Finite Group Databasebeta

← #13076441

Subgroups — #13076441

Order 1408.

344 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 121 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×#400C211yesmaximal, characteristic
2#10622596C211yesmaximal, characteristic
3#10622591C212yesmaximal
4#10622589C211yesmaximal, characteristic
5#10622273C212yesmaximal
6#10622273C212yesmaximal
7#10622268C212yesmaximal
8#10622268C212yesmaximal
9#10622266C212yesmaximal
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic11C2212yes—
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×Dic11⋊C4C2212yes—
16C2×Dic11⋊C4C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×C4×Dic11C2211yescharacteristic
19C2×C4×Dic11C2212yes—
20C11×#95C2212yes—
21C11×#95C2212yes—
22C11×#95C2211yescharacteristic
23C11⋊#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
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—41no—
41C11×C4⋊C4—41no—
42C4⋊Dic11—24no—
43C4⋊Dic11—41no—
44C4⋊Dic11—41no—
45Dic11⋊C4—24no—
46Dic11⋊C4—24no—
47Dic11⋊C4—24no—
48C4×Dic11—22no—
49C4×Dic11—42no—
50#2794—111nomaximal, Sylow
51C23×C11C2411yescharacteristic
52C2×C4×C11—21no—
53C2×C4×C11—21no—
54C2×C4×C11—22no—
55C2×C4×C11—22no—
56C2×C4×C11—22no—
57C2×C4×C11—22no—
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—24no—
63C2×C4×C11#4112yes—
64C2×Dic11—22no—
65C2×Dic11—22no—
66C2×Dic11—22no—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11#4114yes—
76#400—112no—
77#400—112no—
78#400D1111yescharacteristic
79#398—111no—
80#387—112no—
81#387—112no—
82#387—112no—
83#387—112no—
84#384—111no—
85C22×C11C2×#4111yescharacteristic
86C22×C11C2×#4112yes—
87C22×C11H(5,𝔽2)11yescharacteristic
88C22×C112−1+411yescharacteristic
89C22×C112−1+412yes—
90C4×C11—22no—
91C4×C11—42no—
92C4×C11—41no—
93C4×C11—41no—
94C4×C11—42no—
95Dic11—24no—
96Dic11—42no—
97Dic11—42no—
98Dic11—42no—
99C2×C4⋊C4—112no—
100C2×C4⋊C4—112no—
101C2×C4⋊C4—112no—
102C2×C4⋊C4—112no—
103C2×C4⋊C4—111no—
104C2×C4⋊C4—111no—
105C2×C4⋊C4C2×D1111yescharacteristic
106C2×C4⋊C4C2×D1111yescharacteristic
107C2×C42—111no—
108C2×C42—112no—
109#95—112no—
110#95—112no—
111#95—112no—
112#95—112no—
113#95—112no—
114#95—112no—
115#95—112no—
116#95—111no—
117#95C2×D1112yes—
118#95C2×D1112yes—
119#95C2×D1111yescharacteristic
120C2×C11#53911yescharacteristic
121C2×C11#54112yes—
122C2×C11#55212yes—
123C2×C11#55911yescharacteristic
124C2×C11#56311yescharacteristic
125C22×C4—112no—
126C22×C4—112no—
127C22×C4—112no—
128C22×C4—112no—
129C22×C4C22×D1112yes—
130C22×C4C22×D1112yes—
131C22×C4C22×D1111yescharacteristic
132C22×C4C22×D1111yescharacteristic
133C22×C4C22×D1111yescharacteristic
134C4⋊C4—41no—
135C4⋊C4—41no—
136C4⋊C4—224no—
137C4⋊C4—224no—
138C4⋊C4—224no—
139C4⋊C4—224no—
140C4⋊C4—441no—
141C4⋊C4—441no—
142C42—222no—
143C42—442no—
144C11#279411yescharacteristic, complemented, Sylow
145C23C23×D1111yescharacteristic
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—114no—
158C2×C4—222no—
159C2×C4—222no—
160C2×C4—222no—
161C2×C4—222no—
162C2×C4—222no—
163C2×C4—222no—
164C2×C4—222no—
165C2×C4—222no—
166C2×C4—222no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4#434312yes—
170C22#6703711yescharacteristic
171C22C2×#434311yescharacteristic
172C22#41×D1112yes—
173C22#6704311yescharacteristic
174C22#6704312yes—
175C4—22no—
176C4—42no—
177C4—41no—
178C4—41no—
179C4—42no—
180C4—224no—
181C4—442no—
182C4—442no—
183C4—442no—
184C2#1062317611yescharacteristic
185C2#1062319511yescharacteristic
186C2#1062320311yescharacteristic
187C2#1062322512yes—
188C2#1062323212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#400C2
hypercenter#400D11
hypocenterC11#2794
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
144. C11#2794semidirect

Maximal subgroups

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

subgroupindex
C11×#4002
#106225962
#106225912
#106225892
#106222732
#106222682
#106222662
#279411