Finite Group Databasebeta

← #13076106

Subgroups — #13076106

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×#382C211yesmaximal, characteristic
2#10622599C211yesmaximal, characteristic
3#10622596C211yesmaximal, characteristic
4#10622585C212yesmaximal
5#10622546C212yesmaximal
6#10622273C212yesmaximal
7#10622270C212yesmaximal
8#10622265C212yesmaximal
9#10622264C212yesmaximal
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C42×C11C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×Dic11⋊C4C2212yes—
16C2×Dic11⋊C4C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×C4×Dic11C2212yes—
20C11×#95C2212yes—
21C11×#95C2212yes—
22C11⋊#95C2211yescharacteristic
23C11⋊#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C22×C4×C11C2312yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C11×C4⋊C4—41no—
41C11×C4⋊C4—41no—
42C42×C11—22no—
43C4⋊Dic11—41no—
44C4⋊Dic11—41no—
45Dic11⋊C4—24no—
46Dic11⋊C4—24no—
47Dic11⋊C4—24no—
48Dic11⋊C4—42no—
49C4×Dic11—24no—
50#2769—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—22no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11#4112yes—
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—22no—
76C2×Dic11#4114yes—
77#400—111no—
78#400—112no—
79#398—111no—
80#398—112no—
81#389—112no—
82#387—112no—
83#387—112no—
84#383—112no—
85#382D1111yescharacteristic
86C22×C11C2×#4111yescharacteristic
87C22×C11C2×#4112yes—
88C22×C11H(5,𝔽2)11yescharacteristic
89C22×C112−1+411yescharacteristic
90C22×C112−1+412yes—
91C4×C11—22no—
92C4×C11—42no—
93C4×C11—42no—
94C4×C11—41no—
95C4×C11—41no—
96Dic11—24no—
97Dic11—42no—
98Dic11—42no—
99Dic11—42no—
100C2×C4⋊C4—112no—
101C2×C4⋊C4—112no—
102C2×C4⋊C4—112no—
103C2×C4⋊C4—112no—
104C2×C4⋊C4—111no—
105C2×C4⋊C4—111no—
106C2×C4⋊C4C2×D1111yescharacteristic
107C2×C4⋊C4C2×D1111yescharacteristic
108C2×C42—112no—
109C2×C42C2×D1111yescharacteristic
110#95—111no—
111#95—112no—
112#95—112no—
113#95—112no—
114#95—112no—
115#95—111no—
116#95—112no—
117#95—112no—
118#95—112no—
119#95C2×D1112yes—
120#95C2×D1112yes—
121C2×C11#53911yescharacteristic
122C2×C11#54112yes—
123C2×C11#55212yes—
124C2×C11#55511yescharacteristic
125C2×C11#56311yescharacteristic
126C22×C4—112no—
127C22×C4—112no—
128C22×C4—112no—
129C22×C4—112no—
130C22×C4C22×D1112yes—
131C22×C4C22×D1111yescharacteristic
132C22×C4C22×D1111yescharacteristic
133C22×C4C22×D1112yes—
134C22×C4C22×D1111yescharacteristic
135C4⋊C4—41no—
136C4⋊C4—41no—
137C4⋊C4—224no—
138C4⋊C4—224no—
139C4⋊C4—224no—
140C4⋊C4—442no—
141C4⋊C4—441no—
142C4⋊C4—441no—
143C42—22no—
144C42—224no—
145C11#276911yescharacteristic, complemented, Sylow
146C23C23×D1111yescharacteristic
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—114no—
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—222no—
170C2×C4—222no—
171C2×C4#433912yes—
172C22C2×#433911yescharacteristic
173C22#6703711yescharacteristic
174C22#6704011yescharacteristic
175C22#41×D1112yes—
176C22#6704312yes—
177C4—22no—
178C4—42no—
179C4—42no—
180C4—41no—
181C4—41no—
182C4—224no—
183C4—442no—
184C4—442no—
185C4—442no—
186C2#1062304611yescharacteristic
187C2#1062306012yes—
188C2#1062320111yescharacteristic
189C2#1062320311yescharacteristic
190C2#1062322712yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#382C2
hypercenter#382D11
hypocenterC11#2769
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
145. C11#2769semidirect

Maximal subgroups

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

subgroupindex
C11×#3822
#106225992
#106225962
#106225852
#106225462
#106222732
#106222702
#106222652
#106222642
#276911