Finite Group Databasebeta

← #30615145

Subgroups — #30615145

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×#16840787C212yesmaximal, complemented
2#21461713C212yesmaximal, complemented
3#21461678C212yesmaximal, complemented
4#21461675C211yesmaximal, characteristic, complemented
5#21461673C211yesmaximal, characteristic, complemented
6#21461642C211yesmaximal, characteristic
7#21461642C211yesmaximal, characteristic
8#21461548C212yesmaximal, complemented
9#21461545C211yesmaximal, characteristic, complemented
10C4×C22⋊#92420C211yesmaximal, characteristic, complemented
11C22×#14519735C211yesmaximal, characteristic
12#16840787—28no—
13C2×#14519844C2212yescomplemented
14C2×C4⋊#92420C2212yescomplemented
15C2×#14519834C2212yes—
16C2×#14519834C2212yes—
17C2×#14519834C2212yes—
18C2×#14519834C2212yes—
19C2×C22⋊#92420C2211yescharacteristic
20C2×C22⋊#92420C2211yescharacteristic
21C2×C22⋊#92420C2211yescharacteristic
22C2×C22⋊#92420C2211yescharacteristic
23C2×#14519832C2212yescomplemented
24C2×C4×#92420C2212yescomplemented
25#16840628C2212yescomplemented
26#16840628C2212yescomplemented
27#16840628C2212yescomplemented
28#16840628C2212yescomplemented
29C23×C4×D61C2211yescharacteristic
30C2×#14519735—28no—
31C2×#14519735C411yescharacteristic
32C2×#14519735C411yescharacteristic
33C2×#14519735C411yescharacteristic
34C2×#14519735C411yescharacteristic
35C2×#14519735C2211yescharacteristic
36C2×#14519735C2211yescharacteristic
37C2×#14519735C2211yescharacteristic
38C2×#14519735C2211yescharacteristic
39C22×C4⋊Dic61C411yescharacteristic
40C22×#11758198C411yescharacteristic
41C22×#11758198C411yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43C22×C4×Dic61C2211yescharacteristic
44C22×C4⋊C4×C61C411yescharacteristic
45C22×#92420C2312yes—
46C22×#92420C2312yes—
47C22×#92420C2312yes—
48C22×#92420C2312yes—
49#14519844—24no—
50C4⋊#92420—24no—
51#14519834—24no—
52#14519834—24no—
53#14519834—24no—
54#14519834—24no—
55C22⋊#92420—22no—
56C22⋊#92420—22no—
57C22⋊#92420—22no—
58C22⋊#92420—22no—
59#14519832—24no—
60C4×#92420—24no—
61C24×D61C2×C411yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C23×Dic61C2311yescharacteristic
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73#14519735—24no—
74#14519735—24no—
75#14519735—24no—
76#14519735—24no—
77#14519735—24no—
78#14519735—24no—
79#14519735—24no—
80#14519735D418yes—
81C2×C4⋊Dic61—24no—
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×C4⋊Dic61C2×C411yescharacteristic
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×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
106C23×C4×C61C2×C411yescharacteristic
107C23×C4×C61C2×C411yescharacteristic
108C23×C4×C61C2×C411yescharacteristic
109C2×C4⋊C4×C61—24no—
110C2×C4⋊C4×C61C2×C411yescharacteristic
111C2×C4⋊C4×C61C2×C411yescharacteristic
112C2×C4⋊C4×C61C2×C411yescharacteristic
113C2×C4⋊C4×C61C2×C411yescharacteristic
114C24×C61C22×C411yescharacteristic
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—22no—
120C23×D61—41no—
121C23×D61—41no—
122C23×D61C22×C411yescharacteristic
123C23×D61C22×C411yescharacteristic
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×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×Dic61—22no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—41no—
146C22×Dic61—41no—
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61#4112yes—
153C22×Dic61#4112yes—
154C22×Dic61C2411yescharacteristic
155C2×C4×D61—216no—
156C2×C4×D61—216no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—22no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61C2×D414yes—
170C2×C4×D61#4114yes—
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—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61C22⋊C414yes—
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198C22⋊C414yes—
194#11758198C22⋊C414yes—
195C4⋊Dic61—22no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61C22⋊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#11712yes—
212C23×C61#13112yes—
213C23×C61#13112yes—
214C23×C61C23×C411yescharacteristic
215C22×D61—28no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—44no—
229C22×D61—44no—
230C22×D61—44no—
231C22×D61—44no—
232C22×D61—44no—
233C22×D61—44no—
234C22×D61C2×C22⋊C412yes—
235C22×D61#11712yes—
236C2×C4×C61—28no—
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—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—44no—
252C2×C4×C61—44no—
253C2×C4×C61C2×C22⋊C412yes—
254C2×C4×C61C2×C22⋊C412yes—
255C2×C4×C61C2×C22⋊C412yes—
256C2×C4×C61#11712yes—
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—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—44no—
272C2×Dic61—44no—
273C2×Dic61C2×C22⋊C412yes—
274C2×Dic61C2×C22⋊C412yes—
275C2×Dic61#11712yes—
276C2×Dic61C22×D412yes—
277C2×Dic61C2×#4111yescharacteristic
278C2×Dic61C2×#4111yescharacteristic
279C2×Dic61C2×#4112yes—
280C4×D61—28no—
281C4×D61—28no—
282C4×D61—24no—
283C4×D61—24no—
284C4×D61—24no—
285C4×D61—24no—
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#43314yescomplemented
298C22×C61C22×C22⋊C411yescharacteristic
299C22×C61C2×#11711yescharacteristic
300C22×C61C2×#11711yescharacteristic
301C22×C61C2×#13111yescharacteristic
302C22×C61C2×#13111yescharacteristic
303C22×C61#56811yescharacteristic
304C22×C61#56811yescharacteristic
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—22no—
309C2×D61—22no—
310C2×D61—22no—
311C2×D61—416no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C2×D61—41no—
318C2×D61—41no—
319C2×D61—41no—
320C4×C61—22no—
321C4×C61—22no—
322C4×C61—22no—
323C4×C61—22no—
324C4×C61—41no—
325C4×C61—41no—
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#228011yescharacteristic
346C2×C61#288011yescharacteristic
347C2×C61#288011yescharacteristic
348C2×C61C2×#43311yescharacteristic
349C2×C61#292111yescharacteristic
350C2×C61#292411yescharacteristic
351C2×C61#292411yescharacteristic
352D61—42no—
353D61—42no—
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#692311yescharacteristic
366C22×C22⋊C4—611no—
367C22×C22⋊C4—611no—
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
388C25—611no—
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—1224no—
397C23×C4—1222no—
398C23×C4—1222no—
399C23×C4—1224no—
400C23×C4C2×#692311yescharacteristic
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—24no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—1224no—
421C2×C4⋊C4C2×#692311yescharacteristic
422C2×C4⋊C4C2×#692311yescharacteristic
423C2×C4⋊C4C2×#692311yescharacteristic
424C2×C4⋊C4C2×#692311yescharacteristic
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—611no—
433C2×C22⋊C4—1224no—
434C2×C22⋊C4—1224no—
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—611no—
458C24—611no—
459C24—1222no—
460C24—1222no—
461C24—1222no—
462C24—1222no—
463C24—1222no—
464C24—2441no—
465C24—2441no—
466C24C22×#692311yescharacteristic
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—611no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—614no—
483C22×C4—614no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—1222no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1222no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—12216no—
497C22×C4—12216no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—2441no—
507C22×C4—2441no—
508C22×C4C22×#692311yescharacteristic
509C22×C4C22×#692311yescharacteristic
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—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—614no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—1222no—
533C4⋊C4C22⋊#692314yes—
534C22⋊C4—614no—
535C22⋊C4—614no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1222no—
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—612no—
555C23—612no—
556C23—1228no—
557C23—1221no—
558C23—1221no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23—1221no—
564C23—1221no—
565C23—1221no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23—2444no—
570C23—2444no—
571C23—2444no—
572C23—2444no—
573C23—2444no—
574C23—2444no—
575C23#1451985612yes—
576C23#1451986412yes—
577C23#1451986512yes—
578C23C23×#692311yescharacteristic
579C2×C4—28no—
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—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—612no—
597C2×C4—611no—
598C2×C4—611no—
599C2×C4—612no—
600C2×C4—612no—
601C2×C4—612no—
602C2×C4—612no—
603C2×C4—1224no—
604C2×C4—1224no—
605C2×C4—1224no—
606C2×C4—1224no—
607C2×C4—1228no—
608C2×C4—1228no—
609C2×C4—1224no—
610C2×C4—1224no—
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—2444no—
624C2×C4—2444no—
625C2×C4C2×C22⋊#692312yes—
626C2×C4C2×C22⋊#692312yes—
627C2×C4C2×C22⋊#692312yes—
628C2×C4#1451985612yes—
629C8—2442no—
630C8—2442no—
631C8—2442no—
632C8—2442no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—1222no—
640C22—1222no—
641C22—1222no—
642C22—1222no—
643C22—1222no—
644C22—1222no—
645C22—24416no—
646C22—2441no—
647C22—2441no—
648C22—2441no—
649C22—2441no—
650C22—2441no—
651C22—2441no—
652C22—2441no—
653C22—2441no—
654C22#1684078714yescomplemented
655C22C22×C22⋊#692311yescharacteristic
656C22C2×#1451985611yescharacteristic
657C22C2×#1451985611yescharacteristic
658C22C2×#1451986411yescharacteristic
659C22C2×#1451986511yescharacteristic
660C22#1684084011yescharacteristic
661C22#1684084211yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—612no—
669C4—612no—
670C4—1222no—
671C4—1222no—
672C4—1222no—
673C4—2441no—
674C4—2441no—
675C2—24no—
676C2—2442no—
677C2—2442no—
678C2#2146226311yescharacteristic
679C2#2146240711yescharacteristic
680C2#2146240811yescharacteristic
681C2C2×#1684078711yescharacteristic
682C2#2146250111yescharacteristic
683C2#2146250911yescharacteristic
684C2#2146251011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC22×C4⋊C4×C61C4
prime radicalC24×D61C2×C4
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61#20716
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840787C2semidirect
2. #21461713C2semidirect
3. #21461678C2semidirect
4. #21461675C2semidirect
5. #21461673C2semidirect
8. #21461548C2semidirect
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
297. C22×C61#433semidirect
387. C61#20716semidirect
654. C22#16840787semidirect

Maximal subgroups

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

subgroupindex
C2×#168407872
#214617132
#214616782
#214616752
#214616732
#214616422
#214615482
#214615452
C4×C22⋊#924202
C22×#145197352
#2071661