Finite Group Databasebeta

← #28407050

Subgroups — #28407050

Order 14464.

672 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 162 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#20299548C218yesmaximal, complemented
2#20299540C212yesmaximal, complemented
3#20299539C212yesmaximal
4C4×C22⋊#90673C212yesmaximal, complemented
5C2×C22⋊C4×D113C211yesmaximal, characteristic
6C2×C4⋊#90673C2214yescomplemented
7C2×C22⋊#90673C2214yes—
8C2×C22⋊#90673C2214yes—
9C2×C22⋊#90673C2214yes—
10C2×C4×#90673C2214yescomplemented
11(C2×#90673)⋊C4C2214yescomplemented
12(C2×#90673)⋊C4C2214yescomplemented
13C24×D113C2211yescharacteristic
14C22×C4×D113C2211yescharacteristic
15C22×C4×D113C2211yescharacteristic
16C2×C22⋊Dic113C411yescharacteristic, complemented
17C2×#14268624C411yescharacteristic, complemented
18C2×#14268624C411yescharacteristic, complemented
19C22⋊C4×D113C414yescomplemented
20C22⋊C4×D113C2214yes—
21C2×C22⋊C4×C113C411yescharacteristic, complemented
22C22×#90673C2318yes—
23C4⋊#90673—44no—
24C22⋊#90673—28no—
25C22⋊#90673—44no—
26C22⋊#90673—44no—
27C4×#90673—44no—
28C23×D113—24no—
29C23×D113—42no—
30C23×D113—42no—
31C23×D113C2×C412yes—
32C23×D113C2×C411yescharacteristic
33C23×D113C2312yes—
34C23×D113C2311yescharacteristic
35C22×Dic113C2×C411yescharacteristic
36C22×Dic113C2×C411yescharacteristic
37C2×C4×D113—42no—
38C2×C4×D113—42no—
39C2×C4×D113C2×C412yes—
40C2×C4×D113C2×C412yes—
41C2×C4×D113C2312yes—
42C2×C4×D113C2312yes—
43C22⋊Dic113C2×C414yes—
44#14268624C2×C414yes—
45#14268624C2×C414yes—
46C24×C113C2×C411yescharacteristic
47C22×C4×C113C2×C411yescharacteristic
48C22×C4×C113C2×C411yescharacteristic
49C22⋊C4×C113C2×C414yes—
50C23×C113—22no—
51C23×C113—41no—
52C23×C113—41no—
53C23×C113C22×C412yes—
54C23×C113C22×C411yescharacteristic
55C22×D113—22no—
56C22×D113—22no—
57C22×D113—22no—
58C22×D113—24no—
59C22×D113—24no—
60C22×D113—24no—
61C22×D113—24no—
62C22×D113—42no—
63C22×D113—42no—
64C22×D113—41no—
65C22×D113—41no—
66C22×D113—416no—
67C22×D113C22×C412yes—
68C22×D113C22×C411yescharacteristic
69C22×D113#4114yes—
70C22×D113C2411yescharacteristic
71C2×#90673—28no—
72C2×#90673—28no—
73C2×#90673—28no—
74C2×C4×C113—41no—
75C2×C4×C113—41no—
76C2×C4×C113C22×C412yes—
77C2×C4×C113C22×C412yes—
78C2×Dic113—41no—
79C2×Dic113—41no—
80C2×Dic113C22×C412yes—
81C2×Dic113C22×C412yes—
82C4×D113—24no—
83C4×D113—24no—
84C4×D113—42no—
85C4×D113—42no—
86C22×C113—21no—
87C22×C113—21no—
88C22×C113—22no—
89C22×C113—22no—
90C22×C113—22no—
91C22×C113—44no—
92C22×C113#11712yes—
93C22×C113C23×C411yescharacteristic
94C2×D113—21no—
95C2×D113—21no—
96C2×D113—28no—
97C2×D113—22no—
98C2×D113—22no—
99C2×D113—22no—
100C2×D113—48no—
101C2×D113—44no—
102C2×D113—48no—
103C2×D113#11712yes—
104C2×D113C2×#4112yes—
105C2×D113H(5,𝔽2)12yes—
106C2×D113H(5,𝔽2)12yes—
107#90673—48no—
108C4×C113—22no—
109C4×C113—22no—
110Dic113—22no—
111Dic113—22no—
112C2×C113—22no—
113C2×C113—42no—
114C2×C113C2×#11711yescharacteristic
115C2×C113#51811yescharacteristic
116C2×C113#51811yescharacteristic
117D113—22no—
118D113—42no—
119D113#53814yes—
120#2312—1131nomaximal, Sylow
121C113#231211yescharacteristic, complemented, Sylow
122C22×C22⋊C4—1131no—
123#388—1138no—
124#380—1132no—
125#379—1132no—
126C4×C22⋊C4—1132no—
127C25—1131no—
128C23×C4—1131no—
129C23×C4—1131no—
130C2×C4⋊C4—1134no—
131C2×C22⋊C4—1131no—
132C2×C22⋊C4—1131no—
133C2×C22⋊C4—1131no—
134C2×C22⋊C4—1134no—
135C2×C22⋊C4—1134no—
136C2×C22⋊C4—1134no—
137C2×C22⋊C4—1134no—
138C2×C22⋊C4—1134no—
139C2×C22⋊C4#9067311yescharacteristic, complemented
140C2×C42—1134no—
141#95—1134no—
142#95—1134no—
143C24—1131no—
144C24—1132no—
145C24—1131no—
146C24—1132no—
147C24—4522no—
148C24—4522no—
149C24—2264no—
150C24C2×#9067311yescharacteristic
151C22×C4—1131no—
152C22×C4—1131no—
153C22×C4—1132no—
154C22×C4—1132no—
155C22×C4—1132no—
156C22×C4—1132no—
157C22×C4—1138no—
158C22×C4—4522no—
159C22×C4—4522no—
160C22×C4C2×#9067311yescharacteristic
161C22×C4C2×#9067311yescharacteristic
162C4⋊C4—4524no—
163C22⋊C4—1134no—
164C22⋊C4—1134no—
165C22⋊C4—1134no—
166C22⋊C4—4524no—
167C22⋊C4—4524no—
168C22⋊C4—2268no—
169C22⋊C4C2×#9067314yes—
170C42—4524no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—1131no—
175C23—1134no—
176C23—1131no—
177C23—1132no—
178C23—4521no—
179C23—4521no—
180C23—4522no—
181C23—4522no—
182C23—45216no—
183C23—2264no—
184C23—2264no—
185C23—2264no—
186C23—2264no—
187C23—2262no—
188C23—2262no—
189C23—2262no—
190C23C22×#9067312yes—
191C23C22×#9067311yescharacteristic
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1132no—
195C2×C4—1132no—
196C2×C4—4522no—
197C2×C4—4522no—
198C2×C4—4521no—
199C2×C4—4521no—
200C2×C4—2264no—
201C2×C4—2264no—
202C2×C4—2268no—
203C2×C4—2268no—
204C2×C4—2268no—
205C2×C4C22×#9067312yes—
206C2×C4C22×#9067312yes—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—22no—
211C22—22no—
212C22—44no—
213C22—1132no—
214C22—1132no—
215C22—1132no—
216C22—1132no—
217C22—4524no—
218C22—4528no—
219C22—4528no—
220C22—2268no—
221C22—2262no—
222C22—2262no—
223C22—2262no—
224C22—2261no—
225C22—2261no—
226C22#1681370112yes—
227C22C23×#9067311yescharacteristic
228C4—22no—
229C4—22no—
230C4—4528no—
231C4—2262no—
232C4—2262no—
233C2—22no—
234C2—42no—
235C2—1134no—
236C2—4522no—
237C2—2262no—
238C2C2×#1681370111yescharacteristic
239C2#2029966511yescharacteristic
240C2#2029966511yescharacteristic
subgroupG/H
center, FrattiniC22C23×#90673
commutator, socleC22×C113C23×C4
FittingC2×C22⋊C4×C113C4
prime radicalC24×D113C22
cosocleC22×D113C24
hypercenterC2×C22⋊C4#90673
hypocenterC113#2312
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20299548C2semidirect
2. #20299540C2semidirect
4. C4×C22⋊#90673C2semidirect
6. C2×C4⋊#90673C22semidirect
10. C2×C4×#90673C22semidirect
11. (C2×#90673)⋊C4C22semidirect
12. (C2×#90673)⋊C4C22semidirect
16. C2×C22⋊Dic113C4semidirect
17. C2×#14268624C4semidirect
18. C2×#14268624C4semidirect
19. C22⋊C4×D113C4semidirect
21. C2×C22⋊C4×C113C4semidirect
121. C113#2312semidirect
139. C2×C22⋊C4#90673semidirect

Maximal subgroups

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

subgroupindex
#202995482
#202995402
#202995392
C4×C22⋊#906732
C2×C22⋊C4×D1132
#2312113