Finite Group Databasebeta

← #29680016

Subgroups — #29680016

Order 15616.

1758 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2C2×#16839813C211yesmaximal, characteristic, complemented
3#21448215C211yesmaximal, characteristic, complemented
4#21445908C212yesmaximal, complemented
5#21445828C212yesmaximal, complemented
6#21445827C212yesmaximal, complemented
7#21445748C212yesmaximal
8C4×#14519697C211yesmaximal, characteristic, complemented
9C4×#14519699C211yesmaximal, characteristic, complemented
10C4×#14519698C211yesmaximal, characteristic, complemented
11C4×#102×C61C211yesmaximal, characteristic, complemented
12C22×D4×D61C2211yescharacteristic
13C23×C4×D61—21no—
14C2×C4×D244C2211yescharacteristic
15C2×D4×Dic61C2211yescharacteristic
16C2×#14519739C2211yescharacteristic
17C2×C4×C22⋊D61—21no—
18C2×#14519737—21no—
19C4×D4×D61—24no—
20C4×D4×D61C418yescomplemented
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23C2×C42×D61C2211yescharacteristic
24#16839813—24no—
25C2×#14519706C2212yescomplemented
26C2×#14519699C2212yes—
27C2×#14519698C2212yes—
28C2×#14519697C2212yes—
29C2×#14519689C2212yes—
30C2×C4×#92418C2211yescharacteristic, complemented
31#16839629—21no—
32#16839627C2212yescomplemented
33#16839624—21no—
34#16839619C2212yes—
35C4×C4⋊Dic61C2211yescharacteristic, complemented
36C4×#11758198—21no—
37#16839608—21no—
38#16839525C2212yescomplemented
39#16839524C2212yescomplemented
40#16839524C2212yescomplemented
41C2×C4×D4×C61C2211yescharacteristic
42C2×#102×C61C2212yes—
43C2×C4×C8×C61C2211yescharacteristic, complemented
44C4×C4⋊C4×C61C2211yescharacteristic, complemented
45C61×#340C2212yescomplemented
46C24×D61—21no—
47C22×D244C2311yescharacteristic
48C22×C22⋊D61—21no—
49C2×D4×D61—24no—
50C2×D4×D61—24no—
51C2×D4×D61—22no—
52C2×D4×D61C2×C414yes—
53C23×Dic61—21no—
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—28no—
58C22×C4×D61—44no—
59C22×C4×D61—44no—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2312yes—
64C4×D244—22no—
65C4×D244C2×C414yes—
66D4×Dic61—22no—
67D4×Dic61C2×C414yes—
68#14519739—22no—
69#14519739C2×C414yes—
70C4×C22⋊D61—28no—
71#14519737—28no—
72C2×C4⋊Dic61C2312yes—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C4⋊C4×D61—22no—
76C4⋊C4×D61C2×C414yes—
77C2×C22⋊Dic61—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—22no—
81C22⋊C4×D61—28no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C42×D61C2×C414yes—
87C42×D61D414yes—
88#14519706—24no—
89#14519699—24no—
90#14519698—24no—
91#14519697—24no—
92#14519689—24no—
93C4×#92418—22no—
94#14519684—21no—
95#14519684—22no—
96#14519684—22no—
97#14519684—22no—
98C22×D4×C61C2311yescharacteristic
99C23×C4×C61—21no—
100C22×C8×C61C2312yes—
101C4×D4×C61—22no—
102C4×D4×C61C2×C414yes—
103C2×C4⋊C4×C61C2312yes—
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C22⋊C4×C61—21no—
106C2×C42×C61—21no—
107C2×C42×C61C2311yescharacteristic
108#102×C61—24no—
109C4×C8×C61—22no—
110#95×C61—21no—
111C24×C61—21no—
112C23×D61—28no—
113C23×D61—21no—
114C23×D61—24no—
115C23×D61—42no—
116C23×D61—42no—
117C23×D61—44no—
118C23×D61C2×D411yescharacteristic
119C2×D4×C61—21no—
120C2×D4×C61—22no—
121C2×D4×C61C22×C412yes—
122C2×D4×C61#4114yes—
123C22×C4×C61—21no—
124C22×C4×C61—24no—
125C22×C4×C61—22no—
126C22×C4×C61—42no—
127C22×C4×C61—42no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2411yescharacteristic
131C2×C22⋊D61—28no—
132C2×C22⋊D61—24no—
133C22×Dic61—21no—
134C22×Dic61—24no—
135C22×Dic61—22no—
136C22×Dic61—42no—
137C22×Dic61—42no—
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141D4×D61—216no—
142D4×D61—28no—
143D4×D61—28no—
144C2×D244—21no—
145C2×D244—22no—
146C2×D244C22×C412yes—
147C2×D244#4114yes—
148C2×C4×D61—24no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—24no—
154C2×C4×D61—24no—
155C2×C4×D61—24no—
156C2×C4×D61—432no—
157C2×C4×D61—42no—
158C2×C4×D61—42no—
159C2×C4×D61—42no—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×C4×D61—42no—
163C2×C4×D61C22⋊C414yes—
164C2×C4×D61C22⋊C414yes—
165C2×C4×D61C22×C412yes—
166C2×C4×D61C2×D412yes—
167C2×C8×C61—22no—
168C2×C8×C61—22no—
169C2×C8×C61—22no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61C22×C412yes—
174C22⋊C4×C61—24no—
175C42×C61—42no—
176C42×C61C22×C412yes—
177C42×C61C2×D412yes—
178C22⋊Dic61—24no—
179#11758198—24no—
180#11758198—24no—
181#11758198—44no—
182C4⋊Dic61—21no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61C22×C412yes—
186#11758196—24no—
187C4×Dic61—42no—
188C4×Dic61C22⋊C414yes—
189C4×Dic61C22⋊C414yes—
190C4×Dic61C22×C412yes—
191C4×Dic61C2×D412yes—
192C2×#92418—22no—
193C2×#92418—22no—
194C2×#92418—22no—
195C23×C61—22no—
196C23×C61—24no—
197C23×C61—42no—
198C23×C61—41no—
199C23×C61—41no—
200C23×C61C22×D411yescharacteristic
201C22×D61—22no—
202C22×D61—21no—
203C22×D61—21no—
204C22×D61—216no—
205C22×D61—22no—
206C22×D61—24no—
207C22×D61—48no—
208C22×D61—416no—
209C22×D61—416no—
210C22×D61—42no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—48no—
214C22×D61C2×C22⋊C412yes—
215C22×D61#13514yes—
216D4×C61—22no—
217D4×C61—24no—
218D4×C61#11714yes—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—48no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61C2×C22⋊C412yes—
228C2×C4×C61C2×C22⋊C412yes—
229C2×C4×C61AGL(1,ℤ/8)12yes—
230C2×C4×C61AGL(1,ℤ/8)12yes—
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C2×#4112yes—
234C2×C4×C61C2×#4112yes—
235C22⋊D61—216no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—22no—
241C2×Dic61—48no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61C2×C22⋊C412yes—
248C2×Dic61C2×C22⋊C412yes—
249C2×Dic61C2×C22⋊C412yes—
250D244—22no—
251D244—24no—
252D244#11714yes—
253C4×D61—28no—
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—24no—
257C4×D61—28no—
258C4×D61—48no—
259C4×D61—48no—
260C4×D61—48no—
261C8×C61—42no—
262#92418—42no—
263#20733—611nomaximal, Sylow
264C22×C61—24no—
265C22×C61—44no—
266C22×C61—44no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61C22×C22⋊C411yescharacteristic
270C22×C61#52512yes—
271C22×C61C2×#13512yes—
272C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
274C2×D61—24no—
275C2×D61—24no—
276C2×D61—22no—
277C2×D61—22no—
278C2×D61—24no—
279C2×D61—432no—
280C2×D61—44no—
281C2×D61—44no—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61#41614yes—
285C4×C61—22no—
286C4×C61—42no—
287C4×C61—82no—
288C4×C61#41814yes—
289C4×C61C2×#11711yescharacteristic
290C4×C61C2×#11711yescharacteristic
291C4×C61#52512yes—
292Dic61—22no—
293Dic61—22no—
294Dic61—22no—
295Dic61—42no—
296Dic61—82no—
297C22×C4×D4—611no—
298C2×#431—611no—
299#2283—611no—
300#1824—612no—
301#1804—612no—
302#1804—612no—
303#1786—612no—
304C4×#102—611no—
305C4×#102—611no—
306C4×#102—611no—
307C4×#102D6111yescharacteristic, complemented
308C2×C61—44no—
309C2×C61#228011yescharacteristic
310C2×C61C2×#41611yescharacteristic
311C2×C61C2×#41811yescharacteristic
312C2×C61#310512yes—
313C2×C61#310512yes—
314D61—24no—
315D61—44no—
316C23×D4—611no—
317C24×C4—1221no—
318C2×C4×D4—611no—
319C2×C4×D4—618no—
320C2×C4×D4—611no—
321C2×C4×D4—611no—
322C2×C4×D4—1221no—
323C2×C4×D4—1224no—
324C2×C4×D4—1221no—
325C2×C4×D4C2×D6111yescharacteristic
326C22×C4⋊C4—611no—
327C22×C22⋊C4—1221no—
328C22×C42—611no—
329#431—1224no—
330C2×C4⋊C8—612no—
331C2×#102—612no—
332C2×#102—612no—
333C2×#102—612no—
334C2×#102C2×D6112yes—
335C2×C22⋊C8—612no—
336C2×C4×C8—611no—
337C2×C4×C8C2×D6111yescharacteristic, complemented
338#383—1221no—
339#382—612no—
340#381—1221no—
341#380—612no—
342C4×C4⋊C4—611no—
343C4×C4⋊C4C2×D6111yescharacteristic, complemented
344C4×C22⋊C4—1221no—
345#376—1221no—
346#340—612no—
347#340—612no—
348#340—612no—
349#340C2×D6112yescomplemented
350C61#2073311yescharacteristic, complemented, Sylow
351C25—1221no—
352C22×D4—614no—
353C22×D4—611no—
354C22×D4—1222no—
355C22×D4—1221no—
356C22×D4—1224no—
357C22×D4—1224no—
358C22×D4C22×D6111yescharacteristic
359C23×C4—21no—
360C23×C4—611no—
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—1221no—
364C23×C4—1228no—
365C23×C4—1221no—
366C23×C4—1221no—
367C23×C4—1221no—
368C23×C4—2444no—
369C23×C4—2444no—
370C22×C8—612no—
371C22×C8C22×D6112yes—
372C4×D4—22no—
373C4×D4—614no—
374C4×D4—614no—
375C4×D4—614no—
376C4×D4—1228no—
377C4×D4—1222no—
378C4×D4—1228no—
379C4×D4—1222no—
380C4×D4—1222no—
381C4×D4C4×D6114yes—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—614no—
384C2×C4⋊C4—612no—
385C2×C4⋊C4—1222no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4C22×D6112yes—
388C2×C4⋊C4C22×D6111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—1228no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C22⋊C4—1222no—
395C2×C42—21no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—614no—
400C2×C42—614no—
401C2×C42—1221no—
402C2×C42C22×D6111yescharacteristic
403C4⋊C8—1224no—
404#102—24no—
405#102—1224no—
406#102—1224no—
407#102—1224no—
408C22⋊C8—1224no—
409C4×C8—22no—
410C4×C8—1222no—
411#95—21no—
412#95—1222no—
413#95—1222no—
414#95—1222no—
415#95—1221no—
416C24—21no—
417C24—611no—
418C24—1224no—
419C24—1228no—
420C24—1221no—
421C24—2444no—
422C24—2442no—
423C24—2442no—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—612no—
427C2×D4—614no—
428C2×D4—1224no—
429C2×D4—1228no—
430C2×D4—12216no—
431C2×D4—1228no—
432C2×D4—1228no—
433C2×D4—1221no—
434C2×D4—1222no—
435C2×D4C2×C4×D6112yes—
436C2×D4#1175822214yes—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—612no—
446C22×C4—612no—
447C22×C4—614no—
448C22×C4—614no—
449C22×C4—1224no—
450C22×C4—1224no—
451C22×C4—1224no—
452C22×C4—1224no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1221no—
458C22×C4—1224no—
459C22×C4—1222no—
460C22×C4—2442no—
461C22×C4—2442no—
462C22×C4—24432no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4—2442no—
466C22×C4—2442no—
467C22×C4—2442no—
468C22×C4—2442no—
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4C23×D6111yescharacteristic
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—1222no—
476C2×C8—1222no—
477C2×C8—1222no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—612no—
482C4⋊C4—1224no—
483C4⋊C4—1221no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4C2×C4×D6112yes—
487C22⋊C4—24no—
488C22⋊C4—1224no—
489C22⋊C4—1224no—
490C22⋊C4—1224no—
491C22⋊C4—2444no—
492C42—42no—
493C42—612no—
494C42—612no—
495C42—614no—
496C42—614no—
497C42—2442no—
498C42C2×C4×D6112yes—
499C42D4×D6112yes—
500C23—22no—
501C23—24no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23—612no—
506C23—614no—
507C23—12216no—
508C23—1222no—
509C23—1221no—
510C23—1221no—
511C23—1222no—
512C23—1224no—
513C23—2448no—
514C23—2448no—
515C23—24416no—
516C23—24416no—
517C23—2442no—
518C23—2441no—
519C23—2441no—
520C23C2×D4×D6111yescharacteristic
521D4—22no—
522D4—24no—
523D4—614no—
524D4—12216no—
525D4—1222no—
526D4—1224no—
527D4#1451973414yes—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—48no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—612no—
537C2×C4—612no—
538C2×C4—612no—
539C2×C4—1228no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1224no—
547C2×C4—1228no—
548C2×C4—1222no—
549C2×C4—2448no—
550C2×C4—2448no—
551C2×C4—2448no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2448no—
558C2×C4C22⋊C4×D6112yes—
559C2×C4C22⋊C4×D6112yes—
560C2×C4#1451980112yes—
561C2×C4#1451980412yes—
562C2×C4C22×C4×D6111yescharacteristic
563C2×C4C2×D4×D6111yescharacteristic
564C2×C4#41×D6112yes—
565C2×C4C2×#1175822212yes—
566C8—42no—
567C8—2442no—
568C22—24no—
569C22—42no—
570C22—42no—
571C22—44no—
572C22—44no—
573C22—614no—
574C22—1222no—
575C22—1222no—
576C22—1224no—
577C22—1224no—
578C22—1224no—
579C22—24432no—
580C22—2442no—
581C22—2442no—
582C22—2444no—
583C22—2444no—
584C22C2×C22⋊C4×D6111yescharacteristic
585C22#1684027112yes—
586C22#135×D6112yes—
587C22C2×#1451980111yescharacteristic
588C22C2×#1451980411yescharacteristic
589C4—22no—
590C4—42no—
591C4—82no—
592C4—1222no—
593C4—1222no—
594C4—1222no—
595C4—4882no—
596C4—2442no—
597C4#1683976514yes—
598C4#117×D6111yescharacteristic
599C4C2×#1451973411yescharacteristic
600C4#1684027112yes—
601C2—44no—
602C2—1224no—
603C2—2444no—
604C2#2144820011yescharacteristic
605C2#416×D6111yescharacteristic
606C2C2×#1683976511yescharacteristic
607C2#2145586412yes—
608C2#2145587012yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenterC4×#102D61
hypocenterC61#20733
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16839813C2semidirect
3. #21448215C2semidirect
4. #21445908C2semidirect
5. #21445828C2semidirect
6. #21445827C2semidirect
8. C4×#14519697C2semidirect
9. C4×#14519699C2semidirect
10. C4×#14519698C2semidirect
11. C4×#102×C61C2semidirect
20. C4×D4×D61C4semidirect
25. C2×#14519706C22semidirect
30. C2×C4×#92418C22semidirect
32. #16839627C22semidirect
35. C4×C4⋊Dic61C22semidirect
38. #16839525C22semidirect
39. #16839524C22semidirect
40. #16839524C22semidirect
43. C2×C4×C8×C61C22semidirect
44. C4×C4⋊C4×C61C22semidirect
45. C61×#340C22semidirect
307. C4×#102D61semidirect
337. C2×C4×C8C2×D61semidirect
343. C4×C4⋊C4C2×D61semidirect
349. #340C2×D61semidirect
350. C61#20733semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
C2×#168398132
#214482152
#214459082
#214458282
#214458272
#214457482
C4×#145196972
C4×#145196992
C4×#145196982
C4×#102×C612
#2073361