Finite Group Databasebeta

← #28405993

Subgroups — #28405993

Order 14464.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#20299620C211yesmaximal, characteristic, complemented
2#20299543C211yesmaximal, characteristic, complemented
3#20299450C212yesmaximal, complemented
4#20299449C212yesmaximal, complemented
5#20299145C211yesmaximal, characteristic
6C4⋊#11744753—21no—
7#16813679C2212yes—
8#16813677—21no—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4C2212yes—
12C2×#14268647—21no—
13#16813621C411yescharacteristic, complemented
14#16813618C411yescharacteristic, complemented
15#16813608—21no—
16#16813597C2211yescharacteristic
17#16813595—21no—
18#16813593C2211yescharacteristic
19C4×D452C411yescharacteristic, complemented
20C4×C22⋊D113—21no—
21C42×D113C2211yescharacteristic
22C4×D4×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24C2×#11744753—22no—
25#14268647—44no—
26C2×Dic226—21no—
27C2×D452—21no—
28C2×D452C2×C411yescharacteristic
29C2×C22⋊D113—21no—
30C2×C22⋊D113—21no—
31C2×C22⋊D113—21no—
32C2×C4×D113—21no—
33C2×C4×D113D411yescharacteristic
34C2×C4×D113D411yescharacteristic
35C2×C4×D113C2311yescharacteristic
36C4⋊Dic113C2×C411yescharacteristic
37#14268626—21no—
38C22⋊Dic113—21no—
39#14268624—21no—
40#14268624—21no—
41C4×Dic113C2×C411yescharacteristic
42C4×Dic113D411yescharacteristic
43C4×Dic113D411yescharacteristic
44C2×D4×C113C2×C411yescharacteristic
45C22×C4×C113—21no—
46C4⋊C4×C113C2×C411yescharacteristic
47C22⋊C4×C113—21no—
48C42×C113C2×C411yescharacteristic
49C23×C113—21no—
50C22×D113—21no—
51C22×D113C2×D411yescharacteristic
52C2×#90673—42no—
53C2×#90673—42no—
54C2×#90673—42no—
55D4×C113—41no—
56C2×C4×C113—21no—
57C2×C4×C113—42no—
58C2×C4×C113C22⋊C411yescharacteristic
59C2×C4×C113C22⋊C411yescharacteristic
60C2×C4×C113C22×C411yescharacteristic
61C22⋊D113—42no—
62C22⋊D113—42no—
63C22⋊D113—42no—
64C2×Dic113—21no—
65C2×Dic113C22⋊C411yescharacteristic
66C2×Dic113C22⋊C411yescharacteristic
67C2×Dic113C2×D411yescharacteristic
68D452—41no—
69D452—42no—
70C4×D113—22no—
71C4×D113—41no—
72C4×D113—41no—
73C4×D113—42no—
74Dic226—42no—
75#11744753—42no—
76C22×C113—41no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113C2×C22⋊C411yescharacteristic
80C2×D113—21no—
81C2×D113—21no—
82C2×D113—41no—
83C2×D113—41no—
84C2×D113—41no—
85C2×D113AGL(1,ℤ/8)12yes—
86#90673—82no—
87C4×C113—21no—
88C4×C113—21no—
89C4×C113—21no—
90C4×C113—41no—
91Dic113—21no—
92Dic113—21no—
93Dic113—21no—
94Dic113—41no—
95C2×C113—81no—
96C2×C113#41011yescharacteristic
97C2×C113#41811yescharacteristic
98C2×C113#42111yescharacteristic
99D113—22no—
100D113—81no—
101#1514—1131nomaximal, Sylow
102C113#151411yescharacteristic, complemented, Sylow
103#532—1131no—
104#432—1131no—
105#383—1131no—
106#327—1132no—
107#327—1132no—
108C2×#41—2261no—
109C4⋊Q8—1131no—
110#127—1131no—
111#124—2261no—
112#121—1131no—
113#121—1131no—
114#121—2261no—
115C4×D4—1131no—
116C4×D4—2261no—
117C4×D4#9067311yescharacteristic, complemented
118C2×C42—1131no—
119C4⋊C8—2261no—
120C22⋊C8—1132no—
121#97—2261no—
122#95—1132no—
123#95—2261no—
124#95—2261no—
125#41—4524no—
126C2×Q8—2261no—
127C2×D4—1131no—
128C2×D4—2261no—
129C2×D4—2261no—
130C2×D4—2261no—
131C2×D4—2261no—
132C2×D4C2×#9067311yescharacteristic
133C22×C4—21no—
134C22×C4—1131no—
135C22×C4—1131no—
136C22×C4—1131no—
137C22×C4—2262no—
138C22×C4—2261no—
139C2×C8—2262no—
140C4⋊C4—1131no—
141C4⋊C4—2261no—
142C4⋊C4C2×#9067311yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—2261no—
145C22⋊C4—2261no—
146C22⋊C4—2261no—
147C42—1131no—
148C42—1131no—
149C42—1131no—
150C42C2×#9067311yescharacteristic
151C23—21no—
152C23—1131no—
153C23—2261no—
154Q8—4522no—
155D4—41no—
156D4—4521no—
157D4—4522no—
158D4—4522no—
159D4—4522no—
160D4—4522no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—1131no—
164C2×C4—1131no—
165C2×C4—1131no—
166C2×C4—4522no—
167C2×C4—4521no—
168C2×C4—4521no—
169C2×C4—4522no—
170C2×C4—4522no—
171C2×C4—4522no—
172C2×C4—2262no—
173C2×C4—2261no—
174C2×C4C22⋊#9067311yescharacteristic
175C2×C4C22⋊#9067311yescharacteristic
176C2×C4C22×#9067311yescharacteristic
177C8—4522no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1132no—
182C22—4521no—
183C22—4521no—
184C22—4521no—
185C22—2261no—
186C22—2261no—
187C22C2×C22⋊#9067311yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—9042no—
193C4—4521no—
194C4—2261no—
195C4—2261no—
196C4—2261no—
197C2—81no—
198C2—9041no—
199C2—2262no—
200C2#2029957711yescharacteristic
201C2#2029959011yescharacteristic
202C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4×D4×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299145C2
cosocleC2×C4×D113C23
hypercenterC4×D4#90673
hypocenterC113#1514
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20299620C2semidirect
2. #20299543C2semidirect
3. #20299450C2semidirect
4. #20299449C2semidirect
13. #16813621C4semidirect
14. #16813618C4semidirect
19. C4×D452C4semidirect
22. C4×D4×C113C4semidirect
102. C113#1514semidirect
117. C4×D4#90673semidirect

Maximal subgroups

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

subgroupindex
#202996202
#202995432
#202994502
#202994492
#202991452
#1514113