Finite Group Databasebeta

← #13075645

Subgroups — #13075645

Order 1408.

456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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×#66941C212yesmaximal
2C11×#398C211yesmaximal, characteristic
3#10622596C211yesmaximal, characteristic
4#10622592C212yesmaximal
5#10622587C211yesmaximal, characteristic
6#10622585C212yesmaximal
7#10622269C212yesmaximal
8#10622268C212yesmaximal
9#10622265C212yesmaximal
10C22×Dic22C2212yes—
11C22×Dic22C2211yescharacteristic
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic11C2212yes—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23#66941—28no—
24C11×#95C2212yes—
25C11×#95C2211yescharacteristic
26C11⋊#95C2211yescharacteristic
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C2×Dic22—24no—
42C2×Dic22—41no—
43C2×Dic22—41no—
44C2×Dic22—42no—
45C2×Dic22—42no—
46C2×Dic22D414yes—
47C11×C4⋊C4—24no—
48C11×C4⋊C4—41no—
49C11×C4⋊C4—41no—
50C4⋊Dic11—24no—
51C4⋊Dic11—41no—
52Dic11⋊C4—24no—
53Dic11⋊C4—24no—
54Dic11⋊C4—42no—
55Dic11⋊C4Q818yescomplemented
56C4×Dic11—24no—
57C4×Dic11—41no—
58#2734—111nomaximal, Sylow
59C23×C11C2411yescharacteristic
60C2×C4×C11—22no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11C2×D412yes—
72C2×C4×C11C2×Q814yes—
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×Dic11C2×D414yes—
83C2×Dic11C2×Q814yes—
84C2×Dic11C2×Q814yes—
85Dic22—44no—
86Dic22—48no—
87C2×C4⋊Q8—112no—
88#398—111no—
89#398D1111yescharacteristic
90#395—112no—
91#395—112no—
92#391—111no—
93#389—112no—
94#387—112no—
95#387—112no—
96C22×C11C22×D411yescharacteristic
97C22×C11C22×Q812yes—
98C22×C11H(5,𝔽2)11yescharacteristic
99C22×C11H(5,𝔽2)11yescharacteristic
100C22×C112−1+412yes—
101C4×C11—22no—
102C4×C11—24no—
103C4×C11—42no—
104C4×C11—41no—
105C4×C11—41no—
106Dic11—24no—
107Dic11—24no—
108Dic11—24no—
109Dic11—42no—
110C22×Q8—111no—
111C22×Q8—112no—
112C4⋊Q8—228no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—111no—
119C2×C4⋊C4C2×D1112yes—
120C2×C4⋊C4C2×D1111yescharacteristic
121C2×C4⋊C4C2×D1111yescharacteristic
122C2×C42—112no—
123C2×C42—111no—
124#95—111no—
125#95—112no—
126#95—112no—
127#95—112no—
128#95—112no—
129#95—112no—
130#95C2×D1111yescharacteristic
131#95C2×D1112yes—
132C2×C11#53411yescharacteristic
133C2×C11#54412yes—
134C2×C11D4×Q812yes—
135C2×C11Q8211yescharacteristic
136C2×C11#56311yescharacteristic
137C2×Q8—114no—
138C2×Q8—224no—
139C2×Q8—441no—
140C2×Q8—441no—
141C2×Q8—442no—
142C2×Q8—442no—
143C22×C4—112no—
144C22×C4—112no—
145C22×C4—112no—
146C22×C4—112no—
147C22×C4C22×D1111yescharacteristic
148C22×C4C22×D1111yescharacteristic
149C22×C4C22×D1112yes—
150C22×C4C22×D1111yescharacteristic
151C22×C4C22×D1112yes—
152C4⋊C4—24no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—118no—
156C4⋊C4—224no—
157C4⋊C4—224no—
158C4⋊C4—224no—
159C4⋊C4—442no—
160C4⋊C4—441no—
161C42—224no—
162C42—441no—
163C11#273411yescharacteristic, complemented, Sylow
164C23C23×D1111yescharacteristic
165Q8—444no—
166Q8—448no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—114no—
179C2×C4—114no—
180C2×C4—114no—
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×C4D4×D1112yes—
191C2×C4Q8×D1114yes—
192C22C2×D4×D1111yescharacteristic
193C22#6703711yescharacteristic
194C22C2×Q8×D1112yes—
195C22#6704211yescharacteristic
196C22#6704312yes—
197C4—22no—
198C4—24no—
199C4—42no—
200C4—41no—
201C4—41no—
202C4—224no—
203C4—224no—
204C4—224no—
205C4—442no—
206C2#1062313611yescharacteristic
207C2#1062316312yes—
208C2#1062318211yescharacteristic
209C2#1062322012yes—
210C2#1062325311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#398C2
hypercenter#398D11
hypocenterC11#2734
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
55. Dic11⋊C4Q8semidirect
163. C11#2734semidirect

Maximal subgroups

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

subgroupindex
C2×#669412
C11×#3982
#106225962
#106225922
#106225872
#106225852
#106222692
#106222682
#106222652
#273411