Finite Group Databasebeta

← #14670726

Subgroups — #14670726

Order 2816.

530 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622729C211yesmaximal, characteristic
2C2×#10622130C212yesmaximal, complemented
3C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic
4#13066707C212yesmaximal, complemented
5C2×C11×#427C211yesmaximal, characteristic
6C23×C8×C11C2211yescharacteristic
7C2×C11×#117—21no—
8C2×#66977—21no—
9C22×Dic44C2211yescharacteristic
10C11×#427—24no—
11C2×C11×#107C2212yes—
12C2×C11×#106—21no—
13#10622729—22no—
14#10622729C414yescomplemented
15C2×#66882C2211yescharacteristic
16C2×#66880—21no—
17C22×C11⋊C16C2212yes—
18C22⋊(C11⋊C16)—22no—
19#10622130—24no—
20C23×C4×C11D411yescharacteristic
21C22×Dic22—21no—
22C22×C8×C11—22no—
23C22×C8×C11—22no—
24C22×C8×C11C2×C412yes—
25C22×C8×C11D412yes—
26C22×C8×C11D411yescharacteristic
27C22×C8×C11C2311yescharacteristic
28C11×#117—24no—
29C11×#117—42no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C22⋊C4—41no—
32C2×C42×C11—41no—
33C2×C22⋊Dic11—41no—
34C2×C4⋊Dic11—21no—
35#66977—24no—
36#66977—42no—
37C2×Dic11⋊C4—41no—
38C2×Dic44—22no—
39C2×Dic44—22no—
40C2×Dic44—21no—
41C2×Dic44C2×C412yes—
42C11×#107—22no—
43C11×#107D414yes—
44C11×#106—24no—
45#66882—21no—
46#66882C2×C412yes—
47#66880—24no—
48C2×C11⋊C16—22no—
49C2×C11⋊C16—22no—
50C2×C11⋊C16—22no—
51#12994—111nomaximal, Sylow
52C24×C11D811yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—42no—
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11D811yescharacteristic
60C22×C4×C11SD1612yes—
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—41no—
63C22×Dic11—41no—
64C2×Dic22—22no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C2×Dic22—41no—
70C2×C8×C11—24no—
71C2×C8×C11—24no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11C22⋊C412yes—
75C2×C8×C11C22×C411yescharacteristic
76C2×C8×C11C2×D411yescharacteristic
77C2×C8×C11C2×D412yes—
78C2×C8×C11#4112yes—
79C11×C4⋊C4—24no—
80C11×C4⋊C4—42no—
81C11×C22⋊C4—44no—
82C42×C11—44no—
83C22⋊Dic11—44no—
84C4⋊Dic11—22no—
85C4⋊Dic11—41no—
86Dic11⋊C4—44no—
87Dic44—24no—
88Dic44—42no—
89C11⋊C16—42no—
90C2×#467—111no—
91C2×#427D1111yescharacteristic
92C2×#358—112no—
93C2×C22⋊C16—111no—
94#1380—112no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11#10212yes—
100C23×C11C2×D811yescharacteristic
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—44no—
108C2×C4×C11—82no—
109C2×C4×C11—82no—
110C2×C4×C11#10212yes—
111C2×C4×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11#12311yescharacteristic
114C2×C4×C11C2×SD1611yescharacteristic
115C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C11#13711yescharacteristic
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—81no—
120C2×Dic11—81no—
121C2×Dic11—82no—
122Dic22—42no—
123Dic22—42no—
124Dic22—81no—
125Dic22—81no—
126C8×C11—22no—
127C8×C11C4×D412yes—
128C8×C11#12112yes—
129C22×Q16—111no—
130C23×C8C2×D1111yescharacteristic
131C2×C22⋊Q8—221no—
132C2×#117—21no—
133C22×C16—112no—
134#467—114no—
135#467—222no—
136#427—24no—
137C2×#107—111no—
138C2×#107C2×D1112yes—
139C2×#106—21no—
140C2×#103—221no—
141#358—224no—
142C22⋊C16—222no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—42no—
147C22×C11—42no—
148C22×C11C2×#10211yescharacteristic
149C22×C11#44711yescharacteristic
150C22×C11#48011yescharacteristic
151C22×C11#50812yes—
152C22×C11#51012yes—
153C4×C11—22no—
154C4×C11—84no—
155C4×C11#38611yescharacteristic
156C4×C11#41711yescharacteristic
157C4×C11#44811yescharacteristic
158C4×C11#48111yescharacteristic
159Dic11—82no—
160Dic11—82no—
161C22×Q8—221no—
162C23×C4C22⋊D1111yescharacteristic
163C2×Q16—112no—
164C2×Q16—221no—
165C2×Q16—222no—
166C2×Q16—222no—
167C22×C8—22no—
168C22×C8—22no—
169C22×C8C4×D1112yes—
170C22×C8D4412yes—
171C22×C8C22⋊D1111yescharacteristic
172C22×C8C22×D1111yescharacteristic
173C22⋊Q8—224no—
174C22⋊Q8—442no—
175#117—24no—
176#117—42no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—221no—
179C2×C4⋊C4—441no—
180C2×C22⋊C4—41no—
181C2×C22⋊C4—441no—
182C2×C42—41no—
183C2×C16—222no—
184C2×C16—222no—
185C2×C16—222no—
186#107—22no—
187#107—112no—
188#107—221no—
189#107C22⋊D1114yes—
190#106—24no—
191#103—224no—
192C2×C11—42no—
193C2×C11#187411yescharacteristic
194C2×C11#213811yescharacteristic
195C2×C11#214111yescharacteristic
196C2×C11#218912yes—
197C2×C11#223712yes—
198C24#432311yescharacteristic
199C2×Q8—222no—
200C2×Q8—441no—
201C2×Q8—441no—
202C2×Q8—441no—
203C2×Q8—441no—
204C2×Q8—441no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—42no—
210C22×C4—441no—
211C22×C4—441no—
212C22×C4(C2×D11)⋊C412yes—
213C22×C4#432311yescharacteristic
214C22×C4#432512yes—
215C22×C4C2×C22⋊D1111yescharacteristic
216Q16—224no—
217Q16—442no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—24no—
221C2×C8—24no—
222C2×C8(C2×D11)⋊C412yes—
223C2×C8C2×C4×D1111yescharacteristic
224C2×C8C2×D4411yescharacteristic
225C2×C8#433912yes—
226C2×C8C2×C22⋊D1112yes—
227C4⋊C4—24no—
228C4⋊C4—42no—
229C4⋊C4—222no—
230C4⋊C4—444no—
231C4⋊C4—441no—
232C22⋊C4—44no—
233C22⋊C4—444no—
234C42—44no—
235C16—442no—
236C11#1299411yescharacteristic, complemented, Sylow
237C23—22no—
238C23—22no—
239C23—21no—
240C23—21no—
241C23#6687312yes—
242C23C2×#432311yescharacteristic
243Q8—442no—
244Q8—442no—
245Q8—881no—
246Q8—881no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—44no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—882no—
259C2×C4—881no—
260C2×C4—881no—
261C2×C4#6687312yes—
262C2×C4C2×(C2×D11)⋊C411yescharacteristic
263C2×C4#6698211yescharacteristic
264C2×C4#6698511yescharacteristic
265C2×C4C2×#432511yescharacteristic
266C2×C4#6699511yescharacteristic
267C2×C4#6700611yescharacteristic
268C8—22no—
269C8C4×C22⋊D1112yes—
270C8#6698312yes—
271C22—22no—
272C22—22no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22C2×#6687311yescharacteristic
277C22#1062258011yescharacteristic
278C22#1062280712yes—
279C22#1062280812yes—
280C22#1062283011yescharacteristic
281C4—22no—
282C4—84no—
283C4—882no—
284C4—882no—
285C4#1062257911yescharacteristic
286C4#1062258111yescharacteristic
287C4#1062282611yescharacteristic
288C4#1062284011yescharacteristic
289C2—42no—
290C2#1306893311yescharacteristic
291C2#1307032111yescharacteristic
292C2#1307033511yescharacteristic
293C2#1307055612yes—
294C2#1307082412yes—
subgroupG/H
centerC23C2×#4323
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#427C2
socleC23×C11C2×D8
prime radicalC24×C11D8
cosocleC22×C8×C11C23
hypercenterC2×#427D11
hypocenterC11#12994
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#10622130C2semidirect
4. #13066707C2semidirect
14. #10622729C4semidirect
236. C11#12994semidirect

Maximal subgroups

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

subgroupindex
C2×#106227292
C2×#106221302
C2×C22⋊(C11⋊C16)2
#130667072
C2×C11×#4272
#1299411