Finite Group Databasebeta

← #14649776

Subgroups — #14649776

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#13074437C211yesmaximal, characteristic
2#13067298C212yesmaximal, complemented
3#13066930C211yesmaximal, characteristic
4#13066476C212yesmaximal, complemented
5C11×#2905C211yesmaximal, characteristic
6C22×C11×M16—21no—
7C2×C11×#117C2211yescharacteristic
8C2×#66922C2211yescharacteristic
9C11×#424—24no—
10C11×#423—21no—
11C11×#423C2212yes—
12#10622825—21no—
13#10622599—21no—
14#10622592C412yes—
15#10622562—21no—
16#10622560C412yes—
17#10622549C2211yescharacteristic
18#10622541—21no—
19#10622538C2212yes—
20#10622166—21no—
21#10622163—21no—
22#10622119—24no—
23C23×C4×C11D411yescharacteristic
24C22×Dic22C2×C412yes—
25C2×C11×M16—22no—
26C2×C11×M16—22no—
27C2×C11×M16—42no—
28C2×C11×M16—42no—
29C22×C8×C11—22no—
30C11×#117—22no—
31C11×#117—22no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×C22⋊Dic11—22no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×Dic11⋊C4—22no—
43#66922—22no—
44#66922—22no—
45C11×C4⋊C8—24no—
46C11×C4⋊C8—22no—
47C11×C4⋊C8D414yes—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—21no—
51C11⋊#95C2×C412yes—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54C4×C11⋊C8—22no—
55#9191—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11SD1612yes—
65C22×C4×C11Q1612yes—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—22no—
70C22×Dic11—22no—
71C2×Dic22—24no—
72C2×Dic22—82no—
73C11×M16—44no—
74C11×M16—42no—
75C11×M16—42no—
76C2×C8×C11—24no—
77C2×C8×C11—44no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C22⋊C4—22no—
81C11×C22⋊C4—22no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11C2×D412yes—
85C42×C11#4112yes—
86C22⋊Dic11—82no—
87C4⋊Dic11—41no—
88C4⋊Dic11—42no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92Dic11⋊C4—82no—
93C2×C11⋊C8—42no—
94#2905D1111yescharacteristic
95#2628—111no—
96#1548—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
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11#10312yes—
118C2×C4×C11C4×D412yes—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12112yes—
121C2×C4×C11#12311yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C2×C4×C11C2×Q1611yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132Dic22—84no—
133C8×C11—44no—
134C11⋊C8—82no—
135C22×M16—21no—
136C2×C4⋊Q8—111no—
137C2×#117C2×D1111yescharacteristic
138#431—112no—
139#424—24no—
140#423—21no—
141#423C2×D1112yes—
142#400—221no—
143#399—221no—
144#395—112no—
145#393—112no—
146#389—221no—
147#382—111no—
148#380—221no—
149#333—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#45011yescharacteristic
168C4×C11#45111yescharacteristic
169C4×C11#48311yescharacteristic
170C4×C11#48411yescharacteristic
171Dic11—82no—
172Dic11—82no—
173C22×Q8—112no—
174C23×C4C22⋊D1111yescharacteristic
175C2×M16—22no—
176C2×M16—22no—
177C2×M16—42no—
178C2×M16—42no—
179C22×C8—22no—
180C4⋊Q8—222no—
181C4⋊Q8—222no—
182#117—22no—
183#117—22no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—222no—
188C2×C4⋊C4C4×D1111yescharacteristic
189C2×C4⋊C4D4411yescharacteristic
190C2×C22⋊C4—222no—
191C2×C22⋊C4C4×D1111yescharacteristic
192C2×C22⋊C4D4411yescharacteristic
193C2×C42C22⋊D1111yescharacteristic
194C2×C42C22×D1111yescharacteristic
195C4⋊C8—24no—
196C4⋊C8—22no—
197C4⋊C8—222no—
198C4⋊C8C22⋊D1114yes—
199C22⋊C8—222no—
200C4×C8—222no—
201#95—112no—
202#95—222no—
203#95—222no—
204#95—221no—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11—42no—
208C2×C11#187211yescharacteristic
209C2×C11#190911yescharacteristic
210C2×C11#191411yescharacteristic
211C24(C2×D11)⋊C411yescharacteristic
212C2×Q8—224no—
213C2×Q8—882no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—222no—
219C22×C4—222no—
220C22×C4(C2×D11)⋊C411yescharacteristic
221C22×C4(C2×D11)⋊C411yescharacteristic
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4#432412yes—
224C22×C4#432612yes—
225C22×C4C2×C4×D1111yescharacteristic
226C22×C4C2×D4411yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—44no—
229M16—42no—
230M16—42no—
231C2×C8—24no—
232C2×C8—44no—
233C2×C8—442no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—441no—
237C4⋊C4—442no—
238C4⋊C4—441no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C4⋊C4—882no—
242C22⋊C4—22no—
243C22⋊C4—22no—
244C22⋊C4—882no—
245C42—21no—
246C42—21no—
247C42#433912yes—
248C42C2×C22⋊D1112yes—
249C11#919111yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23#6687412yes—
255C23C2×(C2×D11)⋊C411yescharacteristic
256Q8—884no—
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—442no—
270C2×C4—442no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4#6687412yes—
276C2×C4C4×C22⋊D1112yes—
277C2×C4#6698211yescharacteristic
278C2×C4#6698312yes—
279C2×C4#6698511yescharacteristic
280C2×C4C2×#432411yescharacteristic
281C2×C4#6699511yescharacteristic
282C2×C4C2×#432611yescharacteristic
283C2×C4#6700611yescharacteristic
284C8—44no—
285C8—882no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22#1062257911yescharacteristic
294C22C2×#6687411yescharacteristic
295C22#1062282611yescharacteristic
296C4—22no—
297C4—22no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—882no—
302C4—882no—
303C4#1062258311yescharacteristic
304C4#1062258411yescharacteristic
305C4#1062283111yescharacteristic
306C4#1062284111yescharacteristic
307C2—21no—
308C2—21no—
309C2—42no—
310C2#1306892311yescharacteristic
311C2#1306913811yescharacteristic
312C2#1306916311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2905C2
socleC22×C11#386
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2905D11
hypocenterC11#9191
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2905

Complements

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

NH ≅ G/Ntype
2. #13067298C2semidirect
4. #13066476C2semidirect
249. C11#9191semidirect

Maximal subgroups

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

subgroupindex
#130744372
#130672982
#130669302
#130664762
C11×#29052
#919111