Finite Group Databasebeta

← #14673668

Subgroups — #14673668

Order 2816.

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

normal subgroups only

This group has 276 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#13070411C211yesmaximal, characteristic, complemented
2#13068670C212yesmaximal
3#13066718C211yesmaximal, characteristic, complemented
4#13066712C212yesmaximal, complemented
5C11×#2113C211yesmaximal, characteristic
6C2×C11×#131C2211yescharacteristic
7C2×C11×M32C2211yescharacteristic
8C22×C11×C16C2211yescharacteristic
9#10622849—22no—
10C2×#66883C2212yes—
11#10622719C2212yes—
12C11×C22⋊C16—22no—
13#10622197—22no—
14#10622144—22no—
15C2×C11×#41D411yescharacteristic
16C11×#131—22no—
17C11×#131—22no—
18C2×C11×M16—21no—
19C2×C11×M16D411yescharacteristic
20C22×C8×C11—21no—
21C22×C8×C11C2311yescharacteristic
22#66979—22no—
23C2×#4318—22no—
24C11×M32—22no—
25C2×C11×C16—21no—
26C2×C11×C16—22no—
27C2×C11×C16D412yes—
28#66901—44no—
29#66883—22no—
30#66883—22no—
31#66882—22no—
32#66881—22no—
33#13499—111nomaximal, Sylow
34C11×#41—22no—
35C11×#41—22no—
36C2×Q8×C11Q1611yescharacteristic
37C2×D4×C11—21no—
38C2×D4×C11Q1611yescharacteristic
39C22×C4×C11—21no—
40C22×C4×C11C2×D411yescharacteristic
41C11×M16—22no—
42C11×M16—42no—
43C2×C8×C11—21no—
44C2×C8×C11—41no—
45C2×C8×C11—41no—
46C2×C8×C11C2×D411yescharacteristic
47C2×C8×C11#4111yescharacteristic
48C2×C8×C11#4112yes—
49C2×C8×C11#4112yes—
50C22⋊Dic11—42no—
51C4⋊Dic11—42no—
52C4×Dic11—42no—
53#4318—42no—
54#4318—42no—
55C2×C11⋊C8—42no—
56C11×C16—22no—
57C11×C16—41no—
58#2161—111no—
59#2113D1111yescharacteristic
60#1814—112no—
61#1384—111no—
62#1382—112no—
63C23×C11—21no—
64C23×C11#13511yescharacteristic
65Q8×C11—22no—
66D4×C11—22no—
67D4×C11—42no—
68C2×C4×C11—21no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11#12111yescharacteristic
72C2×C4×C11#12312yes—
73C2×C4×C11C2×Q1611yescharacteristic
74C2×C4×C11AGL(1,ℤ/8)12yes—
75C2×Dic11—82no—
76C8×C11—41no—
77C8×C11#12311yescharacteristic
78C8×C11#12411yescharacteristic
79C8×C11#12612yes—
80C11⋊C8—82no—
81C2×#131C2×D1111yescharacteristic
82C2×M32C2×D1111yescharacteristic
83C22×C16C2×D1111yescharacteristic
84C2×#108—112no—
85#427—112no—
86#421—222no—
87#368—222no—
88C22⋊C16—22no—
89#344—222no—
90C22×C11—41no—
91C22×C11—42no—
92C22×C11—41no—
93C22×C11#46711yescharacteristic
94C22×C11#48212yes—
95C4×C11—41no—
96C4×C11#39711yescharacteristic
97C4×C11#46911yescharacteristic
98C4×C11#48412yes—
99Dic11—162no—
100C2×#41D4411yescharacteristic
101#131—22no—
102#131—22no—
103C2×M16—21no—
104C2×M16—222no—
105C2×M16D4411yescharacteristic
106C22×C8—21no—
107C22×C8C22×D1111yescharacteristic
108#117—222no—
109M32—22no—
110C2×C16—22no—
111C2×C16—21no—
112C2×C16C22⋊D1112yes—
113#108—222no—
114#108—222no—
115#107—222no—
116#106—222no—
117#104—444no—
118C2×C11—22no—
119C2×C11—21no—
120C2×C11—81no—
121C2×C11#207611yescharacteristic
122#41—22no—
123#41—22no—
124C2×Q8Dic4411yescharacteristic
125C2×D4—21no—
126C2×D4Dic4411yescharacteristic
127C22×C4—21no—
128C22×C4C2×D4411yescharacteristic
129M16—22no—
130M16—42no—
131M16—442no—
132M16—442no—
133C2×C8—21no—
134C2×C8—41no—
135C2×C8—41no—
136C2×C8—442no—
137C2×C8#433911yescharacteristic
138C2×C8#434112yes—
139C2×C8#434112yes—
140C2×C8C2×C22⋊D1111yescharacteristic
141C4⋊C4—442no—
142C22⋊C4—442no—
143C42—442no—
144C16—22no—
145C16—41no—
146C11#1349911yescharacteristic, complemented, Sylow
147C23—21no—
148C23#6695711yescharacteristic
149Q8—22no—
150D4—22no—
151D4—42no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—882no—
156C2×C4#6693912yes—
157C2×C4C2×Dic4411yescharacteristic
158C2×C4#6696112yes—
159C2×C4#6698311yescharacteristic
160C8—41no—
161C8—882no—
162C8#6693212yes—
163C8#6698811yescharacteristic
164C8#6698911yescharacteristic
165C22—41no—
166C22—42no—
167C22—41no—
168C22#1062235012yes—
169C22#1062272911yescharacteristic
170C4—41no—
171C4—1762no—
172C4#1062233512yes—
173C4#1062256611yescharacteristic
174C4#1062274811yescharacteristic
175C2—22no—
176C2—21no—
177C2—81no—
178C2#1307004411yescharacteristic
subgroupG/H
centerC4#10622748
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2113C2
socleC2×C11#2076
prime radicalC2×C11×#41D4
hypercenter#2113D11
hypocenterC11#13499
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
1. #13070411C2semidirect
3. #13066718C2semidirect
4. #13066712C2semidirect
146. C11#13499semidirect

Maximal subgroups

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

subgroupindex
#130704112
#130686702
#130667182
#130667122
C11×#21132
#1349911