Finite Group Databasebeta

← #14658765

Subgroups — #14658765

Order 2816.

320 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 101 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#13069556C211yesmaximal, characteristic
2#13068791C211yesmaximal, characteristic
3#13067387C212yesmaximal
4#13067046C212yesmaximal
5C11×#1275C211yesmaximal, characteristic
6C2×C4×Dic22C2211yescharacteristic
7C11×#431C2212yes—
8C2×C11×#97C2211yescharacteristic
9C2×#66883—22no—
10#10622537C2212yes—
11C2×C4⋊(C11⋊C8)C2211yescharacteristic
12#10622188—22no—
13#10622095—24no—
14#10622094—24no—
15C22×Dic22Q811yescharacteristic
16C22×C8×C11D412yes—
17C2×C42×C11C2311yescharacteristic
18C2×C4⋊Dic11Q811yescharacteristic
19C2×Dic11⋊C4—21no—
20C2×C4×Dic11—21no—
21C2×#4318—22no—
22C22×C11⋊C8—21no—
23C4×Dic22—22no—
24C4×Dic22—22no—
25C11×C4⋊C8—22no—
26C11×C22⋊C8—22no—
27C11×#97—22no—
28C4×C8×C11D414yes—
29#66883—44no—
30C4⋊(C11⋊C8)—22no—
31C4⋊(C11⋊C8)—22no—
32C4⋊(C11⋊C8)—22no—
33#10663—111nomaximal, Sylow
34C22×C4×C11C2×D411yescharacteristic
35C22×C4×C11C2×Q811yescharacteristic
36C22×C4×C11#4111yescharacteristic
37C22×Dic11—21no—
38C22×Dic11—21no—
39C2×Dic22—22no—
40C2×Dic22—42no—
41C2×C8×C11—22no—
42C2×C8×C11—24no—
43C2×C8×C11—22no—
44C2×C8×C11SD1614yes—
45C42×C11C2×D412yes—
46C42×C11#4112yes—
47C4⋊Dic11—22no—
48Dic11⋊C4—42no—
49C4×Dic11—41no—
50C4×Dic11—41no—
51#4318—44no—
52C2×C11⋊C8—41no—
53C2×C11⋊C8—42no—
54C2×C11⋊C8—42no—
55#1985—111no—
56#1849—111no—
57#1570—112no—
58#1487—112no—
59#1275D1111yescharacteristic
60C23×C11C22⋊Q811yescharacteristic
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11C22⋊Q812yes—
64C2×C4×C11#12312yes—
65C2×C4×C11#12311yescharacteristic
66C2×C4×C11#12711yescharacteristic
67C2×C4×C11C2×SD1612yes—
68C2×C4×C11#13712yes—
69C2×Dic11—22no—
70C2×Dic11—41no—
71C2×Dic11—41no—
72C2×Dic11—42no—
73C2×Dic11—41no—
74Dic22—24no—
75Dic22—42no—
76C8×C11—24no—
77C8×C11—44no—
78C11⋊C8—82no—
79C11⋊C8—81no—
80C2×C4×Q8—111no—
81#431C2×D1112yes—
82C2×#108—222no—
83#423—112no—
84C2×C4⋊C8—111no—
85C2×#97C2×D1111yescharacteristic
86#336—222no—
87#334—224no—
88Q8⋊C8—224no—
89C22×C11—21no—
90C22×C11—21no—
91C22×C11#39911yescharacteristic
92C22×C11#47512yes—
93C4×C11—22no—
94C4×C11—22no—
95C4×C11#48312yes—
96C4×C11#49211yescharacteristic
97C4×C11#49711yescharacteristic
98Dic11—42no—
99Dic11—81no—
100C22×Q8—111no—
101C2×M16—222no—
102C22×C8—221no—
103C22×C8D4412yes—
104C4×Q8—222no—
105C4×Q8—222no—
106C2×C4⋊C4—111no—
107C2×C4⋊C4—221no—
108C2×C42—221no—
109C2×C42C22×D1111yescharacteristic
110#108—444no—
111C4⋊C8—22no—
112C4⋊C8—222no—
113C4⋊C8—222no—
114C4⋊C8—222no—
115C22⋊C8—22no—
116#97—22no—
117C4×C8D4414yes—
118C2×C11—22no—
119C2×C11#209111yescharacteristic
120C2×C11#209611yescharacteristic
121C2×C11#209811yescharacteristic
122C2×Q8—222no—
123C2×Q8—442no—
124C22×C4—221no—
125C22×C4—221no—
126C22×C4C2×D4411yescharacteristic
127C22×C4#434111yescharacteristic
128C22×C4Q8×D1111yescharacteristic
129M16—444no—
130C2×C8—22no—
131C2×C8—22no—
132C2×C8—24no—
133C2×C8—441no—
134C2×C8—442no—
135C2×C8—442no—
136C2×C8#431414yes—
137C4⋊C4—222no—
138C4⋊C4—442no—
139C42—441no—
140C42—441no—
141C42C2×D4412yes—
142C42#434112yes—
143C11#1066311yescharacteristic, complemented, Sylow
144C23#6695011yescharacteristic
145Q8—224no—
146Q8—442no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—222no—
150C2×C4—441no—
151C2×C4—441no—
152C2×C4—442no—
153C2×C4—441no—
154C2×C4#6692711yescharacteristic
155C2×C4#6693912yes—
156C2×C4#6693911yescharacteristic
157C2×C4#6695012yes—
158C2×C4C2×#431412yes—
159C2×C4#6696212yes—
160C8—24no—
161C8—44no—
162C8—882no—
163C8—881no—
164C22—21no—
165C22—21no—
166C22#1062229011yescharacteristic
167C22#1062246412yes—
168C4—22no—
169C4—22no—
170C4—442no—
171C4—881no—
172C4#1062230611yescharacteristic
173C4#1062232811yescharacteristic
174C4#1062233412yes—
175C2—22no—
176C2#1307013311yescharacteristic
177C2#1307015811yescharacteristic
178C2#1307017011yescharacteristic
subgroupG/H
centerC2×C4#66927
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1275C2
socleC22×C11#399
prime radicalC23×C11C22⋊Q8
hypercenter#1275D11
hypocenterC11#10663
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
143. C11#10663semidirect

Maximal subgroups

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

subgroupindex
#130695562
#130687912
#130673872
#130670462
C11×#12752
#1066311