Finite Group Databasebeta

← #28389615

Subgroups — #28389615

Order 14464.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299229C211yesmaximal, characteristic
2#20298933C212yesmaximal
3#20298334C212yesmaximal
4#20298324C211yesmaximal, characteristic
5#400×C113C211yesmaximal, characteristic
6#16813621—22no—
7#16813613—22no—
8#16813601—21no—
9#16813601C2212yes—
10#16813581—21no—
11#16813555—22no—
12#16813545—22no—
13C22⋊#11744751C2212yes—
14C2×C4⋊C4×C113C2211yescharacteristic
15C2×C4⋊C4×C113C2211yescharacteristic
16#95×C113—21no—
17#95×C113—21no—
18#95×C113C2211yescharacteristic
19C2×Dic226—21no—
20C2×Dic226D412yes—
21C2×#11744751—22no—
22C4⋊Dic113—21no—
23C4⋊Dic113—21no—
24C4⋊Dic113—21no—
25C4⋊Dic113D412yes—
26#14268626—22no—
27#14268626—22no—
28C22⋊Dic113—22no—
29C4×Dic113—22no—
30C22×C4×C113—21no—
31C22×C4×C113—21no—
32C22×C4×C113D411yescharacteristic
33C22×C4×C113D411yescharacteristic
34C22×C4×C113C2311yescharacteristic
35C4⋊C4×C113—22no—
36C4⋊C4×C113—22no—
37C23×C113C2×D411yescharacteristic
38C2×C4×C113—21no—
39C2×C4×C113—21no—
40C2×C4×C113—21no—
41C2×C4×C113—41no—
42C2×C4×C113—41no—
43C2×C4×C113—41no—
44C2×C4×C113—41no—
45C2×C4×C113—42no—
46C2×C4×C113—41no—
47C2×C4×C113—41no—
48C2×C4×C113Q1612yes—
49C2×C4×C113C2×D412yes—
50C2×Dic113—22no—
51C2×Dic113—22no—
52Dic226—42no—
53Dic226—81no—
54#11744751—42no—
55C22×C113—21no—
56C22×C113—21no—
57C22×C113#12011yescharacteristic
58C22×C113C2×Q1611yescharacteristic
59C22×C113#13711yescharacteristic
60C4×C113—22no—
61C4×C113—22no—
62C4×C113—41no—
63C4×C113—81no—
64C4×C113—81no—
65Dic113—42no—
66Dic113—42no—
67C2×C113—21no—
68C2×C113—21no—
69C2×C113#45111yescharacteristic
70C2×C113#45411yescharacteristic
71C2×C113#45811yescharacteristic
72#1617—1131nomaximal, Sylow
73C113#161711yescharacteristic, complemented, Sylow
74#544—1131no—
75#484—1132no—
76#400D11311yescharacteristic
77#328—1132no—
78#324—1131no—
79C4⋊Q8—2262no—
80#125—2262no—
81C22⋊Q8—1132no—
82C22⋊Q8—2261no—
83#117—2261no—
84C2×C4⋊C4C2×D11311yescharacteristic
85C2×C4⋊C4C2×D11311yescharacteristic
86#107—2262no—
87#103—2262no—
88C22⋊C8—1132no—
89#95—21no—
90#95—21no—
91#95C2×D11311yescharacteristic
92C2×Q8—1132no—
93C2×Q8—2261no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4C22⋊D11311yescharacteristic
97C22×C4C22⋊D11311yescharacteristic
98C22×C4C22×D11311yescharacteristic
99C2×C8—2262no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4—1132no—
103C4⋊C4—2261no—
104C4⋊C4—2261no—
105C4⋊C4—2261no—
106C4⋊C4—2262no—
107C4⋊C4—2262no—
108C22⋊C4—2262no—
109C42—2262no—
110C23C2×C22⋊D11311yescharacteristic
111Q8—9041no—
112Q8—4522no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—2262no—
124C2×C4—2262no—
125C2×C4#1426863712yes—
126C2×C4D4×D11312yes—
127C8—4522no—
128C22—21no—
129C22—21no—
130C22#1681359011yescharacteristic
131C22C2×#1426863711yescharacteristic
132C22#1681365211yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—81no—
137C4—81no—
138C4—4522no—
139C4—4522no—
140C2—21no—
141C2—21no—
142C2#2029875311yescharacteristic
143C2#2029877011yescharacteristic
144C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#400×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
hypercenter#400D113
hypocenterC113#1617
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
73. C113#1617semidirect

Maximal subgroups

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

subgroupindex
#202992292
#202989332
#202983342
#202983242
#400×C1132
#1617113