Finite Group Databasebeta

← #14666857

Subgroups — #14666857

Order 2816.

330 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069966C211yesmaximal, characteristic
2#13067657C212yesmaximal
3#13066643C212yesmaximal
4#13066560C211yesmaximal, characteristic
5C11×#2844C211yesmaximal, characteristic
6#10623031C2211yescharacteristic
7C11×#400—22no—
8C11×#400C2212yes—
9C11×#395—22no—
10C11×#395—21no—
11C11×#382—21no—
12C11×#382C2211yescharacteristic
13#10622583—22no—
14#10622577—21no—
15#10622168C2211yescharacteristic
16#10622166C2212yes—
17#10622161—21no—
18#10622090—22no—
19C22×Q8×C11—21no—
20C2×C11×C4⋊C4—21no—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C11×C4⋊C4D412yes—
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C42×C11D411yescharacteristic
27#66979—21no—
28#66977—22no—
29C2×#4318—21no—
30#66943—41no—
31#66941—41no—
32C11×#95—22no—
33C11×#95—21no—
34C11×#95—22no—
35C11×#95—22no—
36C11×#95—22no—
37C11×#95D412yes—
38C22⋊(C11⋊C8)—22no—
39#66874—42no—
40#66872—41no—
41#66871—41no—
42#66871—42no—
43#12261—111nomaximal, Sylow
44C2×Q8×C11—82no—
45C2×Q8×C11—81no—
46C22×C4×C11—21no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—21no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D412yes—
52C2×Dic22—22no—
53C11×C4⋊C4—41no—
54C11×C4⋊C4—41no—
55C11×C4⋊C4—42no—
56C11×C4⋊C4—81no—
57C11×C4⋊C4—81no—
58C11×C4⋊C4—82no—
59C42×C11—21no—
60C42×C11Q1612yes—
61C22⋊Dic11—41no—
62C4⋊Dic11—22no—
63C4⋊Dic11—21no—
64C4⋊Dic11—21no—
65Dic11⋊C4—42no—
66C4×Dic11—41no—
67#4318—22no—
68#4318—41no—
69C2×C11⋊C8—41no—
70C2×C11⋊C8—42no—
71#2844D1111yescharacteristic
72#2061—111no—
73#1617—112no—
74#1353—112no—
75#1324—111no—
76C23×C11#12011yescharacteristic
77Q8×C11—84no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11C2×Q1611yescharacteristic
94C2×C4×C11#13711yescharacteristic
95C2×Dic11—41no—
96C2×Dic11—41no—
97Dic22—82no—
98C11⋊C8—42no—
99C11⋊C8—82no—
100#544—111no—
101#484—222no—
102#428—221no—
103#400—22no—
104#400C2×D1112yes—
105#395—22no—
106#395—21no—
107#382—21no—
108#382C2×D1111yescharacteristic
109#343—111no—
110#339—221no—
111#328—222no—
112#324—112no—
113C22×C11—21no—
114C22×C11—21no—
115C22×C11#45111yescharacteristic
116C22×C11#45611yescharacteristic
117C22×C11B(4,𝔽2)11yescharacteristic
118C4×C11—21no—
119C4×C11—21no—
120C4×C11—42no—
121C4×C11—42no—
122C4×C11—82no—
123C4×C11—81no—
124C4×C11—82no—
125Dic11—81no—
126Dic11—81no—
127C22×Q8—21no—
128C2×M16—221no—
129C4⋊Q8—441no—
130#125—441no—
131C22⋊Q8—222no—
132#117—221no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4C22⋊D1111yescharacteristic
137C2×C4⋊C4C22⋊D1112yes—
138C2×C4⋊C4C22×D1111yescharacteristic
139C2×C42C22⋊D1111yescharacteristic
140#107—441no—
141#107—442no—
142#106—441no—
143#103—442no—
144C22⋊C8—222no—
145#95—22no—
146#95—21no—
147#95—22no—
148#95—22no—
149#95—22no—
150#95C22⋊D1112yes—
151C2×C11—21no—
152C2×C11—21no—
153C2×C11#160511yescharacteristic
154C2×C11#220111yescharacteristic
155C2×C11#220211yescharacteristic
156C2×Q8—82no—
157C2×Q8—81no—
158C2×Q8—222no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—21no—
163C22×C4C2×C22⋊D1111yescharacteristic
164C22×C4C2×C22⋊D1112yes—
165M16—222no—
166M16—441no—
167C2×C8—441no—
168C2×C8—442no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C4⋊C4—41no—
172C4⋊C4—81no—
173C4⋊C4—81no—
174C4⋊C4—82no—
175C4⋊C4—221no—
176C4⋊C4—221no—
177C4⋊C4—222no—
178C4⋊C4—442no—
179C22⋊C4—441no—
180C42—21no—
181C42—441no—
182C42#432612yes—
183C11#1226111yescharacteristic, complemented, Sylow
184C23#6700611yescharacteristic
185Q8—84no—
186Q8—882no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—42no—
202C2×C4—441no—
203C2×C4—441no—
204C2×C4#6699511yescharacteristic
205C2×C4C2×#432611yescharacteristic
206C8—442no—
207C8—882no—
208C22—21no—
209C22—21no—
210C22#1062284111yescharacteristic
211C22#1062285711yescharacteristic
212C22#1062285911yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—82no—
218C4—82no—
219C4—81no—
220C4—881no—
221C4—881no—
222C2—21no—
223C2—21no—
224C2#1306759011yescharacteristic
225C2#1307062911yescharacteristic
226C2#1307063311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2844C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2844D11
hypocenterC11#12261
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2844

Complements

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

NH ≅ G/Ntype
183. C11#12261semidirect

Maximal subgroups

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

subgroupindex
#130699662
#130676572
#130666432
#130665602
C11×#28442
#1226111