Finite Group Databasebeta

← C2×#20298911 #28400445

Subgroups — C2×#20298911 #28400445

Order 14464.

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

normal subgroups only

This group has 512 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×#16813596C211yesmaximal, characteristic
2#20298911C218yesmaximal, direct product factor
3C2×#16813555C212yesmaximal, complemented
4C2×#16813542C212yesmaximal, complemented
5C2×C22⋊#11744751C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C113C211yesmaximal, characteristic, complemented
7C22×D452C2211yescharacteristic
8C22×C22⋊D113—21no—
9C22×#11744751C2212yes—
10#16813596—22no—
11#16813596C2214yes—
12C2×C4⋊Dic113C2211yescharacteristic
13C2×#14268624—21no—
14#16813555C2218yescomplemented
15#16813542C2218yescomplemented
16C22⋊#11744751C2214yescomplemented
17C23×C4×C113—21no—
18C23×C4×C113C2211yescharacteristic
19C2×C4⋊C4×C113—22no—
20C2×C4⋊C4×C113—21no—
21C2×C4⋊C4×C113C2212yes—
22C2×C4⋊C4×C113C2214yescomplemented
23C23×D113—21no—
24C2×D452—24no—
25C2×D452—21no—
26C2×D452C2312yes—
27C2×C22⋊D113—24no—
28C2×C22⋊D113—44no—
29C22×Dic113—21no—
30C2×#11744751—24no—
31C2×#11744751C2314yes—
32C4⋊Dic113—21no—
33C4⋊Dic113C2312yes—
34#14268624—24no—
35C24×C113D411yescharacteristic
36C22×C4×C113—24no—
37C22×C4×C113—22no—
38C22×C4×C113—24no—
39C22×C4×C113—44no—
40C22×C4×C113D411yescharacteristic
41C22×C4×C113D412yes—
42C22×C4×C113C2312yes—
43C22×C4×C113C2311yescharacteristic
44C4⋊C4×C113—22no—
45C4⋊C4×C113—24no—
46C4⋊C4×C113C2314yes—
47C23×C113—22no—
48C23×C113—22no—
49C23×C113D814yes—
50C23×C113C2×D412yes—
51C23×C113C2×D411yescharacteristic
52C22×D113—22no—
53C22×D113—42no—
54C22×D113—42no—
55C22×D113—42no—
56C2×C4×C113—22no—
57C2×C4×C113—24no—
58C2×C4×C113—24no—
59C2×C4×C113—24no—
60C2×C4×C113—48no—
61C2×C4×C113—44no—
62C2×C4×C113C2×D412yes—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113#4114yes—
65C2×C4×C113C2411yescharacteristic
66C22⋊D113—48no—
67C2×Dic113—22no—
68C2×Dic113—42no—
69D452—24no—
70D452—42no—
71#11744751—24no—
72C22×C113—22no—
73C22×C113—22no—
74C22×C113—28no—
75C22×C113#12312yes—
76C22×C113C2×D814yes—
77C22×C113C2×D812yes—
78C22×C113#13712yes—
79C22×C113C22×D411yescharacteristic
80C2×D113—42no—
81C2×D113—42no—
82C2×D113—42no—
83C2×D113—84no—
84C4×C113—22no—
85C4×C113—44no—
86C4×C113#12312yes—
87C4×C113C2×#4112yes—
88Dic113—42no—
89C2×C113—24no—
90C2×C113#48014yescomplemented
91C2×C113C2×#12311yescharacteristic
92C2×C113C22×D811yescharacteristic
93C2×C113C2×#13711yescharacteristic
94D113—82no—
95C2×#480—1131nomaximal, Sylow
96C113C2×#48011yescharacteristic, complemented, Sylow
97C2×#121—1131no—
98C22×C4⋊C4D11311yescharacteristic, complemented
99#480—1138no—
100C2×#107—1132no—
101C2×#102—1132no—
102C2×C22⋊C8—1131no—
103C22×D4—1131no—
104C22×D4—2261no—
105C23×C4—21no—
106C23×C4C2×D11311yescharacteristic
107C22×C8—1132no—
108#121—1134no—
109#121—2262no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—1131no—
113C2×C4⋊C4C2×D11312yes—
114C2×C4⋊C4C2×D11314yescomplemented
115C2×C22⋊C4—2261no—
116#107—1138no—
117#102—1138no—
118C22⋊C8—1134no—
119C24—2261no—
120C24C22⋊D11311yescharacteristic
121C2×D4—1132no—
122C2×D4—4524no—
123C2×D4—2264no—
124C2×D4—2261no—
125C2×D4—2264no—
126C22×C4—24no—
127C22×C4—24no—
128C22×C4—22no—
129C22×C4—44no—
130C22×C4—2261no—
131C22×C4C22⋊D11312yes—
132C22×C4C22⋊D11311yescharacteristic
133C22×C4C22×D11312yes—
134C22×C4C22×D11311yescharacteristic
135C2×C8—1134no—
136C2×C8—2264no—
137C4⋊C4—22no—
138C4⋊C4—24no—
139C4⋊C4—1132no—
140C4⋊C4—2261no—
141C4⋊C4C22×D11314yes—
142C22⋊C4—2264no—
143C23—22no—
144C23—22no—
145C23—4522no—
146C23—4522no—
147C23—4522no—
148C23—2262no—
149C23#1426863214yes—
150C23C2×C22⋊D11312yes—
151C23C2×C22⋊D11311yescharacteristic
152D4—4528no—
153D4—4522no—
154D4—2264no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—48no—
160C2×C4—44no—
161C2×C4—4522no—
162C2×C4—2262no—
163C2×C4C2×C22⋊D11312yes—
164C2×C4C2×C22⋊D11311yescharacteristic
165C2×C4#1426864714yes—
166C2×C4C23×D11311yescharacteristic
167C8—2264no—
168C22—22no—
169C22—22no—
170C22—28no—
171C22—9044no—
172C22—4522no—
173C22—4522no—
174C22—4522no—
175C22#1681360512yes—
176C22C2×#1426863214yes—
177C22C2×#1426863212yes—
178C22#1681365312yes—
179C22C22×C22⋊D11311yescharacteristic
180C4—22no—
181C4—44no—
182C4—4522no—
183C4#1681360512yes—
184C4C2×#1426864712yes—
185C2—24no—
186C2—9042no—
187C2#2029891114yesdirect product factor
188C2C2×#1681360511yescharacteristic
189C2C22×#1426863211yescharacteristic
190C2C2×#1681365311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×C4⋊C4×C113C2
socleC23×C113C2×D4
prime radicalC2×#16813596C2
hypercenterC22×C4⋊C4D113
hypocenterC113C2×#480
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. #20298911C2direct (N × H)
3. C2×#16813555C2semidirect
4. C2×#16813542C2semidirect
5. C2×C22⋊#11744751C2semidirect
6. C22×C4⋊C4×C113C2semidirect
14. #16813555C22semidirect
15. #16813542C22semidirect
16. C22⋊#11744751C22semidirect
22. C2×C4⋊C4×C113C22semidirect
90. C2×C113#480semidirect
96. C113C2×#480semidirect
98. C22×C4⋊C4D113semidirect
114. C2×C4⋊C4C2×D113semidirect
187. C2#20298911direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168135962
#202989112
C2×#168135552
C2×#168135422
C2×C22⋊#117447512
C22×C4⋊C4×C1132
C2×#480113