Finite Group Databasebeta

← #14643079

Subgroups — #14643079

Order 2816.

494 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 83 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#13075642C211yesmaximal, characteristic
2#13070154C211yesmaximal, characteristic, complemented
3#13070148C212yesmaximal, complemented
4#13066436C212yesmaximal, complemented
5C11×#1272C211yesmaximal, characteristic, complemented
6C2×#67000—21no—
7C11×#391C2211yescharacteristic
8C2×#66899—21no—
9C2×#66885—22no—
10C2×#66881—22no—
11#10622604—21no—
12C2×#66871—21no—
13#10622552C2212yes—
14#10622548C2211yescharacteristic
15#10622284—22no—
16#10622283—22no—
17C11×#336C2212yes—
18#10622162C2211yescharacteristic
19C22×Q8×C11D411yescharacteristic
20C22×D44—21no—
21C22×D44—21no—
22C22×D44D412yes—
23C22×C8×C11—22no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C42×C11C2311yescharacteristic
26#67000—42no—
27#67000—42no—
28C2×(C2×D11)⋊C4—22no—
29C2×(C2×D11)⋊C4—22no—
30C2×(C2×D11)⋊C4—22no—
31C2×(C2×D11)⋊C4—22no—
32C2×C4⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11D412yes—
35C2×C4×Dic11—21no—
36C22×C11⋊C8—21no—
37C11×#95—22no—
38#66899—42no—
39C11⋊#95—21no—
40#66885—44no—
41#66881—44no—
42#66871—42no—
43#7830—111nomaximal, Sylow
44C23×D11—22no—
45C2×Q8×C11—21no—
46C2×Q8×C11—41no—
47C2×Q8×C11—41no—
48C2×Q8×C11SD1612yes—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D412yes—
53C22×Dic11—22no—
54C22×Dic11—41no—
55C2×D44—22no—
56C2×D44—22no—
57C2×D44—42no—
58C2×D44—42no—
59C2×D44—42no—
60C2×D44—81no—
61C2×D44—81no—
62C2×D44—82no—
63C2×D44—81no—
64C2×C8×C11—24no—
65C2×C8×C11—42no—
66C2×C8×C11—42no—
67C11×C4⋊C4—41no—
68C42×C11—41no—
69(C2×D11)⋊C4—44no—
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4—42no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—82no—
75C4⋊Dic11—42no—
76C4⋊Dic11—41no—
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79C4⋊Dic11—41no—
80C4×Dic11—42no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84#2733—111no—
85#2095—111no—
86#2094—112no—
87#1272D1111yescharacteristic, complemented
88#1270—112no—
89C23×C11#12011yescharacteristic
90C22×D11—42no—
91C22×D11—42no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96C22×D11—42no—
97Q8×C11—42no—
98Q8×C11—81no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—41no—
108C2×C4×C11C2×SD1611yescharacteristic
109C2×C4×C11#13512yes—
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C11#13712yes—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—81no—
116C2×Dic11—82no—
117D44—44no—
118D44—82no—
119D44—84no—
120D44—84no—
121C8×C11—44no—
122C11⋊C8—42no—
123C2×#124—221no—
124C2×#107—221no—
125C2×#106—222no—
126C2×#103—221no—
127C2×#102—222no—
128#394—221no—
129#392—222no—
130#391C2×D1111yescharacteristic
131#390—112no—
132#388—222no—
133#384—111no—
134#336—111no—
135#336C2×D1112yes—
136C22×C11#45011yescharacteristic
137C22×C11#45212yes—
138C22×C11#45311yescharacteristic
139C22×C11#45312yes—
140C22×C11#45811yescharacteristic
141C2×D11—82no—
142C2×D11—82no—
143C2×D11—82no—
144C2×D11—82no—
145C2×D11—82no—
146C2×D11—82no—
147C2×D11—82no—
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—22no—
151C4×C11—22no—
152C4×C11—42no—
153C4×C11—81no—
154Dic11—82no—
155Dic11—161no—
156C22×Q8D4411yescharacteristic
157C22×D4—112no—
158C22×D4—221no—
159C22×D4—221no—
160C22×C8—22no—
161C22×C8—221no—
162#124—442no—
163#124—442no—
164C2×C4⋊C4—112no—
165C2×C4⋊C4—221no—
166C2×C4⋊C4—222no—
167C2×C4⋊C4D4411yescharacteristic
168C2×C22⋊C4—222no—
169C2×C22⋊C4—222no—
170C2×C22⋊C4—222no—
171C2×C22⋊C4—222no—
172C2×C42—221no—
173C2×C42C22×D1111yescharacteristic
174#107—442no—
175#106—444no—
176#103—442no—
177#102—444no—
178#95—22no—
179#95—221no—
180C2×C11#161311yescharacteristic
181C2×C11#161812yes—
182C2×C11#163112yes—
183C2×C11#163411yescharacteristic
184C2×C11#165511yescharacteristic
185D11—162no—
186C24—222no—
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8#431412yes—
191C2×D4—222no—
192C2×D4—222no—
193C2×D4—442no—
194C2×D4—442no—
195C2×D4—442no—
196C2×D4—881no—
197C2×D4—881no—
198C2×D4—881no—
199C2×D4—882no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—222no—
203C22×C4—441no—
204C22×C4C2×D4411yescharacteristic
205C22×C4D4×D1112yes—
206C2×C8—24no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—222no—
210C2×C8—441no—
211C2×C8—441no—
212C4⋊C4—41no—
213C4⋊C4—442no—
214C4⋊C4—442no—
215C4⋊C4—441no—
216C4⋊C4—442no—
217C4⋊C4—441no—
218C22⋊C4—444no—
219C22⋊C4—442no—
220C22⋊C4—442no—
221C22⋊C4—442no—
222C22⋊C4—442no—
223C22⋊C4—882no—
224C42—41no—
225C42—442no—
226C11#783011yescharacteristic, complemented, Sylow
227C23—442no—
228C23—442no—
229C23—442no—
230C23—442no—
231C23—442no—
232C23—442no—
233C23—442no—
234C23#6693511yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—444no—
238D4—882no—
239D4—884no—
240D4—884no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4—442no—
253C2×C4—881no—
254C2×C4—882no—
255C2×C4C2×#431411yescharacteristic
256C2×C4#6696111yescharacteristic
257C2×C4#6696912yes—
258C2×C4#6697112yes—
259C8—44no—
260C8—442no—
261C22—882no—
262C22—882no—
263C22—882no—
264C22—882no—
265C22—882no—
266C22—882no—
267C22—882no—
268C22#1062234411yescharacteristic
269C22#1062235511yescharacteristic
270C22#1062236011yescharacteristic
271C22#1062242312yes—
272C22#1062243512yes—
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—81no—
279C4—882no—
280C4—1761no—
281C2—1762no—
282C2#1306763811yescharacteristic
283C2#1306766712yes—
284C2#1306774512yes—
285C2#1306776211yescharacteristic
286C2#1306790611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11#120
prime radical#13075642C2
hypercenter#1272D11
hypocenterC11#7830
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #13070154C2semidirect
3. #13070148C2semidirect
4. #13066436C2semidirect
5. C11×#1272C2semidirect
87. #1272D11semidirect
226. C11#7830semidirect

Maximal subgroups

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

subgroupindex
#130756422
#130701542
#130701482
#130664362
C11×#12722
#783011