Finite Group Databasebeta

← #28390973

Subgroups — #28390973

Order 14464.

444 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 97 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
1#20299073C211yesmaximal, characteristic, complemented
2#20298603C212yesmaximal, complemented
3C2×#16813539C211yesmaximal, characteristic, complemented
4#20298358C212yesmaximal, complemented
5C2×#127×C113C211yesmaximal, characteristic
6C2×#14268631C2212yes—
7D4×Dic113—24no—
8#16813581C2212yes—
9C2×C22⋊Dic113—22no—
10#16813543—24no—
11#16813539—22no—
12C22×D4×C113—22no—
13C22×D4×C113C2211yescharacteristic
14C22×D4×C113C2211yescharacteristic
15#127×C113—22no—
16#127×C113C414yescomplemented
17C2×C42×C113C2211yescharacteristic
18C22×Dic113—24no—
19#14268631—22no—
20#14268631—22no—
21C2×#11744751—22no—
22C4⋊Dic113D414yescomplemented
23C22⋊Dic113—24no—
24C22⋊Dic113—22no—
25C4×Dic113—22no—
26C24×C113—21no—
27C24×C113D412yes—
28C2×D4×C113—28no—
29C2×D4×C113—22no—
30C2×D4×C113—22no—
31C2×D4×C113—21no—
32C2×D4×C113—22no—
33C2×D4×C113—22no—
34C2×D4×C113—48no—
35C2×D4×C113C2×C412yes—
36C2×D4×C113C2×C412yescomplemented
37C2×D4×C113D412yes—
38C22×C4×C113—21no—
39C22×C4×C113C2311yescharacteristic
40C42×C113—21no—
41C42×C113C2×C412yescomplemented
42C23×C113—22no—
43C23×C113—22no—
44C23×C113—22no—
45C23×C113—44no—
46C23×C113—44no—
47C23×C113—41no—
48C23×C113—41no—
49C23×C113C22⋊C414yes—
50C23×C113C2×D411yescharacteristic
51D4×C113—24no—
52D4×C113—24no—
53D4×C113—24no—
54D4×C113—416no—
55D4×C113—42no—
56C2×C4×C113—24no—
57C2×C4×C113—22no—
58C2×C4×C113C22×C411yescharacteristic
59C2×C4×C113C2×D412yes—
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113#4112yes—
62C2×Dic113—24no—
63C2×Dic113—84no—
64#11744751—42no—
65C22×C113—22no—
66C22×C113—24no—
67C22×C113—44no—
68C22×C113—44no—
69C22×C113—44no—
70C22×C113—42no—
71C22×C113—82no—
72C22×C113—82no—
73C22×C113—82no—
74C22×C113C2×C22⋊C411yescharacteristic
75C22×C113#12011yescharacteristic
76C22×C113#12311yescharacteristic
77C4×C113—24no—
78C4×C113C4×D412yes—
79C4×C113#12112yes—
80Dic113—44no—
81C2×C113—21no—
82C2×C113—21no—
83C2×C113—44no—
84C2×C113—82no—
85C2×C113#38611yescharacteristic
86C2×C113#45312yes—
87#1887—1131nomaximal, Sylow
88C113#188711yescharacteristic, complemented, Sylow
89C2×#127D11311yescharacteristic
90#518—1131no—
91#418—1132no—
92C2×#100—1131no—
93#339—1132no—
94C22×D4—22no—
95C22×D4C2×D11311yescharacteristic
96C22×D4C2×D11311yescharacteristic
97C2×M16—1132no—
98#127—22no—
99#127Dic11314yescomplemented
100C4×D4—2264no—
101#117—1132no—
102C2×C22⋊C4—2262no—
103C2×C42C2×D11311yescharacteristic
104#102—2264no—
105#100—2262no—
106C24—21no—
107C24C22⋊D11312yes—
108C2×D4—28no—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—48no—
115C2×D4C2×Dic11312yes—
116C2×D4C2×Dic11312yescomplemented
117C2×D4C22⋊D11312yes—
118C22×C4—21no—
119C22×C4—2264no—
120C22×C4C22×D11311yescharacteristic
121M16—2262no—
122M16—2262no—
123C2×C8—2262no—
124C4⋊C4—1134no—
125C22⋊C4—2264no—
126C22⋊C4—2262no—
127C42—21no—
128C42—2262no—
129C42C2×Dic11312yescomplemented
130C23—22no—
131C23—22no—
132C23—22no—
133C23—44no—
134C23—44no—
135C23—41no—
136C23—41no—
137C23C22⋊Dic11314yes—
138C23C2×C22⋊D11311yescharacteristic
139D4—24no—
140D4—24no—
141D4—24no—
142D4—416no—
143D4—42no—
144C2×C4—24no—
145C2×C4—22no—
146C2×C4—9044no—
147C2×C4—2264no—
148C2×C4C22×Dic11311yescharacteristic
149C2×C4D4×D11312yes—
150C2×C4C2×C22⋊D11311yescharacteristic
151C2×C4#1426864612yes—
152C8—4522no—
153C22—22no—
154C22—24no—
155C22—44no—
156C22—44no—
157C22—44no—
158C22—42no—
159C22—82no—
160C22—82no—
161C22—82no—
162C22C2×C22⋊Dic11311yescharacteristic
163C22#1681359011yescharacteristic
164C22#1681360311yescharacteristic
165C4—24no—
166C4—4524no—
167C4D4×Dic11312yes—
168C4#1681359412yes—
169C2—21no—
170C2—21no—
171C2—44no—
172C2—82no—
173C2#2029847811yescharacteristic
174C2#2029876512yes—
subgroupG/H
centerC22#16813590
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting, prime radicalC2×#127×C113C2
socleC22×C113#120
cosocleC22×C4×C113C23
hypercenterC2×#127D113
hypocenterC113#1887
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #20299073C2semidirect
2. #20298603C2semidirect
3. C2×#16813539C2semidirect
4. #20298358C2semidirect
16. #127×C113C4semidirect
22. C4⋊Dic113D4semidirect
36. C2×D4×C113C2×C4semidirect
41. C42×C113C2×C4semidirect
88. C113#1887semidirect
99. #127Dic113semidirect
116. C2×D4C2×Dic113semidirect
129. C42C2×Dic113semidirect

Maximal subgroups

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

subgroupindex
#202990732
#202986032
C2×#168135392
#202983582
C2×#127×C1132
#1887113