Finite Group Databasebeta

← #29679957

Subgroups — #29679957

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840234C211yesmaximal, characteristic
2#21448414C212yesmaximal, complemented
3#21445892C212yesmaximal, complemented
4#21445806C212yesmaximal, complemented
5#21445805C212yesmaximal, complemented
6#21445732C212yesmaximal
7C4×#14519691C212yesmaximal, complemented
8C4×#14519692C211yesmaximal, characteristic, complemented
9C4×#99×C61C211yesmaximal, characteristic, complemented
10C22×D4×D61C2211yescharacteristic
11#16840234—24no—
12#16840234—24no—
13C2×C4×D244C411yescharacteristic, complemented
14C2×D4×Dic61C2211yescharacteristic
15C2×#14519739C411yescharacteristic, complemented
16C2×C4×C22⋊D61C411yescharacteristic, complemented
17C2×C4×C22⋊D61C2211yescharacteristic
18C2×#14519737C411yescharacteristic, complemented
19C2×#14519737C2211yescharacteristic
20C2×#14519735C411yescharacteristic, complemented
21C2×#14519734C411yescharacteristic, complemented
22C22×#11758198C411yescharacteristic, complemented
23C22×#11758198C2211yescharacteristic
24C2×C22⋊C4×D61C411yescharacteristic, complemented
25C2×C22⋊C4×D61C2211yescharacteristic
26C2×#14519692C2212yes—
27C2×#14519691C2214yes—
28#16839653—24no—
29#16839651—24no—
30#16839620C2214yescomplemented
31#16839617C2214yes—
32C4×C22⋊Dic61C2212yescomplemented
33#16839529C2212yescomplemented
34#16839528C2214yescomplemented
35C2×C4×D4×C61C2211yescharacteristic
36C2×#99×C61C2212yes—
37C4×C22⋊C4×C61C2212yescomplemented
38C61×#342C2212yescomplemented
39C24×D61C2×C411yescharacteristic
40C24×D61C2311yescharacteristic
41C22×D244C2×C411yescharacteristic
42C22×C22⋊D61C2×C411yescharacteristic
43C22×C22⋊D61C2311yescharacteristic
44C2×D4×D61—24no—
45C2×D4×D61—24no—
46C2×D4×D61—24no—
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2311yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C4×D244—22no—
55C4×D244—22no—
56D4×Dic61—24no—
57#14519739—24no—
58C4×C22⋊D61—22no—
59C4×C22⋊D61—22no—
60C4×C22⋊D61—22no—
61C4×C22⋊D61—22no—
62#14519737—24no—
63#14519737—24no—
64#14519735—24no—
65#14519734—22no—
66#14519734—22no—
67C2×C4⋊Dic61C2×C411yescharacteristic
68C2×#11758196—24no—
69C2×#11758196C2×C411yescharacteristic
70C2×#11758196C2×C411yescharacteristic
71C2×C22⋊Dic61C2×C411yescharacteristic
72C2×C22⋊Dic61C2314yes—
73C2×C22⋊Dic61C2311yescharacteristic
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—24no—
77C2×#11758198—24no—
78C2×#11758198C2×C411yescharacteristic
79C2×#11758198C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×#11758198D414yes—
87C2×#11758198D414yes—
88C22⋊C4×D61—24no—
89C22⋊C4×D61—24no—
90C2×C4×Dic61—22no—
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94#14519692—24no—
95#14519691—28no—
96#14519684—22no—
97#14519684—24no—
98C22×D4×C61C2311yescharacteristic
99C23×C4×C61C2×C411yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103C2×C4⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61C2×C411yescharacteristic
105C2×C22⋊C4×C61C2314yes—
106C2×C22⋊C4×C61C2311yescharacteristic
107C2×C42×C61—22no—
108C2×C42×C61C2×C411yescharacteristic
109#99×C61—24no—
110#95×C61—22no—
111C24×C61C22×C411yescharacteristic
112C24×C61C2411yescharacteristic
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—81no—
119C23×D61—81no—
120C23×D61—81no—
121C23×D61—81no—
122C23×D61C22×C411yescharacteristic
123C23×D61C22×C411yescharacteristic
124C23×D61C22×C411yescharacteristic
125C23×D61C2×D414yes—
126C2×D4×C61—22no—
127C2×D4×C61—22no—
128C2×D4×C61#4114yes—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—24no—
132C22×C4×C61—81no—
133C22×C4×C61—81no—
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2×D412yes—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61#4114yes—
147C22×Dic61—22no—
148C22×Dic61—24no—
149C22×Dic61—81no—
150C22×Dic61—81no—
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C2×D414yes—
157D4×D61—232no—
158C2×D244—22no—
159C2×D244—22no—
160C2×D244—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—22no—
168C2×C4×D61—81no—
169C2×C4×D61—81no—
170C2×C4×D61—81no—
171C2×C4×D61—81no—
172C4⋊C4×C61—22no—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—24no—
176C22⋊C4×C61—24no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—82no—
180C22⋊Dic61—22no—
181C22⋊Dic61—22no—
182C22⋊Dic61—24no—
183C22⋊Dic61—24no—
184#11758198—22no—
185#11758198—22no—
186#11758198—21no—
187#11758198—21no—
188#11758198—22no—
189#11758198—84no—
190#11758198—84no—
191#11758198C22⋊C414yes—
192#11758198C22⋊C412yes—
193#11758198C22⋊C412yes—
194#11758198C22⋊C414yes—
195#11758198C22⋊C412yes—
196#11758198C22⋊C412yes—
197C4⋊Dic61—22no—
198#11758196—21no—
199#11758196—21no—
200#11758196—22no—
201#11758196—84no—
202C4×Dic61—22no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61—82no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61#11712yes—
213C23×C61C23×C411yescharacteristic
214C23×C61C22×D412yes—
215C23×C61C2×#4112yes—
216C23×C61C2×#4112yes—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—28no—
224C22×D61—28no—
225C22×D61—41no—
226C22×D61—41no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—44no—
230C22×D61—44no—
231C22×D61—41no—
232C22×D61—41no—
233C22×D61—82no—
234C22×D61—82no—
235C22×D61—84no—
236C22×D61—84no—
237C22×D61—84no—
238C22×D61—84no—
239C22×D61C2×C22⋊C412yes—
240C22×D61C2×C22⋊C412yes—
241C22×D61#11712yes—
242D4×C61—28no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—44no—
254C2×C4×C61—44no—
255C2×C4×C61—44no—
256C2×C4×C61—81no—
257C2×C4×C61—81no—
258C2×C4×C61C2×C22⋊C412yes—
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61#11712yes—
262C22⋊D61—28no—
263C22⋊D61—28no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—44no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—44no—
274C2×Dic61—44no—
275C2×Dic61—44no—
276C2×Dic61—82no—
277C2×Dic61C2×C22⋊C412yes—
278C2×Dic61C2×C22⋊C412yes—
279C2×Dic61#11712yes—
280D244—28no—
281C4×D61—28no—
282C4×D61—82no—
283C4×D61—82no—
284C4×D61—82no—
285C4×D61—82no—
286#20724—611nomaximal, Sylow
287C22×C61—22no—
288C22×C61—21no—
289C22×C61—22no—
290C22×C61—21no—
291C22×C61—22no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61C22×C22⋊C411yescharacteristic
299C22×C61C2×#11711yescharacteristic
300C22×C61C2×#11711yescharacteristic
301C22×C61#52514yes—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—22no—
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—22no—
309C2×D61—42no—
310C2×D61—42no—
311C2×D61—42no—
312C2×D61—42no—
313C2×D61—42no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—42no—
317C2×D61—88no—
318C2×D61—88no—
319C4×C61—22no—
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—22no—
323C4×C61—41no—
324C4×C61—41no—
325C4×C61—84no—
326Dic61—22no—
327Dic61—22no—
328Dic61—22no—
329Dic61—41no—
330Dic61—41no—
331Dic61—84no—
332C2×#518—611no—
333#2312—612no—
334#1819—612no—
335#1799—612no—
336#1799—612no—
337#1781—612no—
338C4×#99—612no—
339C4×#99—611no—
340C4×#99D6111yescharacteristic, complemented
341C2×C61—24no—
342C2×C61—21no—
343C2×C61—21no—
344C2×C61—42no—
345C2×C61#228011yescharacteristic
346C2×C61#288311yescharacteristic
347C2×C61#288311yescharacteristic
348D61—42no—
349D61—42no—
350D61—42no—
351C23×D4—611no—
352#518—1224no—
353#518—1224no—
354C2×C4×D4—611no—
355C2×C4×D4—611no—
356C2×C4×D4—611no—
357C2×C4×D4—611no—
358C2×C4×D4—611no—
359C2×C4×D4—611no—
360C2×C4×D4—611no—
361C2×C4×D4C2×D6111yescharacteristic
362C2×#117—611no—
363C2×#117—611no—
364C22×C22⋊C4—611no—
365C22×C22⋊C4—611no—
366C22×C22⋊C4—611no—
367C22×C22⋊C4—611no—
368C2×#99—612no—
369C2×#99—614no—
370C2×#99C2×D6112yes—
371#388—1224no—
372#388—1224no—
373#380—614no—
374#379—614no—
375C4×C22⋊C4—612no—
376C4×C22⋊C4C2×D6112yescomplemented
377#342—614no—
378#342—612no—
379#342C2×D6112yescomplemented
380C61#2072411yescharacteristic, complemented, Sylow
381C25—611no—
382C25—611no—
383C22×D4—611no—
384C22×D4—611no—
385C22×D4—611no—
386C22×D4—1224no—
387C22×D4—1224no—
388C22×D4—1224no—
389C22×D4C22×D6111yescharacteristic
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4C4×D6111yescharacteristic
398C23×C4C22×D6111yescharacteristic
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4—1224no—
404C4×D4—1224no—
405C4×D4—1224no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1224no—
409C4×D4—1222no—
410C4×D4—1222no—
411#117—1222no—
412#117—1222no—
413#117—1224no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—1224no—
418C2×C4⋊C4C4×D6111yescharacteristic
419C2×C22⋊C4—611no—
420C2×C22⋊C4—611no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—611no—
423C2×C22⋊C4—614no—
424C2×C22⋊C4—614no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—614no—
432C2×C22⋊C4—1224no—
433C2×C22⋊C4—1224no—
434C2×C22⋊C4—1222no—
435C2×C22⋊C4—1222no—
436C2×C22⋊C4—1224no—
437C2×C22⋊C4—1224no—
438C2×C22⋊C4C4×D6111yescharacteristic
439C2×C22⋊C4C22×D6114yes—
440C2×C22⋊C4C22×D6111yescharacteristic
441C2×C42—22no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—1222no—
446C2×C42C4×D6111yescharacteristic
447#99—24no—
448#99—1228no—
449#99—1224no—
450#95—22no—
451#95—1224no—
452#95—1222no—
453C24—611no—
454C24—611no—
455C24—611no—
456C24—614no—
457C24—1222no—
458C24—1222no—
459C24—1222no—
460C24—1222no—
461C24—1222no—
462C24—4881no—
463C24—4881no—
464C24—4881no—
465C24—4881no—
466C24C2×C4×D6111yescharacteristic
467C24C23×D6111yescharacteristic
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—614no—
471C2×D4—1222no—
472C2×D4—1222no—
473C2×D4—1222no—
474C2×D4—12232no—
475C2×D4—1222no—
476C2×D4—1222no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4#1175822214yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—614no—
490C22×C4—611no—
491C22×C4—611no—
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—1224no—
501C22×C4—4881no—
502C22×C4—4881no—
503C22×C4—4881no—
504C22×C4—4881no—
505C22×C4—4881no—
506C22×C4—4881no—
507C22×C4C2×C4×D6111yescharacteristic
508C22×C4C2×C4×D6111yescharacteristic
509C22×C4C2×C4×D6111yescharacteristic
510C22×C4C2×C4×D6111yescharacteristic
511C22×C4C2×C4×D6111yescharacteristic
512C22×C4D4×D6112yes—
513C22×C4D4×D6112yes—
514C4⋊C4—22no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—4884no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—612no—
525C22⋊C4—612no—
526C22⋊C4—614no—
527C22⋊C4—612no—
528C22⋊C4—612no—
529C22⋊C4—614no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1221no—
536C22⋊C4—1221no—
537C22⋊C4—1224no—
538C22⋊C4—1224no—
539C22⋊C4—4884no—
540C22⋊C4—4884no—
541C42—21no—
542C42—21no—
543C42—82no—
544C42—1222no—
545C42—1222no—
546C42—1222no—
547C42—4882no—
548C23—21no—
549C23—21no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—612no—
555C23—612no—
556C23—612no—
557C23—1228no—
558C23—1228no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23—1221no—
564C23—1221no—
565C23—4882no—
566C23—4882no—
567C23—4884no—
568C23—4884no—
569C23—4884no—
570C23—4884no—
571C23—2444no—
572C23—2444no—
573C23—2441no—
574C23—2441no—
575C23—2441no—
576C23—2441no—
577C23—2441no—
578C23—2441no—
579C23#1451973412yes—
580C23C22×C4×D6111yescharacteristic
581C23C2×D4×D6112yes—
582C23#41×D6112yes—
583C23C2×#1175822212yes—
584D4—28no—
585D4—1228no—
586D4—1228no—
587D4—1228no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—612no—
604C2×C4—612no—
605C2×C4—612no—
606C2×C4—1228no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—4882no—
612C2×C4—4882no—
613C2×C4—4882no—
614C2×C4—4882no—
615C2×C4—4882no—
616C2×C4—2444no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2444no—
620C2×C4—2444no—
621C2×C4—2444no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4C22⋊C4×D6111yescharacteristic
625C2×C4C22⋊C4×D6111yescharacteristic
626C2×C4C22⋊C4×D6112yes—
627C2×C4#1451973412yes—
628C22—22no—
629C22—21no—
630C22—22no—
631C22—21no—
632C22—22no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—41no—
638C22—41no—
639C22—1222no—
640C22—1222no—
641C22—1222no—
642C22—1222no—
643C22—1222no—
644C22—1222no—
645C22—1222no—
646C22—4888no—
647C22—4888no—
648C22—2442no—
649C22—2442no—
650C22—2442no—
651C22—2442no—
652C22—2442no—
653C22—2442no—
654C22—2441no—
655C22—2441no—
656C22C2×C22⋊C4×D6111yescharacteristic
657C22#117×D6111yescharacteristic
658C22C2×#1451973411yescharacteristic
659C22#1684027114yes—
660C4—22no—
661C4—21no—
662C4—21no—
663C4—22no—
664C4—41no—
665C4—41no—
666C4—84no—
667C4—1222no—
668C4—1222no—
669C4—1222no—
670C4—4884no—
671C4—2441no—
672C4—2441no—
673C2—24no—
674C2—21no—
675C2—21no—
676C2—42no—
677C2—2442no—
678C2—2442no—
679C2—2442no—
680C2#2144820011yescharacteristic
681C2#2145427711yescharacteristic
682C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC24×C61C24
hypercenterC4×#99D61
hypocenterC61#20724
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21448414C2semidirect
3. #21445892C2semidirect
4. #21445806C2semidirect
5. #21445805C2semidirect
7. C4×#14519691C2semidirect
8. C4×#14519692C2semidirect
9. C4×#99×C61C2semidirect
13. C2×C4×D244C4semidirect
15. C2×#14519739C4semidirect
16. C2×C4×C22⋊D61C4semidirect
18. C2×#14519737C4semidirect
20. C2×#14519735C4semidirect
21. C2×#14519734C4semidirect
22. C22×#11758198C4semidirect
24. C2×C22⋊C4×D61C4semidirect
30. #16839620C22semidirect
32. C4×C22⋊Dic61C22semidirect
33. #16839529C22semidirect
34. #16839528C22semidirect
37. C4×C22⋊C4×C61C22semidirect
38. C61×#342C22semidirect
340. C4×#99D61semidirect
376. C4×C22⋊C4C2×D61semidirect
379. #342C2×D61semidirect
380. C61#20724semidirect

Maximal subgroups

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

subgroupindex
C2×#168402342
#214484142
#214458922
#214458062
#214458052
#214457322
C4×#145196912
C4×#145196922
C4×#99×C612
#2072461