Finite Group Databasebeta

← #14673925

Subgroups — #14673925

Order 2816.

268 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 87 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#13069362C211yesmaximal, characteristic
2#13068771C211yesmaximal, characteristic
3#13066723C211yesmaximal, characteristic
4#13066722C211yesmaximal, characteristic
5#13066716C211yesmaximal, characteristic
6#13066697C211yesmaximal, characteristic
7C11×#1383C211yesmaximal, characteristic
8C2×C11×M32C2211yescharacteristic
9C2×C11×#108C2211yescharacteristic
10C2×C11×#106C2211yescharacteristic
11#10622732—21no—
12#10622719C2211yescharacteristic
13C2×#66881C2211yescharacteristic
14C2×C8×Dic11C2211yescharacteristic
15C2×#66876C2211yescharacteristic
16#10622589—21no—
17C2×#66872—21no—
18#10622193—21no—
19C2×C11×M16—21no—
20C22×C8×C11C2311yescharacteristic
21C2×C11×C4⋊C4—21no—
22#66979—21no—
23C2×C4⋊Dic11—21no—
24C2×Dic11⋊C4—42no—
25C2×C4×Dic11D411yescharacteristic
26C22×C11⋊C8D411yescharacteristic
27C11×M32—21no—
28C11×M32—21no—
29C2×C11×C16—21no—
30C11×#108—21no—
31C11×#108—21no—
32C11×#106—21no—
33C11×#106—21no—
34#66882Q812yes—
35#66881—21no—
36#66881—21no—
37#66881—21no—
38Dic11⋊C8—42no—
39C8×Dic11—21no—
40C8×Dic11—21no—
41#66876—21no—
42#66876—21no—
43C2×C11⋊C16—21no—
44#66872—42no—
45#13543—111nomaximal, Sylow
46C22×C4×C11—41no—
47C22×C4×C11C2×D411yescharacteristic
48C22×Dic11—21no—
49C22×Dic11—41no—
50C11×M16—41no—
51C11×M16—41no—
52C2×C8×C11—41no—
53C2×C8×C11C2×Q811yescharacteristic
54C2×C8×C11#4111yescharacteristic
55C2×C8×C11#4111yescharacteristic
56C2×C8×C11#4111yescharacteristic
57C2×C8×C11#4111yescharacteristic
58C2×C8×C11#4111yescharacteristic
59C11×C4⋊C4—41no—
60C11×C4⋊C4—41no—
61C22⋊Dic11—41no—
62C4⋊Dic11—22no—
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65Dic11⋊C4—84no—
66C4×Dic11—21no—
67C4×Dic11—41no—
68C4×Dic11Q1612yes—
69C2×C11⋊C8—21no—
70C2×C11⋊C8—21no—
71C2×C11⋊C8SD1612yes—
72C11×C16—41no—
73C11⋊C16—41no—
74#1945—111no—
75#1844—111no—
76#1386—111no—
77#1386—111no—
78#1383—111no—
79#1383D1111yescharacteristic
80#1376—111no—
81C23×C11AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C11—82no—
83C2×C4×C11—81no—
84C2×C4×C11C22⋊Q811yescharacteristic
85C2×C4×C11#12311yescharacteristic
86C2×C4×C11#12411yescharacteristic
87C2×C4×C11C2×SD1611yescharacteristic
88C2×C4×C11C2×Q1611yescharacteristic
89C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
90C2×Dic11—24no—
91C2×Dic11—22no—
92C2×Dic11—42no—
93C2×Dic11—82no—
94C2×Dic11—81no—
95C8×C11—81no—
96C8×C11#12511yescharacteristic
97C8×C11#12511yescharacteristic
98C8×C11#12611yescharacteristic
99C8×C11#12611yescharacteristic
100C11⋊C8—22no—
101C2×M32—111no—
102C2×M32C2×D1111yescharacteristic
103C2×#108C2×D1111yescharacteristic
104#427—111no—
105C2×#106—111no—
106C2×#106—221no—
107C2×#106C2×D1111yescharacteristic
108#424—221no—
109C2×C4×C8—111no—
110#384—221no—
111#339—221no—
112C22×C11—22no—
113C22×C11#47611yescharacteristic
114C22×C11#48411yescharacteristic
115C22×C11#49011yescharacteristic
116C4×C11—161no—
117C4×C11#40011yescharacteristic
118C4×C11#47711yescharacteristic
119C4×C11#48111yescharacteristic
120C4×C11#48711yescharacteristic
121Dic11—24no—
122Dic11—82no—
123Dic11—161no—
124C2×M16—21no—
125C22×C8—111no—
126C22×C8C22×D1111yescharacteristic
127#117—221no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—221no—
130C2×C4⋊C4—442no—
131C2×C42—111no—
132M32—21no—
133M32—21no—
134M32—221no—
135M32—221no—
136C2×C16—21no—
137C2×C16—221no—
138#108—21no—
139#108—21no—
140#107—112no—
141#106—21no—
142#106—21no—
143#106—221no—
144#106—221no—
145#106—221no—
146#106—442no—
147C4⋊C8—442no—
148C4×C8—221no—
149C4×C8—221no—
150C2×C11—21no—
151C2×C11—21no—
152C2×C11#210011yescharacteristic
153C2×C11#223012yes—
154C22×C4—41no—
155C22×C4—221no—
156C22×C4—441no—
157C22×C4D4×D1111yescharacteristic
158M16—41no—
159M16—41no—
160C2×C8—41no—
161C2×C8—112no—
162C2×C8—221no—
163C2×C8—221no—
164C2×C8#433911yescharacteristic
165C2×C8#433911yescharacteristic
166C2×C8#433911yescharacteristic
167C2×C8#434111yescharacteristic
168C2×C8#434111yescharacteristic
169C2×C8Q8×D1111yescharacteristic
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—222no—
173C4⋊C4—441no—
174C4⋊C4—441no—
175C4⋊C4—884no—
176C22⋊C4—441no—
177C42—112no—
178C42—221no—
179C42—441no—
180C16—41no—
181C16—441no—
182C11#1354311yescharacteristic, complemented, Sylow
183C23#6696711yescharacteristic
184C2×C4—82no—
185C2×C4—81no—
186C2×C4—224no—
187C2×C4—222no—
188C2×C4—442no—
189C2×C4—882no—
190C2×C4—881no—
191C2×C4#6693611yescharacteristic
192C2×C4#6693811yescharacteristic
193C2×C4#6694911yescharacteristic
194C2×C4#6696411yescharacteristic
195C2×C4SD16×D1111yescharacteristic
196C2×C4Q16×D1111yescharacteristic
197C8—81no—
198C8—222no—
199C8#6692911yescharacteristic
200C8#6693211yescharacteristic
201C8#6694211yescharacteristic
202C8#6694211yescharacteristic
203C22—22no—
204C22#1062237711yescharacteristic
205C22#1062242211yescharacteristic
206C22#1062248311yescharacteristic
207C4—161no—
208C4—224no—
209C4—882no—
210C4—1761no—
211C4#1062227111yescharacteristic
212C4#1062239011yescharacteristic
213C4#1062240511yescharacteristic
214C4#1062248811yescharacteristic
215C2—21no—
216C2—21no—
217C2#1307018111yescharacteristic
218C2#1307078612yes—
subgroupG/H
centerC22#10622483
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1383C2
socleC22×C11#476
prime radicalC23×C11AGL(1,ℤ/8)
hypercenter#1383D11
hypocenterC11#13543
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1383

Complements

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

NH ≅ G/Ntype
182. C11#13543semidirect

Maximal subgroups

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

subgroupindex
#130693622
#130687712
#130667232
#130667222
#130667162
#130666972
C11×#13832
#1354311