Finite Group Databasebeta

← #29601727

Subgroups — #29601727

Order 15616.

2118 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519735C211yesmaximal, characteristic
2C2×#16839613C212yesmaximal, complemented
3C2×#16839609C211yesmaximal, characteristic
4C2×#16839609C211yesmaximal, characteristic
5#21444083C211yesmaximal, characteristic, complemented
6#21444082C211yesmaximal, characteristic, complemented
7#21444076C211yesmaximal, characteristic, complemented
8#21444063C212yesmaximal
9#21444063C212yesmaximal
10#95×Dic61C212yesmaximal, complemented
11C61×#1442C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C2×#14519735—28no—
14C2×#14519735—24no—
15C22×C4⋊Dic61C2211yescharacteristic
16C22×#11758196C2212yes—
17C22×#11758196C2212yes—
18C22×#11758198C2212yes—
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×C4×Dic61C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2212yes—
25C22×C4×Dic61C2212yes—
26#16839613—28no—
27#16839609—24no—
28#16839609C418yescomplemented
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C2×#95×C61C2212yes—
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2212yes—
39C2×#95×C61C2211yescharacteristic
40C24×D61C2311yescharacteristic
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C23×Dic61C2312yes—
45C23×Dic61C2311yescharacteristic
46C22×C4×D61—24no—
47C22×C4×D61—24no—
48C22×C4×D61C2×C414yes—
49C22×C4×D61D414yes—
50C22×C4×D61Q814yes—
51#14519735—232no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—24no—
54C2×#11758196—24no—
55C2×#11758196—24no—
56C2×#11758196—24no—
57C2×#11758196—24no—
58C2×#11758196—24no—
59C2×#11758196—24no—
60C2×#11758198—24no—
61C2×#11758198—22no—
62C2×#11758198—22no—
63C2×#11758198—24no—
64C2×#11758198—22no—
65C2×#11758198—22no—
66C2×#11758198—24no—
67C2×#11758198—22no—
68C2×#11758198—22no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198C2×C418yes—
72C2×C4×Dic61—24no—
73C2×C4×Dic61—24no—
74C2×C4×Dic61—24no—
75C2×C4×Dic61—24no—
76C2×C4×Dic61—22no—
77C2×C4×Dic61—22no—
78C2×C4×Dic61—24no—
79C2×C4×Dic61—24no—
80C2×C4×Dic61C2×C418yes—
81C2×C4×Dic61D418yes—
82#14519684—22no—
83#14519684—24no—
84#14519684—24no—
85#14519684—24no—
86#14519684—24no—
87#14519684C2×C414yes—
88C23×C4×C61C2312yes—
89C23×C4×C61C2312yes—
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61—24no—
94C2×C4⋊C4×C61—22no—
95#95×C61—22no—
96#95×C61—24no—
97#95×C61—24no—
98#95×C61C2×C414yes—
99C24×C61C2411yescharacteristic
100C23×D61—22no—
101C23×D61—22no—
102C23×D61—22no—
103C23×D61—22no—
104C23×D61—21no—
105C23×D61—21no—
106C23×D61—21no—
107C23×D61—21no—
108C23×D61C22×C412yes—
109C23×D61C2×D412yes—
110C23×D61C2×Q812yes—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61C22×C414yes—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C2×D414yes—
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×Q812yes—
138C22×C4×C61#4112yes—
139C22×C4×C61#4112yes—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61C22×C414yes—
159C22×Dic61C22×C412yes—
160C22×Dic61C2×D414yes—
161C22×Dic61C2×D412yes—
162C22×Dic61C2×D414yes—
163C22×Dic61C2×Q812yes—
164C22×Dic61#4112yes—
165C22×Dic61#4112yes—
166C22×Dic61#4114yes—
167C22×Dic61#4114yes—
168C22×Dic61#4114yes—
169C2×C4×D61—216no—
170C2×C4×D61—28no—
171C2×C4×D61—216no—
172C2×C4×D61—28no—
173C2×C4×D61C4⋊C4116yescomplemented
174C4⋊C4×C61—28no—
175#11758198—28no—
176#11758198—28no—
177#11758198—216no—
178#11758198—216no—
179C4⋊Dic61—28no—
180#11758196—216no—
181#11758196—216no—
182C4×Dic61—216no—
183C4×Dic61—216no—
184C4×Dic61—44no—
185C4×Dic61—44no—
186C23×C61C23×C411yescharacteristic
187C23×C61C22×D411yescharacteristic
188C23×C61C22×D412yes—
189C23×C61C22×Q811yescharacteristic
190C23×C61C2×#4112yes—
191C23×C61C2×#4112yes—
192C23×C61C2×#4112yes—
193C23×C61C2×#4111yescharacteristic
194C23×C61C2×#4111yescharacteristic
195C23×C61C2×#4111yescharacteristic
196C23×C61C2×#4111yescharacteristic
197C22×D61—24no—
198C22×D61—24no—
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—24no—
203C22×D61—22no—
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—22no—
208C22×D61—24no—
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61C2×C4⋊C414yes—
220C2×C4×C61—24no—
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—22no—
224C2×C4×C61—24no—
225C2×C4×C61—24no—
226C2×C4×C61—24no—
227C2×C4×C61—24no—
228C2×C4×C61—24no—
229C2×C4×C61—24no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—41no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—41no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61C2×C4⋊C414yes—
249C2×Dic61—24no—
250C2×Dic61—24no—
251C2×Dic61—24no—
252C2×Dic61—24no—
253C2×Dic61—24no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—41no—
269C2×Dic61—42no—
270C2×Dic61—42no—
271C2×Dic61—41no—
272C2×Dic61C2×C4⋊C414yes—
273C2×Dic61#11718yescomplemented
274C2×Dic61C4×D418yes—
275C2×Dic61#12014yes—
276C2×Dic61C22⋊Q818yes—
277C2×Dic61#12314yes—
278C4×D61—232no—
279#13844—611nomaximal, Sylow
280C22×C61C22×C4⋊C411yescharacteristic
281C22×C61C2×#11712yes—
282C22×C61C2×C4×D412yes—
283C22×C61C4×#4111yescharacteristic
284C22×C61C4×#4111yescharacteristic
285C22×C61C2×#12011yescharacteristic
286C22×C61C2×C22⋊Q812yes—
287C22×C61C2×#12311yescharacteristic
288C22×C61#52512yes—
289C22×C61#52511yescharacteristic
290C22×C61#52511yescharacteristic
291C22×C61#52512yes—
292C22×C61#52912yes—
293C22×C61#52912yes—
294C22×C61#52912yes—
295C22×C61#52912yes—
296C22×C61#53212yes—
297C22×C61#53211yescharacteristic
298C22×C61#53211yescharacteristic
299C22×C61#53212yes—
300C22×C61#53311yescharacteristic
301C22×C61#53312yes—
302C22×C61#53311yescharacteristic
303C2×D61—24no—
304C2×D61—24no—
305C2×D61—24no—
306C2×D61—42no—
307C2×D61—42no—
308C2×D61—42no—
309C2×D61—42no—
310C2×D61—44no—
311C2×D61—44no—
312C2×D61—44no—
313C2×D61—44no—
314C4×C61—24no—
315C4×C61—44no—
316C4×C61—42no—
317C4×C61—42no—
318C4×C61—44no—
319Dic61—28no—
320Dic61—42no—
321Dic61—44no—
322Dic61—42no—
323Dic61#38518yes—
324C22×#117—611no—
325C2×C4×C4⋊C4—612no—
326C2×C4×C22⋊C4—611no—
327C2×C4×C22⋊C4—611no—
328#1444—611no—
329#1444—611no—
330#1442—611no—
331#1442D6111yescharacteristic, complemented
332#1439—612no—
333#1439—612no—
334C4×#95—612no—
335C2×C61#228511yescharacteristic
336C2×C61C2×#38511yescharacteristic
337C2×C61#229012yes—
338C2×C61#229312yes—
339C2×C61#229611yescharacteristic
340C2×C61#238811yescharacteristic
341C2×C61#238811yescharacteristic
342C2×C61#239511yescharacteristic
343C2×C61#239511yescharacteristic
344C2×C61#239612yes—
345C2×C61#239612yes—
346D61—44no—
347C24×C4—611no—
348C2×#117—1228no—
349C2×#117—1224no—
350C22×C4⋊C4—612no—
351C22×C4⋊C4—612no—
352C22×C4⋊C4—611no—
353C22×C4⋊C4C2×D6111yescharacteristic
354C22×C22⋊C4—612no—
355C22×C22⋊C4—612no—
356C22×C22⋊C4—611no—
357C22×C22⋊C4—611no—
358C22×C42—612no—
359C22×C42—612no—
360C22×C42—611no—
361C22×C42—611no—
362C4×C4⋊C4—1228no—
363C4×C22⋊C4—618no—
364C4×C22⋊C4—1224no—
365C2×#95—611no—
366C2×#95—612no—
367C2×#95—612no—
368C2×#95—612no—
369C2×#95—612no—
370C2×#95—611no—
371C2×#95C2×D6112yes—
372C2×#95C2×D6112yes—
373C2×#95C2×D6111yescharacteristic
374C2×#95C2×D6111yescharacteristic
375C61#1384411yescharacteristic, complemented, Sylow
376C25—611no—
377C23×C4—611no—
378C23×C4—612no—
379C23×C4—614no—
380C23×C4—614no—
381C23×C4—614no—
382C23×C4—612no—
383C23×C4—611no—
384C23×C4—611no—
385C23×C4—1224no—
386C23×C4—1224no—
387C23×C4C22×D6112yes—
388C23×C4C22×D6112yes—
389C23×C4C22×D6111yescharacteristic
390C23×C4C22×D6111yescharacteristic
391C23×C4C22×D6111yescharacteristic
392#117—12232no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—1224no—
396C2×C4⋊C4—1224no—
397C2×C4⋊C4—1224no—
398C2×C4⋊C4—1224no—
399C2×C4⋊C4—1224no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1224no—
402C2×C4⋊C4—1224no—
403C2×C22⋊C4—618no—
404C2×C22⋊C4—1224no—
405C2×C22⋊C4—1224no—
406C2×C22⋊C4—1224no—
407C2×C22⋊C4—1222no—
408C2×C22⋊C4—1222no—
409C2×C22⋊C4—1224no—
410C2×C22⋊C4—1222no—
411C2×C22⋊C4—1222no—
412C2×C22⋊C4—1224no—
413C2×C22⋊C4—1222no—
414C2×C22⋊C4—1222no—
415C2×C42—618no—
416C2×C42—618no—
417C2×C42—1224no—
418C2×C42—1224no—
419C2×C42—1224no—
420C2×C42—1224no—
421C2×C42—1222no—
422C2×C42—1222no—
423C2×C42—1224no—
424C2×C42—1224no—
425#95—22no—
426#95—24no—
427#95—24no—
428#95—614no—
429#95—1224no—
430#95—1224no—
431#95—1224no—
432#95—1224no—
433#95—1222no—
434#95C4×D6114yes—
435C24—612no—
436C24—612no—
437C24—612no—
438C24—1222no—
439C24—1222no—
440C24—1222no—
441C24—1221no—
442C24—1221no—
443C24—1222no—
444C24—1221no—
445C24—1221no—
446C24C23×D6111yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—612no—
470C22×C4—614no—
471C22×C4—612no—
472C22×C4—612no—
473C22×C4—614no—
474C22×C4—614no—
475C22×C4—614no—
476C22×C4—614no—
477C22×C4—6116no—
478C22×C4—614no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—1228no—
482C22×C4—12216no—
483C22×C4—12216no—
484C22×C4—1228no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1222no—
503C22×C4C2×C4×D6114yes—
504C22×C4C2×C4×D6112yes—
505C22×C4D4×D6114yes—
506C22×C4D4×D6112yes—
507C22×C4#1175822412yes—
508C22×C4Q8×D6112yes—
509C22×C4#1175822612yes—
510C4⋊C4—28no—
511C4⋊C4—12216no—
512C4⋊C4—12216no—
513C4⋊C4—1228no—
514C22⋊C4—12216no—
515C22⋊C4—12216no—
516C22⋊C4—1228no—
517C22⋊C4—1228no—
518C42—12216no—
519C42—12216no—
520C42—2444no—
521C42—2444no—
522C23—614no—
523C23—1224no—
524C23—1224no—
525C23—1222no—
526C23—1222no—
527C23—1222no—
528C23—1224no—
529C23—1222no—
530C23—1222no—
531C23—1222no—
532C23—1222no—
533C23—1222no—
534C23—1222no—
535C23—1224no—
536C23—1222no—
537C23—2442no—
538C23—2442no—
539C23—2442no—
540C23—2442no—
541C23—2442no—
542C23—2442no—
543C23—2442no—
544C23—2442no—
545C23C22×C4×D6111yescharacteristic
546C23C2×D4×D6111yescharacteristic
547C23C2×D4×D6112yes—
548C23C2×Q8×D6111yescharacteristic
549C23#41×D6112yes—
550C23#41×D6112yes—
551C23#41×D6112yes—
552C23#41×D6111yescharacteristic
553C23#41×D6111yescharacteristic
554C23C2×#1175822411yescharacteristic
555C23C2×#1175822611yescharacteristic
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—614no—
585C2×C4—618no—
586C2×C4—614no—
587C2×C4—618no—
588C2×C4—614no—
589C2×C4—618no—
590C2×C4—12232no—
591C2×C4—1224no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1224no—
598C2×C4—1224no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1224no—
602C2×C4—1224no—
603C2×C4—1224no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4—2442no—
610C2×C4—2441no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2441no—
614C2×C4C4⋊C4×D6114yes—
615C22—1224no—
616C22—1224no—
617C22—1224no—
618C22—2444no—
619C22—2442no—
620C22—2442no—
621C22—2444no—
622C22—2442no—
623C22—2442no—
624C22—2444no—
625C22—2444no—
626C22C2×C4⋊C4×D6111yescharacteristic
627C22#117×D6112yes—
628C22C4×D4×D6112yes—
629C22C4×#1175822411yescharacteristic
630C22C4×#1175822611yescharacteristic
631C22#120×D6111yescharacteristic
632C22C22⋊Q8×D6112yes—
633C22#123×D6111yescharacteristic
634C22#1684027012yes—
635C22#1684027211yescharacteristic
636C22#1684027512yes—
637C22#1684027511yescharacteristic
638C22#1684028912yes—
639C22#1684029512yes—
640C22#1684029512yes—
641C22#1684029712yes—
642C22#1684030712yes—
643C22#1684031111yescharacteristic
644C22#1684031111yescharacteristic
645C22#1684031112yes—
646C22#1684031711yescharacteristic
647C22#1684031812yes—
648C22#1684031811yescharacteristic
649C4—24no—
650C4—44no—
651C4—42no—
652C4—44no—
653C4—42no—
654C4—618no—
655C4—1228no—
656C4—2442no—
657C4—2444no—
658C4—2442no—
659C2—2444no—
660C2#2144822511yescharacteristic
661C2#385×D6111yescharacteristic
662C2#2144825712yes—
663C2#2144827912yes—
664C2#2144830011yescharacteristic
665C2#2144903311yescharacteristic
666C2#2144903611yescharacteristic
667C2#2144908111yescharacteristic
668C2#2144908511yescharacteristic
669C2#2144909212yes—
670C2#2144909612yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1442C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1442D61
hypocenterC61#13844
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#16839613C2semidirect
5. #21444083C2semidirect
6. #21444082C2semidirect
7. #21444076C2semidirect
10. #95×Dic61C2semidirect
11. C61×#1442C2semidirect
28. #16839609C4semidirect
173. C2×C4×D61C4⋊C4semidirect
273. C2×Dic61#117semidirect
331. #1442D61semidirect
375. C61#13844semidirect

Maximal subgroups

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

subgroupindex
C22×#145197352
C2×#168396132
C2×#168396092
#214440832
#214440822
#214440762
#214440632
#95×Dic612
C61×#14422
#1384461