Finite Group Databasebeta

← #14668165

Subgroups — #14668165

Order 2816.

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

normal subgroups only

This group has 172 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#13070892C211yesmaximal, characteristic, complemented
2#13070793C211yesmaximal, characteristic
3#13070789C211yesmaximal, characteristic
4#13070452C211yesmaximal, characteristic
5#13066691C211yesmaximal, characteristic, complemented
6#13066678C211yesmaximal, characteristic, complemented
7C11×#1366C211yesmaximal, characteristic, complemented
8C11×#499C2211yescharacteristic
9#10622520—21no—
10#10622313C2211yescharacteristic
11#10622296C2211yescharacteristic
12C11×#364C2211yescharacteristic
13C11×#364C2211yescharacteristic
14#10622156—21no—
15#10622153—21no—
16#10622151—21no—
17#10622128—21no—
18#10622127—21no—
19#10622126—21no—
20#10622125—21no—
21#10622101C2211yescharacteristic
22C4×C11⋊C16C2211yescharacteristic
23C11×#125—21no—
24#66957D411yescharacteristic
25#66954—21no—
26#66923—21no—
27C11×M32—21no—
28C11×M32—21no—
29C11×#107—21no—
30C11×#106—21no—
31C4×C8×C11C2311yescharacteristic
32#66883D411yescharacteristic
33#66882—21no—
34#66881—21no—
35#66876—21no—
36C2×C11⋊C16D411yescharacteristic
37C2×C11⋊C16D411yescharacteristic
38#66869—21no—
39#66862—41no—
40C16×D11—41no—
41#12463—111nomaximal, Sylow
42#4339—21no—
43C2×C8×C11C2×D411yescharacteristic
44C2×C8×C11C2×D411yescharacteristic
45C11×C4⋊C4—41no—
46C11×C4⋊C4—81no—
47C42×C11#4111yescharacteristic
48C4⋊Dic11—41no—
49Dic11⋊C4—81no—
50#4318—21no—
51Dic44Q1611yescharacteristic
52D88Q1611yescharacteristic
53#4314—21no—
54#4313—41no—
55C8×D11—41no—
56C11×C16—41no—
57C11×C16—41no—
58C11⋊C16—21no—
59C11⋊C16—41no—
60C11⋊C16SD1611yescharacteristic
61C11⋊C16SD1611yescharacteristic
62#2253—111no—
63#2231—111no—
64#2231—111no—
65#2170—111no—
66#1373—111no—
67#1366—111no—
68#1366D1111yescharacteristic, complemented
69C2×C4×C11—21no—
70C2×C4×C11—81no—
71C2×C4×C11#12111yescharacteristic
72C22⋊D11—41no—
73C2×Dic11—81no—
74D44—21no—
75C4×D11—41no—
76Dic22—21no—
77C8×C11C2×SD1611yescharacteristic
78C8×C11C2×Q1611yescharacteristic
79C8×C11#13511yescharacteristic
80C8×C11#13711yescharacteristic
81C11⋊C8—41no—
82#504—221no—
83#499—111no—
84#499C2×D1111yescharacteristic
85#443—111no—
86#367—221no—
87#366—221no—
88#365—221no—
89#365—221no—
90#364—111no—
91#364C2×D1111yescharacteristic
92#364C2×D1111yescharacteristic
93#360—221no—
94#360—221no—
95#350—221no—
96C4×C16—111no—
97C22×C11#47211yescharacteristic
98C2×D11—41no—
99C4×C11—41no—
100C4×C11—161no—
101C4×C11#46111yescharacteristic
102C4×C11#46711yescharacteristic
103Dic11—41no—
104Dic11—161no—
105#135—111no—
106#131—221no—
107#125—21no—
108#125—221no—
109M32—21no—
110M32—21no—
111M32—221no—
112M32—441no—
113C2×C16—111no—
114C2×C16—111no—
115C2×C16—441no—
116#108—111no—
117#107—21no—
118#107—221no—
119#106—21no—
120#106—221no—
121#104—221no—
122C4×C8C22×D1111yescharacteristic
123C2×C11—21no—
124C2×C11#167511yescharacteristic
125D11—81no—
126#41—221no—
127Q16—111no—
128SD16—221no—
129D8—111no—
130M16—221no—
131M16—441no—
132C2×C8—441no—
133C2×C8D4×D1111yescharacteristic
134C2×C8D4×D1111yescharacteristic
135C4⋊C4—41no—
136C4⋊C4—81no—
137C4⋊C4—441no—
138C4⋊C4—881no—
139C42#433911yescharacteristic
140C16—41no—
141C16—41no—
142C16—111no—
143C16—111no—
144C16—221no—
145C16—441no—
146C11#1246311yescharacteristic, complemented, Sylow
147Q8—221no—
148D4—221no—
149D4—441no—
150C2×C4—21no—
151C2×C4—81no—
152C2×C4—441no—
153C2×C4—881no—
154C2×C4#6693711yescharacteristic
155C8—441no—
156C8SD16×D1111yescharacteristic
157C8#6696911yescharacteristic
158C8Q16×D1111yescharacteristic
159C8#6697111yescharacteristic
160C22—441no—
161C22#1062236211yescharacteristic
162C4—41no—
163C4—161no—
164C4—441no—
165C4—1761no—
166C4#1062242611yescharacteristic
167C4#1062243111yescharacteristic
168C2—21no—
169C2—881no—
170C2#1306801411yescharacteristic
subgroupG/H
centerC2#13068014
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1366C2
socleC2×C11#1675
prime radical#66957D4
hypercenter#1366D11
hypocenterC11#12463
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
1. #13070892C2semidirect
5. #13066691C2semidirect
6. #13066678C2semidirect
7. C11×#1366C2semidirect
68. #1366D11semidirect
146. C11#12463semidirect

Maximal subgroups

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

subgroupindex
#130708922
#130707932
#130707892
#130704522
#130666912
#130666782
C11×#13662
#1246311