Finite Group Databasebeta

← #14642255

Subgroups — #14642255

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
2#13068310C211yesmaximal, characteristic
3#13066442C214yesmaximal, complemented
4C11×#2857C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C11×C22⋊Q8C412yes—
7C22×C42×C11C2211yescharacteristic
8C22×#4318—21no—
9C11×#391C2212yes—
10C11×#389—21no—
11C11×#389—21no—
12C11×#384C411yescharacteristic
13C11×#380—21no—
14C11×#380—21no—
15C2×C22⋊(C11⋊C8)—21no—
16C2×C4×C11⋊C8—21no—
17#10622162—21no—
18#10622162C2212yes—
19#10622162C2212yes—
20C22×Q8×C11C2×C412yes—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—42no—
25C11×C22⋊Q8—44no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C22⋊C4—22no—
33C2×C42×C11—42no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×#4318—24no—
39C2×#4318—42no—
40C2×#4318—42no—
41C22×C11⋊C8—22no—
42C22×C11⋊C8—22no—
43C11×#95—22no—
44C11×#95—22no—
45C22⋊(C11⋊C8)—24no—
46C4×C11⋊C8—42no—
47#7687—111nomaximal, Sylow
48C24×C11C22⋊C411yescharacteristic
49C2×Q8×C11—24no—
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11SD1612yes—
66C22×C4×C11Q1612yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—44no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—42no—
76C11×C22⋊C4—44no—
77C42×C11—22no—
78C42×C11—22no—
79C42×C11—41no—
80C42×C11—41no—
81#4318—48no—
82C2×C11⋊C8—24no—
83C2×C11⋊C8—24no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86C2×C11⋊C8—42no—
87C2×C11⋊C8—42no—
88#2857D1111yescharacteristic
89C4×C22⋊C8—111no—
90#1728—111no—
91#1272—114no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11#10312yes—
99C23×C11C2×C22⋊C411yescharacteristic
100Q8×C11—84no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—44no—
114C2×C4×C11—44no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11#9912yes—
122C2×C4×C11#10012yes—
123C2×C4×C11#10312yes—
124C2×C4×C11#10412yes—
125C2×C4×C11#10412yes—
126C2×C4×C11#13112yes—
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11C2×Q1611yescharacteristic
129C2×C4×C11#13712yes—
130C11⋊C8—44no—
131C11⋊C8—44no—
132C22×M16—221no—
133C2×C4⋊Q8Dic1111yescharacteristic
134C2×C22⋊Q8Dic1112yes—
135C22×C42C2×D1111yescharacteristic
136C2×C22⋊C8—221no—
137C2×C4×C8—221no—
138#391C2×D1112yes—
139#389—21no—
140#389—21no—
141#384Dic1111yescharacteristic
142#380—21no—
143#380—21no—
144#336—112no—
145#336—112no—
146#336—221no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11#40811yescharacteristic
155C22×C11C2×#9911yescharacteristic
156C22×C11C2×#10011yescharacteristic
157C22×C11C2×#10311yescharacteristic
158C22×C11#41911yescharacteristic
159C22×C11C2×#10411yescharacteristic
160C22×C11C2×#10411yescharacteristic
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—22no—
166C4×C11—22no—
167C4×C11—82no—
168C4×C11—82no—
169C4×C11#32814yes—
170C22×Q8C2×Dic1112yes—
171C23×C4C2×Dic1111yescharacteristic
172C23×C4C22⋊D1111yescharacteristic
173C23×C4C22⋊D1111yescharacteristic
174C2×M16—224no—
175C2×M16—442no—
176C2×M16—442no—
177C22×C8—222no—
178C22×C8—222no—
179C4⋊Q8—42no—
180C22⋊Q8—44no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C2×Dic1112yes—
187C2×C22⋊C4—22no—
188C2×C42—42no—
189C2×C42C2×Dic1111yescharacteristic
190C2×C42C22⋊D1111yescharacteristic
191C2×C42C22⋊D1111yescharacteristic
192C2×C42C22×D1111yescharacteristic
193C22⋊C8—224no—
194C4×C8—442no—
195#95—22no—
196#95—22no—
197C2×C11—42no—
198C2×C11#147111yescharacteristic
199C2×C11#148511yescharacteristic
200C2×C11#149311yescharacteristic
201C2×C11C2×#32811yescharacteristic
202C2×C11#150811yescharacteristic
203C2×C11#152511yescharacteristic
204C2×C11#154811yescharacteristic
205C24C22⋊Dic1111yescharacteristic
206C2×Q8—24no—
207C2×Q8—42no—
208C2×Q8—42no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4#432512yes—
220C22×C4#432612yes—
221C22×C4C22⋊Dic1111yescharacteristic
222C22×C4C22⋊Dic1111yescharacteristic
223C22×C4C22⋊Dic1111yescharacteristic
224C22×C4C22×Dic1111yescharacteristic
225C22×C4C2×C22⋊D1111yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227M16—448no—
228C2×C8—224no—
229C2×C8—224no—
230C2×C8—442no—
231C2×C8—442no—
232C2×C8—442no—
233C2×C8—442no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—44no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C22⋊C4—44no—
241C42—22no—
242C42—22no—
243C42—41no—
244C42—41no—
245C11#768711yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23#6689912yes—
253C23C2×C22⋊Dic1111yescharacteristic
254Q8—84no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4#6689712yes—
276C2×C4#6689812yes—
277C2×C4#6689912yes—
278C2×C4#6690112yes—
279C2×C4#6690112yes—
280C2×C4C2×#432511yescharacteristic
281C2×C4#6699512yes—
282C2×C4C2×#432611yescharacteristic
283C2×C4#6700112yes—
284C8—444no—
285C8—444no—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22C2×#6689711yescharacteristic
294C22C2×#6689811yescharacteristic
295C22C2×#6689911yescharacteristic
296C22#1062283811yescharacteristic
297C22#1062284711yescharacteristic
298C22C2×#6690111yescharacteristic
299C22C2×#6690111yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—82no—
307C4—82no—
308C4#1062217614yes—
309C2—42no—
310C2#1306697611yescharacteristic
311C2#1306703711yescharacteristic
312C2#1306707111yescharacteristic
313C2C2×#1062217611yescharacteristic
314C2#1306713611yescharacteristic
315C2#1306720811yescharacteristic
316C2#1306729711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2857C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2857D11
hypocenterC11#7687
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
3. #13066442C2semidirect
245. C11#7687semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊(C11⋊C8)2
#130683102
#130664422
C11×#28572
#768711