Finite Group Databasebeta

← #29645913

Subgroups — #29645913

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840235C211yesmaximal, characteristic
2#21454846C212yesmaximal, complemented
3#21444158C212yesmaximal, complemented
4#21444155C212yesmaximal, complemented
5#21444150C212yesmaximal, complemented
6#21444146C211yesmaximal, characteristic, complemented
7#21444134C212yesmaximal, complemented
8#323×D61C212yesmaximal, complemented
9C61×#1462C211yesmaximal, characteristic, complemented
10C23×C22⋊D61C411yescharacteristic
11#16840235—24no—
12#16840235—24no—
13C2×C4×C22⋊D61C411yescharacteristic
14C2×C4×C22⋊D61C411yescharacteristic
15C2×C4×C22⋊D61C2211yescharacteristic
16C2×C4×C22⋊D61C2211yescharacteristic
17C2×#14519737C411yescharacteristic
18C2×#14519737C411yescharacteristic
19C2×#14519737C2211yescharacteristic
20C2×#14519737C2211yescharacteristic
21C2×#14519733C411yescharacteristic
22C2×#14519733C2211yescharacteristic
23C22×C22⋊Dic61C411yescharacteristic
24C2×C22⋊C4×D61C411yescharacteristic
25C2×C22⋊C4×D61C2211yescharacteristic
26#16839836—24no—
27#16839831—24no—
28#16839816C2214yescomplemented
29#16839726C2212yescomplemented
30C22⋊C8×D61C2214yescomplemented
31#16839487C2214yescomplemented
32#16839486C2212yes—
33#16839486C2212yescomplemented
34#16839485C2214yescomplemented
35C22×C22⋊C4×C61C2211yescharacteristic
36C61×#407C2212yescomplemented
37C61×#323C2212yes—
38C61×#323C2212yescomplemented
39C24×D61C2×C411yescharacteristic
40C22×C22⋊D61—24no—
41C22×C22⋊D61—22no—
42C22×C22⋊D61—22no—
43C22×C22⋊D61—24no—
44C22×C22⋊D61C2×C411yescharacteristic
45C22×C22⋊D61C2×C411yescharacteristic
46C22×C22⋊D61C2×C411yescharacteristic
47C22×C22⋊D61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C23×Dic61C2×C411yescharacteristic
50C23×Dic61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2311yescharacteristic
55C2×#11758194—22no—
56C2×C8×D61—24no—
57C4×C22⋊D61—22no—
58C4×C22⋊D61—22no—
59C4×C22⋊D61—22no—
60C4×C22⋊D61—22no—
61C4×C22⋊D61—22no—
62C4×C22⋊D61—22no—
63C4×C22⋊D61D414yes—
64C4×C22⋊D61D414yes—
65#14519737—24no—
66#14519737—24no—
67#14519737—24no—
68#14519737—24no—
69#14519733—24no—
70#14519733—24no—
71C2×#11758196C2×C411yescharacteristic
72C2×#11758196C2×C411yescharacteristic
73C2×#11758196C2×C411yescharacteristic
74C2×#11758196C2311yescharacteristic
75C2×C22⋊Dic61—22no—
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61C2×C411yescharacteristic
78C2×C22⋊Dic61C2×C411yescharacteristic
79C2×C22⋊Dic61C2×C411yescharacteristic
80C2×C22⋊Dic61C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2311yescharacteristic
85C22⋊C4×D61—24no—
86C22⋊C4×D61—24no—
87C2×C4×Dic61C2×C411yescharacteristic
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519706—24no—
92C22⋊#92418—22no—
93C22⋊#92418C2314yes—
94#14519689—24no—
95#14519687—24no—
96C25×C61C2×C411yescharacteristic
97C23×C4×C61C2×C411yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C2×M16×C61—22no—
100C2×C22⋊C4×C61—22no—
101C2×C22⋊C4×C61—22no—
102C2×C22⋊C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61C2311yescharacteristic
105C2×C22⋊C4×C61C2311yescharacteristic
106C22⋊C8×C61—22no—
107C22⋊C8×C61C2314yes—
108C24×C61—21no—
109C24×C61—21no—
110C24×C61—22no—
111C24×C61—22no—
112C24×C61—81no—
113C24×C61—81no—
114C24×C61C22×C411yescharacteristic
115C24×C61C22×C411yescharacteristic
116C24×C61C22×C411yescharacteristic
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—81no—
120C23×D61—81no—
121C23×D61M1614yescomplemented
122C23×D61C22×C411yescharacteristic
123C23×D61C22×C411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—81no—
127C22×C4×C61—81no—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C2×D412yes—
132C22×C4×C61C2×D412yes—
133C22×C4×C61C2411yescharacteristic
134C2×C22⋊D61—216no—
135C2×C22⋊D61—216no—
136C2×C22⋊D61—21no—
137C2×C22⋊D61—21no—
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61C22⋊C412yes—
148C2×C22⋊D61C22⋊C412yes—
149C2×C22⋊D61M1614yescomplemented
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—81no—
156C22×Dic61—81no—
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—22no—
166C2×C4×D61—81no—
167C2×C4×D61—81no—
168C2×C4×D61—81no—
169C2×C4×D61—81no—
170C2×C4×D61C2×D414yes—
171M16×C61—82no—
172C2×C8×C61—24no—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176C22⋊C4×C61—22no—
177C22⋊Dic61—21no—
178C22⋊Dic61—21no—
179C22⋊Dic61—22no—
180C22⋊Dic61—22no—
181C22⋊Dic61C22⋊C412yes—
182C22⋊Dic61C22⋊C412yes—
183#11758198—22no—
184#11758198—22no—
185#11758198—22no—
186#11758198C22⋊C414yes—
187#11758196—22no—
188#11758196—22no—
189#11758196—22no—
190#11758196C22⋊C414yes—
191C4×Dic61—22no—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61C2×D414yes—
195#11758194—82no—
196C2×#92418—24no—
197C8×D61—84no—
198C23×C61—24no—
199C23×C61—24no—
200C23×C61—21no—
201C23×C61—21no—
202C23×C61—21no—
203C23×C61—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—81no—
213C23×C61—81no—
214C23×C61—81no—
215C23×C61—81no—
216C23×C61—84no—
217C23×C61—84no—
218C23×C61C2×C22⋊C411yescharacteristic
219C23×C61C2×C22⋊C411yescharacteristic
220C23×C61C2×M1612yes—
221C23×C61C2×M1612yes—
222C23×C61C23×C411yescharacteristic
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—28no—
226C22×D61—41no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61—82no—
231C22×D61—82no—
232C22×D61—84no—
233C22×D61—84no—
234C22×D61C2×C22⋊C412yes—
235C22×D61C2×M1612yes—
236C22×D61C2×M1612yes—
237C22×D61C2×M1612yes—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—81no—
247C2×C4×C61—81no—
248C2×C4×C61C2×C22⋊C412yes—
249C2×C4×C61C22×D412yes—
250C22⋊D61—28no—
251C22⋊D61—24no—
252C22⋊D61—24no—
253C22⋊D61—24no—
254C22⋊D61—24no—
255C22⋊D61—28no—
256C2×Dic61—28no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—82no—
268C2×Dic61—82no—
269C2×Dic61C2×C22⋊C412yes—
270C2×Dic61C2×C22⋊C412yes—
271C2×Dic61C2×C22⋊C412yes—
272C2×Dic61C2×M1612yes—
273C4×D61—44no—
274C4×D61—82no—
275C4×D61—82no—
276C4×D61—82no—
277C8×C61—44no—
278#92418—44no—
279#17367—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—22no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—22no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—84no—
301C22×C61—84no—
302C22×C61C22×C22⋊C411yescharacteristic
303C22×C61C22×M1611yescharacteristic
304C22×C61C22×M1611yescharacteristic
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—42no—
309C2×D61—42no—
310C2×D61—42no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—42no—
314C2×D61—88no—
315C2×D61#40714yes—
316C4×C61—22no—
317C4×C61—22no—
318C4×C61—41no—
319C4×C61—41no—
320Dic61—22no—
321Dic61—22no—
322Dic61—22no—
323Dic61—22no—
324Dic61—41no—
325Dic61—41no—
326C2×#518—611no—
327#2973—612no—
328#1466—612no—
329#1465—612no—
330#1464—612no—
331#1462—611no—
332#1462D6111yescharacteristic, complemented
333#1459—612no—
334C2×#323—612no—
335C2×C61—21no—
336C2×C61—21no—
337C2×C61—42no—
338C2×C61—41no—
339C2×C61—41no—
340C2×C61—42no—
341C2×C61C2×#40711yescharacteristic
342C2×C61#288311yescharacteristic
343C2×C61#288811yescharacteristic
344D61—24no—
345D61—42no—
346C23×D4—611no—
347#518—1224no—
348#518—1224no—
349C2×C4×D4—611no—
350C2×C4×D4—611no—
351C2×C4×D4—611no—
352C2×C4×D4—611no—
353C2×C4×D4—611no—
354C2×C4×D4—611no—
355C2×C4×D4—611no—
356C2×C4×D4—611no—
357C2×#117—611no—
358C2×#117—611no—
359C22×C22⋊C4—611no—
360C22×C22⋊C4—611no—
361C22×C22⋊C4—611no—
362C22×C22⋊C4C2×D6111yescharacteristic
363#435—1224no—
364#435—1224no—
365#432—614no—
366#407—612no—
367#407C2×D6112yescomplemented
368C2×C22⋊C8—614no—
369#324—614no—
370#323—612no—
371#323—612no—
372#323—614no—
373#323C2×D6112yes—
374#323C2×D6112yescomplemented
375C61#1736711yescharacteristic, complemented, Sylow
376C25—611no—
377C25C4×D6111yescharacteristic
378C22×D4—611no—
379C22×D4—611no—
380C22×D4—611no—
381C22×D4—611no—
382C22×D4—1222no—
383C22×D4—1222no—
384C22×D4—1224no—
385C22×D4—1224no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4C4×D6111yescharacteristic
394C23×C4C22×D6111yescharacteristic
395C2×M16—22no—
396C2×M16—1222no—
397C22×C8—1224no—
398C4×D4—614no—
399C4×D4—614no—
400C4×D4—1224no—
401C4×D4—1224no—
402C4×D4—1224no—
403C4×D4—1224no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4—1222no—
410#117—1224no—
411#117—1224no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—611no—
419C2×C22⋊C4—611no—
420C2×C22⋊C4—611no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—611no—
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—1224no—
427C2×C22⋊C4—1224no—
428C2×C22⋊C4—1222no—
429C2×C22⋊C4—1222no—
430C2×C22⋊C4C4×D6111yescharacteristic
431C2×C22⋊C4C4×D6111yescharacteristic
432C2×C22⋊C4C22×D6111yescharacteristic
433C2×C22⋊C4C22×D6111yescharacteristic
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C4⋊C8—1224no—
439C22⋊C8—22no—
440C22⋊C8—614no—
441C22⋊C8—1224no—
442C22⋊C8—1222no—
443C22⋊C8C22×D6114yes—
444#97—1224no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—81no—
450C24—81no—
451C24—611no—
452C24—614no—
453C24—611no—
454C24—1222no—
455C24—1222no—
456C24—4881no—
457C24—4881no—
458C24C2×C4×D6111yescharacteristic
459C24C2×C4×D6111yescharacteristic
460C24C2×C4×D6111yescharacteristic
461C2×D4—612no—
462C2×D4—612no—
463C2×D4—614no—
464C2×D4—1222no—
465C2×D4—1222no—
466C2×D4—1222no—
467C2×D4—1222no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—1222no—
471C2×D4—1222no—
472C2×D4—12216no—
473C2×D4—12216no—
474C2×D4—1221no—
475C2×D4—1221no—
476C2×D4—1222no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—614no—
486C22×C4—611no—
487C22×C4—611no—
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—4881no—
497C22×C4—4881no—
498C22×C4—4881no—
499C22×C4—4881no—
500C22×C4—4881no—
501C22×C4—4881no—
502C22×C4C2×C4×D6111yescharacteristic
503C22×C4C2×C4×D6111yescharacteristic
504C22×C4C2×C4×D6111yescharacteristic
505C22×C4D4×D6112yes—
506C22×C4D4×D6112yes—
507C22×C4C23×D6111yescharacteristic
508M16—82no—
509M16—4882no—
510C2×C8—24no—
511C2×C8—1224no—
512C2×C8—4884no—
513C4⋊C4—614no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—612no—
522C22⋊C4—612no—
523C22⋊C4—614no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1221no—
529C22⋊C4—1221no—
530C22⋊C4—1222no—
531C42—614no—
532C42—1222no—
533C42—1222no—
534C42—1222no—
535C23—24no—
536C23—24no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—81no—
550C23—81no—
551C23—81no—
552C23—81no—
553C23—84no—
554C23—84no—
555C23—612no—
556C23—612no—
557C23—612no—
558C23—612no—
559C23—1228no—
560C23—1221no—
561C23—1221no—
562C23—4882no—
563C23—4882no—
564C23—4884no—
565C23—4884no—
566C23—2441no—
567C23—2441no—
568C23—2441no—
569C23—2441no—
570C23C22⋊C4×D6111yescharacteristic
571C23C22⋊C4×D6111yescharacteristic
572C23M16×D6112yes—
573C23M16×D6112yes—
574C23C22×C4×D6111yescharacteristic
575D4—1224no—
576D4—1224no—
577D4—1228no—
578D4—1224no—
579D4—1224no—
580D4—1228no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—612no—
592C2×C4—612no—
593C2×C4—612no—
594C2×C4—612no—
595C2×C4—1228no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—4882no—
603C2×C4—4882no—
604C2×C4—4882no—
605C2×C4—4882no—
606C2×C4—4882no—
607C2×C4—2444no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4C22⋊C4×D6112yes—
613C2×C4C2×D4×D6112yes—
614C8—44no—
615C8—2444no—
616C22—21no—
617C22—21no—
618C22—22no—
619C22—21no—
620C22—21no—
621C22—22no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—84no—
637C22—84no—
638C22—614no—
639C22—1222no—
640C22—1222no—
641C22—1222no—
642C22—4888no—
643C22—2442no—
644C22—2442no—
645C22—2442no—
646C22—2442no—
647C22—2441no—
648C22—2441no—
649C22C2×C22⋊C4×D6111yescharacteristic
650C22C2×M16×D6111yescharacteristic
651C22C2×M16×D6111yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—1222no—
657C4—1222no—
658C4—1222no—
659C4—1222no—
660C4—2441no—
661C4—2441no—
662C2—21no—
663C2—21no—
664C2—41no—
665C2—41no—
666C2—42no—
667C2—42no—
668C2—1224no—
669C2—2442no—
670C2#407×D6111yescharacteristic
671C2#2145427711yescharacteristic
672C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1462C2
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC22×C4×C61C24
hypercenter#1462D61
hypocenterC61#17367
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. #21454846C2semidirect
3. #21444158C2semidirect
4. #21444155C2semidirect
5. #21444150C2semidirect
6. #21444146C2semidirect
7. #21444134C2semidirect
8. #323×D61C2semidirect
9. C61×#1462C2semidirect
28. #16839816C22semidirect
29. #16839726C22semidirect
30. C22⋊C8×D61C22semidirect
31. #16839487C22semidirect
33. #16839486C22semidirect
34. #16839485C22semidirect
36. C61×#407C22semidirect
38. C61×#323C22semidirect
121. C23×D61M16semidirect
149. C2×C22⋊D61M16semidirect
332. #1462D61semidirect
367. #407C2×D61semidirect
374. #323C2×D61semidirect
375. C61#17367semidirect

Maximal subgroups

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

subgroupindex
C2×#168402352
#214548462
#214441582
#214441552
#214441502
#214441462
#214441342
#323×D612
C61×#14622
#1736761