Finite Group Databasebeta

← #29646649

Subgroups — #29646649

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459116C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444292C211yesmaximal, characteristic, complemented
5#21444289C211yesmaximal, characteristic, complemented
6#21444287C211yesmaximal, characteristic, complemented
7#21444283C214yesmaximal, complemented
8#21444200C214yesmaximal, complemented
9C61×#1497C211yesmaximal, characteristic, complemented
10#16840317C411yescharacteristic
11#16840317C411yescharacteristic
12#16840313C411yescharacteristic
13#16840313C411yescharacteristic
14#16840312C2211yescharacteristic
15#16840299—21no—
16#16840299C2212yes—
17#16840298—21no—
18#16840298C412yes—
19#16840297—21no—
20#16840297—21no—
21#16840275—21no—
22#16840275C412yes—
23#16840274—21no—
24C4×#11758226—21no—
25C4×#11758226C2212yes—
26#16840230—21no—
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839817—21no—
30#16839815C2211yescharacteristic
31#16839814—21no—
32#16839814C2212yes—
33#16839813C2212yes—
34#16839812—21no—
35#16839812—21no—
36#16839784C2212yes—
37C4⋊C8×D61—21no—
38#16839724—21no—
39C22⋊C8×D61—21no—
40#16839714—21no—
41C4×C8×D61C2212yes—
42Q8⋊#92418C2214yescomplemented
43#16839491C2214yescomplemented
44#16839489C2214yescomplemented
45C61×#533C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C2×#11758226—21no—
50C2×#11758226C2×C412yes—
51C2×#11758222—21no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C2×#11758189—22no—
56C2×C8×D61—22no—
57#14519777C2×C411yescharacteristic
58#14519774C2×C411yescharacteristic
59#14519772—22no—
60#14519772—22no—
61#14519768—21no—
62#14519768C2×C412yes—
63#14519766—21no—
64#14519766C2×C412yes—
65#14519765—21no—
66#14519762—22no—
67#14519762—22no—
68#14519761—22no—
69#14519757—21no—
70#14519757—21no—
71#14519753—21no—
72#14519753C2×C412yes—
73#14519752—21no—
74#14519752—21no—
75#14519752—21no—
76#14519752C2×C412yes—
77#14519751—21no—
78#14519751C2×C412yes—
79#14519747—22no—
80Q8×Dic61—21no—
81Q8×Dic61C2×C412yes—
82#14519742—21no—
83#14519742—21no—
84C4×D244—22no—
85C4×D244—22no—
86C4×D244—21no—
87C4×D244C2312yes—
88#14519739—22no—
89#14519739—22no—
90#14519739—21no—
91#14519739—21no—
92#14519739—21no—
93#14519739C2×C412yes—
94#14519737—22no—
95#14519737—22no—
96#14519735—21no—
97#14519735—22no—
98#14519735—22no—
99#14519735C2×C412yes—
100#14519734—22no—
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61D411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C42×D61—22no—
105C42×D61C2×C411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61C2311yescharacteristic
112C42×D61C2311yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418C2312yes—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119#14519689—22no—
120#14519689—22no—
121#14519688—21no—
122C4×#92418C2312yes—
123C8×Dic61—22no—
124C8×Dic61—22no—
125C4⋊Q8×C61C2×C411yescharacteristic
126C4⋊Q8×C61C2×C411yescharacteristic
127#125×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61C2×C412yes—
130C4×Q8×C61—21no—
131C4×Q8×C61C2312yes—
132#117×C61—21no—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2312yes—
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138#97×C61—21no—
139C4×C8×C61C2312yes—
140C23×D61C22⋊C411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61C22×C412yes—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C2×C22⋊D61—22no—
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150#11758226—28no—
151#11758226—44no—
152#11758222—44no—
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244C22×C412yes—
158C2×C4×D61—24no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—42no—
163C2×C4×D61—42no—
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22×C411yescharacteristic
171C2×C4×D61C22×C411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×Dic122—21no—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61C22×C412yes—
185C22⋊C4×C61—22no—
186C42×C61—22no—
187C42×C61C22×C411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61C2411yescharacteristic
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199C4⋊Dic61—21no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61C22×C412yes—
203#11758196—22no—
204#11758196—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22×C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C2×#92418—22no—
220C2×#92418—22no—
221#11758189—44no—
222C8×D61—44no—
223C23×C61C2×C22⋊C411yescharacteristic
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—41no—
227C22×D61—41no—
228C22×D61C2×C22⋊C411yescharacteristic
229C22×D61C2×C22⋊C411yescharacteristic
230Q8×C61—24no—
231Q8×C61—42no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—41no—
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C23×C411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C22⋊D61—44no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—41no—
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254D244—24no—
255D244—42no—
256D244—42no—
257D244—44no—
258D244—44no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—41no—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—44no—
271C4×D61—44no—
272C4×D61—44no—
273C4×D61#13114yes—
274Dic122—42no—
275C8×C61—42no—
276C8×C61—42no—
277#92418—42no—
278#92418—42no—
279#17477—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61C22×C22⋊C411yescharacteristic
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—44no—
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61#40812yes—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—42no—
299C4×C61—42no—
300C4×C61C2×#13112yes—
301C4×C61#57512yes—
302Dic61—21no—
303Dic61—21no—
304Dic61—21no—
305Dic61—21no—
306Dic61—42no—
307Dic61#40812yes—
308Dic61#42112yes—
309#3444—611no—
310#2920—611no—
311C2×#431—611no—
312#1497—611no—
313#1497D6111yescharacteristic, complemented
314#1496—611no—
315#1496—611no—
316#1495—614no—
317#1476—614no—
318C2×C61—41no—
319C2×C61C2×#40811yescharacteristic
320C2×C61#289611yescharacteristic
321C2×C61C2×#42111yescharacteristic
322D61—22no—
323D61—41no—
324D61—82no—
325#533—611no—
326#533—611no—
327#533C2×D6111yescharacteristic
328#532—611no—
329#532—611no—
330#532—611no—
331#529—612no—
332#529—612no—
333#529—1221no—
334#529—1221no—
335#529—1221no—
336#529—1221no—
337#525—612no—
338#525—1221no—
339#525—1221no—
340C4×#41—612no—
341C4×#41—1221no—
342C4×#41—1221no—
343C22×C42—611no—
344#432—611no—
345#432—1221no—
346#432C2×D6111yescharacteristic
347#431—611no—
348#431—612no—
349#431—612no—
350#431—1221no—
351#431—1221no—
352#431—1221no—
353#431C2×D6111yescharacteristic
354#423—612no—
355C2×C4⋊C8—1221no—
356#407—1221no—
357C2×C22⋊C8—1221no—
358C4×M16—1221no—
359C2×C4×C8—612no—
360Q8⋊C8—614no—
361Q8⋊C8C2×D6114yescomplemented
362D4⋊C8—614no—
363D4⋊C8—614no—
364C61#1747711yescharacteristic, complemented, Sylow
365C2×#41—612no—
366C2×#41—1221no—
367C2×#41—1221no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—611no—
371C2×M16—1222no—
372C22×C8—1222no—
373C4⋊Q8—611no—
374C4⋊Q8C4×D6111yescharacteristic
375C4⋊Q8C4×D6111yescharacteristic
376#127—611no—
377#126—1222no—
378#126—1222no—
379#125—21no—
380#125—612no—
381#125—1221no—
382#124—612no—
383#124—1221no—
384#124—1221no—
385#123—1222no—
386#123—1222no—
387#123—1222no—
388C22⋊Q8—21no—
389C22⋊Q8—612no—
390C22⋊Q8—1221no—
391C22⋊Q8—1221no—
392C22⋊Q8—1221no—
393C22⋊Q8C4×D6112yes—
394#121—612no—
395#121—612no—
396#121—1221no—
397#121—1221no—
398#121—1221no—
399#121—1221no—
400#120—1222no—
401C4×Q8—21no—
402C4×Q8—612no—
403C4×Q8—1221no—
404C4×Q8—1221no—
405C4×Q8—1221no—
406C4×Q8C22×D6112yes—
407C4×D4—612no—
408C4×D4—612no—
409C4×D4—1222no—
410C4×D4—1222no—
411C4×D4—1221no—
412C4×D4—1221no—
413C4×D4—1221no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—1222no—
418C4×D4—1221no—
419#117—21no—
420#117—612no—
421#117—1222no—
422#117—1222no—
423#117—1222no—
424#117—1221no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—1222no—
437C2×C42C22×D6111yescharacteristic
438C4⋊C8—21no—
439C4⋊C8—612no—
440C4⋊C8—1222no—
441C4⋊C8—1222no—
442C4⋊C8—1221no—
443C4⋊C8C22×D6112yes—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—1222no—
447C22⋊C8—1222no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450#97—21no—
451#97—1221no—
452C4×C8—612no—
453C4×C8—1222no—
454C4×C8—1222no—
455C4×C8C22×D6112yes—
456C24—611no—
457#41—1228no—
458#41—2444no—
459#41—2444no—
460C2×Q8—21no—
461C2×Q8—1221no—
462C2×Q8C2×C4×D6112yes—
463C2×D4—612no—
464C2×D4—1222no—
465C2×D4—1222no—
466C2×D4—1222no—
467C2×D4—1221no—
468C2×D4—1221no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—1224no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4C2×C4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4D4×D6111yescharacteristic
493M16—2444no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—1222no—
497C2×C8—1222no—
498C2×C8—2444no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—612no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1221no—
510C4⋊C4C2×C4×D6112yes—
511C22⋊C4—22no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C22⋊C4—1222no—
515C22⋊C4—1222no—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C42—22no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—1222no—
534C42—1222no—
535C42C2×C4×D6111yescharacteristic
536C42D4×D6111yescharacteristic
537C42D4×D6111yescharacteristic
538C42C23×D6111yescharacteristic
539C23—611no—
540C23—611no—
541C23—1222no—
542C23—1222no—
543C23—2441no—
544C23—2441no—
545C23C22⋊C4×D6111yescharacteristic
546Q8—24no—
547Q8—42no—
548Q8—2442no—
549D4—1224no—
550D4—2442no—
551D4—2442no—
552D4—2444no—
553D4—2444no—
554D4—2444no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—614no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2444no—
582C2×C4—2444no—
583C2×C4—2441no—
584C2×C4—2444no—
585C2×C4C22⋊C4×D6111yescharacteristic
586C2×C4C22⋊C4×D6111yescharacteristic
587C2×C4C22⋊C4×D6111yescharacteristic
588C2×C4C22×C4×D6111yescharacteristic
589C2×C4C2×D4×D6111yescharacteristic
590C2×C4C2×D4×D6111yescharacteristic
591C8—42no—
592C8—42no—
593C8—2442no—
594C8—2442no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—612no—
599C22—1221no—
600C22—1221no—
601C22—1221no—
602C22—1221no—
603C22—1221no—
604C22—2444no—
605C22—2442no—
606C22—2442no—
607C22—2442no—
608C22C2×C22⋊C4×D6111yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—42no—
614C4—42no—
615C4—612no—
616C4—612no—
617C4—1221no—
618C4—1221no—
619C4—1221no—
620C4—1221no—
621C4—2442no—
622C4#131×D6112yes—
623C4#1684056112yes—
624C2—41no—
625C2—1222no—
626C2—4882no—
627C2—2441no—
628C2#408×D6111yescharacteristic
629C2#2145433711yescharacteristic
630C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1497C2
socleC22×C61C22×C22⋊C4
prime radical#21459116C2
cosocleC42×C61C24
hypercenter#1497D61
hypocenterC61#17477
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. #431×D61C2semidirect
4. #21444292C2semidirect
5. #21444289C2semidirect
6. #21444287C2semidirect
7. #21444283C2semidirect
8. #21444200C2semidirect
9. C61×#1497C2semidirect
42. Q8⋊#92418C22semidirect
43. #16839491C22semidirect
44. #16839489C22semidirect
48. C61×Q8⋊C8C22semidirect
313. #1497D61semidirect
361. Q8⋊C8C2×D61semidirect
364. C61#17477semidirect

Maximal subgroups

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

subgroupindex
#214591162
#214544492
#431×D612
#214442922
#214442892
#214442872
#214442832
#214442002
C61×#14972
#1747761