Finite Group Databasebeta

← #14642246

Subgroups — #14642246

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 322 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#13066439C214yesmaximal, complemented
4C11×#2857C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C11×C22⋊Q8—21no—
7C22×C42×C11C2211yescharacteristic
8C22×#4318—21no—
9C11×#391—21no—
10C11×#389—21no—
11C11×#389C2212yes—
12C11×#384C411yescharacteristic
13C11×#380—21no—
14C11×#380C412yes—
15C2×C22⋊(C11⋊C8)—21no—
16C2×C4×C11⋊C8—21no—
17#10622162—21no—
18#10622162C2212yes—
19#10622162C2212yes—
20C22×Q8×C11—21no—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—42no—
25C11×C22⋊Q8—42no—
26C11×C22⋊Q8—42no—
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×C4⋊C4C2×C412yes—
33C2×C11×C22⋊C4—22no—
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)—24no—
47C4×C11⋊C8—42no—
48#7685—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C2×Q8×C11—42no—
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—22no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11D812yes—
67C22×C4×C11SD1612yes—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C11×C4⋊C4—24no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C22⋊C4—44no—
79C42×C11—22no—
80C42×C11—22no—
81C42×C11—41no—
82C42×C11—41no—
83#4318—48no—
84C2×C11⋊C8—24no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—42no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90#2857D1111yescharacteristic
91C4×C22⋊C8—111no—
92#1728—111no—
93#1271—114no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11#10212yes—
101C23×C11C2×C22⋊C411yescharacteristic
102Q8×C11—84no—
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—21no—
112C2×C4×C11—21no—
113C2×C4×C11—24no—
114C2×C4×C11—24no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11#9912yes—
124C2×C4×C11#10112yes—
125C2×C4×C11#10212yes—
126C2×C4×C11#10412yes—
127C2×C4×C11#10412yes—
128C2×C4×C11#13112yes—
129C2×C4×C11C2×D811yescharacteristic
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11#13712yes—
132C11⋊C8—44no—
133C11⋊C8—44no—
134C22×M16—221no—
135C2×C4⋊Q8Dic1111yescharacteristic
136C2×C22⋊Q8—21no—
137C22×C42C2×D1111yescharacteristic
138C2×C22⋊C8—221no—
139C2×C4×C8—221no—
140#391—21no—
141#389—21no—
142#389C2×D1112yes—
143#384Dic1111yescharacteristic
144#380—21no—
145#380Dic1112yes—
146#336—112no—
147#336—112no—
148#336—221no—
149C22×C11—22no—
150C22×C11—22no—
151C22×C11—22no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11#40811yescharacteristic
157C22×C11C2×#9911yescharacteristic
158C22×C11C2×#10111yescharacteristic
159C22×C11C2×#10211yescharacteristic
160C22×C11#41911yescharacteristic
161C22×C11C2×#10411yescharacteristic
162C22×C11C2×#10411yescharacteristic
163C4×C11—22no—
164C4×C11—22no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—82no—
170C4×C11—82no—
171C4×C11#32714yes—
172C22×Q8—21no—
173C23×C4C2×Dic1111yescharacteristic
174C23×C4C22⋊D1111yescharacteristic
175C23×C4C22⋊D1111yescharacteristic
176C2×M16—224no—
177C2×M16—442no—
178C2×M16—442no—
179C22×C8—222no—
180C22×C8—222no—
181C4⋊Q8—42no—
182C22⋊Q8—42no—
183C22⋊Q8—42no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4C2×Dic1112yes—
189C2×C4⋊C4C2×Dic1112yes—
190C2×C22⋊C4—22no—
191C2×C42—42no—
192C2×C42C2×Dic1111yescharacteristic
193C2×C42C22⋊D1111yescharacteristic
194C2×C42C22⋊D1111yescharacteristic
195C2×C42C22×D1111yescharacteristic
196C22⋊C8—224no—
197C4×C8—442no—
198#95—22no—
199#95—22no—
200C2×C11—42no—
201C2×C11#147211yescharacteristic
202C2×C11#148511yescharacteristic
203C2×C11#149211yescharacteristic
204C2×C11C2×#32711yescharacteristic
205C2×C11#150811yescharacteristic
206C2×C11#152611yescharacteristic
207C2×C11#154611yescharacteristic
208C24C22⋊Dic1111yescharacteristic
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—42no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4#432312yes—
223C22×C4#432412yes—
224C22×C4C22⋊Dic1111yescharacteristic
225C22×C4C22⋊Dic1111yescharacteristic
226C22×C4C22⋊Dic1111yescharacteristic
227C22×C4C22×Dic1111yescharacteristic
228C22×C4C2×C22⋊D1111yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230M16—448no—
231C2×C8—224no—
232C2×C8—224no—
233C2×C8—442no—
234C2×C8—442no—
235C2×C8—442no—
236C2×C8—442no—
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C22⋊C4—44no—
245C42—22no—
246C42—22no—
247C42—41no—
248C42—41no—
249C11#768511yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23#6689612yes—
257C23C2×C22⋊Dic1111yescharacteristic
258Q8—84no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4#6689612yes—
280C2×C4#6689812yes—
281C2×C4#6690012yes—
282C2×C4#6690112yes—
283C2×C4#6690112yes—
284C2×C4C2×#432311yescharacteristic
285C2×C4C2×#432411yescharacteristic
286C2×C4#6699512yes—
287C2×C4#6700112yes—
288C8—444no—
289C8—444no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×#6689611yescharacteristic
298C22C2×#6689811yescharacteristic
299C22#1062283811yescharacteristic
300C22C2×#6690011yescharacteristic
301C22#1062284711yescharacteristic
302C22C2×#6690111yescharacteristic
303C22C2×#6690111yescharacteristic
304C4—21no—
305C4—21no—
306C4—22no—
307C4—22no—
308C4—22no—
309C4—22no—
310C4—82no—
311C4—82no—
312C4#1062217514yes—
313C2—42no—
314C2#1306698011yescharacteristic
315C2#1306703711yescharacteristic
316C2#1306706711yescharacteristic
317C2C2×#1062217511yescharacteristic
318C2#1306713611yescharacteristic
319C2#1306721111yescharacteristic
320C2#1306728811yescharacteristic
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#7685
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. #13066439C2semidirect
249. C11#7685semidirect

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
#130664392
C11×#28572
#768511