Finite Group Databasebeta

← #29649459

Subgroups — #29649459

Order 15616.

702 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454926C211yesmaximal, characteristic
2#21454898C211yesmaximal, characteristic, complemented
3C4×#14519806C211yesmaximal, characteristic
4#21444639C211yesmaximal, characteristic, complemented
5#21444635C211yesmaximal, characteristic, complemented
6#21444628C211yesmaximal, characteristic, complemented
7#21444625C211yesmaximal, characteristic, complemented
8C8×#11758202C211yesmaximal, characteristic, complemented
9SD16×#92418C211yesmaximal, characteristic, complemented
10C8×#11758200C211yesmaximal, characteristic, complemented
11#21444570C211yesmaximal, characteristic, complemented
12#21444198C211yesmaximal, characteristic
13Q8⋊C8×D61C211yesmaximal, characteristic, complemented
14#21444098C211yesmaximal, characteristic, complemented
15C61×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#14519806C411yescharacteristic
17C4×#11758224C2211yescharacteristic
18C4×Q8×D61C2211yescharacteristic
19Q8×#92418C2211yescharacteristic
20C8×Dic122—21no—
21C8×Dic122C2211yescharacteristic
22C8×Dic122C2211yescharacteristic
23#16839886—21no—
24#16839886C2211yescharacteristic
25#16839886C2211yescharacteristic
26#16839868C411yescharacteristic
27#16839866C411yescharacteristic
28#16839863C411yescharacteristic
29#16839859C411yescharacteristic
30C4×Dic244C2211yescharacteristic
31C4×#11758202C2211yescharacteristic
32C4×#11758200C2211yescharacteristic
33D4×#92418C2211yescharacteristic
34C8×C22⋊D61—21no—
35#16839825—21no—
36#16839814—21no—
37#16839814C2211yescharacteristic
38#16839813—21no—
39#16839813C2211yescharacteristic
40#16839812—21no—
41#16839801C411yescharacteristic
42C2×#14519706—21no—
43C4⋊C8×D61C2211yescharacteristic
44#16839769C411yescharacteristic
45#16839760C411yescharacteristic
46C4×#11758189C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839513C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55#16839492C2211yescharacteristic
56D4⋊#92418C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C8×Q8×C61C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758224C2×C411yescharacteristic
68C2×Q8×D61C2×C411yescharacteristic
69#14519806C818yescomplemented
70C2×Dic244C2×C411yescharacteristic
71C2×#11758202C2×C411yescharacteristic
72C2×#11758200C2×C411yescharacteristic
73C2×#11758189C2×C411yescharacteristic
74C2×#11758189C2×C411yescharacteristic
75C22×#92418—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78Q8×Dic61C2×C411yescharacteristic
79C4×Dic122—21no—
80C4×Dic122C2311yescharacteristic
81C4×Dic122C2311yescharacteristic
82#14519742—21no—
83#14519742C2×C411yescharacteristic
84#14519742C2×C411yescharacteristic
85D4×Dic61C2×C411yescharacteristic
86C4×C22⋊D61—21no—
87#14519737—21no—
88#14519735C2×C411yescharacteristic
89#14519733—21no—
90C4⋊C4×D61—21no—
91C4⋊C4×D61C2×C411yescharacteristic
92C2×C4×Dic61—21no—
93C42×D61—21no—
94C42×D61C2311yescharacteristic
95#14519711C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98C4⋊#92418—21no—
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706D411yescharacteristic
107#14519706D411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519701C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519700C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114C22⋊#92418—21no—
115#14519689—21no—
116#14519689D411yescharacteristic
117#14519689D411yescharacteristic
118#14519687C2×C411yescharacteristic
119#14519687C2×C411yescharacteristic
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C8×Dic61—21no—
130C2×SD16×C61C2×C411yescharacteristic
131C22×C8×C61—21no—
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#106×C61C2×C411yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151Q8×D61—22no—
152Q8×D61C2×C814yescomplemented
153#11758224—22no—
154#11758224C2×C814yes—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61C22×C411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61#4111yescharacteristic
160C2×Dic122—21no—
161C2×Dic122C22×C411yescharacteristic
162C2×Dic122C22×C411yescharacteristic
163SD16×C61C2×C814yescomplemented
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—81no—
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C411yescharacteristic
174C4⋊C4×C61C22×C411yescharacteristic
175C22⋊C4×C61—21no—
176C42×C61—21no—
177C42×C61C2411yescharacteristic
178C22⋊Dic61—21no—
179#11758202C2×C814yescomplemented
180#11758200C2×C814yescomplemented
181#11758198—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61C22×C411yescharacteristic
184C4⋊Dic61C22×C411yescharacteristic
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61C22×C411yescharacteristic
197C4×Dic61C2×D411yescharacteristic
198C4×Dic61#4111yescharacteristic
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—81no—
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207Dic244C2×C814yescomplemented
208#11758189—22no—
209#11758189C2×C814yescomplemented
210C8×D61—42no—
211C8×D61—81no—
212C23×C61—21no—
213C22×D61C4×D411yescharacteristic
214Q8×C61—21no—
215Q8×C61C22×C812yes—
216D4×C61—21no—
217D4×C61C22×C812yes—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61C23×C411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C22⋊D61—24no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—24no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—81no—
233C2×Dic61C4×D411yescharacteristic
234C2×Dic61C4×D411yescharacteristic
235C2×Dic61C4×D411yescharacteristic
236C4×D61—24no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—41no—
240C4×D61—81no—
241C4×D61C22×C812yes—
242C4×D61#13112yes—
243Dic122—21no—
244Dic122—21no—
245Dic122—24no—
246Dic122C22×C812yes—
247Dic122C22×C812yes—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61C22×C812yes—
255#92418—22no—
256#92418—21no—
257#92418—21no—
258#92418—21no—
259#92418—41no—
260#92418—41no—
261#92418C22×C812yes—
262#17853—611nomaximal, Sylow
263C22×C61—22no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C2×C4×D411yescharacteristic
267C2×D61—21no—
268C2×D61—21no—
269C2×D61C8×D412yes—
270C4×C61—22no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61C23×C811yescharacteristic
275C4×C61C2×#13111yescharacteristic
276C4×C61#57711yescharacteristic
277C4×C61#57811yescharacteristic
278Dic61—22no—
279Dic61—22no—
280Dic61—21no—
281Dic61—21no—
282Dic61—41no—
283Dic61—41no—
284Dic61C8×D412yes—
285#2988—611no—
286#2982—611no—
287C4×#137—611no—
288#1579—611no—
289#1579—611no—
290SD16⋊C8—611no—
291SD16⋊C8D6111yescharacteristic, complemented
292C8×Q16—611no—
293C8×Q16—611no—
294C8×SD16—611no—
295C8×SD16—611no—
296#1565—611no—
297#1476—611no—
298C2×Q8⋊C8—611no—
299C8×M16—611no—
300C2×C61—42no—
301C2×C61C2×C8×D411yescharacteristic
302C2×C61#294711yescharacteristic
303C2×C61#295611yescharacteristic
304D61—22no—
305C2×#137—611no—
306C4×#41—611no—
307C2×C4×Q8—611no—
308C8×Q8—611no—
309C8×Q8—611no—
310C8×Q8—611no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—1221no—
314C8×Q8—1221no—
315C8×Q8C2×D6111yescharacteristic
316#441—611no—
317#441—611no—
318#440—611no—
319#440—611no—
320C4×Q16—611no—
321C4×Q16—611no—
322C4×SD16—611no—
323C4×SD16C2×D6111yescharacteristic
324C8×D4—611no—
325C8×D4—1221no—
326C8×D4—1221no—
327C8×D4C2×D6111yescharacteristic
328#431—611no—
329#431—611no—
330#431—1221no—
331#431—1221no—
332#431—1221no—
333#428—611no—
334C2×C4⋊C8—611no—
335C2×C4⋊C8—1221no—
336#419—611no—
337#417—611no—
338C4×M16—611no—
339C2×C4×C8—611no—
340#335—611no—
341#335C2×D6111yescharacteristic
342#334—611no—
343#334—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349Q8⋊C8C2×D6111yescharacteristic
350D4⋊C8—611no—
351D4⋊C8C2×D6111yescharacteristic
352#322—611no—
353#322C2×D6111yescharacteristic
354C82—611no—
355C82—611no—
356C61#1785311yescharacteristic, complemented, Sylow
357C2×#41—611no—
358C22×Q8—611no—
359#137—618no—
360C2×Q16—611no—
361C2×Q16—611no—
362C2×SD16—611no—
363C2×SD16C4×D6111yescharacteristic
364C2×M16—611no—
365C2×M16—611no—
366C22×C8—21no—
367C22×C8—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370C4×Q8—611no—
371C4×Q8—611no—
372C4×Q8—611no—
373C4×Q8—611no—
374C4×Q8—611no—
375C4×Q8—1221no—
376C4×Q8—1221no—
377C4×Q8C22×D6111yescharacteristic
378C4×D4—611no—
379C4×D4—1221no—
380C4×D4—1221no—
381C4×D4C22×D6111yescharacteristic
382#117—611no—
383#117—1221no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—1221no—
386C2×C42—611no—
387C2×C42—1221no—
388C2×C42—1221no—
389#107—611no—
390#107—611no—
391#106—611no—
392#106C4×D6111yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8C22×D6111yescharacteristic
405C4⋊C8C22×D6111yescharacteristic
406#103—611no—
407#103—611no—
408#103—611no—
409#103—611no—
410#103—611no—
411#103C4×D6111yescharacteristic
412#102—611no—
413#102C4×D6111yescharacteristic
414C22⋊C8—21no—
415C22⋊C8—611no—
416C22⋊C8—611no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419#97—611no—
420#97—611no—
421C4×C8—21no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435#41—614no—
436#41—1222no—
437C2×Q8—614no—
438C2×Q8—611no—
439C2×Q8—611no—
440C2×Q8—1221no—
441C2×Q8—1222no—
442C2×Q8C2×C4×D6111yescharacteristic
443C2×D4—1221no—
444C2×D4C2×C4×D6111yescharacteristic
445C22×C4—21no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453Q16—614no—
454Q16—614no—
455SD16—614no—
456SD16C8×D6114yescomplemented
457M16—614no—
458M16—1222no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—81no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—4881no—
471C2×C8—4881no—
472C2×C8—2442no—
473C2×C8C2×C4×D6111yescharacteristic
474C2×C8C2×C4×D6111yescharacteristic
475C2×C8D4×D6111yescharacteristic
476C2×C8D4×D6111yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—611no—
479C4⋊C4—611no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4C2×C4×D6111yescharacteristic
487C4⋊C4C2×C4×D6111yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—21no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—1221no—
496C42—1221no—
497C42—1221no—
498C42—1221no—
499C42—1221no—
500C42—1221no—
501C42C23×D6111yescharacteristic
502C23—21no—
503C23—611no—
504Q8—21no—
505Q8—612no—
506Q8—612no—
507Q8—1224no—
508Q8—1221no—
509Q8—1221no—
510Q8C2×C8×D6112yes—
511D4—21no—
512D4—1224no—
513D4C2×C8×D6112yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—611no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—1224no—
525C2×C4—1224no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—4881no—
533C2×C4—4881no—
534C2×C4—2441no—
535C2×C4C22×C4×D6111yescharacteristic
536C2×C4C2×D4×D6111yescharacteristic
537C2×C4#41×D6111yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—612no—
545C8—1222no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—2441no—
550C8—2441no—
551C8C2×C8×D6112yes—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—612no—
556C22—1221no—
557C22—1221no—
558C22C4×D4×D6111yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—612no—
564C4—1221no—
565C4—1221no—
566C4—1222no—
567C4—1222no—
568C4—2441no—
569C4—2441no—
570C4C22×C8×D6111yescharacteristic
571C4#131×D6111yescharacteristic
572C4#1684057211yescharacteristic
573C4#1684057811yescharacteristic
574C2—42no—
575C2—1222no—
576C2C8×D4×D6111yescharacteristic
577C2#2145465911yescharacteristic
578C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC4×C61C23×C8
FrattiniC42C23×D61
FittingC61×SD16⋊C8C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758224C2×C4
cosocleC42×C61C24
hypercenterSD16⋊C8D61
hypocenterC61#17853
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #21454898C2semidirect
4. #21444639C2semidirect
5. #21444635C2semidirect
6. #21444628C2semidirect
7. #21444625C2semidirect
8. C8×#11758202C2semidirect
9. SD16×#92418C2semidirect
10. C8×#11758200C2semidirect
11. #21444570C2semidirect
13. Q8⋊C8×D61C2semidirect
14. #21444098C2semidirect
15. C61×SD16⋊C8C2semidirect
69. #14519806C8semidirect
152. Q8×D61C2×C8semidirect
163. SD16×C61C2×C8semidirect
179. #11758202C2×C8semidirect
180. #11758200C2×C8semidirect
207. Dic244C2×C8semidirect
209. #11758189C2×C8semidirect
291. SD16⋊C8D61semidirect
356. C61#17853semidirect
456. SD16C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214549262
#214548982
C4×#145198062
#214446392
#214446352
#214446282
#214446252
C8×#117582022
SD16×#924182
C8×#117582002
#214445702
#214441982
Q8⋊C8×D612
#214440982
C61×SD16⋊C82
#1785361