Finite Group Databasebeta

← #14650735

Subgroups — #14650735

Order 2816.

438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079603C211yesmaximal, characteristic
2#13077686C211yesmaximal, characteristic, complemented
3#13067322C211yesmaximal, characteristic, complemented
4#13066968C211yesmaximal, characteristic, complemented
5C11⋊#1308C211yesmaximal, characteristic, complemented
6#13066477C211yesmaximal, characteristic, complemented
7C11×#1533C211yesmaximal, characteristic, complemented
8C2×C11×#124C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12#10622840C412yes—
13#10622830C412yes—
14#10622671—21no—
15#10622670—22no—
16#10622668—21no—
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622449—22no—
21#10622340—22no—
22#10622319—22no—
23C11×#329—22no—
24#10622163—22no—
25#10622124—21no—
26#10622123—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D4×C11C2×C411yescharacteristic
29C2×#4339—21no—
30C11×#124—21no—
31C11×#124—21no—
32C11×#124—21no—
33C11×#124—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4325—22no—
38C2×#4323—22no—
39#66983—21no—
40#66983C2×C412yes—
41C2×#4313—22no—
42C2×C8×D11—22no—
43#66928—21no—
44#66927D411yescharacteristic
45C4×D44—21no—
46C4×D44D412yes—
47#66922D411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#97—21no—
53C11×#97D412yes—
54#66899—22no—
55#66896—22no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)C2×C412yes—
58C22⋊(C11⋊C8)D412yes—
59(C2×D11)⋊C8—24no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
65C4×C11⋊C8—21no—
66#9333—111nomaximal, Sylow
67C24×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—81no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—81no—
74C22×C4×C11—21no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×C22⋊D11—22no—
79#4339—81no—
80#4339—81no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44C22⋊C412yes—
84C2×C4×D11—22no—
85C2×Dic22—21no—
86C2×C8×C11—22no—
87C2×C8×C11—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96#4325—82no—
97#4323—82no—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—22no—
100C4⋊Dic11—21no—
101C4⋊Dic11C22⋊C412yes—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—41no—
105#4313—82no—
106C8×D11—82no—
107#3213—111no—
108#2980—111no—
109#1553—111no—
110#1533D1111yescharacteristic, complemented
111#1469—111no—
112#1308—111no—
113#1287—111no—
114C23×C11—42no—
115C23×C11—41no—
116C23×C11—81no—
117C23×C11—81no—
118C23×C11C4×D411yescharacteristic
119C22×D11—22no—
120Q8×C11—42no—
121Q8×C11—81no—
122D4×C11—42no—
123D4×C11—81no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—81no—
129C2×C4×C11C2×C22⋊C411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12311yescharacteristic
135C22⋊D11—82no—
136C2×Dic11—22no—
137D44—42no—
138D44—81no—
139D44—81no—
140C4×D11—42no—
141C4×D11—42no—
142Dic22—81no—
143C8×C11—42no—
144C8×C11—81no—
145C11⋊C8—42no—
146C11⋊C8—42no—
147C11⋊C8—81no—
148#532—111no—
149C2×#124C2×D1111yescharacteristic
150#496—221no—
151#489—221no—
152#463—222no—
153#448—112no—
154#447—112no—
155#435—222no—
156#435—222no—
157#432—111no—
158#432—111no—
159#432C2×D1111yescharacteristic
160#432C2×D1111yescharacteristic
161#431—111no—
162#408—222no—
163#332—221no—
164#331—221no—
165#329—22no—
166#323—222no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—81no—
171C22×C11—81no—
172C22×C11—81no—
173C22×C11—162no—
174C22×C11#38611yescharacteristic
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—81no—
185Dic11—42no—
186C2×#41—221no—
187C22×Q8C4×D1111yescharacteristic
188C22×D4C4×D1111yescharacteristic
189C2×SD16—222no—
190C2×D8—222no—
191C2×M16—222no—
192C22×C8—222no—
193C4⋊Q8—111no—
194#127—111no—
195#124—21no—
196#124—21no—
197#124—21no—
198#124—21no—
199#124—221no—
200#121—112no—
201#121—221no—
202C4×D4—112no—
203C4×D4—221no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C42C22×D1111yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#103—222no—
213#102—222no—
214C22⋊C8—21no—
215C22⋊C8—21no—
216C22⋊C8—112no—
217C22⋊C8—112no—
218C22⋊C8—224no—
219C22⋊C8—221no—
220#97—21no—
221#97—221no—
222#97—221no—
223#97C22⋊D1112yes—
224C4×C8—221no—
225C2×C11—41no—
226C2×C11—161no—
227C2×C11#188111yescharacteristic
228C2×C11#190411yescharacteristic
229C2×C11#191411yescharacteristic
230D11—82no—
231C24—21no—
232#41—881no—
233#41—881no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—81no—
237C2×Q8—221no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—81no—
241C2×D4—112no—
242C2×D4—222no—
243C2×D4—221no—
244C2×D4—221no—
245C22×C4—21no—
246C22×C4—222no—
247C22×C4C2×C4×D1111yescharacteristic
248C22×C4D4×D1111yescharacteristic
249C22×C4#434111yescharacteristic
250SD16—882no—
251D8—882no—
252M16—882no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—222no—
256C2×C8—222no—
257C2×C8—441no—
258C2×C8—882no—
259C4⋊C4—112no—
260C4⋊C4—221no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—222no—
266C22⋊C4—222no—
267C42#433911yescharacteristic
268C42D4×D1111yescharacteristic
269C42D4×D1111yescharacteristic
270C42C2×C22⋊D1111yescharacteristic
271C11#933311yescharacteristic, complemented, Sylow
272C23—42no—
273C23—41no—
274C23—81no—
275C23—81no—
276C23—222no—
277C23(C22⋊D11)⋊C411yescharacteristic
278Q8—42no—
279Q8—81no—
280Q8—881no—
281D4—42no—
282D4—81no—
283D4—442no—
284D4—881no—
285D4—881no—
286D4—882no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—222no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4C22⋊C4×D1111yescharacteristic
296C2×C4#6693611yescharacteristic
297C2×C4#6693711yescharacteristic
298C2×C4C4×C22⋊D1111yescharacteristic
299C2×C4#6699011yescharacteristic
300C2×C4#6699111yescharacteristic
301C8—42no—
302C8—81no—
303C8—442no—
304C8—442no—
305C8—881no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—162no—
313C22—442no—
314C22—442no—
315C22—442no—
316C22#1062256911yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—442no—
325C2—41no—
326C2—161no—
327C2—882no—
328C2#1306897511yescharacteristic
329C2#1306910011yescharacteristic
330C2#1306916011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1533C2
socleC22×C11#386
prime radical#13079603C2
cosocleC2×C42×C11C23
hypercenter#1533D11
hypocenterC11#9333
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1533

Complements

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

NH ≅ G/Ntype
2. #13077686C2semidirect
3. #13067322C2semidirect
4. #13066968C2semidirect
5. C11⋊#1308C2semidirect
6. #13066477C2semidirect
7. C11×#1533C2semidirect
110. #1533D11semidirect
271. C11#9333semidirect

Maximal subgroups

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

subgroupindex
#130796032
#130776862
#130673222
#130669682
C11⋊#13082
#130664772
C11×#15332
#933311