Finite Group Databasebeta

← #14648283

Subgroups — #14648283

Order 2816.

412 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 111 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#13077683C211yesmaximal, characteristic
2#13069445C211yesmaximal, characteristic
3#13067405C212yesmaximal, complemented
4#13066448C212yesmaximal, complemented
5C11×#1543C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C11×#431C2212yes—
8C2×#66901—22no—
9#10622847—22no—
10#10622625—22no—
11D4×C11⋊C8—22no—
12C42×Dic11C2211yescharacteristic
13#10622538C2212yes—
14#10622537C2211yescharacteristic
15C11×#333C411yescharacteristic, complemented
16C11×#333C411yescharacteristic, complemented
17C11×#331C412yescomplemented
18#10622096—22no—
19#10622095—22no—
20C2×C11×#41D412yes—
21C11×C4⋊Q8C2×C411yescharacteristic
22C11×#127C2×C411yescharacteristic
23C11×#124Q812yes—
24C11×#121—22no—
25C4×D4×C11—22no—
26C2×C42×C11C2311yescharacteristic
27C2×C4×Dic11—21no—
28C2×C4×Dic11—22no—
29C2×#4318—22no—
30C2×#4318—21no—
31C22×C11⋊C8—22no—
32C11×C4⋊C8C2×C412yes—
33C11×C4⋊C8C2×C412yes—
34C11×C22⋊C8—22no—
35C4×C8×C11—22no—
36#66901—44no—
37C22⋊(C11⋊C8)—24no—
38C22⋊(C11⋊C8)—22no—
39C4⋊(C11⋊C8)—22no—
40C4⋊(C11⋊C8)D412yes—
41C4⋊(C11⋊C8)D412yes—
42C4×C11⋊C8—22no—
43#8935—111nomaximal, Sylow
44C11×#41—42no—
45C11×#41—42no—
46C2×Q8×C11C4⋊C412yes—
47C2×D4×C11—22no—
48C2×D4×C11—22no—
49C2×D4×C11C4⋊C412yes—
50C22×C4×C11—22no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11#4112yes—
53C22×Dic11—41no—
54C2×C8×C11—22no—
55C2×C8×C11—22no—
56C11×C4⋊C4—22no—
57C11×C22⋊C4—24no—
58C42×C11C22×C411yescharacteristic
59C42×C11C2×D412yes—
60C42×C11C2×Q811yescharacteristic
61C4×Dic11—22no—
62C4×Dic11—24no—
63C4×Dic11—42no—
64C4×Dic11—41no—
65#4318—42no—
66#4318—82no—
67C2×C11⋊C8—22no—
68C2×C11⋊C8—22no—
69C2×C11⋊C8—41no—
70C2×C11⋊C8—82no—
71#2979—111no—
72#1962—111no—
73#1574—112no—
74#1543D1111yescharacteristic
75#1276—112no—
76C23×C11—22no—
77C23×C11#12311yescharacteristic
78Q8×C11—42no—
79D4×C11—42no—
80D4×C11—42no—
81D4×C11—42no—
82D4×C11—82no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11C2×C4⋊C411yescharacteristic
91C2×C4×C11C4×D412yes—
92C2×C4×C11#12011yescharacteristic
93C2×C4×C11C22⋊Q812yes—
94C2×Dic11—42no—
95C2×Dic11—44no—
96C8×C11—42no—
97C8×C11—42no—
98C11⋊C8—42no—
99C11⋊C8—42no—
100C11⋊C8—81no—
101#532C2×D1111yescharacteristic
102#436—222no—
103C8×D4—222no—
104#431—112no—
105#431C2×D1112yes—
106#423—111no—
107C2×#104—222no—
108#408—222no—
109C43—111no—
110#335—222no—
111#334—222no—
112#333Dic1111yescharacteristic, complemented
113#333Dic1111yescharacteristic, complemented
114#331Dic1112yescomplemented
115C22×C11—21no—
116C22×C11—22no—
117C22×C11—42no—
118C22×C11—44no—
119C22×C11#38511yescharacteristic
120C4×C11—21no—
121C4×C11—22no—
122C4×C11—42no—
123C4×C11#44312yes—
124C4×C11#44412yes—
125C4×C11#45311yescharacteristic
126C4×C11#45511yescharacteristic
127Dic11—44no—
128C2×#41D4412yes—
129C2×M16—222no—
130C2×M16—221no—
131C22×C8—222no—
132C4⋊Q8C2×Dic1111yescharacteristic
133#127C2×Dic1111yescharacteristic
134#124Dic2212yes—
135#121—22no—
136C4×D4—22no—
137C2×C42—221no—
138C2×C42—222no—
139C2×C42C22×D1111yescharacteristic
140C4⋊C8—112no—
141C4⋊C8—112no—
142C4⋊C8—222no—
143C4⋊C8C2×Dic1112yes—
144C4⋊C8C2×Dic1112yes—
145#104—444no—
146C22⋊C8—22no—
147C22⋊C8—224no—
148C22⋊C8—222no—
149C4×C8—22no—
150C4×C8—222no—
151C2×C11—41no—
152C2×C11—82no—
153C2×C11#185611yescharacteristic
154C2×C11#186612yes—
155#41—42no—
156#41—42no—
157C2×Q8C4⋊Dic1112yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4C4⋊Dic1112yes—
161C22×C4—22no—
162C22×C4—441no—
163C22×C4C2×D4411yescharacteristic
164C22×C4#434112yes—
165M16—442no—
166M16—882no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—222no—
170C2×C8—222no—
171C2×C8—441no—
172C2×C8—882no—
173C4⋊C4—22no—
174C22⋊C4—24no—
175C42—222no—
176C42—224no—
177C42—442no—
178C42—441no—
179C42C2×Dic2211yescharacteristic
180C42D4×D1112yes—
181C42C22×Dic1111yescharacteristic
182C11#893511yescharacteristic, complemented, Sylow
183C23—22no—
184C23#6693911yescharacteristic
185Q8—42no—
186D4—42no—
187D4—42no—
188D4—42no—
189D4—82no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—442no—
198C2×C4—444no—
199C2×C4#6693112yes—
200C2×C4#6693511yescharacteristic
201C2×C4C2×C4⋊Dic1111yescharacteristic
202C2×C4D4×Dic1112yes—
203C8—42no—
204C8—42no—
205C8—442no—
206C8—442no—
207C8—881no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—44no—
212C22#1062256311yescharacteristic
213C4—21no—
214C4—22no—
215C4—42no—
216C4—444no—
217C4#1062235911yescharacteristic
218C4#1062236011yescharacteristic
219C4#1062280912yes—
220C4#1062281012yes—
221C2—41no—
222C2—82no—
223C2#1306882811yescharacteristic
224C2#1306889312yes—
subgroupG/H
centerC2×C4#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1543C2
socleC22×C11#385
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1543D11
hypocenterC11#8935
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
3. #13067405C2semidirect
4. #13066448C2semidirect
15. C11×#333C4semidirect
16. C11×#333C4semidirect
17. C11×#331C4semidirect
112. #333Dic11semidirect
113. #333Dic11semidirect
114. #331Dic11semidirect
182. C11#8935semidirect

Maximal subgroups

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

subgroupindex
#130776832
#130694452
#130674052
#130664482
C11×#15432
#893511