#92420C2212yes—
22C2×C22⋊#92420C2212yes—
23C2×#14519832C2212yescomplemented
24C2×C4×#92420C2212yescomplemented
25#16840628C2212yescomplemented
26#16840628C2212yescomplemented
27#16840628C2212yescomplemented
28#16840628C2212yescomplemented
29C24×Dic61C2211yescharacteristic
30C2×#14519733—28no—
31C2×#14519733C411yescharacteristic
32C2×#14519733C411yescharacteristic
33C2×#14519733C411yescharacteristic
34C2×#14519733C411yescharacteristic
35C2×#14519733C2211yescharacteristic
36C2×#14519733C2211yescharacteristic
37C2×#14519733C2211yescharacteristic
38C2×#14519733C2211yescharacteristic
39C22×#11758196C411yescharacteristic
40C22×#11758196C411yescharacteristic
41C22×C22⋊Dic61C411yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43C22×C4×Dic61C2211yescharacteristic
44C22×C22⋊C4×C61C411yescharacteristic
45C22×#92420C2312yes—
46C22×#92420C2312yes—
47C22×#92420C2312yes—
48C22×#92420C2312yes—
49#14519844—24no—
50C4⋊#92420—24no—
51C22⋊#92420—24no—
52C22⋊#92420—24no—
53C22⋊#92420—22no—
54C22⋊#92420—22no—
55C22⋊#92420—22no—
56C22⋊#92420—22no—
57C22⋊#92420—24no—
58C22⋊#92420—24no—
59#14519832—24no—
60C4×#92420—24no—
61C23×Dic61—24no—
62C23×Dic61—24no—
63C23×Dic61—22no—
64C23×Dic61—22no—
65C23×Dic61C2×C411yescharacteristic
66C23×Dic61C2×C411yescharacteristic
67C23×Dic61C2×C411yescharacteristic
68C23×Dic61C2×C411yescharacteristic
69C23×Dic61C2×C411yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73#14519733—24no—
74#14519733—24no—
75#14519733—24no—
76#14519733—24no—
77#14519733—24no—
78#14519733—24no—
79#14519733—24no—
80#14519733D418yes—
81C2×#11758196—24no—
82C2×#11758196—24no—
83C2×#11758196C2×C411yescharacteristic
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2×C411yescharacteristic
86C2×#11758196C2×C411yescharacteristic
87C2×#11758196C2×C411yescharacteristic
88C2×#11758196C2×C411yescharacteristic
89C2×#11758196C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×C22⋊Dic61—24no—
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×C22⋊Dic61C2×C411yescharacteristic
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×C4×Dic61—24no—
97C2×C4×Dic61—24no—
98C2×C4×Dic61C2×C411yescharacteristic
99C2×C4×Dic61C2×C411yescharacteristic
100C2×C4×Dic61C2×C411yescharacteristic
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C25×C61C2×C411yescharacteristic
107C23×C4×C61C2×C411yescharacteristic
108C23×C4×C61C2×C411yescharacteristic
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61C2×C411yescharacteristic
111C2×C22⋊C4×C61C2×C411yescharacteristic
112C2×C22⋊C4×C61C2×C411yescharacteristic
113C2×C22⋊C4×C61C2×C411yescharacteristic
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—41no—
120C24×C61—41no—
121C24×C61C22×C411yescharacteristic
122C24×C61C22×C411yescharacteristic
123C24×C61C22×C411yescharacteristic
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—41no—
129C22×C4×C61—41no—
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×Dic61—216no—
135C22×Dic61—216no—
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—21no—
148C22×Dic61—21no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—41no—
158C22×Dic61—41no—
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C2×D414yes—
167C22×Dic61#4114yes—
168C22×Dic61#4112yes—
169C22×Dic61#4112yes—
170C22×Dic61C2411yescharacteristic
171C2×#92420—22no—
172C2×#92420—22no—
173C2×#92420—22no—
174C2×#92420—22no—
175C2×#92420—22no—
176C2×#92420—22no—
177C2×#92420—22no—
178C2×#92420—22no—
179C2×#92420—22no—
180C2×#92420—22no—
181C2×#92420—22no—
182C2×#92420—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—22no—
186C22⋊C4×C61C22⋊C414yes—
187C22⋊Dic61—22no—
188C22⋊Dic61—22no—
189C22⋊Dic61—22no—
190C22⋊Dic61C22⋊C414yes—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196C22⋊C414yes—
198#11758196C22⋊C414yes—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61C2×D414yes—
206C4×Dic61C2×D414yes—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—28no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—44no—
225C23×C61—44no—
226C23×C61—44no—
227C23×C61—44no—
228C23×C61—44no—
229C23×C61—44no—
230C23×C61C2×C22⋊C412yes—
231C23×C61#11712yes—
232C23×C61#11712yes—
233C23×C61#13112yes—
234C23×C61#13112yes—
235C23×C61C23×C411yescharacteristic
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—44no—
247C2×C4×C61—44no—
248C2×C4×C61C2×C22⋊C412yes—
249C2×C4×C61C2×C22⋊C412yes—
250C2×Dic61—28no—
251C2×Dic61—28no—
252C2×Dic61—28no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—24no—
264C2×Dic61—24no—
265C2×Dic61—24no—
266C2×Dic61—24no—
267C2×Dic61—24no—
268C2×Dic61—24no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—44no—
276C2×Dic61—44no—
277C2×Dic61C2×C22⋊C412yes—
278C2×Dic61C2×C22⋊C412yes—
279C2×Dic61C2×C22⋊C412yes—
280C2×Dic61#11712yes—
281C2×Dic61#11712yes—
282C2×Dic61C22×D412yes—
283C2×Dic61C2×#4111yescharacteristic
284C2×Dic61C2×#4111yescharacteristic
285C2×Dic61C2×#4112yes—
286#92420—42no—
287#92420—42no—
288#92420—42no—
289#92420—42no—
290#20716—611nomaximal, Sylow
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—22no—
294C22×C61—22no—
295C22×C61—22no—
296C22×C61—22no—
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—22no—
300C22×C61—22no—
301C22×C61—22no—
302C22×C61—22no—
303C22×C61—416no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61#43314yescomplemented
313C22×C61C22×C22⋊C411yescharacteristic
314C22×C61C2×#11711yescharacteristic
315C22×C61C2×#11711yescharacteristic
316C22×C61C2×#13111yescharacteristic
317C22×C61C2×#13111yescharacteristic
318C22×C61#56811yescharacteristic
319C22×C61#56811yescharacteristic
320C4×C61—22no—
321C4×C61—22no—
322C4×C61—41no—
323C4×C61—41no—
324Dic61—22no—
325Dic61—22no—
326Dic61—22no—
327Dic61—22no—
328Dic61—22no—
329Dic61—41no—
330Dic61—41no—
331Dic61#52512yes—
332Dic61#52512yes—
333C22×#117—611no—
334C2×#433—612no—
335#1818—612no—
336#1798—612no—
337#1797—611no—
338#1797—611no—
339#1779—611no—
340#1779—611no—
341#1750—612no—
342#1749—611no—
343C4×C22⋊C8—611no—
344C2×C61—24no—
345C2×C61—42no—
346C2×C61—42no—
347C2×C61#228011yescharacteristic
348C2×C61#288011yescharacteristic
349C2×C61#288011yescharacteristic
350C2×C61C2×#43311yescharacteristic
351C2×C61#292111yescharacteristic
352C2×C61#292411yescharacteristic
353C2×C61#292411yescharacteristic
354C24×C4—611no—
355C2×#117—611no—
356C2×#117—611no—
357C2×#117—611no—
358C2×#117—611no—
359C2×#117—611no—
360C2×#117—611no—
361C2×#117—611no—
362C2×#117—611no—
363C2×#117—1228no—
364C22×C4⋊C4—611no—
365C22×C4⋊C4—611no—
366C22×C22⋊C4—611no—
367C22×C22⋊C4#692311yescharacteristic
368C22×C42—611no—
369C22×C42—611no—
370#433—1228no—
371C2×C4⋊C8—612no—
372C2×C4⋊C8—612no—
373C2×C22⋊C8—611no—
374C2×C22⋊C8—611no—
375C2×C22⋊C8—611no—
376C2×C22⋊C8—611no—
377C2×C22⋊C8—612no—
378C2×C22⋊C8—612no—
379C2×C22⋊C8—612no—
380C2×C22⋊C8—612no—
381C2×#97—612no—
382C2×C4×C8—612no—
383#336—612no—
384#336—612no—
385#336—612no—
386#336—612no—
387C61#2071611yescharacteristic, complemented, Sylow
388C25C2×#692311yescharacteristic
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—1224no—
398C23×C4—1224no—
399C23×C4—1222no—
400C23×C4—1222no—
401C23×C4C2×#692311yescharacteristic
402C23×C4C2×#692311yescharacteristic
403C22×C8—612no—
404C22×C8—612no—
405C22×C8—612no—
406C22×C8—612no—
407#117—618no—
408#117—1224no—
409#117—1224no—
410#117—1224no—
411#117—1224no—
412#117—1224no—
413#117—1224no—
414#117—1224no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—1224no—
424C2×C4⋊C4—1224no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—1224no—
431C2×C22⋊C4C2×#692311yescharacteristic
432C2×C22⋊C4C2×#692311yescharacteristic
433C2×C22⋊C4C2×#692311yescharacteristic
434C2×C22⋊C4C2×#692311yescharacteristic
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—1224no—
444C2×C42—1224no—
445C4⋊C8—1224no—
446C4⋊C8—1224no—
447C22⋊C8—1222no—
448C22⋊C8—1222no—
449C22⋊C8—1222no—
450C22⋊C8—1222no—
451C22⋊C8—1224no—
452C22⋊C8—1224no—
453C22⋊C8—1224no—
454C22⋊C8—1224no—
455#97—1224no—
456C4×C8—1224no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—41no—
463C24—41no—
464C24C22×#692311yescharacteristic
465C24C22×#692311yescharacteristic
466C24C22×#692311yescharacteristic
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—611no—
474C22×C4—614no—
475C22×C4—614no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—12216no—
502C22×C4—12216no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—2441no—
509C22×C4—2441no—
510C22×C4C22×#692311yescharacteristic
511C22×C4C22×#692311yescharacteristic
512C22×C4C22×#692311yescharacteristic
513C22×C4C22×#692311yescharacteristic
514C2×C8—1222no—
515C2×C8—1222no—
516C2×C8—1222no—
517C2×C8—1222no—
518C2×C8—1222no—
519C2×C8—1222no—
520C2×C8—1222no—
521C2×C8—1222no—
522C2×C8—1222no—
523C2×C8—1222no—
524C2×C8—1222no—
525C2×C8—1222no—
526C4⋊C4—614no—
527C4⋊C4—614no—
528C4⋊C4—1222no—
529C4⋊C4—1222no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—1222no—
533C4⋊C4—1222no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—614no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4C22⋊#692314yes—
542C42—614no—
543C42—614no—
544C42—1222no—
545C42—1222no—
546C42—1222no—
547C42—1222no—
548C42—1222no—
549C42—1222no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—28no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23—44no—
573C23C2×C22⋊#692312yes—
574C23#1451985612yes—
575C23#1451985612yes—
576C23#1451986412yes—
577C23#1451986412yes—
578C23C23×#692311yescharacteristic
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—612no—
592C2×C4—611no—
593C2×C4—611no—
594C2×C4—612no—
595C2×C4—612no—
596C2×C4—612no—
597C2×C4—612no—
598C2×C4—612no—
599C2×C4—612no—
600C2×C4—1224no—
601C2×C4—1224no—
602C2×C4—1224no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1224no—
606C2×C4—1228no—
607C2×C4—1228no—
608C2×C4—1228no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—2444no—
626C2×C4—2444no—
627C2×C4C2×C22⋊#692312yes—
628C2×C4C2×C22⋊#692312yes—
629C8—2442no—
630C8—2442no—
631C8—2442no—
632C8—2442no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—416no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22#1684078614yescomplemented
655C22C22×C22⋊#692311yescharacteristic
656C22C2×#1451985611yescharacteristic
657C22C2×#1451985611yescharacteristic
658C22C2×#1451986411yescharacteristic
659C22C2×#1451986411yescharacteristic
660C22#1684084011yescharacteristic
661C22#1684084011yescharacteristic
662C4—22no—
663C4—22no—
664C4—41no—
665C4—41no—
666C4—612no—
667C4—612no—
668C4—1222no—
669C4—1222no—
670C4—1222no—
671C4—1222no—
672C4—1222no—
673C4—2441no—
674C4—2441no—
675C2—24no—
676C2—42no—
677C2—42no—
678C2#2146226311yescharacteristic
679C2#2146240711yescharacteristic
680C2#2146240711yescharacteristic
681C2C2×#1684078611yescharacteristic
682C2#2146249911yescharacteristic
683C2#2146250811yescharacteristic
684C2#2146250811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC22×C22⋊C4×C61C4
prime radicalC25×C61C2×C4
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#20716
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840786C2semidirect
2. #21461712C2semidirect
3. #21461677C2semidirect
4. #21461675C2semidirect
5. #21461673C2semidirect
8. #21461549C2semidirect
9. #21461545C2semidirect
10. C4×C22⋊#92420C2semidirect
13. C2×#14519844C22semidirect
14. C2×C4⋊#92420C22semidirect
23. C2×#14519832C22semidirect
24. C2×C4×#92420C22semidirect
25. #16840628C22semidirect
26. #16840628C22semidirect
27. #16840628C22semidirect
28. #16840628C22semidirect
312. C22×C61#433semidirect
387. C61#20716semidirect
654. C22#16840786semidirect

Maximal subgroups

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

subgroupindex
C2×#168407862
#214617122
#214616772
#214616752
#214616732
#214616412
#214615492
#214615452
C4×C22⋊#924202
C22×#145197332
#2071661