Finite Group Databasebeta

← #14521687

Subgroups — #14521687

Order 1984.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×#41×C31C211yesmaximal, characteristic, complemented
2C2×D4×D31C211yesmaximal, characteristic, complemented
3#11758524C211yesmaximal, characteristic, complemented
4#11758523C211yesmaximal, characteristic, complemented
5#11758516C212yesmaximal, complemented
6#11758514C212yesmaximal, complemented
7D4×Dic31C211yesmaximal, characteristic, complemented
8#11758507C211yesmaximal, characteristic, complemented
9#11758506C212yesmaximal, complemented
10C4×C22⋊D31C211yesmaximal, characteristic, complemented
11C2×(C2×D31)⋊C4C212yesmaximal, complemented
12C23×D31C2212yes—
13#41×C31—24no—
14C2×Q8×C31C2211yescharacteristic, complemented
15C2×D4×C31C2211yescharacteristic
16C2×D4×C31C2212yescomplemented
17C22×C4×C31C2212yescomplemented
18C22×C4×C31C2211yescharacteristic, complemented
19C2×C22⋊D31C2211yescharacteristic
20C2×C22⋊D31C2212yes—
21C2×C22⋊D31C2212yescomplemented
22C22×Dic31C2212yescomplemented
23D4×D31—24no—
24C2×D124C2211yescharacteristic
25C2×C4×D31C2211yescharacteristic
26C22⋊Dic31C2211yescharacteristic, complemented
27C22⋊Dic31C2212yescomplemented
28(C2×D31)⋊C4C2211yescharacteristic
29(C2×D31)⋊C4C2212yes—
30(C2×D31)⋊C4C2212yescomplemented
31(C2×D31)⋊C4C2212yescomplemented
32(C2×D31)⋊C4C2212yescomplemented
33C4⋊Dic31C2211yescharacteristic, complemented
34Dic31⋊C4C2211yescharacteristic, complemented
35Dic31⋊C4C2212yescomplemented
36C4×Dic31C2211yescharacteristic, complemented
37C23×C31C2311yescharacteristic
38C23×C31C2312yes—
39C22×D31—24no—
40C22×D31—24no—
41C22×D31—42no—
42C22×D31C2312yes—
43C22×D31C2311yescharacteristic
44Q8×C31—22no—
45D4×C31—24no—
46D4×C31D414yescomplemented
47C2×C4×C31—24no—
48C2×C4×C31—22no—
49C2×C4×C31C2311yescharacteristic
50C2×C4×C31C2312yes—
51C2×C4×C31C2311yescharacteristic
52C22⋊D31—24no—
53C22⋊D31—22no—
54C22⋊D31—42no—
55C2×Dic31—42no—
56C2×Dic31C2311yescharacteristic
57C2×Dic31C2311yescharacteristic
58C2×Dic31C2311yescharacteristic
59C2×Dic31C2312yes—
60D124—22no—
61C4×D31—22no—
62C22×C31—22no—
63C22×C31—22no—
64C22×C31—21no—
65C22×C31—21no—
66C22×C31—21no—
67C22×C31C2×D414yes—
68C22×C31C2411yescharacteristic
69C2×D31—21no—
70C2×D31—21no—
71C2×D31—22no—
72C2×D31—22no—
73C2×D31—22no—
74C2×D31—48no—
75C2×D31#4112yescomplemented
76C4×C31—21no—
77C4×C31—22no—
78C4×C31C2×D412yes—
79Dic31—21no—
80Dic31—21no—
81Dic31—21no—
82Dic31—22no—
83#546—311nomaximal, Sylow
84C2×C31—24no—
85C2×C31—41no—
86C2×C31C22×D411yescharacteristic
87C2×C31C2×#4111yescharacteristic
88C2×C31H(5,𝔽2)11yescharacteristic
89D31—22no—
90D31—42no—
91C2×#41D3111yescharacteristic, complemented
92C22×D4—311no—
93#124—311no—
94#123—312no—
95C22⋊Q8—311no—
96#121—312no—
97#121—311no—
98#120—312no—
99C4×D4—311no—
100C4×D4—311no—
101C2×C22⋊C4—312no—
102C31#54611yescharacteristic, complemented, Sylow
103C24—312no—
104#41—24no—
105C2×Q8C2×D3111yescharacteristic, complemented
106C2×D4—311no—
107C2×D4—312no—
108C2×D4—312no—
109C2×D4—311no—
110C2×D4—624no—
111C2×D4C2×D3111yescharacteristic
112C2×D4C2×D3112yescomplemented
113C22×C4—312no—
114C22×C4—311no—
115C22×C4C2×D3112yescomplemented
116C22×C4C2×D3111yescharacteristic, complemented
117C4⋊C4—311no—
118C4⋊C4—312no—
119C4⋊C4—311no—
120C22⋊C4—312no—
121C22⋊C4—311no—
122C22⋊C4—311no—
123C22⋊C4—312no—
124C22⋊C4—312no—
125C22⋊C4—312no—
126C22⋊C4—312no—
127C42—311no—
128C23—311no—
129C23—312no—
130C23—624no—
131C23—624no—
132C23—1242no—
133C23C22×D3111yescharacteristic
134C23C22×D3112yes—
135Q8—22no—
136D4—24no—
137D4—622no—
138D4—624no—
139D4—622no—
140D4—1242no—
141D4C22⋊D3114yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—311no—
145C2×C4—311no—
146C2×C4—312no—
147C2×C4—311no—
148C2×C4—622no—
149C2×C4—1242no—
150C2×C4C22×D3111yescharacteristic
151C2×C4C22×D3112yes—
152C2×C4C22×D3111yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—312no—
159C22—621no—
160C22—621no—
161C22—622no—
162C22—622no—
163C22—622no—
164C22—1248no—
165C22C2×C22⋊D3114yes—
166C22C23×D3111yescharacteristic
167C4—21no—
168C4—22no—
169C4—621no—
170C4—621no—
171C4—622no—
172C4—621no—
173C4C2×C22⋊D3112yes—
174C2—24no—
175C2—41no—
176C2—622no—
177C2—1242no—
178C2#41×D3111yescharacteristic
179C2#1175856611yescharacteristic
180C2C22×C22⋊D3111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D31
commutator, socle, cosocleC22×C31C24
FittingC2×#41×C31C2
hypercenterC2×#41D31
hypocenterC31#546
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#41×C31C2semidirect
2. C2×D4×D31C2semidirect
3. #11758524C2semidirect
4. #11758523C2semidirect
5. #11758516C2semidirect
6. #11758514C2semidirect
7. D4×Dic31C2semidirect
8. #11758507C2semidirect
9. #11758506C2semidirect
10. C4×C22⋊D31C2semidirect
11. C2×(C2×D31)⋊C4C2semidirect
14. C2×Q8×C31C22semidirect
16. C2×D4×C31C22semidirect
17. C22×C4×C31C22semidirect
18. C22×C4×C31C22semidirect
21. C2×C22⋊D31C22semidirect
22. C22×Dic31C22semidirect
26. C22⋊Dic31C22semidirect
27. C22⋊Dic31C22semidirect
30. (C2×D31)⋊C4C22semidirect
31. (C2×D31)⋊C4C22semidirect
32. (C2×D31)⋊C4C22semidirect
33. C4⋊Dic31C22semidirect
34. Dic31⋊C4C22semidirect
35. Dic31⋊C4C22semidirect
36. C4×Dic31C22semidirect
46. D4×C31D4semidirect
75. C2×D31#41semidirect
91. C2×#41D31semidirect
102. C31#546semidirect
105. C2×Q8C2×D31semidirect
112. C2×D4C2×D31semidirect
115. C22×C4C2×D31semidirect
116. C22×C4C2×D31semidirect
141. D4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C312
C2×D4×D312
#117585242
#117585232
#117585162
#117585142
D4×Dic312
#117585072
#117585062
C4×C22⋊D312
C2×(C2×D31)⋊C42
#54631