Finite Group Databasebeta

← C2×#509×C113 #28388208

Subgroups — C2×#509×C113 #28388208

Order 14464.

400 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 184 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×#135×C113C211yesmaximal, characteristic, complemented
2C22×D8×C113C211yesmaximal, characteristic, complemented
3#509×C113C218yesmaximal, direct product factor
4C2×SD32×C113C212yesmaximal, complemented
5C2×D16×C113C212yesmaximal, complemented
6C2×M32×C113C211yesmaximal, characteristic, complemented
7C2×#41×C113—21no—
8C22×D4×C113—21no—
9#135×C113—22no—
10#135×C113C2214yescomplemented
11C2×Q16×C113C2211yescharacteristic, complemented
12C2×SD16×C113—21no—
13C2×D8×C113—21no—
14C2×D8×C113—22no—
15C2×D8×C113C2212yes—
16C2×D8×C113C2214yescomplemented
17C2×D8×C113C2211yescharacteristic, complemented
18C22×C8×C113C2211yescharacteristic
19SD32×C113C2218yescomplemented
20D16×C113C2218yescomplemented
21M32×C113C2214yescomplemented
22C2×C16×C113C2212yescomplemented
23C24×C113—41no—
24#41×C113—24no—
25#41×C113—42no—
26C2×Q8×C113—21no—
27C2×D4×C113—22no—
28C2×D4×C113—24no—
29C2×D4×C113—21no—
30C2×D4×C113—41no—
31C2×D4×C113—42no—
32C2×D4×C113—41no—
33C22×C4×C113—41no—
34C22×C4×C113D411yescharacteristic
35Q16×C113—21no—
36Q16×C113C2312yescomplemented
37SD16×C113—24no—
38D8×C113—22no—
39D8×C113—24no—
40D8×C113—21no—
41D8×C113C2314yes—
42D8×C113C2312yescomplemented
43C2×C8×C113D411yescharacteristic
44C2×C8×C113D412yes—
45C2×C8×C113C2311yescharacteristic
46C2×C8×C113C2312yes—
47C16×C113C2314yescomplemented
48C23×C113—44no—
49C23×C113—41no—
50C23×C113—42no—
51C23×C113—84no—
52C23×C113D811yescharacteristic
53Q8×C113—22no—
54Q8×C113—41no—
55D4×C113—24no—
56D4×C113—22no—
57D4×C113—44no—
58D4×C113—44no—
59D4×C113—42no—
60D4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113—44no—
63C2×C4×C113D812yes—
64C2×C4×C113D811yescharacteristic
65C2×C4×C113C2×D412yes—
66C2×C4×C113C2×D411yescharacteristic
67C8×C113C2×D411yescharacteristic
68C8×C113C2×D412yes—
69C8×C113C2411yescharacteristic
70C22×C113—22no—
71C22×C113—42no—
72C22×C113—44no—
73C22×C113—88no—
74C22×C113—82no—
75C22×C113—84no—
76C22×C113C2×D812yes—
77C22×C113C2×D811yescharacteristic
78C4×C113—42no—
79C4×C113C2×D812yes—
80C4×C113C2×D811yescharacteristic
81C4×C113C22×D411yescharacteristic
82C2×C113—22no—
83C2×C113—82no—
84C2×C113—84no—
85C2×C113#50912yesdirect product factor
86C2×C113C22×D811yescharacteristic
87C2×#509C11311yesmaximal, characteristic, direct product factor, Sylow
88C113C2×#50911yescharacteristic, direct product factor, Sylow
89C2×#135C2×C11311yescharacteristic, complemented
90C22×D8C2×C11311yescharacteristic, complemented
91#509C2×C11318yesdirect product factor
92C2×SD32C2×C11312yescomplemented
93C2×D16C2×C11312yescomplemented
94C2×M32C2×C11311yescharacteristic, complemented
95C2×#41—21no—
96C22×D4—21no—
97#135—22no—
98#135C22×C11314yescomplemented
99C2×Q16C22×C11311yescharacteristic, complemented
100C2×SD16—21no—
101C2×D8—21no—
102C2×D8—22no—
103C2×D8C22×C11312yes—
104C2×D8C22×C11314yescomplemented
105C2×D8C22×C11311yescharacteristic, complemented
106C22×C8C22×C11311yescharacteristic
107SD32C22×C11318yescomplemented
108D16C22×C11318yescomplemented
109M32C22×C11314yescomplemented
110C2×C16C22×C11312yescomplemented
111C24—41no—
112#41—24no—
113#41—42no—
114C2×Q8—21no—
115C2×D4—22no—
116C2×D4—24no—
117C2×D4—21no—
118C2×D4—41no—
119C2×D4—41no—
120C2×D4—42no—
121C22×C4—41no—
122C22×C4D4×C11311yescharacteristic
123Q16—21no—
124Q16C23×C11312yescomplemented
125SD16—24no—
126D8—22no—
127D8—24no—
128D8—21no—
129D8C23×C11314yes—
130D8C23×C11312yescomplemented
131C2×C8D4×C11311yescharacteristic
132C2×C8D4×C11312yes—
133C2×C8C23×C11311yescharacteristic
134C2×C8C23×C11312yes—
135C16C23×C11314yescomplemented
136C23—41no—
137C23—44no—
138C23—42no—
139C23—84no—
140C23D8×C11311yescharacteristic
141Q8—22no—
142Q8—41no—
143D4—24no—
144D4—22no—
145D4—44no—
146D4—44no—
147D4—42no—
148D4—41no—
149C2×C4—41no—
150C2×C4—44no—
151C2×C4D8×C11311yescharacteristic
152C2×C4D8×C11312yes—
153C2×C4C2×D4×C11311yescharacteristic
154C2×C4C2×D4×C11312yes—
155C8C2×D4×C11311yescharacteristic
156C8C2×D4×C11312yes—
157C8C24×C11311yescharacteristic
158C22—22no—
159C22—42no—
160C22—44no—
161C22—88no—
162C22—84no—
163C22—82no—
164C22C2×D8×C11312yes—
165C22C2×D8×C11311yescharacteristic
166C4—42no—
167C4C2×D8×C11312yes—
168C4C2×D8×C11311yescharacteristic
169C4C22×D4×C11311yescharacteristic
170C2—22no—
171C2—84no—
172C2—82no—
173C2#509×C11312yesdirect product factor
174C2C22×D8×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×D8
commutator, Frattini, cosocleC8C24×C113
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C22×C4×C113 ◁ C22×C8×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#135×C113C2semidirect
2. C22×D8×C113C2semidirect
3. #509×C113C2direct (N × H)
4. C2×SD32×C113C2semidirect
5. C2×D16×C113C2semidirect
6. C2×M32×C113C2semidirect
10. #135×C113C22semidirect
11. C2×Q16×C113C22semidirect
16. C2×D8×C113C22semidirect
17. C2×D8×C113C22semidirect
19. SD32×C113C22semidirect
20. D16×C113C22semidirect
21. M32×C113C22semidirect
22. C2×C16×C113C22semidirect
36. Q16×C113C23semidirect
42. D8×C113C23semidirect
47. C16×C113C23semidirect
85. C2×C113#509direct (N × H)
87. C2×#509C113direct (N × H)
88. C113C2×#509direct (N × H)
89. C2×#135C2×C113semidirect
90. C22×D8C2×C113semidirect
91. #509C2×C113direct (N × H)
92. C2×SD32C2×C113semidirect
93. C2×D16C2×C113semidirect
94. C2×M32C2×C113semidirect
98. #135C22×C113semidirect
99. C2×Q16C22×C113semidirect
104. C2×D8C22×C113semidirect
105. C2×D8C22×C113semidirect
107. SD32C22×C113semidirect
108. D16C22×C113semidirect
109. M32C22×C113semidirect
110. C2×C16C22×C113semidirect
124. Q16C23×C113semidirect
130. D8C23×C113semidirect
135. C16C23×C113semidirect
173. C2#509×C113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#135×C1132
C22×D8×C1132
#509×C1132
C2×SD32×C1132
C2×D16×C1132
C2×M32×C1132
C2×#509113