Finite Group Databasebeta

← #30615141

Subgroups — #30615141

Order 15616.

1974 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840784C212yesmaximal, complemented
2#21461711C212yesmaximal, complemented
3#21461674C212yesmaximal, complemented
4#21461673C212yesmaximal, complemented
5#21461642C212yesmaximal
6#21461546C212yesmaximal, complemented
7#21461545C212yesmaximal, complemented
8C22×C42×D61C211yesmaximal, characteristic
9#16840784—28no—
10C2×C4⋊#92420C2214yescomplemented
11C2×#14519834C2214yes—
12C2×#14519834C2214yes—
13C2×C22⋊#92420C2214yes—
14C2×#14519832C2214yescomplemented
15#16840628C2214yescomplemented
16#16840628C2214yescomplemented
17C23×C4×D61C411yescharacteristic
18C23×C4×D61C411yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C4×Dic61C411yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23C2×C42×D61—28no—
24C2×C42×D61C411yescharacteristic
25C2×C42×D61C411yescharacteristic
26C2×C42×D61C411yescharacteristic
27C2×C42×D61C411yescharacteristic
28C2×C42×D61C2211yescharacteristic
29C2×C42×D61C2211yescharacteristic
30C2×C42×D61C2211yescharacteristic
31C2×C42×D61C2211yescharacteristic
32C22×C42×C61C411yescharacteristic
33C22×#92420C2318yes—
34C4⋊#92420—28no—
35#14519834—28no—
36#14519834—28no—
37C22⋊#92420—28no—
38#14519832—28no—
39C24×D61C2×C411yescharacteristic
40C23×Dic61C2×C411yescharacteristic
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2311yescharacteristic
43C22×C4×D61—24no—
44C22×C4×D61—24no—
45C22×C4×D61—24no—
46C22×C4×D61—24no—
47C22×C4×D61—24no—
48C22×C4×D61—24no—
49C22×C4×D61—24no—
50C22×C4×D61—24no—
51C22×C4×D61—24no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×C4×Dic61—24no—
65C2×C4×Dic61—24no—
66C2×C4×Dic61—24no—
67C2×C4×Dic61C2×C411yescharacteristic
68C2×C4×Dic61C2×C411yescharacteristic
69C2×C4×Dic61C2×C411yescharacteristic
70C2×C4×Dic61C2×C411yescharacteristic
71C2×C4×Dic61C2×C411yescharacteristic
72C2×C4×Dic61C2×C411yescharacteristic
73C2×C4×Dic61C2×C411yescharacteristic
74C2×C4×Dic61C2×C411yescharacteristic
75C2×C4×Dic61C2311yescharacteristic
76C2×C4×Dic61C2311yescharacteristic
77C2×C4×Dic61C2311yescharacteristic
78C2×C4×Dic61C2311yescharacteristic
79C42×D61—24no—
80C42×D61—24no—
81C42×D61—24no—
82C42×D61—24no—
83C42×D61—24no—
84C42×D61—24no—
85C42×D61—24no—
86C42×D61D418yes—
87C23×C4×C61C2×C411yescharacteristic
88C23×C4×C61C2×C411yescharacteristic
89C23×C4×C61C2×C411yescharacteristic
90C2×C42×C61—24no—
91C2×C42×C61C2×C411yescharacteristic
92C2×C42×C61C2×C411yescharacteristic
93C2×C42×C61C2×C411yescharacteristic
94C2×C42×C61C2×C411yescharacteristic
95C24×C61C22×C411yescharacteristic
96C23×D61—22no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—22no—
100C23×D61—22no—
101C23×D61—22no—
102C23×D61M1614yes—
103C23×D61C22×C411yescharacteristic
104C23×D61C22×C411yescharacteristic
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61M1614yes—
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C22×C411yescharacteristic
116C22×C4×C61C22×C411yescharacteristic
117C22×C4×C61C22×C411yescharacteristic
118C22×C4×C61C22×C411yescharacteristic
119C22×C4×C61C22×C411yescharacteristic
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—22no—
123C22×Dic61—22no—
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128C22×Dic61C22×C411yescharacteristic
129C22×Dic61C22×C411yescharacteristic
130C22×Dic61C22×C411yescharacteristic
131C22×Dic61C22×C411yescharacteristic
132C22×Dic61C22×C411yescharacteristic
133C22×Dic61#4114yes—
134C22×Dic61C2411yescharacteristic
135C2×C4×D61—232no—
136C2×C4×D61—232no—
137C2×C4×D61—232no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—22no—
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—22no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
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—22no—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61C22⋊C414yes—
169C2×C4×D61C22⋊C414yes—
170C2×C4×D61M1614yes—
171C2×C4×D61M1614yes—
172C2×C4×D61C2×D414yes—
173C2×C4×D61#4114yes—
174C2×#92420—28no—
175C2×#92420—28no—
176C2×#92420—28no—
177C42×C61—22no—
178C42×C61—22no—
179C42×C61—22no—
180C42×C61C22⋊C414yes—
181C4×Dic61—22no—
182C4×Dic61—22no—
183C4×Dic61—22no—
184C4×Dic61—22no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C4×Dic61—22no—
188C4×Dic61—22no—
189C4×Dic61—22no—
190C4×Dic61C22⋊C414yes—
191C4×Dic61C2×D414yes—
192C4×Dic61C2×D414yes—
193C23×C61—21no—
194C23×C61—21no—
195C23×C61—21no—
196C23×C61—21no—
197C23×C61#11712yes—
198C23×C61C2×M1612yes—
199C23×C61C2×M1612yes—
200C23×C61C23×C411yescharacteristic
201C22×D61—28no—
202C22×D61—28no—
203C22×D61—28no—
204C22×D61—28no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61—28no—
214C22×D61—28no—
215C22×D61—28no—
216C22×D61C2×C22⋊C412yes—
217C22×D61#11712yes—
218C22×D61C2×M1612yes—
219C22×D61C2×M1612yes—
220C22×D61C2×M1612yes—
221C22×D61C2×M1612yes—
222C2×C4×C61—28no—
223C2×C4×C61—28no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—28no—
235C2×C4×C61C2×C22⋊C412yes—
236C2×C4×C61C2×C22⋊C412yes—
237C2×C4×C61C2×C22⋊C412yes—
238C2×C4×C61#11712yes—
239C2×C4×C61C2×M1612yes—
240C2×C4×C61C2×M1612yes—
241C2×C4×C61C2×M1612yes—
242C2×C4×C61C2×M1612yes—
243C2×Dic61—28no—
244C2×Dic61—28no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—28no—
256C2×Dic61C2×C22⋊C412yes—
257C2×Dic61C2×C22⋊C412yes—
258C2×Dic61#11712yes—
259C2×Dic61C2×M1612yes—
260C2×Dic61C2×M1612yes—
261C2×Dic61C22×D412yes—
262C2×Dic61C2×#4112yes—
263C2×Dic61C2×#4112yes—
264C4×D61—28no—
265C4×D61—28no—
266C4×D61—28no—
267C4×D61—28no—
268C4×D61—28no—
269C4×D61—28no—
270C4×D61—28no—
271C4×D61—28no—
272C4×D61—28no—
273C4×D61—28no—
274C4×D61—28no—
275C4×D61—28no—
276#92420—48no—
277#20715—611nomaximal, Sylow
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—22no—
283C22×C61—22no—
284C22×C61#43214yescomplemented
285C22×C61C22×C22⋊C411yescharacteristic
286C22×C61C2×#11711yescharacteristic
287C22×C61C2×#11711yescharacteristic
288C22×C61C22×M1611yescharacteristic
289C22×C61C22×M1611yescharacteristic
290C22×C61C22×M1611yescharacteristic
291C22×C61C22×M1611yescharacteristic
292C2×D61—232no—
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—22no—
305C2×D61#40714yes—
306C2×D61#43214yescomplemented
307C4×C61—22no—
308C4×C61—22no—
309C4×C61—22no—
310C4×C61—22no—
311C4×C61—22no—
312C4×C61#40714yes—
313Dic61—22no—
314Dic61—22no—
315Dic61—22no—
316Dic61—22no—
317Dic61—22no—
318Dic61#52514yes—
319C23×C42—611no—
320C2×#432—612no—
321#1817—612no—
322#1797—612no—
323#1797—612no—
324#1779—612no—
325#1749—612no—
326#1749—612no—
327C2×C61—24no—
328C2×C61#228011yescharacteristic
329C2×C61C2×#40711yescharacteristic
330C2×C61C2×#40711yescharacteristic
331C2×C61C2×#43211yescharacteristic
332C2×C61C2×#43211yescharacteristic
333C2×C61#292011yescharacteristic
334C2×C61#292011yescharacteristic
335D61—24no—
336D61—24no—
337C24×C4—611no—
338C24×C4—611no—
339C24×C4—611no—
340C22×C42—611no—
341C22×C42—611no—
342C22×C42—611no—
343C22×C42—611no—
344C22×C42—611no—
345C22×C42—611no—
346C22×C42—611no—
347C22×C42—611no—
348C22×C42—611no—
349C22×C42—611no—
350C22×C42—611no—
351C22×C42—1228no—
352C22×C42#692311yescharacteristic
353#432—1228no—
354C2×C4⋊C8—614no—
355C2×C22⋊C8—614no—
356C2×C22⋊C8—614no—
357C2×C22⋊C8—614no—
358C2×#97—614no—
359#336—614no—
360#336—614no—
361C61#2071511yescharacteristic, complemented, Sylow
362C25—611no—
363C23×C4—611no—
364C23×C4—611no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—1224no—
379C23×C4—1224no—
380C23×C4—1224no—
381C23×C4—1224no—
382C23×C4—1224no—
383C23×C4—1224no—
384C23×C4—1224no—
385C23×C4—1224no—
386C23×C4—1224no—
387C23×C4C2×#692311yescharacteristic
388C23×C4C2×#692311yescharacteristic
389C23×C4C2×#692311yescharacteristic
390C22×C8—618no—
391C2×C42—24no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—618no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—1224no—
406C2×C42—1224no—
407C2×C42—1224no—
408C2×C42—1224no—
409C2×C42—1224no—
410C2×C42—1224no—
411C2×C42—1224no—
412C2×C42—1224no—
413C2×C42—1224no—
414C2×C42—1224no—
415C2×C42C2×#692311yescharacteristic
416C2×C42C2×#692311yescharacteristic
417C2×C42C2×#692311yescharacteristic
418C2×C42C2×#692311yescharacteristic
419C4⋊C8—1228no—
420C22⋊C8—1228no—
421C22⋊C8—1228no—
422C22⋊C8—1228no—
423#97—1228no—
424C24—611no—
425C24—611no—
426C24—614no—
427C24—1222no—
428C24—1222no—
429C24—1222no—
430C24—1222no—
431C24—1222no—
432C24—1222no—
433C24C22×#692311yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—611no—
443C22×C4—614no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—614no—
450C22×C4—614no—
451C22×C4—614no—
452C22×C4—614no—
453C22×C4—614no—
454C22×C4—614no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—12232no—
476C22×C4—12232no—
477C22×C4—12232no—
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—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4#1175821314yes—
497C22×C4C22×#692311yescharacteristic
498C22×C4C22×#692311yescharacteristic
499C22×C4C22×#692311yescharacteristic
500C22×C4C22×#692311yescharacteristic
501C22×C4C22×#692311yescharacteristic
502C22×C4C22×#692311yescharacteristic
503C2×C8—1228no—
504C2×C8—1228no—
505C2×C8—1228no—
506C42—22no—
507C42—22no—
508C42—22no—
509C42—614no—
510C42—614no—
511C42—614no—
512C42—1222no—
513C42—1222no—
514C42—1222no—
515C42—1222no—
516C42—1222no—
517C42—1222no—
518C42—1222no—
519C42—1222no—
520C42—1222no—
521C42C22⋊#692314yes—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—612no—
527C23—612no—
528C23—612no—
529C23—612no—
530C23—612no—
531C23—612no—
532C23—1228no—
533C23—1228no—
534C23—1228no—
535C23—1228no—
536C23—1228no—
537C23—1228no—
538C23—1228no—
539C23—1221no—
540C23—1221no—
541C23—1221no—
542C23—1221no—
543C23—1221no—
544C23—1221no—
545C23—1221no—
546C23—1221no—
547C23#1451985612yes—
548C23D61⋊M1612yes—
549C23C2×#1175821312yes—
550C23C23×#692311yescharacteristic
551C2×C4—28no—
552C2×C4—28no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—28no—
564C2×C4—612no—
565C2×C4—612no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—612no—
572C2×C4—1228no—
573C2×C4—1228no—
574C2×C4—1228no—
575C2×C4—1228no—
576C2×C4—1228no—
577C2×C4—1228no—
578C2×C4—1228no—
579C2×C4—1228no—
580C2×C4—1228no—
581C2×C4—1228no—
582C2×C4—1228no—
583C2×C4—1228no—
584C2×C4—1228no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1228no—
596C2×C4—1228no—
597C2×C4C2×C22⋊#692312yes—
598C2×C4C2×C22⋊#692312yes—
599C2×C4C2×C22⋊#692312yes—
600C2×C4#1451985612yes—
601C2×C4D61⋊M1612yes—
602C2×C4D61⋊M1612yes—
603C2×C4C2×#1175821312yes—
604C2×C4C2×#1175821312yes—
605C8—2448no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—614no—
613C22—614no—
614C22—12232no—
615C22—1222no—
616C22—1222no—
617C22—1222no—
618C22—1222no—
619C22—1222no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22—1222no—
624C22—1222no—
625C22—1222no—
626C22—1222no—
627C22#1684078414yescomplemented
628C22C22×C22⋊#692311yescharacteristic
629C22C2×#1451985611yescharacteristic
630C22C2×#1451985611yescharacteristic
631C22C2×D61⋊M1611yescharacteristic
632C22C2×D61⋊M1611yescharacteristic
633C22C2×D61⋊M1611yescharacteristic
634C22C22×#1175821311yescharacteristic
635C4—22no—
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—614no—
641C4—1222no—
642C4—1222no—
643C4—1222no—
644C4—1222no—
645C4—1222no—
646C4#1684073314yes—
647C2—24no—
648C2—1224no—
649C2—1224no—
650C2#2146226311yescharacteristic
651C2D61⋊#40711yescharacteristic
652C2C2×#1684073311yescharacteristic
653C2D61⋊#43211yescharacteristic
654C2C2×#1684078411yescharacteristic
655C2#2146249611yescharacteristic
656C2#2146249711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC22×C42×C61C4
prime radicalC24×D61C2×C4
cosocleC22×Dic61C24
hypercenterC22×C42#6923
hypocenterC61#20715
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#16840784C2semidirect
2. #21461711C2semidirect
3. #21461674C2semidirect
4. #21461673C2semidirect
6. #21461546C2semidirect
7. #21461545C2semidirect
10. C2×C4⋊#92420C22semidirect
14. C2×#14519832C22semidirect
15. #16840628C22semidirect
16. #16840628C22semidirect
284. C22×C61#432semidirect
306. C2×D61#432semidirect
361. C61#20715semidirect
627. C22#16840784semidirect

Maximal subgroups

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

subgroupindex
C2×#168407842
#214617112
#214616742
#214616732
#214616422
#214615462
#214615452
C22×C42×D612
#2071561