Finite Group Databasebeta

← #28405569

Subgroups — #28405569

Order 14464.

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

normal subgroups only

This group has 162 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#20298509C211yesmaximal, characteristic
4C2×C22⋊#90673—21no—
5C22⋊#11744753—21no—
6C2×#14268624—21no—
7C2×#14268624C2211yescharacteristic
8#16813529—21no—
9#16813529C411yescharacteristic, complemented
10C22×Q8×C113C411yescharacteristic, complemented
11C22×#90673—41no—
12C2×#11744753—41no—
13C22⋊#90673—22no—
14C22⋊#90673—41no—
15C23×D113D411yescharacteristic
16C22×Dic113—21no—
17C22×Dic113D411yescharacteristic
18#14268624—41no—
19#14268624—42no—
20C2×Q8×C113—42no—
21C2×Q8×C113—41no—
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—
34Q8×C113—42no—
35Q8×C113—42no—
36C2×C4×C113—22no—
37C2×C4×C113—21no—
38C2×C4×C113—41no—
39C2×C4×C113—41no—
40C2×C4×C113—41no—
41C2×Dic113—21no—
42C2×Dic113—41no—
43C2×Dic113—41no—
44C2×Dic113—41no—
45C2×Dic113—41no—
46#11744753—81no—
47C22×C113—21no—
48C22×C113—21no—
49C22×C113#9911yescharacteristic
50C22×C113#10311yescharacteristic
51C22×C113#10411yescharacteristic
52C2×D113—21no—
53C2×D113—21no—
54C2×D113—41no—
55C2×D113—41no—
56C2×D113—41no—
57C2×D113—41no—
58C2×D113—81no—
59#90673—82no—
60C4×C113—42no—
61C4×C113—41no—
62Dic113—41no—
63Dic113—81no—
64C2×C113—21no—
65C2×C113—21no—
66C2×C113#32811yescharacteristic
67C2×C113AΣL(1,𝔽16)11yescharacteristic
68C2×C113#35411yescharacteristic
69D113—41no—
70D113—41no—
71#1351—1131nomaximal, Sylow
72C113#135111yescharacteristic, complemented, Sylow
73#393—1131no—
74#342—1131no—
75#323—1131no—
76C22×Q8#9067311yescharacteristic, complemented
77C2×C22⋊C4—1131no—
78C2×C22⋊C4—2261no—
79C2×C22⋊C4—2261no—
80C22⋊C8—2261no—
81#95—1131no—
82#95—2261no—
83C24—1131no—
84C2×Q8—42no—
85C2×Q8—41no—
86C22×C4—21no—
87C22×C4—1131no—
88C22×C4—4521no—
89C22×C4—2261no—
90C22×C4C2×#9067311yescharacteristic
91C2×C8—4521no—
92C22⋊C4—4522no—
93C22⋊C4—4521no—
94C22⋊C4—4521no—
95C22⋊C4—2262no—
96C23—1131no—
97C23—1131no—
98C23—4521no—
99C23—4521no—
100C23—2261no—
101C23—2261no—
102C23C22⋊#9067311yescharacteristic
103Q8—42no—
104Q8—42no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—9041no—
111C2×C4—9041no—
112C2×C4—4521no—
113C2×C4—4521no—
114C2×C4—4522no—
115C2×C4—4521no—
116C2×C4—4521no—
117C2×C4—2261no—
118C8—9041no—
119C22—21no—
120C22—21no—
121C22—9041no—
122C22—4521no—
123C22—4521no—
124C22—4521no—
125C22—4521no—
126C22—2261no—
127C22—2261no—
128C22#1681368011yescharacteristic
129C22#1681368511yescharacteristic
130C22#1681368711yescharacteristic
131C4—42no—
132C4—41no—
133C4—9041no—
134C4—9042no—
135C4—4521no—
136C2—21no—
137C2—21no—
138C2—4521no—
139C2—4521no—
140C2#2029945211yescharacteristic
141C2#2029949811yescharacteristic
142C2#2029950411yescharacteristic
subgroupG/H
centerC22#16813680
commutatorC22×C4×C113C2×C4
FrattiniC22×C4C2×#90673
FittingC22×Q8×C113C4
socleC22×C113#99
prime radicalC23×D113D4
cosocleC2×#14268624C22
hypercenterC22×Q8#90673
hypocenterC113#1351
LCSG ▷ C22×C4×C113 ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
9. #16813529C4semidirect
10. C22×Q8×C113C4semidirect
72. C113#1351semidirect
76. C22×Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202994762
#202994422
#202985092
#1351113