Finite Group Databasebeta

← #14674456

Subgroups — #14674456

Order 2816.

288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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#13081753C211yesmaximal, characteristic, complemented
2#13070929C211yesmaximal, characteristic, complemented
3#13070733C211yesmaximal, characteristic, complemented
4#13066806C211yesmaximal, characteristic, complemented
5#13066801C211yesmaximal, characteristic, complemented
6#13066757C211yesmaximal, characteristic, complemented
7C2×C11×D32C211yesmaximal, characteristic, complemented
8#10623288—21no—
9C2×C11×D16C2211yescharacteristic
10C2×C11×D16C2211yescharacteristic, complemented
11#10622773—21no—
12#10622760—21no—
13#10622525—21no—
14#10622524—22no—
15D11×D16—21no—
16#10622517C2211yescharacteristic
17#10622514C2211yescharacteristic
18C11×D32—22no—
19C2×C11×C32C2211yescharacteristic, complemented
20#10622201—21no—
21#10622158—21no—
22#10622157—21no—
23#10622144C2211yescharacteristic, complemented
24#10622137C2211yescharacteristic, complemented
25#67037—41no—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28#66985—41no—
29#66985—41no—
30#66965—22no—
31#66964—42no—
32D8×D11—22no—
33#66957—21no—
34#66954D411yescharacteristic
35C11×D16—21no—
36C11×D16—21no—
37C11×D16—21no—
38C11×D16D412yes—
39C2×C11×C16C2311yescharacteristic
40#66897—41no—
41#66891—22no—
42#66890—22no—
43#66883—21no—
44#66876D411yescharacteristic
45Dic88D411yescharacteristic
46#66864—21no—
47D176D411yescharacteristic
48#66862—21no—
49C16×D11—21no—
50C11×C32—21no—
51C11⋊C32—21no—
52#13669—111nomaximal, Sylow
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×C22⋊D11—82no—
56#4341—42no—
57#4341—81no—
58D4×D11—42no—
59D4×D11—81no—
60#4339—41no—
61#4339D811yescharacteristic
62C11×D8—22no—
63C11×D8—41no—
64C11×D8—41no—
65C11×D8—41no—
66C2×C8×C11C2×D411yescharacteristic
67#4324—42no—
68#4324—81no—
69#4323—42no—
70#4323—81no—
71#4318—41no—
72#4318D811yescharacteristic
73Dic44—21no—
74D88—21no—
75#4314—41no—
76#4313—21no—
77C8×D11—21no—
78C11×C16C2×D411yescharacteristic
79C11×C16C2×D411yescharacteristic
80C11⋊C16—21no—
81#3415—111no—
82#2263—111no—
83C2×D32D1111yescharacteristic, complemented
84#2221—111no—
85#1419—111no—
86#1417—111no—
87#1401—111no—
88C23×C11—81no—
89C23×C11—81no—
90C22×D11—82no—
91D4×C11—42no—
92D4×C11—81no—
93D4×C11—81no—
94D4×C11—81no—
95C2×C4×C11C2×D811yescharacteristic
96C22⋊D11—21no—
97C22⋊D11—82no—
98C22⋊D11—82no—
99C22⋊D11—81no—
100C2×Dic11—82no—
101D44—41no—
102D44D1611yescharacteristic
103C4×D11—21no—
104C4×D11—81no—
105Dic22—41no—
106Dic22D1611yescharacteristic
107C8×C11#12011yescharacteristic
108C8×C11AGL(1,ℤ/8)11yescharacteristic
109C11⋊C8—21no—
110C11⋊C8—81no—
111#576—221no—
112#509—221no—
113#509—222no—
114#508—111no—
115#508—221no—
116C2×D16—221no—
117C2×D16C2×D1111yescharacteristic
118C2×D16C2×D1111yescharacteristic, complemented
119#504—111no—
120#472—221no—
121SD64—221no—
122D32—22no—
123D32—221no—
124M64—111no—
125C2×C32C2×D1111yescharacteristic, complemented
126#368—111no—
127#361—221no—
128C22×C11—82no—
129C22×C11—161no—
130C22×C11—321no—
131C22×C11—321no—
132C22×C11#50911yescharacteristic
133C2×D11—21no—
134C2×D11—81no—
135C2×D11—322no—
136C4×C11#44711yescharacteristic
137C4×C11C2×D1611yescharacteristic
138Dic11—21no—
139Dic11—81no—
140H(5,𝔽2)—441no—
141AGL(1,ℤ/8)—441no—
142AGL(1,ℤ/8)—442no—
143AGL(1,ℤ/8)—441no—
144#135—222no—
145#135—221no—
146C2×D8—21no—
147C2×D8—21no—
148C2×D8—222no—
149#131—111no—
150Q32—111no—
151SD32—222no—
152SD32—221no—
153D16—21no—
154D16—21no—
155D16—21no—
156D16—111no—
157D16—222no—
158D16C22⋊D1112yes—
159M32—111no—
160M32—221no—
161C2×C16—221no—
162C2×C16C22×D1111yescharacteristic
163#108—221no—
164#100—441no—
165C32—21no—
166C32—221no—
167C2×C11—21no—
168C2×C11—162no—
169C2×C11—321no—
170C2×C11#218411yescharacteristic
171D11—41no—
172D11—161no—
173#41—111no—
174#41—442no—
175#41—441no—
176#41—881no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4—442no—
180C2×D4—881no—
181C2×D4—882no—
182Q16—221no—
183SD16—442no—
184SD16—441no—
185SD16—881no—
186D8—22no—
187D8—41no—
188D8—41no—
189D8—41no—
190D8—221no—
191D8—442no—
192D8—881no—
193M16—111no—
194M16—221no—
195M16—441no—
196C2×C8—221no—
197C2×C8D4×D1111yescharacteristic
198C16—221no—
199C16D4×D1111yescharacteristic
200C16C2×C22⋊D1111yescharacteristic
201C11#1366911yescharacteristic, complemented, Sylow
202C23—81no—
203C23—81no—
204C23—882no—
205Q8—111no—
206Q8—441no—
207D4—42no—
208D4—81no—
209D4—81no—
210D4—81no—
211D4—111no—
212D4—221no—
213D4—441no—
214D4—882no—
215D4—882no—
216D4—881no—
217C2×C4—221no—
218C2×C4—882no—
219C2×C4—881no—
220C2×C4D8×D1111yescharacteristic
221C8—221no—
222C8—881no—
223C8#6696411yescharacteristic
224C8#6699011yescharacteristic
225C22—82no—
226C22—161no—
227C22—221no—
228C22—321no—
229C22—321no—
230C22—881no—
231C22—3522no—
232C22#1062252411yescharacteristic
233C4—221no—
234C4—881no—
235C4D11×D1611yescharacteristic
236C4#1062276911yescharacteristic
237C2—21no—
238C2—162no—
239C2—321no—
240C2—441no—
241C2—1761no—
242C2#1307052611yescharacteristic
subgroupG/H
centerC2#13070526
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC2×C11×D32C2
socleC2×C11#2184
hypercenterC2×D32D11
hypocenterC11#13669
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D32

Complements

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

NH ≅ G/Ntype
1. #13081753C2semidirect
2. #13070929C2semidirect
3. #13070733C2semidirect
4. #13066806C2semidirect
5. #13066801C2semidirect
6. #13066757C2semidirect
7. C2×C11×D32C2semidirect
10. C2×C11×D16C22semidirect
19. C2×C11×C32C22semidirect
23. #10622144C22semidirect
24. #10622137C22semidirect
83. C2×D32D11semidirect
118. C2×D16C2×D11semidirect
125. C2×C32C2×D11semidirect
201. C11#13669semidirect

Maximal subgroups

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

subgroupindex
#130817532
#130709292
#130707332
#130668062
#130668012
#130667572
C2×C11×D322
#1366911