Finite Group Databasebeta

← #14521853

Subgroups — #14521853

Order 1984.

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

normal subgroups only

This group has 268 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#11758566C211yesmaximal, characteristic, complemented
2#11758561C211yesmaximal, characteristic, complemented
3C31×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4#11758527C211yesmaximal, characteristic, complemented
5C2×#92479C211yesmaximal, characteristic, complemented
6#11758493C212yesmaximal, complemented
7#11758491C212yesmaximal, complemented
8#11758488C212yesmaximal, complemented
9D8×D31C212yesmaximal, complemented
10#11758485C211yesmaximal, characteristic, complemented
11#11758484C211yesmaximal, characteristic, complemented
12#41×C31C2211yescharacteristic, complemented
13C2×D4×C31C2211yescharacteristic, complemented
14C2×C22⋊D31—22no—
15#92499C2212yescomplemented
16#92497—21no—
17#92497C2212yescomplemented
18D4×D31—22no—
19D4×D31—21no—
20D4×D31C2212yescomplemented
21D4×D31C2212yescomplemented
22#92495—21no—
23#92495C2211yescharacteristic
24#92495C2211yescharacteristic, complemented
25C2×D124—21no—
26C2×D124C2211yescharacteristic, complemented
27SD16×C31C2212yescomplemented
28D8×C31C2212yescomplemented
29M16×C31C2211yescharacteristic, complemented
30#92482C2211yescharacteristic, complemented
31#92481C2211yescharacteristic, complemented
32#92480C2211yescharacteristic, complemented
33#92479C2211yescharacteristic, complemented
34#92479C2212yescomplemented
35#92479C2212yescomplemented
36C2×C31⋊C8C2211yescharacteristic, complemented
37D248C2212yescomplemented
38#92470C2212yescomplemented
39#92469C2212yescomplemented
40C8×D31C2212yescomplemented
41C23×C31—21no—
42C22×D31—21no—
43C22×D31—22no—
44C22×D31—22no—
45Q8×C31C2311yescharacteristic
46D4×C31—21no—
47D4×C31—21no—
48D4×C31C2312yes—
49D4×C31C2311yescharacteristic
50C2×C4×C31—21no—
51C2×C4×C31C2311yescharacteristic
52C22⋊D31—21no—
53C22⋊D31—22no—
54C22⋊D31—22no—
55C22⋊D31—22no—
56C22⋊D31D412yes—
57C2×Dic31—22no—
58D124—22no—
59D124—21no—
60D124D411yescharacteristic
61D124C2312yes—
62D124C2311yescharacteristic
63C4×D31—21no—
64C4×D31—22no—
65C4×D31C2312yes—
66Dic62D411yescharacteristic
67Dic62C2311yescharacteristic
68C8×C31C2312yes—
69C31⋊C8C2311yescharacteristic
70C31⋊C8C2311yescharacteristic
71C22×C31—22no—
72C22×C31—21no—
73C22×C31—81no—
74C22×C31C2×D411yescharacteristic
75C2×D31—22no—
76C2×D31—21no—
77C2×D31—82no—
78C2×D31—82no—
79C2×D31—81no—
80C2×D31C2×D412yes—
81C4×C31—21no—
82C4×C31C2×D411yescharacteristic
83C4×C31C2411yescharacteristic
84Dic31—21no—
85Dic31C2×D412yes—
86#576—311nomaximal, Sylow
87C2×C31—21no—
88C2×C31—41no—
89C2×C31—42no—
90C2×C31C22×D411yescharacteristic
91D31—22no—
92D31—42no—
93D31—41no—
94H(5,𝔽2)—311no—
95H(5,𝔽2)—311no—
96AGL(1,ℤ/8)—312no—
97AGL(1,ℤ/8)—312no—
98AGL(1,ℤ/8)—311no—
99AGL(1,ℤ/8)D3111yescharacteristic, complemented
100#135—311no—
101#135—312no—
102C2×D8—311no—
103C2×D8—312no—
104#131—311no—
105C31#57611yescharacteristic, complemented, Sylow
106#41—311no—
107#41—312no—
108#41—312no—
109#41—311no—
110#41—621no—
111#41—621no—
112#41C2×D3111yescharacteristic, complemented
113C2×D4—312no—
114C2×D4—312no—
115C2×D4—311no—
116C2×D4—621no—
117C2×D4—622no—
118C2×D4—621no—
119C2×D4—622no—
120C2×D4C2×D3111yescharacteristic, complemented
121Q16—311no—
122SD16—311no—
123SD16—311no—
124SD16—312no—
125SD16C2×D3112yescomplemented
126D8—312no—
127D8—311no—
128D8—312no—
129D8—312no—
130D8C2×D3112yescomplemented
131M16—312no—
132M16C2×D3111yescharacteristic, complemented
133C2×C8—311no—
134C2×C8—312no—
135C23—21no—
136C23—622no—
137C23—622no—
138C23—621no—
139Q8—311no—
140Q8—311no—
141Q8C22×D3111yescharacteristic
142D4—21no—
143D4—21no—
144D4—312no—
145D4—311no—
146D4—312no—
147D4—311no—
148D4—622no—
149D4—622no—
150D4—622no—
151D4—622no—
152D4—621no—
153D4—621no—
154D4C22×D3112yes—
155D4C22×D3111yescharacteristic
156C2×C4—21no—
157C2×C4—312no—
158C2×C4—622no—
159C2×C4—622no—
160C2×C4—621no—
161C2×C4C22×D3111yescharacteristic
162C8—311no—
163C8—311no—
164C8C22×D3112yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—312no—
169C22—622no—
170C22—621no—
171C22—2481no—
172C22—2482no—
173C22—2482no—
174C22D4×D3111yescharacteristic
175C4—21no—
176C4—312no—
177C4—621no—
178C4D4×D3111yescharacteristic
179C4C23×D3111yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—622no—
184C2—1242no—
185C2—1241no—
186C2C2×D4×D3111yescharacteristic
subgroupG/H
centerC2C2×D4×D31
commutator, cosocleC4×C31C24
FrattiniC4C23×D31
FittingC31×AGL(1,ℤ/8)C2
socleC2×C31C22×D4
hypercenterAGL(1,ℤ/8)D31
hypocenterC31#576
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #11758566C2semidirect
2. #11758561C2semidirect
3. C31×AGL(1,ℤ/8)C2semidirect
4. #11758527C2semidirect
5. C2×#92479C2semidirect
6. #11758493C2semidirect
7. #11758491C2semidirect
8. #11758488C2semidirect
9. D8×D31C2semidirect
10. #11758485C2semidirect
11. #11758484C2semidirect
12. #41×C31C22semidirect
13. C2×D4×C31C22semidirect
15. #92499C22semidirect
17. #92497C22semidirect
20. D4×D31C22semidirect
21. D4×D31C22semidirect
24. #92495C22semidirect
26. C2×D124C22semidirect
27. SD16×C31C22semidirect
28. D8×C31C22semidirect
29. M16×C31C22semidirect
30. #92482C22semidirect
31. #92481C22semidirect
32. #92480C22semidirect
33. #92479C22semidirect
34. #92479C22semidirect
35. #92479C22semidirect
36. C2×C31⋊C8C22semidirect
37. D248C22semidirect
38. #92470C22semidirect
39. #92469C22semidirect
40. C8×D31C22semidirect
99. AGL(1,ℤ/8)D31semidirect
105. C31#576semidirect
112. #41C2×D31semidirect
120. C2×D4C2×D31semidirect
125. SD16C2×D31semidirect
130. D8C2×D31semidirect
132. M16C2×D31semidirect

Maximal subgroups

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

subgroupindex
#117585662
#117585612
C31×AGL(1,ℤ/8)2
#117585272
C2×#924792
#117584932
#117584912
#117584882
D8×D312
#117584852
#117584842
#57631