Finite Group Databasebeta

← #14664439

Subgroups — #14664439

Order 2816.

486 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 79 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#13071852C211yesmaximal, characteristic
2#13068693C211yesmaximal, characteristic, complemented
3#13066617C212yesmaximal, complemented
4#13066614C212yesmaximal
5C11×#1464C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×C4×C22⋊D11—21no—
8C2×C4×D44C411yescharacteristic, complemented
9C11×#432—21no—
10#10622824—21no—
11#10622607—21no—
12#10622604C411yescharacteristic, complemented
13#10622596C411yescharacteristic, complemented
14#10622574—21no—
15#10622573C2211yescharacteristic
16#10622566C2211yescharacteristic
17C4×(C2×D11)⋊C4—21no—
18C4×C4⋊Dic11C411yescharacteristic, complemented
19C11×#324—21no—
20C11×#323C2212yes—
21#10622164—21no—
22#10622164C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C22×C4×D11—21no—
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—22no—
37C4×C22⋊D11—44no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C4×D44—41no—
47C4×D44—41no—
48C11×C4⋊C8—41no—
49C11×C22⋊C8—22no—
50C11×#97—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—41no—
54C11⋊#95—41no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57#11798—111nomaximal, Sylow
58C24×C11C2×D411yescharacteristic
59C23×D11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—41no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C2×C22⋊D11—42no—
71C2×C22⋊D11—42no—
72C2×C22⋊D11—42no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—42no—
77C2×D44—41no—
78C2×D44—42no—
79C2×C4×D11—42no—
80C2×C4×D11—42no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C8×C11—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C22⋊Dic11—42no—
93C22⋊Dic11—42no—
94C22⋊Dic11—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99C4⋊Dic11—41no—
100C4⋊Dic11—42no—
101Dic11⋊C4—42no—
102C4×Dic11—42no—
103#2392—111no—
104#1820—111no—
105#1464D1111yescharacteristic, complemented
106#1344—112no—
107#1343—112no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11AGL(1,ℤ/8)12yes—
114C22×D11—22no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11#9911yescharacteristic
137C2×C4×C11#9911yescharacteristic
138C22⋊D11—48no—
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—82no—
149C2×Dic11—82no—
150C2×Dic11—82no—
151D44—42no—
152D44—42no—
153C4×D11—82no—
154C4×D11—82no—
155C8×C11—82no—
156C2×C4×D4—111no—
157C2×C4×D4—221no—
158C2×#117C2×D1111yescharacteristic
159#432—21no—
160#398—111no—
161#397—111no—
162#396—221no—
163#394—111no—
164#394—221no—
165#392—111no—
166#381—221no—
167C4×C4⋊C4—111no—
168C4×C22⋊C4—221no—
169#342—112no—
170#342—221no—
171#324—21no—
172#323C2×D1112yes—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—42no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—81no—
180C22×C11C2×#9911yescharacteristic
181C22×C11#41811yescharacteristic
182C22×C11#42111yescharacteristic
183C2×D11—42no—
184C2×D11—42no—
185C2×D11—42no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197Dic11—42no—
198Dic11—81no—
199Dic11—81no—
200Dic11—162no—
201C22×D4—111no—
202C22×D4—221no—
203C23×C4—221no—
204C23×C4D4411yescharacteristic
205C4×D4—441no—
206C4×D4—441no—
207C4×D4—444no—
208#117—41no—
209#117—41no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4C4×D1111yescharacteristic
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C22⋊C4—222no—
221C2×C22⋊C4D4411yescharacteristic
222C2×C22⋊C4C22×D1111yescharacteristic
223C2×C42—221no—
224C2×C42C4×D1111yescharacteristic
225C2×C42C22⋊D1111yescharacteristic
226C4⋊C8—41no—
227C22⋊C8—22no—
228#97—41no—
229#95—111no—
230#95—111no—
231#95—221no—
232#95—221no—
233#95—441no—
234#95—441no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—42no—
238C2×C11#151011yescharacteristic
239C2×C11#212011yescharacteristic
240C2×C11#212611yescharacteristic
241D11—82no—
242C24—221no—
243C24C2×D4411yescharacteristic
244C2×D4—441no—
245C2×D4—442no—
246C2×D4—442no—
247C2×D4—442no—
248C2×D4—442no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—442no—
257C22×C4—442no—
258C22×C4—441no—
259C22×C4—441no—
260C22×C4—442no—
261C22×C4(C2×D11)⋊C411yescharacteristic
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4(C2×D11)⋊C411yescharacteristic
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267C2×C8—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—441no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C22⋊C4—442no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C42—21no—
283C42—21no—
284C42—21no—
285C42—21no—
286C42—442no—
287C11#1179811yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—222no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23—441no—
298C23—441no—
299C23#6696112yes—
300C23C2×(C2×D11)⋊C411yescharacteristic
301D4—442no—
302D4—442no—
303D4—448no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—222no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—882no—
329C2×C4—882no—
330C2×C4—882no—
331C2×C4—882no—
332C2×C4—882no—
333C2×C4#6687011yescharacteristic
334C2×C4#6687011yescharacteristic
335C8—82no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—81no—
343C22—442no—
344C22—442no—
345C22—442no—
346C22—881no—
347C22—881no—
348C22—881no—
349C22—881no—
350C22C2×#6687011yescharacteristic
351C22#1062274411yescharacteristic
352C22#1062275211yescharacteristic
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—442no—
361C4—881no—
362C4—881no—
363C4—1762no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—882no—
368C2#1306714611yescharacteristic
369C2#1307025811yescharacteristic
370C2#1307027911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radical#10622573C22
cosocleC2×C11×C22⋊C4C23
hypercenter#1464D11
hypocenterC11#11798
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. #13068693C2semidirect
3. #13066617C2semidirect
5. C11×#1464C2semidirect
8. C2×C4×D44C4semidirect
12. #10622604C4semidirect
13. #10622596C4semidirect
18. C4×C4⋊Dic11C4semidirect
105. #1464D11semidirect
287. C11#11798semidirect

Maximal subgroups

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

subgroupindex
#130718522
#130686932
#130666172
#130666142
C11×#14642
#1179811