Finite Group Databasebeta

← #14645913

Subgroups — #14645913

Order 2816.

1026 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 119 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#13082380C211yesmaximal, characteristic
2#13067309C212yesmaximal, complemented
3#13067226C212yesmaximal, complemented
4#13066957C211yesmaximal, characteristic, complemented
5C11×#1955C211yesmaximal, characteristic, complemented
6C2×#67037C412yes—
7C2×C4×D4×C11C2211yescharacteristic
8C2×#66983—22no—
9#10623086—22no—
10#10623085—24no—
11D4×D44—22no—
12#10623041C412yes—
13#10623024—22no—
14#10623008C2212yes—
15C2×C11×C4⋊C8C2211yescharacteristic, complemented
16C2×C11×C22⋊C8—22no—
17C2×C11×#97C2211yescharacteristic, complemented
18#10622539C2212yescomplemented
19#10622163—22no—
20#10622123—22no—
21#10622119—22no—
22#10622102—24no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D412yes—
25C22×C22⋊D11—24no—
26#67037—48no—
27C2×#4341—24no—
28C2×D4×D11—24no—
29C2×#4339C2×C414yes—
30C22×D44—22no—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C4×D4×C11—22no—
34C4×D4×C11—22no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D412yes—
37C2×C42×C11C2311yescharacteristic
38#66983—24no—
39#66983—24no—
40#66983—24no—
41#66983—22no—
42#66983—22no—
43C2×(C2×D11)⋊C4—24no—
44C2×C4⋊Dic11—22no—
45#66950—24no—
46#66948—24no—
47#66939—28no—
48#66935—28no—
49#66928D414yes—
50#66927D412yes—
51C4×D44—22no—
52C4×D44—22no—
53#66922D412yes—
54C11×C4⋊C8—22no—
55C11×C22⋊C8—44no—
56C11×#97—22no—
57C22⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59#66867—22no—
60#8456—111nomaximal, Sylow
61C24×C11C22⋊C412yes—
62C23×D11—24no—
63C2×D4×C11—24no—
64C2×D4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11C22⋊C412yes—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—28no—
74C2×C22⋊D11—24no—
75C2×C22⋊D11—48no—
76C2×C22⋊D11—48no—
77C22×Dic11—24no—
78#4341—416no—
79D4×D11—416no—
80#4339—48no—
81C2×D44—24no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—82no—
85C2×D44—82no—
86C2×D44C22⋊C414yes—
87C2×C4×D11—24no—
88C2×Dic22C22⋊C414yes—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C2×C8×C11—42no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—22no—
95C11×C22⋊C4—24no—
96C42×C11C2×D412yes—
97C42×C11C2×D412yes—
98(C2×D11)⋊C4—28no—
99(C2×D11)⋊C4—24no—
100(C2×D11)⋊C4—24no—
101C4⋊Dic11—24no—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104C2×C11⋊C8—42no—
105#3496—111no—
106#1955D1111yescharacteristic, complemented
107#1551—112no—
108#1530—112no—
109#1466—111no—
110C23×C11—22no—
111C23×C11—22no—
112C23×C11—42no—
113C23×C11—42no—
114C23×C11#10014yes—
115C23×C11C2×C22⋊C411yescharacteristic
116C22×D11—24no—
117C22×D11—48no—
118C22×D11—84no—
119C22×D11—84no—
120D4×C11—28no—
121C2×C4×C11—22no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—82no—
130C2×C4×C11C2×C22⋊C412yes—
131C2×C4×C11#12012yes—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C22⋊D11—416no—
135C22⋊D11—48no—
136C2×Dic11—24no—
137C2×Dic11—48no—
138D44—44no—
139D44—42no—
140D44—42no—
141D44—82no—
142D44—84no—
143C4×D11—48no—
144Dic22—44no—
145C8×C11—42no—
146C8×C11—81no—
147C11⋊C8—82no—
148C2×H(5,𝔽2)—112no—
149#547—222no—
150#546—224no—
151D42—222no—
152#537—112no—
153#534—222no—
154#532—112no—
155C2×#121—222no—
156C2×C4×D4C2×D1111yescharacteristic
157#432—112no—
158C2×C4⋊C8C2×D1111yescharacteristic, complemented
159C2×C22⋊C8—22no—
160C2×#97C2×D1111yescharacteristic, complemented
161#333—222no—
162#331—222no—
163#329—224no—
164#323—222no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—24no—
168C22×C11—44no—
169C22×C11—42no—
170C22×C11—42no—
171C22×C11—82no—
172C22×C11#37911yescharacteristic
173C22×C11C2×#10012yes—
174C2×D11—44no—
175C2×D11—44no—
176C2×D11—44no—
177C2×D11—168no—
178C4×C11—21no—
179C4×C11—22no—
180C4×C11—22no—
181C4×C11—42no—
182C4×C11#45311yescharacteristic
183C4×C11#45511yescharacteristic
184Dic11—44no—
185H(5,𝔽2)—448no—
186C2×#41—114no—
187C2×#41—224no—
188C22×D4—222no—
189C22×D4—224no—
190C22×D4—224no—
191C22×D4C4×D1111yescharacteristic
192C23×C4C22⋊D1112yes—
193C22×C8—21no—
194C22×C8—21no—
195C4⋊Q8—112no—
196#127—112no—
197#124—114no—
198#123—228no—
199C22⋊Q8—224no—
200#121—224no—
201#121—224no—
202#121—224no—
203#121—224no—
204#121—222no—
205#121—222no—
206#120—228no—
207C4×D4—22no—
208C4×D4—22no—
209C4×D4—222no—
210C4×D4—222no—
211C2×C4⋊C4—222no—
212C2×C4⋊C4C4×D1111yescharacteristic
213C2×C22⋊C4—224no—
214C2×C22⋊C4D4412yes—
215C2×C42C22×D1111yescharacteristic
216C4⋊C8—22no—
217C4⋊C8—222no—
218C22⋊C8—44no—
219C22⋊C8—222no—
220#97—22no—
221#97—222no—
222C2×C11—22no—
223C2×C11—44no—
224C2×C11#178311yescharacteristic
225C2×C11#179211yescharacteristic
226C2×C11#179411yescharacteristic
227D11—84no—
228C24—224no—
229C24(C2×D11)⋊C412yes—
230#41—448no—
231#41—4416no—
232C2×Q8—114no—
233C2×D4—24no—
234C2×D4—22no—
235C2×D4—114no—
236C2×D4—224no—
237C2×D4—228no—
238C2×D4—224no—
239C2×D4—222no—
240C2×D4—222no—
241C2×D4—4416no—
242C2×D4—448no—
243C2×D4—448no—
244C2×D4—882no—
245C2×D4—882no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—224no—
251C22×C4—224no—
252C22×C4(C2×D11)⋊C412yes—
253C22×C4C2×C4×D1111yescharacteristic
254C22×C4C2×D4411yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—442no—
262C4⋊C4—22no—
263C4⋊C4—224no—
264C4⋊C4—222no—
265C4⋊C4—222no—
266C22⋊C4—24no—
267C22⋊C4—228no—
268C22⋊C4—224no—
269C22⋊C4—224no—
270C42D4×D1112yes—
271C42D4×D1112yes—
272C11#845611yescharacteristic, complemented, Sylow
273C23—22no—
274C23—22no—
275C23—42no—
276C23—42no—
277C23—224no—
278C23—448no—
279C23—884no—
280C23—884no—
281C23#6688714yes—
282C23C2×(C2×D11)⋊C411yescharacteristic
283Q8—444no—
284D4—28no—
285D4—444no—
286D4—4416no—
287D4—448no—
288D4—442no—
289D4—442no—
290D4—882no—
291D4—884no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—224no—
302C2×C4—448no—
303C2×C4—448no—
304C2×C4C22⋊C4×D1112yes—
305C2×C4#6693512yes—
306C2×C4#6699011yescharacteristic
307C2×C4#6699011yescharacteristic
308C8—42no—
309C8—81no—
310C8—882no—
311C22—21no—
312C22—21no—
313C22—24no—
314C22—44no—
315C22—42no—
316C22—42no—
317C22—82no—
318C22—444no—
319C22—444no—
320C22—444no—
321C22—1768no—
322C22#1062256811yescharacteristic
323C22C2×#6688712yes—
324C4—21no—
325C4—22no—
326C4—22no—
327C4—42no—
328C4—444no—
329C4#1062267411yescharacteristic
330C4#1062269011yescharacteristic
331C2—22no—
332C2—44no—
333C2—884no—
334C2#1306853611yescharacteristic
335C2#1306856911yescharacteristic
336C2#1306857911yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1955C2
socleC22×C11#379
prime radical#13082380C2
cosocleC2×C42×C11C23
hypercenter#1955D11
hypocenterC11#8456
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. #13067309C2semidirect
3. #13067226C2semidirect
4. #13066957C2semidirect
5. C11×#1955C2semidirect
15. C2×C11×C4⋊C8C22semidirect
17. C2×C11×#97C22semidirect
18. #10622539C22semidirect
106. #1955D11semidirect
158. C2×C4⋊C8C2×D11semidirect
160. C2×#97C2×D11semidirect
272. C11#8456semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130673092
#130672262
#130669572
C11×#19552
#845611