Finite Group Databasebeta

← #28399937

Subgroups — #28399937

Order 14464.

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

normal subgroups only

This group has 698 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×#16813670C211yesmaximal, characteristic, complemented
2#20299396C212yesmaximal, complemented
3#20298780C214yesmaximal, complemented
4#20298770C214yesmaximal, complemented
5#20298616C212yesmaximal, complemented
6C2×#16813541C211yesmaximal, characteristic, complemented
7#536×C113C211yesmaximal, characteristic, complemented
8#16813670—24no—
9#16813670—22no—
10#16813670C2214yes—
11C2×#14268648—22no—
12C2×#14268647—22no—
13C2×#14268647C2212yes—
14C2×Q8×D113—22no—
15#16813653C2214yescomplemented
16#16813652—22no—
17#16813648C2214yescomplemented
18#16813647—22no—
19#16813642—24no—
20C2×#14268631C2212yes—
21#16813550C2218yescomplemented
22#16813541C2214yescomplemented
23C2×#41×C113C2211yescharacteristic
24C22×Q8×C113C2211yescharacteristic
25C4⋊Q8×C113C2212yescomplemented
26#124×C113C2212yescomplemented
27#123×C113—22no—
28C22⋊Q8×C113—22no—
29#117×C113C2211yescharacteristic
30#14268648—28no—
31#14268648—28no—
32#14268647—28no—
33#14268647—28no—
34#14268647—22no—
35#14268647—22no—
36#14268647D414yes—
37#14268647C2314yes—
38C2×Dic226—22no—
39C2×Dic226D412yes—
40Q8×D113—28no—
41Q8×D113—28no—
42C2×D452—22no—
43C2×D452D412yes—
44C2×C22⋊D113—22no—
45C2×C4×D113—24no—
46C2×C4×D113—22no—
47#14268637—24no—
48#14268635—24no—
49#14268634—24no—
50#14268632—24no—
51#14268631—22no—
52#14268631C2314yes—
53C2×#11744751—22no—
54#41×C113—22no—
55#41×C113—22no—
56C2×Q8×C113—22no—
57C2×Q8×C113—22no—
58C2×Q8×C113D412yes—
59C2×Q8×C113C2311yescharacteristic
60C2×Q8×C113C2312yes—
61C2×D4×C113—21no—
62C2×D4×C113C2311yescharacteristic
63C22×C4×C113—21no—
64C22×C4×C113D412yes—
65C22×C4×C113C2311yescharacteristic
66C4⋊C4×C113—21no—
67C4⋊C4×C113—24no—
68C22⋊C4×C113—21no—
69C22⋊C4×C113—24no—
70C42×C113C2312yes—
71C23×C113—21no—
72C23×C113C2×D411yescharacteristic
73C22×D113—22no—
74Q8×C113—24no—
75Q8×C113—24no—
76Q8×C113—22no—
77D4×C113—22no—
78D4×C113—41no—
79D4×C113—41no—
80C2×C4×C113—22no—
81C2×C4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113—21no—
84C2×C4×C113—42no—
85C2×C4×C113C2×D412yes—
86C2×C4×C113C2×D412yes—
87C2×C4×C113C2×D414yes—
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2411yescharacteristic
90C22⋊D113—24no—
91C22⋊D113—24no—
92C2×Dic113—22no—
93D452—28no—
94D452—22no—
95D452C2×D414yes—
96C4×D113—216no—
97C4×D113—24no—
98C4×D113—24no—
99Dic226—28no—
100Dic226—22no—
101Dic226C2×D414yes—
102#11744751—24no—
103C22×C113—41no—
104C22×C113—42no—
105C22×C113—41no—
106C22×C113#12011yescharacteristic
107C22×C113#12011yescharacteristic
108C22×C113C22×D411yescharacteristic
109C2×D113—24no—
110C2×D113—44no—
111C4×C113—24no—
112C4×C113—42no—
113C4×C113—41no—
114C4×C113#12012yes—
115C4×C113C22×D412yes—
116Dic113—24no—
117C2×C113—21no—
118C2×C113—21no—
119C2×C113—21no—
120C2×C113—81no—
121C2×C113C2×#12011yescharacteristic
122D113—44no—
123#3020—1131nomaximal, Sylow
124C113#302011yescharacteristic, complemented, Sylow
125C2×2−1+4—1131no—
126#575—1132no—
127#536D11311yescharacteristic, complemented
128#456—1134no—
129#454—1134no—
130#421—1132no—
131C2×#101—1131no—
1322−1+4—1134no—
1332−1+4—2264no—
1342−1+4—2262no—
135C2×#41—1132no—
136C2×#41—2262no—
137C2×#41—2262no—
138C2×#41C2×D11311yescharacteristic
139C22×Q8—2262no—
140C22×Q8C2×D11311yescharacteristic
141#137—1134no—
142#137—2262no—
143AGL(1,ℤ/8)—1134no—
144AGL(1,ℤ/8)—2262no—
145#135—2264no—
146C2×M16—1132no—
147C4⋊Q8C2×D11312yescomplemented
148#124C2×D11312yescomplemented
149#123—22no—
150C22⋊Q8—22no—
151#117C2×D11311yescharacteristic
152#104—1138no—
153#101—1134no—
154#41—22no—
155#41—22no—
156#41—1134no—
157#41—1134no—
158#41—2268no—
159#41—2268no—
160#41—2268no—
161#41—2262no—
162#41—2262no—
163#41—2268no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—1132no—
167C2×Q8—2262no—
168C2×Q8—2268no—
169C2×Q8—2268no—
170C2×Q8C22⋊D11312yes—
171C2×Q8C22×D11311yescharacteristic
172C2×Q8C22×D11312yes—
173C2×D4—21no—
174C2×D4—1132no—
175C2×D4—2262no—
176C2×D4—2262no—
177C2×D4C22×D11311yescharacteristic
178C22×C4—21no—
179C22×C4—2264no—
180C22×C4—2262no—
181C22×C4C22⋊D11312yes—
182C22×C4C22×D11311yescharacteristic
183Q16—2264no—
184SD16—2264no—
185SD16—2264no—
186D8—2264no—
187M16—1134no—
188M16—2262no—
189C2×C8—2262no—
190C4⋊C4—21no—
191C4⋊C4—24no—
192C22⋊C4—21no—
193C22⋊C4—24no—
194C42C22×D11312yes—
195C23—21no—
196C23—2262no—
197C23C2×C22⋊D11311yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—22no—
201Q8—1134no—
202Q8—2268no—
203Q8—2262no—
204D4—22no—
205D4—41no—
206D4—41no—
207D4—1134no—
208D4—2268no—
209D4—2264no—
210D4—2264no—
211D4—2262no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—22616no—
218C2×C4—2262no—
219C2×C4—2264no—
220C2×C4—2264no—
221C2×C4D4×D11312yes—
222C2×C4D4×D11312yes—
223C2×C4C2×C22⋊D11314yes—
224C2×C4C2×C22⋊D11311yescharacteristic
225C2×C4C23×D11311yescharacteristic
226C8—2264no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—4524no—
231C22—2264no—
232C22#1681359011yescharacteristic
233C22#1681359011yescharacteristic
234C22C22×C22⋊D11311yescharacteristic
235C4—24no—
236C4—42no—
237C4—41no—
238C4—2264no—
239C4#1681359012yes—
240C4C2×D4×D11312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—81no—
245C2—4524no—
246C2C2×#1681359011yescharacteristic
subgroupG/H
centerC2C2×#16813590
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#536×C113C2
socleC2×C113C2×#120
hypercenter#536D113
hypocenterC113#3020
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#16813670C2semidirect
2. #20299396C2semidirect
3. #20298780C2semidirect
4. #20298770C2semidirect
5. #20298616C2semidirect
6. C2×#16813541C2semidirect
7. #536×C113C2semidirect
15. #16813653C22semidirect
17. #16813648C22semidirect
21. #16813550C22semidirect
22. #16813541C22semidirect
25. C4⋊Q8×C113C22semidirect
26. #124×C113C22semidirect
124. C113#3020semidirect
127. #536D113semidirect
147. C4⋊Q8C2×D113semidirect
148. #124C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136702
#202993962
#202987802
#202987702
#202986162
C2×#168135412
#536×C1132
#3020113