Finite Group Databasebeta

← #14674461

Subgroups — #14674461

Order 2816.

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

normal subgroups only

This group has 278 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#13081766C211yesmaximal, characteristic, complemented
2C2×#10622158C211yesmaximal, characteristic, complemented
3#13070733C211yesmaximal, characteristic, complemented
4#13066810C211yesmaximal, characteristic, complemented
5#13066800C211yesmaximal, characteristic, complemented
6#13066759C211yesmaximal, characteristic, complemented
7C11×#2263C211yesmaximal, characteristic, complemented
8#10623302—21no—
9C11×#508C2211yescharacteristic
10C2×C11×D16C2211yescharacteristic
11#10622808—21no—
12#10622773—21no—
13D11×Q32—21no—
14#10622528—22no—
15#10622525—21no—
16C2×Dic88C2211yescharacteristic
17#10622514C2211yescharacteristic
18C11×SD64—21no—
19C11×D32—21no—
20C11×M64C2211yescharacteristic
21#10622201—21no—
22#10622158—22no—
23#10622144C2211yescharacteristic
24C2×C11⋊C32C2211yescharacteristic
25#67043—41no—
26C11×#135—21no—
27C2×C11×D8—21no—
28#67004—41no—
29#66985—41no—
30Q16×D11—22no—
31#66968—42no—
32#66965—22no—
33C2×Dic44—21no—
34#66954D411yescharacteristic
35C11×Q32D411yescharacteristic
36C11×SD32—21no—
37C11×D16—21no—
38C11×D16—21no—
39C11×D16D411yescharacteristic
40C2×C11×C16C2311yescharacteristic
41#66897—41no—
42#66893—22no—
43#66891—22no—
44#66883—21no—
45#66876D411yescharacteristic
46Dic88—21no—
47Dic88D412yes—
48#66862—21no—
49C16×D11—21no—
50C11×C32—21no—
51C11⋊C32—21no—
52#13670—111nomaximal, Sylow
53C11×#41—41no—
54C2×D4×C11—41no—
55Q8×D11—42no—
56#4341—42no—
57#4341—82no—
58#4339—81no—
59#4339D811yescharacteristic
60C2×Dic22—41no—
61C2×Dic22—81no—
62C11×Q16—21no—
63C11×SD16—41no—
64C11×D8—21no—
65C11×D8—41no—
66C11×D8—41no—
67C2×C8×C11C2×D411yescharacteristic
68#4326—42no—
69#4324—42no—
70#4324—81no—
71#4323—81no—
72#4318—41no—
73#4318D811yescharacteristic
74Dic44—22no—
75Dic44—41no—
76#4313—21no—
77C8×D11—21no—
78C11×C16C2×D411yescharacteristic
79C11×C16C2×D411yescharacteristic
80C11⋊C16—21no—
81#3417—111no—
82#2263D1111yescharacteristic, complemented
83C2×SD64—111no—
84#2221—111no—
85#1420—111no—
86#1417—111no—
87#1401—111no—
88C23×C11—81no—
89Q8×C11—41no—
90D4×C11—41no—
91D4×C11—81no—
92D4×C11—81no—
93D4×C11—81no—
94C2×C4×C11—81no—
95C2×C4×C11C2×D811yescharacteristic
96C22⋊D11—21no—
97C22⋊D11—82no—
98C2×Dic11—82no—
99C2×Dic11—81no—
100D44D1611yescharacteristic
101C4×D11—21no—
102C4×D11—82no—
103Dic22—42no—
104Dic22—82no—
105Dic22—81no—
106Dic22D1611yescharacteristic
107C8×C11#12011yescharacteristic
108C8×C11AGL(1,ℤ/8)11yescharacteristic
109C11⋊C8—21no—
110C11⋊C8—81no—
111#578—221no—
112#510—221no—
113#510—222no—
114#508—221no—
115#508C2×D1111yescharacteristic
116C2×Q32—111no—
117C2×Q32—221no—
118C2×D16C2×D1111yescharacteristic
119#504—111no—
120#472—221no—
121SD64—21no—
122SD64—222no—
123D32—21no—
124M64C2×D1111yescharacteristic
125C2×C32—111no—
126#368—111no—
127#361—221no—
128C22×C11—81no—
129C22×C11—161no—
130C22×C11—321no—
131C22×C11#50911yescharacteristic
132C2×D11—21no—
133C4×C11—81no—
134C4×C11#44711yescharacteristic
135C4×C11C2×D1611yescharacteristic
136Dic11—21no—
137Dic11—82no—
1382−1+4—441no—
139#137—441no—
140#137—442no—
141AGL(1,ℤ/8)—441no—
142#135—21no—
143#135—222no—
144C2×Q16—222no—
145C2×Q16—221no—
146C2×D8—21no—
147#131—111no—
148Q32—112no—
149Q32—222no—
150Q32—221no—
151Q32C22⋊D1111yescharacteristic
152SD32—21no—
153SD32—222no—
154D16—21no—
155D16—21no—
156D16C22⋊D1111yescharacteristic
157M32—111no—
158M32—221no—
159C2×C16—221no—
160C2×C16C22×D1111yescharacteristic
161#108—221no—
162#100—441no—
163C32—21no—
164C32—221no—
165C2×C11—21no—
166C2×C11—161no—
167C2×C11—321no—
168C2×C11#218411yescharacteristic
169D11—41no—
170#41—41no—
171#41—111no—
172#41—442no—
173#41—881no—
174#41—882no—
175C2×Q8—442no—
176C2×Q8—441no—
177C2×Q8—881no—
178C2×D4—41no—
179Q16—21no—
180Q16—222no—
181Q16—442no—
182Q16—441no—
183SD16—41no—
184SD16—442no—
185SD16—881no—
186D8—21no—
187D8—41no—
188D8—41no—
189D8—881no—
190M16—111no—
191M16—221no—
192M16—441no—
193C2×C8—221no—
194C2×C8D4×D1111yescharacteristic
195C16—221no—
196C16D4×D1111yescharacteristic
197C16C2×C22⋊D1111yescharacteristic
198C11#1367011yescharacteristic, complemented, Sylow
199C23—81no—
200Q8—41no—
201Q8—111no—
202Q8—442no—
203Q8—882no—
204Q8—881no—
205D4—41no—
206D4—81no—
207D4—81no—
208D4—81no—
209D4—111no—
210D4—221no—
211D4—882no—
212C2×C4—81no—
213C2×C4—221no—
214C2×C4—882no—
215C2×C4—882no—
216C2×C4—881no—
217C2×C4D8×D1111yescharacteristic
218C8—221no—
219C8—881no—
220C8#6696411yescharacteristic
221C8#6699011yescharacteristic
222C22—81no—
223C22—161no—
224C22—221no—
225C22—321no—
226C22#1062252411yescharacteristic
227C4—81no—
228C4—221no—
229C4—882no—
230C4D11×D1611yescharacteristic
231C4#1062276911yescharacteristic
232C2—21no—
233C2—161no—
234C2—321no—
235C2—441no—
236C2#1307052611yescharacteristic
subgroupG/H
centerC2#13070526
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×#2263C2
socleC2×C11#2184
hypercenter#2263D11
hypocenterC11#13670
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2263

Complements

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

NH ≅ G/Ntype
1. #13081766C2semidirect
2. C2×#10622158C2semidirect
3. #13070733C2semidirect
4. #13066810C2semidirect
5. #13066800C2semidirect
6. #13066759C2semidirect
7. C11×#2263C2semidirect
82. #2263D11semidirect
198. C11#13670semidirect

Maximal subgroups

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

subgroupindex
#130817662
C2×#106221582
#130707332
#130668102
#130668002
#130667592
C11×#22632
#1367011