Finite Group Databasebeta

← C2×#22583637 #31827253

Subgroups — C2×#22583637 #31827253

Order 18112.

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

normal subgroups only

This group has 298 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
1C2×#17985393C211yesmaximal, characteristic, complemented
2C2×D4×D283C211yesmaximal, characteristic, complemented
3#22583637C218yesmaximal, direct product factor
4C2×#17985379C211yesmaximal, characteristic, complemented
5C2×D2264C211yesmaximal, characteristic, complemented
6C2×#17985377C211yesmaximal, characteristic, complemented
7C2×#17985375C211yesmaximal, characteristic, complemented
8C2×SD16×C283C211yesmaximal, characteristic, complemented
9C23×D283—21no—
10#17985393—22no—
11#17985393C2214yescomplemented
12C2×D1132—21no—
13C2×D1132C2211yescharacteristic
14C2×D1132C2211yescharacteristic, complemented
15C2×C22⋊D283—21no—
16D4×D283—22no—
17D4×D283C2214yescomplemented
18C2×C4×D283—21no—
19C2×C4×D283C2211yescharacteristic
20#17985379C2214yescomplemented
21D2264C2214yescomplemented
22#17985377C2214yescomplemented
23#17985375C2214yescomplemented
24C2×C283⋊C8C2211yescharacteristic, complemented
25C2×Q8×C283C2211yescharacteristic, complemented
26C2×D4×C283C2211yescharacteristic
27SD16×C283C2214yescomplemented
28C2×C8×C283C2211yescharacteristic, complemented
29C22×D283—21no—
30C22×D283—21no—
31C22×D283—24no—
32C22×D283—44no—
33C22×D283D411yescharacteristic
34D1132—24no—
35D1132—21no—
36D1132—21no—
37D1132C2312yes—
38D1132C2312yescomplemented
39C22⋊D283—24no—
40C2×Dic283D411yescharacteristic
41C4×D283—24no—
42C4×D283D412yes—
43C4×D283C2312yes—
44C283⋊C8C2312yescomplemented
45C23×C283—21no—
46Q8×C283—21no—
47Q8×C283C2312yescomplemented
48D4×C283—21no—
49D4×C283C2312yes—
50C2×C4×C283—21no—
51C2×C4×C283C2311yescharacteristic
52C8×C283C2312yescomplemented
53C22×C283—22no—
54C22×C283—42no—
55C22×C283C2×D411yescharacteristic
56C2×D283—22no—
57C2×D283—22no—
58C2×D283—22no—
59C2×D283—48no—
60C2×D283—42no—
61C2×D283—42no—
62C2×D283C2×D412yes—
63C4×C283—22no—
64C4×C283C2×D411yescharacteristic
65C4×C283C2411yescharacteristic
66Dic283C2×D412yes—
67C2×C283—42no—
68C2×C283AGL(1,ℤ/8)12yescomplemented
69C2×C283C22×D411yescharacteristic
70D283—22no—
71D283—42no—
72D283—42no—
73C283C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
74C2×AGL(1,ℤ/8)—2831nomaximal, Sylow
75C2×#41—2831no—
76C22×D4—2831no—
77AGL(1,ℤ/8)—2838no—
78C2×SD16—2831no—
79C2×SD16D28311yescharacteristic, complemented
80C2×D8—2831no—
81C2×D8—2831no—
82C2×M16—2831no—
83C24—5661no—
84#41—2834no—
85#41—5662no—
86C2×Q8C2×D28311yescharacteristic, complemented
87C2×D4—2834no—
88C2×D4—2831no—
89C2×D4—2831no—
90C2×D4—5661no—
91C2×D4—5662no—
92C2×D4—5661no—
93C2×D4C2×D28311yescharacteristic
94C22×C4—2831no—
95C22×C4—5661no—
96SD16—2834no—
97SD16C2×D28314yescomplemented
98D8—2834no—
99D8—2834no—
100M16—2834no—
101C2×C8—2831no—
102C2×C8C2×D28311yescharacteristic, complemented
103C23—21no—
104C23—2831no—
105C23—5664no—
106C23—5661no—
107C23—5661no—
108C23—11324no—
109Q8—21no—
110Q8C22×D28312yescomplemented
111D4—21no—
112D4—2832no—
113D4—2832no—
114D4—5664no—
115D4—5664no—
116D4—5661no—
117D4—5661no—
118D4C22×D28312yes—
119C2×C4—21no—
120C2×C4—2831no—
121C2×C4—2832no—
122C2×C4—2832no—
123C2×C4—5664no—
124C2×C4C22×D28311yescharacteristic
125C8—2832no—
126C8C22×D28312yescomplemented
127C22—22no—
128C22—42no—
129C22—2832no—
130C22—5662no—
131C22—5662no—
132C22—5662no—
133C22—11328no—
134C22—11322no—
135C22—11322no—
136C22D4×D28311yescharacteristic
137C4—22no—
138C4—2832no—
139C4D4×D28311yescharacteristic
140C4C23×D28311yescharacteristic
141C2—42no—
142C2—5662no—
143C2—11322no—
144C2—11322no—
145C2#2258363712yesdirect product factor
146C2C2×D4×D28311yescharacteristic
subgroupG/H
centerC22D4×D283
commutator, cosocleC4×C283C24
FrattiniC4C23×D283
FittingC2×SD16×C283C2
socleC22×C283C2×D4
hypercenterC2×SD16D283
hypocenterC283C2×AGL(1,ℤ/8)
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#17985393C2semidirect
2. C2×D4×D283C2semidirect
3. #22583637C2direct (N × H)
4. C2×#17985379C2semidirect
5. C2×D2264C2semidirect
6. C2×#17985377C2semidirect
7. C2×#17985375C2semidirect
8. C2×SD16×C283C2semidirect
11. #17985393C22semidirect
14. C2×D1132C22semidirect
17. D4×D283C22semidirect
20. #17985379C22semidirect
21. D2264C22semidirect
22. #17985377C22semidirect
23. #17985375C22semidirect
24. C2×C283⋊C8C22semidirect
25. C2×Q8×C283C22semidirect
27. SD16×C283C22semidirect
28. C2×C8×C283C22semidirect
38. D1132C23semidirect
44. C283⋊C8C23semidirect
47. Q8×C283C23semidirect
52. C8×C283C23semidirect
68. C2×C283AGL(1,ℤ/8)semidirect
73. C283C2×AGL(1,ℤ/8)semidirect
79. C2×SD16D283semidirect
86. C2×Q8C2×D283semidirect
97. SD16C2×D283semidirect
102. C2×C8C2×D283semidirect
110. Q8C22×D283semidirect
126. C8C22×D283semidirect
145. C2#22583637direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179853932
C2×D4×D2832
#225836372
C2×#179853792
C2×D22642
C2×#179853772
C2×#179853752
C2×SD16×C2832
C2×AGL(1,ℤ/8)283