Finite Group Databasebeta

← #28406436

Subgroups — #28406436

Order 14464.

380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 78 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×#16813680C212yesmaximal
2#20299540C212yesmaximal, complemented
3#20299476C212yesmaximal, complemented
4C2×#16813582C211yesmaximal, characteristic
5C2×C4⋊#90673—22no—
6C2×C22⋊#90673C2214yes—
7#16813680—24no—
8(C2×#90673)⋊C4—22no—
9C22×C22⋊D113C2211yescharacteristic
10C23×Dic113C411yescharacteristic, complemented
11C22×C4×D113C2211yescharacteristic
12#16813582—22no—
13#16813582—22no—
14C2×#14268626C411yescharacteristic, complemented
15C2×#14268624C2211yescharacteristic
16C2×C4×Dic113C411yescharacteristic, complemented
17C2×C22⋊C4×C113C411yescharacteristic, complemented
18C22×#90673—24no—
19C4⋊#90673—44no—
20C22⋊#90673—24no—
21C22⋊#90673—24no—
22C23×D113C2311yescharacteristic
23C2×C22⋊D113—22no—
24C2×C22⋊D113—22no—
25C2×C22⋊D113D412yes—
26C2×C22⋊D113Q812yes—
27C22×Dic113—21no—
28C22×Dic113—21no—
29C22×Dic113—42no—
30C22×Dic113C2×C411yescharacteristic
31C22×Dic113C2×C411yescharacteristic
32C22×Dic113C2×C411yescharacteristic
33C2×C4×D113—42no—
34C2×C4×D113D412yes—
35C2×C4×D113D412yes—
36#14268626—22no—
37#14268624—22no—
38C4×Dic113—21no—
39C4×Dic113—21no—
40C24×C113C2×C411yescharacteristic
41C22×C4×C113C2×C411yescharacteristic
42C22×C4×C113C2×C411yescharacteristic
43C22⋊C4×C113—22no—
44C23×C113—21no—
45C23×C113—21no—
46C23×C113—41no—
47C23×C113—41no—
48C23×C113C4⋊C412yescomplemented
49C23×C113C22×C411yescharacteristic
50C22×D113—41no—
51C22×D113—41no—
52C22×D113C2×D412yes—
53C22×D113C2×D411yescharacteristic
54C22×D113C2×Q811yescharacteristic
55C22×D113#4112yes—
56C2×#90673—44no—
57C2×#90673—44no—
58C2×#90673—44no—
59C2×C4×C113—21no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113C22⋊C412yes—
63C22⋊D113—24no—
64C22⋊D113—24no—
65C2×Dic113—21no—
66C2×Dic113—21no—
67C2×Dic113—22no—
68C2×Dic113—21no—
69C2×Dic113—42no—
70C2×Dic113—42no—
71C2×Dic113—41no—
72C2×Dic113C22⋊C411yescharacteristic
73C2×Dic113C22⋊C411yescharacteristic
74C2×Dic113C4⋊C412yescomplemented
75C4×D113—24no—
76C4×D113—42no—
77C22×C113—21no—
78C22×C113—21no—
79C22×C113—22no—
80C22×C113—42no—
81C22×C113—42no—
82C22×C113—41no—
83C22×C113—41no—
84C22×C113C2×C22⋊C411yescharacteristic
85C22×C113C2×C4⋊C411yescharacteristic
86C22×C113#11711yescharacteristic
87C2×D113—22no—
88C2×D113—22no—
89C2×D113—41no—
90C2×D113—41no—
91C2×D113—42no—
92C2×D113#12112yes—
93C2×D113C22⋊Q812yes—
94#90673—84no—
95C4×C113—22no—
96C4×C113—41no—
97Dic113—22no—
98Dic113—21no—
99Dic113—41no—
100Dic113#9912yescomplemented
101C2×C113—21no—
102C2×C113—21no—
103C2×C113—42no—
104C2×C113#38011yescharacteristic
105C2×C113C2×#9911yescharacteristic
106C2×C113#41011yescharacteristic
107D113—22no—
108D113—22no—
109#1799—1131nomaximal, Sylow
110C113#179911yescharacteristic, complemented, Sylow
111C2×C4×D4—1131no—
112C2×#99—1132no—
113#380—1132no—
114#342—1132no—
115C22×D4—1131no—
116C23×C4—1131no—
117C23×C4—1131no—
118C4×D4—2262no—
119C4×D4—2262no—
120C2×C4⋊C4—1131no—
121C2×C4⋊C4—2262no—
122C2×C22⋊C4—1131no—
123C2×C22⋊C4—1134no—
124C2×C22⋊C4#9067311yescharacteristic, complemented
125C2×C42—1131no—
126#99—2264no—
127#95—2262no—
128C24—1131no—
129C24C2×#9067311yescharacteristic
130C2×D4—1132no—
131C2×D4—1132no—
132C2×D4—2262no—
133C2×D4—2262no—
134C22×C4—1131no—
135C22×C4—1131no—
136C22×C4—1132no—
137C22×C4—1132no—
138C22×C4—1131no—
139C22×C4—4522no—
140C22×C4—4522no—
141C22×C4—2261no—
142C22×C4—2261no—
143C22×C4—2264no—
144C22×C4C2×#9067311yescharacteristic
145C22×C4C2×#9067311yescharacteristic
146C4⋊C4—4524no—
147C4⋊C4—2262no—
148C22⋊C4—22no—
149C22⋊C4—2262no—
150C22⋊C4—2264no—
151C22⋊C4—2264no—
152C42—2261no—
153C42—2261no—
154C23—21no—
155C23—21no—
156C23—41no—
157C23—41no—
158C23—1131no—
159C23—1131no—
160C23—1132no—
161C23—1132no—
162C23—4521no—
163C23—4521no—
164C23C4⋊#9067312yescomplemented
165C23C22×#9067311yescharacteristic
166D4—2264no—
167D4—2264no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1131no—
172C2×C4—1131no—
173C2×C4—1132no—
174C2×C4—4522no—
175C2×C4—4522no—
176C2×C4—4524no—
177C2×C4—4524no—
178C2×C4—4524no—
179C2×C4—4522no—
180C2×C4—4521no—
181C2×C4—2264no—
182C2×C4—2262no—
183C2×C4—2261no—
184C2×C4—2261no—
185C2×C4—2261no—
186C2×C4C22⋊#9067312yes—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22—1132no—
195C22—1132no—
196C22—4521no—
197C22—4521no—
198C22—4522no—
199C22—2262no—
200C22—2262no—
201C22C2×C22⋊#9067311yescharacteristic
202C22C2×C4⋊#9067311yescharacteristic
203C22#1681370111yescharacteristic
204C4—22no—
205C4—41no—
206C4—1132no—
207C4—9044no—
208C4—4521no—
209C4—2262no—
210C4—2261no—
211C2—21no—
212C2—21no—
213C2—42no—
214C2—2262no—
215C2—2262no—
216C2#2029954011yescharacteristic
217C2D113⋊#9911yescharacteristic
218C2#2029957811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC23×C113C22×C4
FrattiniC23C22×#90673
FittingC2×C22⋊C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×C22⋊D113C22
cosocleC23×D113C23
hypercenterC2×C22⋊C4#90673
hypocenterC113#1799
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20299540C2semidirect
3. #20299476C2semidirect
10. C23×Dic113C4semidirect
14. C2×#14268626C4semidirect
16. C2×C4×Dic113C4semidirect
17. C2×C22⋊C4×C113C4semidirect
48. C23×C113C4⋊C4semidirect
74. C2×Dic113C4⋊C4semidirect
100. Dic113#99semidirect
110. C113#1799semidirect
124. C2×C22⋊C4#90673semidirect
164. C23C4⋊#90673semidirect

Maximal subgroups

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

subgroupindex
C2×#168136802
#202995402
#202994762
C2×#168135822
#1799113