Finite Group Databasebeta

← #13076607

Subgroups — #13076607

Order 1408.

344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C11×#389C211yesmaximal, characteristic
2#10622599C212yesmaximal
3#10622595C212yesmaximal
4#10622594C212yesmaximal
5#10622591C212yesmaximal
6#10622541C211yesmaximal, characteristic
7#10622541C211yesmaximal, characteristic
8#10622272C212yesmaximal
9#10622268C212yesmaximal
10C2×C11×C4⋊C4C2212yes—
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C42×C11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×C4×Dic11C2212yes—
21C11×#95C2212yes—
22C11⋊#95C2212yes—
23C11⋊#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C22×C4×C11C2312yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C11×C4⋊C4—22no—
41C11×C4⋊C4—24no—
42C11×C4⋊C4—41no—
43C42×C11—41no—
44C4⋊Dic11—22no—
45C4⋊Dic11—22no—
46C4⋊Dic11—41no—
47C4⋊Dic11—41no—
48Dic11⋊C4—24no—
49Dic11⋊C4—24no—
50C4×Dic11—42no—
51#2810—111nomaximal, Sylow
52C23×C11C2411yescharacteristic
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11#4112yes—
66C2×C4×C11#4112yes—
67C2×C4×C11#4112yes—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80#400—112no—
81#400—112no—
82#400—112no—
83#389—111no—
84#389—111no—
85#389D1111yescharacteristic
86#387—112no—
87#387—112no—
88#387—112no—
89C22×C11C2×#4111yescharacteristic
90C22×C11C2×#4111yescharacteristic
91C22×C11C2×#4111yescharacteristic
92C22×C11H(5,𝔽2)11yescharacteristic
93C22×C112−1+411yescharacteristic
94C22×C112−1+411yescharacteristic
95C22×C112−1+411yescharacteristic
96C4×C11—22no—
97C4×C11—22no—
98C4×C11—22no—
99C4×C11—42no—
100C4×C11—42no—
101Dic11—42no—
102Dic11—42no—
103Dic11—42no—
104Dic11—42no—
105C2×C4⋊C4—112no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—111no—
108C2×C4⋊C4—111no—
109C2×C4⋊C4—111no—
110C2×C4⋊C4—111no—
111C2×C4⋊C4C2×D1112yes—
112C2×C4⋊C4C2×D1111yescharacteristic
113C2×C4⋊C4C2×D1111yescharacteristic
114C2×C42—112no—
115C2×C42C2×D1111yescharacteristic
116#95—112no—
117#95—112no—
118#95—112no—
119#95—112no—
120#95—112no—
121#95—112no—
122#95—112no—
123#95—112no—
124#95—112no—
125#95C2×D1112yes—
126C2×C11#53911yescharacteristic
127C2×C11#53911yescharacteristic
128C2×C11#53911yescharacteristic
129C2×C11#55611yescharacteristic
130C2×C11#55611yescharacteristic
131C2×C11#55611yescharacteristic
132C2×C11#56411yescharacteristic
133C22×C4—112no—
134C22×C4—112no—
135C22×C4—112no—
136C22×C4—112no—
137C22×C4C22×D1112yes—
138C22×C4C22×D1112yes—
139C22×C4C22×D1111yescharacteristic
140C22×C4C22×D1111yescharacteristic
141C22×C4C22×D1111yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—24no—
144C4⋊C4—41no—
145C4⋊C4—224no—
146C4⋊C4—222no—
147C4⋊C4—224no—
148C4⋊C4—222no—
149C4⋊C4—441no—
150C4⋊C4—441no—
151C42—41no—
152C42—442no—
153C11#281011yescharacteristic, complemented, Sylow
154C23C23×D1111yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4—222no—
170C2×C4—222no—
171C2×C4—222no—
172C2×C4—222no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4#433912yes—
180C2×C4#434112yes—
181C2×C4#434312yes—
182C22C2×#433911yescharacteristic
183C22C2×#434111yescharacteristic
184C22#6703711yescharacteristic
185C22C2×#434311yescharacteristic
186C22#6704011yescharacteristic
187C22#6704311yescharacteristic
188C22#6704311yescharacteristic
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—442no—
195C4—442no—
196C4—442no—
197C4—442no—
198C2#1062304611yescharacteristic
199C2#1062307311yescharacteristic
200C2#1062311511yescharacteristic
201C2#1062313311yescharacteristic
202C2#1062317611yescharacteristic
203C2C11⋊#56411yescharacteristic
204C2#1062326311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#389C2
hypercenter#389D11
hypocenterC11#2810
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
153. C11#2810semidirect

Maximal subgroups

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

subgroupindex
C11×#3892
#106225992
#106225952
#106225942
#106225912
#106225412
#106222722
#106222682
#281011