Finite Group Databasebeta

← #14665777

Subgroups — #14665777

Order 2816.

206 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C4×Dic88C211yesmaximal, characteristic
2#13067514C212yesmaximal
3#13066690C211yesmaximal, characteristic
4#13066581C212yesmaximal
5C11×#1311C211yesmaximal, characteristic
6C2×Dic88C411yescharacteristic
7C4×Dic44C2212yes—
8#10622292—22no—
9C4×C11×C16C2211yescharacteristic
10C4×C11×C16C2211yescharacteristic
11C82×C11C2211yescharacteristic
12#10622142C411yescharacteristic
13#10622141C412yes—
14#10622096C2212yes—
15#10622094—22no—
16C2×Dic44C2×C412yes—
17C4×Dic22—22no—
18C2×C11×C16—21no—
19C2×C11×C16C2×C411yescharacteristic
20C2×C11×C16C2×C411yescharacteristic
21C4×C8×C11D411yescharacteristic
22C4×C8×C11D411yescharacteristic
23C4×C8×C11C2311yescharacteristic
24#66882C2×C412yes—
25#66880—22no—
26#66879—42no—
27Dic11⋊C8—42no—
28C4⋊(C11⋊C8)—22no—
29Dic88—22no—
30#12085—111nomaximal, Sylow
31C2×Dic22—22no—
32C2×C8×C11—21no—
33C2×C8×C11D812yes—
34C2×C8×C11C22×C411yescharacteristic
35C2×C8×C11#4111yescharacteristic
36C42×C11C2×D411yescharacteristic
37C4⋊Dic11—22no—
38Dic11⋊C4—42no—
39C4×Dic11—42no—
40C2×C11⋊C8—42no—
41Dic44—22no—
42Dic44—22no—
43C11×C16—22no—
44C11×C16—21no—
45C11×C16M1612yes—
46C4×Q32—111no—
47#1591—112no—
48#1372—111no—
49#1332—112no—
50#1311D1111yescharacteristic
51C2×C4×C11C4×D411yescharacteristic
52C2×C4×C11C2×D811yescharacteristic
53C2×C4×C11#13511yescharacteristic
54C2×Dic11—42no—
55C2×Dic11—42no—
56Dic22—42no—
57Dic22—42no—
58C8×C11—21no—
59C8×C11—22no—
60C8×C11—41no—
61C8×C11C2×M1611yescharacteristic
62C8×C11#13111yescharacteristic
63C11⋊C8—82no—
64C2×Q32—111no—
65#446—222no—
66C4×Q16—112no—
67#366—111no—
68#358—112no—
69C4×C16C2×D1111yescharacteristic
70C4×C16C2×D1111yescharacteristic
71#335—112no—
72Q8⋊C8—222no—
73C82C2×D1111yescharacteristic
74C22×C11C4×D811yescharacteristic
75C4×C11—21no—
76C4×C11#43611yescharacteristic
77C4×C11#44311yescharacteristic
78C4×C11#51012yes—
79Dic11—82no—
80Dic11—82no—
81C2×Q16—112no—
82C4×Q8—222no—
83Q32—222no—
84C2×C16—21no—
85C2×C16C4×D1111yescharacteristic
86C2×C16C4×D1111yescharacteristic
87#107—112no—
88C4⋊C8—222no—
89C4⋊C8—442no—
90#103—222no—
91#97—442no—
92C4×C8D4411yescharacteristic
93C4×C8D4411yescharacteristic
94C4×C8C22×D1111yescharacteristic
95C2×C11#158911yescharacteristic
96C2×C11#217611yescharacteristic
97C2×C11#217911yescharacteristic
98C2×Q8—222no—
99Q16—222no—
100Q16—222no—
101C2×C8—21no—
102C2×C8—442no—
103C2×C8D8812yes—
104C2×C8C2×C4×D1111yescharacteristic
105C2×C8#433911yescharacteristic
106C4⋊C4—222no—
107C4⋊C4—442no—
108C42—442no—
109C42C2×D4411yescharacteristic
110C16—22no—
111C16—21no—
112C16#431312yes—
113C11#1208511yescharacteristic, complemented, Sylow
114Q8—442no—
115Q8—442no—
116C2×C4—442no—
117C2×C4—442no—
118C2×C4C4×D4411yescharacteristic
119C2×C4C2×D8811yescharacteristic
120C2×C4#6695711yescharacteristic
121C8—22no—
122C8—21no—
123C8—41no—
124C8—882no—
125C8C2×#431311yescharacteristic
126C8#6695411yescharacteristic
127C22C4×D8811yescharacteristic
128C4—21no—
129C4—882no—
130C4—882no—
131C4#1062230111yescharacteristic
132C4#1062231311yescharacteristic
133C4#1062252212yes—
134C2#1306750211yescharacteristic
135C2#1307048811yescharacteristic
136C2#1307050311yescharacteristic
subgroupG/H
centerC2×C4C2×D88
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1311C2
socle, prime radicalC22×C11C4×D8
cosocleC4×C8×C11C23
hypercenter#1311D11
hypocenterC11#12085
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C82 ◁ #1311

Complements

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

NH ≅ G/Ntype
113. C11#12085semidirect

Maximal subgroups

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

subgroupindex
C4×Dic882
#130675142
#130666902
#130665812
C11×#13112
#1208511