Finite Group Databasebeta

← #14521693

Subgroups — #14521693

Order 1984.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×D4×C31C211yesmaximal, characteristic, complemented
2C2×#92497C211yesmaximal, characteristic, complemented
3#11758530C212yesmaximal, complemented
4C2×C22⋊Dic31C212yesmaximal, complemented
5#11758516C212yesmaximal, complemented
6#11758515C211yesmaximal, characteristic, complemented
7#11758513C211yesmaximal, characteristic, complemented
8#11758512C212yesmaximal, complemented
9D4×Dic31C211yesmaximal, characteristic, complemented
10C4×C22⋊D31C211yesmaximal, characteristic, complemented
11#11758501C211yesmaximal, characteristic, complemented
12C24×C31C2212yes—
13C2×D4×C31—24no—
14C2×D4×C31C2212yes—
15C2×D4×C31C2211yescharacteristic
16C2×D4×C31C2211yescharacteristic
17C22×C4×C31C2211yescharacteristic
18C2×C22⋊D31C2211yescharacteristic
19C2×C22⋊D31C2212yescomplemented
20C2×C22⋊D31C2212yescomplemented
21C22×Dic31C2212yescomplemented
22C22×Dic31C2212yescomplemented
23#92497—24no—
24C2×C4×D31C2211yescharacteristic, complemented
25C2×Dic62C2211yescharacteristic, complemented
26C22⋊Dic31C2212yes—
27C22⋊Dic31C2211yescharacteristic
28C22⋊Dic31C2212yescomplemented
29C22⋊Dic31C2212yescomplemented
30C22⋊Dic31C2212yescomplemented
31C22⋊Dic31C2212yescomplemented
32(C2×D31)⋊C4C2211yescharacteristic, complemented
33C4⋊Dic31C2211yescharacteristic, complemented
34Dic31⋊C4C2212yescomplemented
35Dic31⋊C4C2211yescharacteristic, complemented
36C4×Dic31C2211yescharacteristic, complemented
37C23×C31—24no—
38C23×C31—24no—
39C23×C31—42no—
40C23×C31C2312yes—
41C23×C31C2312yes—
42C23×C31C2311yescharacteristic
43C22×D31C2311yescharacteristic
44D4×C31—24no—
45D4×C31—22no—
46D4×C31D414yescomplemented
47C2×C4×C31—22no—
48C2×C4×C31C2311yescharacteristic
49C2×C4×C31C2311yescharacteristic
50C22⋊D31—24no—
51C22⋊D31—22no—
52C22⋊D31—42no—
53C2×Dic31—24no—
54C2×Dic31—42no—
55C2×Dic31C2311yescharacteristic
56C2×Dic31C2311yescharacteristic
57C2×Dic31C2312yes—
58C2×Dic31C2312yes—
59C2×Dic31C2311yescharacteristic
60C4×D31—22no—
61Dic62—22no—
62C22×C31—21no—
63C22×C31—22no—
64C22×C31—22no—
65C22×C31—21no—
66C22×C31—22no—
67C22×C31—22no—
68C22×C31—22no—
69C22×C31—48no—
70C22×C31C2×D414yes—
71C22×C31#4112yescomplemented
72C22×C31C2411yescharacteristic
73C2×D31—21no—
74C2×D31—21no—
75C2×D31—21no—
76C4×C31—21no—
77C4×C31C2×D412yes—
78Dic31—22no—
79Dic31—21no—
80Dic31—21no—
81Dic31—21no—
82Dic31—22no—
83#546—311nomaximal, Sylow
84C2×C31—22no—
85C2×C31—24no—
86C2×C31—42no—
87C2×C31C22×D411yescharacteristic
88C2×C31C2×#4111yescharacteristic
89C2×C31H(5,𝔽2)11yescharacteristic
90D31—41no—
91C2×#41—311no—
92C22×D4D3111yescharacteristic, complemented
93#124—311no—
94#123—312no—
95C22⋊Q8—311no—
96#121—311no—
97#121—312no—
98#120—312no—
99C4×D4—311no—
100C4×D4—311no—
101C2×C22⋊C4—312no—
102C31#54611yescharacteristic, complemented, Sylow
103C24C2×D3112yes—
104#41—624no—
105C2×Q8—311no—
106C2×D4—24no—
107C2×D4—311no—
108C2×D4—312no—
109C2×D4—312no—
110C2×D4C2×D3112yes—
111C2×D4C2×D3111yescharacteristic
112C2×D4C2×D3111yescharacteristic
113C22×C4—312no—
114C22×C4—312no—
115C22×C4—311no—
116C22×C4C2×D3111yescharacteristic
117C4⋊C4—311no—
118C4⋊C4—312no—
119C4⋊C4—311no—
120C22⋊C4—311no—
121C22⋊C4—312no—
122C22⋊C4—312no—
123C22⋊C4—312no—
124C22⋊C4—312no—
125C22⋊C4—312no—
126C22⋊C4—311no—
127C42—311no—
128C23—24no—
129C23—24no—
130C23—42no—
131C23—311no—
132C23C22×D3112yes—
133C23C22×D3111yescharacteristic
134C23C22×D3112yes—
135Q8—622no—
136D4—24no—
137D4—22no—
138D4—622no—
139D4—624no—
140D4—1242no—
141D4C22⋊D3114yescomplemented
142C2×C4—22no—
143C2×C4—311no—
144C2×C4—311no—
145C2×C4—312no—
146C2×C4—311no—
147C2×C4—312no—
148C2×C4—624no—
149C2×C4—622no—
150C2×C4—1242no—
151C2×C4C22×D3111yescharacteristic
152C2×C4C22×D3111yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—48no—
161C22—621no—
162C22—621no—
163C22—621no—
164C22#9249712yescomplemented
165C22C2×C22⋊D3114yes—
166C22C23×D3111yescharacteristic
167C4—21no—
168C4—621no—
169C4—621no—
170C4—622no—
171C4—621no—
172C4—622no—
173C4C2×C22⋊D3112yes—
174C2—22no—
175C2—24no—
176C2—42no—
177C2—1241no—
178C2C2×#9249711yescharacteristic
179C2#1175856111yescharacteristic
180C2C22×C22⋊D3111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D31
commutator, socle, cosocleC22×C31C24
FittingC22×D4×C31C2
hypercenterC22×D4D31
hypocenterC31#546
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C31C2semidirect
2. C2×#92497C2semidirect
3. #11758530C2semidirect
4. C2×C22⋊Dic31C2semidirect
5. #11758516C2semidirect
6. #11758515C2semidirect
7. #11758513C2semidirect
8. #11758512C2semidirect
9. D4×Dic31C2semidirect
10. C4×C22⋊D31C2semidirect
11. #11758501C2semidirect
19. C2×C22⋊D31C22semidirect
20. C2×C22⋊D31C22semidirect
21. C22×Dic31C22semidirect
22. C22×Dic31C22semidirect
24. C2×C4×D31C22semidirect
25. C2×Dic62C22semidirect
28. C22⋊Dic31C22semidirect
29. C22⋊Dic31C22semidirect
30. C22⋊Dic31C22semidirect
31. C22⋊Dic31C22semidirect
32. (C2×D31)⋊C4C22semidirect
33. C4⋊Dic31C22semidirect
34. Dic31⋊C4C22semidirect
35. Dic31⋊C4C22semidirect
36. C4×Dic31C22semidirect
46. D4×C31D4semidirect
71. C22×C31#41semidirect
92. C22×D4D31semidirect
102. C31#546semidirect
141. D4C22⋊D31semidirect
164. C22#92497semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C312
C2×#924972
#117585302
C2×C22⋊Dic312
#117585162
#117585152
#117585132
#117585122
D4×Dic312
C4×C22⋊D312
#117585012
#54631