Finite Group Databasebeta

← #14652881

Subgroups — #14652881

Order 2816.

486 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 155 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#13076994C211yesmaximal, characteristic
2#13068768C211yesmaximal, characteristic
3C2×#10622120C212yesmaximal
4C2×#10622124C212yesmaximal
5C11×#1767C211yesmaximal, characteristic
6C2×#66922C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C2×C11×C4⋊C8C2212yes—
9C2×C11×#97—21no—
10C43×C11C2211yescharacteristic
11#10622549C414yes—
12#10622542—22no—
13#10622542—21no—
14#10622542—21no—
15C2×C4⋊(C11⋊C8)—22no—
16C2×C4⋊(C11⋊C8)C2212yes—
17C11×#336—21no—
18#10622124—24no—
19#10622120—24no—
20C22×Dic22—21no—
21C22×Dic22—21no—
22C22×C8×C11—22no—
23C2×C42×C11C2×C412yes—
24C2×C42×C11D412yes—
25C2×C42×C11D411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11C2×C412yes—
31C2×C4⋊Dic11C2×C412yes—
32C22×C11⋊C8—22no—
33#66922—22no—
34#66922—22no—
35#66922—22no—
36#66922—22no—
37C11×C4⋊C8—22no—
38C11×C4⋊C8D414yes—
39C11×#97—42no—
40C11⋊#95—24no—
41C11⋊#95—24no—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—44no—
45#9708—111nomaximal, Sylow
46C22×C4×C11C22⋊C412yes—
47C22×C4×C11C22⋊C412yes—
48C22×C4×C11C22×C411yescharacteristic
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C22×Dic11—22no—
52C22×Dic11—22no—
53C2×Dic22—42no—
54C2×Dic22—41no—
55C2×Dic22—41no—
56C2×Dic22—42no—
57C2×Dic22—42no—
58C2×Dic22—41no—
59C2×Dic22—42no—
60C2×Dic22—41no—
61C2×C8×C11—24no—
62C2×C8×C11—42no—
63C2×C8×C11—42no—
64C42×C11—24no—
65C42×C11—22no—
66C42×C11—22no—
67C42×C11—21no—
68C42×C11—22no—
69C42×C11—21no—
70C42×C11C2×D412yes—
71C42×C11#4112yes—
72C4⋊Dic11—24no—
73C4⋊Dic11—24no—
74C4⋊Dic11—42no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—44no—
79#2862—111no—
80#1842—111no—
81#1767D1111yescharacteristic
82C2×#332—112no—
83C2×#332—112no—
84C23×C11C2×C22⋊C411yescharacteristic
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11#10114yes—
92C2×C4×C11C4×D412yes—
93C2×C4×C11#12112yes—
94C2×C4×C11#12411yescharacteristic
95C2×C4×C11#12711yescharacteristic
96C2×C4×C11#13512yes—
97C2×C4×C11AGL(1,ℤ/8)12yes—
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C11#13712yes—
100C2×C4×C11#13711yescharacteristic
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—44no—
105C2×Dic11—42no—
106Dic22—82no—
107Dic22—82no—
108Dic22—82no—
109Dic22—81no—
110Dic22—81no—
111C8×C11—44no—
112C11⋊C8—82no—
113C2×C4⋊Q8—111no—
114C2×C4⋊Q8—111no—
115C2×C4⋊C8—112no—
116C2×C4⋊C8—222no—
117C2×C4⋊C8C2×D1112yes—
118C2×#97—21no—
119#391—222no—
120#391—221no—
121#391—221no—
122#382—114no—
123C43C2×D1111yescharacteristic
124#336—21no—
125#332—224no—
126#332—224no—
127C22×C11#39011yescharacteristic
128C22×C11C2×#10112yes—
129C22×C11#41611yescharacteristic
130C22×C11#41712yes—
131C22×C11#41711yescharacteristic
132C4×C11—24no—
133C4×C11—22no—
134C4×C11—42no—
135C4×C11#46312yes—
136C4×C11#46412yes—
137C4×C11#48912yes—
138C4×C11#49611yescharacteristic
139C4×C11#49711yescharacteristic
140Dic11—82no—
141Dic11—82no—
142C22×Q8—221no—
143C22×Q8—221no—
144C22×C8—22no—
145C22×C8—222no—
146C4⋊Q8—222no—
147C4⋊Q8—222no—
148C4⋊Q8—222no—
149C4⋊Q8—222no—
150C2×C4⋊C4—112no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4—221no—
154C2×C42C4×D1112yes—
155C2×C42D4412yes—
156C2×C42C22⋊D1111yescharacteristic
157C2×C42C22⋊D1111yescharacteristic
158C2×C42C22×D1111yescharacteristic
159C4⋊C8—22no—
160C4⋊C8—222no—
161C4⋊C8—222no—
162C4⋊C8—444no—
163C4⋊C8D4414yes—
164#97—42no—
165#95—224no—
166#95—224no—
167C2×C11#155212yes—
168C2×C11#156112yes—
169C2×C11#195911yescharacteristic
170C2×C11#196611yescharacteristic
171C2×C11#198311yescharacteristic
172C2×Q8—441no—
173C2×Q8—441no—
174C2×Q8—442no—
175C2×Q8—442no—
176C2×Q8—442no—
177C2×Q8—441no—
178C2×Q8—441no—
179C2×Q8—442no—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4(C2×D11)⋊C412yes—
183C22×C4(C2×D11)⋊C412yes—
184C22×C4C2×C4×D1111yescharacteristic
185C22×C4C2×D4411yescharacteristic
186C22×C4C2×C22⋊D1111yescharacteristic
187C2×C8—24no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—442no—
191C2×C8—444no—
192C4⋊C4—224no—
193C4⋊C4—224no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C4⋊C4—442no—
197C42—24no—
198C42—22no—
199C42—22no—
200C42—21no—
201C42—21no—
202C42—22no—
203C42C2×D4412yes—
204C42#433912yes—
205C11#970811yescharacteristic, complemented, Sylow
206C23C2×(C2×D11)⋊C411yescharacteristic
207Q8—881no—
208Q8—882no—
209Q8—881no—
210Q8—882no—
211Q8—882no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—444no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4#6688814yes—
224C2×C4C4×D4412yes—
225C2×C4#6692711yescharacteristic
226C2×C4#6692811yescharacteristic
227C2×C4#6696112yes—
228C2×C4#6696212yes—
229C2×C4#6698312yes—
230C2×C4#6698511yescharacteristic
231C2×C4#6699511yescharacteristic
232C2×C4#6700312yes—
233C8—44no—
234C8—882no—
235C22#1062255211yescharacteristic
236C22#1062257911yescharacteristic
237C22#1062261511yescharacteristic
238C22#1062274612yes—
239C22C2×#6688812yes—
240C4—24no—
241C4—22no—
242C4—42no—
243C4—882no—
244C4—882no—
245C4#1062232511yescharacteristic
246C4#1062232712yes—
247C4#1062232811yescharacteristic
248C4#1062262912yes—
249C4#1062264112yes—
250C2#1306731712yes—
251C2#1306735312yes—
252C2#1306943211yescharacteristic
253C2#1306946011yescharacteristic
254C2#1306954811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1767C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1767D11
hypocenterC11#9708
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
205. C11#9708semidirect

Maximal subgroups

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

subgroupindex
#130769942
#130687682
C2×#106221202
C2×#106221242
C11×#17672
#970811