Finite Group Databasebeta

← #14658578

Subgroups — #14658578

Order 2816.

346 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068757C211yesmaximal, characteristic, complemented
2#13067284C212yesmaximal
3#13066474C212yesmaximal, complemented
4#13066461C211yesmaximal, characteristic, complemented
5C11×#1961C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×C11×#102—22no—
8C2×C11×#97C2211yescharacteristic
9C11×#382C2211yescharacteristic
10#10622538C2212yes—
11#10622537C2212yes—
12#10622190—22no—
13#10622182—24no—
14C22×D4×C11—21no—
15C22×D4×C11—22no—
16C22×C8×C11D412yes—
17C11×#127—21no—
18C11×#127—22no—
19C11×#127D412yes—
20C2×C11×C4⋊C4—21no—
21C2×C42×C11C2311yescharacteristic
22C2×#4318—22no—
23C11×#102—44no—
24C11×#97—22no—
25C11×#95—22no—
26C22⋊(C11⋊C8)—22no—
27C4⋊(C11⋊C8)—22no—
28C4⋊(C11⋊C8)—22no—
29C4⋊(C11⋊C8)—22no—
30C4×C11⋊C8—22no—
31#10634—111nomaximal, Sylow
32C24×C11—41no—
33C2×D4×C11—22no—
34C2×D4×C11—24no—
35C2×D4×C11—41no—
36C2×D4×C11—42no—
37C2×D4×C11—42no—
38C2×D4×C11—42no—
39C2×D4×C11—84no—
40C22×C4×C11—41no—
41C22×C4×C11C2×D411yescharacteristic
42C22×C4×C11#4112yes—
43C2×C8×C11—22no—
44C2×C8×C11—22no—
45C2×C8×C11—22no—
46C11×C4⋊C4—42no—
47C42×C11C2×D411yescharacteristic
48C42×C11#4111yescharacteristic
49C42×C11#4112yes—
50#4318—42no—
51#4318—42no—
52C2×C11⋊C8—42no—
53C2×C11⋊C8—42no—
54#1961D1111yescharacteristic
55#1838—111no—
56#1545—112no—
57#1286—112no—
58#1281—111no—
59C23×C11—42no—
60C23×C11—84no—
61C23×C11—81no—
62C23×C11—81no—
63C23×C11#12411yescharacteristic
64D4×C11—44no—
65D4×C11—84no—
66D4×C11—84no—
67D4×C11—82no—
68C2×C4×C11—42no—
69C2×C4×C11—82no—
70C2×C4×C11—81no—
71C2×C4×C11#12111yescharacteristic
72C2×C4×C11#12312yes—
73C2×C4×C11#12311yescharacteristic
74C2×C4×C11#12612yes—
75C2×C4×C11#13512yes—
76C2×C4×C11AGL(1,ℤ/8)12yes—
77C8×C11—42no—
78C11⋊C8—82no—
79C11⋊C8—82no—
80C2×#127C2×D1111yescharacteristic
81#431—112no—
82#423—112no—
83C2×#102—22no—
84C2×#97C2×D1111yescharacteristic
85#382C2×D1111yescharacteristic
86#341—222no—
87#331—224no—
88C22×C11—22no—
89C22×C11—82no—
90C22×C11—84no—
91C22×C11—162no—
92C22×C11—162no—
93C22×C11#39711yescharacteristic
94C22×C11#48811yescharacteristic
95C22×C11#49011yescharacteristic
96C4×C11—22no—
97C4×C11—22no—
98C4×C11—161no—
99C4×C11#46312yes—
100C4×C11#48212yes—
101C22×D4—22no—
102C22×D4—21no—
103C2×M16—222no—
104C22×C8C22⋊D1112yes—
105#127—21no—
106#127—22no—
107#127D4412yes—
108C2×C4⋊C4—21no—
109C2×C42C22×D1111yescharacteristic
110C4⋊C8—222no—
111C4⋊C8—222no—
112C4⋊C8—222no—
113#102—44no—
114C22⋊C8—222no—
115#97—22no—
116C4×C8—222no—
117#95—22no—
118C2×C11—21no—
119C2×C11—21no—
120C2×C11—162no—
121C2×C11#207311yescharacteristic
122C2×C11#208112yes—
123C24—41no—
124C2×D4—24no—
125C2×D4—22no—
126C2×D4—42no—
127C2×D4—42no—
128C2×D4—41no—
129C2×D4—42no—
130C2×D4—84no—
131C22×C4—41no—
132C22×C4#434112yes—
133C22×C4C2×C22⋊D1111yescharacteristic
134M16—442no—
135M16—442no—
136C2×C8—22no—
137C2×C8—22no—
138C2×C8—22no—
139C2×C8—442no—
140C2×C8—442no—
141C4⋊C4—42no—
142C42C2×D4411yescharacteristic
143C42#433911yescharacteristic
144C42#434112yes—
145C11#1063411yescharacteristic, complemented, Sylow
146C23—42no—
147C23—84no—
148C23—81no—
149C23—81no—
150C23#6698911yescharacteristic
151D4—44no—
152D4—84no—
153D4—84no—
154D4—82no—
155C2×C4—42no—
156C2×C4—82no—
157C2×C4—81no—
158C2×C4#6693212yes—
159C2×C4#6693912yes—
160C2×C4#6698311yescharacteristic
161C2×C4#6698512yes—
162C2×C4#6698811yescharacteristic
163C2×C4#6700312yes—
164C8—42no—
165C8—882no—
166C8—882no—
167C22—22no—
168C22—82no—
169C22—84no—
170C22—162no—
171C22—162no—
172C22#1062256611yescharacteristic
173C22#1062266911yescharacteristic
174C22#1062268411yescharacteristic
175C4—22no—
176C4—22no—
177C4—161no—
178C4#1062262912yes—
179C4#1062264812yes—
180C2—21no—
181C2—21no—
182C2—162no—
183C2#1307002911yescharacteristic
184C2#1307007312yes—
subgroupG/H
centerC22#10622566
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1961C2
socleC22×C11#397
prime radicalC2×C11×#127C22
hypercenter#1961D11
hypocenterC11#10634
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
1. #13068757C2semidirect
3. #13066474C2semidirect
4. #13066461C2semidirect
145. C11#10634semidirect

Maximal subgroups

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

subgroupindex
#130687572
#130672842
#130664742
#130664612
C11×#19612
#1063411