Finite Group Databasebeta

← #14651428

Subgroups — #14651428

Order 2816.

516 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077254C211yesmaximal, characteristic, complemented
2#13068693C211yesmaximal, characteristic, complemented
3#13067145C212yesmaximal
4#13066469C212yesmaximal, complemented
5C11×#2500C211yesmaximal, characteristic
6C2×C11×#121C2211yescharacteristic
7C2×C11×#117C2211yescharacteristic
8C11×#394—21no—
9C11×#394—21no—
10C11×#390C411yescharacteristic, complemented
11C11×#390C411yescharacteristic, complemented
12C11×#388—21no—
13C11×#388—21no—
14C11×#384C411yescharacteristic, complemented
15C11×#382C411yescharacteristic, complemented
16C4×C11×C22⋊C4C2211yescharacteristic
17#10622824C2212yes—
18#10622820C2212yes—
19#10622613—24no—
20#10622537—21no—
21C4×#4318—21no—
22#10622175—24no—
23#10622164—21no—
24#10622164—21no—
25C22×D4×C11—21no—
26C22×D4×C11C2×C411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C11×#121—22no—
29C11×#121—22no—
30C11×#117—22no—
31C11×#117—22no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4D411yescharacteristic
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C22⋊Dic11—22no—
50C2×#4318—22no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11⋊#95—22no—
55C11⋊#95—22no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)D414yes—
58C4⋊(C11⋊C8)—24no—
59#66867—22no—
60C4×C11⋊C8—22no—
61#9446—111nomaximal, Sylow
62C24×C11—21no—
63C24×C11C2×D411yescharacteristic
64C2×D4×C11—22no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C2×D4×C11—81no—
69C2×D4×C11—81no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11#4112yes—
83C22×Dic11—42no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—81no—
88C11×C4⋊C4—81no—
89C11×C22⋊C4—22no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—81no—
97C11×C22⋊C4—81no—
98C42×C11—21no—
99C42×C11—21no—
100C42×C11—21no—
101C42×C11—21no—
102C42×C11—41no—
103C42×C11—41no—
104C22⋊Dic11—42no—
105C22⋊Dic11—42no—
106#4318—42no—
107#4318—42no—
108C2×C11⋊C8—24no—
109#2921—111no—
110#2500D1111yescharacteristic
111#1820—111no—
112#1510—112no—
113#1284—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11#12112yes—
127D4×C11—82no—
128D4×C11—84no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11C4×D412yes—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12311yescharacteristic
155C2×Dic11—82no—
156C2×Dic11—82no—
157C2×Dic11—82no—
158C11⋊C8—44no—
159C2×#121C2×D1111yescharacteristic
160C2×#117C2×D1111yescharacteristic
161#433—224no—
162#423—221no—
163#407—112no—
164C4×M16—221no—
165#394—21no—
166#394—21no—
167#390Dic1111yescharacteristic, complemented
168#390Dic1111yescharacteristic, complemented
169#388—21no—
170#388—21no—
171#384Dic1111yescharacteristic, complemented
172#382Dic1111yescharacteristic, complemented
173#381—112no—
174C4×C22⋊C4C2×D1111yescharacteristic
175#342—221no—
176#342—221no—
177#327—224no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#38611yescharacteristic
193C22×C11#41011yescharacteristic
194C22×C11#41011yescharacteristic
195C4×C11—22no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—42no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—81no—
204C4×C11—81no—
205Dic11—162no—
206C22×D4—21no—
207C22×D4C2×Dic1111yescharacteristic
208C23×C4C22×D1111yescharacteristic
209C2×M16—222no—
210#121—22no—
211#121—22no—
212#117—22no—
213#117—22no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C2×Dic1111yescharacteristic
217C2×C4⋊C4C2×Dic1111yescharacteristic
218C2×C4⋊C4C2×Dic1111yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—222no—
226C2×C22⋊C4C22⋊D1111yescharacteristic
227C2×C22⋊C4C22⋊D1111yescharacteristic
228C2×C42C2×Dic1111yescharacteristic
229C2×C42C2×Dic1111yescharacteristic
230C2×C42C22⋊D1111yescharacteristic
231C2×C42C22⋊D1111yescharacteristic
232C4⋊C8—224no—
233C22⋊C8—114no—
234C22⋊C8—222no—
235#97—222no—
236C4×C8—222no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—222no—
241#95—222no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—42no—
245C2×C11—161no—
246C2×C11#188411yescharacteristic
247C2×C11#189911yescharacteristic
248C2×C11#191011yescharacteristic
249C24—21no—
250C24C2×C22⋊D1111yescharacteristic
251C2×D4—22no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—42no—
255C2×D4—81no—
256C2×D4—81no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—442no—
263C22×C4C22⋊Dic1111yescharacteristic
264C22×C4C22⋊Dic1111yescharacteristic
265C22×C4C22⋊Dic1111yescharacteristic
266C22×C4C22⋊Dic1111yescharacteristic
267C22×C4D4×D1112yes—
268C22×C4#434112yes—
269C22×C4C22×Dic1111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271M16—442no—
272M16—442no—
273C2×C8—224no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—81no—
287C22⋊C4—81no—
288C22⋊C4—442no—
289C22⋊C4—442no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—41no—
295C42—41no—
296C11#944611yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23#6699212yes—
309C23C2×C22⋊Dic1111yescharacteristic
310D4—82no—
311D4—84no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—882no—
336C2×C4—882no—
337C2×C4—882no—
338C2×C4D4×Dic1112yes—
339C2×C4#6698811yescharacteristic
340C2×C4#6699011yescharacteristic
341C8—444no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1062283311yescharacteristic
357C22#1062285311yescharacteristic
358C22#1062285311yescharacteristic
359C4—21no—
360C4—22no—
361C4—21no—
362C4—42no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—1762no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2#1306900011yescharacteristic
375C2#1306907511yescharacteristic
376C2#1306914411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2500C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2500D11
hypocenterC11#9446
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2500

Complements

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

NH ≅ G/Ntype
1. #13077254C2semidirect
2. #13068693C2semidirect
4. #13066469C2semidirect
10. C11×#390C4semidirect
11. C11×#390C4semidirect
14. C11×#384C4semidirect
15. C11×#382C4semidirect
167. #390Dic11semidirect
168. #390Dic11semidirect
171. #384Dic11semidirect
172. #382Dic11semidirect
296. C11#9446semidirect

Maximal subgroups

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

subgroupindex
#130772542
#130686932
#130671452
#130664692
C11×#25002
#944611