Finite Group Databasebeta

← #49130526

Subgroups — #49130526

Order 36224.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583656C211yesmaximal, characteristic, complemented
2C2×#22583637C211yesmaximal, characteristic, complemented
3C2×D8×D283C211yesmaximal, characteristic, complemented
4#31827031C211yesmaximal, characteristic, complemented
5#31826613C211yesmaximal, characteristic, complemented
6#31826610C211yesmaximal, characteristic, complemented
7#31826609C211yesmaximal, characteristic, complemented
8#31826601C211yesmaximal, characteristic, complemented
9#31826600C211yesmaximal, characteristic, complemented
10#31826598C211yesmaximal, characteristic, complemented
11#31826597C211yesmaximal, characteristic, complemented
12#31826468C211yesmaximal, characteristic, complemented
13#31826460C211yesmaximal, characteristic, complemented
14#31826430C211yesmaximal, characteristic, complemented
15#449×C283C211yesmaximal, characteristic, complemented
16#22583656—24no—
17#22583656—24no—
18C2×#17985393C2211yescharacteristic
19C2×#17985393C2211yescharacteristic, complemented
20C2×#17985392—21no—
21C2×#17985392C2211yescharacteristic
22C22×D1132—21no—
23C22×D1132C2211yescharacteristic, complemented
24C2×D4×D283—21no—
25C2×D4×D283—21no—
26C2×D4×D283C2211yescharacteristic
27C2×D4×D283C2211yescharacteristic, complemented
28C2×D4×D283C2211yescharacteristic, complemented
29#22583637—24no—
30C2×#17985379C2211yescharacteristic, complemented
31C2×D2264C2211yescharacteristic, complemented
32C2×D2264C2211yescharacteristic, complemented
33C2×#17985377C2211yescharacteristic, complemented
34C2×#17985377C2211yescharacteristic, complemented
35C2×#17985377C2211yescharacteristic, complemented
36D8×D283—24no—
37C2×#17985375C2211yescharacteristic, complemented
38C2×C8×D283C2211yescharacteristic, complemented
39#22583606—21no—
40#22583596—21no—
41#22583585C2211yescharacteristic, complemented
42#22583584C2211yescharacteristic, complemented
43#22583581C2211yescharacteristic, complemented
44#22583580—21no—
45#22583578—21no—
46#22583568C2211yescharacteristic, complemented
47#22583534C2211yescharacteristic, complemented
48#22583532C2211yescharacteristic, complemented
49#22583532C2211yescharacteristic, complemented
50#22583531C2211yescharacteristic, complemented
51#22583530C2211yescharacteristic, 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×D283—21no—
66C23×D283—21no—
67#17985393—22no—
68#17985393—22no—
69#17985393—22no—
70#17985393D414yescomplemented
71#17985392—28no—
72#17985392—22no—
73#17985392—22no—
74C2×Dic566D411yescharacteristic
75C2×D1132—28no—
76C2×D1132—21no—
77C2×D1132—21no—
78C2×D1132—22no—
79C2×D1132—22no—
80C2×D1132—21no—
81C2×D1132—21no—
82C2×D1132D411yescharacteristic
83C2×D1132C2311yescharacteristic
84C2×D1132C2311yescharacteristic
85C2×D1132C2311yescharacteristic
86C2×C22⋊D283—21no—
87C2×C22⋊D283—21no—
88C2×C22⋊D283—21no—
89C2×C22⋊D283—21no—
90C2×C22⋊D283—21no—
91C2×C22⋊D283D411yescharacteristic
92C2×C22⋊D283D411yescharacteristic
93D4×D283—28no—
94D4×D283—28no—
95D4×D283—22no—
96D4×D283—22no—
97D4×D283—22no—
98D4×D283—22no—
99D4×D283—22no—
100D4×D283D414yescomplemented
101C2×C4×D283—21no—
102C2×C4×D283—21no—
103C2×C4×D283C2311yescharacteristic
104C2×C4×D283C2311yescharacteristic
105#17985379—22no—
106D2264—22no—
107D2264—22no—
108#17985377—22no—
109#17985377—22no—
110#17985377—22no—
111#17985375—22no—
112C2×C283⋊C8C2311yescharacteristic
113C2×C283⋊C8C2311yescharacteristic
114C8×D283—22no—
115C4⋊Dic283C2311yescharacteristic
116C22⋊Dic283—21no—
117(C2×D283)⋊C4—21no—
118(C2×D283)⋊C4—21no—
119(C2×D283)⋊C4—21no—
120C4×Dic283—21no—
121#41×C283—22no—
122#41×C283—22no—
123C2×Q8×C283C2311yescharacteristic
124C2×D4×C283—21no—
125C2×D4×C283—21no—
126C2×D4×C283C2311yescharacteristic
127C2×D4×C283C2311yescharacteristic
128C22×C4×C283—21no—
129C22×C4×C283C2311yescharacteristic
130SD16×C283—22no—
131D8×C283—22no—
132C2×C8×C283C2311yescharacteristic
133C2×C8×C283C2311yescharacteristic
134C4⋊C4×C283C2311yescharacteristic
135C22⋊C4×C283—21no—
136C22×D283—21no—
137C22×D283—21no—
138C22×D283—24no—
139C22×D283—24no—
140C22×D283—24no—
141C22×D283—21no—
142C22×D283—42no—
143C22×D283—81no—
144C22×D283—81no—
145C22×D283—81no—
146C22×D283—81no—
147C22×D283—81no—
148C22×D283—81no—
149C22×D283—81no—
150C22×D283—81no—
151C22×D283C2×D411yescharacteristic
152C22×D283C2×D411yescharacteristic
153Dic566—22no—
154D1132—24no—
155D1132—24no—
156D1132—24no—
157D1132—22no—
158D1132—21no—
159D1132—21no—
160D1132—21no—
161D1132—21no—
162D1132—81no—
163D1132C2×D412yes—
164D1132C2×D412yes—
165C22⋊D283—24no—
166C22⋊D283—22no—
167C22⋊D283—22no—
168C22⋊D283—24no—
169C22⋊D283—42no—
170C22⋊D283—81no—
171C22⋊D283—81no—
172C2×Dic283—21no—
173C2×Dic283C2×D411yescharacteristic
174C2×Dic283C2×D411yescharacteristic
175C4×D283—24no—
176C4×D283—21no—
177C4×D283—21no—
178C4×D283—24no—
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×D412yes—
188D4×C283—24no—
189D4×C283—21no—
190D4×C283—21no—
191D4×C283—21no—
192D4×C283—81no—
193D4×C283C2×D412yes—
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—22no—
217C2×D283—22no—
218C2×D283—21no—
219C2×D283—21no—
220C2×D283—41no—
221C2×D283—41no—
222C2×D283—41no—
223C2×D283—41no—
224C2×D283—41no—
225C2×D283—41no—
226C2×D283—41no—
227C2×D283—84no—
228C2×D283—84no—
229C2×D283—84no—
230C2×D283—84no—
231C2×D283#12012yes—
232C4×C283—21no—
233C4×C283—22no—
234C4×C283—41no—
235C4×C283C22×D411yescharacteristic
236C4×C283C22×D411yescharacteristic
237Dic283—21no—
238Dic283—41no—
239Dic283#12012yes—
240C2×C283—41no—
241C2×C283—42no—
242C2×C283—81no—
243C2×C283C2×#12011yescharacteristic
244C2×C283#57611yescharacteristic
245C2×C283#57611yescharacteristic
246D283—22no—
247D283—41no—
248D283—42no—
249D283—42no—
250D283—81no—
251C283#300811yescharacteristic, complemented, Sylow
252#3008—2831nomaximal, Sylow
253C2×H(5,𝔽2)—2831no—
254C2×AGL(1,ℤ/8)—2831no—
255C22×D8—2831no—
256#535—2831no—
257#449—2831no—
258#449—2831no—
259#449—2831no—
260#449D28311yescharacteristic, complemented
261#447—2831no—
262#447—2831no—
263#447—2831no—
264#447—2831no—
265#418—2831no—
266#416—2831no—
267#408—2831no—
268H(5,𝔽2)—5664no—
269H(5,𝔽2)—5664no—
270C2×#41—2831no—
271C2×#41—2831no—
272C2×#41—2831no—
273C2×#41—5661no—
274C2×#41C2×D28311yescharacteristic, complemented
275C22×D4—2831no—
276C22×D4—2831no—
277C22×D4—2831no—
278C22×D4—2831no—
279C22×D4—5661no—
280C22×D4—5661no—
281C22×D4—5661no—
282AGL(1,ℤ/8)—5664no—
283C2×SD16—2831no—
284C2×SD16C2×D28311yescharacteristic, complemented
285C2×D8—2831no—
286C2×D8—2831no—
287C2×D8—2831no—
288C2×D8—2831no—
289C2×D8—2831no—
290C2×D8—5664no—
291C2×D8C2×D28311yescharacteristic, complemented
292C2×M16—2831no—
293C22×C8—2831no—
294#127—5661no—
295#124—5661no—
296#121—2831no—
297#121—2831no—
298#121—2831no—
299#121C2×D28311yescharacteristic, complemented
300#120—5661no—
301#120—5661no—
302#117—2831no—
303#103—2831no—
304#103C2×D28311yescharacteristic, complemented
305#102—2831no—
306#102—2831no—
307#102—2831no—
308#102—2831no—
309#102—2831no—
310#102C2×D28311yescharacteristic, complemented
311C22⋊C8—2831no—
312C22⋊C8—2831no—
313C22⋊C8—2831no—
314C22⋊C8C2×D28311yescharacteristic, complemented
315C24—5661no—
316C24—5661no—
317C24—5661no—
318C24—5661no—
319#41—22no—
320#41—22no—
321#41—2834no—
322#41—5662no—
323#41—5662no—
324#41—5668no—
325#41—5662no—
326#41—5662no—
327#41—5662no—
328C2×Q8—2831no—
329C2×Q8C22×D28311yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—2834no—
333C2×D4—2831no—
334C2×D4—2831no—
335C2×D4—2831no—
336C2×D4—2831no—
337C2×D4—2831no—
338C2×D4—2831no—
339C2×D4—5662no—
340C2×D4—5662no—
341C2×D4—5661no—
342C2×D4—5661no—
343C2×D4—5668no—
344C2×D4—5661no—
345C2×D4—5662no—
346C2×D4—5662no—
347C2×D4—5662no—
348C2×D4—5661no—
349C2×D4—5661no—
350C2×D4—5661no—
351C2×D4—5662no—
352C2×D4—5668no—
353C2×D4—5668no—
354C2×D4—5662no—
355C2×D4—5661no—
356C2×D4—5661no—
357C2×D4—5661no—
358C2×D4C22×D28311yescharacteristic
359C2×D4C22×D28311yescharacteristic
360C22×C4—21no—
361C22×C4—2831no—
362C22×C4—2831no—
363C22×C4—5661no—
364C22×C4—5661no—
365C22×C4C22×D28311yescharacteristic
366SD16—22no—
367SD16—5662no—
368D8—22no—
369D8—5662no—
370D8—5662no—
371D8—5662no—
372D8—5662no—
373D8—5662no—
374M16—5662no—
375C2×C8—2831no—
376C2×C8—2831no—
377C2×C8—5662no—
378C2×C8C22×D28311yescharacteristic
379C2×C8C22×D28311yescharacteristic
380C4⋊C4—2831no—
381C4⋊C4C22×D28311yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—5661no—
384C22⋊C4—5661no—
385C22⋊C4—5661no—
386C22⋊C4—5661no—
387C42—5661no—
388C23—21no—
389C23—21no—
390C23—2831no—
391C23—2831no—
392C23—5664no—
393C23—5664no—
394C23—5664no—
395C23—5661no—
396C23—5661no—
397C23—5661no—
398C23—11322no—
399C23—22641no—
400C23—22641no—
401C23—22641no—
402C23—22641no—
403C23—22641no—
404C23—22641no—
405C23—22641no—
406C23—22641no—
407C23D4×D28311yescharacteristic
408Q8—21no—
409Q8—5662no—
410Q8D4×D28312yes—
411D4—24no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—81no—
416D4—2832no—
417D4—2832no—
418D4—5662no—
419D4—5664no—
420D4—5664no—
421D4—5664no—
422D4—5662no—
423D4—5664no—
424D4—5662no—
425D4—5664no—
426D4—5661no—
427D4—5661no—
428D4—5661no—
429D4—5661no—
430D4—11322no—
431D4—22641no—
432D4—22641no—
433D4—22641no—
434D4D4×D28312yes—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—2831no—
441C2×C4—2832no—
442C2×C4—2832no—
443C2×C4—2831no—
444C2×C4—5664no—
445C2×C4—5664no—
446C2×C4—5661no—
447C2×C4—5661no—
448C2×C4—5661no—
449C2×C4D4×D28311yescharacteristic
450C2×C4C23×D28311yescharacteristic
451C8—21no—
452C8—21no—
453C8—5661no—
454C8—5661no—
455C22—21no—
456C22—22no—
457C22—21no—
458C22—21no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—2832no—
465C22—5661no—
466C22—5661no—
467C22—5662no—
468C22—5662no—
469C22—5661no—
470C22—5661no—
471C22—5661no—
472C22—11321no—
473C22—11321no—
474C22—11321no—
475C22—11321no—
476C22—11321no—
477C22—11321no—
478C22—11321no—
479C22—22644no—
480C22—22644no—
481C22—22644no—
482C22—22644no—
483C22C2×D4×D28311yescharacteristic
484C4—21no—
485C4—22no—
486C4—41no—
487C4—2832no—
488C4—5661no—
489C4—11321no—
490C4C2×D4×D28311yescharacteristic
491C4C2×D4×D28311yescharacteristic
492C2—41no—
493C2—42no—
494C2—81no—
495C2—5662no—
496C2—11321no—
497C2—11322no—
498C2—11322no—
499C2—22641no—
500C2#120×D28311yescharacteristic
501C2#3182726711yescharacteristic
502C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#449×C283C2
socleC22×C283C22×D4
hypercenter#449D283
hypocenterC283#3008
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×#22583656C2semidirect
2. C2×#22583637C2semidirect
3. C2×D8×D283C2semidirect
4. #31827031C2semidirect
5. #31826613C2semidirect
6. #31826610C2semidirect
7. #31826609C2semidirect
8. #31826601C2semidirect
9. #31826600C2semidirect
10. #31826598C2semidirect
11. #31826597C2semidirect
12. #31826468C2semidirect
13. #31826460C2semidirect
14. #31826430C2semidirect
15. #449×C283C2semidirect
19. C2×#17985393C22semidirect
23. C22×D1132C22semidirect
27. C2×D4×D283C22semidirect
28. C2×D4×D283C22semidirect
30. C2×#17985379C22semidirect
31. C2×D2264C22semidirect
32. C2×D2264C22semidirect
33. C2×#17985377C22semidirect
34. C2×#17985377C22semidirect
35. C2×#17985377C22semidirect
37. C2×#17985375C22semidirect
38. C2×C8×D283C22semidirect
41. #22583585C22semidirect
42. #22583584C22semidirect
43. #22583581C22semidirect
46. #22583568C22semidirect
47. #22583534C22semidirect
48. #22583532C22semidirect
49. #22583532C22semidirect
50. #22583531C22semidirect
51. #22583530C22semidirect
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
70. #17985393D4semidirect
100. D4×D283D4semidirect
251. C283#3008semidirect
260. #449D283semidirect
274. C2×#41C2×D283semidirect
284. C2×SD16C2×D283semidirect
291. C2×D8C2×D283semidirect
299. #121C2×D283semidirect
304. #103C2×D283semidirect
310. #102C2×D283semidirect
314. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836562
C2×#225836372
C2×D8×D2832
#318270312
#318266132
#318266102
#318266092
#318266012
#318266002
#318265982
#318265972
#318264682
#318264602
#318264302
#449×C2832
#3008283