Finite Group Databasebeta

← #13074021

Subgroups — #13074021

Order 1408.

412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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×#398C211yesmaximal, characteristic
2#10622592C212yesmaximal
3#10622592C211yesmaximal, characteristic
4C4⋊C4×Dic11C212yesmaximal
5#10622587C211yesmaximal, characteristic
6#10622585C212yesmaximal
7#10622267C212yesmaximal
8#10622266C212yesmaximal
9#10622259C212yesmaximal
10C22×Dic22C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic11C2212yes—
16C2×Dic11⋊C4C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×C4×Dic11C2212yes—
20C2×C4×Dic11C2212yes—
21C2×C4×Dic11C2211yescharacteristic
22C11×#95C2212yes—
23C11×#95C2211yescharacteristic
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C22×C4×C11C2311yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×Dic22—24no—
41C2×Dic22—22no—
42C2×Dic22—41no—
43C2×Dic22—41no—
44C2×Dic22—41no—
45C11×C4⋊C4—24no—
46C11×C4⋊C4—41no—
47C11×C4⋊C4—41no—
48C4⋊Dic11Q818yescomplemented
49Dic11⋊C4—24no—
50Dic11⋊C4—42no—
51Dic11⋊C4—42no—
52C4×Dic11—24no—
53C4×Dic11—41no—
54C4×Dic11—42no—
55#2586—111nomaximal, Sylow
56C23×C11C2411yescharacteristic
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—22no—
65C2×C4×C11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11C2×Q814yes—
69C2×C4×C11#4112yes—
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×Dic11C2×Q814yes—
80C2×Dic11C2×Q814yes—
81C2×Dic11#4114yes—
82Dic22—44no—
83Dic22—44no—
84#398D1111yescharacteristic
85#395—111no—
86#395—112no—
87#391—111no—
88#391—112no—
89#389—112no—
90#387—112no—
91#387—112no—
92C4×C4⋊C4—112no—
93C22×C11C22×Q812yes—
94C22×C11C2×#4111yescharacteristic
95C22×C11C2×#4112yes—
96C22×C11H(5,𝔽2)11yescharacteristic
97C22×C11H(5,𝔽2)11yescharacteristic
98C4×C11—24no—
99C4×C11—22no—
100C4×C11—42no—
101C4×C11—41no—
102C4×C11—41no—
103Dic11—24no—
104Dic11—24no—
105Dic11—24no—
106Dic11—42no—
107C22×Q8—111no—
108C22×Q8—111no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—112no—
111C2×C4⋊C4—112no—
112C2×C4⋊C4—112no—
113C2×C4⋊C4C2×D1112yes—
114C2×C4⋊C4C2×D1111yescharacteristic
115C2×C4⋊C4C2×D1111yescharacteristic
116C2×C42—112no—
117C2×C42—111no—
118C2×C42—112no—
119#95—112no—
120#95—112no—
121#95—111no—
122#95—112no—
123#95—112no—
124#95—112no—
125#95—112no—
126#95C2×D1111yescharacteristic
127#95C2×D1112yes—
128C2×C11#53312yes—
129C2×C11#53811yescharacteristic
130C2×C11#55111yescharacteristic
131C2×C11#55412yes—
132C2×C11Q8211yescharacteristic
133C2×Q8—224no—
134C2×Q8—222no—
135C2×Q8—441no—
136C2×Q8—441no—
137C2×Q8—441no—
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—118no—
151C4⋊C4—224no—
152C4⋊C4—442no—
153C4⋊C4—442no—
154C42—224no—
155C42—441no—
156C42—442no—
157C11#258611yescharacteristic, complemented, Sylow
158C23C23×D1111yescharacteristic
159Q8—444no—
160Q8—444no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—114no—
173C2×C4—114no—
174C2×C4—114no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4#434112yes—
185C2×C4Q8×D1114yes—
186C22C2×#434111yescharacteristic
187C22#6703711yescharacteristic
188C22C2×Q8×D1112yes—
189C22#41×D1112yes—
190C22#6704211yescharacteristic
191C4—22no—
192C4—24no—
193C4—42no—
194C4—41no—
195C4—41no—
196C4—224no—
197C4—224no—
198C4—224no—
199C4—442no—
200C2#1062314811yescharacteristic
201C2#1062315312yes—
202C2#1062319011yescharacteristic
203C2#1062322112yes—
204C2#1062325311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#398C2
hypercenter#398D11
hypocenterC11#2586
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
48. C4⋊Dic11Q8semidirect
157. C11#2586semidirect

Maximal subgroups

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

subgroupindex
C11×#3982
#106225922
C4⋊C4×Dic112
#106225872
#106225852
#106222672
#106222662
#106222592
#258611