Finite Group Databasebeta

← #28406487

Subgroups — #28406487

Order 14464.

272 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 62 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×#16813682C212yesmaximal
2#20299479C214yesmaximal, complemented
3#20299071C211yesmaximal, characteristic
4C2×#14268656C2214yes—
5#16813682—22no—
6#16813682—22no—
7C22×C22⋊D113C2211yescharacteristic
8C4×C22⋊D113—22no—
9#16813582—22no—
10#16813578C2212yes—
11C2×C22⋊Dic113C411yescharacteristic
12C22⋊C4×D113C412yes—
13C2×C22⋊C4×C113C411yescharacteristic
14#14268656—24no—
15#14268656—24no—
16C2×#11744753—24no—
17C23×D113C2×C411yescharacteristic
18C2×C22⋊D113—24no—
19C2×C22⋊D113D412yes—
20C2×C22⋊D113D412yes—
21C22×Dic113—21no—
22C22×Dic113C2311yescharacteristic
23C2×C4×D113—22no—
24#14268626—22no—
25C22⋊Dic113—21no—
26C22⋊Dic113C2×C412yes—
27#14268624—22no—
28C4×Dic113—22no—
29C24×C113C2×C411yescharacteristic
30C22×C4×C113—21no—
31C22⋊C4×C113—21no—
32C22⋊C4×C113C2×C412yes—
33C23×C113—22no—
34C23×C113—81no—
35C23×C113C22⋊C411yescharacteristic
36C23×C113C22⋊C411yescharacteristic
37C23×C113C22×C411yescharacteristic
38C22×D113—22no—
39C22×D113—81no—
40C22×D113C22⋊C412yes—
41C2×C4×C113—22no—
42C2×C4×C113—81no—
43C22⋊D113—24no—
44C22⋊D113—24no—
45C2×Dic113—22no—
46C2×Dic113—81no—
47C2×Dic113C2×D412yes—
48C2×Dic113#4114yes—
49C4×D113—82no—
50#11744753—44no—
51C22×C113—21no—
52C22×C113—21no—
53C22×C113—41no—
54C22×C113—41no—
55C22×C113—41no—
56C22×C113—82no—
57C22×C113C2×C22⋊C411yescharacteristic
58C22×C113#11712yes—
59C2×D113—22no—
60C2×D113—42no—
61C2×D113—82no—
62C4×C113—42no—
63Dic113—42no—
64Dic113#12314yes—
65C2×C113—21no—
66C2×C113—22no—
67C2×C113—41no—
68C2×C113—41no—
69C2×C113#38111yescharacteristic
70D113—42no—
71#1829—1131nomaximal, Sylow
72C113#182911yescharacteristic, complemented, Sylow
73#518—1131no—
74C2×#100—1132no—
75#344—1134no—
76C22×D4—1131no—
77C2×M16—1134no—
78C4×D4—2262no—
79C4×D4—2262no—
80#117—1132no—
81C2×C22⋊C4—1131no—
82C2×C22⋊C4—1132no—
83C2×C22⋊C4#9067311yescharacteristic
84#100—2262no—
85#100—2262no—
86C24—1131no—
87C24C2×#9067311yescharacteristic
88C2×D4—1132no—
89C2×D4—1132no—
90C2×D4—2264no—
91C22×C4—21no—
92C22×C4—1131no—
93C22×C4—2262no—
94C22×C4—2261no—
95M16—2264no—
96M16—2264no—
97C2×C8—2264no—
98C4⋊C4—2262no—
99C22⋊C4—21no—
100C22⋊C4—1132no—
101C22⋊C4—2262no—
102C22⋊C4—2261no—
103C22⋊C4C2×#9067312yes—
104C42—2262no—
105C23—22no—
106C23—81no—
107C23—1132no—
108C23—9041no—
109C23—2262no—
110C23C22⋊#9067311yescharacteristic
111C23C22⋊#9067311yescharacteristic
112C23C22×#9067311yescharacteristic
113D4—2264no—
114D4—2264no—
115C2×C4—22no—
116C2×C4—81no—
117C2×C4—1132no—
118C2×C4—1134no—
119C2×C4—9042no—
120C2×C4—9041no—
121C2×C4—2262no—
122C8—4524no—
123C22—21no—
124C22—21no—
125C22—41no—
126C22—41no—
127C22—41no—
128C22—82no—
129C22—9042no—
130C22—4522no—
131C22—2262no—
132C22C2×C22⋊#9067311yescharacteristic
133C22#1681370112yes—
134C4—42no—
135C4—1134no—
136C4—4522no—
137C2—21no—
138C2—22no—
139C2—41no—
140C2—41no—
141C2—4522no—
142C2#2029954111yescharacteristic
subgroupG/H
centerC2#20299541
commutatorC23×C113C22×C4
FrattiniC23C22×#90673
FittingC2×C22⋊C4×C113C4
socleC2×C113#381
prime radicalC22×C22⋊D113C22
cosocleC22×Dic113C23
hypercenterC2×C22⋊C4#90673
hypocenterC113#1829
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20299479C2semidirect
72. C113#1829semidirect

Maximal subgroups

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

subgroupindex
C2×#168136822
#202994792
#202990712
#1829113