Finite Group Databasebeta

← #14667105

Subgroups — #14667105

Order 2816.

324 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 55 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#13079440C211yesmaximal, characteristic
2#13070836C212yesmaximal, complemented
3#13070132C211yesmaximal, characteristic
4#13066611C212yesmaximal, complemented
5C11×#1320C211yesmaximal, characteristic
6C2×#66977—21no—
7C11×#407C2211yescharacteristic
8#10622820—21no—
9#10622750—21no—
10#10622750C2212yes—
11#10622738C2211yescharacteristic
12#10622737—21no—
13#10622352—22no—
14#10622334—22no—
15C11×#349C2212yes—
16C11⋊#338C2211yescharacteristic
17#10622155—22no—
18#10622151—22no—
19C23×C4×C11D411yescharacteristic
20C22×Dic22—21no—
21C2×C11×M16D411yescharacteristic
22C2×C11×M16C2311yescharacteristic
23C2×C22⋊Dic11—41no—
24C2×C4⋊Dic11—21no—
25#66977—22no—
26#66977—22no—
27#66977—41no—
28#66977—41no—
29C2×Dic11⋊C4—41no—
30C2×#4318—21no—
31C2×#4318—21no—
32C2×Dic44—21no—
33C2×Dic44D412yes—
34C11×M32—22no—
35C11×C22⋊C8—22no—
36C22⋊(C11⋊C8)—42no—
37#66886—42no—
38#66883—22no—
39#66881—21no—
40#66881D412yes—
41#66880—22no—
42#66880—22no—
43#12299—111nomaximal, Sylow
44C24×C11SD1611yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11—41no—
48C22×C4×C11—41no—
49C22×C4×C11SD1611yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C22×Dic11—41no—
52C22×Dic11—41no—
53C2×Dic22—22no—
54C2×Dic22—41no—
55C2×Dic22—81no—
56C2×Dic22—81no—
57C11×M16—41no—
58C11×M16—41no—
59C2×C8×C11—21no—
60C2×C8×C11C2×D412yes—
61C22⋊Dic11—42no—
62C22⋊Dic11—42no—
63C4⋊Dic11—22no—
64C4⋊Dic11—41no—
65Dic11⋊C4—42no—
66Dic11⋊C4—42no—
67#4318—41no—
68#4318—41no—
69#4318—41no—
70#4318—41no—
71C2×C11⋊C8—22no—
72C2×C11⋊C8—41no—
73Dic44—42no—
74Dic44—81no—
75C11×C16—42no—
76#3195—111no—
77#2239—112no—
78#2091—111no—
79#1342—112no—
80#1320D1111yescharacteristic
81C23×C11—21no—
82C23×C11—41no—
83C23×C11—42no—
84C23×C11C2×SD1611yescharacteristic
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—81no—
92C2×C4×C11#12011yescharacteristic
93C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11—82no—
97C2×Dic11—82no—
98Dic22—42no—
99Dic22—42no—
100Dic22—82no—
101C8×C11—22no—
102C8×C11—41no—
103C11⋊C8—42no—
104C11⋊C8—81no—
105C2×C22⋊Q8—221no—
106#483—222no—
107#470—112no—
108#470—221no—
109#451—222no—
110#430—111no—
111#430—221no—
112#407—221no—
113#407C2×D1111yescharacteristic
114#365—222no—
115#362—222no—
116#349C2×D1112yes—
117#338—111no—
118C22×C11—22no—
119C22×C11—21no—
120C22×C11—41no—
121C22×C11—41no—
122C22×C11—42no—
123C22×C11—41no—
124C22×C11—81no—
125C22×C11#45011yescharacteristic
126C4×C11—21no—
127C4×C11—41no—
128C4×C11#45311yescharacteristic
129C4×C11#45811yescharacteristic
130Dic11—82no—
131Dic11—82no—
132C22×Q8—221no—
133C23×C4D4411yescharacteristic
134C2×Q16—112no—
135C2×Q16—221no—
136C2×M16—221no—
137C2×M16—221no—
138C2×M16D4411yescharacteristic
139C2×M16C22×D1111yescharacteristic
140C22⋊Q8—222no—
141C22⋊Q8—222no—
142C22⋊Q8—441no—
143C22⋊Q8—441no—
144C2×C4⋊C4—221no—
145C2×C4⋊C4—441no—
146C2×C22⋊C4—441no—
147M32—22no—
148#108—222no—
149#108—442no—
150#106—112no—
151#106—221no—
152#103—222no—
153#103—222no—
154C22⋊C8—22no—
155C22⋊C8—442no—
156C2×C11—21no—
157C2×C11—42no—
158C2×C11—41no—
159C2×C11#161311yescharacteristic
160C24#431411yescharacteristic
161C2×Q8—222no—
162C2×Q8—441no—
163C2×Q8—881no—
164C2×Q8—881no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—441no—
170C22×C4—441no—
171C22×C4#431411yescharacteristic
172C22×C4C2×D4411yescharacteristic
173Q16—442no—
174Q16—881no—
175M16—41no—
176M16—41no—
177M16—441no—
178M16—441no—
179M16—441no—
180M16—441no—
181C2×C8—21no—
182C2×C8—222no—
183C2×C8—441no—
184C2×C8D4×D1112yes—
185C4⋊C4—222no—
186C4⋊C4—441no—
187C4⋊C4—442no—
188C4⋊C4—442no—
189C22⋊C4—442no—
190C22⋊C4—442no—
191C16—42no—
192C11#1229911yescharacteristic, complemented, Sylow
193C23—21no—
194C23—41no—
195C23—42no—
196C23C2×#431411yescharacteristic
197Q8—442no—
198Q8—442no—
199Q8—882no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—81no—
207C2×C4—442no—
208C2×C4—442no—
209C2×C4—882no—
210C2×C4—882no—
211C2×C4#6693511yescharacteristic
212C2×C4#6696111yescharacteristic
213C8—22no—
214C8—41no—
215C8—442no—
216C8—881no—
217C22—22no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22#1062234411yescharacteristic
225C4—21no—
226C4—41no—
227C4—882no—
228C4—882no—
229C4#1062235511yescharacteristic
230C4#1062236011yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1306763811yescharacteristic
subgroupG/H
centerC2#13067638
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#1320C2
socleC2×C11#1613
prime radicalC24×C11SD16
hypercenter#1320D11
hypocenterC11#12299
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #13070836C2semidirect
4. #13066611C2semidirect
192. C11#12299semidirect

Maximal subgroups

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

subgroupindex
#130794402
#130708362
#130701322
#130666112
C11×#13202
#1229911