Finite Group Databasebeta

← #13073985

Subgroups — #13073985

Order 1408.

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

normal subgroups only

This group has 484 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×#66940C212yesmaximal
2C11×#398C211yesmaximal, characteristic
3#10622597C212yesmaximal
4#10622596C211yesmaximal, characteristic
5#10622589C211yesmaximal, characteristic
6#10622585C212yesmaximal
7#10622260C212yesmaximal
8#10622259C212yesmaximal
9#10622259C212yesmaximal
10C22×Dic22C2212yes—
11C2×C11×C4⋊C4C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×Dic11⋊C4C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2212yes—
22C2×C4×Dic11C2212yes—
23C2×C4×Dic11C2211yescharacteristic
24#66940—28no—
25C11×#95C2211yescharacteristic
26C11×#95C2212yes—
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C2×Dic22—24no—
42C2×Dic22—24no—
43C2×Dic22Q818yescomplemented
44C11×C4⋊C4—24no—
45C11×C4⋊C4—41no—
46C11×C4⋊C4—41no—
47C4⋊Dic11—41no—
48C4⋊Dic11—41no—
49Dic11⋊C4—24no—
50Dic11⋊C4—24no—
51Dic11⋊C4—24no—
52Dic11⋊C4—24no—
53Dic11⋊C4—42no—
54C4×Dic11—24no—
55C4×Dic11—24no—
56C4×Dic11D414yes—
57#2582—111nomaximal, Sylow
58C23×C11C2411yescharacteristic
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—22no—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×Q814yes—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11C2×D414yes—
81C2×Dic11C2×Q814yes—
82C2×Dic11C2×Q814yes—
83C2×Dic11#4114yes—
84Dic22—216no—
85C2×C4×Q8—112no—
86#398—111no—
87#398—112no—
88#398D1111yescharacteristic
89#391—112no—
90#391—112no—
91#389—112no—
92#389—112no—
93#384—111no—
94C22×C11C22×D411yescharacteristic
95C22×C11C22×Q812yes—
96C22×C11C2×#4112yes—
97C22×C11H(5,𝔽2)11yescharacteristic
98C22×C112−1+411yescharacteristic
99C4×C11—24no—
100C4×C11—22no—
101C4×C11—42no—
102C4×C11—41no—
103C4×C11—41no—
104Dic11—24no—
105Dic11—42no—
106Dic11—42no—
107Dic11C22⋊Q818yes—
108C22×Q8—112no—
109C4×Q8—228no—
110C2×C4⋊C4—112no—
111C2×C4⋊C4—112no—
112C2×C4⋊C4—112no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—111no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—111no—
117C2×C4⋊C4C2×D1112yes—
118C2×C4⋊C4C2×D1111yescharacteristic
119C2×C4⋊C4C2×D1111yescharacteristic
120C2×C42—111no—
121C2×C42—112no—
122C2×C42—112no—
123#95—112no—
124#95—112no—
125#95—112no—
126#95—111no—
127#95—112no—
128#95C2×D1112yes—
129#95C2×D1111yescharacteristic
130C2×C11C2×C22⋊Q812yes—
131C2×C11#53711yescharacteristic
132C2×C11#55712yes—
133C2×C11Q8211yescharacteristic
134C2×C11#55911yescharacteristic
135C2×Q8—118no—
136C2×Q8—224no—
137C2×Q8—224no—
138C22×C4—112no—
139C22×C4—112no—
140C22×C4—112no—
141C22×C4—112no—
142C22×C4C22×D1111yescharacteristic
143C22×C4C22×D1111yescharacteristic
144C22×C4C22×D1112yes—
145C22×C4C22×D1111yescharacteristic
146C22×C4C22×D1112yes—
147C4⋊C4—24no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—224no—
151C4⋊C4—224no—
152C4⋊C4—224no—
153C4⋊C4—224no—
154C4⋊C4—442no—
155C4⋊C4—441no—
156C4⋊C4—441no—
157C42—114no—
158C42—224no—
159C42—224no—
160C11#258211yescharacteristic, complemented, Sylow
161C23C23×D1111yescharacteristic
162Q8—2216no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—114no—
175C2×C4—114no—
176C2×C4—114no—
177C2×C4—114no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4D4×D1112yes—
187C2×C4Q8×D1114yes—
188C22C2×D4×D1111yescharacteristic
189C22#6703711yescharacteristic
190C22C2×Q8×D1112yes—
191C22#41×D1112yes—
192C22#6704311yescharacteristic
193C4—22no—
194C4—24no—
195C4—42no—
196C4—41no—
197C4—41no—
198C4—118no—
199C4—224no—
200C4—442no—
201C4—442no—
202C2#1062312811yescharacteristic
203C2D11×C22⋊Q812yes—
204C2#1062319511yescharacteristic
205C2#1062321612yes—
206C2#1062325311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#398C2
hypercenter#398D11
hypocenterC11#2582
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
43. C2×Dic22Q8semidirect
160. C11#2582semidirect

Maximal subgroups

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

subgroupindex
C2×#669402
C11×#3982
#106225972
#106225962
#106225892
#106225852
#106222602
#106222592
#258211