Finite Group Databasebeta

← #13069784

Subgroups — #13069784

Order 1408.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#10623014C211yesmaximal, characteristic
2#10622556C211yesmaximal, characteristic
3#10622556C212yesmaximal
4C11×#342C211yesmaximal, characteristic
5#10622165C212yesmaximal
6C23×Dic11C2211yescharacteristic
7C2×C11×C22⋊C4C2212yes—
8C2×C11×C22⋊C4C2211yescharacteristic
9C2×C22⋊Dic11C2211yescharacteristic
10C2×C22⋊Dic11C2212yes—
11#66977—22no—
12#66931—24no—
13C11⋊#95—22no—
14C11⋊#95—24no—
15C24×C11C2311yescharacteristic
16C22×C4×C11—22no—
17C22×C4×C11D412yes—
18C22×Dic11—21no—
19C22×Dic11—22no—
20C22×Dic11—21no—
21C22×Dic11—22no—
22C22×Dic11—21no—
23C22×Dic11D414yes—
24C22×Dic11Q812yescomplemented
25C2×Dic22—22no—
26C11×C22⋊C4—22no—
27C11×C22⋊C4—22no—
28C11×C22⋊C4—22no—
29C22⋊Dic11—22no—
30C22⋊Dic11—22no—
31C22⋊Dic11—22no—
32C4⋊Dic11—22no—
33Dic11⋊C4—24no—
34#2030—111nomaximal, Sylow
35C23×C11—42no—
36C23×C11C2×D411yescharacteristic
37C23×C11C2×D412yes—
38C23×C11C2×Q811yescharacteristic
39C23×C11#4112yes—
40C23×C11#4111yescharacteristic
41C2×C4×C11—22no—
42C2×C4×C11—42no—
43C2×C4×C11—44no—
44C2×C4×C11—42no—
45C2×Dic11—24no—
46C2×Dic11—24no—
47C2×Dic11—22no—
48C2×Dic11—41no—
49C2×Dic11—41no—
50C2×Dic11—42no—
51C2×Dic11—44no—
52C2×Dic11—42no—
53C2×Dic11—41no—
54Dic22—82no—
55#543—111no—
56#381—112no—
57#381—111no—
58#342—112no—
59#342D1111yescharacteristic
60C22×C11—22no—
61C22×C11—24no—
62C22×C11—41no—
63C22×C11—42no—
64C22×C11—41no—
65C22×C11#12011yescharacteristic
66C22×C11C22⋊Q812yes—
67C22×C11C22⋊Q811yescharacteristic
68C22×C11#12411yescharacteristic
69C22×C11#12412yes—
70C4×C11—42no—
71C4×C11—82no—
72Dic11—42no—
73Dic11—44no—
74Dic11—81no—
75C23×C4—111no—
76C22⋊Q8—224no—
77C22⋊Q8—222no—
78C2×C22⋊C4—112no—
79C2×C22⋊C4—111no—
80C2×C22⋊C4C2×D1112yes—
81C2×C22⋊C4C2×D1111yescharacteristic
82#95—224no—
83#95—222no—
84C2×C11—21no—
85C2×C11—22no—
86C2×C11—22no—
87C2×C11—21no—
88C2×C11#39311yescharacteristic
89C2×C11#45812yes—
90C24C22×D1111yescharacteristic
91C2×Q8—222no—
92C22×C4—22no—
93C22×C4—112no—
94C22×C4—114no—
95C22×C4—221no—
96C22×C4—222no—
97C22×C4—222no—
98C22×C4—221no—
99C22×C4—221no—
100C22×C4D4412yes—
101C4⋊C4—224no—
102C4⋊C4—222no—
103C22⋊C4—22no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—222no—
107C22⋊C4—222no—
108C22⋊C4—222no—
109C11#203011yescharacteristic, complemented, Sylow
110C23—42no—
111C23C2×D4411yescharacteristic
112C23#433912yes—
113C23D4×D1112yes—
114C23#434111yescharacteristic
115C23Q8×D1111yescharacteristic
116Q8—882no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—224no—
122C2×C4—224no—
123C2×C4—222no—
124C2×C4—441no—
125C2×C4—441no—
126C2×C4—442no—
127C2×C4—444no—
128C2×C4—442no—
129C2×C4—441no—
130C22—22no—
131C22—24no—
132C22—42no—
133C22—41no—
134C22—41no—
135C22#6692811yescharacteristic
136C22#6693511yescharacteristic
137C22#6693812yes—
138C22#6694912yes—
139C22#6695011yescharacteristic
140C4—42no—
141C4—82no—
142C4—442no—
143C4—444no—
144C4—881no—
145C2—22no—
146C2—21no—
147C2—22no—
148C2—21no—
149C2#1062228611yescharacteristic
150C2#1062235512yes—
subgroupG/H
centerC22#66935
commutator, prime radical, cosocleC24×C11C23
FrattiniC24C22×D11
FittingC11×#342C2
socleC22×C11#120
hypercenter#342D11
hypocenterC11#2030
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
24. C22×Dic11Q8semidirect
109. C11#2030semidirect

Maximal subgroups

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

subgroupindex
#106230142
#106225562
C11×#3422
#106221652
#203011