Finite Group Databasebeta

← #29645916

Subgroups — #29645916

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840234C211yesmaximal, characteristic
2#21454848C211yesmaximal, characteristic, complemented
3#21444159C212yesmaximal, complemented
4#21444155C212yesmaximal, complemented
5#21444151C212yesmaximal, complemented
6#21444145C212yesmaximal, complemented
7#21444135C212yesmaximal, complemented
8C2×#16839485C212yesmaximal, complemented
9C61×#2973C211yesmaximal, characteristic, complemented
10C22×D4×D61C411yescharacteristic
11#16840234—24no—
12#16840234—24no—
13C2×C4×D244C2211yescharacteristic
14C2×D4×Dic61C411yescharacteristic
15C2×#14519739C411yescharacteristic
16C2×C4×C22⋊D61C2211yescharacteristic
17C2×C4×C22⋊D61C2211yescharacteristic
18C2×#14519737C411yescharacteristic
19C2×#14519737C411yescharacteristic
20C2×#14519735C411yescharacteristic
21C2×#14519734C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C2×C22⋊C4×D61C411yescharacteristic
25C2×C22⋊C4×D61C411yescharacteristic
26#16839834—24no—
27#16839819C2212yescomplemented
28#16839726C2212yescomplemented
29C2×C22⋊#92418C2212yescomplemented
30#16839487C2214yescomplemented
31#16839485C2214yes—
32#16839485C2214yescomplemented
33#16839485C2214yescomplemented
34C2×C4×D4×C61C2211yescharacteristic
35C61×#435—24no—
36C61×#432C2212yescomplemented
37C61×#407C2212yescomplemented
38C2×C22⋊C8×C61C2212yescomplemented
39C24×D61C2×C411yescharacteristic
40C24×D61C2×C411yescharacteristic
41C22×D244C2×C411yescharacteristic
42C22×C22⋊D61C2×C411yescharacteristic
43C22×C22⋊D61C2×C411yescharacteristic
44C2×D4×D61—24no—
45C2×D4×D61—24no—
46C2×D4×D61—24no—
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C2×#11758194—22no—
55C22×#92418—22no—
56C4×D244—22no—
57C4×D244—22no—
58D4×Dic61—24no—
59#14519739—24no—
60C4×C22⋊D61—22no—
61C4×C22⋊D61—22no—
62C4×C22⋊D61—22no—
63C4×C22⋊D61—22no—
64#14519737—24no—
65#14519737—24no—
66#14519735—24no—
67#14519734—22no—
68#14519734—22no—
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×#11758196C2×C411yescharacteristic
71C2×#11758196C2311yescharacteristic
72C2×C22⋊Dic61C2×C411yescharacteristic
73C2×C22⋊Dic61C2×C411yescharacteristic
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198C2×C411yescharacteristic
79C2×#11758198C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2311yescharacteristic
84C2×#11758198C2311yescharacteristic
85C2×#11758198C2311yescharacteristic
86C22⋊C4×D61—24no—
87C22⋊C4×D61—24no—
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C4⋊#92418—22no—
92C22⋊#92418—22no—
93C22⋊#92418—22no—
94C22⋊#92418C2314yes—
95#14519688—22no—
96C22×D4×C61C2×C411yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C2×M16×C61—22no—
100C22×C8×C61—22no—
101C4×D4×C61D414yes—
102C4×D4×C61D414yes—
103C2×C4⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61C2×C411yescharacteristic
105C2×C22⋊C4×C61C2×C411yescharacteristic
106C2×C42×C61C2311yescharacteristic
107C4⋊C8×C61—22no—
108C22⋊C8×C61—22no—
109C22⋊C8×C61—22no—
110C22⋊C8×C61C2314yes—
111#97×C61—22no—
112C24×C61C22×C411yescharacteristic
113C24×C61C22×C411yescharacteristic
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—81no—
120C23×D61—81no—
121C23×D61—81no—
122C23×D61—81no—
123C23×D61M1614yescomplemented
124C23×D61C22×C411yescharacteristic
125C23×D61C22×C411yescharacteristic
126C23×D61C22×C411yescharacteristic
127C2×D4×C61—22no—
128C2×D4×C61—22no—
129C2×D4×C61C22⋊C414yes—
130C22×C4×C61—81no—
131C22×C4×C61—81no—
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×D412yes—
138C22×C4×C61C2×D412yes—
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2411yescharacteristic
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61M1614yescomplemented
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—81no—
150C22×Dic61—81no—
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156D4×D61—232no—
157C2×D244—22no—
158C2×D244—22no—
159C2×D244—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—81no—
168C2×C4×D61—81no—
169C2×C4×D61—81no—
170C2×C4×D61—81no—
171M16×C61—82no—
172C2×C8×C61—24no—
173C2×C8×C61—82no—
174C4⋊C4×C61C22⋊C414yes—
175C22⋊C4×C61C22⋊C414yes—
176C22⋊C4×C61C22⋊C414yes—
177C42×C61C2×D412yes—
178C42×C61C2×D412yes—
179C22⋊Dic61—22no—
180C22⋊Dic61—22no—
181#11758198—22no—
182#11758198—22no—
183#11758198—22no—
184#11758198—22no—
185#11758198—22no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61—22no—
193#11758196—22no—
194#11758196—21no—
195#11758196—21no—
196C4×Dic61—22no—
197C4×Dic61—22no—
198C4×Dic61—22no—
199#11758194—82no—
200C2×#92418—24no—
201C2×#92418—82no—
202C23×C61—21no—
203C23×C61—21no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61C2×C22⋊C412yes—
209C23×C61C2×C22⋊C412yes—
210C23×C61C2×M1612yes—
211C23×C61C2×M1612yes—
212C23×C61C23×C411yescharacteristic
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—28no—
220C22×D61—28no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61—41no—
227C22×D61—82no—
228C22×D61—82no—
229C22×D61—82no—
230C22×D61—82no—
231C22×D61—84no—
232C22×D61—84no—
233C22×D61—84no—
234C22×D61—84no—
235C22×D61C2×M1612yes—
236C22×D61C2×M1612yes—
237C22×D61C2×M1612yes—
238D4×C61—28no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61C2×C22⋊C412yes—
250C2×C4×C61C2×C22⋊C412yes—
251C2×C4×C61C2×C22⋊C412yes—
252C2×C4×C61C2×C22⋊C412yes—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C22⋊D61—28no—
256C22⋊D61—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×M1612yes—
270D244—28no—
271C4×D61—28no—
272C4×D61—82no—
273C4×D61—82no—
274C4×D61—82no—
275C4×D61—82no—
276C8×C61—44no—
277#92418—44no—
278#17367—611nomaximal, Sylow
279C22×C61—21no—
280C22×C61—22no—
281C22×C61—21no—
282C22×C61—22no—
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61#40714yes—
291C22×C61C22×C22⋊C411yescharacteristic
292C22×C61C22×M1611yescharacteristic
293C22×C61C22×M1611yescharacteristic
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—42no—
307C2×D61—42no—
308C2×D61—42no—
309C2×D61—88no—
310C2×D61—88no—
311C4×C61—22no—
312C4×C61—21no—
313C4×C61—21no—
314C4×C61—22no—
315C4×C61—22no—
316C4×C61—22no—
317Dic61—22no—
318Dic61—41no—
319Dic61—41no—
320Dic61—41no—
321Dic61—41no—
322C2×#518—611no—
323#2973—611no—
324#2973D6111yescharacteristic, complemented
325#1466—612no—
326#1465—612no—
327#1464—612no—
328#1462—612no—
329#1459—612no—
330C2×#323—612no—
331C2×C61—21no—
332C2×C61—21no—
333C2×C61—24no—
334C2×C61—42no—
335C2×C61C2×#40711yescharacteristic
336C2×C61#288311yescharacteristic
337C2×C61#288811yescharacteristic
338D61—42no—
339D61—42no—
340D61—42no—
341C23×D4—611no—
342#518—1224no—
343#518—1224no—
344C2×C4×D4—611no—
345C2×C4×D4—611no—
346C2×C4×D4—611no—
347C2×C4×D4—611no—
348C2×C4×D4—611no—
349C2×C4×D4—611no—
350C2×C4×D4—611no—
351C2×C4×D4C2×D6111yescharacteristic
352C2×#117—611no—
353C2×#117—611no—
354C22×C22⋊C4—611no—
355C22×C22⋊C4—611no—
356C22×C22⋊C4—611no—
357C22×C22⋊C4—611no—
358#435—24no—
359#435—1224no—
360#432—612no—
361#432C2×D6112yescomplemented
362#407—612no—
363#407C2×D6112yescomplemented
364C2×C22⋊C8—612no—
365C2×C22⋊C8C2×D6112yescomplemented
366#324—614no—
367#323—614no—
368#323—614no—
369#323—614no—
370C61#1736711yescharacteristic, complemented, Sylow
371C25—611no—
372C25—611no—
373C22×D4—611no—
374C22×D4—611no—
375C22×D4—611no—
376C22×D4—1224no—
377C22×D4—1224no—
378C22×D4—1224no—
379C22×D4C4×D6111yescharacteristic
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—611no—
385C23×C4—611no—
386C23×C4—611no—
387C23×C4C22×D6111yescharacteristic
388C23×C4C22×D6111yescharacteristic
389C2×M16—22no—
390C2×M16—1222no—
391C22×C8—22no—
392C22×C8—1222no—
393C4×D4—1224no—
394C4×D4—1222no—
395C4×D4—1222no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—1224no—
399C4×D4—1224no—
400C4×D4—1224no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4D24414yes—
404C4×D4C22⋊D6114yes—
405#117—1224no—
406#117—1222no—
407#117—1222no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4C4×D6111yescharacteristic
412C2×C22⋊C4—611no—
413C2×C22⋊C4—611no—
414C2×C22⋊C4—611no—
415C2×C22⋊C4—611no—
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—611no—
419C2×C22⋊C4—611no—
420C2×C22⋊C4—611no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—1222no—
423C2×C22⋊C4—1222no—
424C2×C22⋊C4—1222no—
425C2×C22⋊C4—1222no—
426C2×C22⋊C4—1224no—
427C2×C22⋊C4—1224no—
428C2×C22⋊C4C4×D6111yescharacteristic
429C2×C22⋊C4C4×D6111yescharacteristic
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42C22×D6111yescharacteristic
434C4⋊C8—22no—
435C4⋊C8—1222no—
436C22⋊C8—22no—
437C22⋊C8—22no—
438C22⋊C8—614no—
439C22⋊C8—1222no—
440C22⋊C8—1222no—
441C22⋊C8C22×D6114yes—
442#97—22no—
443#97—1222no—
444C24—614no—
445C24—611no—
446C24—611no—
447C24—611no—
448C24—1222no—
449C24—1222no—
450C24—1222no—
451C24—1222no—
452C24—1222no—
453C24—4881no—
454C24—4881no—
455C24—4881no—
456C24—4881no—
457C24C2×C4×D6111yescharacteristic
458C24C2×C4×D6111yescharacteristic
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—614no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—1222no—
465C2×D4—12232no—
466C2×D4—1222no—
467C2×D4—1222no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—1222no—
471C2×D4#1175819814yes—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
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—4881no—
489C22×C4—4881no—
490C22×C4—4881no—
491C22×C4—4881no—
492C22×C4—4881no—
493C22×C4—4881no—
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C2×C4×D6111yescharacteristic
496C22×C4C2×C4×D6111yescharacteristic
497C22×C4C2×C4×D6111yescharacteristic
498C22×C4C2×D24412yes—
499C22×C4C2×D24412yes—
500C22×C4C2×C22⋊D6112yes—
501C22×C4C2×C22⋊D6112yes—
502C22×C4C23×D6111yescharacteristic
503M16—82no—
504M16—4882no—
505C2×C8—24no—
506C2×C8—82no—
507C2×C8—1224no—
508C2×C8—4882no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4#1175819814yes—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C22⋊C4—1221no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C22⋊C4—1221no—
521C22⋊C4—1221no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4#1175819814yes—
528C22⋊C4#1175819814yes—
529C42—1222no—
530C42—1222no—
531C42—1222no—
532C42C2×D24412yes—
533C42C2×C22⋊D6112yes—
534C23—21no—
535C23—21no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—612no—
541C23—612no—
542C23—612no—
543C23—1228no—
544C23—1228no—
545C23—1221no—
546C23—1221no—
547C23—1221no—
548C23—1221no—
549C23—1221no—
550C23—1221no—
551C23—4882no—
552C23—4882no—
553C23—4882no—
554C23—4882no—
555C23—4884no—
556C23—4884no—
557C23—4884no—
558C23—4884no—
559C23—2441no—
560C23—2441no—
561C23—2441no—
562C23—2441no—
563C23—2441no—
564C23—2441no—
565C23C2×#1175819812yes—
566C23C2×#1175819812yes—
567C23M16×D6112yes—
568C23M16×D6112yes—
569C23C22×C4×D6111yescharacteristic
570D4—28no—
571D4—1228no—
572D4—1228no—
573D4—1228no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—612no—
585C2×C4—1228no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—4882no—
593C2×C4—4882no—
594C2×C4—4882no—
595C2×C4—4882no—
596C2×C4—4882no—
597C2×C4—4882no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4C2×#1175819812yes—
603C2×C4C2×#1175819812yes—
604C2×C4C2×#1175819812yes—
605C2×C4C2×#1175819812yes—
606C2×C4C22×C22⋊D6111yescharacteristic
607C2×C4C22×D24411yescharacteristic
608C8—44no—
609C8—2444no—
610C22—21no—
611C22—22no—
612C22—21no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—1222no—
622C22—1222no—
623C22—1222no—
624C22—4888no—
625C22—4888no—
626C22—2442no—
627C22—2442no—
628C22—2442no—
629C22—2442no—
630C22—2442no—
631C22—2442no—
632C22—2441no—
633C22—2441no—
634C22—2441no—
635C22—2441no—
636C22—2441no—
637C22—2441no—
638C22#1683972514yes—
639C22C22×#1175819811yescharacteristic
640C22C2×M16×D6111yescharacteristic
641C22C2×M16×D6111yescharacteristic
642C4—22no—
643C4—21no—
644C4—21no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—1222no—
649C4—2441no—
650C4—2441no—
651C4—2441no—
652C4—2441no—
653C2—21no—
654C2—21no—
655C2—24no—
656C2—42no—
657C2—2442no—
658C2—2442no—
659C2—2442no—
660C2C2×#1683972511yescharacteristic
661C2#2145427911yescharacteristic
662C2#2145429711yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2973C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC22×C4×C61C24
hypercenter#2973D61
hypocenterC61#17367
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #21454848C2semidirect
3. #21444159C2semidirect
4. #21444155C2semidirect
5. #21444151C2semidirect
6. #21444145C2semidirect
7. #21444135C2semidirect
8. C2×#16839485C2semidirect
9. C61×#2973C2semidirect
27. #16839819C22semidirect
28. #16839726C22semidirect
29. C2×C22⋊#92418C22semidirect
30. #16839487C22semidirect
32. #16839485C22semidirect
33. #16839485C22semidirect
36. C61×#432C22semidirect
37. C61×#407C22semidirect
38. C2×C22⋊C8×C61C22semidirect
123. C23×D61M16semidirect
146. C2×C22⋊D61M16semidirect
324. #2973D61semidirect
361. #432C2×D61semidirect
363. #407C2×D61semidirect
365. C2×C22⋊C8C2×D61semidirect
370. C61#17367semidirect

Maximal subgroups

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

subgroupindex
C2×#168402342
#214548482
#214441592
#214441552
#214441512
#214441452
#214441352
C2×#168394852
C61×#29732
#1736761