Finite Group Databasebeta

← #28399930

Subgroups — #28399930

Order 14464.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#16813667C211yesmaximal, characteristic, complemented
2#20299396C212yesmaximal, complemented
3#20298775C214yesmaximal, complemented
4#20298765C214yesmaximal, complemented
5#20298616C212yesmaximal, complemented
6C2×#16813539C211yesmaximal, characteristic, complemented
7#535×C113C211yesmaximal, characteristic, complemented
8#16813667—24no—
9#16813667—22no—
10#16813667C2214yes—
11C2×#14268647C2212yes—
12C2×#14268646—22no—
13C22×C22⋊D113—22no—
14C2×D4×D113—22no—
15#16813653C2214yescomplemented
16#16813652—22no—
17#16813648C2214yescomplemented
18#16813647—22no—
19#16813642—24no—
20C2×#14268631C2212yescomplemented
21#16813550C2218yescomplemented
22#16813539C2214yescomplemented
23C2×#41×C113C2211yescharacteristic, complemented
24C22×D4×C113C2211yescharacteristic
25#127×C113C2212yescomplemented
26#124×C113C2212yescomplemented
27#121×C113—22no—
28#120×C113—22no—
29#117×C113C2211yescharacteristic, complemented
30C23×D113—22no—
31#14268647—22no—
32#14268647—22no—
33#14268647D414yescomplemented
34#14268647C2314yes—
35#14268646—28no—
36#14268646—28no—
37C2×Dic226D412yescomplemented
38C2×D452D412yescomplemented
39C2×C22⋊D113—24no—
40C2×C22⋊D113—28no—
41C2×C22⋊D113—22no—
42C2×C22⋊D113—28no—
43D4×D113—28no—
44D4×D113—28no—
45C22×Dic113—22no—
46C2×C4×D113—22no—
47#14268637—24no—
48#14268635—24no—
49#14268634—24no—
50#14268632—24no—
51#14268631—22no—
52#14268631C2314yescomplemented
53C2×#11744751—22no—
54C24×C113D412yes—
55#41×C113—22no—
56#41×C113—22no—
57C2×Q8×C113C2311yescharacteristic, complemented
58C2×D4×C113—21no—
59C2×D4×C113—24no—
60C2×D4×C113—22no—
61C2×D4×C113—22no—
62C2×D4×C113D412yes—
63C2×D4×C113C2312yes—
64C2×D4×C113C2311yescharacteristic, complemented
65C22×C4×C113—21no—
66C22×C4×C113C2311yescharacteristic
67C4⋊C4×C113—21no—
68C22⋊C4×C113—21no—
69C22⋊C4×C113—24no—
70C42×C113C2312yescomplemented
71C23×C113—22no—
72C23×C113—22no—
73C23×C113—21no—
74C23×C113—82no—
75C23×C113C2×D414yes—
76C23×C113C2×D411yescharacteristic
77C22×D113—22no—
78C22×D113—28no—
79C22×D113—84no—
80Q8×C113—22no—
81D4×C113—24no—
82D4×C113—24no—
83D4×C113—22no—
84D4×C113—41no—
85D4×C113—41no—
86D4×C113—84no—
87C2×C4×C113—22no—
88C2×C4×C113—21no—
89C2×C4×C113—42no—
90C2×C4×C113C2×D412yes—
91C2×C4×C113C2×D412yes—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2411yescharacteristic
94C22⋊D113—216no—
95C22⋊D113—24no—
96C22⋊D113—24no—
97C2×Dic113—28no—
98C2×Dic113—22no—
99D452—22no—
100D452C2×D414yes—
101C4×D113—24no—
102C4×D113—24no—
103Dic226—22no—
104Dic226C2×D414yes—
105#11744751—24no—
106C22×C113—24no—
107C22×C113—41no—
108C22×C113—44no—
109C22×C113—44no—
110C22×C113—42no—
111C22×C113—41no—
112C22×C113—82no—
113C22×C113#12011yescharacteristic
114C22×C113#12011yescharacteristic
115C22×C113C22×D411yescharacteristic
116C2×D113—24no—
117C2×D113—44no—
118C2×D113—88no—
119C4×C113—42no—
120C4×C113—41no—
121C4×C113#12012yes—
122C4×C113C22×D412yes—
123Dic113—24no—
124C2×C113—21no—
125C2×C113—21no—
126C2×C113—21no—
127C2×C113—44no—
128C2×C113—81no—
129C2×C113C2×#12011yescharacteristic
130D113—44no—
131#3019—1131nomaximal, Sylow
132C113#301911yescharacteristic, complemented, Sylow
133C2×H(5,𝔽2)—1131no—
134#575—1132no—
135#535D11311yescharacteristic, complemented
136#455—1134no—
137#453—1134no—
138#421—1132no—
139C2×#100—1131no—
140H(5,𝔽2)—1134no—
141H(5,𝔽2)—2264no—
142H(5,𝔽2)—2262no—
143C2×#41—1132no—
144C2×#41—2262no—
145C2×#41C2×D11311yescharacteristic, complemented
146C22×D4—2262no—
147C22×D4—2262no—
148C22×D4C2×D11311yescharacteristic
149#137—1134no—
150#137—2262no—
151AGL(1,ℤ/8)—1134no—
152AGL(1,ℤ/8)—2262no—
153#135—2264no—
154C2×M16—1132no—
155#127C2×D11312yescomplemented
156#124C2×D11312yescomplemented
157#121—22no—
158#120—22no—
159#117C2×D11311yescharacteristic, complemented
160#104—1138no—
161#100—1134no—
162C24—2262no—
163C24C22⋊D11312yes—
164#41—22no—
165#41—22no—
166#41—1134no—
167#41—1134no—
168#41—2268no—
169#41—2268no—
170#41—2262no—
171#41—2262no—
172C2×Q8—1132no—
173C2×Q8C22×D11311yescharacteristic, complemented
174C2×D4—21no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—1132no—
179C2×D4—2268no—
180C2×D4—2268no—
181C2×D4—2264no—
182C2×D4—2268no—
183C2×D4—2262no—
184C2×D4—2268no—
185C2×D4C22⋊D11312yes—
186C2×D4C22×D11312yes—
187C2×D4C22×D11311yescharacteristic, complemented
188C22×C4—21no—
189C22×C4—2262no—
190C22×C4—2262no—
191C22×C4C22×D11311yescharacteristic
192Q16—2264no—
193SD16—2264no—
194SD16—2264no—
195D8—2264no—
196M16—1134no—
197M16—2262no—
198C2×C8—2262no—
199C4⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—24no—
202C42C22×D11312yescomplemented
203C23—22no—
204C23—22no—
205C23—21no—
206C23—82no—
207C23—9044no—
208C23—2268no—
209C23—2262no—
210C23C2×C22⋊D11314yes—
211C23C2×C22⋊D11311yescharacteristic
212Q8—22no—
213Q8—1134no—
214Q8—2262no—
215D4—24no—
216D4—24no—
217D4—22no—
218D4—41no—
219D4—41no—
220D4—84no—
221D4—1134no—
222D4—22616no—
223D4—2264no—
224D4—2264no—
225D4—2262no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—2268no—
230C2×C4—2262no—
231C2×C4—2264no—
232C2×C4—2264no—
233C2×C4D4×D11312yes—
234C2×C4D4×D11312yes—
235C2×C4C2×C22⋊D11311yescharacteristic
236C2×C4C23×D11311yescharacteristic
237C8—2264no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—41no—
244C22—82no—
245C22—9048no—
246C22—4524no—
247C22—2264no—
248C22#1681359011yescharacteristic
249C22#1681359011yescharacteristic
250C22C22×C22⋊D11311yescharacteristic
251C4—42no—
252C4—41no—
253C4—2264no—
254C4#1681359012yes—
255C4C2×D4×D11312yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—81no—
261C2—4524no—
262C2C2×#1681359011yescharacteristic
subgroupG/H
centerC2C2×#16813590
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#535×C113C2
socleC2×C113C2×#120
hypercenter#535D113
hypocenterC113#3019
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#16813667C2semidirect
2. #20299396C2semidirect
3. #20298775C2semidirect
4. #20298765C2semidirect
5. #20298616C2semidirect
6. C2×#16813539C2semidirect
7. #535×C113C2semidirect
15. #16813653C22semidirect
17. #16813648C22semidirect
20. C2×#14268631C22semidirect
21. #16813550C22semidirect
22. #16813539C22semidirect
23. C2×#41×C113C22semidirect
25. #127×C113C22semidirect
26. #124×C113C22semidirect
29. #117×C113C22semidirect
33. #14268647D4semidirect
37. C2×Dic226D4semidirect
38. C2×D452D4semidirect
52. #14268631C23semidirect
57. C2×Q8×C113C23semidirect
64. C2×D4×C113C23semidirect
70. C42×C113C23semidirect
132. C113#3019semidirect
135. #535D113semidirect
145. C2×#41C2×D113semidirect
155. #127C2×D113semidirect
156. #124C2×D113semidirect
159. #117C2×D113semidirect
173. C2×Q8C22×D113semidirect
187. C2×D4C22×D113semidirect
202. C42C22×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136672
#202993962
#202987752
#202987652
#202986162
C2×#168135392
#535×C1132
#3019113