Finite Group Databasebeta

← #13073077

Subgroups — #13073077

Order 1408.

568 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 145 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×#66991C211yesmaximal, characteristic
2C2×#66945C211yesmaximal, characteristic, complemented
3C11×#390C211yesmaximal, characteristic, complemented
4#10622834C211yesmaximal, characteristic, complemented
5#10622589C211yesmaximal, characteristic, complemented
6#10622572C214yesmaximal, complemented
7#10622558C214yesmaximal, complemented
8C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
9#10622549C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×C4×D11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2214yes—
15C2×C42×C11C2211yescharacteristic
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2214yes—
18#66991—24no—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2214yes—
24C2×C4×Dic11C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26#66945—24no—
27C11⋊#95C2214yes—
28C11⋊#95C2212yes—
29C24×C11C2312yes—
30C23×D11C2311yescharacteristic
31C2×D4×C11—22no—
32C2×D4×C11—22no—
33C2×D4×C11—22no—
34C22×C4×C11C2312yes—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—24no—
38C2×C22⋊D11—44no—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2312yes—
43C2×C4×D11—22no—
44C2×C4×D11—22no—
45C2×C4×D11D414yes—
46C11×C4⋊C4—22no—
47C11×C22⋊C4—44no—
48C42×C11—22no—
49C22⋊Dic11—24no—
50C22⋊Dic11—28no—
51(C2×D11)⋊C4—24no—
52(C2×D11)⋊C4—24no—
53C4⋊Dic11—22no—
54C4⋊Dic11—22no—
55Dic11⋊C4—44no—
56C4×Dic11—24no—
57C4×Dic11—22no—
58#2500—111nomaximal, Sylow
59C23×C11—22no—
60C23×C11—24no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—24no—
64C23×C11C2411yescharacteristic
65C22×D11—22no—
66C22×D11—21no—
67C22×D11—21no—
68C22×D11—22no—
69C22×D11C2×D412yes—
70D4×C11—44no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—24no—
75C2×C4×C11—22no—
76C2×C4×C11C2×D412yes—
77C2×C4×C11#4112yes—
78C2×C4×C11#4112yes—
79C22⋊D11—48no—
80C2×Dic11—22no—
81C2×Dic11—21no—
82C2×Dic11—21no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—24no—
87C2×Dic11—24no—
88C2×Dic11C2×D412yes—
89C2×Dic11#4114yes—
90C4×D11—28no—
91C2×#121—111no—
92C2×#117—111no—
93#394—114no—
94#390—111no—
95#390D1111yescharacteristic, complemented
96#388—114no—
97#384—111no—
98#382—111no—
99C4×C22⋊C4—111no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11—42no—
103C22×C11—44no—
104C22×C11—44no—
105C22×C11C22×D411yescharacteristic
106C22×C11C2×#4111yescharacteristic
107C22×C11C2×#4111yescharacteristic
108C22×C11C2×#4112yes—
109C22×C11H(5,𝔽2)12yes—
110C2×D11—22no—
111C2×D11—22no—
112C2×D11—22no—
113C2×D11—42no—
114C2×D11—42no—
115C4×C11—42no—
116C4×C11—42no—
117C4×C11#12314yes—
118Dic11—22no—
119Dic11—24no—
120Dic11—42no—
121Dic11—42no—
122C22×D4—112no—
123C22×D4C2×D1111yescharacteristic
124C23×C4—111no—
125#121—224no—
126#117—224no—
127C2×C4⋊C4—111no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4—114no—
130C2×C4⋊C4C2×D1111yescharacteristic
131C2×C22⋊C4—112no—
132C2×C22⋊C4—114no—
133C2×C22⋊C4—112no—
134C2×C22⋊C4—112no—
135C2×C22⋊C4C2×D1114yes—
136C2×C42—112no—
137C2×C42—111no—
138C2×C42C2×D1111yescharacteristic
139#95—112no—
140#95—114no—
141C2×C11—82no—
142C2×C11C2×#12311yescharacteristic
143C2×C11#53211yescharacteristic
144C2×C11#53511yescharacteristic
145C2×C11#55312yes—
146C2×C11#55512yes—
147D11—42no—
148C24—111no—
149C24C22×D1112yes—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—224no—
154C2×D4—444no—
155C22×C4—111no—
156C22×C4—112no—
157C22×C4—114no—
158C22×C4—112no—
159C22×C4—112no—
160C22×C4—222no—
161C22×C4—222no—
162C22×C4C22×D1112yes—
163C22×C4C22×D1112yes—
164C22×C4C22×D1111yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—222no—
167C4⋊C4—222no—
168C4⋊C4—444no—
169C22⋊C4—44no—
170C22⋊C4—224no—
171C22⋊C4—224no—
172C22⋊C4—224no—
173C22⋊C4—228no—
174C42—22no—
175C42—224no—
176C42—222no—
177C11#250011yescharacteristic, complemented, Sylow
178C23—22no—
179C23—22no—
180C23—22no—
181C23—24no—
182C23—24no—
183C23—112no—
184C23—221no—
185C23—221no—
186C23—222no—
187C23—222no—
188C23C23×D1111yescharacteristic
189D4—44no—
190D4—448no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—22no—
196C2×C4—112no—
197C2×C4—114no—
198C2×C4—222no—
199C2×C4—221no—
200C2×C4—221no—
201C2×C4—222no—
202C2×C4—228no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—224no—
206C2×C4—224no—
207C2×C4#433912yes—
208C2×C4D4×D1112yes—
209C2×C4#434112yes—
210C22—42no—
211C22—42no—
212C22—44no—
213C22—44no—
214C22—42no—
215C22—222no—
216C22—222no—
217C22—222no—
218C22—442no—
219C22—442no—
220C22C2×#433911yescharacteristic
221C22C2×D4×D1111yescharacteristic
222C22C2×#434111yescharacteristic
223C22#6703712yes—
224C22#41×D1112yes—
225C4—42no—
226C4—42no—
227C4—222no—
228C4—224no—
229C4—442no—
230C4—442no—
231C4#6693614yes—
232C2—82no—
233C2—442no—
234C2C2×#6693611yescharacteristic
235C2#1062308912yes—
236C2#1062314712yes—
237C2#1062319911yescharacteristic
238C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC2×#66991C2
hypercenter#390D11
hypocenterC11#2500
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#66945C2semidirect
3. C11×#390C2semidirect
4. #10622834C2semidirect
5. #10622589C2semidirect
6. #10622572C2semidirect
7. #10622558C2semidirect
8. C4×(C2×D11)⋊C4C2semidirect
9. #10622549C2semidirect
95. #390D11semidirect
177. C11#2500semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×#669452
C11×#3902
#106228342
#106225892
#106225722
#106225582
C4×(C2×D11)⋊C42
#106225492
#250011