Finite Group Databasebeta

← #49133041

Subgroups — #49133041

Order 36224.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827280C211yesmaximal, characteristic, complemented
2#31827272C211yesmaximal, characteristic, complemented
3#31827268C211yesmaximal, characteristic, complemented
4#31826846C211yesmaximal, characteristic, complemented
5#31826738C211yesmaximal, characteristic, complemented
6#31826733C211yesmaximal, characteristic, complemented
7#31826728C211yesmaximal, characteristic, complemented
8#31826725C211yesmaximal, characteristic, complemented
9#31826643C211yesmaximal, characteristic, complemented
10#31826641C211yesmaximal, characteristic, complemented
11#31826638C211yesmaximal, characteristic, complemented
12#31826636C211yesmaximal, characteristic, complemented
13#31826582C211yesmaximal, characteristic, complemented
14#31826580C211yesmaximal, characteristic, complemented
15#577×C283C211yesmaximal, characteristic, complemented
16#22583657C2211yescharacteristic, complemented
17#22583656C2211yescharacteristic
18#22583642—21no—
19#22583641—21no—
20#22583641C2211yescharacteristic, complemented
21#22583640—21no—
22#22583640C2211yescharacteristic
23#22583640C2211yescharacteristic, complemented
24#22583636—21no—
25#22583636C2211yescharacteristic
26#22583635—21no—
27#22583635C2211yescharacteristic
28#22583635C2211yescharacteristic, complemented
29#22583634—21no—
30#22583631—21no—
31#22583630—21no—
32#22583630—21no—
33#22583630C2211yescharacteristic
34C2×#17985382—21no—
35C2×#17985382C2211yescharacteristic, complemented
36C2×#17985381C2211yescharacteristic, complemented
37SD16×D283—21no—
38C2×#17985377—21no—
39C2×#17985377C2211yescharacteristic
40#22583617C2211yescharacteristic
41#22583617C2211yescharacteristic, complemented
42#22583616C2211yescharacteristic, complemented
43#22583599C2211yescharacteristic, complemented
44#22583597C2211yescharacteristic, complemented
45#22583546C2211yescharacteristic, complemented
46#22583545C2211yescharacteristic, complemented
47#22583537C2211yescharacteristic
48#22583537C2211yescharacteristic, complemented
49#22583537C2211yescharacteristic, complemented
50#22583536C2211yescharacteristic, complemented
51#22583529C2211yescharacteristic, complemented
52#22583528C2211yescharacteristic, complemented
53#22583527C2211yescharacteristic, complemented
54#22583526C2211yescharacteristic, complemented
55C8×Dic283C2211yescharacteristic, complemented
562−1+4×C283C2211yescharacteristic, complemented
57H(5,𝔽2)×C283C2211yescharacteristic
58#137×C283—21no—
59#137×C283C2211yescharacteristic
60AGL(1,ℤ/8)×C283—21no—
61AGL(1,ℤ/8)×C283C2211yescharacteristic, complemented
62#135×C283—21no—
63#135×C283C2211yescharacteristic
64C2×SD16×C283—21no—
65C2×SD16×C283C2211yescharacteristic, complemented
66#131×C283C2211yescharacteristic, complemented
67#17985393—21no—
68#17985392—21no—
69#17985392—21no—
70#17985392C2311yescharacteristic
71#17985391—21no—
72#17985391—41no—
73C2×Dic566—21no—
74C2×Dic566C2311yescharacteristic
75Q8×D283—21no—
76C2×D1132—21no—
77C2×D1132C2311yescharacteristic
78D4×D283—21no—
79D4×D283—41no—
80#17985382—21no—
81#17985382—21no—
82#17985382—21no—
83#17985382—21no—
84#17985382—21no—
85#17985382D411yescharacteristic
86#17985381—21no—
87#17985381—21no—
88#17985380—21no—
89#17985380—21no—
90#17985380—21no—
91#17985380D411yescharacteristic
92#17985379—21no—
93#17985379—21no—
94#17985379—21no—
95#17985379D411yescharacteristic
96#17985377—21no—
97#17985377—21no—
98#17985377—21no—
99#17985377—21no—
100#17985377—21no—
101#17985377D411yescharacteristic
102#17985376—21no—
103#17985376—21no—
104#17985376C2311yescharacteristic
105#17985376C2311yescharacteristic
106#17985376C2311yescharacteristic
107#17985375—21no—
108C2×C283⋊C8—21no—
109C2×C283⋊C8—21no—
110C2×C283⋊C8C2311yescharacteristic
111C8×D283—21no—
112C22⋊Dic283—41no—
113(C2×D283)⋊C4—41no—
114C4×Dic283C2311yescharacteristic
115#41×C283—21no—
116#41×C283—21no—
117#41×C283—21no—
118#41×C283—21no—
119#41×C283—41no—
120#41×C283C2311yescharacteristic
121#41×C283C2311yescharacteristic
122#41×C283C2311yescharacteristic
123C2×Q8×C283—21no—
124C2×Q8×C283—21no—
125C2×Q8×C283C2311yescharacteristic
126C2×D4×C283—21no—
127C2×D4×C283—21no—
128C2×D4×C283—41no—
129C2×D4×C283C2311yescharacteristic
130Q16×C283—21no—
131Q16×C283D411yescharacteristic
132SD16×C283—21no—
133SD16×C283—21no—
134SD16×C283—21no—
135SD16×C283—21no—
136SD16×C283D411yescharacteristic
137SD16×C283D411yescharacteristic
138D8×C283—21no—
139D8×C283D411yescharacteristic
140M16×C283—21no—
141M16×C283C2311yescharacteristic
142C2×C8×C283—21no—
143C2×C8×C283C2311yescharacteristic
144C22×D283—21no—
145C22×D283—41no—
146Dic566—21no—
147Dic566—21no—
148Dic566—41no—
149Dic566C2×D411yescharacteristic
150D1132—21no—
151D1132—21no—
152D1132—41no—
153D1132C2×D411yescharacteristic
154C22⋊D283—21no—
155C22⋊D283—41no—
156C22⋊D283—41no—
157C2×Dic283—21no—
158C2×Dic283—21no—
159C2×Dic283—41no—
160C4×D283—21no—
161C4×D283—41no—
162C4×D283—41no—
163C283⋊C8—21no—
164C283⋊C8—21no—
165C283⋊C8—21no—
166C283⋊C8C2×D411yescharacteristic
167C283⋊C8C2×D411yescharacteristic
168C23×C283—21no—
169C23×C283—41no—
170Q8×C283—21no—
171Q8×C283—21no—
172Q8×C283—41no—
173Q8×C283C2×D411yescharacteristic
174Q8×C283C2×D411yescharacteristic
175Q8×C283C2×D411yescharacteristic
176D4×C283—21no—
177D4×C283—21no—
178D4×C283—21no—
179D4×C283—21no—
180D4×C283—21no—
181D4×C283—41no—
182D4×C283—41no—
183D4×C283—41no—
184D4×C283C2×D411yescharacteristic
185D4×C283C2×D411yescharacteristic
186D4×C283C2×D411yescharacteristic
187C2×C4×C283—21no—
188C2×C4×C283—21no—
189C2×C4×C283—21no—
190C2×C4×C283—21no—
191C2×C4×C283—41no—
192C2×C4×C283—41no—
193C2×C4×C283—41no—
194C2×C4×C283C2411yescharacteristic
195C8×C283—21no—
196C8×C283C2×D411yescharacteristic
197C8×C283C2×D411yescharacteristic
198C22×C283—21no—
199C22×C283—21no—
200C22×C283—21no—
201C22×C283—41no—
202C22×C283—81no—
203C22×C283—161no—
204C22×C283H(5,𝔽2)11yescharacteristic
205C2×D283—21no—
206C2×D283—41no—
207C2×D283—81no—
208C2×D283—161no—
209C4×C283—21no—
210C4×C283—21no—
211C4×C283—21no—
212C4×C283—41no—
213C4×C283C22×D411yescharacteristic
214C4×C283C22×D411yescharacteristic
215Dic283—21no—
216Dic283—41no—
217Dic283—41no—
218C2×C283—21no—
219C2×C283—41no—
220C2×C283—41no—
221C2×C283—41no—
222C2×C283—81no—
223C2×C283D4211yescharacteristic
224D283—41no—
225D283—81no—
226C283#329011yescharacteristic, complemented, Sylow
227#3290—2831nomaximal, Sylow
228#578—2831no—
229#577—2831no—
230#577D28311yescharacteristic, complemented
231#576—2831no—
232#495—2831no—
233#473—2831no—
234#472—2831no—
235#471—2831no—
236#471—2831no—
237#455—2831no—
238#455—2831no—
239#454—2831no—
240#454—2831no—
241#443—2831no—
242#443—2831no—
2432−1+4—2831no—
2442−1+4C2×D28311yescharacteristic, complemented
245H(5,𝔽2)—2831no—
246H(5,𝔽2)C2×D28311yescharacteristic
247#137—21no—
248#137—2831no—
249#137—2831no—
250#137—2831no—
251#137—5661no—
252#137—5661no—
253#137—5661no—
254#137C2×D28311yescharacteristic
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—2831no—
257AGL(1,ℤ/8)—2831no—
258AGL(1,ℤ/8)—2831no—
259AGL(1,ℤ/8)—5661no—
260AGL(1,ℤ/8)—5661no—
261AGL(1,ℤ/8)—5661no—
262AGL(1,ℤ/8)C2×D28311yescharacteristic, complemented
263#135—21no—
264#135—2831no—
265#135—5661no—
266#135—5661no—
267#135—5661no—
268#135C2×D28311yescharacteristic
269C2×Q16—2831no—
270C2×Q16—5661no—
271C2×SD16—21no—
272C2×SD16—2831no—
273C2×SD16—5661no—
274C2×SD16C2×D28311yescharacteristic, complemented
275C2×D8—2831no—
276C2×D8—5661no—
277#131—2831no—
278#131—2831no—
279#131—2831no—
280#131C2×D28311yescharacteristic, complemented
281#124—2831no—
282#124—2831no—
283#108—2831no—
284#108—2831no—
285#104—2831no—
286#104—2831no—
287#104—2831no—
288#104—2831no—
289#101—2831no—
290#101—2831no—
291#100—2831no—
292#100—2831no—
293C4×C8—2831no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—2831no—
300#41—5661no—
301#41—5661no—
302#41—5661no—
303#41—5661no—
304#41—11321no—
305#41C22×D28311yescharacteristic
306#41C22×D28311yescharacteristic
307#41C22×D28311yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—2831no—
311C2×Q8—5661no—
312C2×Q8—5661no—
313C2×Q8C22×D28311yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—2831no—
318C2×D4—5661no—
319C2×D4—5661no—
320C2×D4—11321no—
321C2×D4C22×D28311yescharacteristic
322Q16—21no—
323Q16—2831no—
324Q16—5661no—
325Q16—5661no—
326Q16—5661no—
327Q16—5661no—
328Q16—5661no—
329Q16C22⋊D28311yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—2831no—
335SD16—2831no—
336SD16—5661no—
337SD16—5661no—
338SD16—5661no—
339SD16—5661no—
340SD16—5661no—
341SD16—5661no—
342SD16—5661no—
343SD16—5661no—
344SD16C22⋊D28311yescharacteristic
345SD16C22⋊D28311yescharacteristic
346D8—21no—
347D8—2831no—
348D8—5661no—
349D8—5661no—
350D8—5661no—
351D8—5661no—
352D8—5661no—
353D8C22⋊D28311yescharacteristic
354M16—21no—
355M16—2831no—
356M16—2831no—
357M16—2831no—
358M16—5661no—
359M16—5661no—
360M16—5661no—
361M16C22×D28311yescharacteristic
362C2×C8—21no—
363C2×C8—2831no—
364C2×C8—5661no—
365C2×C8—5661no—
366C2×C8—5661no—
367C2×C8C22×D28311yescharacteristic
368C22⋊C4—11321no—
369C22⋊C4—11321no—
370C42—2831no—
371C23—21no—
372C23—41no—
373C23—5661no—
374C23—11321no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—2831no—
379Q8—5661no—
380Q8—5661no—
381Q8—11321no—
382Q8D4×D28311yescharacteristic
383Q8C2×C22⋊D28311yescharacteristic
384Q8C2×C22⋊D28311yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—2831no—
394D4—5661no—
395D4—5661no—
396D4—5661no—
397D4—11321no—
398D4—11321no—
399D4—11321no—
400D4D4×D28311yescharacteristic
401D4C2×C22⋊D28311yescharacteristic
402D4C2×C22⋊D28311yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—5661no—
411C2×C4—5661no—
412C2×C4—5661no—
413C2×C4—11321no—
414C2×C4—11321no—
415C2×C4—11321no—
416C2×C4C23×D28311yescharacteristic
417C8—21no—
418C8—2831no—
419C8—2831no—
420C8—5661no—
421C8—5661no—
422C8—5661no—
423C8C2×C22⋊D28311yescharacteristic
424C8C2×C22⋊D28311yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—5661no—
432C22—11321no—
433C22—45281no—
434C22—22641no—
435C22#2258365511yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—5661no—
441C4—11321no—
442C4—11321no—
443C4C2×D4×D28311yescharacteristic
444C4C22×C22⋊D28311yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—11321no—
451C2—22641no—
452C2D4×C22⋊D28311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#577×C283C2
socleC2×C283D42
hypercenter#577D283
hypocenterC283#3290
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #31827280C2semidirect
2. #31827272C2semidirect
3. #31827268C2semidirect
4. #31826846C2semidirect
5. #31826738C2semidirect
6. #31826733C2semidirect
7. #31826728C2semidirect
8. #31826725C2semidirect
9. #31826643C2semidirect
10. #31826641C2semidirect
11. #31826638C2semidirect
12. #31826636C2semidirect
13. #31826582C2semidirect
14. #31826580C2semidirect
15. #577×C283C2semidirect
16. #22583657C22semidirect
20. #22583641C22semidirect
23. #22583640C22semidirect
28. #22583635C22semidirect
35. C2×#17985382C22semidirect
36. C2×#17985381C22semidirect
41. #22583617C22semidirect
42. #22583616C22semidirect
43. #22583599C22semidirect
44. #22583597C22semidirect
45. #22583546C22semidirect
46. #22583545C22semidirect
48. #22583537C22semidirect
49. #22583537C22semidirect
50. #22583536C22semidirect
51. #22583529C22semidirect
52. #22583528C22semidirect
53. #22583527C22semidirect
54. #22583526C22semidirect
55. C8×Dic283C22semidirect
56. 2−1+4×C283C22semidirect
61. AGL(1,ℤ/8)×C283C22semidirect
65. C2×SD16×C283C22semidirect
66. #131×C283C22semidirect
226. C283#3290semidirect
230. #577D283semidirect
244. 2−1+4C2×D283semidirect
262. AGL(1,ℤ/8)C2×D283semidirect
274. C2×SD16C2×D283semidirect
280. #131C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272802
#318272722
#318272682
#318268462
#318267382
#318267332
#318267282
#318267252
#318266432
#318266412
#318266382
#318266362
#318265822
#318265802
#577×C2832
#3290283