Finite Group Databasebeta

← #13066950

Subgroups — #13066950

Order 1408.

252 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 85 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×C11×#117C211yesmaximal, characteristic
2#10622539C212yesmaximal, complemented
3#10622166C212yesmaximal, complemented
4#10622163C212yesmaximal
5C23×C4×C11C411yescharacteristic
6C11×#117—22no—
7C11×#117—22no—
8C2×C11×C4⋊C4C411yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C11×C22⋊C4C411yescharacteristic
11C2×C11×C22⋊C4C2211yescharacteristic
12C2×C42×C11C411yescharacteristic
13C2×C42×C11C2211yescharacteristic
14C22⋊(C11⋊C8)C2214yes—
15C4⋊(C11⋊C8)—22no—
16#66867—22no—
17C24×C11C2×C411yescharacteristic
18C22×C4×C11—22no—
19C22×C4×C11—21no—
20C22×C4×C11—21no—
21C22×C4×C11—22no—
22C22×C4×C11C2×C411yescharacteristic
23C22×C4×C11C2×C411yescharacteristic
24C22×C4×C11C2×C411yescharacteristic
25C22×C4×C11C2×C411yescharacteristic
26C22×C4×C11C2×C411yescharacteristic
27C22×C4×C11C2311yescharacteristic
28C11×C4⋊C4—22no—
29C11×C4⋊C4—22no—
30C11×C22⋊C4—22no—
31C11×C22⋊C4—22no—
32C42×C11—21no—
33C42×C11—21no—
34C42×C11D412yes—
35C42×C11D412yes—
36C2×C11⋊C8—24no—
37#1464—111nomaximal, Sylow
38C23×C11—21no—
39C23×C11—21no—
40C23×C11—41no—
41C23×C11—41no—
42C23×C11M1612yes—
43C23×C11C22×C411yescharacteristic
44C2×C4×C11—24no—
45C2×C4×C11—24no—
46C2×C4×C11—21no—
47C2×C4×C11—21no—
48C2×C4×C11—21no—
49C2×C4×C11—21no—
50C2×C4×C11—21no—
51C2×C4×C11—21no—
52C2×C4×C11—41no—
53C2×C4×C11—41no—
54C2×C4×C11—41no—
55C2×C4×C11—41no—
56C2×C4×C11C22⋊C411yescharacteristic
57C2×C4×C11C22⋊C411yescharacteristic
58C2×C4×C11C22⋊C412yes—
59C2×C4×C11M1612yes—
60C2×C4×C11C2×D412yes—
61C11⋊C8—44no—
62C2×#117D1111yescharacteristic
63#432—112no—
64#324—112no—
65#323—112no—
66C22×C11—21no—
67C22×C11—21no—
68C22×C11—22no—
69C22×C11—42no—
70C22×C11—42no—
71C22×C11—41no—
72C22×C11—41no—
73C22×C11C2×C22⋊C411yescharacteristic
74C22×C11C2×M1611yescharacteristic
75C22×C11C2×M1611yescharacteristic
76C4×C11—21no—
77C4×C11—21no—
78C4×C11—22no—
79C4×C11—22no—
80C4×C11—22no—
81C4×C11—41no—
82C4×C11—41no—
83C23×C4Dic1111yescharacteristic
84#117—22no—
85#117—22no—
86C2×C4⋊C4Dic1111yescharacteristic
87C2×C4⋊C4C2×D1111yescharacteristic
88C2×C22⋊C4Dic1111yescharacteristic
89C2×C22⋊C4C2×D1111yescharacteristic
90C2×C42Dic1111yescharacteristic
91C2×C42C2×D1111yescharacteristic
92C4⋊C8—222no—
93C22⋊C8—114no—
94#97—222no—
95C2×C11—21no—
96C2×C11—21no—
97C2×C11—42no—
98C2×C11#40711yescharacteristic
99C2×C11#41011yescharacteristic
100C2×C11#41311yescharacteristic
101C24C2×Dic1111yescharacteristic
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4C2×Dic1111yescharacteristic
107C22×C4C2×Dic1111yescharacteristic
108C22×C4C2×Dic1111yescharacteristic
109C22×C4C2×Dic1111yescharacteristic
110C22×C4C2×Dic1111yescharacteristic
111C22×C4C22×D1111yescharacteristic
112C2×C8—224no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—22no—
117C42—21no—
118C42—21no—
119C42C22⋊D1112yes—
120C42C22⋊D1112yes—
121C11#146411yescharacteristic, complemented, Sylow
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#431812yes—
127C23C22×Dic1111yescharacteristic
128C2×C4—24no—
129C2×C4—24no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4#431812yes—
141C2×C4C22⋊Dic1111yescharacteristic
142C2×C4C22⋊Dic1111yescharacteristic
143C2×C4C22⋊Dic1112yes—
144C2×C4C2×C22⋊D1112yes—
145C8—444no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×#431811yescharacteristic
154C22C2×#431811yescharacteristic
155C22C2×C22⋊Dic1111yescharacteristic
156C4—22no—
157C4—21no—
158C4—21no—
159C4—22no—
160C4—22no—
161C4—41no—
162C4—41no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1062282011yescharacteristic
167C2#1062285011yescharacteristic
168C2#1062285311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic11
commutatorC23×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C11×#117C2
socleC22×C11C2×C22⋊C4
prime radicalC24×C11C2×C4
cosocleC22×C4×C11C23
hypercenterC2×#117D11
hypocenterC11#1464
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #10622539C2semidirect
3. #10622166C2semidirect
121. C11#1464semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1172
#106225392
#106221662
#106221632
#146411