Finite Group Databasebeta

← #28388598

Subgroups — #28388598

Order 14464.

154 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 37 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#20298365C211yesmaximal, characteristic
2#20298322C211yesmaximal, characteristic
3#399×C113C211yesmaximal, characteristic
4C2×C22⋊Dic113—21no—
5C22⋊#11744751—21no—
6C2×C4⋊C4×C113—21no—
7C2×C4⋊C4×C113C411yescharacteristic, complemented
8C2×C22⋊C4×C113—21no—
9C2×C22⋊C4×C113C2211yescharacteristic
10#95×C113C411yescharacteristic, complemented
11C22×Dic113—41no—
12C2×#11744751—41no—
13C22⋊Dic113—22no—
14C22⋊Dic113—41no—
15C24×C113D411yescharacteristic
16C22×C4×C113—21no—
17C22×C4×C113—21no—
18C22×C4×C113C2×C411yescharacteristic
19C22×C4×C113D411yescharacteristic
20C4⋊C4×C113—41no—
21C4⋊C4×C113—42no—
22C22⋊C4×C113—41no—
23C22⋊C4×C113—42no—
24C23×C113—21no—
25C23×C113—21no—
26C23×C113—41no—
27C23×C113—41no—
28C23×C113C22⋊C411yescharacteristic
29C23×C113SD1611yescharacteristic
30C23×C113Q1611yescharacteristic
31C2×C4×C113—22no—
32C2×C4×C113—21no—
33C2×C4×C113—21no—
34C2×C4×C113—41no—
35C2×C4×C113—41no—
36C2×C4×C113—41no—
37C2×C4×C113—41no—
38C2×C4×C113—41no—
39C2×C4×C113—41no—
40C2×C4×C113—41no—
41C2×Dic113—42no—
42C2×Dic113—81no—
43C2×Dic113—81no—
44#11744751—81no—
45C22×C113—21no—
46C22×C113—21no—
47C22×C113—21no—
48C22×C113—21no—
49C22×C113—41no—
50C22×C113—41no—
51C22×C113—41no—
52C22×C113—41no—
53C22×C113—81no—
54C22×C113#9911yescharacteristic
55C22×C113#10311yescharacteristic
56C22×C113#10411yescharacteristic
57C4×C113—42no—
58C4×C113—41no—
59C4×C113—41no—
60C4×C113—81no—
61Dic113—82no—
62C2×C113—21no—
63C2×C113—21no—
64C2×C113—41no—
65C2×C113—41no—
66C2×C113#32811yescharacteristic
67C2×C113#35211yescharacteristic
68C2×C113#35311yescharacteristic
69#1352—1131nomaximal, Sylow
70C113#135211yescharacteristic, complemented, Sylow
71#399D11311yescharacteristic
72#342—1131no—
73#323—1131no—
74C2×C4⋊C4—21no—
75C2×C4⋊C4Dic11311yescharacteristic, complemented
76C2×C22⋊C4—21no—
77C2×C22⋊C4—2261no—
78C2×C22⋊C4C2×D11311yescharacteristic
79C22⋊C8—2261no—
80#95Dic11311yescharacteristic, complemented
81C24C22⋊D11311yescharacteristic
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—4521no—
85C22×C4C2×Dic11311yescharacteristic
86C22×C4C22⋊D11311yescharacteristic
87C2×C8—4521no—
88C4⋊C4—41no—
89C4⋊C4—42no—
90C22⋊C4—41no—
91C22⋊C4—42no—
92C22⋊C4—4521no—
93C22⋊C4—2262no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23C22⋊Dic11311yescharacteristic
99C23#1426863411yescharacteristic
100C23#1426863711yescharacteristic
101C2×C4—22no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—9041no—
112C2×C4—9041no—
113C2×C4—4522no—
114C8—9041no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#1681353711yescharacteristic
125C22#1681354611yescharacteristic
126C22#1681354911yescharacteristic
127C4—42no—
128C4—41no—
129C4—41no—
130C4—81no—
131C4—9042no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#2029833511yescharacteristic
137C2#2029838811yescharacteristic
138C2#2029839111yescharacteristic
subgroupG/H
centerC22#16813537
commutatorC22×C4×C113C2×C4
FrattiniC2×C22⋊C4C2×D113
Fitting#399×C113C2
socleC22×C113#99
prime radicalC24×C113D4
cosocleC2×C22⋊C4×C113C22
hypercenter#399D113
hypocenterC113#1352
LCSG ▷ C22×C4×C113 ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #399

Complements

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

NH ≅ G/Ntype
7. C2×C4⋊C4×C113C4semidirect
10. #95×C113C4semidirect
70. C113#1352semidirect
75. C2×C4⋊C4Dic113semidirect
80. #95Dic113semidirect

Maximal subgroups

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

subgroupindex
#202983652
#202983222
#399×C1132
#1352113