Finite Group Databasebeta

← #14735074

Subgroups — #14735074

Order 2816.

808 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C2×C11⋊#564C211yesmaximal, characteristic, complemented
2#13079802C212yesmaximal
3#13067942C214yesmaximal, complemented
4#13067917C214yesmaximal, complemented
5#13067243C211yesmaximal, characteristic, complemented
6#13067217C212yesmaximal, complemented
7C11×#3142C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C11⋊#564—22no—
11C11⋊#564—24no—
12C11⋊#564C2214yes—
13C2×#66943—22no—
14C2×#66942—22no—
15C2×#66942—22no—
16C2×#66923C2212yes—
17C11×#491C2212yes—
18C11×#490C2212yes—
19C11×#488—22no—
20C11×#417—22no—
21C4×C11×M16C2211yescharacteristic
22#10622693C2214yes—
23#10622684C2214yes—
24#10622647—22no—
25#10622646—22no—
26#10622622—24no—
27#10622539C2212yes—
28#10622181C2214yes—
29#10622103C2218yes—
30C2×C11×#41—21no—
31C2×C11×M16—21no—
32C11×C4⋊Q8C2311yescharacteristic
33C11×#127C2311yescharacteristic
34C11×#125—22no—
35C11×#125D412yes—
36C11×#125C2312yes—
37C11×#124—21no—
38C11×#121—22no—
39C4×D4×C11—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4D412yes—
42C2×C42×C11C2311yescharacteristic
43C2×C4⋊Dic11—22no—
44C2×C4⋊Dic11D412yes—
45C2×C4⋊Dic11D412yes—
46C2×Dic11⋊C4—22no—
47C2×Dic11⋊C4—22no—
48C2×Dic11⋊C4—22no—
49C2×Dic11⋊C4—22no—
50C2×C4×Dic11—22no—
51#66943—28no—
52#66943—28no—
53#66942—28no—
54#66942—28no—
55#66942—28no—
56#66942—28no—
57#66923—22no—
58#66923—22no—
59#66923D414yes—
60#66923C2314yes—
61C11×#103—24no—
62C11×#102—24no—
63C11×#97C2312yes—
64C4×C8×C11—21no—
65#66896—24no—
66#66896—24no—
67C22⋊(C11⋊C8)—22no—
68#66872—24no—
69#66871—24no—
70C4⋊(C11⋊C8)—22no—
71#66867C2314yes—
72#19003—111nomaximal, Sylow
73C11×#41—44no—
74C2×Q8×C11—21no—
75C2×D4×C11—22no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C22×C4×C11—22no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×Dic11—22no—
83C22×Dic11—22no—
84C11×M16—42no—
85C2×C8×C11—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4C2×D414yes—
91C11×C22⋊C4—42no—
92C42×C11C2×D412yes—
93C42×C11C2×D411yescharacteristic
94C42×C11C2411yescharacteristic
95C4⋊Dic11—28no—
96C4⋊Dic11—22no—
97C4⋊Dic11—22no—
98C4⋊Dic11C2×D414yes—
99C4⋊Dic11C2×D414yes—
100Dic11⋊C4—28no—
101Dic11⋊C4—28no—
102Dic11⋊C4—24no—
103Dic11⋊C4—24no—
104Dic11⋊C4—24no—
105Dic11⋊C4—24no—
106C4×Dic11—28no—
107C2×C11⋊C8—24no—
108C2×#564—111no—
109#3234—112no—
110#3142D1111yescharacteristic
111#1663—114no—
112#1658—114no—
113#1534—111no—
114#1528—112no—
115C23×C11—41no—
116C23×C11#12011yescharacteristic
117Q8×C11—42no—
118D4×C11—44no—
119D4×C11—42no—
120D4×C11—82no—
121C2×C4×C11—22no—
122C2×C4×C11—24no—
123C2×C4×C11—42no—
124C2×C4×C11—44no—
125C2×C4×C11—41no—
126C2×C4×C11—82no—
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12012yes—
129C2×C4×C11C22×D412yes—
130C2×C4×C11C22×D411yescharacteristic
131C2×Dic11—24no—
132C2×Dic11—24no—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C8×C11—42no—
136C11⋊C8—44no—
137#564—114no—
138#564—224no—
139#564—222no—
140#532C2×D1111yescharacteristic
141C2×#125—112no—
142C2×#125—222no—
143C2×#125—222no—
144C2×#125—222no—
145C2×#125C2×D1111yescharacteristic
146#501—114no—
147#491C2×D1112yes—
148#490—114no—
149#490C2×D1112yes—
150#488—22no—
151#481—222no—
152#480—222no—
153#478—224no—
154#432—112no—
155#417—22no—
156C4×M16C2×D1111yescharacteristic
157#330—114no—
158#330—118no—
159C22×C11—22no—
160C22×C11—81no—
161C22×C11—82no—
162C22×C11#45412yes—
163C22×C11C2×#12011yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—44no—
169C4×C11—81no—
170Dic11—44no—
171Dic11—44no—
172C2×#41—21no—
173C2×M16—21no—
174C4⋊Q8C22×D1111yescharacteristic
175#127C22×D1111yescharacteristic
176#125—22no—
177#125—114no—
178#125—114no—
179#125—228no—
180#125—228no—
181#125—228no—
182#125—228no—
183#125—228no—
184#125—228no—
185#125—222no—
186#125—222no—
187#125C22⋊D1112yes—
188#125C22×D1112yes—
189#124—21no—
190#121—22no—
191C4×D4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—112no—
194C2×C4⋊C4—112no—
195C2×C4⋊C4—222no—
196C2×C4⋊C4—222no—
197C2×C4⋊C4—222no—
198C2×C4⋊C4—222no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4C22⋊D1112yes—
201C2×C42—222no—
202C2×C42C22×D1111yescharacteristic
203#107—224no—
204#106—224no—
205C4⋊C8—222no—
206#103—24no—
207#102—24no—
208#102—224no—
209#102—224no—
210C22⋊C8—222no—
211#97—114no—
212#97C22×D1112yes—
213C4×C8—21no—
214C2×C11—22no—
215C2×C11—161no—
216C2×C11C2×#45411yescharacteristic
217C2×C11#302012yes—
218#41—44no—
219C2×Q8—21no—
220C2×D4—22no—
221C2×D4—21no—
222C2×D4—41no—
223C22×C4—22no—
224C22×C4—41no—
225C22×C4—222no—
226C22×C4—222no—
227C22×C4D4×D1112yes—
228C22×C4C2×C22⋊D1111yescharacteristic
229M16—42no—
230C2×C8—22no—
231C2×C8—224no—
232C4⋊C4—24no—
233C4⋊C4—22no—
234C4⋊C4—24no—
235C4⋊C4—22no—
236C4⋊C4—114no—
237C4⋊C4—114no—
238C4⋊C4—228no—
239C4⋊C4—228no—
240C4⋊C4—228no—
241C4⋊C4—222no—
242C4⋊C4—222no—
243C4⋊C4—224no—
244C4⋊C4—224no—
245C4⋊C4—224no—
246C4⋊C4—224no—
247C4⋊C4C2×C22⋊D1114yes—
248C22⋊C4—42no—
249C42—228no—
250C42D4×D1112yes—
251C42C2×C22⋊D1111yescharacteristic
252C42C23×D1111yescharacteristic
253C11#1900311yescharacteristic, complemented, Sylow
254C23—41no—
255C23#6699011yescharacteristic
256Q8—42no—
257D4—44no—
258D4—42no—
259D4—82no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—42no—
263C2×C4—44no—
264C2×C4—41no—
265C2×C4—82no—
266C2×C4—224no—
267C2×C4—224no—
268C2×C4—444no—
269C2×C4—444no—
270C2×C4#6699011yescharacteristic
271C2×C4#6699012yes—
272C2×C4C2×D4×D1112yes—
273C2×C4C22×C22⋊D1111yescharacteristic
274C8—42no—
275C8—444no—
276C22—22no—
277C22—81no—
278C22—82no—
279C22#1062267512yes—
280C22C2×#6699011yescharacteristic
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—44no—
286C4—81no—
287C4—444no—
288C4—444no—
289C2—22no—
290C2—161no—
291C2C2×#1062267511yescharacteristic
292C2#1307797812yes—
subgroupG/H
centerC22C2×#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3142C2
socleC22×C11C2×#120
prime radicalC11×#532C22
hypercenter#3142D11
hypocenterC11#19003
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. C2×C11⋊#564C2semidirect
3. #13067942C2semidirect
4. #13067917C2semidirect
5. #13067243C2semidirect
6. #13067217C2semidirect
253. C11#19003semidirect

Maximal subgroups

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

subgroupindex
C2×C11⋊#5642
#130798022
#130679422
#130679172
#130672432
#130672172
C11×#31422
#1900311