Finite Group Databasebeta

← #28389616

Subgroups — #28389616

Order 14464.

202 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 57 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#20298931C212yesmaximal
2#20298537C211yesmaximal, characteristic
3#20298335C212yesmaximal
4#20298324C211yesmaximal, characteristic
5#544×C113C211yesmaximal, characteristic
6C2×C4⋊Dic113C2211yescharacteristic
7#16813555—22no—
8#16813546—22no—
9C22⋊#11744751C2212yes—
10#16813529—21no—
11#16813529—21no—
12#16813529C2211yescharacteristic
13C4⋊Q8×C113—22no—
14#125×C113—22no—
15C22⋊Q8×C113—21no—
16C22⋊Q8×C113C2212yes—
17#117×C113—21no—
18C2×C4⋊C4×C113C2211yescharacteristic
19C22×Dic113—21no—
20C22×Dic113—21no—
21C2×#11744751—22no—
22C4⋊Dic113—22no—
23C2×Q8×C113—21no—
24C2×Q8×C113D412yes—
25C22×C4×C113D411yescharacteristic
26C22×C4×C113D411yescharacteristic
27C22×C4×C113C2311yescharacteristic
28C4⋊C4×C113—21no—
29C4⋊C4×C113—21no—
30C4⋊C4×C113—21no—
31C4⋊C4×C113—22no—
32C4⋊C4×C113—22no—
33C4⋊C4×C113—22no—
34C4⋊C4×C113D412yes—
35C22⋊C4×C113—22no—
36C42×C113—22no—
37C23×C113C2×D411yescharacteristic
38Q8×C113—42no—
39Q8×C113—81no—
40C2×C4×C113—21no—
41C2×C4×C113—21no—
42C2×C4×C113—22no—
43C2×C4×C113—22no—
44C2×C4×C113—21no—
45C2×C4×C113—41no—
46C2×C4×C113—41no—
47C2×C4×C113Q1612yes—
48C2×C4×C113C2×D412yes—
49C2×Dic113—41no—
50C2×Dic113—41no—
51C2×Dic113—42no—
52C2×Dic113—41no—
53C2×Dic113—41no—
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—42no—
63C4×C113—41no—
64C4×C113—42no—
65Dic113—81no—
66Dic113—81no—
67C2×C113—21no—
68C2×C113—21no—
69C2×C113#45111yescharacteristic
70C2×C113#45411yescharacteristic
71C2×C113#45811yescharacteristic
72#1617—1131nomaximal, Sylow
73C113#161711yescharacteristic, complemented, Sylow
74#544D11311yescharacteristic
75#484—1132no—
76#400—1131no—
77#328—1132no—
78#324—1131no—
79C4⋊Q8—22no—
80#125—22no—
81C22⋊Q8—21no—
82C22⋊Q8C2×D11312yes—
83#117—21no—
84C2×C4⋊C4—1131no—
85C2×C4⋊C4C2×D11311yescharacteristic
86#107—2262no—
87#103—2262no—
88C22⋊C8—1132no—
89#95—1131no—
90#95—2261no—
91#95—2261no—
92C2×Q8—21no—
93C2×Q8C22⋊D11312yes—
94C22×C4—2261no—
95C22×C4—2261no—
96C22×C4C22⋊D11311yescharacteristic
97C22×C4C22⋊D11311yescharacteristic
98C22×C4C22×D11311yescharacteristic
99C2×C8—2262no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—2262no—
107C4⋊C4C22⋊D11312yes—
108C22⋊C4—22no—
109C42—22no—
110C23C2×C22⋊D11311yescharacteristic
111Q8—42no—
112Q8—81no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—4521no—
121C2×C4—4521no—
122C2×C4—4522no—
123C2×C4—4521no—
124C2×C4—4521no—
125C2×C4#1426863712yes—
126C2×C4C2×C22⋊D11312yes—
127C8—4522no—
128C22—21no—
129C22—21no—
130C22#1681359111yescharacteristic
131C22C2×#1426863711yescharacteristic
132C22#1681365311yescharacteristic
133C4—22no—
134C4—22no—
135C4—42no—
136C4—41no—
137C4—42no—
138C4—9041no—
139C4—9041no—
140C2—21no—
141C2—21no—
142C2#2029875411yescharacteristic
143C2#2029877111yescharacteristic
144C2#2029878811yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#544×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
hypercenter#544D113
hypocenterC113#1617
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

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
#202989312
#202985372
#202983352
#202983242
#544×C1132
#1617113