Finite Group Databasebeta

← #14649787

Subgroups — #14649787

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077180C211yesmaximal, characteristic
2#13067301C212yesmaximal, complemented
3#13066930C211yesmaximal, characteristic
4#13066474C212yesmaximal, complemented
5C11×#2628C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×#117C2211yescharacteristic
8C22×#4318—21no—
9C11×#400C412yes—
10C11×#399C412yes—
11C11×#395—21no—
12C11×#393—21no—
13C11×#389—21no—
14C11×#382C2211yescharacteristic
15C11×#380—21no—
16#10622612—24no—
17#10622538C2212yes—
18#10622537—21no—
19#10622537C2212yes—
20#10622185—24no—
21#10622166—21no—
22#10622163—21no—
23C22×Q8×C11—21no—
24C23×C4×C11D411yescharacteristic
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8—22no—
27C11×#117—22no—
28C11×#117—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C2×#4318—22no—
41C2×#4318—22no—
42C2×#4318—42no—
43C2×#4318—42no—
44C22×C11⋊C8—22no—
45C11×#95—22no—
46C11×#95—22no—
47C11×#95—21no—
48C11×#95C2×C412yes—
49C22⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—24no—
51C4⋊(C11⋊C8)—22no—
52C4⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)D414yes—
54C4×C11⋊C8—22no—
55#9193—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C2×Q8×C11—42no—
58C2×Q8×C11—82no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11SD1612yes—
69C22×C4×C11Q1612yes—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—24no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—82no—
81C11×C22⋊C4—22no—
82C11×C22⋊C4—22no—
83C11×C22⋊C4—82no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11C2×D412yes—
87C42×C11#4112yes—
88#4318—44no—
89#4318—42no—
90#4318—42no—
91C2×C11⋊C8—24no—
92C2×C11⋊C8—44no—
93C2×C11⋊C8—42no—
94#2905—111no—
95#2628D1111yescharacteristic
96#1549—112no—
97#1458—111no—
98#1286—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11#10312yes—
104C23×C11C2×C22⋊C411yescharacteristic
105Q8×C11—84no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11#10312yes—
125C2×C4×C11C4×D412yes—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12112yes—
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11C2×SD1611yescharacteristic
130C2×C4×C11C2×Q1611yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C11⋊C8—44no—
134C11⋊C8—82no—
135C22×M16—221no—
136C2×C4⋊Q8C2×D1111yescharacteristic
137C2×#117C2×D1111yescharacteristic
138#431—112no—
139#424—224no—
140#423—112no—
141#423—221no—
142#400Dic1112yes—
143#399Dic1112yes—
144#395—21no—
145#393—21no—
146#389—21no—
147#382C2×D1111yescharacteristic
148#380—21no—
149#332—224no—
150#324—221no—
151#323—221no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—22no—
155C22×C11—42no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—81no—
159C22×C11#38611yescharacteristic
160C22×C11C2×#10311yescharacteristic
161C22×C11#41711yescharacteristic
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—22no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—82no—
168C4×C11—82no—
169C4×C11#45011yescharacteristic
170C4×C11#45111yescharacteristic
171C4×C11#48311yescharacteristic
172C4×C11#48411yescharacteristic
173C22×Q8—21no—
174C23×C4C22⋊D1111yescharacteristic
175C2×M16—222no—
176C2×M16—222no—
177C2×M16—442no—
178C2×M16—442no—
179C22×C8—222no—
180C4⋊Q8—22no—
181C4⋊Q8—22no—
182#117—22no—
183#117—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4C2×Dic1112yes—
188C2×C4⋊C4C2×Dic1111yescharacteristic
189C2×C4⋊C4C22⋊D1111yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4C2×Dic1111yescharacteristic
192C2×C22⋊C4C22⋊D1111yescharacteristic
193C2×C42C22⋊D1111yescharacteristic
194C2×C42C22×D1111yescharacteristic
195C4⋊C8—114no—
196C4⋊C8—224no—
197C4⋊C8—222no—
198C4⋊C8—222no—
199C22⋊C8—222no—
200C4×C8—222no—
201#95—22no—
202#95—22no—
203#95—21no—
204#95C2×Dic1112yes—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11—42no—
208C2×C11#187211yescharacteristic
209C2×C11#191011yescharacteristic
210C2×C11#191511yescharacteristic
211C24C22⋊Dic1111yescharacteristic
212C2×Q8—42no—
213C2×Q8—82no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4#432512yes—
221C22×C4#432612yes—
222C22×C4C22⋊Dic1111yescharacteristic
223C22×C4C22⋊Dic1111yescharacteristic
224C22×C4C22⋊Dic1111yescharacteristic
225C22×C4C22×Dic1111yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—444no—
229M16—442no—
230M16—442no—
231C2×C8—224no—
232C2×C8—444no—
233C2×C8—442no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—24no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—82no—
242C22⋊C4—22no—
243C22⋊C4—22no—
244C22⋊C4—82no—
245C42—21no—
246C42—21no—
247C42D4×D1112yes—
248C42#434112yes—
249C11#919311yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23#6689912yes—
255C23C2×C22⋊Dic1111yescharacteristic
256Q8—84no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4#6689912yes—
276C2×C4D4×Dic1112yes—
277C2×C4#6698811yescharacteristic
278C2×C4#6699011yescharacteristic
279C2×C4#6699212yes—
280C2×C4C2×#432511yescharacteristic
281C2×C4C2×#432611yescharacteristic
282C2×C4#6700211yescharacteristic
283C2×C4#6700411yescharacteristic
284C8—444no—
285C8—882no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22#1062283311yescharacteristic
294C22C2×#6689911yescharacteristic
295C22#1062284511yescharacteristic
296C4—22no—
297C4—22no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—82no—
302C4—82no—
303C4#1062265611yescharacteristic
304C4#1062265711yescharacteristic
305C4#1062265911yescharacteristic
306C4#1062266311yescharacteristic
307C2—21no—
308C2—21no—
309C2—42no—
310C2#1306892411yescharacteristic
311C2#1306914411yescharacteristic
312C2#1306916911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2628C2
socleC22×C11#386
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2628D11
hypocenterC11#9193
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2628

Complements

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

NH ≅ G/Ntype
2. #13067301C2semidirect
4. #13066474C2semidirect
249. C11#9193semidirect

Maximal subgroups

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

subgroupindex
#130771802
#130673012
#130669302
#130664742
C11×#26282
#919311