Finite Group Databasebeta

← #13076801

Subgroups — #13076801

Order 1408.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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×#397C211yesmaximal, characteristic
2#10622596C212yesmaximal, complemented
3#10622565C212yesmaximal
4#10622563C212yesmaximal
5#10622562C211yesmaximal, characteristic
6#10622559C211yesmaximal, characteristic
7C11⋊#401C212yesmaximal, complemented
8#10622274C212yesmaximal, complemented
9#10622270C212yesmaximal, complemented
10C23×Dic11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C22⋊C4C2212yes—
13C2×C11×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic11C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C11×#95C2211yescharacteristic
23C11×#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C24×C11C2311yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11—42no—
37C22×Dic11—41no—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C11×C4⋊C4—41no—
43C11×C22⋊C4—24no—
44C11×C22⋊C4—41no—
45C22⋊Dic11—22no—
46C22⋊Dic11—42no—
47C4⋊Dic11—42no—
48C4⋊Dic11—41no—
49C4⋊Dic11—42no—
50Dic11⋊C4—42no—
51Dic11⋊C4—42no—
52Dic11⋊C4—42no—
53#2834—111nomaximal, Sylow
54C23×C11—22no—
55C23×C11—21no—
56C23×C11—21no—
57C23×C11—22no—
58C23×C11#4112yes—
59C23×C11C2411yescharacteristic
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—21no—
65C2×C4×C11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—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—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—44no—
83#401—112no—
84#399—111no—
85#398—112no—
86#398—112no—
87#398—112no—
88#397—112no—
89#397D1111yescharacteristic
90#385—111no—
91#385—112no—
92C22×C11—22no—
93C22×C11—24no—
94C22×C11—41no—
95C22×C11—42no—
96C22×C11—41no—
97C22×C11C2×#4111yescharacteristic
98C22×C11H(5,𝔽2)11yescharacteristic
99C22×C11H(5,𝔽2)12yes—
100C22×C112−1+411yescharacteristic
101C22×C112−1+412yes—
102C4×C11—42no—
103C4×C11—42no—
104C4×C11—41no—
105C4×C11—41no—
106Dic11—42no—
107Dic11—42no—
108Dic11—42no—
109Dic11—42no—
110C23×C4—111no—
111C2×C4⋊C4—112no—
112C2×C4⋊C4—112no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—111no—
117C2×C4⋊C4C2×D1111yescharacteristic
118C2×C22⋊C4—111no—
119C2×C22⋊C4—112no—
120C2×C22⋊C4C2×D1112yes—
121C2×C22⋊C4C2×D1111yescharacteristic
122#95—112no—
123#95—112no—
124#95—112no—
125#95—112no—
126#95—112no—
127#95—112no—
128#95—111no—
129#95C2×D1111yescharacteristic
130#95C2×D1112yes—
131C2×C11—42no—
132C2×C11#53911yescharacteristic
133C2×C11#53912yes—
134C2×C11#56011yescharacteristic
135C2×C11#56312yes—
136C2×C11#56311yescharacteristic
137C24C22×D1111yescharacteristic
138C22×C4—112no—
139C22×C4—112no—
140C22×C4—112no—
141C22×C4—112no—
142C22×C4—441no—
143C22×C4—442no—
144C22×C4C22×D1111yescharacteristic
145C22×C4C22×D1112yes—
146C22×C4C22×D1112yes—
147C22×C4C22×D1111yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—442no—
150C4⋊C4—442no—
151C4⋊C4—442no—
152C4⋊C4—441no—
153C4⋊C4—442no—
154C4⋊C4—442no—
155C22⋊C4—24no—
156C22⋊C4—41no—
157C22⋊C4—222no—
158C22⋊C4—442no—
159C11#283411yescharacteristic, complemented, Sylow
160C23—21no—
161C23—22no—
162C23—21no—
163C23—22no—
164C23#434112yes—
165C23C23×D1111yescharacteristic
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
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—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—444no—
189C22—22no—
190C22—24no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22C2×#434111yescharacteristic
195C22#6703711yescharacteristic
196C22#6704212yes—
197C22#6704311yescharacteristic
198C22#6704312yes—
199C4—42no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—442no—
204C4—442no—
205C4—442no—
206C4—442no—
207C2—42no—
208C2#1062313311yescharacteristic
209C2#1062319612yes—
210C2#1062319711yescharacteristic
211C2#1062320311yescharacteristic
212C2#1062324312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC24×C11C23
hypercenter#397D11
hypocenterC11#2834
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #10622596C2semidirect
7. C11⋊#401C2semidirect
8. #10622274C2semidirect
9. #10622270C2semidirect
159. C11#2834semidirect

Maximal subgroups

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

subgroupindex
C11×#3972
#106225962
#106225652
#106225632
#106225622
#106225592
C11⋊#4012
#106222742
#106222702
#283411