Finite Group Databasebeta

← #49133026

Subgroups — #49133026

Order 36224.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827274C211yesmaximal, characteristic, complemented
2#31827271C211yesmaximal, characteristic, complemented
3#31827270C211yesmaximal, characteristic, complemented
4#31827269C211yesmaximal, characteristic, complemented
5#31826851C211yesmaximal, characteristic, complemented
6#31826736C211yesmaximal, characteristic, complemented
7#31826734C211yesmaximal, characteristic, complemented
8#31826731C211yesmaximal, characteristic, complemented
9#31826641C211yesmaximal, characteristic, complemented
10#31826640C211yesmaximal, characteristic, complemented
11#31826635C211yesmaximal, characteristic, complemented
12#31826631C211yesmaximal, characteristic, complemented
13#31826586C211yesmaximal, characteristic, complemented
14#31826585C211yesmaximal, characteristic, complemented
15#471×C283C211yesmaximal, characteristic, complemented
16#22583658C2211yescharacteristic, complemented
17#22583656C2211yescharacteristic
18#22583656C2211yescharacteristic, complemented
19#22583655C2211yescharacteristic, complemented
20#22583642—21no—
21#22583641C2211yescharacteristic, complemented
22#22583639—21no—
23#22583638—21no—
24#22583638—21no—
25#22583638C2211yescharacteristic
26#22583638C2211yescharacteristic, complemented
27#22583638C2211yescharacteristic, complemented
28#22583638C2211yescharacteristic, complemented
29#22583637—21no—
30#22583637—21no—
31#22583637—21no—
32#22583636C2211yescharacteristic, complemented
33#22583634—21no—
34#22583633—21no—
35#22583632—21no—
36#22583632C2211yescharacteristic
37#22583631—21no—
38#22583631—21no—
39#22583630C2211yescharacteristic
40C2×#17985379C2211yescharacteristic, complemented
41SD16×D283—21no—
42SD16×D283—21no—
43C2×D2264—21no—
44C2×D2264C2211yescharacteristic, complemented
45C2×#17985377C2211yescharacteristic, complemented
46D8×D283—21no—
47#22583618C2211yescharacteristic, complemented
48#22583618C2211yescharacteristic, complemented
49#22583616C2211yescharacteristic, complemented
50#22583606C2211yescharacteristic, complemented
51#22583599C2211yescharacteristic, complemented
52#22583545C2211yescharacteristic, complemented
53#22583537C2211yescharacteristic, complemented
54#22583536C2211yescharacteristic, complemented
55#22583536C2211yescharacteristic, complemented
56#22583536C2211yescharacteristic, complemented
57#22583526C2211yescharacteristic, complemented
58#22583526C2211yescharacteristic, complemented
59#22583520C2211yescharacteristic, complemented
60#137×C283C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C283C2211yescharacteristic
62C2×SD16×C283C2211yescharacteristic, complemented
63#131×C283C2211yescharacteristic, complemented
64#108×C283C2211yescharacteristic, complemented
65#101×C283C2211yescharacteristic, complemented
66#100×C283C2211yescharacteristic, complemented
67#17985393—21no—
68#17985393—21no—
69#17985393—21no—
70#17985393—21no—
71#17985392—21no—
72#17985392—21no—
73#17985392—41no—
74#17985392C2311yescharacteristic
75#17985392C2311yescharacteristic
76#17985392C2311yescharacteristic
77#17985391—21no—
78#17985391—21no—
79Q8×D283—21no—
80Q8×D283—21no—
81C2×D1132—21no—
82C2×D1132—21no—
83C2×D1132C2311yescharacteristic
84C2×D1132C2311yescharacteristic
85C2×C22⋊D283—41no—
86C2×C22⋊D283—41no—
87D4×D283—21no—
88D4×D283—21no—
89D4×D283—21no—
90D4×D283—21no—
91D4×D283—41no—
92D4×D283—41no—
93Dic1132D411yescharacteristic, complemented
94#17985382—21no—
95#17985382D411yescharacteristic, complemented
96#17985381—21no—
97#17985381—21no—
98#17985381—21no—
99#17985381—21no—
100#17985381D411yescharacteristic, complemented
101#17985381D411yescharacteristic, complemented
102#17985380—21no—
103#17985380D411yescharacteristic, complemented
104#17985379—21no—
105#17985379—21no—
106#17985379—21no—
107#17985379D411yescharacteristic, complemented
108D2264—21no—
109D2264—21no—
110D2264—21no—
111D2264—21no—
112D2264—21no—
113D2264—21no—
114D2264D411yescharacteristic, complemented
115#17985377—21no—
116#17985377—21no—
117#17985377—21no—
118#17985377D411yescharacteristic, complemented
119#17985376C2311yescharacteristic
120#17985375—21no—
121#17985375—21no—
122#17985375—21no—
123C2×C283⋊C8C2311yescharacteristic
124C8×D283—21no—
125C8×D283—21no—
126C8×D283—21no—
127(C2×D283)⋊C4—41no—
128C4×Dic283C2311yescharacteristic
129#41×C283C2311yescharacteristic
130C2×Q8×C283C2311yescharacteristic
131C2×D4×C283C2311yescharacteristic
132Q16×C283—21no—
133SD16×C283—21no—
134SD16×C283—21no—
135SD16×C283—21no—
136SD16×C283—21no—
137D8×C283—21no—
138M16×C283—21no—
139M16×C283C2311yescharacteristic
140M16×C283C2311yescharacteristic
141M16×C283C2311yescharacteristic
142C2×C8×C283—21no—
143C2×C8×C283C2311yescharacteristic
144C22×D283—21no—
145C22×D283—21no—
146C22×D283—41no—
147C22×D283—41no—
148C22×D283—41no—
149Dic566—41no—
150Dic566C2×D411yescharacteristic
151Dic566C2×D411yescharacteristic
152Dic566C2×D411yescharacteristic
153D1132—21no—
154D1132—21no—
155D1132—21no—
156D1132—21no—
157D1132—41no—
158D1132—41no—
159D1132—41no—
160D1132C2×D411yescharacteristic
161D1132C2×D411yescharacteristic
162D1132C2×D411yescharacteristic
163C22⋊D283—21no—
164C22⋊D283—21no—
165C22⋊D283—21no—
166C22⋊D283—41no—
167C22⋊D283—41no—
168C22⋊D283—41no—
169C22⋊D283—41no—
170C22⋊D283—82no—
171C2×Dic283—21no—
172C2×Dic283—41no—
173C4×D283—21no—
174C4×D283—21no—
175C4×D283—21no—
176C4×D283—41no—
177C4×D283—41no—
178C4×D283—41no—
179C4×D283—41no—
180C283⋊C8—21no—
181C283⋊C8C2×D411yescharacteristic
182C283⋊C8C2×D411yescharacteristic
183C23×C283—21no—
184Q8×C283—21no—
185Q8×C283—21no—
186Q8×C283C2×D411yescharacteristic
187D4×C283—21no—
188D4×C283—21no—
189D4×C283—21no—
190D4×C283C2×D411yescharacteristic
191C2×C4×C283—21no—
192C2×C4×C283—21no—
193C2×C4×C283C2411yescharacteristic
194C8×C283—21no—
195C8×C283—21no—
196C8×C283—21no—
197C8×C283C2×D411yescharacteristic
198C8×C283C2×D411yescharacteristic
199C22×C283—21no—
200C22×C283—41no—
201C22×C283—81no—
202C22×C283H(5,𝔽2)11yescharacteristic
203C2×D283—21no—
204C2×D283—21no—
205C2×D283—21no—
206C2×D283—41no—
207C2×D283—41no—
208C2×D283—81no—
209C2×D283—81no—
210C2×D283—161no—
211C2×D283—161no—
212C2×D283—161no—
213C4×C283—21no—
214C4×C283—41no—
215C4×C283C22×D411yescharacteristic
216C4×C283C22×D411yescharacteristic
217Dic283—21no—
218Dic283—21no—
219Dic283—21no—
220Dic283—41no—
221C2×C283—21no—
222C2×C283—41no—
223C2×C283—81no—
224C2×C283D4211yescharacteristic
225D283—41no—
226D283—41no—
227D283—41no—
228D283—81no—
229D283—81no—
230C283#328811yescharacteristic, complemented, Sylow
231#3288—2831nomaximal, Sylow
232#577—2831no—
233#577—2831no—
234#576—2831no—
235#576—2831no—
236#496—2831no—
237#472—2831no—
238#472—2831no—
239#471—2831no—
240#471D28311yescharacteristic, complemented
241#455—2831no—
242#454—2831no—
243#453—2831no—
244#453—2831no—
245#444—2831no—
246#444—2831no—
2472−1+4—2831no—
248H(5,𝔽2)—2831no—
249H(5,𝔽2)—2831no—
250H(5,𝔽2)—2831no—
251#137—2831no—
252#137—5661no—
253#137—5661no—
254#137C2×D28311yescharacteristic, complemented
255AGL(1,ℤ/8)—2831no—
256AGL(1,ℤ/8)—2831no—
257AGL(1,ℤ/8)—2831no—
258AGL(1,ℤ/8)—2831no—
259AGL(1,ℤ/8)—2831no—
260AGL(1,ℤ/8)—5661no—
261AGL(1,ℤ/8)—5661no—
262AGL(1,ℤ/8)—5661no—
263AGL(1,ℤ/8)—5661no—
264AGL(1,ℤ/8)—5661no—
265AGL(1,ℤ/8)—5661no—
266AGL(1,ℤ/8)C2×D28311yescharacteristic
267#135—2831no—
268#135—2831no—
269#135—5661no—
270#135—5661no—
271#135—5661no—
272#135—5661no—
273C2×SD16—2831no—
274C2×SD16—5661no—
275C2×SD16—5661no—
276C2×SD16C2×D28311yescharacteristic, complemented
277C2×D8—2831no—
278C2×D8—2831no—
279C2×D8—5661no—
280C2×D8—5661no—
281#131—2831no—
282#131—2831no—
283#131—2831no—
284#131C2×D28311yescharacteristic, complemented
285#127—2831no—
286#124—2831no—
287#108—2831no—
288#108C2×D28311yescharacteristic, complemented
289#104—2831no—
290#104—2831no—
291#104—2831no—
292#104—2831no—
293#101C2×D28311yescharacteristic, complemented
294#100—2831no—
295#100—2831no—
296#100C2×D28311yescharacteristic, complemented
297#97—2831no—
298#41—2831no—
299#41—2831no—
300#41—2831no—
301#41—5661no—
302#41—5661no—
303#41—5661no—
304#41—5661no—
305#41—5661no—
306#41—5661no—
307#41—5661no—
308#41—5661no—
309#41—11321no—
310#41C22×D28311yescharacteristic
311C2×Q8—5661no—
312C2×Q8—5661no—
313C2×Q8C22×D28311yescharacteristic
314C2×D4—2831no—
315C2×D4—2831no—
316C2×D4—5661no—
317C2×D4—5661no—
318C2×D4—5661no—
319C2×D4—5661no—
320C2×D4—5661no—
321C2×D4—5661no—
322C2×D4—11321no—
323C2×D4—11321no—
324C2×D4—11321no—
325C2×D4—11321no—
326C2×D4C22×D28311yescharacteristic
327Q16—21no—
328Q16—2831no—
329Q16—2831no—
330Q16—5661no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—2831no—
336SD16—2831no—
337SD16—2831no—
338SD16—2831no—
339SD16—5661no—
340SD16—5661no—
341SD16—5661no—
342SD16—5661no—
343SD16—5661no—
344SD16—5661no—
345SD16—5661no—
346SD16—5661no—
347D8—21no—
348D8—2831no—
349D8—2831no—
350D8—5661no—
351D8—5661no—
352D8—5661no—
353D8—5661no—
354D8—5661no—
355D8—5661no—
356D8—5661no—
357D8—5661no—
358D8—5661no—
359M16—21no—
360M16—2831no—
361M16—5661no—
362M16—5661no—
363M16—5661no—
364M16C22×D28311yescharacteristic
365M16C22×D28311yescharacteristic
366M16C22×D28311yescharacteristic
367C2×C8—21no—
368C2×C8—2831no—
369C2×C8—5661no—
370C2×C8—5661no—
371C2×C8—5661no—
372C2×C8C22×D28311yescharacteristic
373C22⋊C4—11321no—
374C42—2831no—
375C23—21no—
376C23—5661no—
377C23—5661no—
378C23—11321no—
379C23—11321no—
380C23—11321no—
381Q8—21no—
382Q8—21no—
383Q8—2831no—
384Q8—2831no—
385Q8—2831no—
386Q8—11321no—
387Q8D4×D28311yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—2831no—
392D4—2831no—
393D4—2831no—
394D4—5661no—
395D4—5661no—
396D4—5661no—
397D4—5661no—
398D4—5661no—
399D4—5661no—
400D4—5661no—
401D4—11321no—
402D4—11321no—
403D4—11321no—
404D4—11321no—
405D4—11321no—
406D4—11321no—
407D4—11321no—
408D4—22642no—
409D4D4×D28311yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—5661no—
413C2×C4—5661no—
414C2×C4—5661no—
415C2×C4—5661no—
416C2×C4—11321no—
417C2×C4—11321no—
418C2×C4—11321no—
419C2×C4—11321no—
420C2×C4—11321no—
421C2×C4C23×D28311yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—2831no—
426C8—2831no—
427C8—5661no—
428C8D4×D28311yescharacteristic
429C8D4×D28311yescharacteristic
430C22—21no—
431C22—41no—
432C22—81no—
433C22—5661no—
434C22—5661no—
435C22—5661no—
436C22—11321no—
437C22—11321no—
438C22—45281no—
439C22—45281no—
440C22—45281no—
441C22—22641no—
442C22—22641no—
443C22#2258365611yescharacteristic
444C4—21no—
445C4—41no—
446C4—5661no—
447C4—5661no—
448C4—5661no—
449C4—11321no—
450C4C2×D4×D28311yescharacteristic
451C4C2×D4×D28311yescharacteristic
452C2—21no—
453C2—41no—
454C2—81no—
455C2—11321no—
456C2—11321no—
457C2—11321no—
458C2—22641no—
459C2—22641no—
460C2#3182709911yescharacteristic
subgroupG/H
centerC2#31827099
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#471×C283C2
socleC2×C283D42
hypercenter#471D283
hypocenterC283#3288
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #31827274C2semidirect
2. #31827271C2semidirect
3. #31827270C2semidirect
4. #31827269C2semidirect
5. #31826851C2semidirect
6. #31826736C2semidirect
7. #31826734C2semidirect
8. #31826731C2semidirect
9. #31826641C2semidirect
10. #31826640C2semidirect
11. #31826635C2semidirect
12. #31826631C2semidirect
13. #31826586C2semidirect
14. #31826585C2semidirect
15. #471×C283C2semidirect
16. #22583658C22semidirect
18. #22583656C22semidirect
19. #22583655C22semidirect
21. #22583641C22semidirect
26. #22583638C22semidirect
27. #22583638C22semidirect
28. #22583638C22semidirect
32. #22583636C22semidirect
40. C2×#17985379C22semidirect
44. C2×D2264C22semidirect
45. C2×#17985377C22semidirect
47. #22583618C22semidirect
48. #22583618C22semidirect
49. #22583616C22semidirect
50. #22583606C22semidirect
51. #22583599C22semidirect
52. #22583545C22semidirect
53. #22583537C22semidirect
54. #22583536C22semidirect
55. #22583536C22semidirect
56. #22583536C22semidirect
57. #22583526C22semidirect
58. #22583526C22semidirect
59. #22583520C22semidirect
60. #137×C283C22semidirect
62. C2×SD16×C283C22semidirect
63. #131×C283C22semidirect
64. #108×C283C22semidirect
65. #101×C283C22semidirect
66. #100×C283C22semidirect
93. Dic1132D4semidirect
95. #17985382D4semidirect
100. #17985381D4semidirect
101. #17985381D4semidirect
103. #17985380D4semidirect
107. #17985379D4semidirect
114. D2264D4semidirect
118. #17985377D4semidirect
230. C283#3288semidirect
240. #471D283semidirect
254. #137C2×D283semidirect
276. C2×SD16C2×D283semidirect
284. #131C2×D283semidirect
288. #108C2×D283semidirect
293. #101C2×D283semidirect
296. #100C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272742
#318272712
#318272702
#318272692
#318268512
#318267362
#318267342
#318267312
#318266412
#318266402
#318266352
#318266312
#318265862
#318265852
#471×C2832
#3288283