Finite Group Databasebeta

← #30616751

Subgroups — #30616751

Order 15616.

1318 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462295C211yesmaximal, characteristic, complemented
2#21462255C211yesmaximal, characteristic, complemented
3#21462009C212yesmaximal, complemented
4#21461960C212yesmaximal, complemented
5#21461841C212yesmaximal, complemented
6#21461840C212yesmaximal, complemented
7#21461564C212yesmaximal, complemented
8C4×#14519835C212yesmaximal, complemented
9C2×#16840348C211yesmaximal, characteristic
10C22×C22⋊#6923C2212yes—
11C2×#14519836C2214yes—
12C2×#14519835C2214yes—
13#16840712—24no—
14#16840704C2212yes—
15#16840703C2212yes—
16C22⋊C4×#6923—24no—
17C4×C22⋊#6923C2212yes—
18C4×C22⋊#6923C2212yes—
19C4×C22⋊#6923C2212yes—
20#16840640C2214yes—
21#16840640C2214yes—
22#16840348—24no—
23#16840348—24no—
24C2×#14519772C411yescharacteristic, complemented
25C2×#14519770C411yescharacteristic, complemented
26C2×#14519763C411yescharacteristic, complemented
27C2×#14519763C411yescharacteristic, complemented
28C2×#14519762C411yescharacteristic, complemented
29C2×#14519757C2211yescharacteristic
30C2×#14519751C411yescharacteristic, complemented
31C2×#14519750C2211yescharacteristic
32C2×#14519748C411yescharacteristic, complemented
33C2×#14519747C2211yescharacteristic
34C2×#14519745C2211yescharacteristic
35C2×#14519739C2211yescharacteristic
36C2×C4×C22⋊D61C2211yescharacteristic
37C2×C22⋊C4×D61C2211yescharacteristic
38C2×#123×C61C411yescharacteristic, complemented
39C23×#6923—22no—
40C2×C4⋊#6923—22no—
41C2×C22⋊#6923—22no—
42C2×C22⋊#6923—28no—
43C2×C22⋊#6923—22no—
44C2×C22⋊#6923—22no—
45C2×C22⋊#6923C2314yes—
46C2×C22⋊#6923C2314yes—
47C2×C4×#6923—22no—
48C2×C4×#6923—22no—
49C2×C4×#6923—22no—
50#14519836—28no—
51#14519835—28no—
52(C2×#6923)⋊C4—22no—
53(C2×#6923)⋊C4—22no—
54(C2×#6923)⋊C4—22no—
55(C2×#6923)⋊C4—22no—
56C24×D61C2311yescharacteristic
57C22×Dic122C2×C411yescharacteristic, complemented
58C22×D244C2×C411yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic, complemented
63C22×C22⋊D61C2311yescharacteristic
64C22×C4×D61C2×C411yescharacteristic, complemented
65C22×C4×D61C2311yescharacteristic
66C22×C4×D61C2311yescharacteristic
67#14519772—24no—
68#14519770—24no—
69#14519763—24no—
70#14519763—24no—
71#14519762—24no—
72#14519757—22no—
73#14519757—22no—
74#14519751—24no—
75#14519750—22no—
76#14519750—22no—
77#14519748—24no—
78#14519747—22no—
79#14519747—22no—
80#14519745—22no—
81#14519745—22no—
82#14519739—22no—
83#14519739—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C2×C4⋊Dic61C2×C411yescharacteristic, complemented
87C2×C4⋊Dic61C2×C411yescharacteristic, complemented
88C2×#11758196C2×C411yescharacteristic, complemented
89C2×#11758196C2×C411yescharacteristic, complemented
90C2×C22⋊Dic61C2×C411yescharacteristic
91C2×C22⋊Dic61C2×C411yescharacteristic
92C2×C22⋊Dic61C2×C411yescharacteristic, complemented
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic, complemented
98C2×#11758198C2×C411yescharacteristic, complemented
99C2×#11758198C2311yescharacteristic
100C2×#11758198C2311yescharacteristic
101C22⋊C4×D61D414yes—
102C22⋊C4×D61D414yes—
103C2×C4×Dic61C2×C411yescharacteristic, complemented
104C2×C4×Dic61C2×C411yescharacteristic, complemented
105C22×D4×C61C2×C411yescharacteristic
106C23×C4×C61C2×C411yescharacteristic, complemented
107#123×C61—24no—
108C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
109C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
110C2×C22⋊C4×C61C2×C411yescharacteristic
111C2×C22⋊C4×C61C2×C411yescharacteristic
112C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
113C24×C61C22×C411yescharacteristic
114C24×C61C22×C411yescharacteristic
115C23×D61—24no—
116C23×D61—81no—
117C23×D61—81no—
118C23×D61C22×C411yescharacteristic
119C23×D61C22×C411yescharacteristic
120C23×D61C2×D412yes—
121C23×D61C2×D412yes—
122C23×D61C2411yescharacteristic
123C22×#6923—24no—
124C22×#6923—28no—
125C22×#6923—24no—
126C22×#6923—82no—
127C22×#6923—82no—
128C2×D4×C61—22no—
129C2×D4×C61—81no—
130C22×C4×C61—22no—
131C22×C4×C61—81no—
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C2×C22⋊D61—21no—
138C2×C22⋊D61—21no—
139C2×C22⋊D61—24no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—81no—
144C2×C22⋊D61—81no—
145C2×C22⋊D61—81no—
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—24no—
154C2×D244—22no—
155C2×D244—81no—
156C2×C4×D61—22no—
157C2×C4×D61—81no—
158C2×C4×D61—81no—
159C2×C4×D61—81no—
160C2×C4×D61C2×D412yes—
161C2×C4×D61C2×D412yes—
162C2×C4×D61C2×D412yes—
163C2×C4×D61C2×D412yes—
164C2×Dic122—22no—
165C2×Dic122—81no—
166C22⋊#6923—28no—
167C22⋊#6923—24no—
168C22⋊#6923—24no—
169C22⋊#6923—24no—
170C22⋊#6923—82no—
171C22⋊#6923—82no—
172C22⋊#6923#4118yes—
173C4⋊#6923—82no—
174C4×#6923—82no—
175C4×#6923—82no—
176C4×#6923—82no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—22no—
179C22⋊C4×C61—22no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61C22⋊C414yes—
182C22⋊Dic61—22no—
183C22⋊Dic61—22no—
184C22⋊Dic61C22⋊C414yes—
185#11758198—22no—
186#11758198—22no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—22no—
192#11758198—22no—
193#11758198C22⋊C414yes—
194#11758198C22⋊C414yes—
195C4⋊Dic61—22no—
196C4⋊Dic61—22no—
197#11758196—22no—
198#11758196—22no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C23×C61—22no—
202C23×C61—21no—
203C23×C61—22no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61C2×C22⋊C412yes—
209C23×C61C23×C411yescharacteristic
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—24no—
214C22×D61—21no—
215C22×D61—22no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61—88no—
227C22×D61C2×C22⋊C412yes—
228C22×D61C22×D411yescharacteristic
229C22×D61C22×D411yescharacteristic
230C22×D61C2×#4114yes—
231C2×#6923—28no—
232C2×#6923—44no—
233C2×#6923—44no—
234C2×#6923—44no—
235C2×#6923—44no—
236C2×#6923—44no—
237C2×#6923—88no—
238D4×C61—82no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—22no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—82no—
248C2×C4×C61C2×C22⋊C412yes—
249C2×C4×C61C2×C22⋊C412yes—
250C22⋊D61—42no—
251C22⋊D61—42no—
252C22⋊D61—82no—
253C22⋊D61—82no—
254C22⋊D61—82no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—22no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61C2×C22⋊C412yes—
264C2×Dic61C2×C22⋊C412yes—
265D244—42no—
266D244—42no—
267D244—82no—
268C4×D61—42no—
269C4×D61—42no—
270C4×D61—42no—
271C4×D61—42no—
272C4×D61—82no—
273Dic122—82no—
274#21422—611nomaximal, Sylow
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—82no—
284C22×C61—82no—
285C22×C61C22×C22⋊C411yescharacteristic
286C22×C61C4×#4112yes—
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—21no—
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—44no—
295C2×D61—44no—
296C2×D61—44no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—84no—
301C2×D61—82no—
302C2×D61—82no—
303C2×D61#52512yes—
304C2×D61#53212yes—
305#6923—48no—
306#6923—84no—
307C4×C61—22no—
308C4×C61—22no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312Dic61—22no—
313Dic61—22no—
314Dic61—41no—
315Dic61—41no—
316Dic61—41no—
317C2×#538—611no—
318#2312—611no—
319#2273—611no—
320#1996—612no—
321#1964—612no—
322#1898—612no—
323#1898—612no—
324C4×#99—612no—
325C4×#99—612no—
326C2×C61—22no—
327C2×C61—42no—
328C2×C61—81no—
329C2×C61#229711yescharacteristic
330C2×C61#288311yescharacteristic
331C2×C61#288311yescharacteristic
332D61—22no—
333D61—22no—
334D61—42no—
335D61—81no—
336#538—1224no—
337#538—1224no—
338C2×#126—611no—
339C2×#126—611no—
340C2×#124—611no—
341C2×#124—611no—
342C2×#123—611no—
343C2×#123#692311yescharacteristic, complemented
344C2×C22⋊Q8—611no—
345C2×#121—611no—
346C2×#121—611no—
347C2×#121—611no—
348C2×#120—611no—
349C2×#120—611no—
350C2×C4×D4—611no—
351C2×C4×D4—611no—
352C22×C22⋊C4—611no—
353C22×C22⋊C4—612no—
354C2×#99—614no—
355C2×#99—614no—
356#388—1224no—
357#380—612no—
358#379—612no—
359C4×C22⋊C4—612no—
360C4×C22⋊C4—612no—
361C4×C22⋊C4—612no—
362C4×C22⋊C4—1224no—
363#342—614no—
364#342—614no—
365C61#2142211yescharacteristic, complemented, Sylow
366C25—611no—
367C22×Q8—611no—
368C22×D4—611no—
369C22×D4—611no—
370C22×D4—611no—
371C22×D4—611no—
372C22×D4—611no—
373C22×D4—611no—
374C22×D4C2×#692311yescharacteristic
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—1222no—
379C23×C4C2×#692311yescharacteristic, complemented
380#126—1224no—
381#126—1224no—
382#124—1224no—
383#124—1224no—
384#123—24no—
385#123—1224no—
386C22⋊Q8—1222no—
387C22⋊Q8—1222no—
388#121—1222no—
389#121—1222no—
390#121—1224no—
391#121—1224no—
392#120—1222no—
393#120—1222no—
394#120—1222no—
395#120—1222no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—1222no—
399C4×D4—1222no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4C2×#692311yescharacteristic, complemented
406C2×C4⋊C4C2×#692311yescharacteristic, complemented
407C2×C22⋊C4—611no—
408C2×C22⋊C4—611no—
409C2×C22⋊C4—611no—
410C2×C22⋊C4—614no—
411C2×C22⋊C4—614no—
412C2×C22⋊C4—614no—
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—614no—
422C2×C22⋊C4—1228no—
423C2×C22⋊C4—1222no—
424C2×C22⋊C4—1222no—
425C2×C22⋊C4—1222no—
426C2×C22⋊C4C2×#692311yescharacteristic
427C2×C22⋊C4C2×#692311yescharacteristic
428C2×C22⋊C4C2×#692311yescharacteristic, complemented
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—1222no—
432C2×C42—1222no—
433C2×C42—1222no—
434#99—1228no—
435#99—1228no—
436#95—1222no—
437#95—1222no—
438#95—1222no—
439#95—1222no—
440C24—611no—
441C24—612no—
442C24—612no—
443C24—611no—
444C24—611no—
445C24—1224no—
446C24—4881no—
447C24—4881no—
448C24C22×#692311yescharacteristic
449C24C22×#692311yescharacteristic
450C2×Q8—1222no—
451C2×Q8—4881no—
452C2×D4—22no—
453C2×D4—81no—
454C2×D4—1222no—
455C2×D4—1224no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—1224no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4—4881no—
465C2×D4—4881no—
466C2×D4—4881no—
467C2×D4—4881no—
468C22×C4—22no—
469C22×C4—81no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—612no—
473C22×C4—612no—
474C22×C4—612no—
475C22×C4—612no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—1222no—
480C22×C4—1228no—
481C22×C4—1224no—
482C22×C4—1224no—
483C22×C4—4881no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4—4882no—
487C22×C4—4882no—
488C22×C4C22×#692311yescharacteristic
489C22×C4C22×#692311yescharacteristic
490C22×C4C22×#692311yescharacteristic
491C22×C4C22×#692311yescharacteristic
492C22×C4C22×#692311yescharacteristic
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—4882no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—614no—
503C22⋊C4—614no—
504C22⋊C4—614no—
505C22⋊C4—618no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—1222no—
513C22⋊C4—1224no—
514C22⋊C4—1228no—
515C22⋊C4—1222no—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C22⋊C4—1224no—
519C22⋊C4—1224no—
520C22⋊C4—4882no—
521C22⋊C4—4882no—
522C22⋊C4C22⋊#692314yes—
523C42—1222no—
524C42—1222no—
525C42—4882no—
526C42—4882no—
527C42—4882no—
528C23—22no—
529C23—21no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—611no—
536C23—611no—
537C23—614no—
538C23—612no—
539C23—1224no—
540C23—1222no—
541C23—1222no—
542C23—1222no—
543C23—1222no—
544C23—1221no—
545C23—4888no—
546C23—2442no—
547C23—2442no—
548C23—2441no—
549C23—2441no—
550C23—2441no—
551C23—2441no—
552C23—2442no—
553C23—2442no—
554C23—2441no—
555C23—2441no—
556C23C2×C22⋊#692312yes—
557C23C23×#692311yescharacteristic
558Q8—4882no—
559D4—82no—
560D4—4882no—
561D4—4882no—
562D4—4882no—
563D4—4882no—
564D4—2442no—
565D4—2442no—
566D4—2442no—
567D4—2442no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—1228no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1222no—
584C2×C4—4882no—
585C2×C4—4888no—
586C2×C4—2442no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2444no—
593C2×C4—2444no—
594C2×C4—2444no—
595C2×C4—2444no—
596C2×C4—2444no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4C2×C22⋊#692312yes—
600C2×C4C2×C22⋊#692312yes—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—82no—
610C22—82no—
611C22—612no—
612C22—612no—
613C22—1221no—
614C22—1221no—
615C22—1221no—
616C22—1221no—
617C22—1222no—
618C22—1222no—
619C22—1222no—
620C22—4882no—
621C22—4882no—
622C22—4884no—
623C22—2444no—
624C22—2444no—
625C22—2444no—
626C22—2441no—
627C22—2441no—
628C22—2441no—
629C22C22×C22⋊#692311yescharacteristic
630C22#41×#692312yes—
631C4—22no—
632C4—22no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—1222no—
637C4—1222no—
638C4—4884no—
639C4—2448no—
640C4—2441no—
641C4—2441no—
642C4—2441no—
643C2—22no—
644C2—42no—
645C2—81no—
646C2—1222no—
647C2—1222no—
648C2—4881no—
649C2—2442no—
650C2#2146228011yescharacteristic
651C2#2146241811yescharacteristic
652C2#2146241911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840348C2
cosocleC23×D61C24
hypercenterC2×#123#6923
hypocenterC61#21422
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462295C2semidirect
2. #21462255C2semidirect
3. #21462009C2semidirect
4. #21461960C2semidirect
5. #21461841C2semidirect
6. #21461840C2semidirect
7. #21461564C2semidirect
8. C4×#14519835C2semidirect
24. C2×#14519772C4semidirect
25. C2×#14519770C4semidirect
26. C2×#14519763C4semidirect
27. C2×#14519763C4semidirect
28. C2×#14519762C4semidirect
30. C2×#14519751C4semidirect
32. C2×#14519748C4semidirect
38. C2×#123×C61C4semidirect
57. C22×Dic122C2×C4semidirect
62. C22×C22⋊D61C2×C4semidirect
64. C22×C4×D61C2×C4semidirect
86. C2×C4⋊Dic61C2×C4semidirect
87. C2×C4⋊Dic61C2×C4semidirect
88. C2×#11758196C2×C4semidirect
89. C2×#11758196C2×C4semidirect
92. C2×C22⋊Dic61C2×C4semidirect
97. C2×#11758198C2×C4semidirect
98. C2×#11758198C2×C4semidirect
103. C2×C4×Dic61C2×C4semidirect
104. C2×C4×Dic61C2×C4semidirect
106. C23×C4×C61C2×C4semidirect
108. C2×C4⋊C4×C61C2×C4semidirect
109. C2×C4⋊C4×C61C2×C4semidirect
112. C2×C22⋊C4×C61C2×C4semidirect
343. C2×#123#6923semidirect
365. C61#21422semidirect
379. C23×C4C2×#6923semidirect
405. C2×C4⋊C4C2×#6923semidirect
406. C2×C4⋊C4C2×#6923semidirect
428. C2×C22⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214622952
#214622552
#214620092
#214619602
#214618412
#214618402
#214615642
C4×#145198352
C2×#168403482
#2142261