Finite Group Databasebeta

← #14667165

Subgroups — #14667165

Order 2816.

406 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 61 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#13080416C211yesmaximal, characteristic, complemented
2#13070689C211yesmaximal, characteristic, complemented
3#13068230C211yesmaximal, characteristic, complemented
4#13066652C211yesmaximal, characteristic, complemented
5#13066589C211yesmaximal, characteristic, complemented
6#13066588C211yesmaximal, characteristic, complemented
7C11×#2213C211yesmaximal, characteristic, complemented
8#10623300—21no—
9#10623283—21no—
10C11×#509—21no—
11C11×#493C2211yescharacteristic, complemented
12C11×#443C2211yescharacteristic
13#10622760—21no—
14#10622755—21no—
15#10622686—22no—
16#10622510—21no—
17#10622435—22no—
18#10622313C2211yescharacteristic
19#10622308C2211yescharacteristic
20C11×#364C2211yescharacteristic, complemented
21C11×#361—21no—
22#10622201—21no—
23#10622101C2211yescharacteristic, complemented
24C8×C11⋊C8C2211yescharacteristic, complemented
25#67042—22no—
26C11×#135D411yescharacteristic
27C2×C11×D8—21no—
28C2×C11×D8—21no—
29C11×#131—21no—
30C11×#127—21no—
31#67002—22no—
32C2×#4323—44no—
33#66972—41no—
34#66967—42no—
35D8×D11—41no—
36#66961—22no—
37#66961—42no—
38#66957—41no—
39#66957D411yescharacteristic
40C2×D88—21no—
41C2×D88—21no—
42C2×D88—41no—
43#66954—21no—
44#66927D412yes—
45C11×SD32—41no—
46C11×D16—41no—
47C11×M32—21no—
48C11×#108D411yescharacteristic
49C11×#104—21no—
50C4×C8×C11C2311yescharacteristic
51#66891—41no—
52#66890—41no—
53#66887—22no—
54#66883D411yescharacteristic
55#66876—21no—
56#66869—21no—
57C4×C11⋊C8—21no—
58#12310—111nomaximal, Sylow
59C11×#41—21no—
60C2×D4×C11—42no—
61C2×D4×C11—41no—
62#4343—42no—
63D4×D11—42no—
64D4×D11—82no—
65#4339—21no—
66#4339—42no—
67C2×D44—22no—
68C2×D44—42no—
69C2×D44—42no—
70C11×Q16D811yescharacteristic, complemented
71C11×SD16—21no—
72C11×D8—41no—
73C11×D8—41no—
74C11×D8—41no—
75C11×D8—41no—
76C11×D8D811yescharacteristic, complemented
77C11×M16—21no—
78C11×M16—41no—
79C2×C8×C11—41no—
80C2×C8×C11C2×D411yescharacteristic
81C2×C8×C11C2×D411yescharacteristic
82C42×C11C2×D411yescharacteristic
83#4325—42no—
84#4323—42no—
85#4323—88no—
86#4318—21no—
87C2×C11⋊C8—22no—
88Dic44D811yescharacteristic, complemented
89D88—42no—
90D88—41no—
91D88—41no—
92D88—41no—
93D88—41no—
94D88D811yescharacteristic, complemented
95#4314—21no—
96#4314—42no—
97#4313—41no—
98C8×D11—41no—
99C11×C16—41no—
100C11⋊C16—41no—
101#3292—111no—
102#2213—111no—
103#2213D1111yescharacteristic, complemented
104#1712—111no—
105#1357—111no—
106#1335—111no—
107#1335—111no—
108C23×C11—81no—
109C22×D11—42no—
110C22×D11—82no—
111Q8×C11—21no—
112D4×C11—21no—
113D4×C11—41no—
114D4×C11—84no—
115D4×C11—81no—
116D4×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11#12011yescharacteristic
120C22⋊D11—41no—
121C22⋊D11—82no—
122D44—21no—
123D44—42no—
124D44—42no—
125D44—84no—
126D44—82no—
127C4×D11—41no—
128C4×D11—82no—
129Dic22—21no—
130C8×C11—41no—
131C8×C11C2×D811yescharacteristic
132C8×C11C2×D811yescharacteristic
133C8×C11AGL(1,ℤ/8)11yescharacteristic
134C8×C11AGL(1,ℤ/8)11yescharacteristic
135C11⋊C8—24no—
136C11⋊C8—41no—
137#576—221no—
138#576—221no—
139#509—21no—
140#509—221no—
141#493—111no—
142#493—222no—
143#493C2×D1111yescharacteristic, complemented
144#472—221no—
145#472—221no—
146#453—222no—
147#443—111no—
148#443C2×D1111yescharacteristic
149#364—111no—
150#364C2×D1111yescharacteristic, complemented
151#361—21no—
152#361—221no—
153C82—111no—
154C22×C11—41no—
155C22×C11—162no—
156C22×C11—161no—
157C22×C11#45311yescharacteristic
158C2×D11—41no—
159C2×D11—82no—
160C2×D11—162no—
161C2×D11—322no—
162C4×C11—22no—
163C4×C11—41no—
164C4×C11#44711yescharacteristic
165C4×C11#44711yescharacteristic
166Dic11—41no—
167H(5,𝔽2)—222no—
168AGL(1,ℤ/8)—222no—
169AGL(1,ℤ/8)—222no—
170AGL(1,ℤ/8)—442no—
171AGL(1,ℤ/8)—442no—
172#135—111no—
173#135—441no—
174#135—441no—
175#135C22⋊D1111yescharacteristic
176C2×D8—21no—
177C2×D8—21no—
178C2×D8—221no—
179C2×D8—221no—
180C2×D8—441no—
181C2×D8—444no—
182C2×D8—441no—
183#131—21no—
184#131—221no—
185#127—21no—
186#127—112no—
187SD32—41no—
188SD32—441no—
189D16—41no—
190D16—441no—
191M32—21no—
192M32—221no—
193#108—111no—
194#108C22⋊D1111yescharacteristic
195#104—21no—
196#104—221no—
197#100—222no—
198C4×C8—221no—
199C4×C8C22×D1111yescharacteristic
200C2×C11—21no—
201C2×C11—81no—
202C2×C11—321no—
203C2×C11#161911yescharacteristic
204D11—81no—
205D11—162no—
206#41—21no—
207#41—221no—
208#41—442no—
209#41—442no—
210C2×D4—42no—
211C2×D4—41no—
212C2×D4—222no—
213C2×D4—442no—
214C2×D4—442no—
215C2×D4—442no—
216C2×D4—882no—
217Q16—111no—
218Q16#432311yescharacteristic, complemented
219SD16—21no—
220SD16—221no—
221SD16—442no—
222SD16—442no—
223D8—41no—
224D8—41no—
225D8—41no—
226D8—41no—
227D8—111no—
228D8—442no—
229D8—442no—
230D8—441no—
231D8—441no—
232D8—441no—
233D8—441no—
234D8—888no—
235D8#432311yescharacteristic, complemented
236M16—21no—
237M16—41no—
238M16—221no—
239M16—441no—
240C2×C8—41no—
241C2×C8—222no—
242C2×C8—441no—
243C2×C8D4×D1111yescharacteristic
244C2×C8C2×C22⋊D1111yescharacteristic
245C42D4×D1111yescharacteristic
246C16—41no—
247C16—441no—
248C11#1231011yescharacteristic, complemented, Sylow
249C23—81no—
250C23—442no—
251C23—882no—
252Q8—21no—
253Q8—221no—
254D4—21no—
255D4—41no—
256D4—84no—
257D4—81no—
258D4—81no—
259D4—221no—
260D4—441no—
261D4—442no—
262D4—442no—
263D4—884no—
264D4—882no—
265D4—882no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—441no—
269C2×C4—882no—
270C2×C4#6699011yescharacteristic
271C8—41no—
272C8—224no—
273C8—441no—
274C8D8×D1111yescharacteristic
275C8#6696411yescharacteristic
276C8C2×#432311yescharacteristic
277C8#6700211yescharacteristic
278C22—41no—
279C22—162no—
280C22—161no—
281C22—441no—
282C22—882no—
283C22—3522no—
284C22—1762no—
285C22#1062281111yescharacteristic
286C4—22no—
287C4—41no—
288C4—441no—
289C4#1062264911yescharacteristic
290C4#1062276911yescharacteristic
291C2—21no—
292C2—81no—
293C2—321no—
294C2—881no—
295C2—1762no—
296C2#1306766911yescharacteristic
subgroupG/H
centerC2#13067669
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2213C2
socleC2×C11#1619
hypercenter#2213D11
hypocenterC11#12310
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #13080416C2semidirect
2. #13070689C2semidirect
3. #13068230C2semidirect
4. #13066652C2semidirect
5. #13066589C2semidirect
6. #13066588C2semidirect
7. C11×#2213C2semidirect
11. C11×#493C22semidirect
20. C11×#364C22semidirect
23. #10622101C22semidirect
24. C8×C11⋊C8C22semidirect
70. C11×Q16D8semidirect
76. C11×D8D8semidirect
88. Dic44D8semidirect
94. D88D8semidirect
103. #2213D11semidirect
143. #493C2×D11semidirect
150. #364C2×D11semidirect
218. Q16#4323semidirect
235. D8#4323semidirect
248. C11#12310semidirect

Maximal subgroups

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

subgroupindex
#130804162
#130706892
#130682302
#130666522
#130665892
#130665882
C11×#22132
#1231011