Finite Group Databasebeta

← C2×#26045819 #37560210

Subgroups — C2×#26045819 #37560210

Order 23872.

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×#20238611C211yesmaximal, characteristic, complemented
2C2×D4×D373C211yesmaximal, characteristic, complemented
3#26045819C218yesmaximal, direct product factor
4C2×#20238597C211yesmaximal, characteristic, complemented
5C2×D2984C211yesmaximal, characteristic, complemented
6C2×#20238595C211yesmaximal, characteristic, complemented
7C2×#20238593C211yesmaximal, characteristic, complemented
8C2×SD16×C373C211yesmaximal, characteristic, complemented
9C23×D373—21no—
10#20238611—22no—
11#20238611C2214yescomplemented
12C2×D1492—21no—
13C2×D1492C2211yescharacteristic
14C2×D1492C2211yescharacteristic, complemented
15C2×C22⋊D373—21no—
16D4×D373—22no—
17D4×D373C2214yescomplemented
18C2×C4×D373—21no—
19C2×C4×D373C2211yescharacteristic
20#20238597C2214yescomplemented
21D2984C2214yescomplemented
22#20238595C2214yescomplemented
23#20238593C2214yescomplemented
24C2×#15688412C2211yescharacteristic, complemented
25C2×Q8×C373C2211yescharacteristic, complemented
26C2×D4×C373C2211yescharacteristic
27SD16×C373C2214yescomplemented
28C2×C8×C373C2211yescharacteristic, complemented
29C22×D373—21no—
30C22×D373—21no—
31C22×D373—24no—
32C22×D373—44no—
33C22×D373D411yescharacteristic
34D1492—24no—
35D1492—21no—
36D1492—21no—
37D1492C2312yes—
38D1492C2312yescomplemented
39C22⋊D373—24no—
40C2×Dic373D411yescharacteristic
41C4×D373—24no—
42C4×D373D412yes—
43C4×D373C2312yes—
44#15688412C2312yescomplemented
45C23×C373—21no—
46Q8×C373—21no—
47Q8×C373C2312yescomplemented
48D4×C373—21no—
49D4×C373C2312yes—
50C2×C4×C373—21no—
51C2×C4×C373C2311yescharacteristic
52C8×C373C2312yescomplemented
53C22×C373—22no—
54C22×C373—42no—
55C22×C373C2×D411yescharacteristic
56C2×D373—22no—
57C2×D373—22no—
58C2×D373—22no—
59C2×D373—48no—
60C2×D373—42no—
61C2×D373—42no—
62C2×D373C2×D412yes—
63C4×C373—22no—
64C4×C373C2×D411yescharacteristic
65C4×C373C2411yescharacteristic
66Dic373C2×D412yes—
67C2×C373—42no—
68C2×C373AGL(1,ℤ/8)12yescomplemented
69C2×C373C22×D411yescharacteristic
70D373—22no—
71D373—42no—
72D373—42no—
73C373C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
74C2×AGL(1,ℤ/8)—3731nomaximal, Sylow
75C2×#41—3731no—
76C22×D4—3731no—
77AGL(1,ℤ/8)—3738no—
78C2×SD16—3731no—
79C2×SD16D37311yescharacteristic, complemented
80C2×D8—3731no—
81C2×D8—3731no—
82C2×M16—3731no—
83C24—7461no—
84#41—3734no—
85#41—7462no—
86C2×Q8C2×D37311yescharacteristic, complemented
87C2×D4—3734no—
88C2×D4—3731no—
89C2×D4—3731no—
90C2×D4—7461no—
91C2×D4—7462no—
92C2×D4—7461no—
93C2×D4C2×D37311yescharacteristic
94C22×C4—3731no—
95C22×C4—7461no—
96SD16—3734no—
97SD16C2×D37314yescomplemented
98D8—3734no—
99D8—3734no—
100M16—3734no—
101C2×C8—3731no—
102C2×C8C2×D37311yescharacteristic, complemented
103C23—21no—
104C23—3731no—
105C23—14924no—
106C23—7464no—
107C23—7461no—
108C23—7461no—
109Q8—21no—
110Q8C22×D37312yescomplemented
111D4—21no—
112D4—3732no—
113D4—3732no—
114D4—7464no—
115D4—7464no—
116D4—7461no—
117D4—7461no—
118D4C22×D37312yes—
119C2×C4—21no—
120C2×C4—3731no—
121C2×C4—3732no—
122C2×C4—3732no—
123C2×C4—7464no—
124C2×C4C22×D37311yescharacteristic
125C8—3732no—
126C8C22×D37312yescomplemented
127C22—22no—
128C22—42no—
129C22—3732no—
130C22—14928no—
131C22—14922no—
132C22—14922no—
133C22—7462no—
134C22—7462no—
135C22—7462no—
136C22D4×D37311yescharacteristic
137C4—22no—
138C4—3732no—
139C4D4×D37311yescharacteristic
140C4C23×D37311yescharacteristic
141C2—42no—
142C2—14922no—
143C2—14922no—
144C2—7462no—
145C2#2604581912yesdirect product factor
146C2C2×D4×D37311yescharacteristic
subgroupG/H
centerC22D4×D373
commutator, cosocleC4×C373C24
FrattiniC4C23×D373
FittingC2×SD16×C373C2
socleC22×C373C2×D4
hypercenterC2×SD16D373
hypocenterC373C2×AGL(1,ℤ/8)
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#20238611C2semidirect
2. C2×D4×D373C2semidirect
3. #26045819C2direct (N × H)
4. C2×#20238597C2semidirect
5. C2×D2984C2semidirect
6. C2×#20238595C2semidirect
7. C2×#20238593C2semidirect
8. C2×SD16×C373C2semidirect
11. #20238611C22semidirect
14. C2×D1492C22semidirect
17. D4×D373C22semidirect
20. #20238597C22semidirect
21. D2984C22semidirect
22. #20238595C22semidirect
23. #20238593C22semidirect
24. C2×#15688412C22semidirect
25. C2×Q8×C373C22semidirect
27. SD16×C373C22semidirect
28. C2×C8×C373C22semidirect
38. D1492C23semidirect
44. #15688412C23semidirect
47. Q8×C373C23semidirect
52. C8×C373C23semidirect
68. C2×C373AGL(1,ℤ/8)semidirect
73. C373C2×AGL(1,ℤ/8)semidirect
79. C2×SD16D373semidirect
86. C2×Q8C2×D373semidirect
97. SD16C2×D373semidirect
102. C2×C8C2×D373semidirect
110. Q8C22×D373semidirect
126. C8C22×D373semidirect
145. C2#26045819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202386112
C2×D4×D3732
#260458192
C2×#202385972
C2×D29842
C2×#202385952
C2×#202385932
C2×SD16×C3732
C2×AGL(1,ℤ/8)373