Finite Group Databasebeta

← C22×D8×D113 #28405288

Subgroups — C22×D8×D113 #28405288

Order 14464.

1976 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 565 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
1C22×D4×D113C212yesmaximal, complemented
2C22×D904C211yesmaximal, characteristic, complemented
3C22×#14268632C212yesmaximal, complemented
4C2×D8×D113C2124yesmaximal, direct product factor
5C22×C8×D113C211yesmaximal, characteristic, complemented
6C22×D8×C113C211yesmaximal, characteristic, complemented
7C24×D113—22no—
8C22×D452C2212yescomplemented
9C22×C22⋊D113—22no—
10C2×D4×D113—212no—
11C2×D4×D113C22124yescomplemented
12C22×C4×D113C2211yescharacteristic
13C2×D904C22112yescomplemented
14C2×#14268632C22124yescomplemented
15D8×D113C22164yesdirect product factor
16C22×#11744751C2211yescharacteristic, complemented
17C2×C8×D113C22112yescomplemented
18C22×D4×C113C2212yescomplemented
19C2×D8×C113C22112yescomplemented
20C22×C8×C113C2211yescharacteristic, complemented
21C23×D113—22no—
22C23×D113—224no—
23C23×D113—416no—
24C23×D113D411yescharacteristic
25C2×D452—26no—
26C2×D452C23112yescomplemented
27C2×C22⋊D113—224no—
28D4×D113—248no—
29D4×D113C23132yescomplemented
30C22×Dic113D411yescharacteristic
31C2×C4×D113D416yes—
32C2×C4×D113C2316yes—
33D904C23116yescomplemented
34#14268632C23132yescomplemented
35C2×#11744751C2316yescomplemented
36C8×D113C23116yescomplemented
37C24×C113—22no—
38C2×D4×C113—26no—
39C2×D4×C113C23112yescomplemented
40C22×C4×C113C2311yescharacteristic
41D8×C113C23116yescomplemented
42C2×C8×C113C2316yescomplemented
43C23×C113—212no—
44C23×C113—48no—
45C23×C113C2×D411yescharacteristic
46C22×D113—212no—
47C22×D113—232no—
48C22×D113—48no—
49C22×D113—496no—
50C22×D113D818yesdirect product factor
51C22×D113C2×D416yes—
52D4×C113—212no—
53D4×C113C2418yescomplemented
54C2×C4×C113C2×D413yes—
55C2×C4×C113C2413yes—
56C22⋊D113—232no—
57C2×Dic113C2×D416yes—
58D452—212no—
59D452C2418yescomplemented
60C4×D113C2×D4112yes—
61C4×D113C2414yes—
62C8×C113C2414yescomplemented
63#11744751C2414yescomplemented
64C22×C113—28no—
65C22×C113—424no—
66C22×C113C2×D814yescomplemented
67C22×C113C22×D413yes—
68C2×D113—28no—
69C2×D113—424no—
70C2×D113—464no—
71C2×D113C2×D8124yesdirect product factor
72C2×D113C22×D414yes—
73C4×C113C22×D413yes—
74C4×C113C2511yescharacteristic
75Dic113C22×D414yes—
76C2×C113—48no—
77C2×C113C22×D816yescomplemented
78C2×C113C23×D411yescharacteristic
79D113—48no—
80D113C22×D818yesdirect product factor
81C23×D8—1131nomaximal, Sylow
82C113C23×D811yescharacteristic, complemented, Sylow
83C23×D4—1132no—
84C22×D8—1132no—
85C22×D8—11324no—
86C22×D8—1131no—
87C22×D8D11311yescharacteristic, direct product factor
88C23×C8—1131no—
89C25—2262no—
90C22×D4—11324no—
91C22×D4—1132no—
92C22×D4—22612no—
93C22×D4—2262no—
94C22×D4C2×D11312yescomplemented
95C23×C4—1131no—
96C2×D8—11324no—
97C2×D8—11364no—
98C2×D8—11312no—
99C2×D8C2×D113112yesdirect product factor
100C22×C8—1131no—
101C22×C8—11312no—
102C22×C8C2×D11311yescharacteristic, complemented
103C24—22no—
104C24—1131no—
105C24—45216no—
106C24—22624no—
107C24—2262no—
108C2×D4—26no—
109C2×D4—11332no—
110C2×D4—11312no—
111C2×D4—22648no—
112C2×D4—22624no—
113C2×D4—2266no—
114C2×D4C22×D113112yescomplemented
115C22×C4—1131no—
116C22×C4—1136no—
117C22×C4—1136no—
118C22×C4C22×D11311yescharacteristic
119D8—11332no—
120D8—11316no—
121D8C22×D113116yesdirect product factor
122C2×C8—1136no—
123C2×C8—11316no—
124C2×C8C22×D11316yescomplemented
125C23—212no—
126C23—48no—
127C23—1138no—
128C23—1136no—
129C23—45296no—
130C23—4528no—
131C23—22632no—
132C23—22612no—
133C23D4×D11311yescharacteristic
134D4—212no—
135D4—1138no—
136D4—22632no—
137D4—22612no—
138D4C23×D11318yescomplemented
139C2×C4—1136no—
140C2×C4—11312no—
141C2×C4—1134no—
142C2×C4D4×D11313yes—
143C2×C4C23×D11313yes—
144C8—1134no—
145C8C23×D11314yescomplemented
146C22—28no—
147C22—424no—
148C22—11324no—
149C22—1134no—
150C22—45264no—
151C22—45224no—
152C22—2268no—
153C22D8×D11314yesdirect product factor
154C22C2×D4×D11313yes—
155C4—1134no—
156C4C2×D4×D11313yes—
157C4C24×D11311yescharacteristic
158C2—48no—
159C2—1138no—
160C2—4528no—
161C2C2×D8×D11316yesdirect product factor
162C2C22×D4×D11311yescharacteristic
subgroupG/H
centerC23D4×D113
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
FittingC22×D8×C113C2
socleC23×C113C2×D4
hypercenterC22×D8D113
hypocenterC113C23×D8
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D113C2semidirect
2. C22×D904C2semidirect
3. C22×#14268632C2semidirect
4. C2×D8×D113C2direct (N × H)
5. C22×C8×D113C2semidirect
6. C22×D8×C113C2semidirect
8. C22×D452C22semidirect
11. C2×D4×D113C22semidirect
13. C2×D904C22semidirect
14. C2×#14268632C22semidirect
15. D8×D113C22direct (N × H)
16. C22×#11744751C22semidirect
17. C2×C8×D113C22semidirect
18. C22×D4×C113C22semidirect
19. C2×D8×C113C22semidirect
20. C22×C8×C113C22semidirect
26. C2×D452C23semidirect
29. D4×D113C23semidirect
33. D904C23semidirect
34. #14268632C23semidirect
35. C2×#11744751C23semidirect
36. C8×D113C23semidirect
39. C2×D4×C113C23semidirect
41. D8×C113C23semidirect
42. C2×C8×C113C23semidirect
50. C22×D113D8direct (N × H)
53. D4×C113C24semidirect
59. D452C24semidirect
62. C8×C113C24semidirect
63. #11744751C24semidirect
66. C22×C113C2×D8semidirect
71. C2×D113C2×D8direct (N × H)
77. C2×C113C22×D8semidirect
80. D113C22×D8direct (N × H)
82. C113C23×D8semidirect
87. C22×D8D113direct (N × H)
94. C22×D4C2×D113semidirect
99. C2×D8C2×D113direct (N × H)
102. C22×C8C2×D113semidirect
114. C2×D4C22×D113semidirect
121. D8C22×D113direct (N × H)
124. C2×C8C22×D113semidirect
138. D4C23×D113semidirect
145. C8C23×D113semidirect
153. C22D8×D113direct (N × H)
161. C2C2×D8×D113direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1132
C22×D9042
C22×#142686322
C2×D8×D1132
C22×C8×D1132
C22×D8×C1132
C23×D8113