Finite Group Databasebeta

← #14651425

Subgroups — #14651425

Order 2816.

516 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 95 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#13073074C211yesmaximal, characteristic
3#13067144C212yesmaximal
4#13066468C212yesmaximal, complemented
5C11×#1820C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C11×#381C2212yes—
9C4×C22⋊Dic11C2211yescharacteristic
10#10622820C2212yes—
11#10622613—24no—
12#10622601C411yescharacteristic, complemented
13#10622601C411yescharacteristic, complemented
14#10622590C411yescharacteristic, complemented
15#10622589C411yescharacteristic, complemented
16#10622572—21no—
17#10622572—21no—
18#10622553—21no—
19#10622553—21no—
20#10622537—21no—
21C4×#4318—21no—
22C11×#342—21no—
23C11×#342—21no—
24#10622089—24no—
25C23×C4×C11C2311yescharacteristic
26C22×C22⋊D11—21no—
27C22×D44C2×C411yescharacteristic
28C11×#117—22no—
29C11×#117—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38#66983—22no—
39#66983—22no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11C2×C411yescharacteristic
50C2×#4318—22no—
51C11×#95—22no—
52C11×#95—22no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)D414yes—
58C4⋊(C11⋊C8)—24no—
59#66867—22no—
60C4×C11⋊C8—22no—
61#9446—111nomaximal, Sylow
62C24×C11C2×D411yescharacteristic
63C23×D11—21no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11#4112yes—
75C2×C22⋊D11—42no—
76C2×C22⋊D11—81no—
77C2×C22⋊D11—81no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C2×D44—22no—
82C2×D44—41no—
83C2×D44—41no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—42no—
89C11×C22⋊C4—42no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—21no—
94C22⋊Dic11—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—81no—
100(C2×D11)⋊C4—81no—
101C4⋊Dic11—22no—
102Dic11⋊C4—81no—
103Dic11⋊C4—81no—
104C4×Dic11—41no—
105C4×Dic11—41no—
106#4318—42no—
107#4318—42no—
108C2×C11⋊C8—24no—
109#2921—111no—
110#2500—111no—
111#1820D1111yescharacteristic, complemented
112#1510—112no—
113#1284—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11C2×C22⋊C411yescharacteristic
119C23×C11#12112yes—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C2×C4×C11—21no—
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—42no—
136C2×C4×C11—42no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—82no—
142C2×C4×C11—82no—
143C2×C4×C11—82no—
144C2×C4×C11C4×D412yes—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C22⋊D11—84no—
148C2×Dic11—22no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157D44—82no—
158C11⋊C8—44no—
159C2×#121—111no—
160C2×#117C2×D1111yescharacteristic
161#433—224no—
162#423—221no—
163#407—112no—
164C4×M16—221no—
165#394—221no—
166#394—221no—
167#390—111no—
168#390—111no—
169#388—221no—
170#388—221no—
171#384—111no—
172#382—111no—
173#381C2×D1112yes—
174C4×C22⋊C4—111no—
175#342—21no—
176#342—21no—
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#38611yescharacteristic
186C22×C11#41011yescharacteristic
187C22×C11#41011yescharacteristic
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C4×C11—22no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—162no—
203Dic11—42no—
204Dic11—81no—
205Dic11—81no—
206C22×D4—111no—
207C22×D4—221no—
208C23×C4C22×D1111yescharacteristic
209C2×M16—222no—
210#121—222no—
211#121—222no—
212#117—22no—
213#117—22no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4C4×D1111yescharacteristic
218C2×C4⋊C4C4×D1111yescharacteristic
219C2×C22⋊C4—22no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4C22⋊D1111yescharacteristic
227C2×C22⋊C4C22⋊D1111yescharacteristic
228C2×C42—111no—
229C2×C42—111no—
230C2×C42D4411yescharacteristic
231C2×C42D4411yescharacteristic
232C4⋊C8—224no—
233C22⋊C8—114no—
234C22⋊C8—222no—
235#97—222no—
236C4×C8—222no—
237#95—22no—
238#95—22no—
239#95—221no—
240#95—221no—
241#95—221no—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—42no—
245C2×C11#188411yescharacteristic
246C2×C11#189911yescharacteristic
247C2×C11#191011yescharacteristic
248D11—161no—
249C24—221no—
250C24C2×C22⋊D1111yescharacteristic
251C2×D4—222no—
252C2×D4—441no—
253C2×D4—441no—
254C2×D4—442no—
255C2×D4—881no—
256C2×D4—881no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—42no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4(C2×D11)⋊C411yescharacteristic
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4(C2×D11)⋊C411yescharacteristic
266C22×C4(C2×D11)⋊C411yescharacteristic
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4C2×D4411yescharacteristic
269C22×C4D4×D1112yes—
270C22×C4#434112yes—
271M16—442no—
272M16—442no—
273C2×C8—224no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—222no—
277C4⋊C4—881no—
278C4⋊C4—881no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—441no—
287C22⋊C4—441no—
288C22⋊C4—881no—
289C22⋊C4—881no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—441no—
295C42—441no—
296C11#944611yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—441no—
302C23—441no—
303C23—441no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23C2×(C2×D11)⋊C411yescharacteristic
309C23#6699212yes—
310D4—882no—
311D4—884no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—222no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4(C22⋊D11)⋊C412yes—
339C2×C4#6693511yescharacteristic
340C2×C4#6693911yescharacteristic
341C8—444no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—81no—
348C22—81no—
349C22—881no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22—881no—
355C22—881no—
356C22#1062257111yescharacteristic
357C22#1062261911yescharacteristic
358C22#1062261911yescharacteristic
359C4—21no—
360C4—22no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—162no—
367C4—442no—
368C4—881no—
369C4—881no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—1761no—
374C2#1306899711yescharacteristic
375C2#1306907211yescharacteristic
376C2#1306914111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1820C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1820D11
hypocenterC11#9446
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
1. #13077254C2semidirect
4. #13066468C2semidirect
5. C11×#1820C2semidirect
12. #10622601C4semidirect
13. #10622601C4semidirect
14. #10622590C4semidirect
15. #10622589C4semidirect
111. #1820D11semidirect
296. C11#9446semidirect

Maximal subgroups

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

subgroupindex
#130772542
#130730742
#130671442
#130664682
C11×#18202
#944611