Finite Group Databasebeta

← #14651373

Subgroups — #14651373

Order 2816.

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

normal subgroups only

This group has 504 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#13067351C211yesmaximal, characteristic
3#13067301C212yesmaximal, complemented
4#13066506C212yesmaximal, complemented
5C11×#3152C211yesmaximal, characteristic
6C2×C11×#137—22no—
7C11×#532C2211yescharacteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C11×#497C414yes—
10C11×#494—21no—
11C11×#492—21no—
12C4×C11×M16C2211yescharacteristic
13#10622847—22no—
14#10622625—22no—
15D4×C11⋊C8—22no—
16#10622538C2212yes—
17#10622537C2212yes—
18#10622185—22no—
19#10622185—22no—
20#10622184—21no—
21#10622182—21no—
22C2×C11×#41D412yes—
23C22×Q8×C11—21no—
24C11×#137—44no—
25C11×#137—44no—
26C2×C11×Q16—24no—
27C2×C11×SD16—24no—
28C2×C11×M16—21no—
29C11×C4⋊Q8—22no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8C2×C412yes—
32C11×C4⋊Q8D411yescharacteristic
33C11×#127D411yescharacteristic
34C11×#124C2×C412yes—
35C11×#121—22no—
36C4×D4×C11—22no—
37C2×C11×C4⋊C4—22no—
38C2×C42×C11C2311yescharacteristic
39C2×#4318—22no—
40C2×#4318—22no—
41C22×C11⋊C8—22no—
42C11×#97C2×C412yes—
43C4×C8×C11—21no—
44C22⋊(C11⋊C8)—24no—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)D412yes—
49C4⋊(C11⋊C8)D412yes—
50C4×C11⋊C8—22no—
51#9435—111nomaximal, Sylow
52C11×#41—42no—
53C11×#41—42no—
54C2×Q8×C11—22no—
55C2×Q8×C11—42no—
56C2×Q8×C11—42no—
57C2×Q8×C11—41no—
58C2×Q8×C11C22⋊C412yes—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11C22⋊C412yes—
62C22×C4×C11—22no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11#4112yes—
66C11×Q16—48no—
67C11×SD16—48no—
68C11×M16—22no—
69C11×M16—22no—
70C2×C8×C11—22no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—24no—
73C11×C4⋊C4—42no—
74C11×C22⋊C4—24no—
75C42×C11C22×C411yescharacteristic
76C42×C11C2×D411yescharacteristic
77C42×C11C2×D412yes—
78#4318—82no—
79#4318—82no—
80C2×C11⋊C8—22no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—82no—
84#3152D1111yescharacteristic
85#2979—111no—
86#1560—111no—
87#1549—112no—
88#1299—112no—
89C23×C11—22no—
90C23×C11#12311yescharacteristic
91Q8×C11—42no—
92Q8×C11—44no—
93Q8×C11—81no—
94Q8×C11—81no—
95D4×C11—42no—
96D4×C11—42no—
97D4×C11—42no—
98D4×C11—82no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—82no—
108C2×C4×C11C2×C22⋊C411yescharacteristic
109C2×C4×C11C4×D412yes—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11#12112yes—
112C8×C11—24no—
113C11⋊C8—42no—
114C11⋊C8—42no—
115C11⋊C8—82no—
116C2×#137—22no—
117#532C2×D1111yescharacteristic
118C2×C4⋊Q8C2×D1111yescharacteristic
119#497Dic1114yes—
120#494—21no—
121#492—21no—
122#436—222no—
123C8×D4—222no—
124#431—112no—
125#423—112no—
126#408—222no—
127C4×M16C2×D1111yescharacteristic
128#333—221no—
129#332—222no—
130#332—222no—
131#331—221no—
132C22×C11—21no—
133C22×C11—22no—
134C22×C11—42no—
135C22×C11—44no—
136C22×C11#38611yescharacteristic
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—42no—
140C4×C11—82no—
141C4×C11#45311yescharacteristic
142C4×C11#45311yescharacteristic
143C4×C11#47112yes—
144C4×C11#47312yes—
145C2×#41C22⋊D1112yes—
146C22×Q8—21no—
147#137—44no—
148#137—44no—
149C2×Q16—24no—
150C2×SD16—24no—
151C2×M16—21no—
152C2×M16—222no—
153C2×M16—222no—
154C22×C8—222no—
155C4⋊Q8—22no—
156C4⋊Q8—21no—
157C4⋊Q8C2×Dic1112yes—
158C4⋊Q8C22⋊D1111yescharacteristic
159#127C22⋊D1111yescharacteristic
160#124C2×Dic1112yes—
161#121—22no—
162C4×D4—22no—
163C2×C4⋊C4—22no—
164C2×C42C22×D1111yescharacteristic
165C4⋊C8—112no—
166C4⋊C8—112no—
167C4⋊C8—222no—
168C4⋊C8—222no—
169C22⋊C8—224no—
170C22⋊C8—222no—
171#97C2×Dic1112yes—
172C4×C8—21no—
173C4×C8—222no—
174C2×C11—41no—
175C2×C11—82no—
176C2×C11#188711yescharacteristic
177C2×C11#190812yes—
178#41—42no—
179#41—42no—
180C2×Q8—22no—
181C2×Q8—42no—
182C2×Q8—42no—
183C2×Q8—41no—
184C2×Q8C22⋊Dic1112yes—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4C22⋊Dic1112yes—
188C22×C4—22no—
189C22×C4—41no—
190C22×C4#434112yes—
191C22×C4C2×C22⋊D1111yescharacteristic
192Q16—48no—
193SD16—48no—
194M16—22no—
195M16—22no—
196M16—882no—
197M16—882no—
198C2×C8—22no—
199C2×C8—222no—
200C2×C8—222no—
201C2×C8—442no—
202C2×C8—882no—
203C4⋊C4—22no—
204C4⋊C4—24no—
205C4⋊C4—42no—
206C22⋊C4—24no—
207C42D4×D1112yes—
208C42C22×Dic1111yescharacteristic
209C42C2×C22⋊D1111yescharacteristic
210C11#943511yescharacteristic, complemented, Sylow
211C23—22no—
212C23#6698811yescharacteristic
213Q8—42no—
214Q8—44no—
215Q8—81no—
216Q8—81no—
217D4—42no—
218D4—42no—
219D4—42no—
220D4—82no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4D4×Dic1112yes—
231C2×C4#6699011yescharacteristic
232C2×C4#6699212yes—
233C2×C4C2×C22⋊Dic1111yescharacteristic
234C8—24no—
235C8—442no—
236C8—442no—
237C8—882no—
238C22—22no—
239C22—21no—
240C22—44no—
241C22—42no—
242C22#1062283311yescharacteristic
243C4—22no—
244C4—21no—
245C4—42no—
246C4—82no—
247C4#1062269011yescharacteristic
248C4#1062269011yescharacteristic
249C4#1062281612yes—
250C4#1062281712yes—
251C2—41no—
252C2—82no—
253C2#1306901511yescharacteristic
254C2#1306913312yes—
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3152C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#3152D11
hypocenterC11#9435
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
3. #13067301C2semidirect
4. #13066506C2semidirect
210. C11#9435semidirect

Maximal subgroups

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

subgroupindex
#130776832
#130673512
#130673012
#130665062
C11×#31522
#943511