Finite Group Databasebeta

← #28391742

Subgroups — #28391742

Order 14464.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#20299224C211yesmaximal, characteristic
2#20298459C211yesmaximal, characteristic
3#20298459C212yesmaximal
4#20298364C212yesmaximal
5#342×C113C211yesmaximal, characteristic
6C23×Dic113C2211yescharacteristic
7#16813601—22no—
8#16813599—24no—
9C2×C22⋊Dic113C2211yescharacteristic
10C2×C22⋊Dic113C2212yes—
11#16813529—24no—
12#16813529—22no—
13C2×C22⋊C4×C113C2212yes—
14C2×C22⋊C4×C113C2211yescharacteristic
15C2×Dic226—22no—
16C22×Dic113—22no—
17C22×Dic113—21no—
18C22×Dic113—21no—
19C22×Dic113—22no—
20C22×Dic113—21no—
21C22×Dic113D414yes—
22C22×Dic113Q812yescomplemented
23C4⋊Dic113—22no—
24#14268626—24no—
25C22⋊Dic113—22no—
26C22⋊Dic113—22no—
27C22⋊Dic113—22no—
28C24×C113C2311yescharacteristic
29C22×C4×C113—22no—
30C22×C4×C113D412yes—
31C22⋊C4×C113—22no—
32C22⋊C4×C113—22no—
33C22⋊C4×C113—22no—
34C23×C113—42no—
35C23×C113C2×D412yes—
36C23×C113C2×D411yescharacteristic
37C23×C113C2×Q811yescharacteristic
38C23×C113#4111yescharacteristic
39C23×C113#4112yes—
40C2×C4×C113—22no—
41C2×C4×C113—42no—
42C2×C4×C113—44no—
43C2×C4×C113—42no—
44C2×Dic113—24no—
45C2×Dic113—24no—
46C2×Dic113—22no—
47C2×Dic113—41no—
48C2×Dic113—42no—
49C2×Dic113—41no—
50C2×Dic113—44no—
51C2×Dic113—42no—
52C2×Dic113—41no—
53Dic226—82no—
54C22×C113—24no—
55C22×C113—22no—
56C22×C113—41no—
57C22×C113—41no—
58C22×C113—42no—
59C22×C113#12011yescharacteristic
60C22×C113C22⋊Q812yes—
61C22×C113C22⋊Q811yescharacteristic
62C22×C113#12412yes—
63C22×C113#12411yescharacteristic
64C4×C113—42no—
65C4×C113—82no—
66Dic113—42no—
67Dic113—44no—
68Dic113—81no—
69C2×C113—21no—
70C2×C113—22no—
71C2×C113—22no—
72C2×C113—21no—
73C2×C113#39311yescharacteristic
74C2×C113#45812yes—
75#2030—1131nomaximal, Sylow
76C113#203011yescharacteristic, complemented, Sylow
77#543—1131no—
78#381—1132no—
79#381—1131no—
80#342—1132no—
81#342D11311yescharacteristic
82C23×C4—1131no—
83C22⋊Q8—2264no—
84C22⋊Q8—2262no—
85C2×C22⋊C4—1132no—
86C2×C22⋊C4—1131no—
87C2×C22⋊C4C2×D11312yes—
88C2×C22⋊C4C2×D11311yescharacteristic
89#95—2264no—
90#95—2262no—
91C24C22×D11311yescharacteristic
92C2×Q8—2262no—
93C22×C4—22no—
94C22×C4—1134no—
95C22×C4—1132no—
96C22×C4—2261no—
97C22×C4—2262no—
98C22×C4—2261no—
99C22×C4—2261no—
100C22×C4—2262no—
101C22×C4D45212yes—
102C4⋊C4—2264no—
103C4⋊C4—2262no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—22no—
107C22⋊C4—2262no—
108C22⋊C4—2262no—
109C22⋊C4—2262no—
110C23—42no—
111C23D4×D11312yes—
112C23C2×D45211yescharacteristic
113C23Q8×D11311yescharacteristic
114C23#1426864611yescharacteristic
115C23#1426864712yes—
116Q8—9042no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—4522no—
122C2×C4—4521no—
123C2×C4—4521no—
124C2×C4—4522no—
125C2×C4—4521no—
126C2×C4—4524no—
127C2×C4—2264no—
128C2×C4—2264no—
129C2×C4—2262no—
130C22—24no—
131C22—22no—
132C22—41no—
133C22—41no—
134C22—42no—
135C22#1681359211yescharacteristic
136C22#1681360012yes—
137C22#1681360211yescharacteristic
138C22#1681360812yes—
139C22#1681361011yescharacteristic
140C4—42no—
141C4—82no—
142C4—9041no—
143C4—4522no—
144C4—4524no—
145C2—22no—
146C2—21no—
147C2—22no—
148C2—21no—
149C2#2029851111yescharacteristic
150C2#2029878912yes—
subgroupG/H
centerC22#16813592
commutator, prime radical, cosocleC24×C113C23
FrattiniC24C22×D113
Fitting#342×C113C2
socleC22×C113#120
hypercenter#342D113
hypocenterC113#2030
LCSG ▷ C24×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
22. C22×Dic113Q8semidirect
76. C113#2030semidirect

Maximal subgroups

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

subgroupindex
#202992242
#202984592
#202983642
#342×C1132
#2030113