Finite Group Databasebeta

← #28389097

Subgroups — #28389097

Order 14464.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#20299132C211yesmaximal, characteristic
2#20298655C211yesmaximal, characteristic, complemented
3#20298334C212yesmaximal, complemented
4#20298331C212yesmaximal
5C4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
6#16813616—21no—
7#16813614C411yescharacteristic, complemented
8#16813610C411yescharacteristic, complemented
9#16813605—21no—
10#16813601C2211yescharacteristic
11#16813596C2211yescharacteristic
12C4×Dic226C411yescharacteristic, complemented
13C4×D452C411yescharacteristic, complemented
14C4×C22⋊D113—21no—
15#16813579—21no—
16C4⋊#11744751—21no—
17C22⋊#11744751C2212yes—
18#16813533—21no—
19C2×C4⋊C4×C113—21no—
20C2×C42×C113—21no—
21C2×C42×C113C2211yescharacteristic
22#95×C113C2212yes—
23C2×Dic226C2×C411yescharacteristic
24C2×D452C2×C411yescharacteristic
25C2×C22⋊D113—21no—
26C2×C4×D113—21no—
27C2×#11744751—22no—
28C4⋊Dic113C2×C411yescharacteristic
29C4⋊Dic113C2×C411yescharacteristic
30#14268626—21no—
31#14268626—21no—
32#14268626—21no—
33#14268626—21no—
34C22⋊Dic113—21no—
35#14268624—21no—
36#14268624—21no—
37#14268624—21no—
38#14268624—21no—
39C4×Dic113—21no—
40C22×C4×C113—22no—
41C22×C4×C113D411yescharacteristic
42C22×C4×C113D411yescharacteristic
43C22×C4×C113C2311yescharacteristic
44C4⋊C4×C113—24no—
45C42×C113—42no—
46C42×C113C2×C411yescharacteristic
47C42×C113C2×C411yescharacteristic
48C42×C113D411yescharacteristic
49C42×C113D411yescharacteristic
50C23×C113C2×D411yescharacteristic
51C22×D113—21no—
52C2×C4×C113—21no—
53C2×C4×C113—21no—
54C2×C4×C113—22no—
55C2×C4×C113—24no—
56C2×C4×C113—41no—
57C2×C4×C113—42no—
58C2×C4×C113—42no—
59C2×C4×C113C22⋊C411yescharacteristic
60C2×C4×C113C22⋊C411yescharacteristic
61C2×C4×C113C22⋊C411yescharacteristic
62C2×C4×C113C22⋊C411yescharacteristic
63C2×C4×C113C22×C411yescharacteristic
64C2×C4×C113C2×D411yescharacteristic
65C22⋊D113—41no—
66C22⋊D113—41no—
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113—21no—
70D452—41no—
71C4×D113—42no—
72Dic226—41no—
73#11744751—42no—
74C22×C113—21no—
75C22×C113—21no—
76C22×C113C2×C22⋊C411yescharacteristic
77C22×C113AGL(1,ℤ/8)11yescharacteristic
78C22×C113#13711yescharacteristic
79C2×D113—41no—
80C2×D113—41no—
81C2×D113—41no—
82C4×C113—21no—
83C4×C113—21no—
84C4×C113—21no—
85C4×C113—21no—
86C4×C113—21no—
87C4×C113—44no—
88C4×C113#10412yes—
89Dic113—41no—
90Dic113—41no—
91Dic113—41no—
92C2×C113—21no—
93C2×C113—21no—
94C2×C113#41011yescharacteristic
95C2×C113#41711yescharacteristic
96C2×C113C2×#10411yescharacteristic
97D113—81no—
98#1509—1131nomaximal, Sylow
99C113#150911yescharacteristic, complemented, Sylow
100#529—1131no—
101#432—1131no—
102C4×C4⋊C4D11311yescharacteristic, complemented
103#328—1132no—
104#327—1132no—
105#126—2261no—
106#125—1131no—
107#124—1131no—
108#123—2261no—
109C22⋊Q8—1131no—
110#121—1131no—
111C4×Q8—1131no—
112C4×D4—1131no—
113C4×D4—2261no—
114#117—2261no—
115C2×C4⋊C4—21no—
116C2×C42—21no—
117C2×C42C2×D11311yescharacteristic
118C4⋊C8—2261no—
119C22⋊C8—1132no—
120#97—2261no—
121#95C2×D11312yes—
122C2×Q8—1131no—
123C2×D4—1131no—
124C2×D4—2261no—
125C22×C4—22no—
126C22×C4—2261no—
127C22×C4C22⋊D11311yescharacteristic
128C22×C4C22⋊D11311yescharacteristic
129C22×C4C22×D11311yescharacteristic
130C2×C8—2262no—
131C4⋊C4—24no—
132C4⋊C4—1131no—
133C4⋊C4—1131no—
134C4⋊C4—2261no—
135C4⋊C4—2261no—
136C4⋊C4—2261no—
137C4⋊C4—2261no—
138C22⋊C4—2261no—
139C22⋊C4—2261no—
140C22⋊C4—2261no—
141C22⋊C4—2261no—
142C22⋊C4—2261no—
143C42—42no—
144C42—2261no—
145C42C4×D11311yescharacteristic
146C42C4×D11311yescharacteristic
147C42D45211yescharacteristic
148C42D45211yescharacteristic
149C23—2261no—
150C23C2×C22⋊D11311yescharacteristic
151Q8—4521no—
152D4—4521no—
153D4—4521no—
154D4—4521no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—4522no—
163C2×C4—2261no—
164C2×C4—2261no—
165C2×C4—2261no—
166C2×C4#1426862411yescharacteristic
167C2×C4#1426862411yescharacteristic
168C2×C4#1426862411yescharacteristic
169C2×C4#1426862411yescharacteristic
170C2×C4C2×C4×D11311yescharacteristic
171C2×C4C2×D45211yescharacteristic
172C8—4522no—
173C22—21no—
174C22—21no—
175C22—4521no—
176C22—4521no—
177C22—4521no—
178C22C2×#1426862411yescharacteristic
179C22#1681364811yescharacteristic
180C22#1681365311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—44no—
187C4—4521no—
188C4—4521no—
189C4—4521no—
190C4#1681355012yes—
191C2—21no—
192C2—21no—
193C2—9041no—
194C2#2029857111yescharacteristic
195C2#2029859711yescharacteristic
196C2C2×#1681355011yescharacteristic
subgroupG/H
centerC22C2×#14268624
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC4×C4⋊C4×C113C2
socleC22×C113C2×C22⋊C4
prime radical#16813596C22
cosocleC22×C4×C113C23
hypercenterC4×C4⋊C4D113
hypocenterC113#1509
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20298655C2semidirect
3. #20298334C2semidirect
5. C4×C4⋊C4×C113C2semidirect
7. #16813614C4semidirect
8. #16813610C4semidirect
12. C4×Dic226C4semidirect
13. C4×D452C4semidirect
99. C113#1509semidirect
102. C4×C4⋊C4D113semidirect

Maximal subgroups

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

subgroupindex
#202991322
#202986552
#202983342
#202983312
C4×C4⋊C4×C1132
#1509113