Finite Group Databasebeta

← #14651291

Subgroups — #14651291

Order 2816.

488 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077687C211yesmaximal, characteristic
2#13067333C212yesmaximal, complemented
3#13067251C211yesmaximal, characteristic
4#13066488C212yesmaximal, complemented
5C11×#3152C211yesmaximal, characteristic
6C2×C11×#137—22no—
7C11×#532C2211yescharacteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C11×#497—22no—
10C11×#494C412yes—
11C11×#492C412yes—
12C4×C11×M16C2211yescharacteristic
13#10622847—22no—
14#10622624—24no—
15#10622539C2212yes—
16#10622539C2212yes—
17#10622185—24no—
18#10622178—22no—
19C2×C11×#41D412yes—
20C22×Q8×C11—21no—
21C11×#137—44no—
22C11×#137—44no—
23C2×C11×Q16—24no—
24C2×C11×SD16—24no—
25C2×C11×M16—21no—
26C11×C4⋊Q8—22no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8C2×C412yes—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#127C2×C411yescharacteristic
31C11×#124D412yes—
32C11×#121—22no—
33C4×D4×C11—22no—
34C2×C11×C4⋊C4—22no—
35C2×C42×C11C2311yescharacteristic
36C2×#4318—22no—
37C22×C11⋊C8—22no—
38C11×#97—21no—
39C4×C8×C11C2×C412yes—
40C22⋊(C11⋊C8)—24no—
41C22⋊(C11⋊C8)—22no—
42C22⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)D414yes—
45#66867—22no—
46#66867—22no—
47#9421—111nomaximal, Sylow
48C11×#41—42no—
49C11×#41—42no—
50C2×Q8×C11—22no—
51C2×Q8×C11—42no—
52C2×Q8×C11—42no—
53C2×Q8×C11—41no—
54C2×Q8×C11C22⋊C412yes—
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11C22⋊C412yes—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11#4112yes—
62C11×Q16—48no—
63C11×SD16—48no—
64C11×M16—24no—
65C2×C8×C11—22no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—24no—
68C11×C4⋊C4—42no—
69C11×C22⋊C4—24no—
70C42×C11C22×C411yescharacteristic
71C42×C11C2×D411yescharacteristic
72C42×C11C2×D412yes—
73#4318—82no—
74C2×C11⋊C8—24no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—82no—
77#3152D1111yescharacteristic
78#2980—111no—
79#1556—112no—
80#1536—111no—
81#1291—112no—
82C23×C11—22no—
83C23×C11#12311yescharacteristic
84Q8×C11—42no—
85Q8×C11—44no—
86Q8×C11—82no—
87D4×C11—42no—
88D4×C11—82no—
89D4×C11—82no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—81no—
97C2×C4×C11—81no—
98C2×C4×C11C2×C22⋊C411yescharacteristic
99C2×C4×C11C4×D412yes—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11#12112yes—
102C8×C11—24no—
103C11⋊C8—44no—
104C11⋊C8—82no—
105C2×#137—22no—
106#532C2×D1111yescharacteristic
107C2×C4⋊Q8C2×D1111yescharacteristic
108#497—22no—
109#494Dic1112yes—
110#492Dic1112yes—
111#435—224no—
112#432—112no—
113#432—112no—
114#408—222no—
115C4×M16C2×D1111yescharacteristic
116#332—224no—
117#329—222no—
118C22×C11—21no—
119C22×C11—22no—
120C22×C11—42no—
121C22×C11—44no—
122C22×C11#38611yescharacteristic
123C4×C11—21no—
124C4×C11—22no—
125C4×C11—22no—
126C4×C11—42no—
127C4×C11—82no—
128C4×C11#45312yes—
129C2×#41C22⋊D1112yes—
130C22×Q8—21no—
131#137—44no—
132#137—44no—
133C2×Q16—24no—
134C2×SD16—24no—
135C2×M16—21no—
136C2×M16—222no—
137C22×C8—222no—
138C4⋊Q8—22no—
139C4⋊Q8—21no—
140C4⋊Q8C2×Dic1112yes—
141C4⋊Q8C2×Dic1111yescharacteristic
142#127C2×Dic1111yescharacteristic
143#124C22⋊D1112yes—
144#121—22no—
145C4×D4—22no—
146C2×C4⋊C4—22no—
147C2×C42C22×D1111yescharacteristic
148C4⋊C8—114no—
149C4⋊C8—222no—
150C22⋊C8—224no—
151C22⋊C8—222no—
152C22⋊C8—222no—
153#97—21no—
154#97—222no—
155#97—222no—
156C4×C8C2×Dic1112yes—
157C2×C11—41no—
158C2×C11—82no—
159C2×C11#188711yescharacteristic
160C2×C11#190212yes—
161#41—42no—
162#41—42no—
163C2×Q8—22no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C2×Q8C22⋊Dic1112yes—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4C22⋊Dic1112yes—
171C22×C4—22no—
172C22×C4—41no—
173C22×C4#434112yes—
174C22×C4C2×C22⋊D1111yescharacteristic
175Q16—48no—
176SD16—48no—
177M16—24no—
178M16—882no—
179C2×C8—22no—
180C2×C8—224no—
181C2×C8—442no—
182C2×C8—882no—
183C4⋊C4—22no—
184C4⋊C4—24no—
185C4⋊C4—42no—
186C22⋊C4—24no—
187C42D4×D1112yes—
188C42C22×Dic1111yescharacteristic
189C42C2×C22⋊D1111yescharacteristic
190C11#942111yescharacteristic, complemented, Sylow
191C23—22no—
192C23#6698811yescharacteristic
193Q8—42no—
194Q8—44no—
195Q8—82no—
196D4—42no—
197D4—82no—
198D4—82no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4D4×Dic1112yes—
208C2×C4#6699011yescharacteristic
209C2×C4#6699212yes—
210C2×C4C2×C22⋊Dic1111yescharacteristic
211C8—24no—
212C8—444no—
213C8—882no—
214C22—22no—
215C22—21no—
216C22—44no—
217C22—42no—
218C22#1062283311yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—42no—
223C4—82no—
224C4#1062269012yes—
225C2—41no—
226C2—82no—
227C2#1306901511yescharacteristic
228C2#1306909112yes—
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3152C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#3152D11
hypocenterC11#9421
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. #13067333C2semidirect
4. #13066488C2semidirect
190. C11#9421semidirect

Maximal subgroups

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

subgroupindex
#130776872
#130673332
#130672512
#130664882
C11×#31522
#942111