Finite Group Databasebeta

← #13074428

Subgroups — #13074428

Order 1408.

508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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×#66999C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic
3C11×#395C211yesmaximal, characteristic, complemented
4#10622842C211yesmaximal, characteristic, complemented
5#10622602C212yesmaximal
6#10622599C211yesmaximal, characteristic, complemented
7#10622593C212yesmaximal, complemented
8#10622280C211yesmaximal, characteristic
9#10622277C212yesmaximal
10#10622272C211yesmaximal, characteristic, complemented
11#10622270C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18#66999—24no—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C4⋊C4×D11—24no—
29C11×#95C2212yes—
30C11×#95C2211yescharacteristic
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C23×D11C2311yescharacteristic
38C2×Q8×C11—22no—
39C2×Q8×C11—42no—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C2×C4×D11—22no—
51C2×C4×D11—22no—
52C2×C4×D11—22no—
53C2×C4×D11—42no—
54C2×C4×D11—42no—
55C2×C4×D11D414yes—
56C2×C4×D11Q814yescomplemented
57C11×C4⋊C4—22no—
58C11×C4⋊C4—42no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4—24no—
61C4⋊Dic11—22no—
62C4⋊Dic11—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—24no—
65Dic11⋊C4—22no—
66Dic11⋊C4—42no—
67Dic11⋊C4—42no—
68#2627—111nomaximal, Sylow
69C23×C11C2411yescharacteristic
70C22×D11—22no—
71C22×D11—22no—
72C22×D11C2×D412yes—
73C22×D11C2×Q812yes—
74C22×D11#4112yes—
75Q8×C11—44no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11C2×D412yes—
88C2×C4×C11C2×Q812yes—
89C2×Dic11—21no—
90C2×Dic11—21no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—24no—
98C2×Dic11—22no—
99C2×Dic11C2×D412yes—
100C2×Dic11C2×Q812yes—
101C4×D11—28no—
102C4×D11—44no—
103C4×D11—44no—
104C2×C22⋊Q8—111no—
105C22×C4⋊C4—111no—
106#400—111no—
107#400—111no—
108#398—112no—
109#398—112no—
110#395—111no—
111#395D1111yescharacteristic, complemented
112#385—112no—
113#381—112no—
114#380—111no—
115C22×C11C22×D411yescharacteristic
116C22×C11C22×Q811yescharacteristic
117C22×C11C2×#4111yescharacteristic
118C22×C11H(5,𝔽2)12yes—
119C22×C112−1+412yes—
120C2×D11—22no—
121C2×D11—22no—
122C2×D11—24no—
123C2×D11—24no—
124C2×D11C22⋊Q814yes—
125C4×C11—22no—
126C4×C11—22no—
127C4×C11—42no—
128C4×C11—41no—
129C4×C11—42no—
130Dic11—22no—
131Dic11—22no—
132Dic11—41no—
133Dic11—42no—
134Dic11—42no—
135C22×Q8C2×D1111yescharacteristic
136C23×C4—111no—
137C23×C4—111no—
138C23×C4—111no—
139C22⋊Q8—224no—
140C2×C4⋊C4—111no—
141C2×C4⋊C4—111no—
142C2×C4⋊C4—111no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—111no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4—112no—
147C2×C4⋊C4—224no—
148C2×C4⋊C4C2×D1111yescharacteristic
149C2×C4⋊C4C2×D1112yes—
150C2×C22⋊C4—112no—
151C2×C22⋊C4—112no—
152#95—111no—
153#95—112no—
154#95—112no—
155#95—112no—
156#95—112no—
157#95—112no—
158#95C2×D1111yescharacteristic
159#95C2×D1112yes—
160C2×C11C2×C22⋊Q811yescharacteristic
161C2×C11#53411yescharacteristic
162C2×C11#53611yescharacteristic
163C2×C11#53912yes—
164C2×C11#54412yes—
165D11—24no—
166C24—111no—
167C2×Q8—22no—
168C2×Q8—42no—
169C22×C4—111no—
170C22×C4—111no—
171C22×C4—114no—
172C22×C4—114no—
173C22×C4—112no—
174C22×C4—112no—
175C22×C4—111no—
176C22×C4—222no—
177C22×C4—222no—
178C22×C4—222no—
179C22×C4—442no—
180C22×C4—442no—
181C22×C4C22×D1112yes—
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1112yes—
184C22×C4C22×D1111yescharacteristic
185C22×C4C22×D1111yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—42no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—224no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C22⋊C4—224no—
196C22⋊C4—224no—
197C11#262711yescharacteristic, complemented, Sylow
198C23—112no—
199C23—112no—
200C23—112no—
201C23—222no—
202C23—222no—
203C23C23×D1111yescharacteristic
204Q8—44no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—112no—
217C2×C4—112no—
218C2×C4—228no—
219C2×C4—221no—
220C2×C4—222no—
221C2×C4—221no—
222C2×C4—222no—
223C2×C4—221no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—224no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—444no—
230C2×C4—444no—
231C2×C4D4×D1112yes—
232C2×C4Q8×D1112yes—
233C22—114no—
234C22—222no—
235C22—224no—
236C22—222no—
237C22—224no—
238C22C2×D4×D1111yescharacteristic
239C22#6703712yes—
240C22C2×Q8×D1111yescharacteristic
241C22#6704012yes—
242C22#41×D1111yescharacteristic
243C4—22no—
244C4—22no—
245C4—41no—
246C4—42no—
247C4—42no—
248C4—222no—
249C4—222no—
250C4—442no—
251C4—441no—
252C4—442no—
253C2—224no—
254C2#1062312011yescharacteristic
255C2D11×C22⋊Q811yescharacteristic
256C2#1062316912yes—
257C2#1062325511yescharacteristic
258C2#1062326012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
prime radicalC23×D11C23
hypercenter#395D11
hypocenterC11#2627
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. C11×#395C2semidirect
4. #10622842C2semidirect
6. #10622599C2semidirect
7. #10622593C2semidirect
10. #10622272C2semidirect
11. #10622270C2semidirect
56. C2×C4×D11Q8semidirect
111. #395D11semidirect
197. C11#2627semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×C4⋊C4×D112
C11×#3952
#106228422
#106226022
#106225992
#106225932
#106222802
#106222772
#106222722
#106222702
#262711