Finite Group Databasebeta

← #13075451

Subgroups — #13075451

Order 1408.

512 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 137 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×C11×#124C211yesmaximal, characteristic
2C2×#66988C211yesmaximal, characteristic
3#10622842C212yesmaximal, complemented
4#10622833C211yesmaximal, characteristic
5#10622565C212yesmaximal, complemented
6#10622565C212yesmaximal, complemented
7#10622559C212yesmaximal, complemented
8#10622555C212yesmaximal, complemented
9#10622546C212yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D4×C11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C11×#124—24no—
15C2×C11×C22⋊C4C2212yes—
16C2×C11×C22⋊C4C2212yes—
17C2×C42×C11C2211yescharacteristic
18C2×C22⋊Dic11C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2211yescharacteristic
22#66988—24no—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C24×C11C2311yescharacteristic
34C24×C11C2311yescharacteristic
35C2×Q8×C11—22no—
36C2×Q8×C11—41no—
37C2×Q8×C11—41no—
38C2×D4×C11—41no—
39C2×D4×C11—41no—
40C2×D4×C11D414yes—
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×Dic11—24no—
45C22×Dic11—22no—
46C22×Dic11—41no—
47C22×Dic11—41no—
48C22×Dic11—41no—
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C11×C22⋊C4—24no—
54C11×C22⋊C4—24no—
55C42×C11—22no—
56C22⋊Dic11—24no—
57C22⋊Dic11—24no—
58C22⋊Dic11—22no—
59C22⋊Dic11—41no—
60Dic11⋊C4—24no—
61Dic11⋊C4—24no—
62Dic11⋊C4—42no—
63Dic11⋊C4—42no—
64#2717—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—21no—
68C23×C11—21no—
69C23×C11—21no—
70C23×C11—21no—
71C23×C11—22no—
72C23×C11—22no—
73C23×C11C2×D412yes—
74C23×C11C2×D412yes—
75C23×C11C2411yescharacteristic
76Q8×C11—44no—
77D4×C11—44no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11C2×D412yes—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—44no—
99C2×Dic11—44no—
100C2×Dic11#4114yes—
101C2×#124D1111yescharacteristic
102C2×#123—111no—
103#397—112no—
104#397—112no—
105#395—112no—
106#387—112no—
107#386—111no—
108#385—112no—
109#380—112no—
110C22×C11—22no—
111C22×C11—22no—
112C22×C11—24no—
113C22×C11—24no—
114C22×C11—42no—
115C22×C11—42no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11—41no—
120C22×C11C22×D411yescharacteristic
121C22×C11C2×#4112yes—
122C22×C11H(5,𝔽2)11yescharacteristic
123C22×C11H(5,𝔽2)11yescharacteristic
124C22×C112−1+412yes—
125C4×C11—22no—
126C4×C11—42no—
127C4×C11—42no—
128Dic11—24no—
129Dic11—42no—
130Dic11—42no—
131Dic11—42no—
132C22×Q8C2×D1111yescharacteristic
133C22×D4C2×D1111yescharacteristic
134C23×C4—111no—
135C23×C4—111no—
136#124—24no—
137#123—224no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—112no—
142C2×C22⋊C4—112no—
143C2×C22⋊C4—111no—
144C2×C22⋊C4—112no—
145C2×C22⋊C4—111no—
146C2×C22⋊C4C2×D1112yes—
147C2×C22⋊C4C2×D1112yes—
148C2×C42C2×D1111yescharacteristic
149#95—112no—
150#95—112no—
151#95—112no—
152#95—112no—
153#95—112no—
154#95—112no—
155C2×C11—42no—
156C2×C11—42no—
157C2×C11#53411yescharacteristic
158C2×C11#54212yes—
159C2×C11#54712yes—
160C2×C11#55111yescharacteristic
161C2×C11#56311yescharacteristic
162C24C22×D1111yescharacteristic
163C24C22×D1111yescharacteristic
164C2×Q8—22no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×D4—41no—
168C2×D4—41no—
169C2×D4C22⋊D1114yes—
170C22×C4—112no—
171C22×C4—112no—
172C22×C4—112no—
173C22×C4—112no—
174C22×C4—224no—
175C22×C4—222no—
176C22×C4—441no—
177C22×C4—441no—
178C22×C4—441no—
179C22×C4C22×D1112yes—
180C22×C4C22×D1112yes—
181C22×C4C22×D1111yescharacteristic
182C4⋊C4—224no—
183C4⋊C4—224no—
184C4⋊C4—442no—
185C4⋊C4—442no—
186C22⋊C4—24no—
187C22⋊C4—24no—
188C22⋊C4—224no—
189C22⋊C4—222no—
190C22⋊C4—224no—
191C22⋊C4—441no—
192C42—22no—
193C11#271711yescharacteristic, complemented, Sylow
194C23—21no—
195C23—21no—
196C23—21no—
197C23—21no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23C2×C22⋊D1112yes—
203C23C2×C22⋊D1112yes—
204C23C23×D1111yescharacteristic
205Q8—44no—
206D4—44no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—114no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—444no—
228C2×C4—444no—
229C2×C4C2×C22⋊D1112yes—
230C22—22no—
231C22—22no—
232C22—24no—
233C22—24no—
234C22—42no—
235C22—42no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22#6703711yescharacteristic
241C22#6703711yescharacteristic
242C22#41×D1112yes—
243C22#6704312yes—
244C22C22×C22⋊D1111yescharacteristic
245C4—22no—
246C4—42no—
247C4—42no—
248C4—224no—
249C4—442no—
250C4—442no—
251C4—442no—
252C2—42no—
253C2—42no—
254C2#1062320012yes—
255C2#1062320311yescharacteristic
256C2#1062321011yescharacteristic
257C2#1062333511yescharacteristic
258C2#1062335512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radicalC22×D4×C11C22
hypercenterC2×#124D11
hypocenterC11#2717
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
3. #10622842C2semidirect
5. #10622565C2semidirect
6. #10622565C2semidirect
7. #10622559C2semidirect
8. #10622555C2semidirect
9. #10622546C2semidirect
193. C11#2717semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#669882
#106228422
#106228332
#106225652
#106225592
#106225552
#106225462
#271711