Finite Group Databasebeta

← #14521855

Subgroups — #14521855

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#11758564C211yesmaximal, characteristic, complemented
2#11758561C211yesmaximal, characteristic, complemented
3C2×SD16×C31C211yesmaximal, characteristic, complemented
4#11758519C211yesmaximal, characteristic, complemented
5#11758509C211yesmaximal, characteristic, complemented
6#11758493C212yesmaximal, complemented
7#11758492C212yesmaximal, complemented
8#11758491C212yesmaximal, complemented
9SD16×D31C212yesmaximal, complemented
10#11758481C211yesmaximal, characteristic, complemented
11#11758478C211yesmaximal, characteristic, complemented
12C2×Q8×C31C2211yescharacteristic, complemented
13C2×D4×C31C2211yescharacteristic
14C2×C22⋊D31—22no—
15#92499—21no—
16#92499C2212yescomplemented
17Q8×D31—21no—
18Q8×D31C2212yescomplemented
19#92497—21no—
20#92497C2212yes—
21D4×D31—21no—
22D4×D31C2212yes—
23#92495—22no—
24#92495C2211yescharacteristic
25#92495C2211yescharacteristic
26#92495C2211yescharacteristic, complemented
27SD16×C31C2212yescomplemented
28SD16×C31C2212yescomplemented
29C2×C8×C31C2211yescharacteristic, complemented
30#92482C2212yescomplemented
31#92481C2212yescomplemented
32#92480C2212yescomplemented
33#92479C2212yescomplemented
34#92474C2211yescharacteristic, complemented
35Dic124C2211yescharacteristic, complemented
36D248C2211yescharacteristic, complemented
37#92470C2211yescharacteristic, complemented
38#92470C2211yescharacteristic, complemented
39#92469C2212yescomplemented
40C8×D31C2212yescomplemented
41C23×C31—21no—
42C22×D31—22no—
43Q8×C31—21no—
44Q8×C31C2312yes—
45D4×C31—21no—
46D4×C31C2312yes—
47C2×C4×C31—21no—
48C2×C4×C31C2311yescharacteristic
49C22⋊D31—21no—
50C22⋊D31—21no—
51C22⋊D31—22no—
52C22⋊D31—22no—
53C22⋊D31D412yes—
54C2×Dic31—22no—
55D124—22no—
56D124D411yescharacteristic
57D124C2311yescharacteristic
58D124C2311yescharacteristic
59C4×D31—22no—
60C4×D31—21no—
61C4×D31—21no—
62C4×D31—22no—
63C4×D31C2312yes—
64Dic62—22no—
65Dic62D411yescharacteristic
66Dic62C2311yescharacteristic
67Dic62C2311yescharacteristic
68C8×C31C2311yescharacteristic
69C8×C31C2311yescharacteristic
70C31⋊C8C2312yes—
71C22×C31—22no—
72C22×C31—81no—
73C22×C31C2×D411yescharacteristic
74C2×D31—21no—
75C2×D31—21no—
76C2×D31—82no—
77C2×D31C2×D412yes—
78C4×C31—22no—
79C4×C31C2×D411yescharacteristic
80C4×C31C2411yescharacteristic
81Dic31—21no—
82Dic31—21no—
83Dic31C2×D412yes—
84#577—311nomaximal, Sylow
85C2×C31—21no—
86C2×C31—42no—
87C2×C31C22×D411yescharacteristic
88D31—22no—
89D31—41no—
90D31—41no—
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#135—311no—
99C2×SD16—312no—
100C2×SD16D3111yescharacteristic, complemented
101#131—311no—
102C31#57711yescharacteristic, complemented, Sylow
103#41—311no—
104#41—312no—
105#41—312no—
106#41—311no—
107#41—311no—
108#41—622no—
109#41—621no—
110#41—621no—
111C2×Q8—312no—
112C2×Q8—621no—
113C2×Q8C2×D3111yescharacteristic, complemented
114C2×D4—312no—
115C2×D4—621no—
116C2×D4—622no—
117C2×D4C2×D3111yescharacteristic
118Q16—312no—
119Q16—311no—
120SD16—312no—
121SD16—312no—
122SD16—311no—
123SD16—311no—
124SD16C2×D3112yescomplemented
125SD16C2×D3112yescomplemented
126D8—312no—
127D8—311no—
128M16—311no—
129M16—312no—
130C2×C8—312no—
131C2×C8C2×D3111yescharacteristic, complemented
132C23—21no—
133C23—622no—
134Q8—21no—
135Q8—311no—
136Q8—311no—
137Q8—311no—
138Q8—622no—
139Q8C22×D3112yes—
140D4—21no—
141D4—312no—
142D4—311no—
143D4—311no—
144D4—311no—
145D4—622no—
146D4—622no—
147D4—622no—
148D4—621no—
149D4—621no—
150D4C22×D3112yes—
151C2×C4—21no—
152C2×C4—312no—
153C2×C4—622no—
154C2×C4—622no—
155C2×C4—622no—
156C2×C4—621no—
157C2×C4—621no—
158C2×C4C22×D3111yescharacteristic
159C8—312no—
160C8C22×D3111yescharacteristic
161C8C22×D3111yescharacteristic
162C22—22no—
163C22—81no—
164C22—312no—
165C22—621no—
166C22—621no—
167C22—2482no—
168C22D4×D3111yescharacteristic
169C4—22no—
170C4—312no—
171C4—621no—
172C4—621no—
173C4D4×D3111yescharacteristic
174C4C23×D3111yescharacteristic
175C2—21no—
176C2—42no—
177C2—622no—
178C2—1241no—
179C2—1241no—
180C2C2×D4×D3111yescharacteristic
subgroupG/H
centerC2C2×D4×D31
commutator, cosocleC4×C31C24
FrattiniC4C23×D31
FittingC2×SD16×C31C2
socleC2×C31C22×D4
hypercenterC2×SD16D31
hypocenterC31#577
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #11758564C2semidirect
2. #11758561C2semidirect
3. C2×SD16×C31C2semidirect
4. #11758519C2semidirect
5. #11758509C2semidirect
6. #11758493C2semidirect
7. #11758492C2semidirect
8. #11758491C2semidirect
9. SD16×D31C2semidirect
10. #11758481C2semidirect
11. #11758478C2semidirect
12. C2×Q8×C31C22semidirect
16. #92499C22semidirect
18. Q8×D31C22semidirect
26. #92495C22semidirect
27. SD16×C31C22semidirect
28. SD16×C31C22semidirect
29. C2×C8×C31C22semidirect
30. #92482C22semidirect
31. #92481C22semidirect
32. #92480C22semidirect
33. #92479C22semidirect
34. #92474C22semidirect
35. Dic124C22semidirect
36. D248C22semidirect
37. #92470C22semidirect
38. #92470C22semidirect
39. #92469C22semidirect
40. C8×D31C22semidirect
100. C2×SD16D31semidirect
102. C31#577semidirect
113. C2×Q8C2×D31semidirect
124. SD16C2×D31semidirect
125. SD16C2×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
#117585642
#117585612
C2×SD16×C312
#117585192
#117585092
#117584932
#117584922
#117584912
SD16×D312
#117584812
#117584782
#57731