Finite Group Databasebeta

← #13073089

Subgroups — #13073089

Order 1408.

544 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 161 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×#66949C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic
3C11×#398C211yesmaximal, characteristic, complemented
4#10622602C212yesmaximal
5#10622596C211yesmaximal, characteristic, complemented
6#10622593C211yesmaximal, characteristic, complemented
7#10622589C212yesmaximal, complemented
8#10622281C212yesmaximal
9#10622279C211yesmaximal, characteristic
10#10622274C211yesmaximal, characteristic, complemented
11#10622259C212yesmaximal, complemented
12C22×C4×D11C2211yescharacteristic
13C22×C4×D11C2212yes—
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2212yes—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊Dic11C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2212yes—
29#66949—24no—
30C4⋊C4×D11—24no—
31C11×#95C2212yes—
32C11×#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C23×D11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2312yes—
47C22×Dic11C2311yescharacteristic
48C2×C4×D11—24no—
49C2×C4×D11—24no—
50C2×C4×D11—42no—
51C2×C4×D11—42no—
52C2×C4×D11D414yes—
53C2×Dic22—22no—
54C2×Dic22—24no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—42no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—22no—
60(C2×D11)⋊C4Q818yescomplemented
61C4⋊Dic11—22no—
62C4⋊Dic11—42no—
63Dic11⋊C4—24no—
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—42no—
67Dic11⋊C4—42no—
68C4×Dic11—24no—
69#2502—111nomaximal, Sylow
70C23×C11C2411yescharacteristic
71C22×D11—22no—
72C22×D11—21no—
73C22×D11—21no—
74C22×D11C2×D412yes—
75C22×D11C2×Q814yes—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11C2×D412yes—
88C2×C4×C11C2×Q814yes—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11C2×D412yes—
100C2×Dic11C2×Q814yes—
101C2×Dic11#4114yes—
102C4×D11—28no—
103C4×D11—48no—
104Dic22—44no—
105C2×C22⋊Q8—111no—
106C22×C4⋊C4—111no—
107#398—111no—
108#398—111no—
109#398—111no—
110#398D1111yescharacteristic, complemented
111#391—112no—
112#385—112no—
113#385—112no—
114#384—112no—
115C4×C22⋊C4—111no—
116C22×C11C22×D411yescharacteristic
117C22×C11C22×Q812yes—
118C22×C11C2×#4112yes—
119C22×C11H(5,𝔽2)11yescharacteristic
120C22×C11H(5,𝔽2)11yescharacteristic
121C2×D11—22no—
122C2×D11—22no—
123C2×D11—24no—
124C2×D11—24no—
125C2×D11C4⋊Q814yes—
126C4×C11—22no—
127C4×C11—24no—
128C4×C11—41no—
129C4×C11—41no—
130C4×C11—42no—
131Dic11—24no—
132Dic11—41no—
133Dic11—42no—
134Dic11—41no—
135Dic11#12314yes—
136C22×Q8—111no—
137C23×C4—111no—
138C23×C4—112no—
139C22⋊Q8—224no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—111no—
142C2×C4⋊C4—111no—
143C2×C4⋊C4—111no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4—112no—
147C2×C4⋊C4—224no—
148C2×C4⋊C4C2×D1111yescharacteristic
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C4⋊C4C2×D1112yes—
151C2×C22⋊C4—112no—
152C2×C22⋊C4—111no—
153C2×C22⋊C4—111no—
154C2×C42—112no—
155#95—111no—
156#95—112no—
157#95—112no—
158#95—112no—
159#95C2×D1111yescharacteristic
160#95C2×D1112yes—
161C2×C11C2×#12311yescharacteristic
162C2×C11C2×C4⋊Q811yescharacteristic
163C2×C11#53511yescharacteristic
164C2×C11#55412yes—
165C2×C11#55412yes—
166D11—24no—
167C24—111no—
168C2×Q8—222no—
169C2×Q8—224no—
170C22×C4—111no—
171C22×C4—112no—
172C22×C4—114no—
173C22×C4—111no—
174C22×C4—112no—
175C22×C4—111no—
176C22×C4—224no—
177C22×C4—224no—
178C22×C4—442no—
179C22×C4—442no—
180C22×C4C22×D1111yescharacteristic
181C22×C4C22×D1112yes—
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1111yescharacteristic
184C22×C4C22×D1112yes—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—42no—
188C4⋊C4—224no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—222no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C22⋊C4—118no—
196C22⋊C4—222no—
197C22⋊C4—222no—
198C42—224no—
199C11#250211yescharacteristic, complemented, Sylow
200C23—112no—
201C23—114no—
202C23—221no—
203C23—222no—
204C23—221no—
205C23C23×D1111yescharacteristic
206Q8—444no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—112no—
219C2×C4—114no—
220C2×C4—114no—
221C2×C4—228no—
222C2×C4—222no—
223C2×C4—222no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—222no—
227C2×C4—221no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—221no—
231C2×C4—222no—
232C2×C4—448no—
233C2×C4D4×D1112yes—
234C2×C4Q8×D1114yes—
235C22—114no—
236C22—222no—
237C22—224no—
238C22—222no—
239C22—224no—
240C22C2×D4×D1111yescharacteristic
241C22#6703711yescharacteristic
242C22C2×Q8×D1112yes—
243C22#41×D1112yes—
244C22#6704211yescharacteristic
245C4—24no—
246C4—22no—
247C4—42no—
248C4—41no—
249C4—41no—
250C4—114no—
251C4—224no—
252C4—442no—
253C4—441no—
254C4—441no—
255C2—224no—
256C2#1062313811yescharacteristic
257C2#1062316712yes—
258C2D11×#12311yescharacteristic
259C2#1062322112yes—
260C2D11×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#398C2
prime radicalC23×D11C23
hypercenter#398D11
hypocenterC11#2502
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C11×#398C2semidirect
5. #10622596C2semidirect
6. #10622593C2semidirect
7. #10622589C2semidirect
10. #10622274C2semidirect
11. #10622259C2semidirect
60. (C2×D11)⋊C4Q8semidirect
110. #398D11semidirect
199. C11#2502semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×C4⋊C4×D112
C11×#3982
#106226022
#106225962
#106225932
#106225892
#106222812
#106222792
#106222742
#106222592
#250211