Finite Group Databasebeta

← #14667136

Subgroups — #14667136

Order 2816.

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

normal subgroups only

This group has 262 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#13080070C211yesmaximal, characteristic
2#13070835C212yesmaximal
3#13066609C212yesmaximal
4#13066569C211yesmaximal, characteristic
5C11×#2103C211yesmaximal, characteristic
6#10623049—21no—
7C11×#430C2211yescharacteristic
8C11×#424C2211yescharacteristic
9#10622750C2212yes—
10#10622729—21no—
11#10622462—22no—
12#10622442—22no—
13C11×#344—21no—
14C11×#341—21no—
15C11×#338C2211yescharacteristic
16#10622191C2212yes—
17#10622134—22no—
18#10622132—22no—
19C2×C11×M16—21no—
20C2×C11×M16—21no—
21C2×C11×M16C2311yescharacteristic
22C22×C8×C11D411yescharacteristic
23C11×#117D411yescharacteristic
24#66977—22no—
25C2×Dic44—21no—
26C2×Dic44D412yes—
27#66942—42no—
28#66932—42no—
29#66923—21no—
30#66922—21no—
31C4×Dic22—22no—
32C11×#108—22no—
33C11×C4⋊C8—22no—
34#66882—21no—
35#66881D412yes—
36#66880—22no—
37#66880—22no—
38#66876—22no—
39#12305—111nomaximal, Sylow
40C22×C4×C11C2×D411yescharacteristic
41C2×Dic22—22no—
42C11×M16—41no—
43C11×M16—41no—
44C11×M16—41no—
45C11×M16—41no—
46C11×M16—41no—
47C2×C8×C11—21no—
48C2×C8×C11—41no—
49C2×C8×C11—41no—
50C2×C8×C11—41no—
51C2×C8×C11C2×D412yes—
52C11×C4⋊C4—21no—
53C11×C22⋊C4SD1612yes—
54C42×C11—21no—
55C22⋊Dic11—42no—
56C4⋊Dic11—22no—
57C4⋊Dic11—42no—
58Dic11⋊C4—42no—
59Dic11⋊C4—42no—
60Dic11⋊C4—42no—
61C4×Dic11—42no—
62Dic44—42no—
63Dic44—81no—
64C11⋊C16—42no—
65#3261—111no—
66#2239—112no—
67#2103D1111yescharacteristic
68#1342—112no—
69#1328—111no—
70C23×C11C2×SD1611yescharacteristic
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11#12011yescharacteristic
75C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
76C2×Dic11—42no—
77C2×Dic11—42no—
78Dic22—42no—
79Dic22—42no—
80C8×C11—22no—
81C8×C11—41no—
82C8×C11—81no—
83C8×C11—81no—
84#541—221no—
85#479—222no—
86#470—112no—
87#467—221no—
88#462—222no—
89#430C2×D1111yescharacteristic
90#424C2×D1111yescharacteristic
91#365—222no—
92#362—222no—
93#349—112no—
94#344—21no—
95#341—21no—
96#338C2×D1111yescharacteristic
97C22×C11—21no—
98C22×C11—41no—
99C22×C11#45011yescharacteristic
100C4×C11—21no—
101C4×C11—42no—
102C4×C11#45411yescharacteristic
103C4×C11#45811yescharacteristic
104Dic11—82no—
105Dic11—82no—
106C2×Q16—112no—
107C2×Q16—221no—
108C2×M16—21no—
109C2×M16—21no—
110C2×M16C22×D1111yescharacteristic
111C22×C8C22⋊D1111yescharacteristic
112C4⋊Q8—221no—
113#126—442no—
114#125—221no—
115#125—442no—
116C22⋊Q8—222no—
117C4×Q8—222no—
118#117C22⋊D1111yescharacteristic
119M32—222no—
120#108—22no—
121#107—221no—
122#106—112no—
123C4⋊C8—22no—
124#103—222no—
125#103—222no—
126C2×C11—21no—
127C2×C11—41no—
128C2×C11#161611yescharacteristic
129C2×Q8—222no—
130C22×C4C2×C22⋊D1111yescharacteristic
131Q16—442no—
132Q16—881no—
133M16—41no—
134M16—41no—
135M16—41no—
136M16—41no—
137M16—41no—
138C2×C8—21no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8D4×D1112yes—
143C4⋊C4—21no—
144C4⋊C4—222no—
145C4⋊C4—442no—
146C4⋊C4—442no—
147C4⋊C4—442no—
148C4⋊C4—442no—
149C22⋊C4—442no—
150C22⋊C4#432512yes—
151C42—21no—
152C42—442no—
153C16—442no—
154C11#1230511yescharacteristic, complemented, Sylow
155C23C2×#432511yescharacteristic
156Q8—442no—
157Q8—442no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—442no—
162C2×C4—442no—
163C2×C4#6699011yescharacteristic
164C2×C4#6700211yescharacteristic
165C8—22no—
166C8—41no—
167C8—81no—
168C8—81no—
169C22—21no—
170C22—41no—
171C22#1062265911yescharacteristic
172C4—21no—
173C4—42no—
174C4—882no—
175C4—882no—
176C4#1062266611yescharacteristic
177C4#1062267511yescharacteristic
178C2—21no—
179C2—41no—
180C2#1306765211yescharacteristic
subgroupG/H
centerC2#13067652
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#2103C2
socleC2×C11#1616
prime radicalC23×C11C2×SD16
hypercenter#2103D11
hypocenterC11#12305
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2103

Complements

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

NH ≅ G/Ntype
154. C11#12305semidirect

Maximal subgroups

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

subgroupindex
#130800702
#130708352
#130666092
#130665692
C11×#21032
#1230511