Finite Group Databasebeta

← #30615224

Subgroups — #30615224

Order 15616.

1428 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462496C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21461725C212yesmaximal, complemented
4#21461691C214yesmaximal, complemented
5#21461660C212yesmaximal
6C4×#14519841C214yesmaximal, complemented
7C2×C4×#11758224C211yesmaximal, characteristic
8C2×#14519856—21no—
9#16840784—21no—
10#16840783—21no—
11#16840781—21no—
12#16840778—21no—
13#16840766C2212yescomplemented
14C2×#14519841C2218yes—
15#16840733C2212yes—
16C4×#11758213C2212yescomplemented
17C4×C4⋊#6923—21no—
18C4×C4⋊#6923C2212yescomplemented
19C4×C22⋊#6923—21no—
20C4×C22⋊#6923C2212yes—
21#16840698—21no—
22C42×#6923C2212yescomplemented
23#16840632C2218yescomplemented
24C22×#11758224C2211yescharacteristic
25C4×#11758224—21no—
26C4×#11758224—21no—
27C4×#11758224—21no—
28C4×#11758224—21no—
29C4×#11758224C412yescomplemented
30C4×#11758224C412yescomplemented
31C4×#11758224C2212yes—
32C4×#11758224C2212yes—
33C2×C4×Dic122C411yescharacteristic, complemented
34C2×#14519742C411yescharacteristic, complemented
35C2×D4×Dic61C411yescharacteristic, complemented
36C2×C4×C22⋊D61—21no—
37C2×#14519737—21no—
38C2×#14519735C2211yescharacteristic
39C2×#14519733—21no—
40C22×C4×Dic61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×D4×C61C411yescharacteristic, complemented
43C2×#11758213C2314yes—
44#14519856—28no—
45C2×C4⋊#6923—22no—
46C2×C22⋊#6923—22no—
47C2×C4×#6923—22no—
48C2×C4×#6923—22no—
49C2×C4×#6923C2314yes—
50C4⋊#92420—22no—
51C4⋊#92420—22no—
52#14519841—216no—
53#14519834—22no—
54C22⋊#92420—22no—
55#14519832—22no—
56C4×#92420—22no—
57(C2×#6923)⋊C4—22no—
58(C2×#6923)⋊C4—22no—
59C2×#11758224—28no—
60C2×#11758224—21no—
61C2×#11758224—21no—
62C2×#11758224C2×C412yes—
63C2×#11758224C2312yes—
64C22×Dic122C2×C411yescharacteristic
65C22×C22⋊D61—21no—
66C23×Dic61—21no—
67C23×Dic61—21no—
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C4×Dic122—21no—
72C4×Dic122—21no—
73C4×Dic122C2×C412yes—
74C4×Dic122C2×C412yes—
75#14519742—21no—
76#14519742—21no—
77#14519742C2×C412yes—
78#14519742C2×C412yes—
79D4×Dic61—21no—
80D4×Dic61—21no—
81D4×Dic61C2×C412yes—
82D4×Dic61C2×C412yes—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87#14519737—22no—
88#14519737—22no—
89#14519737—22no—
90#14519737—22no—
91#14519735—21no—
92#14519735—21no—
93#14519735C2×C412yes—
94#14519735C2312yes—
95#14519733—22no—
96#14519733—22no—
97#14519733—22no—
98#14519733—22no—
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61C2×C411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61C2311yescharacteristic
121C42×D61C2311yescharacteristic
122C22×D4×C61C2×C411yescharacteristic
123C23×C4×C61—21no—
124C4×D4×C61—21no—
125C4×D4×C61—21no—
126C4×D4×C61C2×C412yes—
127C4×D4×C61C2×C412yes—
128C2×C4⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C42×C61C2×C411yescharacteristic
131C24×C61—21no—
132C23×D61C2×D411yescharacteristic
133C22×#6923—24no—
134C2×D4×C61—24no—
135C2×D4×C61—21no—
136C2×D4×C61C22×C412yes—
137C22×C4×C61—21no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—44no—
141C22×C4×C61C22⋊C411yescharacteristic
142C22×C4×C61C22⋊C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C2×C22⋊D61—28no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C22×Dic61—28no—
148C22×Dic61—21no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—21no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—44no—
155C22×Dic61C22⋊C411yescharacteristic
156C22×Dic61C22⋊C411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158#11758224—28no—
159#11758224—28no—
160#11758224—24no—
161#11758224—24no—
162#11758224—24no—
163#11758224#4118yes—
164C2×C4×D61—24no—
165C2×C4×D61—24no—
166C2×C4×D61—42no—
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22×C411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61C2411yescharacteristic
179C2×Dic122—21no—
180C2×Dic122—24no—
181C2×Dic122C22×C412yes—
182C22⋊#6923—28no—
183C2×#92420—24no—
184C4⋊#6923—28no—
185C4×#6923—28no—
186C4×#6923—28no—
187C4×#6923—44no—
188#11758213—28no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61C22×C412yes—
191C22⋊C4×C61—22no—
192C22⋊C4×C61—22no—
193C42×C61C22⋊C411yescharacteristic
194C42×C61C22⋊C411yescharacteristic
195C42×C61C22×C411yescharacteristic
196C42×C61C22×C411yescharacteristic
197C22⋊Dic61—22no—
198C22⋊Dic61—22no—
199#11758198—22no—
200#11758198—22no—
201C4⋊Dic61—21no—
202C4⋊Dic61C22×C412yes—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22×C411yescharacteristic
220C4×Dic61C22×C411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C23×C61—24no—
226C23×C61—22no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61C2×C22⋊C411yescharacteristic
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—41no—
233C22×D61C2×C22⋊C411yescharacteristic
234C22×D61C22×D411yescharacteristic
235C2×#6923—28no—
236C2×#6923—44no—
237C2×#6923—44no—
238D4×C61—24no—
239D4×C61—22no—
240D4×C61#11714yescomplemented
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—41no—
244C2×C4×C61—42no—
245C2×C4×C61—44no—
246C2×C4×C61—44no—
247C2×C4×C61#10414yescomplemented
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C23×C411yescharacteristic
254C22⋊D61—28no—
255C22⋊D61—28no—
256C2×Dic61—24no—
257C2×Dic61—28no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—28no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—44no—
265C2×Dic61—42no—
266C2×Dic61—44no—
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C22×D411yescharacteristic
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61C2×#4114yes—
285Dic122—24no—
286Dic122—22no—
287Dic122#11714yescomplemented
288#92420—44no—
289#20747—611nomaximal, Sylow
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—24no—
293C22×C61—48no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61C2×#10412yes—
297C22×C61C22×C22⋊C411yescharacteristic
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—21no—
302C2×D61—21no—
303C2×D61—44no—
304C2×D61#52512yes—
305#6923—48no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—42no—
310C4×C61C2×#10412yes—
311C4×C61C2×#10412yes—
312C4×C61C2×#11712yes—
313Dic61—21no—
314Dic61—21no—
315Dic61—21no—
316Dic61—24no—
317Dic61—21no—
318Dic61—42no—
319Dic61#42112yes—
320Dic61#52512yes—
321C2×C4×#41—611no—
322#2920—611no—
323C4×#117—611no—
324#1826—612no—
325#1806—614no—
326#1789—612no—
327C4×#104—614no—
328C2×C61—22no—
329C2×C61—44no—
330C2×C61#228011yescharacteristic
331C2×C61C22×#10411yescharacteristic
332C2×C61C2×#42111yescharacteristic
333D61—22no—
334D61—41no—
335C22×#41—611no—
336C4×#41—612no—
337C4×#41—612no—
338C4×#41—612no—
339C4×#41—612no—
340C4×#41—1221no—
341C4×#41—1221no—
342C4×#41—1221no—
343C4×#41—1221no—
344C2×C4×Q8—611no—
345C2×C4×Q8—611no—
346C2×C4×D4—611no—
347C2×C4×D4—1221no—
348C2×C4×D4—1221no—
349C2×C4×D4#692311yescharacteristic, complemented
350C2×#117—611no—
351C2×#117—1221no—
352C2×#117—1221no—
353C22×C42—611no—
354C22×C42—1221no—
355#432—1221no—
356#432—1221no—
357#431—1221no—
358#431—1221no—
359#423—612no—
360C2×#104—618no—
361#407—612no—
362C4×M16—612no—
363C4×C4⋊C4—612no—
364C4×C4⋊C4—1221no—
365C4×C22⋊C4—612no—
366C4×C22⋊C4—1221no—
367#376—1221no—
368C43—612no—
369#339—618no—
370C61#2074711yescharacteristic, complemented, Sylow
371C2×#41—612no—
372C2×#41—612no—
373C2×#41—1221no—
374C2×#41—1221no—
375C2×#41—1228no—
376C22×Q8—611no—
377C22×D4—1221no—
378C22×D4C2×#692311yescharacteristic
379C23×C4—21no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—1221no—
384C23×C4—1221no—
385C2×M16—614no—
386C4×Q8—612no—
387C4×Q8—612no—
388C4×Q8—612no—
389C4×Q8—612no—
390C4×Q8—1221no—
391C4×Q8—1221no—
392C4×Q8—1221no—
393C4×Q8—1221no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—612no—
397C4×D4—612no—
398C4×D4—1221no—
399C4×D4—1221no—
400C4×D4—1222no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4—1222no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4C2×#692312yes—
409C4×D4C2×#692312yes—
410#117—612no—
411#117—612no—
412#117—1222no—
413#117—1222no—
414#117—1222no—
415#117—1222no—
416#117—1221no—
417#117—1221no—
418#117—1228no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1222no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4C2×#692311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1222no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—614no—
440C2×C42—1222no—
441C2×C42—1222no—
442C2×C42—1222no—
443C2×C42—1222no—
444C2×C42—1221no—
445C2×C42—1221no—
446C2×C42—1222no—
447C2×C42—1221no—
448C2×C42—1222no—
449C2×C42C2×#692311yescharacteristic
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452#104—12216no—
453C22⋊C8—1222no—
454C22⋊C8—1222no—
455#97—1222no—
456C4×C8—1222no—
457#95—1222no—
458#95—1222no—
459C24—21no—
460C24—611no—
461#41—618no—
462#41—1224no—
463#41—1224no—
464#41—1228no—
465#41—1228no—
466#41—1224no—
467C2×Q8—612no—
468C2×Q8—1224no—
469C2×Q8—1221no—
470C2×D4—24no—
471C2×D4—21no—
472C2×D4—1222no—
473C2×D4—1222no—
474C2×D4—1228no—
475C2×D4C22×#692312yes—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—44no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—1224no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1228no—
501C22×C4—1221no—
502C22×C4—1224no—
503C22×C4—1224no—
504C22×C4—1221no—
505C22×C4—2442no—
506C22×C4—2444no—
507C22×C4C22⋊#692311yescharacteristic
508C22×C4C22⋊#692311yescharacteristic
509C22×C4C22×#692311yescharacteristic
510M16—1228no—
511C2×C8—1224no—
512C4⋊C4—21no—
513C4⋊C4—612no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1228no—
517C4⋊C4—1221no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4C22×#692312yes—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1228no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—1222no—
541C42—1222no—
542C42—1222no—
543C42—1222no—
544C42—1228no—
545C42—1228no—
546C42—1222no—
547C42—1222no—
548C42—2444no—
549C42C22⋊#692311yescharacteristic
550C42C22⋊#692311yescharacteristic
551C42C22×#692311yescharacteristic
552C42C22×#692311yescharacteristic
553C23—24no—
554C23—22no—
555C23—42no—
556C23—42no—
557C23—611no—
558C23—611no—
559C23—1222no—
560C23—1222no—
561C23—2441no—
562C23C2×C22⋊#692311yescharacteristic
563Q8—614no—
564Q8—1224no—
565Q8—1222no—
566D4—24no—
567D4—22no—
568D4—1228no—
569D4—1228no—
570D4#1451985614yescomplemented
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—611no—
578C2×C4—611no—
579C2×C4—614no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1228no—
591C2×C4—1224no—
592C2×C4—1228no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1228no—
601C2×C4—1222no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2444no—
605C2×C4—2444no—
606C2×C4—2442no—
607C2×C4—2444no—
608C2×C4—2444no—
609C2×C4#1451984114yescomplemented
610C2×C4C2×C22⋊#692311yescharacteristic
611C2×C4C2×C22⋊#692311yescharacteristic
612C2×C4C2×C22⋊#692311yescharacteristic
613C2×C4C2×C22⋊#692311yescharacteristic
614C2×C4C2×C22⋊#692311yescharacteristic
615C2×C4C23×#692311yescharacteristic
616C8—2444no—
617C22—21no—
618C22—21no—
619C22—24no—
620C22—48no—
621C22—42no—
622C22—42no—
623C22—612no—
624C22—1221no—
625C22—1221no—
626C22—1221no—
627C22—1221no—
628C22—1221no—
629C22—2444no—
630C22C2×#1451984112yes—
631C22C22×C22⋊#692311yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—42no—
636C4—612no—
637C4—612no—
638C4—1221no—
639C4—1221no—
640C4—1221no—
641C4—1221no—
642C4—1224no—
643C4—2448no—
644C4—2442no—
645C4C2×#1451984112yes—
646C4C2×#1451984112yes—
647C4C2×#1451985612yes—
648C2—22no—
649C2—44no—
650C2—1222no—
651C2—2441no—
652C2#2146226311yescharacteristic
653C2C22×#1451984111yescharacteristic
654C2D61⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758224C22
cosocleC2×C4×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61#20747
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462496C2semidirect
2. C4×#14519856C2semidirect
3. #21461725C2semidirect
4. #21461691C2semidirect
6. C4×#14519841C2semidirect
13. #16840766C22semidirect
16. C4×#11758213C22semidirect
18. C4×C4⋊#6923C22semidirect
22. C42×#6923C22semidirect
23. #16840632C22semidirect
29. C4×#11758224C4semidirect
30. C4×#11758224C4semidirect
33. C2×C4×Dic122C4semidirect
34. C2×#14519742C4semidirect
35. C2×D4×Dic61C4semidirect
42. C2×C4×D4×C61C4semidirect
240. D4×C61#117semidirect
247. C2×C4×C61#104semidirect
287. Dic122#117semidirect
349. C2×C4×D4#6923semidirect
370. C61#20747semidirect
570. D4#14519856semidirect
609. C2×C4#14519841semidirect

Maximal subgroups

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

subgroupindex
#214624962
C4×#145198562
#214617252
#214616912
#214616602
C4×#145198412
C2×C4×#117582242
#2074761