Finite Group Databasebeta

← #28391703

Subgroups — #28391703

Order 14464.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16813603C212yesmaximal, complemented
2C2×#16813537C212yesmaximal, complemented
3#20298459C211yesmaximal, characteristic, complemented
4#20298365C211yesmaximal, characteristic, complemented
5#534×C113C211yesmaximal, characteristic
6C23×Dic113C2211yescharacteristic
7#16813603—24no—
8#16813603—24no—
9C2×#14268626—22no—
10C2×C22⋊Dic113—22no—
11C2×C22⋊Dic113C2211yescharacteristic
12C2×C22⋊Dic113C2212yes—
13#16813537—24no—
14#16813529—22no—
15C22×D4×C113C2212yes—
16#123×C113—22no—
17#121×C113—22no—
18#120×C113—22no—
19C2×C22⋊C4×C113C2211yescharacteristic
20C22×Dic113—22no—
21C22×Dic113—22no—
22C22×Dic113—22no—
23C22×Dic113—21no—
24C22×Dic113—21no—
25C22×Dic113—21no—
26C22×Dic113D412yescomplemented
27#14268626—28no—
28C22⋊Dic113—28no—
29C22⋊Dic113—22no—
30C22⋊Dic113—22no—
31C22⋊Dic113D414yescomplemented
32C24×C113D412yes—
33C24×C113C2311yescharacteristic
34C2×D4×C113—22no—
35C2×D4×C113—22no—
36C2×D4×C113—22no—
37C2×D4×C113—22no—
38C2×D4×C113—22no—
39C2×D4×C113—22no—
40C2×D4×C113—22no—
41C22×C4×C113D412yes—
42C22×C4×C113D412yes—
43C4⋊C4×C113—22no—
44C22⋊C4×C113—24no—
45C22⋊C4×C113—22no—
46C23×C113—22no—
47C23×C113—22no—
48C23×C113—22no—
49C23×C113—42no—
50C23×C113—44no—
51C23×C113C2×D411yescharacteristic
52C23×C113C2×D412yes—
53C23×C113C2×D412yes—
54C23×C113C2×D411yescharacteristic
55C23×C113#4111yescharacteristic
56D4×C113—42no—
57D4×C113—42no—
58D4×C113—42no—
59D4×C113—42no—
60D4×C113—82no—
61C2×C4×C113—22no—
62C2×C4×C113—22no—
63C2×C4×C113—22no—
64C2×C4×C113—22no—
65C2×C4×C113—42no—
66C2×Dic113—24no—
67C2×Dic113—24no—
68C2×Dic113—22no—
69C2×Dic113—44no—
70C2×Dic113—41no—
71C2×Dic113—42no—
72C2×Dic113—41no—
73C2×Dic113—42no—
74C2×Dic113—41no—
75C22×C113—22no—
76C22×C113—24no—
77C22×C113—41no—
78C22×C113—42no—
79C22×C113—41no—
80C22×C113—44no—
81C22×C113—42no—
82C22×C113—44no—
83C22×C113—82no—
84C22×C113#12012yes—
85C22×C113#12011yescharacteristic
86C22×C113#12111yescharacteristic
87C22×C113#12112yes—
88C22×C113#12711yescharacteristic
89C4×C113—42no—
90C4×C113—42no—
91Dic113—44no—
92Dic113—42no—
93Dic113—81no—
94C2×C113—22no—
95C2×C113—21no—
96C2×C113—22no—
97C2×C113—21no—
98C2×C113—82no—
99C2×C113#39211yescharacteristic
100C2×C113#45812yes—
101#2022—1131nomaximal, Sylow
102C113#202211yescharacteristic, complemented, Sylow
103#534D11311yescharacteristic
104C2×#123—1132no—
105C2×#99—1132no—
106#381—1131no—
107#342—1131no—
108C22×D4C2×D11312yes—
109C23×C4—1131no—
110#123—22no—
111#123—2264no—
112#123—2264no—
113#121—22no—
114#120—22no—
115C2×C4⋊C4—2262no—
116C2×C22⋊C4—1132no—
117C2×C22⋊C4—1131no—
118C2×C22⋊C4—2262no—
119C2×C22⋊C4C2×D11311yescharacteristic
120#99—2264no—
121#95—2262no—
122C24C22⋊D11312yes—
123C24C22×D11311yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—22no—
131C22×C4—1132no—
132C22×C4—2261no—
133C22×C4—2262no—
134C22×C4—2261no—
135C22×C4—2262no—
136C22×C4—2262no—
137C22×C4—2261no—
138C22×C4C22⋊D11312yes—
139C22×C4C22⋊D11312yes—
140C4⋊C4—22no—
141C4⋊C4—2268no—
142C22⋊C4—24no—
143C22⋊C4—22no—
144C22⋊C4—1134no—
145C22⋊C4—2262no—
146C22⋊C4—2268no—
147C22⋊C4—2262no—
148C23—22no—
149C23—22no—
150C23—22no—
151C23—42no—
152C23—44no—
153C23D4×D11311yescharacteristic
154C23D4×D11312yes—
155C23C2×C22⋊D11312yes—
156C23C2×C22⋊D11311yescharacteristic
157C23#1426864611yescharacteristic
158D4—42no—
159D4—42no—
160D4—42no—
161D4—42no—
162D4—82no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—4522no—
169C2×C4—4521no—
170C2×C4—4524no—
171C2×C4—4521no—
172C2×C4—4522no—
173C2×C4—4521no—
174C2×C4—2264no—
175C2×C4—2264no—
176C2×C4—2262no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—44no—
183C22—42no—
184C22—44no—
185C22—82no—
186C22#1681359012yes—
187C22#1681359111yescharacteristic
188C22#1681359311yescharacteristic
189C22#1681359412yes—
190C22#1681361811yescharacteristic
191C4—42no—
192C4—42no—
193C4—9041no—
194C4—4524no—
195C4—4522no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—82no—
201C2#2029850611yescharacteristic
202C2#2029878812yes—
subgroupG/H
centerC22#16813591
commutator, cosocleC24×C113C23
FrattiniC24C22×D113
Fitting, prime radical#534×C113C2
socleC22×C113#120
hypercenter#534D113
hypocenterC113#2022
LCSG ▷ C24×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#16813603C2semidirect
2. C2×#16813537C2semidirect
3. #20298459C2semidirect
4. #20298365C2semidirect
26. C22×Dic113D4semidirect
31. C22⋊Dic113D4semidirect
102. C113#2022semidirect

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
#534×C1132
#2022113