Finite Group Databasebeta

← #29648411

Subgroups — #29648411

Order 15616.

1252 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840313C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444513C214yesmaximal, complemented
5#21444500C211yesmaximal, characteristic, complemented
6#21444488C211yesmaximal, characteristic, complemented
7#21444486C211yesmaximal, characteristic, complemented
8#21444480C214yesmaximal, complemented
9C61×#1548C211yesmaximal, characteristic, complemented
10C22×#11758226C412yes—
11#16840313—21no—
12#16840313—21no—
13#16840313—21no—
14#16840313—21no—
15#16840313C412yes—
16#16840313C412yes—
17#16840313C2212yes—
18#16840313C2212yes—
19C2×#14519774C2211yescharacteristic
20C2×#14519766C412yes—
21C2×#14519752—21no—
22C2×#14519752—21no—
23C2×#14519739—21no—
24C2×#14519739—21no—
25C2×C42×D61C2211yescharacteristic
26#16839818—21no—
27#16839818C2212yescomplemented
28#16839815C2211yescharacteristic
29#16839814—21no—
30#16839814C2212yescomplemented
31#16839814C2212yescomplemented
32#16839813—21no—
33#16839812—21no—
34#16839786C2211yescharacteristic
35C4⋊C8×D61C2212yescomplemented
36#16839725—21no—
37C22⋊C8×D61—21no—
38M16×Dic61—21no—
39C4×C8×D61—21no—
40#16839511C2214yescomplemented
41#16839505C2214yescomplemented
42#16839505C2214yescomplemented
43C2×C4⋊Q8×C61C2211yescharacteristic
44C61×#431C2211yescharacteristic
45C61×#423C2211yescharacteristic
46C61×#333C2214yescomplemented
47C2×#11758226—22no—
48C2×#11758226—22no—
49C2×#11758226—48no—
50C2×#11758226C2×C414yes—
51C2×#11758226C2×C414yes—
52C22×D244—22no—
53C22×D244—21no—
54C22×D244—21no—
55C22×D244C2×C412yes—
56C22×C4×D61—22no—
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C2×#11758194—21no—
61C2×C8×D61—22no—
62#14519774—21no—
63#14519774—21no—
64#14519774C2×C412yes—
65#14519774C2312yes—
66#14519766—22no—
67#14519766—22no—
68#14519766C2×C414yes—
69#14519766C2×C414yes—
70#14519752—22no—
71#14519752—22no—
72#14519752—22no—
73#14519752—22no—
74#14519752—22no—
75#14519752—22no—
76#14519752—22no—
77#14519752—22no—
78#14519739—22no—
79#14519739—22no—
80#14519739—22no—
81#14519739—22no—
82#14519739—22no—
83#14519739—22no—
84#14519739—22no—
85#14519739—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×C4×Dic61C2×C411yescharacteristic
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61D411yescharacteristic
91C42×D61C2×C411yescharacteristic
92C42×D61C2×C411yescharacteristic
93C42×D61D411yescharacteristic
94C42×D61D411yescharacteristic
95C42×D61D411yescharacteristic
96C42×D61D411yescharacteristic
97C42×D61C2311yescharacteristic
98C42×D61C2311yescharacteristic
99C4⋊#92418—21no—
100C4⋊#92418C2312yes—
101C4⋊#92418C2312yes—
102#14519706—22no—
103C22⋊#92418—21no—
104#14519689—22no—
105#14519689—22no—
106#14519689—22no—
107#14519687—22no—
108C4×#92418—21no—
109C8×Dic61—22no—
110C8×Dic61—22no—
111C22×Q8×C61C2×C412yes—
112C2×M16×C61—21no—
113C4⋊Q8×C61—21no—
114C4⋊Q8×C61—21no—
115C4⋊Q8×C61C2×C412yes—
116C4⋊Q8×C61C2312yes—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C42×C61C2311yescharacteristic
120C4⋊C8×C61—21no—
121C4⋊C8×C61C2312yes—
122C4⋊C8×C61C2312yes—
123C22⋊C8×C61—21no—
124C4×C8×C61—21no—
125C23×D61—22no—
126C23×D61C22⋊C411yescharacteristic
127C2×Q8×C61—22no—
128C2×Q8×C61—44no—
129C2×Q8×C61C22×C414yes—
130C22×C4×C61—22no—
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×Dic61C22⋊C411yescharacteristic
135C22×Dic61C22⋊C411yescharacteristic
136C22×Dic61C22⋊C411yescharacteristic
137#11758226—48no—
138#11758226—48no—
139#11758226—48no—
140#11758226—48no—
141C2×D244—24no—
142C2×D244—24no—
143C2×D244—22no—
144C2×D244—22no—
145C2×D244—22no—
146C2×D244—22no—
147C2×D244—22no—
148C2×D244—44no—
149C2×D244—48no—
150C2×D244—42no—
151C2×D244—42no—
152C2×D244—44no—
153C2×D244C22×C414yes—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—24no—
157C2×C4×D61—24no—
158C2×C4×D61—24no—
159C2×C4×D61—42no—
160C2×C4×D61—48no—
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22×C411yescharacteristic
168C2×C4×D61C22×C411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173M16×C61—42no—
174C2×C8×C61—22no—
175C2×C8×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C42×C61C22×C411yescharacteristic
181C42×C61C2×D411yescharacteristic
182C42×C61C2×D411yescharacteristic
183C42×C61C2411yescharacteristic
184#11758198—24no—
185#11758198—24no—
186#11758198—24no—
187#11758198—24no—
188C4×Dic61C22⋊C411yescharacteristic
189C4×Dic61C22⋊C411yescharacteristic
190C4×Dic61C22⋊C411yescharacteristic
191C4×Dic61C22⋊C411yescharacteristic
192C4×Dic61C22⋊C411yescharacteristic
193C4×Dic61C22⋊C411yescharacteristic
194C4×Dic61C22×C411yescharacteristic
195C4×Dic61C22×C411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61C2×D411yescharacteristic
198C4×Dic61C2×D411yescharacteristic
199C4×Dic61C2×D411yescharacteristic
200#11758194—42no—
201C2×#92418—22no—
202C2×#92418—22no—
203C8×D61—44no—
204C23×C61C2×C22⋊C411yescharacteristic
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—24no—
208C22×D61—41no—
209C22×D61—44no—
210C22×D61—44no—
211C22×D61—44no—
212C22×D61C2×C22⋊C411yescharacteristic
213C22×D61C2×C22⋊C411yescharacteristic
214Q8×C61—44no—
215Q8×C61—44no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—24no—
219C2×C4×C61—44no—
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C2×C22⋊C411yescharacteristic
223C2×C4×C61#13512yes—
224C2×C4×C61#13512yes—
225C2×C4×C61C23×C411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—41no—
231C2×Dic61C2×C22⋊C411yescharacteristic
232C2×Dic61C2×C22⋊C411yescharacteristic
233C2×Dic61C2×C22⋊C411yescharacteristic
234C2×Dic61C2×C22⋊C411yescharacteristic
235C2×Dic61C2×C22⋊C411yescharacteristic
236C2×Dic61C2×C22⋊C411yescharacteristic
237D244—44no—
238D244—44no—
239D244—48no—
240D244—48no—
241D244—42no—
242D244—42no—
243D244—44no—
244D244—44no—
245D244—44no—
246C4×D61—22no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—21no—
251C4×D61—22no—
252C4×D61—22no—
253C4×D61—22no—
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—48no—
260C4×D61—48no—
261C4×D61#10014yes—
262C8×C61—42no—
263C8×C61—42no—
264#92418—42no—
265#92418—42no—
266#17714—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61#41612yes—
270C22×C61C22×C22⋊C411yescharacteristic
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—44no—
277C2×D61—44no—
278C2×D61—44no—
279C2×D61—44no—
280C2×D61—88no—
281C2×D61C2×#10012yes—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—44no—
285C4×C61C2×#10012yes—
286C4×C61#41612yes—
287C4×C61C2×#13511yescharacteristic
288C4×C61C2×#13511yescharacteristic
289C4×C61#57512yes—
290Dic61—21no—
291Dic61—21no—
292Dic61—21no—
293Dic61—21no—
294Dic61—21no—
295Dic61C2×#10012yes—
296C2×#532—611no—
297#2920—611no—
298C2×#431—611no—
299#1551—614no—
300#1548—611no—
301#1548D6111yescharacteristic, complemented
302#1545—611no—
303#1545—611no—
304#1543—614no—
305C2×C61—22no—
306C2×C61C22×#10011yescharacteristic
307C2×C61C2×#41611yescharacteristic
308C2×C61#289611yescharacteristic
309D61—22no—
310D61—41no—
311D61—84no—
312C22×#41—612no—
313#532—612no—
314#532—612no—
315#532—612no—
316#532—612no—
317#532—1221no—
318#532—1221no—
319#532—1221no—
320#532—1221no—
321C2×C4⋊Q8C2×D6111yescharacteristic
322C2×#127—611no—
323C2×#124—612no—
324C2×#121—1221no—
325C2×#121—1221no—
326C2×C4×D4—1221no—
327C2×C4×D4—1221no—
328C22×C42—611no—
329#432—612no—
330#432—1221no—
331#431—611no—
332#431—612no—
333#431—612no—
334#431—1221no—
335#431—1221no—
336#431—1221no—
337#431C2×D6111yescharacteristic
338#423—611no—
339#423C2×D6111yescharacteristic
340C2×C4⋊C8—612no—
341#407—1221no—
342C2×C22⋊C8—1221no—
343C4×M16—1221no—
344C2×C4×C8—1221no—
345#333—614no—
346#333C2×D6114yescomplemented
347#331—614no—
348#331—614no—
349C61#1771411yescharacteristic, complemented, Sylow
350C2×#41—614no—
351C2×#41—614no—
352C2×#41—1222no—
353C2×#41—1222no—
354C2×#41—2448no—
355C22×Q8C4×D6112yes—
356C22×D4—612no—
357C22×D4—1222no—
358C22×D4—1221no—
359C22×D4—1221no—
360C23×C4—611no—
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—1222no—
364C2×M16—21no—
365C2×M16—1221no—
366C22×C8—1222no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8C4×D6112yes—
370C4⋊Q8C22×D6112yes—
371#127—612no—
372#127—612no—
373#127—1221no—
374#127—1221no—
375#124—614no—
376#124—614no—
377#124—1222no—
378#124—1222no—
379#121—1222no—
380#121—1222no—
381#121—1222no—
382#121—1222no—
383#121—1222no—
384#121—1222no—
385#121—1222no—
386#121—1222no—
387C4×D4—1222no—
388C4×D4—1222no—
389C4×D4—1222no—
390C4×D4—1222no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4—1222no—
394C4×D4—1222no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C22⋊C4—1222no—
398C2×C22⋊C4—1222no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42C22×D6111yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—612no—
413C4⋊C8—612no—
414C4⋊C8—1222no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6112yes—
417C4⋊C8C22×D6112yes—
418C22⋊C8—21no—
419C22⋊C8—1222no—
420C22⋊C8—1222no—
421C22⋊C8—1222no—
422C22⋊C8—1221no—
423#97—1222no—
424C4×C8—21no—
425C4×C8—1222no—
426C4×C8—1222no—
427C4×C8—1221no—
428C24—611no—
429C24—1222no—
430#41—2448no—
431#41—2448no—
432#41—2448no—
433#41—2448no—
434C2×Q8—22no—
435C2×Q8—44no—
436C2×Q8C2×C4×D6114yes—
437C2×D4—614no—
438C2×D4—1224no—
439C2×D4—1224no—
440C2×D4—1222no—
441C2×D4—1222no—
442C2×D4—1222no—
443C2×D4—1222no—
444C2×D4—1222no—
445C2×D4—2444no—
446C2×D4—2444no—
447C2×D4—2448no—
448C2×D4—2442no—
449C2×D4—2442no—
450C22×C4—22no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—1224no—
467C22×C4—1224no—
468C22×C4—1224no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—2442no—
472C22×C4—2448no—
473C22×C4C2×C4×D6111yescharacteristic
474C22×C4D4×D6111yescharacteristic
475C22×C4D4×D6111yescharacteristic
476M16—42no—
477M16—2442no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—1222no—
481C2×C8—1222no—
482C2×C8—2444no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C22⋊C4—1224no—
488C22⋊C4—1224no—
489C22⋊C4—1224no—
490C22⋊C4—1224no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—611no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—611no—
502C42—611no—
503C42C2×C4×D6111yescharacteristic
504C42D4×D6111yescharacteristic
505C42D4×D6111yescharacteristic
506C42C23×D6111yescharacteristic
507C23—611no—
508C23—611no—
509C23—1222no—
510C23—1222no—
511C23—1224no—
512C23—2441no—
513C23—2444no—
514C23—2444no—
515C23—2444no—
516C23C22⋊C4×D6111yescharacteristic
517Q8—44no—
518Q8—44no—
519D4—2444no—
520D4—2444no—
521D4—2448no—
522D4—2448no—
523D4—2444no—
524D4—2444no—
525D4—2442no—
526D4—2442no—
527D4—2444no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—44no—
532C2×C4—611no—
533C2×C4—614no—
534C2×C4—611no—
535C2×C4—611no—
536C2×C4—611no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—1222no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2448no—
555C2×C4—2448no—
556C2×C4—2441no—
557C2×C4C22⋊C4×D6111yescharacteristic
558C2×C4C22⋊C4×D6111yescharacteristic
559C2×C4C22⋊C4×D6111yescharacteristic
560C2×C4#1451979812yes—
561C2×C4#1451980012yes—
562C2×C4C22×C4×D6111yescharacteristic
563C2×C4C2×D4×D6111yescharacteristic
564C2×C4C2×D4×D6111yescharacteristic
565C8—42no—
566C8—42no—
567C8—2442no—
568C8—2442no—
569C22—21no—
570C22—21no—
571C22—612no—
572C22—1221no—
573C22—1221no—
574C22—1221no—
575C22—1221no—
576C22—1221no—
577C22—4888no—
578C22—2444no—
579C22—2444no—
580C22—2444no—
581C22—2444no—
582C22#1683975712yes—
583C22C2×C22⋊C4×D6111yescharacteristic
584C4—21no—
585C4—21no—
586C4—44no—
587C4—612no—
588C4—1221no—
589C4—1221no—
590C4—1221no—
591C4—1221no—
592C4—1221no—
593C4#100×D6112yes—
594C4#1683975712yes—
595C4C2×#1451979811yescharacteristic
596C4C2×#1451980011yescharacteristic
597C4#1684056112yes—
598C2—22no—
599C2—1222no—
600C2—4884no—
601C2—2441no—
602C2C2×#100×D6111yescharacteristic
603C2C2×#1683975711yescharacteristic
604C2#2145433711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1548C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840313C2
cosocleC42×C61C24
hypercenter#1548D61
hypocenterC61#17714
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
2. #21454451C2semidirect
3. #431×D61C2semidirect
4. #21444513C2semidirect
5. #21444500C2semidirect
6. #21444488C2semidirect
7. #21444486C2semidirect
8. #21444480C2semidirect
9. C61×#1548C2semidirect
27. #16839818C22semidirect
30. #16839814C22semidirect
31. #16839814C22semidirect
35. C4⋊C8×D61C22semidirect
40. #16839511C22semidirect
41. #16839505C22semidirect
42. #16839505C22semidirect
46. C61×#333C22semidirect
301. #1548D61semidirect
346. #333C2×D61semidirect
349. C61#17714semidirect

Maximal subgroups

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

subgroupindex
C2×#168403132
#214544512
#431×D612
#214445132
#214445002
#214444882
#214444862
#214444802
C61×#15482
#1771461