Finite Group Databasebeta

← #13075546

Subgroups — #13075546

Order 1408.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#66988C212yesmaximal
2C11×#390C211yesmaximal, characteristic
3#10622596C212yesmaximal, complemented
4#10622566C214yesmaximal, complemented
5#10622563C214yesmaximal, complemented
6#10622541C212yesmaximal, complemented
7C22×D4×C11C2211yescharacteristic
8C23×Dic11C2212yes—
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C11×C22⋊C4C2214yes—
11C2×C42×C11C2211yescharacteristic
12C2×C22⋊Dic11C2214yes—
13C2×C22⋊Dic11C2212yes—
14#66988—28no—
15C2×C4⋊Dic11C2212yes—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2212yes—
18C2×Dic11⋊C4C2214yes—
19C11⋊#95C2214yes—
20C11⋊#95C2214yes—
21C11⋊#95C2212yes—
22C24×C11C2312yes—
23C2×D4×C11—41no—
24C2×D4×C11—41no—
25C2×D4×C11D414yes—
26C22×C4×C11C2312yes—
27C22×C4×C11C2311yescharacteristic
28C22×C4×C11C2312yes—
29C22×Dic11—24no—
30C22×Dic11—42no—
31C22×Dic11—42no—
32C22×Dic11C2314yes—
33C22×Dic11C2314yes—
34C11×C4⋊C4—41no—
35C11×C22⋊C4—28no—
36C42×C11—41no—
37C22⋊Dic11—24no—
38C22⋊Dic11—28no—
39C4⋊Dic11—24no—
40C4⋊Dic11—42no—
41C4⋊Dic11—42no—
42Dic11⋊C4—28no—
43#2724—111nomaximal, Sylow
44C23×C11—24no—
45C23×C11—22no—
46C23×C11—22no—
47C23×C11—24no—
48C23×C11C2×D414yes—
49C23×C11C2411yescharacteristic
50D4×C11—44no—
51C2×C4×C11—22no—
52C2×C4×C11—21no—
53C2×C4×C11—21no—
54C2×C4×C11—22no—
55C2×C4×C11—24no—
56C2×C4×C11—22no—
57C2×C4×C11C2×D412yes—
58C2×C4×C11#4114yes—
59C2×Dic11—24no—
60C2×Dic11—24no—
61C2×Dic11—24no—
62C2×Dic11—24no—
63C2×Dic11—24no—
64C2×Dic11—24no—
65C2×Dic11—48no—
66C2×#123—112no—
67#398—112no—
68#397—114no—
69#390D1111yescharacteristic
70#389—112no—
71#385—114no—
72C22×C11—24no—
73C22×C11—28no—
74C22×C11—44no—
75C22×C11—42no—
76C22×C11—42no—
77C22×C11C22×D411yescharacteristic
78C22×C11C2×#4112yes—
79C22×C11H(5,𝔽2)11yescharacteristic
80C22×C11H(5,𝔽2)11yescharacteristic
81C22×C112−1+412yes—
82C4×C11—22no—
83C4×C11—24no—
84C4×C11—42no—
85Dic11—44no—
86Dic11—44no—
87C22×D4C2×D1111yescharacteristic
88C23×C4—112no—
89#123—228no—
90C2×C4⋊C4—114no—
91C2×C4⋊C4—112no—
92C2×C4⋊C4—112no—
93C2×C4⋊C4—112no—
94C2×C4⋊C4C2×D1111yescharacteristic
95C2×C22⋊C4—114no—
96C2×C22⋊C4—112no—
97C2×C22⋊C4C2×D1114yes—
98C2×C42C2×D1111yescharacteristic
99#95—114no—
100#95—114no—
101#95—112no—
102C2×C11—44no—
103C2×C11#53411yescharacteristic
104C2×C11#53912yes—
105C2×C11#54712yes—
106C2×C11#55911yescharacteristic
107C2×C11#56311yescharacteristic
108C24C22×D1112yes—
109C2×D4—41no—
110C2×D4—41no—
111C2×D4D4414yes—
112C22×C4—114no—
113C22×C4—114no—
114C22×C4—224no—
115C22×C4—442no—
116C22×C4—442no—
117C22×C4C22×D1112yes—
118C22×C4C22×D1111yescharacteristic
119C22×C4C22×D1112yes—
120C4⋊C4—41no—
121C4⋊C4—228no—
122C4⋊C4—224no—
123C4⋊C4—442no—
124C4⋊C4—442no—
125C22⋊C4—28no—
126C22⋊C4—224no—
127C22⋊C4—228no—
128C42—41no—
129C11#272411yescharacteristic, complemented, Sylow
130C23—24no—
131C23—22no—
132C23—22no—
133C23—24no—
134C23C2×D4414yes—
135C23C23×D1111yescharacteristic
136D4—44no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—24no—
142C2×C4—22no—
143C2×C4—224no—
144C2×C4—224no—
145C2×C4—224no—
146C2×C4—224no—
147C2×C4—224no—
148C2×C4—224no—
149C2×C4—448no—
150C2×C4C2×D4412yes—
151C2×C4#434114yes—
152C22—24no—
153C22—28no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22C22×D4411yescharacteristic
158C22C2×#434112yes—
159C22#6703711yescharacteristic
160C22#6703711yescharacteristic
161C22#6704312yes—
162C4—22no—
163C4—24no—
164C4—42no—
165C4—444no—
166C4—444no—
167C2—44no—
168C2#1062302411yescharacteristic
169C2#1062308612yes—
170C2#1062313312yes—
171C2#1062320311yescharacteristic
172C2#1062324411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2724
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
3. #10622596C2semidirect
4. #10622566C2semidirect
5. #10622563C2semidirect
6. #10622541C2semidirect
129. C11#2724semidirect

Maximal subgroups

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

subgroupindex
C2×#669882
C11×#3902
#106225962
#106225662
#106225632
#106225412
#272411