Finite Group Databasebeta

← #28393169

Subgroups — #28393169

Order 14464.

672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C22×#14268624C211yesmaximal, characteristic
2#20298489C214yesmaximal, complemented
3#20298487C214yesmaximal, complemented
4#20298456C212yesmaximal, complemented
5#20298453C212yesmaximal
6C4×C22⋊Dic113C211yesmaximal, characteristic, complemented
7C4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
8C24×D113C2211yescharacteristic
9C23×Dic113C2211yescharacteristic
10C2×#14268626C2214yescomplemented
11C2×C22⋊Dic113C2212yes—
12C2×#14268624C418yescomplemented
13C2×#14268624C2214yes—
14C2×#14268624C2214yes—
15C2×#14268624C2212yes—
16C2×#14268624C2212yes—
17C2×C4×Dic113C2212yescomplemented
18#16813529C2212yescomplemented
19#16813529C2214yescomplemented
20C23×C4×C113C2211yescharacteristic
21C2×C22⋊C4×C113C2212yes—
22C2×C42×C113C2212yescomplemented
23#95×C113C2212yescomplemented
24C23×D113—24no—
25C23×D113—42no—
26C23×D113—42no—
27C23×D113C2×C414yes—
28C23×D113C2312yes—
29C22×Dic113—42no—
30C22×Dic113C2×C414yes—
31C22×Dic113C2314yes—
32C22×Dic113C2312yes—
33#14268626—44no—
34C22⋊Dic113—24no—
35#14268624—44no—
36#14268624—44no—
37#14268624C2×C418yes—
38#14268624C2×C418yes—
39C4×Dic113—42no—
40C24×C113C2311yescharacteristic
41C22×C4×C113—42no—
42C22×C4×C113C2×C414yes—
43C22×C4×C113C2314yes—
44C22×C4×C113C2311yescharacteristic
45C22×C4×C113C2311yescharacteristic
46C22⋊C4×C113—24no—
47C42×C113—42no—
48C23×C113—22no—
49C23×C113—22no—
50C23×C113C22×C412yes—
51C23×C113#4114yes—
52C23×C113C2411yescharacteristic
53C22×D113—28no—
54C22×D113—24no—
55C22×D113—24no—
56C22×D113—24no—
57C22×D113—44no—
58C22×D113—44no—
59C22×D113—416no—
60C22×D113C22×C414yes—
61C2×C4×C113—22no—
62C2×C4×C113—22no—
63C2×C4×C113—24no—
64C2×C4×C113—24no—
65C2×C4×C113—24no—
66C2×C4×C113—44no—
67C2×C4×C113C22×C412yes—
68C2×C4×C113C22×C412yes—
69C2×Dic113—24no—
70C2×Dic113—24no—
71C2×Dic113—24no—
72C2×Dic113—24no—
73C2×Dic113—44no—
74C2×Dic113C22×C414yes—
75C22×C113—22no—
76C22×C113—22no—
77C22×C113—28no—
78C22×C113#11714yes—
79C22×C113C23×C411yescharacteristic
80C22×C113C2×#4112yes—
81C22×C113H(5,𝔽2)12yes—
82C22×C113H(5,𝔽2)12yes—
83C2×D113—24no—
84C2×D113—24no—
85C2×D113—24no—
86C2×D113—416no—
87C2×D113—48no—
88C4×C113—22no—
89C4×C113—22no—
90C4×C113—44no—
91Dic113—24no—
92Dic113—44no—
93C2×C113—24no—
94C2×C113C2×#11711yescharacteristic
95C2×C113#51811yescharacteristic
96C2×C113#51811yescharacteristic
97C2×C113#53814yes—
98D113—44no—
99#2312—1131nomaximal, Sylow
100C113#231211yescharacteristic, complemented, Sylow
101C22×C22⋊C4—1131no—
102#388—1134no—
103#388—1134no—
104#380—1132no—
105#379—1132no—
106C4×C22⋊C4—1131no—
107C4×C22⋊C4D11311yescharacteristic, complemented
108C25—1131no—
109C23×C4—1131no—
110C23×C4C2×D11311yescharacteristic
111C2×C4⋊C4—1134no—
112C2×C22⋊C4—1138no—
113C2×C22⋊C4—1132no—
114C2×C22⋊C4—1132no—
115C2×C22⋊C4—1134no—
116C2×C22⋊C4—1134no—
117C2×C22⋊C4—1132no—
118C2×C22⋊C4C2×D11312yes—
119C2×C42—1132no—
120C2×C42C2×D11312yescomplemented
121#95—1132no—
122#95—1134no—
123#95C2×D11312yescomplemented
124C24—1134no—
125C24—1132no—
126C24—4522no—
127C24—4522no—
128C24—2264no—
129C24C22×D11311yescharacteristic
130C22×C4—42no—
131C22×C4—1134no—
132C22×C4—1132no—
133C22×C4—1134no—
134C22×C4—4522no—
135C22×C4C4×D11314yes—
136C22×C4C22×D11314yes—
137C22×C4C22×D11311yescharacteristic
138C22×C4C22×D11311yescharacteristic
139C4⋊C4—4524no—
140C22⋊C4—24no—
141C22⋊C4—1138no—
142C22⋊C4—1138no—
143C22⋊C4—4524no—
144C22⋊C4—4524no—
145C22⋊C4—2264no—
146C42—42no—
147C42—4522no—
148C23—22no—
149C23—22no—
150C23—1134no—
151C23—45216no—
152C23—4524no—
153C23—4524no—
154C23—2268no—
155C23—2264no—
156C23—2264no—
157C23—2264no—
158C23C2×C4×D11312yes—
159C23#1426864714yes—
160C23C23×D11311yescharacteristic
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—24no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—44no—
167C2×C4—1134no—
168C2×C4—4524no—
169C2×C4—2264no—
170C2×C4—2264no—
171C2×C4—2264no—
172C2×C4—2264no—
173C2×C4C2×C4×D11312yes—
174C2×C4C2×C4×D11312yes—
175C22—22no—
176C22—22no—
177C22—28no—
178C22—45216no—
179C22—4528no—
180C22—2264no—
181C22—2264no—
182C22—2264no—
183C22#1681357914yes—
184C22C22×C4×D11311yescharacteristic
185C22C2×#1426864712yes—
186C22#1681366712yes—
187C22#1681366812yes—
188C4—22no—
189C4—22no—
190C4—44no—
191C4—4524no—
192C4—2264no—
193C2—24no—
194C2—4524no—
195C2C2×#1681357911yescharacteristic
196C2#2029907111yescharacteristic
197C2#2029907211yescharacteristic
198C2#2029918114yes—
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
FittingC4×C22⋊C4×C113C2
socle, cosocleC23×C113C24
prime radicalC24×D113C22
hypercenterC4×C22⋊C4D113
hypocenterC113#2312
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20298489C2semidirect
3. #20298487C2semidirect
4. #20298456C2semidirect
6. C4×C22⋊Dic113C2semidirect
7. C4×C22⋊C4×C113C2semidirect
10. C2×#14268626C22semidirect
12. C2×#14268624C4semidirect
17. C2×C4×Dic113C22semidirect
18. #16813529C22semidirect
19. #16813529C22semidirect
22. C2×C42×C113C22semidirect
23. #95×C113C22semidirect
100. C113#2312semidirect
107. C4×C22⋊C4D113semidirect
120. C2×C42C2×D113semidirect
123. #95C2×D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686242
#202984892
#202984872
#202984562
#202984532
C4×C22⋊Dic1132
C4×C22⋊C4×C1132
#2312113