Finite Group Databasebeta

← #28400826

Subgroups — #28400826

Order 14464.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299210C211yesmaximal, characteristic, complemented
2#20298939C212yesmaximal, complemented
3#20298898C212yesmaximal, complemented
4#20298803C212yesmaximal, complemented
5#20298749C212yesmaximal
6#20298698C212yesmaximal, complemented
7C4×#14268635C212yesmaximal, complemented
8#20298659C211yesmaximal, characteristic, complemented
9#518×C113C211yesmaximal, characteristic
10C2×#14268635C2212yes—
11C2×#14268635C2212yes—
12#16813622C2211yescharacteristic, complemented
13#16813615—22no—
14#16813614C2211yescharacteristic, complemented
15#16813612—22no—
16#16813601C2212yes—
17C4×Dic226C2212yescomplemented
18#16813555C2212yescomplemented
19#16813553C2212yescomplemented
20C4⋊#11744751C2212yescomplemented
21#16813545C2212yescomplemented
22#16813545C2212yescomplemented
23#16813543C2212yes—
24#16813543C2212yes—
25C22⋊#11744751C2212yes—
26#16813533C2211yescharacteristic, complemented
27C4×#11744751C2211yescharacteristic, complemented
28C22×D4×C113C2211yescharacteristic
29C4×D4×C113—22no—
30C4×D4×C113C2212yes—
31C4×D4×C113C2212yes—
32#117×C113C2211yescharacteristic
33#117×C113C2211yescharacteristic
34C2×C22⋊C4×C113—22no—
35C2×Dic226C2312yes—
36#14268635—24no—
37#14268635—24no—
38C2×#11744751C2312yes—
39C2×#11744751C2312yes—
40C4⋊Dic113—22no—
41C4⋊Dic113C2312yes—
42#14268626—22no—
43#14268626—22no—
44#14268626—22no—
45C22⋊Dic113—22no—
46C4×Dic113—22no—
47C24×C113—21no—
48C2×D4×C113—24no—
49C2×D4×C113—21no—
50C2×D4×C113C2312yes—
51C22×C4×C113—22no—
52C22×C4×C113—22no—
53C22×C4×C113C2311yescharacteristic
54C4⋊C4×C113D412yes—
55C4⋊C4×C113C2312yes—
56C22⋊C4×C113—21no—
57C22⋊C4×C113—22no—
58C22⋊C4×C113—22no—
59C22⋊C4×C113D412yes—
60C42×C113—21no—
61C42×C113C2311yescharacteristic
62C42×C113C2311yescharacteristic
63C23×C113—24no—
64C23×C113—22no—
65C23×C113—82no—
66C23×C113C2×D411yescharacteristic
67D4×C113—24no—
68D4×C113—22no—
69D4×C113#4114yes—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113—82no—
73C2×C4×C113—82no—
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2×D412yes—
76C2×C4×C113C2×D412yes—
77C2×C4×C113C2411yescharacteristic
78C2×Dic113—22no—
79C2×Dic113—22no—
80Dic226—22no—
81Dic226—22no—
82#11744751—22no—
83#11744751—22no—
84C22×C113—21no—
85C22×C113—24no—
86C22×C113—22no—
87C22×C113—42no—
88C22×C113—42no—
89C22×C113—84no—
90C22×C113C22×D411yescharacteristic
91C4×C113—21no—
92C4×C113—22no—
93C4×C113—22no—
94C4×C113—42no—
95C4×C113C2×#4112yes—
96Dic113—42no—
97Dic113—42no—
98C2×C113—41no—
99C2×C113—44no—
100C2×C113#52511yescharacteristic
101C2×C113#57712yes—
102#3123—1131nomaximal, Sylow
103C113#312311yescharacteristic, complemented, Sylow
104#541—1131no—
105#518D11311yescharacteristic
106#485—1132no—
107#478—1132no—
108#461—1132no—
109#450—1132no—
110#440—1132no—
111C4×SD16—1132no—
112#433—1131no—
113C22×D4C2×D11311yescharacteristic
114C2×SD16—1132no—
115C2×SD16—1132no—
116C4⋊Q8—1131no—
117#126—2262no—
118#125—1131no—
119#125—2262no—
120C22⋊Q8—1132no—
121C4×Q8—1132no—
122C4×D4—22no—
123C4×D4C2×D11312yes—
124C4×D4C2×D11312yes—
125#117C2×D11311yescharacteristic
126#117C2×D11311yescharacteristic
127C2×C22⋊C4—22no—
128#107—1132no—
129#106—1132no—
130C4⋊C8—1132no—
131#103—1132no—
132#103—1132no—
133#102—1132no—
134#102—1132no—
135C22⋊C8—1132no—
136#97—1131no—
137C4×C8—1131no—
138C24—21no—
139C2×Q8—1132no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D11312yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D11311yescharacteristic
146SD16—2264no—
147SD16—2264no—
148C2×C8—1132no—
149C2×C8—1132no—
150C4⋊C4—1132no—
151C4⋊C4—2262no—
152C4⋊C4—2262no—
153C4⋊C4—2262no—
154C4⋊C4—2262no—
155C4⋊C4C22⋊D11312yes—
156C4⋊C4C22×D11312yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—2262no—
161C22⋊C4C22⋊D11312yes—
162C42—21no—
163C42—2262no—
164C42C22×D11311yescharacteristic
165C42C22×D11311yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D11311yescharacteristic
170Q8—2262no—
171Q8—2262no—
172D4—24no—
173D4—22no—
174D4#1426864714yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—2262no—
180C2×C4—2262no—
181C2×C4C2×C22⋊D11311yescharacteristic
182C2×C4C2×C22⋊D11312yes—
183C2×C4C2×C22⋊D11312yes—
184C2×C4C23×D11311yescharacteristic
185C8—2262no—
186C8—2262no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D11311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—4522no—
199C4—4522no—
200C4C2×#1426864712yes—
201C2—41no—
202C2—44no—
203C2#2029910911yescharacteristic
204C2#2029940912yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#518×C113C2
socleC22×C113C22×D4
prime radicalC22×D4×C113C22
hypercenter#518D113
hypocenterC113#3123
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #20299210C2semidirect
2. #20298939C2semidirect
3. #20298898C2semidirect
4. #20298803C2semidirect
6. #20298698C2semidirect
7. C4×#14268635C2semidirect
8. #20298659C2semidirect
12. #16813622C22semidirect
14. #16813614C22semidirect
17. C4×Dic226C22semidirect
18. #16813555C22semidirect
19. #16813553C22semidirect
20. C4⋊#11744751C22semidirect
21. #16813545C22semidirect
22. #16813545C22semidirect
26. #16813533C22semidirect
27. C4×#11744751C22semidirect
103. C113#3123semidirect

Maximal subgroups

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

subgroupindex
#202992102
#202989392
#202988982
#202988032
#202987492
#202986982
C4×#142686352
#202986592
#518×C1132
#3123113