Finite Group Databasebeta

← #14658786

Subgroups — #14658786

Order 2816.

354 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 99 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#13068770C211yesmaximal, characteristic, complemented
2#13067388C212yesmaximal, complemented
3#13067015C212yesmaximal
4#13066445C211yesmaximal, characteristic, complemented
5C11×#1963C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C11×#423C2211yescharacteristic
8C2×C11×#104—22no—
9C11×#376C2211yescharacteristic
10#10622538C2212yes—
11C2×C4⋊(C11⋊C8)—22no—
12C2×C4⋊(C11⋊C8)C2212yes—
13D4⋊(C11⋊C8)—24no—
14#10622118—24no—
15C2×C11×#41—21no—
16C2×C11×M16—21no—
17C11×C4⋊Q8Q811yescharacteristic
18C11×#127Q811yescharacteristic
19C11×#124—21no—
20C11×#121—22no—
21C4×D4×C11—22no—
22C2×C42×C11D412yes—
23C2×C42×C11C2311yescharacteristic
24C22×C11⋊C8—22no—
25C11×C4⋊C8—22no—
26C11×#104—44no—
27C11×#95—22no—
28C22⋊(C11⋊C8)—22no—
29C4⋊(C11⋊C8)—22no—
30C4⋊(C11⋊C8)—22no—
31C4⋊(C11⋊C8)—22no—
32C4⋊(C11⋊C8)—44no—
33C4×C11⋊C8D414yes—
34#10666—111nomaximal, Sylow
35C11×#41—42no—
36C11×#41—42no—
37C2×Q8×C11—21no—
38C2×D4×C11—22no—
39C2×D4×C11—21no—
40C2×D4×C11—41no—
41C22×C4×C11—22no—
42C22×C4×C11—41no—
43C22×C4×C11C2×D411yescharacteristic
44C22×C4×C11#4112yes—
45C11×M16—42no—
46C2×C8×C11—41no—
47C11×C4⋊C4—22no—
48C11×C22⋊C4—42no—
49C42×C11—22no—
50C42×C11SD1614yes—
51C42×C11C2×D412yes—
52C42×C11C2×Q811yescharacteristic
53C42×C11#4111yescharacteristic
54C2×C11⋊C8—24no—
55C2×C11⋊C8—42no—
56C2×C11⋊C8—44no—
57#1963D1111yescharacteristic
58#1843—111no—
59#1570—112no—
60#1480—112no—
61#1274—111no—
62C23×C11—41no—
63C23×C11#12311yescharacteristic
64Q8×C11—42no—
65D4×C11—44no—
66D4×C11—42no—
67D4×C11—82no—
68C2×C4×C11—24no—
69C2×C4×C11—42no—
70C2×C4×C11—44no—
71C2×C4×C11—41no—
72C2×C4×C11—81no—
73C2×C4×C11—81no—
74C2×C4×C11C22⋊Q812yes—
75C2×C4×C11C22⋊Q811yescharacteristic
76C2×C4×C11#12312yes—
77C2×C4×C11#12711yescharacteristic
78C2×C4×C11C2×SD1612yes—
79C2×C4×C11AGL(1,ℤ/8)12yes—
80C8×C11—81no—
81C11⋊C8—44no—
82C11⋊C8—82no—
83#532C2×D1111yescharacteristic
84#431—112no—
85#423C2×D1111yescharacteristic
86C2×C4⋊C8—112no—
87C2×C4⋊C8—222no—
88C2×#104—22no—
89#376C2×D1111yescharacteristic
90#334—224no—
91D4⋊C8—224no—
92C22×C11—22no—
93C22×C11—81no—
94C22×C11—82no—
95C22×C11#39911yescharacteristic
96C22×C11#48112yes—
97C4×C11—22no—
98C4×C11—22no—
99C4×C11—44no—
100C4×C11—81no—
101C4×C11#47612yes—
102C4×C11#49211yescharacteristic
103C4×C11#49611yescharacteristic
104C2×#41—21no—
105C2×M16—21no—
106C22×C8—222no—
107C4⋊Q8Dic2211yescharacteristic
108#127Dic2211yescharacteristic
109#124—21no—
110#121—22no—
111C4×D4—22no—
112C2×C42C22⋊D1112yes—
113C2×C42C22×D1111yescharacteristic
114C4⋊C8—22no—
115C4⋊C8—222no—
116C4⋊C8—222no—
117C4⋊C8—222no—
118C4⋊C8—444no—
119#104—44no—
120C22⋊C8—222no—
121C4×C8—114no—
122#95—22no—
123C2×C11—22no—
124C2×C11—161no—
125C2×C11#209411yescharacteristic
126C2×C11#209812yes—
127#41—42no—
128#41—42no—
129C2×Q8—21no—
130C2×D4—22no—
131C2×D4—21no—
132C2×D4—41no—
133C22×C4—22no—
134C22×C4—41no—
135C22×C4#434112yes—
136C22×C4C2×C22⋊D1111yescharacteristic
137M16—42no—
138C2×C8—41no—
139C2×C8—224no—
140C2×C8—442no—
141C2×C8—444no—
142C4⋊C4—22no—
143C22⋊C4—42no—
144C42—22no—
145C42#432414yes—
146C42C2×Dic2211yescharacteristic
147C42#433911yescharacteristic
148C42D4×D1112yes—
149C11#1066611yescharacteristic, complemented, Sylow
150C23—41no—
151C23#6698811yescharacteristic
152Q8—42no—
153D4—44no—
154D4—42no—
155D4—82no—
156C2×C4—24no—
157C2×C4—42no—
158C2×C4—44no—
159C2×C4—41no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4#6693112yes—
163C2×C4#6693612yes—
164C2×C4#6697711yescharacteristic
165C2×C4C2×#432412yes—
166C2×C4#6699311yescharacteristic
167C2×C4#6700212yes—
168C8—81no—
169C8—444no—
170C8—882no—
171C22—22no—
172C22—81no—
173C22—82no—
174C22#1062256211yescharacteristic
175C22#1062264712yes—
176C4—22no—
177C4—22no—
178C4—44no—
179C4—81no—
180C4#1062262112yes—
181C4#1062267111yescharacteristic
182C4#1062268911yescharacteristic
183C2—22no—
184C2—161no—
185C2#1307014911yescharacteristic
186C2#1307017112yes—
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1963C2
socleC22×C11#399
prime radicalC11×#532C22
hypercenter#1963D11
hypocenterC11#10666
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #13068770C2semidirect
2. #13067388C2semidirect
4. #13066445C2semidirect
149. C11#10666semidirect

Maximal subgroups

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

subgroupindex
#130687702
#130673882
#130670152
#130664452
C11×#19632
#1066611