Finite Group Databasebeta

← #14668054

Subgroups — #14668054

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#13070524C211yesmaximal, characteristic, complemented
2#13067983C211yesmaximal, characteristic, complemented
3#13067973C211yesmaximal, characteristic
4#13066688C211yesmaximal, characteristic, complemented
5#13066665C211yesmaximal, characteristic, complemented
6#13066662C211yesmaximal, characteristic
7C11×#2248C211yesmaximal, characteristic
8C2×C11×SD32—21no—
9C2×C11×SD32—21no—
10C11×#494C2211yescharacteristic
11C11×#493C2211yescharacteristic
12#10622707—21no—
13#10622688—21no—
14C8×Dic22C2211yescharacteristic
15C4×C11×C16C2211yescharacteristic
16#10622185—21no—
17#10622182—21no—
18#10622140—21no—
19Dic11⋊C16—21no—
20C4⋊(C11⋊C16)C2211yescharacteristic
21#10622096C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C11×C4⋊Q8—21no—
28C11×#127—21no—
29C2×#4324—41no—
30C4×Dic22D411yescharacteristic
31C11×SD32—42no—
32C11×SD32—42no—
33C2×C11×C16D411yescharacteristic
34C2×C11×C16D411yescharacteristic
35C4×C8×C11C2311yescharacteristic
36#66896—41no—
37Dic11⋊C8—21no—
38C8×Dic11—21no—
39C2×C11⋊C16—21no—
40#66874—41no—
41#66872—41no—
42C4⋊(C11⋊C8)—21no—
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)D411yescharacteristic
45#12444—111nomaximal, Sylow
46C2×Q8×C11—41no—
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×Dic22D811yescharacteristic
51C11×Q16—41no—
52C11×Q16—41no—
53C11×Q16—81no—
54C11×D8—41no—
55C11×D8—41no—
56C11×D8—81no—
57C2×C8×C11C2×D411yescharacteristic
58C2×C8×C11#4111yescharacteristic
59C11×C4⋊C4—41no—
60C11×C4⋊C4—41no—
61C42×C11C2×D411yescharacteristic
62#4324—82no—
63C4⋊Dic11D811yescharacteristic
64Dic11⋊C4—21no—
65C4×Dic11—21no—
66C2×C11⋊C8—21no—
67C2×C11⋊C8—41no—
68C2×C11⋊C8—41no—
69C11×C16—21no—
70C11×C16SD1612yescomplemented
71C11⋊C16—41no—
72#2248D1111yescharacteristic
73#2183—111no—
74#1670—111no—
75#1668—111no—
76#1371—111no—
77#1362—111no—
78#1361—111no—
79C23×C11—81no—
80Q8×C11—81no—
81Q8×C11—81no—
82D4×C11—81no—
83D4×C11—81no—
84D4×C11—81no—
85D4×C11—81no—
86D4×C11—161no—
87C2×C4×C11—81no—
88C2×C4×C11#12111yescharacteristic
89C2×C4×C11C2×D811yescharacteristic
90C2×C4×C11#13511yescharacteristic
91C2×Dic11—21no—
92C2×Dic11—21no—
93Dic22—21no—
94Dic22—21no—
95C8×C11—21no—
96C8×C11C2×SD1611yescharacteristic
97C8×C11AGL(1,ℤ/8)11yescharacteristic
98C11⋊C8—41no—
99C11⋊C8—81no—
100C11⋊C8—81no—
101C2×SD32—21no—
102C2×SD32—21no—
103#494C2×D1111yescharacteristic
104#493C2×D1111yescharacteristic
105#475—221no—
106#460—221no—
107C8×Q8—111no—
108C4⋊C16—111no—
109C4⋊C16—221no—
110#346—221no—
111C4×C16C2×D1111yescharacteristic
112#335—111no—
113#335—111no—
114#332—221no—
115#331—221no—
116C22×C11—161no—
117C22×C11—161no—
118C22×C11—161no—
119C22×C11#46611yescharacteristic
120C4×C11—21no—
121C4×C11—161no—
122C4×C11#46011yescharacteristic
123C4×C11#47211yescharacteristic
124C4×C11#50911yescharacteristic
125C4×C11#51011yescharacteristic
126Dic11—41no—
127Dic11—41no—
128C2×Q16—21no—
129C2×Q16—21no—
130C2×SD16—441no—
131C2×D8—21no—
132C2×D8—21no—
133C4⋊Q8—21no—
134#127—21no—
135C4×Q8—111no—
136SD32—42no—
137SD32—42no—
138C2×C16—221no—
139C2×C16C22⋊D1111yescharacteristic
140C2×C16C22⋊D1111yescharacteristic
141#106—441no—
142C4⋊C8—111no—
143C4⋊C8—221no—
144C4⋊C8—221no—
145C4⋊C8—221no—
146#103—441no—
147#102—441no—
148C4×C8—221no—
149C4×C8C22×D1111yescharacteristic
150C2×C11—321no—
151C2×C11#166811yescharacteristic
152C2×C11#222011yescharacteristic
153C2×C11#222311yescharacteristic
154C2×Q8—41no—
155C2×Q8—111no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159Q16—41no—
160Q16—41no—
161Q16—81no—
162SD16—882no—
163D8—41no—
164D8—41no—
165D8—81no—
166C2×C8—221no—
167C2×C8—441no—
168C2×C8—441no—
169C2×C8#434111yescharacteristic
170C2×C8C2×C22⋊D1111yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—111no—
174C4⋊C4—221no—
175C42—221no—
176C42D4×D1111yescharacteristic
177C16—21no—
178C16—441no—
179C16#432412yescomplemented
180C11#1244411yescharacteristic, complemented, Sylow
181C23—81no—
182Q8—81no—
183Q8—81no—
184Q8—221no—
185Q8—221no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—81no—
192C2×C4—221no—
193C2×C4—221no—
194C2×C4D8×D1111yescharacteristic
195C2×C4#6696511yescharacteristic
196C2×C4#6699111yescharacteristic
197C8—21no—
198C8—441no—
199C8—881no—
200C8—881no—
201C8#6698511yescharacteristic
202C8C2×#432411yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1062277011yescharacteristic
207C4—21no—
208C4—161no—
209C4—441no—
210C4—441no—
211C4#1062252711yescharacteristic
212C4#1062252811yescharacteristic
213C4#1062268811yescharacteristic
214C4#1062277311yescharacteristic
215C2—321no—
216C2#1306797311yescharacteristic
217C2#1307072611yescharacteristic
218C2#1307074311yescharacteristic
subgroupG/H
centerC22#10622770
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2248C2
socleC22×C11#466
prime radicalC11×#493C22
hypercenter#2248D11
hypocenterC11#12444
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #13070524C2semidirect
2. #13067983C2semidirect
4. #13066688C2semidirect
5. #13066665C2semidirect
70. C11×C16SD16semidirect
179. C16#4324semidirect
180. C11#12444semidirect

Maximal subgroups

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

subgroupindex
#130705242
#130679832
#130679732
#130666882
#130666652
#130666622
C11×#22482
#1244411