Finite Group Databasebeta

← #13076806

Subgroups — #13076806

Order 1408.

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

normal subgroups only

This group has 380 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#10622599C212yesmaximal, complemented
3#10622565C212yesmaximal
4#10622563C212yesmaximal
5#10622560C211yesmaximal, characteristic
6#10622559C211yesmaximal, characteristic
7#10622272C212yesmaximal, complemented
8#10622271C212yesmaximal, complemented
9#10622269C212yesmaximal, complemented
10C23×Dic11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊Dic11C2212yes—
17C2×C4⋊Dic11C2212yes—
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C11×#95C2212yes—
22C11×#95C2211yescharacteristic
23C11⋊#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2211yescharacteristic
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
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—
42C2×Dic22—42no—
43C2×Dic22—41no—
44C11×C4⋊C4—41no—
45C11×C22⋊C4—24no—
46C11×C22⋊C4—41no—
47C22⋊Dic11—22no—
48C22⋊Dic11—42no—
49C4⋊Dic11—42no—
50C4⋊Dic11—42no—
51Dic11⋊C4—42no—
52Dic11⋊C4—42no—
53#2835—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—22no—
65C2×C4×C11—21no—
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—
83Dic22—44no—
84#400—112no—
85#400—112no—
86#400—112no—
87#397—112no—
88#397D1111yescharacteristic
89#395—112no—
90#393—111no—
91#385—111no—
92#385—112no—
93C22×C11—22no—
94C22×C11—24no—
95C22×C11—41no—
96C22×C11—42no—
97C22×C11—41no—
98C22×C11C2×#4111yescharacteristic
99C22×C11H(5,𝔽2)11yescharacteristic
100C22×C11H(5,𝔽2)12yes—
101C22×C112−1+411yescharacteristic
102C22×C112−1+412yes—
103C4×C11—42no—
104C4×C11—42no—
105C4×C11—41no—
106C4×C11—41no—
107Dic11—42no—
108Dic11—42no—
109Dic11—42no—
110Dic11—42no—
111C22×Q8—111no—
112C23×C4—111no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
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—111no—
126#95—112no—
127#95—112no—
128#95—112no—
129#95—112no—
130#95C2×D1112yes—
131#95C2×D1111yescharacteristic
132C2×C11—42no—
133C2×C11#53911yescharacteristic
134C2×C11#53912yes—
135C2×C11H(3,𝔽4)11yescharacteristic
136C2×C11#56312yes—
137C2×C11#56311yescharacteristic
138C24C22×D1111yescharacteristic
139C2×Q8—441no—
140C2×Q8—442no—
141C22×C4—112no—
142C22×C4—112no—
143C22×C4—112no—
144C22×C4—112no—
145C22×C4—441no—
146C22×C4—442no—
147C22×C4C22×D1111yescharacteristic
148C22×C4C22×D1112yes—
149C22×C4C22×D1112yes—
150C22×C4C22×D1111yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—442no—
153C4⋊C4—442no—
154C4⋊C4—442no—
155C4⋊C4—442no—
156C22⋊C4—24no—
157C22⋊C4—41no—
158C22⋊C4—222no—
159C22⋊C4—442no—
160C11#283511yescharacteristic, complemented, Sylow
161C23—21no—
162C23—22no—
163C23—21no—
164C23—22no—
165C23#434112yes—
166C23C23×D1111yescharacteristic
167Q8—444no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
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—222no—
189C2×C4—222no—
190C2×C4—444no—
191C22—22no—
192C22—24no—
193C22—42no—
194C22—41no—
195C22—41no—
196C22C2×#434111yescharacteristic
197C22#6703711yescharacteristic
198C22#6704212yes—
199C22#6704311yescharacteristic
200C22#6704312yes—
201C4—42no—
202C4—41no—
203C4—42no—
204C4—41no—
205C4—442no—
206C4—442no—
207C4—442no—
208C4—442no—
209C2—42no—
210C2#1062313311yescharacteristic
211C2#1062318211yescharacteristic
212C2#1062319612yes—
213C2#1062321411yescharacteristic
214C2#1062324312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC24×C11C23
hypercenter#397D11
hypocenterC11#2835
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #10622599C2semidirect
7. #10622272C2semidirect
8. #10622271C2semidirect
9. #10622269C2semidirect
160. C11#2835semidirect

Maximal subgroups

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

subgroupindex
C11×#3972
#106225992
#106225652
#106225632
#106225602
#106225592
#106222722
#106222712
#106222692
#283511