Finite Group Databasebeta

← #14654749

Subgroups — #14654749

Order 2816.

584 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 105 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#13078643C212yesmaximal, complemented
2#13069556C211yesmaximal, characteristic, complemented
3#13067015C212yesmaximal, complemented
4#13066447C211yesmaximal, characteristic, complemented
5C11×#3150C211yesmaximal, characteristic
6C2×C11×#135—22no—
7C11×#532C2212yes—
8C2×C4×Dic22C2211yescharacteristic
9C11×#497—22no—
10C11×#496—22no—
11C2×C11×#97C2211yescharacteristic
12#10622707—22no—
13#10622688—22no—
14#10622653—22no—
15#10622647—22no—
16C4×#4324—24no—
17#10622538C2212yes—
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19#10622188—22no—
20D4⋊(C11⋊C8)—24no—
21C2×C11×#41—22no—
22C22×Dic22D411yescharacteristic
23C11×#135—44no—
24C11×#135—44no—
25C2×C11×Q16—22no—
26C2×C11×SD16—24no—
27C2×C11×D8—22no—
28C22×C8×C11D412yes—
29C11×C4⋊Q8D412yes—
30C11×#127D412yes—
31C11×#124—22no—
32C11×#121—22no—
33C11×#121—22no—
34C4×D4×C11—22no—
35C4×D4×C11—22no—
36C2×C42×C11C2311yescharacteristic
37C2×#4324—24no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—21no—
41C22×C11⋊C8—21no—
42C4×Dic22—22no—
43C4×Dic22—22no—
44C11×#97—22no—
45#66896—24no—
46C22⋊(C11⋊C8)—22no—
47#66874—24no—
48#66872—24no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51C4×C11⋊C8D414yes—
52#10034—111nomaximal, Sylow
53C11×#41—44no—
54C11×#41—44no—
55C2×Q8×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C2×Dic22—22no—
67C2×Dic22—42no—
68C11×Q16—44no—
69C11×SD16—48no—
70C11×D8—44no—
71C2×C8×C11—22no—
72C2×C8×C11—22no—
73C2×C8×C11SD1614yescomplemented
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C22⋊C4—42no—
77C11×C22⋊C4—42no—
78C42×C11C2×D412yes—
79C42×C11C2×D412yes—
80#4324—48no—
81C4⋊Dic11—22no—
82Dic11⋊C4—42no—
83C4×Dic11—41no—
84C4×Dic11—41no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—42no—
88#3150D1111yescharacteristic
89#3103—112no—
90#1985—111no—
91#1480—112no—
92#1275—111no—
93C23×C11—42no—
94C23×C11#12111yescharacteristic
95Q8×C11—44no—
96D4×C11—44no—
97D4×C11—44no—
98D4×C11—44no—
99D4×C11—84no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—82no—
104C2×C4×C11—82no—
105C2×C4×C11#12012yes—
106C2×C4×C11#12011yescharacteristic
107C2×C4×C11#12112yes—
108C2×C4×C11#12711yescharacteristic
109C2×C4×C11C2×SD1612yes—
110C2×C4×C11AGL(1,ℤ/8)12yes—
111C2×Dic11—22no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—42no—
115C2×Dic11—41no—
116Dic22—24no—
117Dic22—42no—
118C8×C11—24no—
119C11⋊C8—44no—
120C11⋊C8—81no—
121C2×#135—22no—
122#532C2×D1112yes—
123C2×C4×Q8—111no—
124#497—22no—
125#496—22no—
126#481—222no—
127#475—222no—
128#460—222no—
129#448—222no—
130C4×SD16—224no—
131#431—112no—
132C2×C4⋊C8—111no—
133C2×#97C2×D1111yescharacteristic
134#336—222no—
135D4⋊C8—224no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11—82no—
139C22×C11—82no—
140C22×C11—82no—
141C22×C11#39211yescharacteristic
142C22×C11#46012yes—
143C4×C11—22no—
144C4×C11—22no—
145C4×C11—82no—
146C4×C11#45012yes—
147C4×C11#49211yescharacteristic
148C4×C11#49611yescharacteristic
149Dic11—42no—
150Dic11—81no—
151C2×#41—22no—
152C22×Q8—111no—
153#135—44no—
154#135—44no—
155C2×Q16—22no—
156C2×SD16—24no—
157C2×SD16—224no—
158C2×D8—22no—
159C22×C8—221no—
160C22×C8C22⋊D1112yes—
161C4⋊Q8C22⋊D1112yes—
162#127C22⋊D1112yes—
163#124—22no—
164#121—22no—
165#121—22no—
166C4×Q8—222no—
167C4×Q8—222no—
168C4×D4—22no—
169C4×D4—22no—
170C2×C4⋊C4—111no—
171C2×C4⋊C4—221no—
172C2×C42—221no—
173C2×C42C22×D1111yescharacteristic
174#106—224no—
175C4⋊C8—222no—
176C4⋊C8—222no—
177#103—224no—
178#102—224no—
179C22⋊C8—222no—
180#97—22no—
181C4×C8—114no—
182C2×C11—22no—
183C2×C11—162no—
184C2×C11#201011yescharacteristic
185C2×C11#201411yescharacteristic
186C2×C11#201711yescharacteristic
187#41—44no—
188#41—44no—
189C2×Q8—22no—
190C2×Q8—222no—
191C2×Q8—442no—
192C2×D4—22no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—42no—
196C22×C4—42no—
197C22×C4—221no—
198C22×C4—221no—
199C22×C4D4×D1111yescharacteristic
200C22×C4#434111yescharacteristic
201C22×C4C2×C22⋊D1111yescharacteristic
202Q16—44no—
203SD16—48no—
204SD16—448no—
205D8—44no—
206C2×C8—22no—
207C2×C8—22no—
208C2×C8—224no—
209C2×C8—442no—
210C2×C8—441no—
211C2×C8#432414yescomplemented
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—222no—
215C4⋊C4—442no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C42—441no—
219C42—441no—
220C42D4×D1112yes—
221C42C2×C22⋊D1112yes—
222C11#1003411yescharacteristic, complemented, Sylow
223C23—42no—
224C23#6699111yescharacteristic
225Q8—44no—
226Q8—224no—
227Q8—442no—
228D4—44no—
229D4—44no—
230D4—44no—
231D4—84no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4—222no—
238C2×C4—441no—
239C2×C4—441no—
240C2×C4—442no—
241C2×C4—441no—
242C2×C4#6698512yes—
243C2×C4C2×#432412yes—
244C2×C4#6699012yes—
245C2×C4#6699212yes—
246C2×C4#6699311yescharacteristic
247C2×C4#6700611yescharacteristic
248C8—24no—
249C8—444no—
250C8—881no—
251C22—21no—
252C22—21no—
253C22—82no—
254C22—82no—
255C22—82no—
256C22#1062268812yes—
257C22#1062283611yescharacteristic
258C4—22no—
259C4—22no—
260C4—82no—
261C4—442no—
262C4—881no—
263C4#1062268711yescharacteristic
264C4#1062268911yescharacteristic
265C4#1062283112yes—
266C2—22no—
267C2—162no—
268C2#1306968011yescharacteristic
269C2#1306970411yescharacteristic
270C2#1306971911yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3150C2
socleC22×C11#392
hypercenter#3150D11
hypocenterC11#10034
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3150

Complements

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

NH ≅ G/Ntype
1. #13078643C2semidirect
2. #13069556C2semidirect
3. #13067015C2semidirect
4. #13066447C2semidirect
73. C2×C8×C11SD16semidirect
211. C2×C8#4324semidirect
222. C11#10034semidirect

Maximal subgroups

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

subgroupindex
#130786432
#130695562
#130670152
#130664472
C11×#31502
#1003411