Finite Group Databasebeta

← #14650755

Subgroups — #14650755

Order 2816.

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

normal subgroups only

This group has 400 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#13079806C211yesmaximal, characteristic
2#13077686C211yesmaximal, characteristic
3#13067319C211yesmaximal, characteristic
4#13067243C211yesmaximal, characteristic, complemented
5C11⋊#1308C211yesmaximal, characteristic, complemented
6#13066478C211yesmaximal, characteristic, complemented
7C11×#1470C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#431C2211yescharacteristic
12#10622680—21no—
13#10622679—22no—
14#10622678—21no—
15#10622581C412yes—
16#10622580C412yes—
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622539C2211yescharacteristic
20#10622449—22no—
21#10622340—22no—
22#10622319—22no—
23C11×#324—22no—
24#10622181—22no—
25#10622123—21no—
26#10622120—21no—
27C2×#4339—21no—
28C11×#125—21no—
29C11×#125—21no—
30C11×#125—21no—
31C11×#125—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37#66983—21no—
38#66983C2×C412yes—
39C2×#4313—22no—
40C2×C8×D11—22no—
41#66928—21no—
42#66927D411yescharacteristic
43C4×D44—21no—
44C4×D44D412yes—
45#66922D411yescharacteristic
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×C22⋊C8D412yes—
50C11×#97—21no—
51C4×C8×C11—21no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54C22⋊(C11⋊C8)C2×C412yes—
55(C2×D11)⋊C8—24no—
56#66873—22no—
57#66873—22no—
58#66872—22no—
59#66871—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
65#66867D412yes—
66#9335—111nomaximal, Sylow
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C2×C22⋊D11—22no—
73#4339—81no—
74#4339—81no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44C22⋊C412yes—
78C2×C4×D11—22no—
79C2×Dic22—21no—
80C2×C8×C11—22no—
81C2×C8×C11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96C4⋊Dic11—21no—
97C4⋊Dic11C22⋊C412yes—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101#4313—82no—
102C8×D11—82no—
103#3234—111no—
104#2980—111no—
105#1553—111no—
106#1534—111no—
107#1470D1111yescharacteristic, complemented
108#1308—111no—
109#1287—111no—
110C23×C11C4×D411yescharacteristic
111C22×D11—22no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—81no—
119C2×C4×C11C2×C22⋊C411yescharacteristic
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12311yescharacteristic
125C22⋊D11—82no—
126C2×Dic11—22no—
127D44—42no—
128D44—81no—
129D44—81no—
130C4×D11—42no—
131C4×D11—42no—
132Dic22—81no—
133C8×C11—42no—
134C8×C11—81no—
135C11⋊C8—42no—
136C11⋊C8—42no—
137C11⋊C8—81no—
138#532—111no—
139C2×#125C2×D1111yescharacteristic
140#501—221no—
141#490—221no—
142#481—112no—
143#480—112no—
144#478—222no—
145#435—222no—
146#435—222no—
147#432—111no—
148#432—111no—
149#432—111no—
150#432C2×D1111yescharacteristic
151#431C2×D1111yescharacteristic
152#408—222no—
153#332—221no—
154#331—221no—
155#330—222no—
156#324—22no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11#38611yescharacteristic
161C2×D11—42no—
162C2×D11—42no—
163C2×D11—42no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—81no—
171C4×C11—81no—
172Dic11—42no—
173C2×#41—221no—
174C2×M16—222no—
175C22×C8—222no—
176C4⋊Q8—111no—
177#127—111no—
178#125—21no—
179#125—21no—
180#125—21no—
181#125—21no—
182#124—221no—
183#121—112no—
184#121—221no—
185C4×D4—112no—
186C4×D4—221no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C4×D1111yescharacteristic
190C2×C4⋊C4C4×D1111yescharacteristic
191C2×C42C22×D1111yescharacteristic
192#107—222no—
193#106—222no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—221no—
197C4⋊C8—221no—
198C4⋊C8—221no—
199#102—222no—
200#102—222no—
201C22⋊C8—21no—
202C22⋊C8—112no—
203C22⋊C8—224no—
204C22⋊C8—221no—
205C22⋊C8—221no—
206C22⋊C8C22⋊D1112yes—
207#97—21no—
208#97—112no—
209#97—221no—
210#97—221no—
211C4×C8—21no—
212C2×C11—41no—
213C2×C11#188111yescharacteristic
214C2×C11#190411yescharacteristic
215C2×C11#191511yescharacteristic
216D11—82no—
217#41—881no—
218#41—881no—
219C2×Q8—221no—
220C2×D4—112no—
221C2×D4—222no—
222C2×D4—221no—
223C2×D4—221no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—222no—
227C22×C4C2×C4×D1111yescharacteristic
228C22×C4#433911yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230M16—882no—
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—222no—
234C2×C8—222no—
235C2×C8—441no—
236C2×C8—882no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—112no—
246C4⋊C4—221no—
247C22⋊C4—222no—
248C22⋊C4—222no—
249C42D4×D1111yescharacteristic
250C42D4×D1111yescharacteristic
251C42D4×D1111yescharacteristic
252C42#434111yescharacteristic
253C11#933511yescharacteristic, complemented, Sylow
254C23—222no—
255C23C4×C22⋊D1111yescharacteristic
256Q8—881no—
257D4—442no—
258D4—881no—
259D4—881no—
260D4—882no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—81no—
268C2×C4—222no—
269C2×C4—442no—
270C2×C4—442no—
271C2×C4C22⋊C4×D1111yescharacteristic
272C2×C4(C22⋊D11)⋊C411yescharacteristic
273C2×C4#6693611yescharacteristic
274C2×C4#6693711yescharacteristic
275C2×C4#6699011yescharacteristic
276C2×C4#6699111yescharacteristic
277C8—42no—
278C8—81no—
279C8—442no—
280C8—442no—
281C8—881no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—442no—
286C22—442no—
287C22—442no—
288C22#1062256911yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—81no—
296C4—81no—
297C4—442no—
298C2—41no—
299C2—882no—
300C2#1306898111yescharacteristic
301C2#1306910611yescharacteristic
302C2#1306916511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1470C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1470D11
hypocenterC11#9335
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
4. #13067243C2semidirect
5. C11⋊#1308C2semidirect
6. #13066478C2semidirect
7. C11×#1470C2semidirect
107. #1470D11semidirect
253. C11#9335semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130776862
#130673192
#130672432
C11⋊#13082
#130664782
C11×#14702
#933511