Finite Group Databasebeta

← #14664290

Subgroups — #14664290

Order 2816.

470 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074303C211yesmaximal, characteristic
2#13068355C211yesmaximal, characteristic, complemented
3#13066647C212yesmaximal, complemented
4#13066620C212yesmaximal, complemented
5C11×#1464C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C22×#4318—21no—
8C2×#66928C411yescharacteristic
9C11×#432—21no—
10#10622826—21no—
11#10622604C2211yescharacteristic
12#10622603—21no—
13#10622592C2211yescharacteristic
14#10622573C411yescharacteristic
15#10622570—21no—
16#10622560C411yescharacteristic
17#10622553—21no—
18#10622545C411yescharacteristic
19C11×#324C2212yes—
20C11×#323—21no—
21#10622168—21no—
22#10622168C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C2×#4318—24no—
44C2×#4318—22no—
45C2×#4318—41no—
46C2×#4318—42no—
47C22×C11⋊C8—41no—
48#66928—41no—
49#66928—41no—
50C11×C4⋊C8—41no—
51C11×C22⋊C8—22no—
52C11×#97—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C11⋊#95C2×C411yescharacteristic
58#11765—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C23×D11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—42no—
73C2×C22⋊D11—42no—
74C2×C22⋊D11—81no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×D44—41no—
79C2×D44—81no—
80C2×Dic22—41no—
81C2×Dic22—81no—
82C2×C8×C11—42no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C22⋊Dic11—81no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—81no—
99Dic11⋊C4—81no—
100C4×Dic11—42no—
101#4318—24no—
102#4318—44no—
103#4318—42no—
104C2×C11⋊C8—44no—
105C2×C11⋊C8—42no—
106#2610—111no—
107#1742—111no—
108#1464D1111yescharacteristic, complemented
109#1354—112no—
110#1345—112no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#10412yes—
116C23×C11C2×C22⋊C411yescharacteristic
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11#9911yescharacteristic
141C2×C4×C11#9911yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C22⋊D11—84no—
145C2×Dic11—22no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154D44—82no—
155Dic22—82no—
156C8×C11—82no—
157C11⋊C8—44no—
158C22×M16—221no—
159C2×#124—111no—
160C2×#117C2×D1111yescharacteristic
161#432—21no—
162#395—111no—
163#394—111no—
164#393—111no—
165#392—111no—
166#390—221no—
167#388—221no—
168#388—221no—
169#386—221no—
170#376—111no—
171#343—112no—
172#343—221no—
173#324C2×D1112yes—
174#323—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—22no—
178C22×C11—42no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—81no—
182C22×C11C2×#9911yescharacteristic
183C22×C11#41711yescharacteristic
184C22×C11C2×#10411yescharacteristic
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200Dic11—42no—
201Dic11—81no—
202Dic11—81no—
203C22×Q8—111no—
204C22×D4—111no—
205C22×D4—221no—
206C23×C4D4411yescharacteristic
207C2×M16—224no—
208C2×M16—222no—
209C2×M16—441no—
210C2×M16—442no—
211C22×C8—441no—
212#124—441no—
213#124—441no—
214#117—41no—
215#117—41no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4D4411yescharacteristic
218C2×C4⋊C4C22×D1111yescharacteristic
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4C4×D1111yescharacteristic
226C2×C22⋊C4C22⋊D1111yescharacteristic
227C2×C42—221no—
228C2×C42C4×D1111yescharacteristic
229C2×C42C22⋊D1111yescharacteristic
230C4⋊C8—41no—
231C22⋊C8—22no—
232#97—41no—
233#95—111no—
234#95—111no—
235#95—221no—
236#95—221no—
237#95—221no—
238C2×C11—21no—
239C2×C11—21no—
240C2×C11—42no—
241C2×C11#150411yescharacteristic
242C2×C11#212211yescharacteristic
243C2×C11#213211yescharacteristic
244D11—161no—
245C24—221no—
246C24(C2×D11)⋊C411yescharacteristic
247C2×Q8—441no—
248C2×Q8—881no—
249C2×D4—441no—
250C2×D4—442no—
251C2×D4—442no—
252C2×D4—881no—
253C2×D4—881no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4(C2×D11)⋊C411yescharacteristic
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4C2×D4411yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268M16—224no—
269M16—444no—
270M16—442no—
271C2×C8—42no—
272C2×C8—444no—
273C2×C8—442no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—881no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C22⋊C4—881no—
286C22⋊C4—881no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—21no—
291C42—442no—
292C11#1176511yescharacteristic, complemented, Sylow
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—441no—
298C23—441no—
299C23—441no—
300C23—441no—
301C23—441no—
302C23—441no—
303C23—441no—
304C23#6688912yes—
305C23C2×(C2×D11)⋊C411yescharacteristic
306Q8—882no—
307D4—882no—
308D4—884no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—222no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4#6687011yescharacteristic
335C2×C4#6687011yescharacteristic
336C2×C4#6696111yescharacteristic
337C2×C4#6696211yescharacteristic
338C8—82no—
339C8—444no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—881no—
348C22—881no—
349C22—881no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22C2×#6687011yescharacteristic
355C22#1062274611yescharacteristic
356C22C2×#6688911yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—442no—
366C4—881no—
367C4—881no—
368C2—21no—
369C2—21no—
370C2—42no—
371C2—1761no—
372C2#1306712111yescharacteristic
373C2#1307026511yescharacteristic
374C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radical#10622573C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1464D11
hypocenterC11#11765
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13068355C2semidirect
3. #13066647C2semidirect
4. #13066620C2semidirect
5. C11×#1464C2semidirect
108. #1464D11semidirect
292. C11#11765semidirect

Maximal subgroups

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

subgroupindex
#130743032
#130683552
#130666472
#130666202
C11×#14642
#1176511