Finite Group Databasebeta

← #14671243

Subgroups — #14671243

Order 2816.

454 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 131 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#13081719C211yesmaximal, characteristic
2C2×#10622203C212yesmaximal, complemented
3#13068666C211yesmaximal, characteristic
4#13066732C212yesmaximal, complemented
5C11×#3059C211yesmaximal, characteristic
6C22×C11×Q16C2211yescharacteristic
7C2×C11×#131C2211yescharacteristic
8C11×#536—21no—
9C11×#470C414yes—
10C11×#467—22no—
11C11×#427C2211yescharacteristic
12C11×#419—21no—
13#10622850—21no—
14#10622753—24no—
15C2×#66883C2212yes—
16C2×#66876—22no—
17C2×#66876C2212yes—
18#10622203—24no—
19C11⋊#338—21no—
20C2×C11×#41D411yescharacteristic
21C22×Q8×C11—21no—
22C2×C11×Q16—22no—
23C2×C11×Q16—21no—
24C2×C11×Q16—22no—
25C2×C11×Q16C2×C412yes—
26C11×#131—22no—
27C11×#131—22no—
28C2×C11×M16C2×C412yes—
29C2×C11×M16D411yescharacteristic
30C22×C8×C11D412yes—
31C22×C8×C11C2311yescharacteristic
32C11×C4⋊Q8—41no—
33C11×#124—41no—
34C11×#123—42no—
35C11×C22⋊Q8—24no—
36C11×#117—21no—
37C2×#4318—22no—
38C11×#107—21no—
39C11×#106C2×C412yes—
40C11×#103—24no—
41#66900—41no—
42#66897—41no—
43#66883—22no—
44#66883—22no—
45#66876—24no—
46#66876—22no—
47#66876D414yes—
48C2×C11⋊C16—24no—
49C2×C11⋊C16—22no—
50#13078—111nomaximal, Sylow
51C11×#41—22no—
52C11×#41—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—41no—
55C2×Q8×C11—42no—
56C2×Q8×C11—42no—
57C2×Q8×C11D811yescharacteristic
58C2×D4×C11D811yescharacteristic
59C2×D4×C11SD1612yes—
60C22×C4×C11—41no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C2×D411yescharacteristic
63C11×Q16—24no—
64C11×Q16—41no—
65C11×Q16—41no—
66C11×M16—24no—
67C11×M16—22no—
68C2×C8×C11—22no—
69C2×C8×C11—22no—
70C2×C8×C11C22⋊C412yes—
71C2×C8×C11C22×C411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D412yes—
74C2×C8×C11#4112yes—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—44no—
77C11×C22⋊C4—44no—
78C11×C22⋊C4—41no—
79C42×C11—41no—
80#4318—42no—
81#4318—42no—
82C2×C11⋊C8—42no—
83C11⋊C16—24no—
84#3407—111no—
85#3059D1111yescharacteristic
86C2×#362—112no—
87#1813—111no—
88#1389—112no—
89C23×C11#10212yes—
90C23×C11C2×SD1611yescharacteristic
91Q8×C11—22no—
92Q8×C11—42no—
93Q8×C11—42no—
94Q8×C11—82no—
95D4×C11—24no—
96D4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—82no—
102C2×C4×C11#10212yes—
103C2×C4×C11C2×C22⋊C411yescharacteristic
104C2×C4×C11#12112yes—
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11#13512yes—
107C8×C11—22no—
108C8×C11C4×D412yes—
109C8×C11#12011yescharacteristic
110C8×C11#12311yescharacteristic
111C11⋊C8—82no—
112C22×Q16C2×D1111yescharacteristic
113C2×#131C2×D1111yescharacteristic
114#536—21no—
115#504—224no—
116C2×M32—112no—
117C2×M32—222no—
118#470Dic1114yes—
119#467—22no—
120C2×#108—112no—
121#427C2×D1111yescharacteristic
122#419—21no—
123#413—221no—
124#362—224no—
125#338—221no—
126C22×C11—22no—
127C22×C11—41no—
128C22×C11—42no—
129C22×C11C2×#10211yescharacteristic
130C22×C11#46512yes—
131C4×C11—22no—
132C4×C11—82no—
133C4×C11—82no—
134C4×C11#38611yescharacteristic
135C4×C11#41611yescharacteristic
136C4×C11#46612yes—
137C2×#41C22⋊D1111yescharacteristic
138C22×Q8—21no—
139C2×Q16—22no—
140C2×Q16—22no—
141C2×Q16—21no—
142C2×Q16C2×Dic1112yes—
143#131—22no—
144#131—22no—
145C2×M16—222no—
146C2×M16C2×Dic1112yes—
147C2×M16C22⋊D1111yescharacteristic
148C22×C8C22⋊D1112yes—
149C22×C8C22×D1111yescharacteristic
150C4⋊Q8—41no—
151#124—41no—
152#123—42no—
153C22⋊Q8—24no—
154#117—21no—
155M32—114no—
156M32—224no—
157M32—222no—
158C2×C16—224no—
159C2×C16—222no—
160#108—222no—
161#108—222no—
162#107—21no—
163#106C2×Dic1112yes—
164#103—24no—
165#101—441no—
166#100—441no—
167C2×C11—21no—
168C2×C11—22no—
169C2×C11—42no—
170C2×C11#189311yescharacteristic
171#41—22no—
172#41—22no—
173C2×Q8—22no—
174C2×Q8—41no—
175C2×Q8—42no—
176C2×Q8—42no—
177C2×Q8#432311yescharacteristic
178C2×D4#432311yescharacteristic
179C2×D4#432412yes—
180C22×C4—41no—
181C22×C4C22⋊Dic1112yes—
182C22×C4C2×C22⋊D1111yescharacteristic
183Q16—24no—
184Q16—41no—
185Q16—41no—
186M16—22no—
187M16—24no—
188M16—442no—
189M16—442no—
190C2×C8—22no—
191C2×C8—22no—
192C2×C8—442no—
193C2×C8C22⋊Dic1112yes—
194C2×C8D4×D1112yes—
195C2×C8#434112yes—
196C2×C8C22×Dic1111yescharacteristic
197C2×C8C2×C22⋊D1111yescharacteristic
198C4⋊C4—22no—
199C4⋊C4—44no—
200C22⋊C4—44no—
201C22⋊C4—41no—
202C42—41no—
203C16—224no—
204C11#1307811yescharacteristic, complemented, Sylow
205C23#6689612yes—
206C23C2×#432411yescharacteristic
207Q8—22no—
208Q8—42no—
209Q8—42no—
210Q8—82no—
211D4—24no—
212D4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4#6689612yes—
219C2×C4C2×#432311yescharacteristic
220C2×C4#6699212yes—
221C2×C4#6700312yes—
222C2×C4C2×C22⋊Dic1111yescharacteristic
223C8—22no—
224C8—882no—
225C8D4×Dic1112yes—
226C8#6698811yescharacteristic
227C8#6699011yescharacteristic
228C22—22no—
229C22—41no—
230C22—42no—
231C22#1062265412yes—
232C22C2×#6689611yescharacteristic
233C4—22no—
234C4—82no—
235C4—82no—
236C4#1062265112yes—
237C4#1062283311yescharacteristic
238C4#1062284611yescharacteristic
239C2—21no—
240C2—22no—
241C2—42no—
242C2#1306904511yescharacteristic
subgroupG/H
centerC2#13069045
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#3059C2
socleC2×C11#1893
prime radicalC2×C11×#41D4
cosocleC22×C8×C11C23
hypercenter#3059D11
hypocenterC11#13078
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3059

Complements

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

NH ≅ G/Ntype
2. C2×#10622203C2semidirect
4. #13066732C2semidirect
204. C11#13078semidirect

Maximal subgroups

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

subgroupindex
#130817192
C2×#106222032
#130686662
#130667322
C11×#30592
#1307811