Finite Group Databasebeta

← #13075519

Subgroups — #13075519

Order 1408.

448 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×#66932C212yesmaximal
2C11×#397C211yesmaximal, characteristic
3#10622585C212yesmaximal, complemented
4#10622566C211yesmaximal, characteristic
5#10622559C211yesmaximal, characteristic
6#10622555C212yesmaximal
7#10622270C212yesmaximal, complemented
8#10622270C212yesmaximal, complemented
9#10622268C212yesmaximal, complemented
10C23×Dic11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C22⋊C4C2212yes—
13C2×C11×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic11C2212yes—
15C2×C22⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2212yes—
24#66932—28no—
25C11×#95C2212yes—
26C11×#95C2211yescharacteristic
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C24×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×C4×C11C2312yes—
37C22×Dic11—24no—
38C22×Dic11—41no—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C11×C4⋊C4—41no—
44C11×C22⋊C4—24no—
45C11×C22⋊C4—41no—
46C22⋊Dic11—24no—
47C22⋊Dic11D414yes—
48C4⋊Dic11—24no—
49C4⋊Dic11—41no—
50Dic11⋊C4—24no—
51Dic11⋊C4—24no—
52Dic11⋊C4—24no—
53Dic11⋊C4—24no—
54Dic11⋊C4—42no—
55C4×Dic11—24no—
56#2722—111nomaximal, Sylow
57C23×C11—22no—
58C23×C11—21no—
59C23×C11—21no—
60C23×C11—22no—
61C23×C11C2×D412yes—
62C23×C11C2411yescharacteristic
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—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—22no—
83C2×Dic11—44no—
84C2×Dic11C2×D414yes—
85C2×Dic11#4114yes—
86C2×#126—112no—
87#398—112no—
88#398—112no—
89#397—111no—
90#397D1111yescharacteristic
91#389—112no—
92#387—112no—
93#385—111no—
94#380—112no—
95C22×C11—22no—
96C22×C11—24no—
97C22×C11—42no—
98C22×C11—41no—
99C22×C11—41no—
100C22×C11C22×D411yescharacteristic
101C22×C11C2×#4112yes—
102C22×C11H(5,𝔽2)11yescharacteristic
103C22×C112−1+411yescharacteristic
104C22×C112−1+412yes—
105C4×C11—42no—
106C4×C11—42no—
107C4×C11—41no—
108C4×C11—41no—
109Dic11—24no—
110Dic11—24no—
111Dic11—42no—
112Dic11—42no—
113C23×C4—111no—
114#126—228no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—112no—
121C2×C4⋊C4—111no—
122C2×C4⋊C4C2×D1111yescharacteristic
123C2×C22⋊C4—111no—
124C2×C22⋊C4—112no—
125C2×C22⋊C4C2×D1112yes—
126C2×C22⋊C4C2×D1111yescharacteristic
127C2×C42—112no—
128#95—112no—
129#95—112no—
130#95—112no—
131#95—111no—
132#95—112no—
133#95C2×D1112yes—
134#95C2×D1111yescharacteristic
135C2×C11—42no—
136C2×C11#53711yescharacteristic
137C2×C11#54112yes—
138C2×C11#54712yes—
139C2×C11#55111yescharacteristic
140C2×C11#56311yescharacteristic
141C24C22×D1111yescharacteristic
142C22×C4—112no—
143C22×C4—112no—
144C22×C4—112no—
145C22×C4—112no—
146C22×C4—224no—
147C22×C4—441no—
148C22×C4C22×D1111yescharacteristic
149C22×C4C22×D1111yescharacteristic
150C22×C4C22×D1112yes—
151C22×C4C22×D1112yes—
152C4⋊C4—41no—
153C4⋊C4—224no—
154C4⋊C4—224no—
155C4⋊C4—224no—
156C4⋊C4—224no—
157C4⋊C4—224no—
158C4⋊C4—442no—
159C4⋊C4—441no—
160C22⋊C4—24no—
161C22⋊C4—41no—
162C22⋊C4—114no—
163C22⋊C4—224no—
164C42—224no—
165C11#272211yescharacteristic, complemented, Sylow
166C23—21no—
167C23—22no—
168C23—21no—
169C23—22no—
170C23D4×D1112yes—
171C23C23×D1111yescharacteristic
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—114no—
183C2×C4—114no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—444no—
195C22—22no—
196C22—24no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22C2×D4×D1111yescharacteristic
201C22#6703711yescharacteristic
202C22#41×D1112yes—
203C22#6704311yescharacteristic
204C22#6704312yes—
205C4—42no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—224no—
210C4—224no—
211C4—442no—
212C4—442no—
213C2—42no—
214C2#1062312811yescharacteristic
215C2#1062318612yes—
216C2#1062319011yescharacteristic
217C2#1062320311yescharacteristic
218C2#1062323212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC24×C11C23
hypercenter#397D11
hypocenterC11#2722
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #10622585C2semidirect
7. #10622270C2semidirect
8. #10622270C2semidirect
9. #10622268C2semidirect
165. C11#2722semidirect

Maximal subgroups

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

subgroupindex
C2×#669322
C11×#3972
#106225852
#106225662
#106225592
#106225552
#106222702
#106222682
#272211