Finite Group Databasebeta

← #14521690

Subgroups — #14521690

Order 1984.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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×#92499C211yesmaximal, characteristic, complemented
2C22×D124C211yesmaximal, characteristic, complemented
3C31×C22⋊Q8C211yesmaximal, characteristic, complemented
4#11758524C211yesmaximal, characteristic, complemented
5C4×C22⋊D31C211yesmaximal, characteristic, complemented
6#11758472C211yesmaximal, characteristic, complemented
7#11758472C212yesmaximal, complemented
8#11758471C212yesmaximal, complemented
9#11758470C211yesmaximal, characteristic, complemented
10#11758459C212yesmaximal, complemented
11C22⋊C4×D31C212yesmaximal, complemented
12C23×D31C2212yes—
13C2×Q8×C31C2211yescharacteristic, complemented
14C22×C4×C31C2211yescharacteristic
15C2×C22⋊D31C2211yescharacteristic
16#92499—24no—
17C2×D124—24no—
18C2×D124C2212yes—
19C2×D124C2211yescharacteristic
20C2×D124C2211yescharacteristic
21C2×D124C2212yescomplemented
22C2×D124C2212yescomplemented
23C2×C4×D31C2212yescomplemented
24C2×C4×D31C2211yescharacteristic, complemented
25C2×C4×D31C2212yescomplemented
26C4⋊C4×C31C2211yescharacteristic, complemented
27C4⋊C4×C31C2212yescomplemented
28C22⋊C4×C31C2212yes—
29C22⋊Dic31C2211yescharacteristic
30(C2×D31)⋊C4C2212yescomplemented
31(C2×D31)⋊C4C2212yescomplemented
32(C2×D31)⋊C4C2212yescomplemented
33(C2×D31)⋊C4C2212yescomplemented
34(C2×D31)⋊C4C2211yescharacteristic, complemented
35Dic31⋊C4C2211yescharacteristic, complemented
36C4×Dic31C2211yescharacteristic, complemented
37C23×C31C2311yescharacteristic
38C22×D31—24no—
39C22×D31—24no—
40C22×D31—42no—
41C22×D31C2312yes—
42C22×D31C2311yescharacteristic
43C22×D31C2312yes—
44Q8×C31—22no—
45C2×C4×C31—22no—
46C2×C4×C31C2311yescharacteristic
47C2×C4×C31C2312yes—
48C2×C4×C31C2312yes—
49C2×C4×C31C2311yescharacteristic
50C22⋊D31—22no—
51C2×Dic31C2311yescharacteristic
52C2×Dic31C2311yescharacteristic
53C2×Dic31C2311yescharacteristic
54D124—24no—
55D124—24no—
56D124—22no—
57D124—42no—
58D124D414yescomplemented
59C4×D31—24no—
60C4×D31—22no—
61C4×D31—42no—
62C22×C31—21no—
63C22×C31—21no—
64C22×C31#4112yescomplemented
65C22×C31C2411yescharacteristic
66C2×D31—22no—
67C2×D31—22no—
68C2×D31—21no—
69C2×D31—22no—
70C2×D31—21no—
71C2×D31—22no—
72C2×D31—21no—
73C2×D31—22no—
74C2×D31—48no—
75C2×D31C2×D414yes—
76C4×C31—22no—
77C4×C31—21no—
78C4×C31—22no—
79C4×C31C2×D412yes—
80Dic31—21no—
81Dic31—21no—
82Dic31—21no—
83#546—311nomaximal, Sylow
84C2×C31—22no—
85C2×C31C22×D411yescharacteristic
86C2×C31C2×#4111yescharacteristic
87C2×C31H(5,𝔽2)11yescharacteristic
88D31—24no—
89D31—41no—
90D31—42no—
91C2×#41—311no—
92C22×D4—311no—
93#124—311no—
94#123—312no—
95C22⋊Q8D3111yescharacteristic, complemented
96#121—311no—
97#121—312no—
98#120—312no—
99C4×D4—311no—
100C4×D4—311no—
101C2×C22⋊C4—312no—
102C31#54611yescharacteristic, complemented, Sylow
103C24—312no—
104#41—624no—
105C2×Q8C2×D3111yescharacteristic, complemented
106C2×D4—311no—
107C2×D4—311no—
108C2×D4—312no—
109C2×D4—311no—
110C2×D4—312no—
111C2×D4—312no—
112C2×D4—624no—
113C22×C4—312no—
114C22×C4—311no—
115C22×C4—312no—
116C22×C4C2×D3111yescharacteristic
117C4⋊C4—311no—
118C4⋊C4C2×D3111yescharacteristic, complemented
119C4⋊C4C2×D3112yescomplemented
120C22⋊C4—311no—
121C22⋊C4—312no—
122C22⋊C4—312no—
123C22⋊C4—312no—
124C22⋊C4—311no—
125C22⋊C4—312no—
126C22⋊C4C2×D3112yes—
127C42—311no—
128C23—312no—
129C23—312no—
130C23—311no—
131C23—624no—
132C23—624no—
133C23—1242no—
134C23C22×D3111yescharacteristic
135Q8—22no—
136D4—314no—
137D4—624no—
138D4—624no—
139D4—622no—
140D4—622no—
141D4—1242no—
142C2×C4—22no—
143C2×C4—311no—
144C2×C4—311no—
145C2×C4—311no—
146C2×C4—624no—
147C2×C4—622no—
148C2×C4—1242no—
149C2×C4C22×D3112yes—
150C2×C4C22×D3112yes—
151C2×C4C22×D3111yescharacteristic
152C2×C4C22×D3111yescharacteristic
153C22—21no—
154C22—21no—
155C22—314no—
156C22—622no—
157C22—622no—
158C22—621no—
159C22—622no—
160C22—621no—
161C22—622no—
162C22—621no—
163C22—622no—
164C22—1248no—
165C22#9249912yescomplemented
166C22C23×D3111yescharacteristic
167C4—21no—
168C4—22no—
169C4—22no—
170C4—621no—
171C4—621no—
172C4—621no—
173C4D4×D3112yes—
174C2—22no—
175C2—624no—
176C2—1242no—
177C2—1241no—
178C2C2×D4×D3111yescharacteristic
179C2C2×#9249911yescharacteristic
180C2#1175856611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D31
commutator, socle, cosocleC22×C31C24
FittingC31×C22⋊Q8C2
hypercenterC22⋊Q8D31
hypocenterC31#546
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#92499C2semidirect
2. C22×D124C2semidirect
3. C31×C22⋊Q8C2semidirect
4. #11758524C2semidirect
5. C4×C22⋊D31C2semidirect
6. #11758472C2semidirect
7. #11758472C2semidirect
8. #11758471C2semidirect
9. #11758470C2semidirect
10. #11758459C2semidirect
11. C22⋊C4×D31C2semidirect
13. C2×Q8×C31C22semidirect
21. C2×D124C22semidirect
22. C2×D124C22semidirect
23. C2×C4×D31C22semidirect
24. C2×C4×D31C22semidirect
25. C2×C4×D31C22semidirect
26. C4⋊C4×C31C22semidirect
27. C4⋊C4×C31C22semidirect
30. (C2×D31)⋊C4C22semidirect
31. (C2×D31)⋊C4C22semidirect
32. (C2×D31)⋊C4C22semidirect
33. (C2×D31)⋊C4C22semidirect
34. (C2×D31)⋊C4C22semidirect
35. Dic31⋊C4C22semidirect
36. C4×Dic31C22semidirect
58. D124D4semidirect
64. C22×C31#41semidirect
95. C22⋊Q8D31semidirect
102. C31#546semidirect
105. C2×Q8C2×D31semidirect
118. C4⋊C4C2×D31semidirect
119. C4⋊C4C2×D31semidirect
165. C22#92499semidirect

Maximal subgroups

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

subgroupindex
C2×#924992
C22×D1242
C31×C22⋊Q82
#117585242
C4×C22⋊D312
#117584722
#117584712
#117584702
#117584592
C22⋊C4×D312
#54631