Finite Group Databasebeta

← #14668055

Subgroups — #14668055

Order 2816.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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#13070871C211yesmaximal, characteristic
2#13070525C211yesmaximal, characteristic, complemented
3#13067986C211yesmaximal, characteristic, complemented
4#13066687C211yesmaximal, characteristic, complemented
5#13066664C211yesmaximal, characteristic, complemented
6#13066662C211yesmaximal, characteristic
7C11×#1668C211yesmaximal, characteristic
8C11×#493C2211yescharacteristic
9C11×#460—21no—
10C8×Q8×C11C2211yescharacteristic
11C2×#66891—21no—
12C2×#66891—21no—
13#10622633—21no—
14#10622312C2211yescharacteristic
15C11×#335C2211yescharacteristic
16C11×#331—21no—
17#10622120—21no—
18C4⋊(C11⋊C16)—21no—
19C4⋊(C11⋊C16)C2211yescharacteristic
20#10622099—21no—
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×SD16—41no—
24C2×C11×D8—21no—
25C2×C11×D8—21no—
26C11×#127—21no—
27C4×Q8×C11D411yescharacteristic
28C2×Dic44—21no—
29C2×Dic44—21no—
30#66922—21no—
31C11×C4⋊C8—21no—
32C11×C4⋊C8—21no—
33C11×C4⋊C8D411yescharacteristic
34C11×#102—41no—
35C4×C8×C11—21no—
36C4×C8×C11C2311yescharacteristic
37#66899—41no—
38#66891—42no—
39#66891—42no—
40C2×C11⋊C16—21no—
41C2×C11⋊C16D411yescharacteristic
42C2×C11⋊C16D411yescharacteristic
43#66872—41no—
44C4⋊(C11⋊C8)—21no—
45#12444—111nomaximal, Sylow
46C2×Q8×C11D811yescharacteristic
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×Dic22—41no—
51C11×SD16—82no—
52C11×D8—41no—
53C11×D8—41no—
54C11×D8—81no—
55C2×C8×C11—21no—
56C2×C8×C11—41no—
57C2×C8×C11C2×D411yescharacteristic
58C2×C8×C11#4111yescharacteristic
59C11×C4⋊C4—21no—
60C11×C4⋊C4D811yescharacteristic
61C42×C11—21no—
62C42×C11C2×D411yescharacteristic
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65C2×C11⋊C8—41no—
66Dic44—41no—
67Dic44—41no—
68Dic44—81no—
69C11⋊C16—21no—
70C11⋊C16—41no—
71C11⋊C16SD1612yescomplemented
72#2248—111no—
73#2183—111no—
74#1670—111no—
75#1668D1111yescharacteristic
76#1371—111no—
77#1362—111no—
78#1361—111no—
79C23×C11—81no—
80Q8×C11—21no—
81Q8×C11—21no—
82D4×C11—81no—
83D4×C11—81no—
84D4×C11—81no—
85D4×C11—81no—
86D4×C11—161no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11#12111yescharacteristic
90C2×C4×C11C2×D811yescharacteristic
91C2×C4×C11#13511yescharacteristic
92C2×Dic11—81no—
93Dic22—81no—
94Dic22—81no—
95C8×C11—21no—
96C8×C11—41no—
97C8×C11—81no—
98C8×C11C2×SD1611yescharacteristic
99C8×C11AGL(1,ℤ/8)11yescharacteristic
100C11⋊C8—81no—
101C2×SD32—221no—
102C2×SD32—221no—
103#494—111no—
104#493C2×D1111yescharacteristic
105#475—221no—
106#460—21no—
107C8×Q8C2×D1111yescharacteristic
108C4⋊C16—111no—
109C4⋊C16—221no—
110#346—221no—
111C4×C16—111no—
112#335—111no—
113#335C2×D1111yescharacteristic
114#332—221no—
115#331—21no—
116C22×C11—161no—
117C22×C11—161no—
118C22×C11—161no—
119C22×C11#46611yescharacteristic
120C4×C11—21no—
121C4×C11—41no—
122C4×C11—41no—
123C4×C11#46011yescharacteristic
124C4×C11#47211yescharacteristic
125C4×C11#50911yescharacteristic
126C4×C11#51011yescharacteristic
127Dic11—161no—
128C2×Q16—221no—
129C2×Q16—221no—
130C2×SD16—41no—
131C2×D8—21no—
132C2×D8—21no—
133C4⋊Q8—221no—
134#127—21no—
135C4×Q8C22⋊D1111yescharacteristic
136SD32—442no—
137SD32—442no—
138C2×C16—111no—
139C2×C16—111no—
140C2×C16—221no—
141#106—441no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—221no—
145C4⋊C8C22⋊D1111yescharacteristic
146#103—441no—
147#102—41no—
148C4×C8—21no—
149C4×C8C22×D1111yescharacteristic
150C2×C11—321no—
151C2×C11#166811yescharacteristic
152C2×C11#222011yescharacteristic
153C2×C11#222311yescharacteristic
154C2×Q8—441no—
155C2×Q8#432311yescharacteristic
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159Q16—441no—
160Q16—441no—
161Q16—881no—
162SD16—82no—
163D8—41no—
164D8—41no—
165D8—81no—
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—441no—
169C2×C8D4×D1111yescharacteristic
170C2×C8#434111yescharacteristic
171C4⋊C4—21no—
172C4⋊C4—441no—
173C4⋊C4—441no—
174C4⋊C4#432311yescharacteristic
175C42—21no—
176C42C2×C22⋊D1111yescharacteristic
177C16—112no—
178C16—221no—
179C16—441no—
180C11#1244411yescharacteristic, complemented, Sylow
181C23—81no—
182Q8—21no—
183Q8—21no—
184Q8—881no—
185Q8—881no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—881no—
194C2×C4C2×#432311yescharacteristic
195C2×C4#6699211yescharacteristic
196C2×C4#6700311yescharacteristic
197C8—21no—
198C8—41no—
199C8—81no—
200C8—881no—
201C8SD16×D1111yescharacteristic
202C8#6696711yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1062265111yescharacteristic
207C4—21no—
208C4—41no—
209C4—41no—
210C4—1761no—
211C4#1062276011yescharacteristic
212C4#1062277611yescharacteristic
213C4#1062280811yescharacteristic
214C4#1062281211yescharacteristic
215C2—321no—
216C2#1306797411yescharacteristic
217C2#1307072711yescharacteristic
218C2#1307074411yescharacteristic
subgroupG/H
centerC22#10622651
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1668C2
socleC22×C11#466
prime radicalC11×#493C22
hypercenter#1668D11
hypocenterC11#12444
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1668

Complements

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

NH ≅ G/Ntype
2. #13070525C2semidirect
3. #13067986C2semidirect
4. #13066687C2semidirect
5. #13066664C2semidirect
71. C11⋊C16SD16semidirect
180. C11#12444semidirect

Maximal subgroups

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

subgroupindex
#130708712
#130705252
#130679862
#130666872
#130666642
#130666622
C11×#16682
#1244411