Finite Group Databasebeta

← #49129721

Subgroups — #49129721

Order 36224.

800 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 249 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
1C2×#22583655C211yesmaximal, characteristic
2#31826940C211yesmaximal, characteristic, complemented
3#31826438C214yesmaximal, complemented
4C2×#22583524C218yesmaximal, complemented
5#518×C283C211yesmaximal, characteristic, complemented
6#22583655—24no—
7#22583655—24no—
8C2×#17985392C2212yes—
9C2×#17985391C414yescomplemented
10C22×C22⋊D283C2214yes—
11C2×D4×D283C414yescomplemented
12D4×Dic283—24no—
13#22583569C2212yescomplemented
14C2×C22⋊Dic283C2214yescomplemented
15#22583524C22116yescomplemented
16C22×D4×C283C2211yescharacteristic
17C4×D4×C283—24no—
18#117×C283C2212yescomplemented
19C2×C22⋊C4×C283C2214yescomplemented
20C23×D283C2×C414yescomplemented
21#17985392—24no—
22#17985392—24no—
23#17985391—216no—
24C2×Dic566C2×C412yescomplemented
25C2×D1132C2×C412yescomplemented
26C2×C22⋊D283—28no—
27C2×C22⋊D283—28no—
28C2×C22⋊D283C2×C418yescomplemented
29C2×C22⋊D283C2314yes—
30D4×D283—216no—
31C22×Dic283—24no—
32C22×Dic283C2×C414yescomplemented
33C2×C4×D283C2×C414yescomplemented
34C4⋊Dic283—22no—
35C22⋊Dic283—24no—
36C22⋊Dic283C2314yes—
37C4×Dic283—22no—
38C24×C283C2312yes—
39C2×D4×C283C2×C414yes—
40C2×D4×C283D414yes—
41C2×D4×C283D414yes—
42C22×C4×C283—24no—
43C22×C4×C283C2311yescharacteristic
44C4⋊C4×C283—22no—
45C22⋊C4×C283—24no—
46C22⋊C4×C283C2314yes—
47C42×C283—22no—
48C22×D283—28no—
49C22×D283—84no—
50C22×D283C22×C414yes—
51Dic566—24no—
52D1132—24no—
53C22⋊D283—216no—
54C22⋊D283—24no—
55C22⋊D283—24no—
56C2×Dic283—28no—
57C2×Dic283—24no—
58C2×Dic283—84no—
59C2×Dic283C22×C414yes—
60C4×D283—28no—
61C23×C283—82no—
62C23×C283C22×C414yes—
63C23×C283C2×D414yes—
64C23×C283C2×D414yes—
65C23×C283C2411yescharacteristic
66D4×C283C22⋊C4116yes—
67C2×C4×C283—24no—
68C2×C4×C283—84no—
69C2×C4×C283C22×C412yes—
70C2×C4×C283C2×D412yes—
71C2×C4×C283C2×D412yes—
72C22×C283—44no—
73C22×C283—41no—
74C22×C283—44no—
75C22×C283—44no—
76C22×C283C2×C22⋊C418yes—
77C22×C283C23×C411yescharacteristic
78C22×C283C22×D411yescharacteristic
79C22×C283C22×D411yescharacteristic
80C2×D283—24no—
81C2×D283—44no—
82C2×D283—88no—
83C4×C283—44no—
84C4×C283C2×C22⋊C414yes—
85Dic283—24no—
86Dic283—44no—
87C2×C283—21no—
88C2×C283—21no—
89C2×C283—21no—
90C2×C283—28no—
91C2×C283C22×C22⋊C411yescharacteristic
92D283—44no—
93C283#288311yescharacteristic, complemented, Sylow
94#2883—2831nomaximal, Sylow
95C2×H(5,𝔽2)—2831no—
96#518—2831no—
97#518D28311yescharacteristic, complemented
98#410—2834no—
99C2×#99—2838no—
100H(5,𝔽2)—5664no—
101H(5,𝔽2)—5664no—
102C2×#41—2834no—
103C2×#41—2832no—
104C22×D4—2834no—
105C22×D4—2834no—
106C22×D4C2×D28311yescharacteristic
107C4×D4—24no—
108C4×D4—5664no—
109#117—2832no—
110#117C2×D28312yescomplemented
111C2×C22⋊C4—2834no—
112C2×C22⋊C4C2×D28314yescomplemented
113#99—28316no—
114C24—2834no—
115C24C22×D28312yes—
116#41—56616no—
117#41—5664no—
118#41—5664no—
119C2×Q8—2832no—
120C2×D4—2838no—
121C2×D4—2834no—
122C2×D4—2832no—
123C2×D4—5668no—
124C2×D4—5668no—
125C2×D4—56616no—
126C2×D4C4×D28314yes—
127C2×D4C22⋊D28314yes—
128C2×D4D113214yes—
129C22×C4—24no—
130C22×C4—2834no—
131C22×C4—2834no—
132C22×C4—5664no—
133C22×C4C22×D28311yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—5662no—
136C22⋊C4—24no—
137C22⋊C4—2834no—
138C22⋊C4—5664no—
139C22⋊C4C22×D28314yes—
140C42—22no—
141C42—5662no—
142C23—82no—
143C23—2834no—
144C23—5668no—
145C23—22644no—
146C23C2×C4×D28314yes—
147C23C2×C22⋊D28314yes—
148C23C2×D113214yes—
149C23C23×D28311yescharacteristic
150Q8—5664no—
151D4—56616no—
152D4—5664no—
153D4—5664no—
154D4—5664no—
155D4(C2×D283)⋊C4116yes—
156C2×C4—24no—
157C2×C4—84no—
158C2×C4—2834no—
159C2×C4—5668no—
160C2×C4—5668no—
161C2×C4—5664no—
162C2×C4—22644no—
163C2×C4C2×C4×D28312yes—
164C2×C4C2×C22⋊D28312yes—
165C2×C4C2×D113212yes—
166C22—44no—
167C22—44no—
168C22—41no—
169C22—44no—
170C22—5664no—
171C22—11324no—
172C22—22648no—
173C22C2×(C2×D283)⋊C418yes—
174C22C22×C4×D28311yescharacteristic
175C22C22×C22⋊D28311yescharacteristic
176C22C22×D113211yescharacteristic
177C4—44no—
178C4—5664no—
179C4—11324no—
180C4C2×(C2×D283)⋊C414yes—
181C2—21no—
182C2—21no—
183C2—21no—
184C2—28no—
185C2—11324no—
186C2C22×(C2×D283)⋊C411yescharacteristic
subgroupG/H
centerC2C22×(C2×D283)⋊C4
commutatorC22×C283C23×C4
FrattiniC23C23×D283
Fitting#518×C283C2
socleC2×C283C22×C22⋊C4
prime radicalC2×#22583655C2
cosocleC23×C283C24
hypercenter#518D283
hypocenterC283#2883
LCSG ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×D4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #31826940C2semidirect
3. #31826438C2semidirect
4. C2×#22583524C2semidirect
5. #518×C283C2semidirect
9. C2×#17985391C4semidirect
11. C2×D4×D283C4semidirect
13. #22583569C22semidirect
14. C2×C22⋊Dic283C22semidirect
15. #22583524C22semidirect
18. #117×C283C22semidirect
19. C2×C22⋊C4×C283C22semidirect
20. C23×D283C2×C4semidirect
24. C2×Dic566C2×C4semidirect
25. C2×D1132C2×C4semidirect
28. C2×C22⋊D283C2×C4semidirect
32. C22×Dic283C2×C4semidirect
33. C2×C4×D283C2×C4semidirect
93. C283#2883semidirect
97. #518D283semidirect
110. #117C2×D283semidirect
112. C2×C22⋊C4C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836552
#318269402
#318264382
C2×#225835242
#518×C2832
#2883283