Finite Group Databasebeta

← #49130510

Subgroups — #49130510

Order 36224.

806 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D283C211yesmaximal, characteristic, complemented
2C2×#22583637C211yesmaximal, characteristic, complemented
3C2×#22583634C211yesmaximal, characteristic, complemented
4#121×D283C211yesmaximal, characteristic, complemented
5#31826612C211yesmaximal, characteristic, complemented
6#31826610C211yesmaximal, characteristic, complemented
7#31826608C211yesmaximal, characteristic, complemented
8#31826605C211yesmaximal, characteristic, complemented
9#31826602C211yesmaximal, characteristic, complemented
10#31826600C211yesmaximal, characteristic, complemented
11#31826597C211yesmaximal, characteristic, complemented
12#31826465C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic, complemented
14#31826427C211yesmaximal, characteristic, complemented
15#449×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985392—21no—
18C2×#17985392C2211yescharacteristic, complemented
19C2×#17985391—21no—
20C2×#17985391C2211yescharacteristic
21#41×D283—24no—
22#41×D283—24no—
23C2×Q8×D283C2211yescharacteristic, complemented
24C2×D4×D283—21no—
25C2×D4×D283—21no—
26C2×D4×D283C2211yescharacteristic, complemented
27C2×D4×D283C2211yescharacteristic, complemented
28C22×C4×D283—21no—
29C22×C4×D283C2211yescharacteristic
30#22583637—24no—
31#22583634—24no—
32C2×#17985381C2211yescharacteristic, complemented
33C2×#17985380C2211yescharacteristic, complemented
34C2×#17985379C2211yescharacteristic, complemented
35C2×D2264C2211yescharacteristic, complemented
36C2×#17985377C2211yescharacteristic, complemented
37C2×#17985377C2211yescharacteristic, complemented
38C2×#17985375C2211yescharacteristic, complemented
39C2×#17985375C2211yescharacteristic, complemented
40#22583585C2211yescharacteristic
41#22583584C2211yescharacteristic, complemented
42#22583583—21no—
43#22583582—21no—
44#22583581C2211yescharacteristic
45C4⋊C4×D283C2211yescharacteristic, complemented
46C22⋊C4×D283—21no—
47#22583535C2211yescharacteristic, complemented
48#22583534C2211yescharacteristic, complemented
49#22583533C2211yescharacteristic, complemented
50#22583532C2211yescharacteristic, complemented
51#22583531C2211yescharacteristic, complemented
52#22583530C2211yescharacteristic, complemented
53C22⋊(C283⋊C8)C2211yescharacteristic, complemented
54(C2×D283)⋊C8C2211yescharacteristic, complemented
55(C2×D283)⋊C8C2211yescharacteristic, complemented
56C2×#41×C283C2211yescharacteristic, complemented
57C2×SD16×C283C2211yescharacteristic, complemented
58C2×D8×C283C2211yescharacteristic, complemented
59#121×C283C2211yescharacteristic, complemented
60#103×C283C2211yescharacteristic, complemented
61#102×C283C2211yescharacteristic, complemented
62C22⋊C8×C283C2211yescharacteristic, complemented
63C23×D283—21no—
64C23×D283—21no—
65C23×D283D411yescharacteristic
66#17985393—22no—
67#17985393D414yescomplemented
68#17985392—28no—
69#17985392—22no—
70#17985392—22no—
71#17985391—28no—
72#17985391—22no—
73#17985391D414yescomplemented
74C2×Dic566—21no—
75C2×Dic566C2311yescharacteristic
76Q8×D283—22no—
77Q8×D283—22no—
78C2×D1132—21no—
79C2×D1132—21no—
80C2×D1132C2311yescharacteristic
81C2×D1132C2311yescharacteristic
82C2×C22⋊D283—21no—
83C2×C22⋊D283—21no—
84C2×C22⋊D283—21no—
85C2×C22⋊D283—21no—
86C2×C22⋊D283—21no—
87C2×C22⋊D283—21no—
88D4×D283—28no—
89D4×D283—22no—
90D4×D283—22no—
91D4×D283—22no—
92D4×D283—22no—
93D4×D283—44no—
94C22×Dic283—21no—
95C22×Dic283D411yescharacteristic
96C2×C4×D283—28no—
97C2×C4×D283—21no—
98C2×C4×D283—21no—
99C2×C4×D283—22no—
100C2×C4×D283—22no—
101C2×C4×D283—21no—
102C2×C4×D283—21no—
103C2×C4×D283D411yescharacteristic
104C2×C4×D283D411yescharacteristic
105C2×C4×D283C2311yescharacteristic
106C2×C4×D283C2311yescharacteristic
107#17985381—22no—
108#17985380—22no—
109#17985379—22no—
110D2264—22no—
111#17985377—22no—
112#17985377—22no—
113#17985375—22no—
114#17985375—22no—
115C2×C283⋊C8C2311yescharacteristic
116C2×C283⋊C8C2311yescharacteristic
117C4⋊Dic283C2311yescharacteristic
118Dic283⋊C4—21no—
119C22⋊Dic283—21no—
120(C2×D283)⋊C4—21no—
121(C2×D283)⋊C4—21no—
122#41×C283—22no—
123#41×C283—22no—
124C2×Q8×C283C2311yescharacteristic
125C2×D4×C283—21no—
126C2×D4×C283—21no—
127C2×D4×C283C2311yescharacteristic
128C2×D4×C283C2311yescharacteristic
129C22×C4×C283—21no—
130C22×C4×C283C2311yescharacteristic
131SD16×C283—22no—
132D8×C283—22no—
133C2×C8×C283C2311yescharacteristic
134C2×C8×C283C2311yescharacteristic
135C4⋊C4×C283C2311yescharacteristic
136C22⋊C4×C283—21no—
137C22×D283—24no—
138C22×D283—21no—
139C22×D283—22no—
140C22×D283—22no—
141C22×D283—21no—
142C22×D283—41no—
143C22×D283—42no—
144C22×D283—42no—
145C22×D283—42no—
146C22×D283—42no—
147C22×D283—42no—
148C22×D283C2×D411yescharacteristic
149C22×D283C2×D411yescharacteristic
150Dic566—24no—
151Dic566—21no—
152Dic566C2×D412yescomplemented
153D1132—24no—
154D1132—21no—
155D1132—21no—
156D1132—21no—
157D1132—42no—
158D1132C2×D412yescomplemented
159C22⋊D283—24no—
160C22⋊D283—24no—
161C22⋊D283—24no—
162C22⋊D283—42no—
163C22⋊D283—42no—
164C22⋊D283—42no—
165C2×Dic283—21no—
166C2×Dic283—24no—
167C2×Dic283—22no—
168C2×Dic283—21no—
169C2×Dic283C2×D411yescharacteristic
170C2×Dic283C2×D411yescharacteristic
171C4×D283—24no—
172C4×D283—24no—
173C4×D283—22no—
174C4×D283—21no—
175C4×D283—21no—
176C4×D283—22no—
177C4×D283—24no—
178C4×D283—42no—
179C4×D283C2×D412yes—
180C4×D283C2×D412yes—
181C283⋊C8—21no—
182C283⋊C8—21no—
183C23×C283—21no—
184C23×C283—21no—
185C23×C283C2×D411yescharacteristic
186Q8×C283—21no—
187Q8×C283C2×D412yescomplemented
188D4×C283—24no—
189D4×C283—21no—
190D4×C283—21no—
191D4×C283—21no—
192D4×C283—42no—
193D4×C283C2×D412yescomplemented
194C2×C4×C283—24no—
195C2×C4×C283—21no—
196C2×C4×C283—21no—
197C2×C4×C283—21no—
198C2×C4×C283—21no—
199C2×C4×C283C2×D411yescharacteristic
200C2×C4×C283C2411yescharacteristic
201C8×C283—21no—
202C8×C283—21no—
203C22×C283—21no—
204C22×C283—22no—
205C22×C283—21no—
206C22×C283—21no—
207C22×C283—41no—
208C22×C283—41no—
209C22×C283—41no—
210C22×C283—41no—
211C22×C283—41no—
212C22×C283C22×D411yescharacteristic
213C2×D283—21no—
214C2×D283—21no—
215C2×D283—21no—
216C2×D283—21no—
217C2×D283—22no—
218C2×D283—44no—
219C2×D283—48no—
220C2×D283—41no—
221C2×D283—41no—
222C2×D283—41no—
223C2×D283—41no—
224C2×D283—41no—
225C2×D283—84no—
226C2×D283#12012yes—
227C2×D283AGL(1,ℤ/8)12yescomplemented
228C4×C283—21no—
229C4×C283—22no—
230C4×C283—41no—
231C4×C283C22×D411yescharacteristic
232C4×C283C22×D411yescharacteristic
233Dic283—22no—
234Dic283—21no—
235Dic283—41no—
236Dic283#12012yes—
237C2×C283—41no—
238C2×C283—42no—
239C2×C283—81no—
240C2×C283C2×#12011yescharacteristic
241C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
242C2×C283#57511yescharacteristic
243D283—22no—
244D283—22no—
245D283—42no—
246D283—81no—
247C283#300611yescharacteristic, complemented, Sylow
248#3006—2831nomaximal, Sylow
249C22×#41—2831no—
250C2×AGL(1,ℤ/8)—2831no—
251C2×AGL(1,ℤ/8)—2831no—
252C2×#121—2831no—
253#449—2831no—
254#449—2831no—
255#449—2831no—
256#449D28311yescharacteristic, complemented
257#448—2831no—
258#448—2831no—
259#447—2831no—
260#447—2831no—
261#417—2831no—
262#417—2831no—
263#407—2831no—
264C2×#41—2831no—
265C2×#41—2831no—
266C2×#41—2831no—
267C2×#41—5661no—
268C2×#41—5661no—
269C2×#41—5664no—
270C2×#41—5664no—
271C2×#41C2×D28311yescharacteristic, complemented
272C22×Q8—2831no—
273C22×D4—2831no—
274C22×D4—2831no—
275C22×D4—5661no—
276C22×D4—5661no—
277C23×C4—2831no—
278C23×C4—5661no—
279AGL(1,ℤ/8)—5664no—
280AGL(1,ℤ/8)—5664no—
281C2×SD16—2831no—
282C2×SD16—2831no—
283C2×SD16—2831no—
284C2×SD16C2×D28311yescharacteristic, complemented
285C2×D8—2831no—
286C2×D8—2831no—
287C2×D8—2831no—
288C2×D8C2×D28311yescharacteristic, complemented
289C2×M16—2831no—
290C2×M16—2831no—
291#121—2831no—
292#121—2831no—
293#121—2831no—
294#121—5661no—
295#121—5661no—
296#121C2×D28311yescharacteristic, complemented
297C2×C4⋊C4—2831no—
298C2×C22⋊C4—5661no—
299#103—2831no—
300#103—2831no—
301#103—2831no—
302#103C2×D28311yescharacteristic, complemented
303#102—2831no—
304#102—2831no—
305#102—2831no—
306#102C2×D28311yescharacteristic, complemented
307C22⋊C8—2831no—
308C22⋊C8—2831no—
309C22⋊C8—2831no—
310C22⋊C8C2×D28311yescharacteristic, complemented
311C24—2831no—
312C24—5661no—
313C24—5661no—
314#41—22no—
315#41—22no—
316#41—2834no—
317#41—2834no—
318#41—5662no—
319#41—5662no—
320#41—5668no—
321#41—5662no—
322#41—5662no—
323#41—5668no—
324C2×Q8—2831no—
325C2×Q8—5661no—
326C2×Q8—5662no—
327C2×Q8—5662no—
328C2×Q8C22×D28311yescharacteristic
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—2831no—
332C2×D4—2831no—
333C2×D4—5661no—
334C2×D4—5661no—
335C2×D4—5662no—
336C2×D4—5662no—
337C2×D4—5661no—
338C2×D4—5661no—
339C2×D4—5662no—
340C2×D4—5668no—
341C2×D4—5661no—
342C2×D4—5661no—
343C2×D4—5662no—
344C2×D4—5661no—
345C2×D4—5661no—
346C2×D4—11324no—
347C2×D4C22×D28311yescharacteristic
348C2×D4C22×D28311yescharacteristic
349C22×C4—21no—
350C22×C4—2831no—
351C22×C4—2831no—
352C22×C4—2831no—
353C22×C4—2831no—
354C22×C4—2831no—
355C22×C4—5662no—
356C22×C4—5662no—
357C22×C4—5661no—
358C22×C4—5661no—
359C22×C4—5668no—
360C22×C4—5661no—
361C22×C4—5661no—
362C22×C4—5661no—
363C22×C4C22×D28311yescharacteristic
364SD16—22no—
365SD16—5662no—
366SD16—5662no—
367SD16—5662no—
368D8—22no—
369D8—5662no—
370D8—5662no—
371D8—5662no—
372M16—5662no—
373M16—5662no—
374C2×C8—2831no—
375C2×C8—2831no—
376C2×C8C22×D28311yescharacteristic
377C2×C8C22×D28311yescharacteristic
378C4⋊C4—2831no—
379C4⋊C4—5661no—
380C4⋊C4C22×D28311yescharacteristic
381C22⋊C4—21no—
382C22⋊C4—5661no—
383C22⋊C4—5661no—
384C22⋊C4—5661no—
385C23—21no—
386C23—21no—
387C23—2831no—
388C23—2831no—
389C23—5662no—
390C23—5662no—
391C23—5664no—
392C23—5661no—
393C23—5661no—
394C23—11321no—
395C23—11322no—
396C23—11322no—
397C23—11322no—
398C23—11322no—
399C23—11322no—
400C23D4×D28311yescharacteristic
401Q8—21no—
402Q8—2832no—
403Q8—5664no—
404Q8—5661no—
405Q8D4×D28312yescomplemented
406D4—24no—
407D4—21no—
408D4—21no—
409D4—21no—
410D4—42no—
411D4—2832no—
412D4—5664no—
413D4—5664no—
414D4—5664no—
415D4—5664no—
416D4—5661no—
417D4—5661no—
418D4—5661no—
419D4—11322no—
420D4—11322no—
421D4—11322no—
422D4—11322no—
423D4D4×D28312yescomplemented
424C2×C4—24no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—2831no—
430C2×C4—2832no—
431C2×C4—2832no—
432C2×C4—2831no—
433C2×C4—5662no—
434C2×C4—5664no—
435C2×C4—5662no—
436C2×C4—5664no—
437C2×C4—5664no—
438C2×C4—5662no—
439C2×C4—5664no—
440C2×C4—5661no—
441C2×C4—5661no—
442C2×C4—5661no—
443C2×C4—5661no—
444C2×C4—11322no—
445C2×C4D4×D28311yescharacteristic
446C2×C4C23×D28311yescharacteristic
447C8—21no—
448C8—21no—
449C8—5661no—
450C8—5661no—
451C22—21no—
452C22—22no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—2832no—
461C22—2832no—
462C22—5661no—
463C22—5661no—
464C22—5661no—
465C22—5661no—
466C22—5662no—
467C22—11324no—
468C22—11328no—
469C22—11321no—
470C22—11321no—
471C22—11321no—
472C22—11321no—
473C22—11321no—
474C22—22644no—
475C22C2×D4×D28311yescharacteristic
476C4—21no—
477C4—22no—
478C4—41no—
479C4—2832no—
480C4—5661no—
481C4—5662no—
482C4—11321no—
483C4C2×D4×D28311yescharacteristic
484C4C2×D4×D28311yescharacteristic
485C2—41no—
486C2—42no—
487C2—81no—
488C2—5662no—
489C2—5662no—
490C2—11322no—
491C2—22641no—
492C2#120×D28311yescharacteristic
493C2AGL(1,ℤ/8)×D28311yescharacteristic
494C2#3182726211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#449×C283C2
socleC22×C283C22×D4
hypercenter#449D283
hypocenterC283#3006
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#41×D283C2semidirect
2. C2×#22583637C2semidirect
3. C2×#22583634C2semidirect
4. #121×D283C2semidirect
5. #31826612C2semidirect
6. #31826610C2semidirect
7. #31826608C2semidirect
8. #31826605C2semidirect
9. #31826602C2semidirect
10. #31826600C2semidirect
11. #31826597C2semidirect
12. #31826465C2semidirect
13. #31826463C2semidirect
14. #31826427C2semidirect
15. #449×C283C2semidirect
18. C2×#17985392C22semidirect
23. C2×Q8×D283C22semidirect
26. C2×D4×D283C22semidirect
27. C2×D4×D283C22semidirect
32. C2×#17985381C22semidirect
33. C2×#17985380C22semidirect
34. C2×#17985379C22semidirect
35. C2×D2264C22semidirect
36. C2×#17985377C22semidirect
37. C2×#17985377C22semidirect
38. C2×#17985375C22semidirect
39. C2×#17985375C22semidirect
41. #22583584C22semidirect
45. C4⋊C4×D283C22semidirect
47. #22583535C22semidirect
48. #22583534C22semidirect
49. #22583533C22semidirect
50. #22583532C22semidirect
51. #22583531C22semidirect
52. #22583530C22semidirect
53. C22⋊(C283⋊C8)C22semidirect
54. (C2×D283)⋊C8C22semidirect
55. (C2×D283)⋊C8C22semidirect
56. C2×#41×C283C22semidirect
57. C2×SD16×C283C22semidirect
58. C2×D8×C283C22semidirect
59. #121×C283C22semidirect
60. #103×C283C22semidirect
61. #102×C283C22semidirect
62. C22⋊C8×C283C22semidirect
67. #17985393D4semidirect
73. #17985391D4semidirect
152. Dic566C2×D4semidirect
158. D1132C2×D4semidirect
187. Q8×C283C2×D4semidirect
193. D4×C283C2×D4semidirect
227. C2×D283AGL(1,ℤ/8)semidirect
247. C283#3006semidirect
256. #449D283semidirect
271. C2×#41C2×D283semidirect
284. C2×SD16C2×D283semidirect
288. C2×D8C2×D283semidirect
296. #121C2×D283semidirect
302. #103C2×D283semidirect
306. #102C2×D283semidirect
310. C22⋊C8C2×D283semidirect
405. Q8D4×D283semidirect
423. D4D4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2832
C2×#225836372
C2×#225836342
#121×D2832
#318266122
#318266102
#318266082
#318266052
#318266022
#318266002
#318265972
#318264652
#318264632
#318264272
#449×C2832
#3006283