Finite Group Databasebeta

← #13070062

Subgroups — #13070062

Order 1408.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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×#106C211yesmaximal, characteristic, complemented
2#10622723C211yesmaximal, characteristic
3#10622579C212yesmaximal
4#10622190C211yesmaximal, characteristic, complemented
5#10622168C212yesmaximal, complemented
6C2×#4339C2211yescharacteristic
7C22×C8×C11C2211yescharacteristic
8C2×C11×C4⋊C4C2212yes—
9C2×#4318C2211yescharacteristic
10C2×#4318C2212yes—
11C11×#106—22no—
12(C2×D11)⋊C8—22no—
13#66874—22no—
14#66873—22no—
15C22×C4×C11—22no—
16C22×C4×C11C2311yescharacteristic
17C2×C22⋊D11—21no—
18#4339—22no—
19#4339—22no—
20C2×D44D411yescharacteristic
21C2×C4×D11—21no—
22C2×Dic22D411yescharacteristic
23C2×C8×C11—22no—
24C2×C8×C11D412yes—
25C11×C4⋊C4—22no—
26C11×C4⋊C4—22no—
27#4318—22no—
28#4318—22no—
29#4318—22no—
30C2×C11⋊C8—22no—
31C2×C11⋊C8—21no—
32#2079—111nomaximal, Sylow
33C23×C11#4111yescharacteristic
34C22×D11—21no—
35C2×C4×C11—42no—
36C2×C4×C11—82no—
37C2×C4×C11C2×D411yescharacteristic
38C2×C4×C11C2×D411yescharacteristic
39C2×C4×C11#4112yes—
40C2×C4×C11#4112yes—
41C22⋊D11—42no—
42C2×Dic11—21no—
43D44—22no—
44C4×D11—41no—
45C4×D11—41no—
46Dic22—22no—
47C8×C11—22no—
48C11⋊C8—42no—
49C11⋊C8—41no—
50C2×#106D1111yescharacteristic, complemented
51#417—112no—
52#408—111no—
53#343—112no—
54#341—111no—
55C22×C11—22no—
56C22×C11#12111yescharacteristic
57C22×C11#12612yes—
58C2×D11—41no—
59C2×D11—42no—
60C4×C11—82no—
61C4×C11#12312yes—
62C4×C11#12311yescharacteristic
63C4×C11#12411yescharacteristic
64Dic11—41no—
65C2×#41—111no—
66C2×M16—112no—
67C2×M16—111no—
68C22×C8C2×D1111yescharacteristic
69C2×C4⋊C4C2×D1112yes—
70#106—22no—
71#103—222no—
72#102—222no—
73C22⋊C8—222no—
74C2×C11—22no—
75C2×C11#39711yescharacteristic
76C2×C11#47112yes—
77D11—81no—
78#41—222no—
79#41—222no—
80C2×Q8—111no—
81C2×D4—111no—
82C2×D4—221no—
83C22×C4—22no—
84C22×C4—221no—
85C22×C4C22×D1111yescharacteristic
86M16—222no—
87M16—222no—
88M16—222no—
89C2×C8—22no—
90C2×C8—222no—
91C2×C8—221no—
92C2×C8C22⋊D1112yes—
93C4⋊C4—22no—
94C4⋊C4—22no—
95C11#207911yescharacteristic, complemented, Sylow
96C23—221no—
97C23#434111yescharacteristic
98Q8—222no—
99D4—222no—
100D4—442no—
101C2×C4—42no—
102C2×C4—82no—
103C2×C4—221no—
104C2×C4—441no—
105C2×C4—441no—
106C2×C4#433912yes—
107C2×C4D4×D1111yescharacteristic
108C2×C4#434312yes—
109C2×C4C2×C22⋊D1111yescharacteristic
110C8—22no—
111C8—442no—
112C8—441no—
113C22—22no—
114C22—442no—
115C22—441no—
116C22#6695112yes—
117C22#6699111yescharacteristic
118C4—82no—
119C4—441no—
120C4#6694712yes—
121C4#6698211yescharacteristic
122C4#6700011yescharacteristic
123C2—22no—
124C2—881no—
125C2#1062260611yescharacteristic
126C2#1062279012yes—
subgroupG/H
centerC22#66991
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#106C2
socleC22×C11#121
prime radicalC2×#4339C22
hypercenterC2×#106D11
hypocenterC11#2079
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C2×C11×#106C2semidirect
4. #10622190C2semidirect
5. #10622168C2semidirect
50. C2×#106D11semidirect
95. C11#2079semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1062
#106227232
#106225792
#106221902
#106221682
#207911