Finite Group Databasebeta

← #28390987

Subgroups — #28390987

Order 14464.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#16813603C211yesmaximal, characteristic
2C2×#16813537C211yesmaximal, characteristic
3#20298459C212yesmaximal, complemented
4#20298365C212yesmaximal, complemented
5#518×C113C211yesmaximal, characteristic
6C23×Dic113C2211yescharacteristic
7#16813603—22no—
8#16813603C414yescomplemented
9C2×#14268626—21no—
10C2×C22⋊Dic113—21no—
11C2×C22⋊Dic113C2212yes—
12C2×C22⋊Dic113C2211yescharacteristic
13#16813537—22no—
14#16813529—24no—
15C22×D4×C113C2211yescharacteristic
16C4×D4×C113—24no—
17#117×C113—21no—
18C2×C22⋊C4×C113—21no—
19C2×C22⋊C4×C113C2212yes—
20C22×Dic113—21no—
21C22×Dic113—21no—
22C22×Dic113—21no—
23C22×Dic113—22no—
24C22×Dic113—22no—
25C22×Dic113—22no—
26C22×Dic113C2×C412yescomplemented
27#14268626—24no—
28C22⋊Dic113—24no—
29C22⋊Dic113—21no—
30C22⋊Dic113—22no—
31C22⋊Dic113—22no—
32C22⋊Dic113C2×C412yescomplemented
33C24×C113D411yescharacteristic
34C24×C113C2311yescharacteristic
35C2×D4×C113—22no—
36C2×D4×C113—22no—
37C2×D4×C113C2×C412yes—
38C2×D4×C113D412yes—
39C22×C4×C113—22no—
40C22×C4×C113D411yescharacteristic
41C22×C4×C113D414yes—
42C4⋊C4×C113—22no—
43C22⋊C4×C113—22no—
44C22⋊C4×C113—22no—
45C22⋊C4×C113—22no—
46C42×C113—22no—
47C23×C113—21no—
48C23×C113—21no—
49C23×C113—42no—
50C23×C113—42no—
51C23×C113C22⋊C412yes—
52C23×C113C22×C411yescharacteristic
53C23×C113C2×D411yescharacteristic
54C23×C113C2×D412yes—
55C23×C113C2×D411yescharacteristic
56C23×C113#4112yes—
57D4×C113—24no—
58D4×C113—24no—
59C2×C4×C113—21no—
60C2×C4×C113—21no—
61C2×C4×C113—24no—
62C2×C4×C113—44no—
63C2×C4×C113—82no—
64C2×C4×C113C22⋊C412yes—
65C2×Dic113—22no—
66C2×Dic113—22no—
67C2×Dic113—24no—
68C2×Dic113—42no—
69C2×Dic113—41no—
70C2×Dic113—42no—
71C2×Dic113—41no—
72C2×Dic113—44no—
73C2×Dic113—42no—
74C22×C113—24no—
75C22×C113—22no—
76C22×C113—22no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113—42no—
80C22×C113—42no—
81C22×C113—42no—
82C22×C113—81no—
83C22×C113C2×C22⋊C411yescharacteristic
84C22×C113C4×D412yes—
85C22×C113#12011yescharacteristic
86C22×C113#12112yes—
87C22×C113#12311yescharacteristic
88C4×C113—22no—
89C4×C113—44no—
90Dic113—42no—
91Dic113—42no—
92Dic113—82no—
93C2×C113—21no—
94C2×C113—22no—
95C2×C113—21no—
96C2×C113—22no—
97C2×C113—42no—
98C2×C113#38611yescharacteristic
99C2×C113#45812yes—
100#1890—1131nomaximal, Sylow
101C113#189011yescharacteristic, complemented, Sylow
102C2×#123—1131no—
103#518D11311yescharacteristic
104C2×#99—1131no—
105#381—1132no—
106#342—1132no—
107C22×D4C2×D11311yescharacteristic
108C23×C4—1131no—
109#123—1134no—
110#123—2262no—
111C4×D4—24no—
112#117—21no—
113C2×C4⋊C4—2261no—
114C2×C22⋊C4—21no—
115C2×C22⋊C4—1131no—
116C2×C22⋊C4—1132no—
117C2×C22⋊C4—2261no—
118C2×C22⋊C4C2×D11312yes—
119#99—2262no—
120#95—2264no—
121C24C22⋊D11311yescharacteristic
122C24C22×D11311yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C4×D11312yes—
126C2×D4D45212yes—
127C22×C4—22no—
128C22×C4—1132no—
129C22×C4—2262no—
130C22×C4—2262no—
131C22×C4—2261no—
132C22×C4—2261no—
133C22×C4—2261no—
134C22×C4—2262no—
135C22×C4C22⋊D11311yescharacteristic
136C22×C4C22⋊D11314yes—
137C4⋊C4—22no—
138C4⋊C4—2264no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—1132no—
143C22⋊C4—2262no—
144C22⋊C4—2262no—
145C22⋊C4—2264no—
146C22⋊C4—2261no—
147C42—22no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23#1426862412yes—
153C23C2×C4×D11311yescharacteristic
154C23C2×C22⋊D11311yescharacteristic
155C23C2×C22⋊D11312yes—
156C23C2×D45211yescharacteristic
157C23#1426864712yes—
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—24no—
163C2×C4—44no—
164C2×C4—82no—
165C2×C4—4524no—
166C2×C4—4522no—
167C2×C4—4522no—
168C2×C4—4521no—
169C2×C4—4522no—
170C2×C4—4521no—
171C2×C4—2262no—
172C2×C4—2262no—
173C2×C4—2264no—
174C2×C4#1426862412yes—
175C22—24no—
176C22—22no—
177C22—22no—
178C22—41no—
179C22—41no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22C2×#1426862411yescharacteristic
185C22C4×C22⋊D11312yes—
186C22#1681359111yescharacteristic
187C22#1681359612yes—
188C22#1681360511yescharacteristic
189C4—22no—
190C4—44no—
191C4—9042no—
192C4—4522no—
193C4—4522no—
194C2—22no—
195C2—21no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#2029847711yescharacteristic
200C2#2029878812yes—
subgroupG/H
centerC22#16813591
commutatorC23×C113C22×C4
FrattiniC24C22×D113
Fitting#518×C113C2
socleC22×C113#120
prime radicalC22×D4×C113C22
cosocleC24×C113C23
hypercenter#518D113
hypocenterC113#1890
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
3. #20298459C2semidirect
4. #20298365C2semidirect
8. #16813603C4semidirect
26. C22×Dic113C2×C4semidirect
32. C22⋊Dic113C2×C4semidirect
101. C113#1890semidirect

Maximal subgroups

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

subgroupindex
C2×#168136032
C2×#168135372
#202984592
#202983652
#518×C1132
#1890113