Finite Group Databasebeta

← #14654737

Subgroups — #14654737

Order 2816.

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

normal subgroups only

This group has 636 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#13078612C212yesmaximal, complemented
2#13069414C211yesmaximal, characteristic, complemented
3#13067015C212yesmaximal, complemented
4#13066447C211yesmaximal, characteristic, complemented
5C11×#3150C211yesmaximal, characteristic, complemented
6C2×C11×#135—22no—
7C11×#532C2212yes—
8C2×C4×D44C2211yescharacteristic
9C11×#497—22no—
10C11×#496—22no—
11C2×C11×#97C2211yescharacteristic
12C2×(C2×D11)⋊C8—22no—
13#10622700—22no—
14#10622685—22no—
15#10622649—22no—
16#10622646—22no—
17C4×#4323—24no—
18#10622538C2212yes—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20D4⋊(C11⋊C8)—24no—
21C2×C11×#41—22no—
22C22×D44D411yescharacteristic
23C22×C4×D11—21no—
24C11×#135—44no—
25C11×#135—44no—
26C2×C11×Q16—22no—
27C2×C11×SD16—24no—
28C2×C11×D8—22no—
29C22×C8×C11D412yes—
30C11×C4⋊Q8D412yes—
31C11×#127D412yes—
32C11×#124—22no—
33C11×#121—22no—
34C11×#121—22no—
35C4×D4×C11—22no—
36C4×D4×C11—22no—
37C2×C42×C11C2311yescharacteristic
38C2×#4323—24no—
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11D411yescharacteristic
41C22×C11⋊C8—21no—
42C4×D44—22no—
43C4×D44—22no—
44C11×#97—22no—
45#66896—24no—
46C22⋊(C11⋊C8)—22no—
47(C2×D11)⋊C8—44no—
48#66873—24no—
49#66871—24no—
50C4⋊(C11⋊C8)—22no—
51C4⋊(C11⋊C8)—22no—
52C4×C11⋊C8D414yes—
53#10032—111nomaximal, Sylow
54C23×D11—21no—
55C11×#41—44no—
56C11×#41—44no—
57C2×Q8×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C22×Dic11—21no—
67C2×D44—22no—
68C2×D44—42no—
69C2×C4×D11—41no—
70C2×C4×D11—41no—
71C2×C4×D11—42no—
72C2×C4×D11—42no—
73C11×Q16—44no—
74C11×SD16—48no—
75C11×D8—44no—
76C2×C8×C11—22no—
77C2×C8×C11—22no—
78C2×C8×C11D814yescomplemented
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83C42×C11C2×D412yes—
84C42×C11C2×D412yes—
85#4323—48no—
86(C2×D11)⋊C4—42no—
87C4⋊Dic11—22no—
88C2×C11⋊C8—24no—
89C2×C11⋊C8—41no—
90C2×C11⋊C8—42no—
91#3150D1111yescharacteristic, complemented
92#3100—112no—
93#1955—111no—
94#1480—112no—
95#1275—111no—
96C23×C11—42no—
97C23×C11#12111yescharacteristic
98C22×D11—22no—
99C22×D11—41no—
100C22×D11—42no—
101C22×D11—41no—
102C22×D11—42no—
103Q8×C11—44no—
104D4×C11—44no—
105D4×C11—44no—
106D4×C11—44no—
107D4×C11—84no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—82no—
112C2×C4×C11—82no—
113C2×C4×C11#12012yes—
114C2×C4×C11#12011yescharacteristic
115C2×C4×C11#12112yes—
116C2×C4×C11#12711yescharacteristic
117C2×C4×C11C2×D812yes—
118C2×C4×C11AGL(1,ℤ/8)12yes—
119C2×Dic11—41no—
120C2×Dic11—42no—
121D44—24no—
122D44—42no—
123C4×D11—82no—
124C4×D11—81no—
125C4×D11—81no—
126C8×C11—24no—
127C11⋊C8—44no—
128C11⋊C8—81no—
129C2×#135—22no—
130#532C2×D1112yes—
131C2×C4×D4—111no—
132#497—22no—
133#496—22no—
134#480—222no—
135#474—222no—
136#459—222no—
137#447—222no—
138C4×D8—224no—
139#431—112no—
140C2×C4⋊C8—111no—
141C2×C22⋊C8—222no—
142C2×#97C2×D1111yescharacteristic
143D4⋊C8—224no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—82no—
147C22×C11—82no—
148C22×C11—82no—
149C22×C11#39211yescharacteristic
150C22×C11#45912yes—
151C2×D11—44no—
152C2×D11—42no—
153C2×D11—82no—
154C2×D11—81no—
155C2×D11—81no—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11—82no—
159C4×C11#44712yes—
160C4×C11#49311yescharacteristic
161C4×C11#49611yescharacteristic
162Dic11—81no—
163C2×#41—22no—
164C22×D4—111no—
165C23×C4—221no—
166#135—44no—
167#135—44no—
168C2×Q16—22no—
169C2×SD16—24no—
170C2×D8—22no—
171C2×D8—224no—
172C22×C8—221no—
173C22×C8C22⋊D1112yes—
174C4⋊Q8C22⋊D1112yes—
175#127C22⋊D1112yes—
176#124—22no—
177#121—22no—
178#121—22no—
179C4×D4—22no—
180C4×D4—22no—
181C4×D4—222no—
182C4×D4—222no—
183C2×C4⋊C4—111no—
184C2×C22⋊C4—221no—
185C2×C42C22×D1111yescharacteristic
186#107—224no—
187C4⋊C8—222no—
188C4⋊C8—222no—
189#102—224no—
190#102—224no—
191C22⋊C8—222no—
192C22⋊C8—444no—
193#97—22no—
194C4×C8—114no—
195C2×C11—22no—
196C2×C11—162no—
197C2×C11#201011yescharacteristic
198C2×C11#201111yescharacteristic
199C2×C11#201711yescharacteristic
200D11—82no—
201C24—221no—
202#41—44no—
203#41—44no—
204C2×Q8—22no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4—222no—
210C2×D4—442no—
211C22×C4—42no—
212C22×C4—221no—
213C22×C4—442no—
214C22×C4—442no—
215C22×C4—441no—
216C22×C4—441no—
217C22×C4D4×D1111yescharacteristic
218C22×C4#434111yescharacteristic
219C22×C4C2×C22⋊D1111yescharacteristic
220Q16—44no—
221SD16—48no—
222D8—44no—
223D8—448no—
224C2×C8—22no—
225C2×C8—22no—
226C2×C8—224no—
227C2×C8—442no—
228C2×C8—441no—
229C2×C8#432314yescomplemented
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—222no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—442no—
236C42D4×D1112yes—
237C42C2×C22⋊D1112yes—
238C11#1003211yescharacteristic, complemented, Sylow
239C23—42no—
240C23—222no—
241C23—441no—
242C23—442no—
243C23—441no—
244C23—442no—
245C23#6699111yescharacteristic
246Q8—44no—
247D4—44no—
248D4—44no—
249D4—44no—
250D4—84no—
251D4—224no—
252D4—442no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—441no—
259C2×C4—442no—
260C2×C4—882no—
261C2×C4—881no—
262C2×C4—881no—
263C2×C4C2×#432312yes—
264C2×C4#6698512yes—
265C2×C4#6699012yes—
266C2×C4#6699212yes—
267C2×C4#6699311yescharacteristic
268C2×C4#6700611yescharacteristic
269C8—24no—
270C8—444no—
271C8—881no—
272C22—21no—
273C22—21no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—444no—
278C22—442no—
279C22—882no—
280C22—881no—
281C22—881no—
282C22#1062268512yes—
283C22#1062283611yescharacteristic
284C4—22no—
285C4—22no—
286C4—82no—
287C4—881no—
288C4#1062268611yescharacteristic
289C4#1062268711yescharacteristic
290C4#1062283012yes—
291C2—22no—
292C2—162no—
293C2—882no—
294C2#1306968011yescharacteristic
295C2#1306968711yescharacteristic
296C2#1306971911yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3150C2
socleC22×C11#392
hypercenter#3150D11
hypocenterC11#10032
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. #13078612C2semidirect
2. #13069414C2semidirect
3. #13067015C2semidirect
4. #13066447C2semidirect
5. C11×#3150C2semidirect
78. C2×C8×C11D8semidirect
91. #3150D11semidirect
229. C2×C8#4323semidirect
238. C11#10032semidirect

Maximal subgroups

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

subgroupindex
#130786122
#130694142
#130670152
#130664472
C11×#31502
#1003211