Finite Group Databasebeta

← #28390560

Subgroups — #28390560

Order 14464.

380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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×D4×Dic113C211yesmaximal, characteristic
2C2×#16813537C211yesmaximal, characteristic
3#20298456C212yesmaximal, complemented
4#20298364C212yesmaximal, complemented
5C2×#99×C113C211yesmaximal, characteristic
6C23×Dic113C411yescharacteristic, complemented
7C23×Dic113C2211yescharacteristic
8D4×Dic113—22no—
9D4×Dic113—22no—
10C2×C4⋊Dic113C411yescharacteristic, complemented
11C2×#14268626—22no—
12C2×C22⋊Dic113C411yescharacteristic, complemented
13C2×C22⋊Dic113C2212yes—
14C2×C22⋊Dic113C2211yescharacteristic
15C2×C4×Dic113C411yescharacteristic, complemented
16#16813537—22no—
17#16813529—22no—
18C22×D4×C113C2211yescharacteristic
19C2×C22⋊C4×C113C2212yes—
20#99×C113—22no—
21C22×Dic113—21no—
22C22×Dic113—21no—
23C22×Dic113—22no—
24C22×Dic113—42no—
25C22×Dic113—42no—
26C22×Dic113C2×C411yescharacteristic
27C22×Dic113C2×C411yescharacteristic
28C22×Dic113C2×C411yescharacteristic
29C22×Dic113C2×C411yescharacteristic
30C22×Dic113D412yes—
31C22×Dic113D412yes—
32C4⋊Dic113—22no—
33#14268626—44no—
34C22⋊Dic113—22no—
35C22⋊Dic113—22no—
36C22⋊Dic113—22no—
37C22⋊Dic113—22no—
38C4×Dic113—21no—
39C4×Dic113—21no—
40C24×C113C2×C411yescharacteristic
41C24×C113C2311yescharacteristic
42C2×D4×C113—22no—
43C2×D4×C113—22no—
44C2×D4×C113D412yes—
45C2×D4×C113Q812yes—
46C22×C4×C113—22no—
47C22×C4×C113C2×C411yescharacteristic
48C22⋊C4×C113—22no—
49C22⋊C4×C113—22no—
50C23×C113—21no—
51C23×C113—21no—
52C23×C113—41no—
53C23×C113—41no—
54C23×C113—41no—
55C23×C113—41no—
56C23×C113C4⋊C412yescomplemented
57C23×C113C22×C411yescharacteristic
58C23×C113C2×D412yes—
59C23×C113C2×D411yescharacteristic
60C23×C113C2×Q811yescharacteristic
61C23×C113#4112yes—
62D4×C113—24no—
63D4×C113—24no—
64C2×C4×C113—21no—
65C2×C4×C113—21no—
66C2×C4×C113—42no—
67C2×C4×C113—42no—
68C2×C4×C113—42no—
69C2×C4×C113C4⋊C412yescomplemented
70C2×Dic113—24no—
71C2×Dic113—22no—
72C2×Dic113—21no—
73C2×Dic113—21no—
74C2×Dic113—41no—
75C2×Dic113—42no—
76C2×Dic113—42no—
77C2×Dic113—42no—
78C2×Dic113—41no—
79C2×Dic113—41no—
80C2×Dic113—42no—
81C2×Dic113—42no—
82C2×Dic113—42no—
83C2×Dic113C22⋊C411yescharacteristic
84C2×Dic113C22⋊C412yes—
85C2×Dic113C22⋊C411yescharacteristic
86C22×C113—22no—
87C22×C113—21no—
88C22×C113—22no—
89C22×C113—21no—
90C22×C113—22no—
91C22×C113—41no—
92C22×C113—41no—
93C22×C113—42no—
94C22×C113—42no—
95C22×C113—42no—
96C22×C113—41no—
97C22×C113—41no—
98C22×C113C2×C22⋊C411yescharacteristic
99C22×C113C2×C4⋊C411yescharacteristic
100C22×C113#11711yescharacteristic
101C22×C113#12112yes—
102C22×C113C22⋊Q812yes—
103C4×C113—22no—
104C4×C113—82no—
105Dic113—21no—
106Dic113—22no—
107Dic113—41no—
108Dic113—41no—
109Dic113—82no—
110Dic113#9912yescomplemented
111C2×C113—22no—
112C2×C113—21no—
113C2×C113—21no—
114C2×C113—22no—
115C2×C113—42no—
116C2×C113#38011yescharacteristic
117C2×C113C2×#9911yescharacteristic
118C2×C113#41011yescharacteristic
119#1799—1131nomaximal, Sylow
120C113#179911yescharacteristic, complemented, Sylow
121C2×C4×D4—1131no—
122C2×#99—1131no—
123C2×#99D11311yescharacteristic
124#380—1132no—
125#342—1132no—
126C22×D4C2×D11311yescharacteristic
127C23×C4—1131no—
128C23×C4—1131no—
129C4×D4—2262no—
130C4×D4—2262no—
131C2×C4⋊C4—1131no—
132C2×C4⋊C4—2262no—
133C2×C22⋊C4—1131no—
134C2×C22⋊C4—1131no—
135C2×C22⋊C4—1132no—
136C2×C22⋊C4C2×D11312yes—
137C2×C42—1131no—
138#99—22no—
139#99—2262no—
140#95—2262no—
141C24C4×D11311yescharacteristic
142C24C22×D11311yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4Dic22612yes—
146C2×D4C22⋊D11312yes—
147C22×C4—22no—
148C22×C4—1131no—
149C22×C4—1132no—
150C22×C4—1131no—
151C22×C4—1132no—
152C22×C4—1131no—
153C22×C4—1131no—
154C22×C4—4522no—
155C22×C4—4522no—
156C22×C4—2261no—
157C22×C4—2261no—
158C22×C4—2262no—
159C22×C4C4×D11311yescharacteristic
160C4⋊C4—4524no—
161C4⋊C4—2262no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—2262no—
165C22⋊C4—2262no—
166C22⋊C4—2262no—
167C22⋊C4—2262no—
168C42—2261no—
169C42—2261no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23#1426862612yescomplemented
177C23C2×C4×D11311yescharacteristic
178C23D4×D11312yes—
179C23C2×C22⋊D11311yescharacteristic
180C23C2×Dic22611yescharacteristic
181C23#1426864612yes—
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—1131no—
190C2×C4—1131no—
191C2×C4—1132no—
192C2×C4—4522no—
193C2×C4—4522no—
194C2×C4—4522no—
195C2×C4—4522no—
196C2×C4—4522no—
197C2×C4—4521no—
198C2×C4—4521no—
199C2×C4—4522no—
200C2×C4—4521no—
201C2×C4—2264no—
202C2×C4—2262no—
203C2×C4—2261no—
204C2×C4—2261no—
205C2×C4#1426862612yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C22⋊C4×D11311yescharacteristic
219C22C2×#1426862611yescharacteristic
220C22#1681357811yescharacteristic
221C22#1681359412yes—
222C22#1681359912yes—
223C4—22no—
224C4—82no—
225C4—1132no—
226C4—9042no—
227C4—4521no—
228C4—4521no—
229C4—2261no—
230C4—2262no—
231C2—22no—
232C2—21no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2#2029845611yescharacteristic
237C2#99×D11311yescharacteristic
238C2#2029857011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC23×C113C22×C4
FrattiniC24C22×D113
FittingC2×#99×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×D4×C113C22
cosocleC24×C113C23
hypercenterC2×#99D113
hypocenterC113#1799
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #20298456C2semidirect
4. #20298364C2semidirect
6. C23×Dic113C4semidirect
10. C2×C4⋊Dic113C4semidirect
12. C2×C22⋊Dic113C4semidirect
15. C2×C4×Dic113C4semidirect
56. C23×C113C4⋊C4semidirect
69. C2×C4×C113C4⋊C4semidirect
110. Dic113#99semidirect
120. C113#1799semidirect
176. C23#14268626semidirect
205. C2×C4#14268626semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1132
C2×#168135372
#202984562
#202983642
C2×#99×C1132
#1799113