Finite Group Databasebeta

← #14647196

Subgroups — #14647196

Order 2816.

630 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 195 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#13068596C212yesmaximal
2#13066499C214yesmaximal, complemented
3C2×C11×#384C211yesmaximal, characteristic
4C22×C11×C4⋊C4—22no—
5C22×C11×C4⋊C4C412yes—
6C22×C42×C11C2211yescharacteristic
7C11×#384—22no—
8C11×#384C412yes—
9C11×#384C2212yes—
10C2×C22⋊(C11⋊C8)—22no—
11C2×C4⋊(C11⋊C8)C2214yes—
12#10622162—22no—
13C23×C4×C11—22no—
14C23×C4×C11C2×C411yescharacteristic
15C23×C4×C11D412yes—
16C2×C11×C4⋊C4—24no—
17C2×C11×C4⋊C4—22no—
18C2×C11×C4⋊C4—24no—
19C2×C11×C4⋊C4—44no—
20C2×C11×C4⋊C4—48no—
21C2×C11×C4⋊C4C2×C414yes—
22C2×C42×C11—24no—
23C2×C42×C11C2×C411yescharacteristic
24C2×C42×C11D412yes—
25C2×C42×C11C2311yescharacteristic
26C22×C11⋊C8—24no—
27C22⋊(C11⋊C8)—44no—
28C4⋊(C11⋊C8)—28no—
29#8725—111nomaximal, Sylow
30C24×C11C22⋊C411yescharacteristic
31C22×C4×C11—22no—
32C22×C4×C11—22no—
33C22×C4×C11—22no—
34C22×C4×C11—24no—
35C22×C4×C11—24no—
36C22×C4×C11—24no—
37C22×C4×C11—48no—
38C22×C4×C11—44no—
39C22×C4×C11C22⋊C411yescharacteristic
40C22×C4×C11C22⋊C412yes—
41C22×C4×C11SD1614yes—
42C22×C4×C11Q1614yes—
43C22×C4×C11C22×C411yescharacteristic
44C22×C4×C11C2×D412yes—
45C11×C4⋊C4—44no—
46C11×C4⋊C4—48no—
47C11×C4⋊C4—44no—
48C11×C4⋊C4—48no—
49C42×C11—22no—
50C42×C11—24no—
51C42×C11#4114yes—
52C2×C11⋊C8—44no—
53C2×C11⋊C8—44no—
54C2×C11⋊C8—44no—
55C2×#384D1111yescharacteristic
56#1797—112no—
57#1296—114no—
58C23×C11—21no—
59C23×C11—21no—
60C23×C11—22no—
61C23×C11#10012yes—
62C23×C11#10314yes—
63C23×C11C2×C22⋊C411yescharacteristic
64C2×C4×C11—28no—
65C2×C4×C11—21no—
66C2×C4×C11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—28no—
72C2×C4×C11—28no—
73C2×C4×C11—44no—
74C2×C4×C11—48no—
75C2×C4×C11—88no—
76C2×C4×C11#10112yes—
77C2×C4×C11#10314yes—
78C2×C4×C11#11712yes—
79C2×C4×C11#12314yes—
80C2×C4×C11C2×SD1612yes—
81C2×C4×C11C2×Q1612yes—
82C2×C4×C11AGL(1,ℤ/8)14yes—
83C11⋊C8—84no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4Dic1112yes—
86C22×C42C2×D1111yescharacteristic
87C2×C4⋊C8—114no—
88C2×C22⋊C8—222no—
89#384—22no—
90#384Dic1112yes—
91#384C2×D1112yes—
92#336—222no—
93C22×C11—24no—
94C22×C11—22no—
95C22×C11—22no—
96C22×C11—24no—
97C22×C11#33314yes—
98C22×C11#38111yescharacteristic
99C22×C11C2×#10011yescharacteristic
100C22×C11C2×#10111yescharacteristic
101C22×C11C2×#10312yes—
102C22×C11#41812yes—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11—24no—
106C4×C11—84no—
107C4×C11#48114yes—
108C4×C11#48414yes—
109C23×C4—22no—
110C23×C4C2×Dic1111yescharacteristic
111C23×C4C22⋊D1112yes—
112C22×C8—224no—
113C2×C4⋊C4—24no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—24no—
116C2×C4⋊C4—44no—
117C2×C4⋊C4—48no—
118C2×C4⋊C4C2×Dic1114yes—
119C2×C42—24no—
120C2×C42C2×Dic1111yescharacteristic
121C2×C42C22⋊D1112yes—
122C2×C42C22×D1111yescharacteristic
123C4⋊C8—228no—
124C22⋊C8—444no—
125C2×C11—24no—
126C2×C11C2×#33311yescharacteristic
127C2×C11#154912yes—
128C2×C11#155511yescharacteristic
129C2×C11#182111yescharacteristic
130C2×C11#182412yes—
131C24C22⋊Dic1111yescharacteristic
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—48no—
139C22×C4—44no—
140C22×C4#432514yes—
141C22×C4#432614yes—
142C22×C4C22⋊Dic1112yes—
143C22×C4C22⋊Dic1111yescharacteristic
144C22×C4C22×Dic1111yescharacteristic
145C22×C4C2×C22⋊D1112yes—
146C2×C8—444no—
147C2×C8—444no—
148C2×C8—444no—
149C4⋊C4—44no—
150C4⋊C4—48no—
151C4⋊C4—44no—
152C4⋊C4—48no—
153C42—22no—
154C42—24no—
155C42#433914yes—
156C11#872511yescharacteristic, complemented, Sylow
157C23—21no—
158C23—22no—
159C23—21no—
160C23#6689712yes—
161C23#6689914yes—
162C23C2×C22⋊Dic1111yescharacteristic
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—28no—
171C2×C4—28no—
172C2×C4—48no—
173C2×C4—44no—
174C2×C4—88no—
175C2×C4#6689914yes—
176C2×C4#6690012yes—
177C2×C4#6697912yes—
178C2×C4#6698214yes—
179C2×C4#6698514yes—
180C2×C4C2×#432512yes—
181C2×C4C2×#432612yes—
182C8—884no—
183C22—24no—
184C22—22no—
185C22—22no—
186C22—24no—
187C22#1062218414yes—
188C22#1062282411yescharacteristic
189C22#1062282812yes—
190C22C2×#6689711yescharacteristic
191C22C2×#6689912yes—
192C22C2×#6690011yescharacteristic
193C4—22no—
194C4—22no—
195C4—24no—
196C4—84no—
197C4#1062258114yes—
198C4#1062258314yes—
199C2—24no—
200C2C2×#1062218411yescharacteristic
201C2#1306730112yes—
202C2#1306733011yescharacteristic
203C2#1306869611yescharacteristic
204C2#1306870612yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#384C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#384D11
hypocenterC11#8725
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
2. #13066499C2semidirect
156. C11#8725semidirect

Maximal subgroups

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

subgroupindex
#130685962
#130664992
C2×C11×#3842
#872511