Finite Group Databasebeta

← #28405570

Subgroups — #28405570

Order 14464.

154 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 30 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#20299476C211yesmaximal, characteristic
2#20299442C211yesmaximal, characteristic
3#20298535C211yesmaximal, characteristic
4C2×C22⋊#90673—21no—
5C22⋊#11744753—21no—
6C2×C4⋊Dic113—21no—
7C2×C4⋊Dic113C411yescharacteristic, complemented
8C2×#14268624—21no—
9C2×#14268624C2211yescharacteristic
10#95×C113C411yescharacteristic, complemented
11C22×#90673—41no—
12C2×#11744753—41no—
13C22⋊#90673—22no—
14C22⋊#90673—41no—
15C23×D113D411yescharacteristic
16C22×Dic113—21no—
17C22×Dic113D411yescharacteristic
18C4⋊Dic113—42no—
19C4⋊Dic113—41no—
20#14268624—41no—
21#14268624—42no—
22C22×C4×C113—21no—
23C22×C4×C113C2×C411yescharacteristic
24C23×C113C22⋊C411yescharacteristic
25C22×D113—21no—
26C22×D113—21no—
27C22×D113—41no—
28C22×D113—41no—
29C22×D113SD1611yescharacteristic
30C22×D113Q1611yescharacteristic
31C2×#90673—42no—
32C2×#90673—81no—
33C2×#90673—81no—
34C2×C4×C113—22no—
35C2×C4×C113—21no—
36C2×C4×C113—41no—
37C2×C4×C113—41no—
38C2×C4×C113—41no—
39C2×Dic113—21no—
40C2×Dic113—41no—
41C2×Dic113—41no—
42C2×Dic113—41no—
43C2×Dic113—41no—
44#11744753—81no—
45C22×C113—21no—
46C22×C113—21no—
47C22×C113#9911yescharacteristic
48C22×C113#10311yescharacteristic
49C22×C113#10411yescharacteristic
50C2×D113—21no—
51C2×D113—21no—
52C2×D113—41no—
53C2×D113—41no—
54C2×D113—41no—
55C2×D113—41no—
56C2×D113—81no—
57#90673—82no—
58C4×C113—42no—
59C4×C113—41no—
60Dic113—41no—
61Dic113—81no—
62C2×C113—21no—
63C2×C113—21no—
64C2×C113#32811yescharacteristic
65C2×C113#35211yescharacteristic
66C2×C113#35311yescharacteristic
67D113—41no—
68D113—41no—
69#1352—1131nomaximal, Sylow
70C113#135211yescharacteristic, complemented, Sylow
71#399—1131no—
72#342—1131no—
73#323—1131no—
74C2×C4⋊C4—1131no—
75C2×C4⋊C4—2261no—
76C2×C22⋊C4—1131no—
77C2×C22⋊C4—2261no—
78C2×C22⋊C4—2261no—
79C22⋊C8—2261no—
80#95#9067311yescharacteristic, complemented
81C24—1131no—
82C22×C4—21no—
83C22×C4—1131no—
84C22×C4—4521no—
85C22×C4—2261no—
86C22×C4C2×#9067311yescharacteristic
87C2×C8—4521no—
88C4⋊C4—4521no—
89C4⋊C4—4522no—
90C22⋊C4—4522no—
91C22⋊C4—4521no—
92C22⋊C4—4521no—
93C22⋊C4—2262no—
94C23—1131no—
95C23—1131no—
96C23—4521no—
97C23—4521no—
98C23—2261no—
99C23—2261no—
100C23C22⋊#9067311yescharacteristic
101C2×C4—22no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—9041no—
107C2×C4—9041no—
108C2×C4—4521no—
109C2×C4—4521no—
110C2×C4—4522no—
111C2×C4—4521no—
112C2×C4—4521no—
113C2×C4—2261no—
114C8—9041no—
115C22—21no—
116C22—21no—
117C22—9041no—
118C22—4521no—
119C22—4521no—
120C22—4521no—
121C22—4521no—
122C22—2261no—
123C22—2261no—
124C22#1681368111yescharacteristic
125C22#1681368511yescharacteristic
126C22#1681368611yescharacteristic
127C4—42no—
128C4—41no—
129C4—9042no—
130C4—9041no—
131C4—4521no—
132C2—21no—
133C2—21no—
134C2—4521no—
135C2—4521no—
136C2#2029945111yescharacteristic
137C2#2029950111yescharacteristic
138C2#2029950311yescharacteristic
subgroupG/H
centerC22#16813681
commutatorC22×C4×C113C2×C4
FrattiniC22×C4C2×#90673
Fitting#95×C113C4
socleC22×C113#99
prime radicalC23×D113D4
cosocleC2×#14268624C22
hypercenter#95#90673
hypocenterC113#1352
LCSG ▷ C22×C4×C113 ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
7. C2×C4⋊Dic113C4semidirect
10. #95×C113C4semidirect
70. C113#1352semidirect
80. #95#90673semidirect

Maximal subgroups

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

subgroupindex
#202994762
#202994422
#202985352
#1352113