Finite Group Databasebeta

← #14658653

Subgroups — #14658653

Order 2816.

258 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 69 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#13067391C211yesmaximal, characteristic, complemented
2#13067339C211yesmaximal, characteristic
3#13067312C211yesmaximal, characteristic
4#13067086C211yesmaximal, characteristic
5#13066526C211yesmaximal, characteristic, complemented
6#13066485C211yesmaximal, characteristic, complemented
7C11×#1287C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#431C2211yescharacteristic
12#10622539C2211yescharacteristic
13#10622537C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15#10622123—21no—
16#10622123—21no—
17#10622120—21no—
18#10622119—21no—
19#10622097—22no—
20#10622096—22no—
21C2×#4339—21no—
22C2×C42×C11C2311yescharacteristic
23#66983—21no—
24#66983—21no—
25C2×#4318—21no—
26C22×C11⋊C8—21no—
27#66928—21no—
28#66927D411yescharacteristic
29C4×D44—21no—
30C4×D44—21no—
31#66922D411yescharacteristic
32C11×C4⋊C8—21no—
33C11×C4⋊C8—21no—
34C11×C4⋊C8—21no—
35C11×C22⋊C8—21no—
36C11×C22⋊C8—21no—
37C11×C22⋊C8—21no—
38C11×#97—21no—
39C11×#97—21no—
40C4×C8×C11D412yes—
41C22⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47#66867—21no—
48#10645—111nomaximal, Sylow
49C22×C4×C11#4111yescharacteristic
50C22×C4×C11#4111yescharacteristic
51C22×C4×C11#4111yescharacteristic
52C2×C22⋊D11—41no—
53#4339—82no—
54C2×D44—21no—
55C2×D44—21no—
56C2×D44—21no—
57C2×C4×D11—41no—
58C2×Dic22—21no—
59C2×C8×C11—22no—
60C2×C8×C11—41no—
61C2×C8×C11—41no—
62C42×C11C2×D411yescharacteristic
63C42×C11C2×D411yescharacteristic
64C42×C11#4111yescharacteristic
65C42×C11#4111yescharacteristic
66(C2×D11)⋊C4—41no—
67(C2×D11)⋊C4—41no—
68C4⋊Dic11—21no—
69C4⋊Dic11—21no—
70#4318—81no—
71C2×C11⋊C8—41no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—41no—
74C2×C11⋊C8—81no—
75#1571—111no—
76#1557—111no—
77#1551—111no—
78#1496—111no—
79#1307—111no—
80#1290—111no—
81#1287D1111yescharacteristic, complemented
82C23×C11#12611yescharacteristic
83C22×D11—41no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11#12111yescharacteristic
89C2×C4×C11#12311yescharacteristic
90C2×C4×C11#12311yescharacteristic
91C2×C4×C11#12311yescharacteristic
92C2×C4×C11#12411yescharacteristic
93C2×C4×C11#12611yescharacteristic
94C22⋊D11—82no—
95C2×Dic11—41no—
96D44—41no—
97D44—41no—
98D44—81no—
99D44—81no—
100C4×D11—82no—
101Dic22—81no—
102C8×C11—42no—
103C8×C11—81no—
104C8×C11—81no—
105C11⋊C8—81no—
106C11⋊C8—81no—
107C11⋊C8—81no—
108#532—111no—
109#432—111no—
110#432C2×D1111yescharacteristic
111#432C2×D1111yescharacteristic
112#431C2×D1111yescharacteristic
113#423—111no—
114C2×C4⋊C8—111no—
115#335—222no—
116#333—221no—
117#332—221no—
118#331—221no—
119#331—221no—
120D4⋊C8—222no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—21no—
124C22×C11#39711yescharacteristic
125C2×D11—81no—
126C2×D11—81no—
127C2×D11—81no—
128C4×C11—21no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—21no—
133C4×C11#47211yescharacteristic
134C4×C11#47311yescharacteristic
135Dic11—81no—
136C2×#41—221no—
137C2×M16—221no—
138C22×C8—221no—
139C4⋊Q8—111no—
140#127—111no—
141#124—221no—
142#121—221no—
143#121—221no—
144C4×D4—221no—
145C4×D4—221no—
146C2×C42C22×D1111yescharacteristic
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—221no—
151C4⋊C8—221no—
152C4⋊C8—221no—
153C4⋊C8—221no—
154C4⋊C8—221no—
155C22⋊C8—21no—
156C22⋊C8—21no—
157C22⋊C8—21no—
158C22⋊C8—221no—
159#97—21no—
160#97—21no—
161#97—221no—
162C4×C8D4412yes—
163C2×C11—41no—
164C2×C11#207811yescharacteristic
165C2×C11#208011yescharacteristic
166C2×C11#208111yescharacteristic
167D11—161no—
168#41—882no—
169C2×Q8—221no—
170C2×D4—221no—
171C2×D4—221no—
172C2×D4—221no—
173C2×D4—441no—
174C22×C4—441no—
175C22×C4#433911yescharacteristic
176C22×C4#434111yescharacteristic
177C22×C4#434311yescharacteristic
178M16—881no—
179C2×C8—22no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—441no—
183C2×C8—441no—
184C2×C8—441no—
185C2×C8—881no—
186C4⋊C4—221no—
187C4⋊C4—221no—
188C22⋊C4—441no—
189C22⋊C4—441no—
190C42C2×D4411yescharacteristic
191C42#433911yescharacteristic
192C42D4×D1111yescharacteristic
193C42#434111yescharacteristic
194C11#1064511yescharacteristic, complemented, Sylow
195C23—441no—
196C23#6695111yescharacteristic
197Q8—881no—
198D4—441no—
199D4—441no—
200D4—881no—
201D4—881no—
202D4—882no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—441no—
208C2×C4—882no—
209C2×C4#6692811yescharacteristic
210C2×C4#6693611yescharacteristic
211C2×C4#6693611yescharacteristic
212C2×C4#6693911yescharacteristic
213C2×C4#6694811yescharacteristic
214C2×C4#6695111yescharacteristic
215C8—42no—
216C8—81no—
217C8—81no—
218C8—881no—
219C8—881no—
220C8—881no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—881no—
225C22—881no—
226C22—881no—
227C22#1062228711yescharacteristic
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—21no—
233C4—881no—
234C4#1062250911yescharacteristic
235C4#1062251011yescharacteristic
236C2—41no—
237C2—1761no—
238C2#1307005811yescharacteristic
239C2#1307006811yescharacteristic
240C2#1307007511yescharacteristic
subgroupG/H
centerC22#10622287
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1287C2
socleC22×C11#397
prime radical#10623008C22
hypercenter#1287D11
hypocenterC11#10645
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
1. #13067391C2semidirect
5. #13066526C2semidirect
6. #13066485C2semidirect
7. C11×#1287C2semidirect
81. #1287D11semidirect
194. C11#10645semidirect

Maximal subgroups

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

subgroupindex
#130673912
#130673392
#130673122
#130670862
#130665262
#130664852
C11×#12872
#1064511