Finite Group Databasebeta

← #14521856

Subgroups — #14521856

Order 1984.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#11758567C211yesmaximal, characteristic, complemented
2#11758566C211yesmaximal, characteristic, complemented
3C31×#135C211yesmaximal, characteristic, complemented
4#11758528C211yesmaximal, characteristic, complemented
5#11758526C211yesmaximal, characteristic, complemented
6#11758495C212yesmaximal, complemented
7#11758493C212yesmaximal, complemented
8SD16×D31C212yesmaximal, complemented
9#11758488C212yesmaximal, complemented
10C2×#92470C211yesmaximal, characteristic, complemented
11#11758478C211yesmaximal, characteristic, complemented
12#41×C31C2211yescharacteristic
13#41×C31C2211yescharacteristic, complemented
14#92499C2212yes—
15Q8×D31C2212yescomplemented
16#92497—22no—
17#92497C2212yescomplemented
18D4×D31—22no—
19D4×D31C2212yes—
20#92495—21no—
21#92495—21no—
22#92495C2211yescharacteristic
23C2×D124—21no—
24C2×D124C2211yescharacteristic
25C2×Dic62—21no—
26C2×Dic62C2211yescharacteristic, complemented
27Q16×C31C2211yescharacteristic, complemented
28SD16×C31C2211yescharacteristic, complemented
29SD16×C31C2211yescharacteristic, complemented
30D8×C31C2211yescharacteristic, complemented
31C2×C8×C31C2211yescharacteristic, complemented
32#92482C2212yescomplemented
33#92481C2212yescomplemented
34#92480C2212yescomplemented
35#92479C2212yescomplemented
36#92474C2211yescharacteristic, complemented
37#92470C2212yescomplemented
38#92470C2212yescomplemented
39#92469C2212yescomplemented
40C8×D31C2212yescomplemented
41C22×D31—21no—
42C22×D31—22no—
43Q8×C31C2311yescharacteristic
44Q8×C31C2311yescharacteristic
45D4×C31—21no—
46D4×C31—21no—
47D4×C31C2311yescharacteristic
48D4×C31C2311yescharacteristic
49C2×C4×C31—21no—
50C2×C4×C31—21no—
51C2×C4×C31C2311yescharacteristic
52C22⋊D31—22no—
53C22⋊D31—22no—
54C22⋊D31D412yes—
55C2×Dic31—21no—
56C2×Dic31—22no—
57D124—22no—
58D124—21no—
59D124D411yescharacteristic
60D124C2312yes—
61C4×D31—22no—
62C4×D31—22no—
63C4×D31C2312yes—
64Dic62—21no—
65Dic62—22no—
66Dic62D411yescharacteristic
67Dic62C2312yes—
68C8×C31C2311yescharacteristic
69C8×C31C2311yescharacteristic
70C31⋊C8C2312yes—
71C22×C31—21no—
72C22×C31—21no—
73C22×C31C2×D411yescharacteristic
74C2×D31—22no—
75C2×D31—82no—
76C2×D31—81no—
77C2×D31C2×D412yes—
78C4×C31—21no—
79C4×C31—21no—
80C4×C31C2×D411yescharacteristic
81C4×C31C2411yescharacteristic
82Dic31—22no—
83Dic31C2×D412yes—
84#577—311nomaximal, Sylow
85C2×C31—21no—
86C2×C31—41no—
87C2×C31—41no—
88C2×C31C22×D411yescharacteristic
89D31—22no—
90D31—42no—
912−1+4—311no—
92H(5,𝔽2)—311no—
93#137—311no—
94#137—312no—
95AGL(1,ℤ/8)—311no—
96AGL(1,ℤ/8)—312no—
97#135—312no—
98#135D3111yescharacteristic, complemented
99C2×SD16—312no—
100C2×SD16—311no—
101#131—311no—
102C31#57711yescharacteristic, complemented, Sylow
103#41—311no—
104#41—312no—
105#41—312no—
106#41—621no—
107#41—621no—
108#41—622no—
109#41C2×D3111yescharacteristic
110#41C2×D3111yescharacteristic, complemented
111C2×Q8—312no—
112C2×Q8—311no—
113C2×Q8—621no—
114C2×D4—312no—
115C2×D4—311no—
116C2×D4—621no—
117C2×D4—622no—
118Q16—312no—
119Q16C2×D3111yescharacteristic, complemented
120SD16—312no—
121SD16—312no—
122SD16—312no—
123SD16—312no—
124SD16C2×D3111yescharacteristic, complemented
125SD16C2×D3111yescharacteristic, complemented
126D8—312no—
127D8C2×D3111yescharacteristic, complemented
128M16—311no—
129M16—312no—
130C2×C8—312no—
131C2×C8C2×D3111yescharacteristic, complemented
132C23—622no—
133C23—621no—
134Q8—311no—
135Q8—312no—
136Q8—622no—
137Q8—621no—
138Q8C22×D3111yescharacteristic
139Q8C22×D3111yescharacteristic
140D4—21no—
141D4—21no—
142D4—312no—
143D4—311no—
144D4—312no—
145D4—622no—
146D4—622no—
147D4—622no—
148D4—621no—
149D4C22×D3111yescharacteristic
150D4C22×D3111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—312no—
154C2×C4—622no—
155C2×C4—622no—
156C2×C4—622no—
157C2×C4—621no—
158C2×C4C22×D3111yescharacteristic
159C8—312no—
160C8C22×D3111yescharacteristic
161C8C22×D3111yescharacteristic
162C22—21no—
163C22—21no—
164C22—312no—
165C22—622no—
166C22—2481no—
167C22—2482no—
168C22D4×D3111yescharacteristic
169C4—21no—
170C4—21no—
171C4—312no—
172C4—622no—
173C4D4×D3111yescharacteristic
174C4C23×D3111yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—622no—
179C2—1242no—
180C2C2×D4×D3111yescharacteristic
subgroupG/H
centerC2C2×D4×D31
commutator, cosocleC4×C31C24
FrattiniC4C23×D31
FittingC31×#135C2
socleC2×C31C22×D4
hypercenter#135D31
hypocenterC31#577
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #11758567C2semidirect
2. #11758566C2semidirect
3. C31×#135C2semidirect
4. #11758528C2semidirect
5. #11758526C2semidirect
6. #11758495C2semidirect
7. #11758493C2semidirect
8. SD16×D31C2semidirect
9. #11758488C2semidirect
10. C2×#92470C2semidirect
11. #11758478C2semidirect
13. #41×C31C22semidirect
15. Q8×D31C22semidirect
17. #92497C22semidirect
26. C2×Dic62C22semidirect
27. Q16×C31C22semidirect
28. SD16×C31C22semidirect
29. SD16×C31C22semidirect
30. D8×C31C22semidirect
31. C2×C8×C31C22semidirect
32. #92482C22semidirect
33. #92481C22semidirect
34. #92480C22semidirect
35. #92479C22semidirect
36. #92474C22semidirect
37. #92470C22semidirect
38. #92470C22semidirect
39. #92469C22semidirect
40. C8×D31C22semidirect
98. #135D31semidirect
102. C31#577semidirect
110. #41C2×D31semidirect
119. Q16C2×D31semidirect
124. SD16C2×D31semidirect
125. SD16C2×D31semidirect
127. D8C2×D31semidirect
131. C2×C8C2×D31semidirect

Maximal subgroups

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

subgroupindex
#117585672
#117585662
C31×#1352
#117585282
#117585262
#117584952
#117584932
SD16×D312
#117584882
C2×#924702
#117584782
#57731