Finite Group Databasebeta

← #28399801

Subgroups — #28399801

Order 14464.

994 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 173 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×#16813648C212yesmaximal, complemented
2#20299109C211yesmaximal, characteristic, complemented
3#20298749C214yesmaximal, complemented
4#20298732C214yesmaximal, complemented
5#20298603C212yesmaximal, complemented
6#20298562C211yesmaximal, characteristic, complemented
7C23×D4×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic, complemented
9#16813648—28no—
10C2×#14268635C2214yescomplemented
11C2×#14268632C2214yescomplemented
12C2×#14268631C2212yescomplemented
13#16813605—21no—
14#16813601C2212yescomplemented
15#16813596C2212yescomplemented
16#16813591—21no—
17C4×C22⋊D113—22no—
18#16813581C2211yescharacteristic, complemented
19#16813543C2218yescomplemented
20C22⋊#11744751C2214yescomplemented
21C25×C113—21no—
22C22×D4×C113—28no—
23C22×D4×C113—22no—
24C22×D4×C113—21no—
25C22×D4×C113C2214yes—
26C22×D4×C113C2212yes—
27C23×C4×C113C2211yescharacteristic
28#14268647—24no—
29C2×Dic226C2311yescharacteristic, complemented
30C2×D452C2311yescharacteristic, complemented
31C2×C22⋊D113—22no—
32C2×C22⋊D113—21no—
33C2×C4×D113—21no—
34#14268635—28no—
35#14268632—28no—
36#14268631—24no—
37C2×#11744751C2314yescomplemented
38C4⋊Dic113C2312yescomplemented
39#14268626—22no—
40C22⋊Dic113—21no—
41C22⋊Dic113—22no—
42#14268624—22no—
43C4×Dic113—21no—
44C24×C113—28no—
45C24×C113—24no—
46C24×C113—22no—
47C24×C113—48no—
48C24×C113D411yescharacteristic
49C2×D4×C113—28no—
50C2×D4×C113—216no—
51C2×D4×C113—216no—
52C2×D4×C113—24no—
53C2×D4×C113—22no—
54C2×D4×C113—24no—
55C2×D4×C113D418yescomplemented
56C2×D4×C113C2314yes—
57C22×C4×C113—24no—
58C22×C4×C113D412yes—
59C22×C4×C113D411yescharacteristic
60C22×C4×C113C2312yes—
61C22×C4×C113C2311yescharacteristic
62C23×C113—22no—
63C23×C113—24no—
64C23×C113—216no—
65C23×C113—28no—
66C23×C113—24no—
67C23×C113—432no—
68C23×C113—48no—
69C23×C113—48no—
70C23×C113—48no—
71C23×C113C2×D411yescharacteristic
72C23×C113C2×D412yes—
73C22×D113—21no—
74D4×C113—216no—
75D4×C113—28no—
76D4×C113—24no—
77D4×C113C2×D418yes—
78C2×C4×C113—22no—
79C2×C4×C113—24no—
80C2×C4×C113—24no—
81C2×C4×C113C2×D412yes—
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2×D414yes—
84C2×C4×C113C2411yescharacteristic
85C22⋊D113—42no—
86C22⋊D113—44no—
87C2×Dic113—22no—
88C2×Dic113—21no—
89D452—22no—
90C4×D113—42no—
91Dic226—22no—
92#11744751—24no—
93C22×C113—28no—
94C22×C113—22no—
95C22×C113—22no—
96C22×C113—22no—
97C22×C113—28no—
98C22×C113—416no—
99C22×C113—432no—
100C22×C113—48no—
101C22×C113#12012yes—
102C22×C113AGL(1,ℤ/8)14yescomplemented
103C22×C113C22×D411yescharacteristic
104C2×D113—41no—
105C2×D113—42no—
106C4×C113—22no—
107C4×C113#12012yes—
108C4×C113C22×D412yes—
109Dic113—41no—
110Dic113—42no—
111C2×C113—22no—
112C2×C113—24no—
113C2×C113—48no—
114C2×C113C2×#12011yescharacteristic
115C2×C113C2×AGL(1,ℤ/8)12yes—
116D113—81no—
117#3003—1131nomaximal, Sylow
118C113#300311yescharacteristic, complemented, Sylow
119C23×D4D11311yescharacteristic, complemented
120C2×AGL(1,ℤ/8)—1132no—
121#525—1131no—
122#450—1134no—
123#447—1134no—
124#418—1132no—
125#407—1131no—
126C25—21no—
127C2×#41—1131no—
128C22×D4—28no—
129C22×D4—22no—
130C22×D4—21no—
131C22×D4C2×D11314yes—
132C22×D4C2×D11312yes—
133C23×C4C2×D11311yescharacteristic
134AGL(1,ℤ/8)—2268no—
135C2×SD16—1134no—
136C2×D8—1134no—
137C2×M16—1132no—
138#123—2261no—
139C22⋊Q8—1132no—
140#121—1132no—
141#120—2261no—
142C4×D4—2262no—
143#117—1131no—
144#102—1138no—
145C22⋊C8—1134no—
146C24—28no—
147C24—24no—
148C24—22no—
149C24—48no—
150C24C22⋊D11311yescharacteristic
151#41—2264no—
152C2×Q8—1131no—
153C2×D4—28no—
154C2×D4—216no—
155C2×D4—216no—
156C2×D4—24no—
157C2×D4—22no—
158C2×D4—24no—
159C2×D4—1131no—
160C2×D4—2262no—
161C2×D4—2261no—
162C2×D4C22⋊D11318yescomplemented
163C2×D4C22×D11314yes—
164C22×C4—24no—
165C22×C4—2261no—
166C22×C4C22⋊D11312yes—
167C22×C4C22⋊D11311yescharacteristic
168C22×C4C22×D11312yes—
169C22×C4C22×D11311yescharacteristic
170SD16—2268no—
171D8—2268no—
172M16—2264no—
173C2×C8—1134no—
174C4⋊C4—1132no—
175C4⋊C4—2262no—
176C22⋊C4—2261no—
177C22⋊C4—2262no—
178C22⋊C4—2262no—
179C42—2261no—
180C23—22no—
181C23—24no—
182C23—216no—
183C23—28no—
184C23—24no—
185C23—432no—
186C23—48no—
187C23—48no—
188C23—48no—
189C23—2261no—
190C23C2×C22⋊D11311yescharacteristic
191C23C2×C22⋊D11312yes—
192Q8—2262no—
193D4—216no—
194D4—28no—
195D4—24no—
196D4—4522no—
197D4—4524no—
198D4—2262no—
199D4C2×C22⋊D11318yes—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—4522no—
204C2×C4—2262no—
205C2×C4—2261no—
206C2×C4C2×C22⋊D11312yes—
207C2×C4C2×C22⋊D11311yescharacteristic
208C2×C4C2×C22⋊D11314yes—
209C2×C4C23×D11311yescharacteristic
210C8—2264no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—28no—
216C22—416no—
217C22—432no—
218C22—48no—
219C22—4521no—
220C22—4522no—
221C22#1681359112yes—
222C22#1681364814yescomplemented
223C22C22×C22⋊D11311yescharacteristic
224C4—22no—
225C4—4521no—
226C4—4522no—
227C4#1681359112yes—
228C4C22×C22⋊D11312yes—
229C2—22no—
230C2—24no—
231C2—48no—
232C2—9041no—
233C2C2×#1681359111yescharacteristic
234C2C2×#1681364812yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC23×D4×C113C2
socleC22×C113C22×D4
hypercenterC23×D4D113
hypocenterC113#3003
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. #20299109C2semidirect
3. #20298749C2semidirect
4. #20298732C2semidirect
5. #20298603C2semidirect
6. #20298562C2semidirect
7. C23×D4×C113C2semidirect
8. C2×#14268647C22semidirect
10. C2×#14268635C22semidirect
11. C2×#14268632C22semidirect
12. C2×#14268631C22semidirect
14. #16813601C22semidirect
15. #16813596C22semidirect
18. #16813581C22semidirect
19. #16813543C22semidirect
20. C22⋊#11744751C22semidirect
29. C2×Dic226C23semidirect
30. C2×D452C23semidirect
37. C2×#11744751C23semidirect
38. C4⋊Dic113C23semidirect
55. C2×D4×C113D4semidirect
102. C22×C113AGL(1,ℤ/8)semidirect
118. C113#3003semidirect
119. C23×D4D113semidirect
162. C2×D4C22⋊D113semidirect
222. C22#16813648semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
#202991092
#202987492
#202987322
#202986032
#202985622
C23×D4×C1132
#3003113