Finite Group Databasebeta

← #14641908

Subgroups — #14641908

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068684C211yesmaximal, characteristic
2#13068310C211yesmaximal, characteristic
3#13066439C214yesmaximal, complemented
4C2×C11×#389C211yesmaximal, characteristic
5C22×C11×C4⋊C4—21no—
6C22×C11×C4⋊C4C411yescharacteristic
7C22×C11×C4⋊C4C411yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C22×#4318—21no—
10C11×#389—21no—
11C11×#389—21no—
12C11×#389C412yes—
13C11×#389C2212yes—
14C2×C11×#95—21no—
15C2×C22⋊(C11⋊C8)—21no—
16#10622162—21no—
17#10622162—21no—
18#10622162C2212yes—
19#10622162C2212yes—
20C23×C4×C11—21no—
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—24no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—42no—
31C2×C11×C4⋊C4—44no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4C2×C412yes—
34C2×C42×C11—42no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11C2311yescharacteristic
39C2×#4318—24no—
40C2×#4318—42no—
41C2×#4318—42no—
42C22×C11⋊C8—22no—
43C22×C11⋊C8—22no—
44C11×#95—22no—
45C11×#95—22no—
46C22⋊(C11⋊C8)—42no—
47#7607—111nomaximal, Sylow
48C24×C11C22⋊C411yescharacteristic
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—24no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
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—24no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—44no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—44no—
79C11×C4⋊C4M1614yescomplemented
80C42×C11—41no—
81C42×C11—41no—
82C42×C11—41no—
83C42×C11—41no—
84#4318—48no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—42no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—42no—
91C2×#389D1111yescharacteristic
92#1817—111no—
93#1728—111no—
94#1271—114no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11#9912yes—
100C23×C11#10312yes—
101C23×C11#10412yes—
102C23×C11C2×C22⋊C411yescharacteristic
103C2×C4×C11—28no—
104C2×C4×C11—24no—
105C2×C4×C11—24no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—24no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—44no—
121C2×C4×C11—48no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—84no—
128C2×C4×C11#10112yes—
129C2×C4×C11#10312yes—
130C2×C4×C11C2×M1612yes—
131C2×C4×C11C2×SD1611yescharacteristic
132C2×C4×C11C2×Q1611yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)12yes—
134C11⋊C8—44no—
135C11⋊C8—82no—
136C22×M16—221no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4Dic1111yescharacteristic
139C22×C4⋊C4Dic1111yescharacteristic
140C22×C42C2×D1111yescharacteristic
141C2×C22⋊C8—221no—
142#389—21no—
143#389—21no—
144#389Dic1112yes—
145#389C2×D1112yes—
146C2×#95—21no—
147#336—112no—
148#336—112no—
149#336—221no—
150#336—221no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11#32814yes—
158C22×C11#40711yescharacteristic
159C22×C11C2×#9911yescharacteristic
160C22×C11C2×#10111yescharacteristic
161C22×C11C2×#10311yescharacteristic
162C22×C11#41811yescharacteristic
163C22×C11C2×#10411yescharacteristic
164C22×C11#42111yescharacteristic
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—22no—
171C4×C11—44no—
172C4×C11—41no—
173C4×C11—82no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4C2×Dic1111yescharacteristic
177C23×C4C22⋊D1111yescharacteristic
178C23×C4C22⋊D1111yescharacteristic
179C2×M16—224no—
180C2×M16—442no—
181C2×M16—442no—
182C22×C8—222no—
183C22×C8—222no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4C2×Dic1112yes—
192C2×C4⋊C4C2×Dic1112yes—
193C2×C42—42no—
194C2×C42C2×Dic1111yescharacteristic
195C2×C42C22⋊D1111yescharacteristic
196C2×C42C22⋊D1111yescharacteristic
197C2×C42C22×D1111yescharacteristic
198C22⋊C8—442no—
199#95—22no—
200#95—22no—
201C2×C11—24no—
202C2×C11#146311yescharacteristic
203C2×C11#148711yescharacteristic
204C2×C11#149011yescharacteristic
205C2×C11C2×#32811yescharacteristic
206C2×C11#151011yescharacteristic
207C2×C11#152811yescharacteristic
208C2×C11#154911yescharacteristic
209C24C22⋊Dic1111yescharacteristic
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—41no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4#432512yes—
227C22×C4#432612yes—
228C22×C4C22⋊Dic1111yescharacteristic
229C22×C4C22⋊Dic1111yescharacteristic
230C22×C4C22⋊Dic1111yescharacteristic
231C22×C4C22×Dic1111yescharacteristic
232C22×C4C2×C22⋊D1111yescharacteristic
233C22×C4C2×C22⋊D1111yescharacteristic
234M16—448no—
235C2×C8—224no—
236C2×C8—442no—
237C2×C8—442no—
238C2×C8—442no—
239C2×C8—442no—
240C2×C8—442no—
241C4⋊C4—24no—
242C4⋊C4—22no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—44no—
246C4⋊C4—44no—
247C4⋊C4#431814yescomplemented
248C42—41no—
249C42—41no—
250C42—41no—
251C42—41no—
252C11#760711yescharacteristic, complemented, Sylow
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#6689812yes—
258C23#6689912yes—
259C23#6690112yes—
260C23C2×C22⋊Dic1111yescharacteristic
261C2×C4—28no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—44no—
279C2×C4—48no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—84no—
286C2×C4#6689912yes—
287C2×C4#6690012yes—
288C2×C4C2×#431812yes—
289C2×C4#6698512yes—
290C2×C4C2×#432511yescharacteristic
291C2×C4C2×#432611yescharacteristic
292C8—444no—
293C8—882no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22#1062217614yes—
301C22#1062282011yescharacteristic
302C22#1062282811yescharacteristic
303C22C2×#6689811yescharacteristic
304C22C2×#6689911yescharacteristic
305C22C2×#6690011yescharacteristic
306C22C2×#6690111yescharacteristic
307C22#1062284911yescharacteristic
308C4—21no—
309C4—22no—
310C4—21no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—44no—
315C4—41no—
316C4—82no—
317C2—24no—
318C2#1306694611yescharacteristic
319C2#1306704511yescharacteristic
320C2#1306705911yescharacteristic
321C2C2×#1062217611yescharacteristic
322C2#1306714511yescharacteristic
323C2#1306721811yescharacteristic
324C2#1306730111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#389C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#389D11
hypocenterC11#7607
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #13066439C2semidirect
79. C11×C4⋊C4M16semidirect
247. C4⋊C4#4318semidirect
252. C11#7607semidirect

Maximal subgroups

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

subgroupindex
#130686842
#130683102
#130664392
C2×C11×#3892
#760711