Finite Group Databasebeta

← #14647208

Subgroups — #14647208

Order 2816.

514 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 135 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#13071021C211yesmaximal, characteristic
2#13068593C212yesmaximal
3#13066500C212yesmaximal, complemented
4#13066499C211yesmaximal, characteristic, complemented
5C11×#1296C211yesmaximal, characteristic, complemented
6C2×#66945C412yes—
7C2×C42×D11C2211yescharacteristic
8C2×C11×C4⋊C8C2212yes—
9C11×#384C2211yescharacteristic
10C2×(C2×D11)⋊C8—22no—
11#10622600—22no—
12#10622590C412yes—
13C4⋊C4×Dic11—22no—
14#10622548C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2212yes—
16#10622188—22no—
17C22×C4×D11C2×C411yescharacteristic
18C22×C4×D11D412yes—
19C22×C8×C11—22no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4C2×C412yes—
22C2×C42×C11C2311yescharacteristic
23C2×(C2×D11)⋊C4—22no—
24C2×C4⋊Dic11—22no—
25C2×C4⋊Dic11C2×C412yes—
26C2×C4×Dic11—22no—
27C2×C4×Dic11C2×C411yescharacteristic
28C2×C4×Dic11D412yes—
29C22×C11⋊C8—22no—
30#66945—44no—
31C42×D11—22no—
32C42×D11—21no—
33C42×D11—21no—
34C11×C4⋊C8—22no—
35C11×C4⋊C8—22no—
36C11⋊#95—24no—
37(C2×D11)⋊C8—44no—
38C4⋊(C11⋊C8)—22no—
39C4⋊(C11⋊C8)—22no—
40#8728—111nomaximal, Sylow
41C23×D11C22⋊C411yescharacteristic
42C22×C4×C11—22no—
43C22×C4×C11C22×C411yescharacteristic
44C22×C4×C11C2×D412yes—
45C22×Dic11—22no—
46C22×Dic11C22⋊C412yes—
47C22×Dic11C22⋊C411yescharacteristic
48C2×C4×D11—22no—
49C2×C4×D11—22no—
50C2×C4×D11—21no—
51C2×C4×D11—21no—
52C2×C4×D11—22no—
53C2×C4×D11—22no—
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×C4×D11—22no—
57C2×C4×D11—22no—
58C2×C8×C11—42no—
59C2×C8×C11—42no—
60C2×C8×C11—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—42no—
64C42×C11#4112yes—
65C42×C11#4111yescharacteristic
66C42×C11#4111yescharacteristic
67(C2×D11)⋊C4—44no—
68C4⋊Dic11—42no—
69C4⋊Dic11—42no—
70C4⋊Dic11—42no—
71C4×Dic11—21no—
72C4×Dic11—21no—
73C4×Dic11—22no—
74C4×Dic11—22no—
75C4×Dic11—44no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—42no—
79#2285—111no—
80#1797—112no—
81#1296—112no—
82#1296—111no—
83#1296D1111yescharacteristic, complemented
84C23×C11C2×C22⋊C411yescharacteristic
85C22×D11—21no—
86C22×D11—21no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11#10112yes—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—42no—
93C2×C4×C11—44no—
94C2×C4×C11#11711yescharacteristic
95C2×C4×C11#11711yescharacteristic
96C2×C4×C11#12312yes—
97C2×C4×C11#12312yes—
98C2×C4×C11#13512yes—
99C2×C4×C11#13512yes—
100C2×C4×C11AGL(1,ℤ/8)12yes—
101C2×C4×C11#13712yes—
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—42no—
108C2×Dic11—44no—
109C2×Dic11#10012yes—
110C4×D11—24no—
111C4×D11—24no—
112C4×D11—42no—
113C4×D11—42no—
114C4×D11—42no—
115C4×D11—42no—
116C8×C11—82no—
117C11⋊C8—82no—
118C2×#117—112no—
119C22×C42—111no—
120C2×C4⋊C8—112no—
121C2×C4⋊C8C2×D1112yes—
122C2×C22⋊C8—222no—
123#384—111no—
124#384C2×D1111yescharacteristic
125#382—112no—
126#380—222no—
127C4×C4⋊C4—222no—
128#336—222no—
129C22×C11#38111yescharacteristic
130C22×C11C2×#10011yescharacteristic
131C22×C11C2×#10111yescharacteristic
132C22×C11#41612yes—
133C22×C11#41712yes—
134C2×D11—24no—
135C2×D11—22no—
136C2×D11—41no—
137C2×D11—41no—
138C2×D11—42no—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—82no—
142C4×C11#48212yes—
143C4×C11#48212yes—
144C4×C11#48512yes—
145C4×C11#48512yes—
146Dic11—22no—
147Dic11—42no—
148Dic11—82no—
149C23×C4—111no—
150C23×C4—112no—
151C22×C8—22no—
152C22×C8—222no—
153#117—444no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4—222no—
157C2×C4⋊C4C4×D1112yes—
158C2×C22⋊C4—222no—
159C2×C42—111no—
160C2×C42—112no—
161C2×C42—222no—
162C2×C42—221no—
163C2×C42—221no—
164C2×C42—222no—
165C2×C42C22×D1111yescharacteristic
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—222no—
169C4⋊C8—222no—
170C22⋊C8—444no—
171#95—224no—
172C2×C11#154311yescharacteristic
173C2×C11#155212yes—
174C2×C11#156011yescharacteristic
175C2×C11#182111yescharacteristic
176C2×C11#182512yes—
177D11—42no—
178C24—111no—
179C22×C4—22no—
180C22×C4—111no—
181C22×C4—112no—
182C22×C4—222no—
183C22×C4—222no—
184C22×C4—221no—
185C22×C4—221no—
186C22×C4—222no—
187C22×C4—222no—
188C22×C4—222no—
189C22×C4—222no—
190C22×C4—222no—
191C22×C4—222no—
192C22×C4—222no—
193C22×C4C2×C4×D1111yescharacteristic
194C22×C4D4×D1112yes—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—442no—
199C2×C8—442no—
200C2×C8—442no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—442no—
205C4⋊C4—442no—
206C4⋊C4—442no—
207C22⋊C4—444no—
208C42—221no—
209C42—222no—
210C42—221no—
211C42—222no—
212C42—444no—
213C42#433912yes—
214C42#434111yescharacteristic
215C42#434311yescharacteristic
216C11#872811yescharacteristic, complemented, Sylow
217C23—112no—
218C23—221no—
219C23—221no—
220C23—222no—
221C23—222no—
222C23C22⋊C4×D1111yescharacteristic
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—44no—
227C2×C4—112no—
228C2×C4—224no—
229C2×C4—224no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—442no—
236C2×C4—442no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—444no—
241C2×C4#6692511yescharacteristic
242C2×C4#6693612yes—
243C2×C4#6694511yescharacteristic
244C2×C4#6694712yes—
245C2×C4#6696512yes—
246C2×C4#6696712yes—
247C2×C4#6696912yes—
248C2×C4#6697112yes—
249C8—82no—
250C8—882no—
251C22—224no—
252C22—222no—
253C22—441no—
254C22—441no—
255C22—442no—
256C22#1062227711yescharacteristic
257C22D11×#10011yescharacteristic
258C22D11×#10111yescharacteristic
259C22#1062238512yes—
260C22#1062241612yes—
261C4—21no—
262C4—21no—
263C4—82no—
264C4—222no—
265C4—442no—
266C4—882no—
267C4#1062239712yes—
268C4#1062242812yes—
269C4#1062247912yes—
270C4#1062250112yes—
271C2—442no—
272C2#1306727511yescharacteristic
273C2#1306731312yes—
274C2#1306735011yescharacteristic
275C2#1306869511yescharacteristic
276C2#1306870912yes—
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#8728
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #13066500C2semidirect
4. #13066499C2semidirect
5. C11×#1296C2semidirect
83. #1296D11semidirect
216. C11#8728semidirect

Maximal subgroups

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

subgroupindex
#130710212
#130685932
#130665002
#130664992
C11×#12962
#872811