Finite Group Databasebeta

← #14658658

Subgroups — #14658658

Order 2816.

236 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 71 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
2#13067346C211yesmaximal, characteristic
3#13067316C211yesmaximal, characteristic
4#13066526C211yesmaximal, characteristic
5#13066485C211yesmaximal, characteristic
6#13066478C211yesmaximal, characteristic
7C11×#1497C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#431C2211yescharacteristic
11#10622539C2211yescharacteristic
12#10622539C2211yescharacteristic
13#10622537C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C11×Q8⋊C8—22no—
16#10622185—21no—
17#10622185—21no—
18#10622185—21no—
19#10622184—21no—
20#10622096—22no—
21C11×C4⋊Q8D411yescharacteristic
22C11×C4⋊Q8D411yescharacteristic
23C11×#125—21no—
24C11×C22⋊Q8—21no—
25C11×C22⋊Q8—21no—
26C4×Q8×C11—21no—
27C4×Q8×C11—21no—
28C11×#117—21no—
29C2×C42×C11C2311yescharacteristic
30C2×#4318—21no—
31C22×C11⋊C8—21no—
32C11×C4⋊C8—21no—
33C11×C4⋊C8—21no—
34C11×C22⋊C8—21no—
35C11×C22⋊C8—21no—
36C11×#97—21no—
37C4×C8×C11D412yes—
38C22⋊(C11⋊C8)—21no—
39C22⋊(C11⋊C8)—21no—
40C4⋊(C11⋊C8)—21no—
41C4⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46#66867—21no—
47#66867—21no—
48#10646—111nomaximal, Sylow
49C2×Q8×C11—21no—
50C2×Q8×C11—21no—
51C22×C4×C11#4111yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C2×C8×C11—22no—
55C2×C8×C11—41no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4—21no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—41no—
62C11×C22⋊C4—41no—
63C42×C11—41no—
64C42×C11C2×D411yescharacteristic
65C42×C11C2×D411yescharacteristic
66C42×C11#4111yescharacteristic
67C42×C11#4111yescharacteristic
68#4318—81no—
69C2×C11⋊C8—41no—
70C2×C11⋊C8—41no—
71C2×C11⋊C8—41no—
72C2×C11⋊C8—41no—
73C2×C11⋊C8—81no—
74#1571—111no—
75#1559—111no—
76#1552—111no—
77#1497D1111yescharacteristic
78#1307—111no—
79#1290—111no—
80#1287—111no—
81C23×C11#12611yescharacteristic
82Q8×C11—41no—
83Q8×C11—41no—
84Q8×C11—81no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11#12111yescharacteristic
92C2×C4×C11#12311yescharacteristic
93C2×C4×C11#12311yescharacteristic
94C2×C4×C11#12311yescharacteristic
95C2×C4×C11#12411yescharacteristic
96C2×C4×C11#12611yescharacteristic
97C8×C11—42no—
98C8×C11—81no—
99C11⋊C8—81no—
100C11⋊C8—81no—
101C11⋊C8—81no—
102C11⋊C8—81no—
103#533C2×D1111yescharacteristic
104#432—111no—
105#432—111no—
106#432C2×D1111yescharacteristic
107#431C2×D1111yescharacteristic
108#423—111no—
109C2×C4⋊C8—111no—
110#335—222no—
111#333—221no—
112#332—221no—
113#332—221no—
114#332—221no—
115Q8⋊C8—22no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11#39711yescharacteristic
120C4×C11—21no—
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—21no—
125C4×C11—81no—
126C4×C11—81no—
127C4×C11#47211yescharacteristic
128C4×C11#47311yescharacteristic
129C2×M16—221no—
130C22×C8—221no—
131C4⋊Q8D4411yescharacteristic
132C4⋊Q8D4411yescharacteristic
133#125—21no—
134C22⋊Q8—21no—
135C22⋊Q8—21no—
136C4×Q8—21no—
137C4×Q8—21no—
138#117—21no—
139C2×C42C22×D1111yescharacteristic
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8—221no—
143C4⋊C8—221no—
144C4⋊C8—221no—
145C4⋊C8—221no—
146C4⋊C8—221no—
147C4⋊C8—221no—
148C22⋊C8—21no—
149C22⋊C8—21no—
150C22⋊C8—221no—
151C22⋊C8—221no—
152#97—21no—
153#97—221no—
154#97—221no—
155C4×C8C22⋊D1112yes—
156C2×C11—41no—
157C2×C11#207811yescharacteristic
158C2×C11#208011yescharacteristic
159C2×C11#208211yescharacteristic
160C2×Q8—21no—
161C2×Q8—21no—
162C22×C4#433911yescharacteristic
163C22×C4#434111yescharacteristic
164C22×C4#434111yescharacteristic
165M16—881no—
166C2×C8—22no—
167C2×C8—41no—
168C2×C8—441no—
169C2×C8—441no—
170C2×C8—441no—
171C2×C8—441no—
172C2×C8—881no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C22⋊C4—41no—
180C42—41no—
181C42C2×D4411yescharacteristic
182C42#434111yescharacteristic
183C42#434111yescharacteristic
184C42C2×C22⋊D1111yescharacteristic
185C11#1064611yescharacteristic, complemented, Sylow
186C23#6693211yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—81no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4#6693211yescharacteristic
197C2×C4#6693911yescharacteristic
198C2×C4#6693911yescharacteristic
199C2×C4#6698311yescharacteristic
200C2×C4#6698811yescharacteristic
201C2×C4#6698911yescharacteristic
202C8—42no—
203C8—81no—
204C8—881no—
205C8—881no—
206C8—881no—
207C8—881no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1062256611yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—81no—
218C4—81no—
219C4#1062275511yescharacteristic
220C4#1062275611yescharacteristic
221C2—41no—
222C2#1307005611yescharacteristic
223C2#1307006611yescharacteristic
224C2#1307008011yescharacteristic
subgroupG/H
centerC22#10622566
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1497C2
socleC22×C11#397
prime radicalC23×C11#126
hypercenter#1497D11
hypocenterC11#10646
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
185. C11#10646semidirect

Maximal subgroups

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

subgroupindex
#130673912
#130673462
#130673162
#130665262
#130664852
#130664782
C11×#14972
#1064611