Finite Group Databasebeta

← #49133030

Subgroups — #49133030

Order 36224.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827274C212yesmaximal, complemented
2#31827268C212yesmaximal, complemented
3#31826855C211yesmaximal, characteristic, complemented
4#31826734C212yesmaximal, complemented
5#31826730C212yesmaximal, complemented
6#31826637C211yesmaximal, characteristic, complemented
7#31826634C212yesmaximal, complemented
8#31826584C212yesmaximal, complemented
9#455×C283C211yesmaximal, characteristic, complemented
10#22583658C2211yescharacteristic, complemented
11#22583656C2212yescomplemented
12#22583642—22no—
13#22583638C2212yescomplemented
14#22583637—22no—
15#22583636—22no—
16#22583636C2212yescomplemented
17#22583635—22no—
18#22583635C2212yes—
19#22583633—22no—
20#22583630—22no—
21#22583630C2212yes—
22C2×#17985379C2212yescomplemented
23SD16×D283—22no—
24C2×#17985377—22no—
25C2×#17985377C2212yescomplemented
26#22583618C2212yescomplemented
27#22583617C2212yescomplemented
28#22583607C2211yescharacteristic, complemented
29#22583545C2212yescomplemented
30#22583538C2212yescomplemented
31#22583529C2211yescharacteristic, complemented
32#22583526C2212yescomplemented
33#22583521C2211yescharacteristic, complemented
34H(5,𝔽2)×C283C2211yescharacteristic
35#137×C283C2212yescomplemented
36#124×C283C2211yescharacteristic, complemented
37#104×C283C2212yescomplemented
38#100×C283C2211yescharacteristic, complemented
39#17985393—22no—
40#17985393—22no—
41#17985392—22no—
42#17985392—41no—
43#17985392C2312yes—
44Q8×D283—22no—
45C2×D1132—22no—
46C2×D1132—41no—
47C2×D1132C2312yes—
48D4×D283—22no—
49D4×D283—42no—
50#17985382D412yescomplemented
51#17985381—22no—
52#17985380—22no—
53#17985380D412yescomplemented
54#17985379—22no—
55#17985379—22no—
56#17985379—22no—
57#17985379D412yescomplemented
58D2264—22no—
59#17985377—22no—
60#17985377—22no—
61#17985377—22no—
62#17985377—22no—
63#17985377D412yescomplemented
64#17985376—22no—
65#17985376C2312yes—
66#17985375—22no—
67C2×C283⋊C8—22no—
68C2×C283⋊C8C2312yes—
69C8×D283—22no—
70#41×C283—22no—
71#41×C283C2312yes—
72C2×Q8×C283C2311yescharacteristic
73C2×D4×C283—22no—
74C2×D4×C283—41no—
75C2×D4×C283C2311yescharacteristic
76Q16×C283—22no—
77SD16×C283—22no—
78M16×C283C2312yes—
79C22⋊C4×C283—41no—
80C42×C283C2311yescharacteristic
81C22×D283—22no—
82C22×D283—42no—
83Dic566—41no—
84Dic566C2×D412yes—
85D1132—22no—
86D1132—22no—
87D1132—42no—
88D1132—41no—
89D1132—82no—
90D1132C2×D412yes—
91C22⋊D283—22no—
92C22⋊D283—42no—
93C4×D283—22no—
94C4×D283—42no—
95C4×D283—42no—
96C283⋊C8—22no—
97C283⋊C8C2×D412yes—
98C283⋊C8C2×D412yes—
99C23×C283—21no—
100C23×C283—41no—
101Q8×C283—22no—
102Q8×C283C2×D412yes—
103D4×C283—22no—
104D4×C283—22no—
105D4×C283—42no—
106D4×C283C2×D412yes—
107C2×C4×C283—22no—
108C2×C4×C283—21no—
109C2×C4×C283—21no—
110C2×C4×C283—41no—
111C2×C4×C283C2411yescharacteristic
112C8×C283—22no—
113C22×C283—22no—
114C22×C283—41no—
115C22×C283—81no—
116C22×C283—161no—
117C22×C283H(5,𝔽2)11yescharacteristic
118C2×D283—22no—
119C2×D283—42no—
120C2×D283—82no—
121C2×D283—162no—
122C4×C283—22no—
123C4×C283—41no—
124C4×C283—41no—
125C4×C283C22×D412yes—
126Dic283—22no—
127C2×C283—21no—
128C2×C283—42no—
129C2×C283—81no—
130C2×C283D4211yescharacteristic
131D283—42no—
132D283—82no—
133C283#328811yescharacteristic, complemented, Sylow
134#3288—2831nomaximal, Sylow
135#577—2832no—
136#576—2832no—
137#496—2831no—
138#472—2832no—
139#471—2832no—
140#455D28311yescharacteristic, complemented
141#454—2831no—
142#453—2832no—
143#444—2832no—
1442−1+4—2831no—
145H(5,𝔽2)—2832no—
146H(5,𝔽2)C2×D28311yescharacteristic
147#137—5662no—
148#137C2×D28312yescomplemented
149AGL(1,ℤ/8)—2832no—
150AGL(1,ℤ/8)—2832no—
151AGL(1,ℤ/8)—2832no—
152AGL(1,ℤ/8)—5662no—
153AGL(1,ℤ/8)—5662no—
154AGL(1,ℤ/8)—5662no—
155#135—2832no—
156#135—5662no—
157#135—5662no—
158C2×SD16—2832no—
159C2×SD16—5662no—
160C2×D8—2832no—
161C2×D8—5662no—
162#131—2832no—
163#131—2832no—
164#127—2831no—
165#124C2×D28311yescharacteristic, complemented
166#108—2832no—
167#104—2832no—
168#104C2×D28312yescomplemented
169#101—2831no—
170#100—2832no—
171#100C2×D28311yescharacteristic, complemented
172#97—2831no—
173#41—22no—
174#41—2832no—
175#41—5662no—
176#41—5662no—
177#41—5662no—
178#41—11321no—
179#41C22×D28312yes—
180C2×Q8—5662no—
181C2×Q8C22×D28311yescharacteristic
182C2×D4—22no—
183C2×D4—41no—
184C2×D4—2832no—
185C2×D4—5662no—
186C2×D4—5662no—
187C2×D4—11321no—
188C2×D4—11322no—
189C2×D4C22×D28311yescharacteristic
190Q16—22no—
191Q16—2832no—
192SD16—22no—
193SD16—2832no—
194SD16—2832no—
195SD16—5662no—
196SD16—5662no—
197SD16—5662no—
198SD16—5662no—
199SD16—5662no—
200D8—2832no—
201D8—5662no—
202D8—5662no—
203D8—5662no—
204D8—5662no—
205D8—5662no—
206M16—2832no—
207M16—5662no—
208M16—5662no—
209M16C22×D28312yes—
210C2×C8—2832no—
211C2×C8—5662no—
212C2×C8—5662no—
213C22⋊C4—41no—
214C42C22×D28311yescharacteristic
215C23—21no—
216C23—41no—
217C23—5662no—
218C23—11322no—
219Q8—22no—
220Q8—2832no—
221Q8—11321no—
222Q8D4×D28312yes—
223D4—22no—
224D4—22no—
225D4—42no—
226D4—2832no—
227D4—5662no—
228D4—5662no—
229D4—5662no—
230D4—11322no—
231D4—11321no—
232D4—11322no—
233D4—22642no—
234D4D4×D28312yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—5662no—
240C2×C4—11322no—
241C2×C4—11322no—
242C2×C4C23×D28311yescharacteristic
243C8—22no—
244C8—2832no—
245C8—2832no—
246C8—5662no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—161no—
251C22—5662no—
252C22—11322no—
253C22—45282no—
254C22—22642no—
255C22#2258365511yescharacteristic
256C4—22no—
257C4—41no—
258C4—41no—
259C4—5662no—
260C4C2×D4×D28312yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—11322no—
265C2—22642no—
266C2#3182709711yescharacteristic
subgroupG/H
centerC2#31827097
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#455×C283C2
socleC2×C283D42
hypercenter#455D283
hypocenterC283#3288
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #31827274C2semidirect
2. #31827268C2semidirect
3. #31826855C2semidirect
4. #31826734C2semidirect
5. #31826730C2semidirect
6. #31826637C2semidirect
7. #31826634C2semidirect
8. #31826584C2semidirect
9. #455×C283C2semidirect
10. #22583658C22semidirect
11. #22583656C22semidirect
13. #22583638C22semidirect
16. #22583636C22semidirect
22. C2×#17985379C22semidirect
25. C2×#17985377C22semidirect
26. #22583618C22semidirect
27. #22583617C22semidirect
28. #22583607C22semidirect
29. #22583545C22semidirect
30. #22583538C22semidirect
31. #22583529C22semidirect
32. #22583526C22semidirect
33. #22583521C22semidirect
35. #137×C283C22semidirect
36. #124×C283C22semidirect
37. #104×C283C22semidirect
38. #100×C283C22semidirect
50. #17985382D4semidirect
53. #17985380D4semidirect
57. #17985379D4semidirect
63. #17985377D4semidirect
133. C283#3288semidirect
140. #455D283semidirect
148. #137C2×D283semidirect
165. #124C2×D283semidirect
168. #104C2×D283semidirect
171. #100C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272742
#318272682
#318268552
#318267342
#318267302
#318266372
#318266342
#318265842
#455×C2832
#3288283