Finite Group Databasebeta

← C2×#20298933 #28400479

Subgroups — C2×#20298933 #28400479

Order 14464.

460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16813601C211yesmaximal, characteristic
2#20298933C218yesmaximal, direct product factor
3C2×#16813555C212yesmaximal, complemented
4C2×#16813545C212yesmaximal, complemented
5C2×C22⋊#11744751C211yesmaximal, characteristic
6C22×C4⋊C4×C113C211yesmaximal, characteristic
7C22×Dic226C2211yescharacteristic
8C22×#11744751C2212yes—
9#16813601—22no—
10#16813601C2214yes—
11C2×C4⋊Dic113C2211yescharacteristic
12C2×#14268626—21no—
13C2×C22⋊Dic113—21no—
14#16813555C2218yescomplemented
15#16813545C2218yescomplemented
16C22⋊#11744751C2214yes—
17C23×C4×C113—21no—
18C23×C4×C113C2211yescharacteristic
19C2×C4⋊C4×C113—21no—
20C2×C4⋊C4×C113—22no—
21C2×C4⋊C4×C113C2212yes—
22C2×C4⋊C4×C113C2214yes—
23C2×Dic226—24no—
24C2×Dic226—21no—
25C2×Dic226C2312yes—
26C22×Dic113—21no—
27C22×Dic113—21no—
28C2×#11744751—24no—
29C2×#11744751C2314yes—
30C4⋊Dic113—21no—
31C4⋊Dic113C2312yes—
32#14268626—24no—
33C22⋊Dic113—24no—
34C24×C113D411yescharacteristic
35C22×C4×C113—24no—
36C22×C4×C113—24no—
37C22×C4×C113—22no—
38C22×C4×C113—44no—
39C22×C4×C113D411yescharacteristic
40C22×C4×C113D412yes—
41C22×C4×C113C2312yes—
42C22×C4×C113C2311yescharacteristic
43C4⋊C4×C113—24no—
44C4⋊C4×C113—22no—
45C4⋊C4×C113C2314yes—
46C23×C113—22no—
47C23×C113—22no—
48C23×C113Q1614yes—
49C23×C113C2×D412yes—
50C23×C113C2×D411yescharacteristic
51C2×C4×C113—22no—
52C2×C4×C113—24no—
53C2×C4×C113—24no—
54C2×C4×C113—24no—
55C2×C4×C113—48no—
56C2×C4×C113—44no—
57C2×C4×C113C2×D412yes—
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113#4114yes—
60C2×C4×C113C2411yescharacteristic
61C2×Dic113—22no—
62C2×Dic113—22no—
63C2×Dic113—42no—
64C2×Dic113—42no—
65Dic226—24no—
66Dic226—42no—
67#11744751—24no—
68C22×C113—22no—
69C22×C113—22no—
70C22×C113—28no—
71C22×C113#12312yes—
72C22×C113C2×Q1614yes—
73C22×C113C2×Q1612yes—
74C22×C113AGL(1,ℤ/8)12yes—
75C22×C113C22×D411yescharacteristic
76C4×C113—22no—
77C4×C113—44no—
78C4×C113#12312yes—
79C4×C113C2×#4112yes—
80Dic113—42no—
81Dic113—42no—
82C2×C113—24no—
83C2×C113#48414yescomplemented
84C2×C113C2×#12311yescharacteristic
85C2×C113C22×Q1611yescharacteristic
86C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
87C2×#484—1131nomaximal, Sylow
88C113C2×#48411yescharacteristic, complemented, Sylow
89C2×C22⋊Q8—1131no—
90C22×C4⋊C4D11311yescharacteristic
91#484—1138no—
92C2×#107—1132no—
93C2×#103—1132no—
94C2×C22⋊C8—1131no—
95C22×Q8—1131no—
96C23×C4—21no—
97C23×C4C2×D11311yescharacteristic
98C22×C8—1132no—
99C22⋊Q8—1134no—
100C22⋊Q8—2262no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—1131no—
104C2×C4⋊C4—2261no—
105C2×C4⋊C4C2×D11312yes—
106C2×C4⋊C4C2×D11314yes—
107C2×C22⋊C4—2261no—
108#107—1138no—
109#103—1138no—
110C22⋊C8—1134no—
111C24C22⋊D11311yescharacteristic
112C2×Q8—1132no—
113C2×Q8—2264no—
114C2×Q8—2261no—
115C22×C4—24no—
116C22×C4—24no—
117C22×C4—22no—
118C22×C4—44no—
119C22×C4—2261no—
120C22×C4—2261no—
121C22×C4C22⋊D11312yes—
122C22×C4C22⋊D11311yescharacteristic
123C22×C4C22×D11312yes—
124C22×C4C22×D11311yescharacteristic
125C2×C8—1134no—
126C2×C8—2264no—
127C4⋊C4—24no—
128C4⋊C4—22no—
129C4⋊C4—1132no—
130C4⋊C4—2261no—
131C4⋊C4—2264no—
132C4⋊C4C22×D11314yes—
133C22⋊C4—2264no—
134C23—22no—
135C23—22no—
136C23#1426863714yes—
137C23C2×C22⋊D11312yes—
138C23C2×C22⋊D11311yescharacteristic
139Q8—4522no—
140Q8—2264no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—24no—
145C2×C4—48no—
146C2×C4—44no—
147C2×C4—4522no—
148C2×C4—4522no—
149C2×C4—2262no—
150C2×C4—2262no—
151C2×C4C2×C22⋊D11312yes—
152C2×C4C2×C22⋊D11311yescharacteristic
153C2×C4#1426864714yes—
154C2×C4C23×D11311yescharacteristic
155C8—2264no—
156C22—22no—
157C22—22no—
158C22—28no—
159C22#1681360512yes—
160C22C2×#1426863714yes—
161C22C2×#1426863712yes—
162C22#1681364812yes—
163C22C22×C22⋊D11311yescharacteristic
164C4—22no—
165C4—44no—
166C4—4522no—
167C4—4522no—
168C4#1681360512yes—
169C4C2×#1426864712yes—
170C2—24no—
171C2#2029893314yesdirect product factor
172C2C2×#1681360511yescharacteristic
173C2C22×#1426863711yescharacteristic
174C2C2×#1681364811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×C4⋊C4×C113C2
socleC23×C113C2×D4
prime radicalC24×C113D4
hypercenterC22×C4⋊C4D113
hypocenterC113C2×#484
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20298933C2direct (N × H)
3. C2×#16813555C2semidirect
4. C2×#16813545C2semidirect
14. #16813555C22semidirect
15. #16813545C22semidirect
83. C2×C113#484semidirect
88. C113C2×#484semidirect
171. C2#20298933direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168136012
#202989332
C2×#168135552
C2×#168135452
C2×C22⋊#117447512
C22×C4⋊C4×C1132
C2×#484113