Finite Group Databasebeta

← #14521609

Subgroups — #14521609

Order 1984.

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

normal subgroups only

This group has 346 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
1C22×C22⋊D31C211yesmaximal, characteristic, complemented
2C2×D4×D31C211yesmaximal, characteristic, complemented
3C31×#120C211yesmaximal, characteristic, complemented
4#11758530C211yesmaximal, characteristic, complemented
5#11758515C212yesmaximal, complemented
6#11758514C212yesmaximal, complemented
7#11758512C211yesmaximal, characteristic, complemented
8#11758463C211yesmaximal, characteristic, complemented
9#11758461C212yesmaximal, complemented
10#11758460C212yesmaximal, complemented
11C22⋊C4×D31C211yesmaximal, characteristic, complemented
12C24×C31C2211yescharacteristic, complemented
13C23×D31C2211yescharacteristic
14C23×D31C2211yescharacteristic, complemented
15C2×D4×C31C2211yescharacteristic
16C2×D4×C31C2212yescomplemented
17C2×C22⋊D31—24no—
18C2×C22⋊D31C2212yes—
19C2×C22⋊D31C2211yescharacteristic
20C2×C22⋊D31C2212yescomplemented
21C2×C22⋊D31C2211yescharacteristic, complemented
22C2×C22⋊D31C2212yescomplemented
23C22×Dic31C2211yescharacteristic, complemented
24D4×D31—24no—
25C2×D124C2211yescharacteristic, complemented
26C2×C4×D31C2211yescharacteristic, complemented
27C2×C4×D31C2212yescomplemented
28C22⋊C4×C31C2211yescharacteristic, complemented
29C22⋊C4×C31C2212yescomplemented
30C22⋊Dic31C2211yescharacteristic, complemented
31C22⋊Dic31C2212yescomplemented
32C22⋊Dic31C2212yescomplemented
33(C2×D31)⋊C4C2212yescomplemented
34(C2×D31)⋊C4C2212yescomplemented
35C4⋊Dic31C2212yescomplemented
36Dic31⋊C4C2212yescomplemented
37C23×C31—22no—
38C23×C31—42no—
39C23×C31C2311yescharacteristic
40C23×C31C2312yes—
41C23×C31C2311yescharacteristic
42C22×D31—22no—
43C22×D31—42no—
44C22×D31—42no—
45C22×D31D414yescomplemented
46C22×D31C2311yescharacteristic
47C22×D31C2311yescharacteristic
48C22×D31C2311yescharacteristic
49D4×C31—22no—
50D4×C31—42no—
51C2×C4×C31C2311yescharacteristic
52C2×C4×C31C2312yes—
53C22⋊D31—22no—
54C22⋊D31—22no—
55C22⋊D31—24no—
56C22⋊D31—24no—
57C22⋊D31—42no—
58C2×Dic31—22no—
59C2×Dic31C2312yes—
60C2×Dic31C2312yes—
61C2×Dic31C2311yescharacteristic
62D124—22no—
63C4×D31—22no—
64C4×D31—42no—
65C22×C31—22no—
66C22×C31—22no—
67C22×C31—21no—
68C22×C31—22no—
69C22×C31—22no—
70C22×C31—22no—
71C22×C31—44no—
72C22×C31C2×D412yes—
73C22×C31C2411yescharacteristic
74C2×D31—22no—
75C2×D31—22no—
76C2×D31—21no—
77C2×D31—22no—
78C2×D31—44no—
79C2×D31—44no—
80C2×D31C2×D412yes—
81C2×D31C2×D412yes—
82C4×C31—21no—
83C4×C31—22no—
84Dic31—21no—
85Dic31—22no—
86Dic31—22no—
87#534—311nomaximal, Sylow
88C2×C31—22no—
89C2×C31—41no—
90C2×C31—42no—
91C2×C31C22×D411yescharacteristic
92C2×C31H(5,𝔽2)12yes—
93D31—22no—
94D31—22no—
95D31—41no—
96C22×D4—311no—
97C22×D4—311no—
98#123—311no—
99#123—312no—
100#123—311no—
101#121—312no—
102#121—312no—
103#120—311no—
104#120—312no—
105#120D3111yescharacteristic, complemented
106C2×C22⋊C4—311no—
107C31#53411yescharacteristic, complemented, Sylow
108C24—311no—
109C24—311no—
110C24C2×D3111yescharacteristic, complemented
111C2×D4—312no—
112C2×D4—311no—
113C2×D4—311no—
114C2×D4—312no—
115C2×D4—312no—
116C2×D4—311no—
117C2×D4—624no—
118C2×D4—624no—
119C2×D4C2×D3111yescharacteristic
120C2×D4C2×D3112yescomplemented
121C22×C4—311no—
122C22×C4—311no—
123C22×C4—312no—
124C4⋊C4—312no—
125C4⋊C4—312no—
126C22⋊C4—311no—
127C22⋊C4—312no—
128C22⋊C4—312no—
129C22⋊C4—312no—
130C22⋊C4—312no—
131C22⋊C4C2×D3111yescharacteristic, complemented
132C22⋊C4C2×D3112yescomplemented
133C23—22no—
134C23—42no—
135C23—311no—
136C23—311no—
137C23—314no—
138C23—311no—
139C23—622no—
140C23—1242no—
141C23—1242no—
142C23C22×D3111yescharacteristic
143C23C22×D3112yes—
144C23C22×D3111yescharacteristic
145D4—22no—
146D4—42no—
147D4—622no—
148D4—622no—
149D4—624no—
150D4—624no—
151D4—622no—
152D4—1242no—
153C2×C4—312no—
154C2×C4—312no—
155C2×C4—311no—
156C2×C4—622no—
157C2×C4—622no—
158C2×C4—1242no—
159C2×C4C22×D3112yes—
160C2×C4C22×D3111yescharacteristic
161C22—22no—
162C22—21no—
163C22—22no—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—312no—
169C22—312no—
170C22—622no—
171C22—622no—
172C22—621no—
173C22—622no—
174C22—1244no—
175C22—1244no—
176C22D4×D3112yes—
177C22C23×D3111yescharacteristic
178C4—21no—
179C4—22no—
180C4—621no—
181C4—622no—
182C4—622no—
183C2—22no—
184C2—42no—
185C2—41no—
186C2—622no—
187C2—622no—
188C2—1241no—
189C2C2×D4×D3111yescharacteristic
190C2#1175856112yes—
subgroupG/H
center, FrattiniC22C23×D31
commutator, socle, cosocleC22×C31C24
FittingC31×#120C2
hypercenter#120D31
hypocenterC31#534
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D31C2semidirect
2. C2×D4×D31C2semidirect
3. C31×#120C2semidirect
4. #11758530C2semidirect
5. #11758515C2semidirect
6. #11758514C2semidirect
7. #11758512C2semidirect
8. #11758463C2semidirect
9. #11758461C2semidirect
10. #11758460C2semidirect
11. C22⋊C4×D31C2semidirect
12. C24×C31C22semidirect
14. C23×D31C22semidirect
16. C2×D4×C31C22semidirect
20. C2×C22⋊D31C22semidirect
21. C2×C22⋊D31C22semidirect
22. C2×C22⋊D31C22semidirect
23. C22×Dic31C22semidirect
25. C2×D124C22semidirect
26. C2×C4×D31C22semidirect
27. C2×C4×D31C22semidirect
28. C22⋊C4×C31C22semidirect
29. C22⋊C4×C31C22semidirect
30. C22⋊Dic31C22semidirect
31. C22⋊Dic31C22semidirect
32. C22⋊Dic31C22semidirect
33. (C2×D31)⋊C4C22semidirect
34. (C2×D31)⋊C4C22semidirect
35. C4⋊Dic31C22semidirect
36. Dic31⋊C4C22semidirect
45. C22×D31D4semidirect
105. #120D31semidirect
107. C31#534semidirect
110. C24C2×D31semidirect
120. C2×D4C2×D31semidirect
131. C22⋊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
C22×C22⋊D312
C2×D4×D312
C31×#1202
#117585302
#117585152
#117585142
#117585122
#117584632
#117584612
#117584602
C22⋊C4×D312
#53431