Finite Group Databasebeta

← #28406439

Subgroups — #28406439

Order 14464.

336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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#20299601C212yesmaximal, complemented
2C2×#16813682C212yesmaximal
3#20299478C212yesmaximal, complemented
4C2×#16813582C211yesmaximal, characteristic
5C2×#14268656C2214yes—
6#16813689—22no—
7C4⋊#11744753—22no—
8#16813682—24no—
9C22×C22⋊D113C2211yescharacteristic
10C23×Dic113C411yescharacteristic
11C22×C4×D113C411yescharacteristic
12#16813582—22no—
13#16813582—22no—
14C2×#14268626C2211yescharacteristic
15C2×#14268624C411yescharacteristic
16C2×C4×Dic113C2211yescharacteristic
17C2×C22⋊C4×C113C411yescharacteristic
18#14268656—24no—
19#14268656—24no—
20C2×#11744753—24no—
21C23×D113C2×C411yescharacteristic
22C2×C22⋊D113—22no—
23C2×C22⋊D113—22no—
24C2×C22⋊D113D412yes—
25C2×C22⋊D113Q812yes—
26C22×Dic113—21no—
27C22×Dic113—21no—
28C22×Dic113—42no—
29C22×Dic113C2×C411yescharacteristic
30C22×Dic113C2×C411yescharacteristic
31C22×Dic113C2311yescharacteristic
32C2×C4×D113—21no—
33C2×C4×D113—21no—
34C2×C4×D113—42no—
35#14268626—22no—
36#14268624—22no—
37C4×Dic113D412yes—
38C4×Dic113D412yes—
39C24×C113C2×C411yescharacteristic
40C22×C4×C113C2×C411yescharacteristic
41C22×C4×C113C2×C411yescharacteristic
42C22⋊C4×C113—22no—
43C23×C113—21no—
44C23×C113—21no—
45C23×C113—41no—
46C23×C113—41no—
47C23×C113C4⋊C412yes—
48C23×C113C22×C411yescharacteristic
49C22×D113—21no—
50C22×D113—21no—
51C22×D113—41no—
52C22×D113—41no—
53C22×D113C4⋊C412yes—
54C2×C4×C113—21no—
55C2×C4×C113—41no—
56C2×C4×C113—41no—
57C2×C4×C113C22⋊C412yes—
58C22⋊D113—24no—
59C22⋊D113—24no—
60C2×Dic113—22no—
61C2×Dic113—21no—
62C2×Dic113—42no—
63C2×Dic113—42no—
64C2×Dic113—41no—
65C2×Dic113C22⋊C411yescharacteristic
66C2×Dic113C22⋊C411yescharacteristic
67C2×Dic113C2×D411yescharacteristic
68C2×Dic113C2×D412yes—
69C2×Dic113C2×Q811yescharacteristic
70C2×Dic113#4112yes—
71C4×D113—42no—
72C4×D113—42no—
73#11744753—44no—
74C22×C113—21no—
75C22×C113—21no—
76C22×C113—22no—
77C22×C113—42no—
78C22×C113—42no—
79C22×C113—41no—
80C22×C113—41no—
81C22×C113C2×C22⋊C411yescharacteristic
82C22×C113C2×C4⋊C411yescharacteristic
83C22×C113#11711yescharacteristic
84C2×D113—22no—
85C2×D113—42no—
86C2×D113—41no—
87C2×D113—41no—
88C2×D113—42no—
89C4×C113—22no—
90C4×C113—41no—
91Dic113—21no—
92Dic113—41no—
93Dic113#10012yescomplemented
94Dic113#12112yes—
95Dic113C22⋊Q812yes—
96C2×C113—21no—
97C2×C113—21no—
98C2×C113—42no—
99C2×C113#38011yescharacteristic
100C2×C113C2×#10011yescharacteristic
101C2×C113#41311yescharacteristic
102D113—42no—
103#1800—1131nomaximal, Sylow
104C113#180011yescharacteristic, complemented, Sylow
105C2×C4×D4—1131no—
106#423—1132no—
107C2×#100—1132no—
108#343—1132no—
109C22×D4—1131no—
110C23×C4—1131no—
111C23×C4—1131no—
112C2×M16—1134no—
113C4×D4—2262no—
114C4×D4—2262no—
115C2×C4⋊C4—1131no—
116C2×C22⋊C4—1131no—
117C2×C22⋊C4#9067311yescharacteristic
118C2×C42—1131no—
119C4⋊C8—2262no—
120C4⋊C8—2262no—
121#100—2264no—
122C24—1131no—
123C24C2×#9067311yescharacteristic
124C2×D4—1132no—
125C2×D4—1132no—
126C2×D4—2262no—
127C2×D4—2262no—
128C22×C4—1131no—
129C22×C4—1131no—
130C22×C4—1131no—
131C22×C4—4522no—
132C22×C4—4522no—
133C22×C4—2261no—
134C22×C4—2261no—
135C22×C4—2261no—
136C22×C4—2261no—
137C22×C4C2×#9067311yescharacteristic
138C22×C4C2×#9067311yescharacteristic
139M16—2264no—
140M16—2264no—
141C2×C8—2264no—
142C4⋊C4—2262no—
143C22⋊C4—22no—
144C22⋊C4—2262no—
145C42—1132no—
146C42—1132no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—1132no—
152C23—4521no—
153C23—4521no—
154C23—2261no—
155C23—2261no—
156C23C4⋊#9067312yes—
157C23C22×#9067311yescharacteristic
158D4—2264no—
159D4—2264no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—1132no—
164C2×C4—1131no—
165C2×C4—1131no—
166C2×C4—1131no—
167C2×C4—1132no—
168C2×C4—1131no—
169C2×C4—4522no—
170C2×C4—4522no—
171C2×C4—4522no—
172C2×C4—4522no—
173C2×C4—4521no—
174C2×C4—2262no—
175C2×C4—2261no—
176C2×C4C22⋊#9067312yes—
177C8—4524no—
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—4522no—
186C22—4522no—
187C22—4521no—
188C22—4521no—
189C22—2262no—
190C22C2×C22⋊#9067311yescharacteristic
191C22C2×C4⋊#9067311yescharacteristic
192C22#1681370111yescharacteristic
193C4—22no—
194C4—41no—
195C4—1132no—
196C4—1132no—
197C4—1132no—
198C4—4521no—
199C4—2261no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2—4522no—
204C2#2029954011yescharacteristic
205C2D113⋊#10011yescharacteristic
206C2#2029958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC23×C113C22×C4
FrattiniC23C22×#90673
FittingC2×C22⋊C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×C22⋊D113C22
cosocleC22×Dic113C23
hypercenterC2×C22⋊C4#90673
hypocenterC113#1800
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20299601C2semidirect
3. #20299478C2semidirect
93. Dic113#100semidirect
104. C113#1800semidirect

Maximal subgroups

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

subgroupindex
#202996012
C2×#168136822
#202994782
C2×#168135822
#1800113