Finite Group Databasebeta

← #14521615

Subgroups — #14521615

Order 1984.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×D4×D31C211yesmaximal, characteristic, complemented
2C2×#92495C211yesmaximal, characteristic, complemented
3C31×#121C211yesmaximal, characteristic, complemented
4#11758517C212yesmaximal, complemented
5#11758515C211yesmaximal, characteristic, complemented
6#11758514C212yesmaximal, complemented
7#11758507C211yesmaximal, characteristic, complemented
8#11758472C211yesmaximal, characteristic, complemented
9#11758469C211yesmaximal, characteristic, complemented
10#11758462C212yesmaximal, complemented
11#11758459C212yesmaximal, complemented
12C23×D31C2212yes—
13C2×D4×C31C2211yescharacteristic
14C2×D4×C31C2212yescomplemented
15C22×C4×C31C2211yescharacteristic, complemented
16C2×C22⋊D31C2212yes—
17C2×C22⋊D31C2211yescharacteristic
18C2×C22⋊D31C2211yescharacteristic, complemented
19C2×C22⋊D31C2212yescomplemented
20C2×C22⋊D31C2212yescomplemented
21D4×D31—24no—
22#92495—24no—
23C2×D124C2211yescharacteristic
24C2×D124C2211yescharacteristic
25C2×D124C2212yescomplemented
26C2×C4×D31C2211yescharacteristic
27C2×C4×D31C2211yescharacteristic, complemented
28C2×Dic62C2211yescharacteristic, complemented
29C4⋊C4×C31C2211yescharacteristic, complemented
30C22⋊C4×C31C2212yescomplemented
31C22⋊Dic31C2212yescomplemented
32(C2×D31)⋊C4C2212yes—
33(C2×D31)⋊C4C2212yescomplemented
34(C2×D31)⋊C4C2212yescomplemented
35C4⋊Dic31C2211yescharacteristic, complemented
36C4×Dic31C2212yescomplemented
37C23×C31C2312yes—
38C23×C31C2311yescharacteristic
39C22×D31—24no—
40C22×D31—42no—
41C22×D31—42no—
42C22×D31C2312yes—
43C22×D31C2311yescharacteristic
44C22×D31C2311yescharacteristic
45D4×C31—22no—
46D4×C31—42no—
47C2×C4×C31—22no—
48C2×C4×C31C2312yes—
49C2×C4×C31C2311yescharacteristic
50C2×C4×C31C2311yescharacteristic
51C22⋊D31—22no—
52C22⋊D31—22no—
53C22⋊D31—24no—
54C22⋊D31—42no—
55C22⋊D31—42no—
56C2×Dic31C2312yes—
57C2×Dic31C2311yescharacteristic
58C2×Dic31C2311yescharacteristic
59D124—22no—
60D124—22no—
61D124—42no—
62C4×D31—22no—
63C4×D31D414yescomplemented
64Dic62—22no—
65C22×C31—21no—
66C22×C31—22no—
67C22×C31—21no—
68C22×C31—22no—
69C22×C31—21no—
70C22×C31—22no—
71C22×C31C2411yescharacteristic
72C2×D31—21no—
73C2×D31—21no—
74C2×D31—21no—
75C2×D31—22no—
76C2×D31—21no—
77C2×D31—22no—
78C2×D31—21no—
79C2×D31—22no—
80C2×D31—48no—
81C2×D31C2×D412yes—
82C4×C31—21no—
83C4×C31—22no—
84C4×C31C2×D412yes—
85Dic31—21no—
86Dic31—22no—
87Dic31C2×D412yes—
88#535—311nomaximal, Sylow
89C2×C31—42no—
90C2×C31—41no—
91C2×C31C22×D411yescharacteristic
92C2×C31H(5,𝔽2)11yescharacteristic
93C2×C31H(5,𝔽2)11yescharacteristic
94D31—22no—
95D31—41no—
96D31—42no—
97C2×#41—311no—
98C22×D4—311no—
99#127—312no—
100#124—312no—
101#121—311no—
102#121—311no—
103#121—311no—
104#121D3111yescharacteristic, complemented
105#120—312no—
106#120—312no—
107#117—311no—
108C31#53511yescharacteristic, complemented, Sylow
109C24—312no—
110#41—624no—
111C2×Q8—311no—
112C2×D4—311no—
113C2×D4—312no—
114C2×D4—311no—
115C2×D4—312no—
116C2×D4—312no—
117C2×D4—311no—
118C2×D4—311no—
119C2×D4—312no—
120C2×D4—624no—
121C2×D4C2×D3111yescharacteristic
122C2×D4C2×D3112yescomplemented
123C22×C4—311no—
124C22×C4—311no—
125C22×C4C2×D3111yescharacteristic, complemented
126C4⋊C4—311no—
127C4⋊C4C2×D3111yescharacteristic, complemented
128C22⋊C4—312no—
129C22⋊C4—312no—
130C22⋊C4—312no—
131C22⋊C4—312no—
132C22⋊C4C2×D3112yescomplemented
133C42—312no—
134C23—311no—
135C23—312no—
136C23—311no—
137C23—624no—
138C23—1242no—
139C23—1242no—
140C23C22×D3112yes—
141C23C22×D3111yescharacteristic
142Q8—622no—
143D4—22no—
144D4—42no—
145D4—622no—
146D4—624no—
147D4—622no—
148D4—622no—
149D4—622no—
150D4—1242no—
151D4—1242no—
152D4—1242no—
153C2×C4—22no—
154C2×C4—311no—
155C2×C4—314no—
156C2×C4—312no—
157C2×C4—311no—
158C2×C4—622no—
159C2×C4C22×D3112yes—
160C2×C4C22×D3111yescharacteristic
161C2×C4C22×D3111yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—312no—
169C22—621no—
170C22—621no—
171C22—621no—
172C22—622no—
173C22—621no—
174C22—622no—
175C22—621no—
176C22—622no—
177C22—1248no—
178C22C23×D3111yescharacteristic
179C4—21no—
180C4—22no—
181C4—312no—
182C4—621no—
183C4—622no—
184C4D4×D3112yes—
185C2—42no—
186C2—41no—
187C2—622no—
188C2—1242no—
189C2—1241no—
190C2C2×D4×D3111yescharacteristic
191C2#1175856111yescharacteristic
192C2#1175856611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D31
commutator, socle, cosocleC22×C31C24
FittingC31×#121C2
hypercenter#121D31
hypocenterC31#535
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D31C2semidirect
2. C2×#92495C2semidirect
3. C31×#121C2semidirect
4. #11758517C2semidirect
5. #11758515C2semidirect
6. #11758514C2semidirect
7. #11758507C2semidirect
8. #11758472C2semidirect
9. #11758469C2semidirect
10. #11758462C2semidirect
11. #11758459C2semidirect
14. C2×D4×C31C22semidirect
15. C22×C4×C31C22semidirect
18. C2×C22⋊D31C22semidirect
19. C2×C22⋊D31C22semidirect
20. C2×C22⋊D31C22semidirect
25. C2×D124C22semidirect
27. C2×C4×D31C22semidirect
28. C2×Dic62C22semidirect
29. C4⋊C4×C31C22semidirect
30. C22⋊C4×C31C22semidirect
31. C22⋊Dic31C22semidirect
33. (C2×D31)⋊C4C22semidirect
34. (C2×D31)⋊C4C22semidirect
35. C4⋊Dic31C22semidirect
36. C4×Dic31C22semidirect
63. C4×D31D4semidirect
104. #121D31semidirect
108. C31#535semidirect
122. C2×D4C2×D31semidirect
125. C22×C4C2×D31semidirect
127. C4⋊C4C2×D31semidirect
132. C22⋊C4C2×D31semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D312
C2×#924952
C31×#1212
#117585172
#117585152
#117585142
#117585072
#117584722
#117584692
#117584622
#117584592
#53531