Finite Group Databasebeta

← #13069967

Subgroups — #13069967

Order 1408.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#10623031C211yesmaximal, characteristic
2#10622734C212yesmaximal
3#10622590C211yesmaximal, characteristic
4C11×#343C211yesmaximal, characteristic
5#10622193C212yesmaximal
6C2×C11×M16C2212yes—
7C2×C11×C4⋊C4C2211yescharacteristic
8#66979C2212yes—
9C2×C4⋊Dic11C2211yescharacteristic
10#66977—22no—
11C2×C4×Dic11C2211yescharacteristic
12#66943—22no—
13#66941—22no—
14C11⋊#95—22no—
15#66882—22no—
16#66881—22no—
17C22×C4×C11D412yes—
18C22×C4×C11C2311yescharacteristic
19C22×Dic11—21no—
20C22×Dic11—21no—
21C2×Dic22—22no—
22C11×M16—22no—
23C11×M16Q814yescomplemented
24C2×C8×C11—22no—
25C11×C4⋊C4—22no—
26C22⋊Dic11—22no—
27C4⋊Dic11—22no—
28C4⋊Dic11—22no—
29C4⋊Dic11D412yes—
30C4⋊Dic11D412yes—
31Dic11⋊C4—24no—
32C4×Dic11—22no—
33C4×Dic11—21no—
34C4×Dic11Q812yescomplemented
35#2061—111nomaximal, Sylow
36C23×C11C2×D411yescharacteristic
37C2×C4×C11—22no—
38C2×C4×C11—42no—
39C2×C4×C11C2×D412yes—
40C2×C4×C11C2×Q812yes—
41C2×C4×C11C2×Q811yescharacteristic
42C2×C4×C11#4111yescharacteristic
43C2×Dic11—22no—
44C2×Dic11—22no—
45C2×Dic11—22no—
46C2×Dic11—41no—
47C2×Dic11—41no—
48C2×Dic11—42no—
49C2×Dic11—41no—
50Dic22—82no—
51C8×C11—24no—
52#544—111no—
53#428—112no—
54#382—111no—
55#343D1111yescharacteristic
56#339—112no—
57C22×C11—21no—
58C22×C11—21no—
59C22×C11#12011yescharacteristic
60C22×C11C22⋊Q811yescharacteristic
61C22×C11C4⋊Q811yescharacteristic
62C4×C11—42no—
63C4×C11C22⋊Q812yes—
64C4×C11C4⋊Q812yes—
65Dic11—42no—
66Dic11—42no—
67Dic11—42no—
68Dic11—81no—
69C2×M16C2×D1112yes—
70C4⋊Q8—222no—
71#125—222no—
72C22⋊Q8—222no—
73#117—112no—
74C2×C4⋊C4—111no—
75C2×C4⋊C4C2×D1111yescharacteristic
76C2×C42—111no—
77#107—222no—
78#106—222no—
79#95—222no—
80C2×C11—21no—
81C2×C11—21no—
82C2×C11#39511yescharacteristic
83C2×C11#45411yescharacteristic
84C2×C11#45511yescharacteristic
85C2×Q8—222no—
86C22×C4—221no—
87C22×C4—221no—
88C22×C4D4412yes—
89C22×C4C22×D1111yescharacteristic
90M16—22no—
91M16Dic2214yescomplemented
92C2×C8—22no—
93C4⋊C4—22no—
94C4⋊C4—112no—
95C4⋊C4—112no—
96C4⋊C4—222no—
97C4⋊C4—224no—
98C4⋊C4—222no—
99C22⋊C4—222no—
100C42—112no—
101C42—222no—
102C42—221no—
103C11#206111yescharacteristic, complemented, Sylow
104C23C2×D4411yescharacteristic
105Q8—882no—
106C2×C4—22no—
107C2×C4—42no—
108C2×C4—222no—
109C2×C4—222no—
110C2×C4—222no—
111C2×C4—441no—
112C2×C4—441no—
113C2×C4—442no—
114C2×C4—441no—
115C2×C4C2×Dic2212yes—
116C2×C4D4×D1112yes—
117C2×C4#434111yescharacteristic
118C2×C4Q8×D1111yescharacteristic
119C8—24no—
120C22—21no—
121C22—21no—
122C22#6692211yescharacteristic
123C22#6693511yescharacteristic
124C22#6695011yescharacteristic
125C4—42no—
126C4—442no—
127C4—442no—
128C4—442no—
129C4—881no—
130C4#6693112yes—
131C4#6694112yes—
132C2—21no—
133C2—21no—
134C2#1062226911yescharacteristic
135C2#1062235911yescharacteristic
136C2#1062236611yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#343C2
socleC22×C11#120
prime radicalC23×C11C2×D4
hypercenter#343D11
hypocenterC11#2061
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
23. C11×M16Q8semidirect
34. C4×Dic11Q8semidirect
91. M16Dic22semidirect
103. C11#2061semidirect

Maximal subgroups

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

subgroupindex
#106230312
#106227342
#106225902
C11×#3432
#106221932
#206111