Finite Group Databasebeta

← #28399938

Subgroups — #28399938

Order 14464.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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#20299396C212yesmaximal, complemented
2#20299172C211yesmaximal, characteristic, complemented
3#20298781C214yesmaximal, complemented
4#20298771C214yesmaximal, complemented
5#20298615C212yesmaximal, complemented
6C2×#16813541C211yesmaximal, characteristic, complemented
7C2×2−1+4×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9#16813653—22no—
10#16813652C2214yescomplemented
11#16813648—22no—
12#16813647C2214yescomplemented
13#16813642—24no—
14C2×#14268631C2212yes—
15#16813620C2212yescomplemented
16#16813611C2212yescomplemented
17#16813605—22no—
18#16813598—22no—
19#16813581C2211yescharacteristic
20#16813549C2218yescomplemented
21#16813541C2214yescomplemented
222−1+4×C113—24no—
232−1+4×C113—22no—
242−1+4×C113C2214yes—
25C2×#41×C113—22no—
26C2×#41×C113—22no—
27C2×#41×C113C2212yes—
28C22×Q8×C113—22no—
29C22×Q8×C113C2211yescharacteristic
30#14268647—22no—
31#14268647—22no—
32C2×Dic226C2311yescharacteristic
33C2×D452C2311yescharacteristic
34C2×C22⋊D113—21no—
35C2×C4×D113—21no—
36#14268637—24no—
37#14268635—24no—
38#14268634—24no—
39#14268632—24no—
40#14268631—22no—
41#14268631C2314yes—
42C2×#11744751—22no—
43C4⋊Dic113—21no—
44#14268626—24no—
45C22⋊Dic113—21no—
46#14268624—24no—
47C4×Dic113C2312yes—
48#41×C113—28no—
49#41×C113—28no—
50#41×C113—28no—
51#41×C113—28no—
52#41×C113—22no—
53#41×C113—22no—
54#41×C113D414yes—
55#41×C113C2314yes—
56C2×Q8×C113—22no—
57C2×Q8×C113—28no—
58C2×Q8×C113—28no—
59C2×Q8×C113—22no—
60C2×Q8×C113—22no—
61C2×Q8×C113D412yes—
62C2×Q8×C113D412yes—
63C2×Q8×C113C2312yes—
64C2×D4×C113—22no—
65C2×D4×C113—22no—
66C2×D4×C113D412yes—
67C22×C4×C113—24no—
68C22×C4×C113—22no—
69C22×C4×C113D412yes—
70C22×C4×C113C2311yescharacteristic
71C23×C113—22no—
72C23×C113C2×D411yescharacteristic
73C22×D113—21no—
74Q8×C113—28no—
75Q8×C113—22no—
76Q8×C113—24no—
77Q8×C113—24no—
78Q8×C113C2×D414yes—
79D4×C113—28no—
80D4×C113—24no—
81D4×C113—24no—
82D4×C113—22no—
83D4×C113C2×D414yes—
84C2×C4×C113—216no—
85C2×C4×C113—22no—
86C2×C4×C113—22no—
87C2×C4×C113—22no—
88C2×C4×C113—24no—
89C2×C4×C113—24no—
90C2×C4×C113C2×D414yes—
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2×D412yes—
93C2×C4×C113C2×D412yes—
94C2×C4×C113C2411yescharacteristic
95C22⋊D113—41no—
96C22⋊D113—41no—
97C2×Dic113—22no—
98C2×Dic113—21no—
99D452—22no—
100C4×D113—42no—
101Dic226—22no—
102#11744751—24no—
103C22×C113—24no—
104C22×C113—41no—
105C22×C113—44no—
106C22×C113#12011yescharacteristic
107C22×C113#12011yescharacteristic
108C22×C113C22×D411yescharacteristic
109C2×D113—42no—
110C2×D113—41no—
111C4×C113—24no—
112C4×C113—24no—
113C4×C113#12012yes—
114C4×C113C22×D412yes—
115Dic113—42no—
116Dic113—41no—
117C2×C113—21no—
118C2×C113—21no—
119C2×C113—21no—
120C2×C113—44no—
121C2×C113C2×#12011yescharacteristic
122D113—81no—
123#3020—1131nomaximal, Sylow
124C113#302011yescharacteristic, complemented, Sylow
125C2×2−1+4D11311yescharacteristic, complemented
126#575—1132no—
127#536—1131no—
128#456—1134no—
129#454—1134no—
130#421—1132no—
131C2×#101—1131no—
1322−1+4—24no—
1332−1+4—22no—
1342−1+4C2×D11314yes—
135C2×#41—22no—
136C2×#41—22no—
137C2×#41—1131no—
138C2×#41C2×D11312yes—
139C22×Q8—22no—
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⋊Q8—1132no—
148#124—1132no—
149#123—2262no—
150C22⋊Q8—2262no—
151#117—1131no—
152#104—1138no—
153#101—1134no—
154#41—28no—
155#41—28no—
156#41—28no—
157#41—28no—
158#41—22no—
159#41—22no—
160#41—2262no—
161#41—2262no—
162#41C22⋊D11314yes—
163#41C22×D11314yes—
164C2×Q8—22no—
165C2×Q8—28no—
166C2×Q8—28no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—1131no—
170C2×Q8C22⋊D11312yes—
171C2×Q8C22⋊D11312yes—
172C2×Q8C22×D11312yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—1131no—
176C2×D4—2261no—
177C2×D4C22⋊D11312yes—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—2261no—
181C22×C4C22⋊D11312yes—
182C22×C4C22×D11311yescharacteristic
183Q16—2264no—
184SD16—2264no—
185SD16—2264no—
186D8—2264no—
187M16—1134no—
188M16—2262no—
189C2×C8—2262no—
190C4⋊C4—2261no—
191C4⋊C4—2264no—
192C22⋊C4—2261no—
193C22⋊C4—2264no—
194C42—1132no—
195C23—22no—
196C23—2261no—
197C23C2×C22⋊D11311yescharacteristic
198Q8—28no—
199Q8—22no—
200Q8—24no—
201Q8—24no—
202Q8—2262no—
203Q8C2×C22⋊D11314yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—4521no—
209D4—4521no—
210D4—2262no—
211D4C2×C22⋊D11314yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—4522no—
219C2×C4—2262no—
220C2×C4—2261no—
221C2×C4C2×C22⋊D11314yes—
222C2×C4C2×C22⋊D11311yescharacteristic
223C2×C4C2×C22⋊D11312yes—
224C2×C4C2×C22⋊D11312yes—
225C2×C4C23×D11311yescharacteristic
226C8—2264no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—4522no—
231C22—4521no—
232C22#1681359111yescharacteristic
233C22#1681359111yescharacteristic
234C22C22×C22⋊D11311yescharacteristic
235C4—24no—
236C4—24no—
237C4—4522no—
238C4—4521no—
239C4#1681359112yes—
240C4C22×C22⋊D11312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—9041no—
246C2C2×#1681359111yescharacteristic
subgroupG/H
centerC2C2×#16813591
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×2−1+4×C113C2
socleC2×C113C2×#120
hypercenterC2×2−1+4D113
hypocenterC113#3020
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20299396C2semidirect
2. #20299172C2semidirect
3. #20298781C2semidirect
4. #20298771C2semidirect
5. #20298615C2semidirect
6. C2×#16813541C2semidirect
7. C2×2−1+4×C113C2semidirect
10. #16813652C22semidirect
12. #16813647C22semidirect
15. #16813620C22semidirect
16. #16813611C22semidirect
20. #16813549C22semidirect
21. #16813541C22semidirect
124. C113#3020semidirect
125. C2×2−1+4D113semidirect

Maximal subgroups

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

subgroupindex
#202993962
#202991722
#202987812
#202987712
#202986152
C2×#168135412
C2×2−1+4×C1132
#3020113