Finite Group Databasebeta

← #14674429

Subgroups — #14674429

Order 2816.

324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×#10622158C212yesmaximal, complemented
2#13070707C211yesmaximal, characteristic, complemented
3#13066794C212yesmaximal, complemented
4C22⋊(C11⋊C32)C211yesmaximal, characteristic, complemented
5C22×C11×D16C211yesmaximal, characteristic
6C22×C11×D8—21no—
7C2×C11×D16—24no—
8C2×C11×D16—21no—
9C2×C11×D16C2212yes—
10C22×C11×C16C2211yescharacteristic
11#10622729—21no—
12C2×Dic88C2211yescharacteristic, complemented
13#10622158—24no—
14#10622142C2211yescharacteristic, complemented
15#10622141—21no—
16C2×C11⋊C32C2212yescomplemented
17C22×D4×C11—41no—
18C2×C11×D8—24no—
19C2×C11×D8—22no—
20C2×C11×D8—42no—
21C2×C11×D8—41no—
22C22×C8×C11D411yescharacteristic
23#66977—41no—
24C2×Dic44—21no—
25C11×D16—24no—
26C11×D16—22no—
27C11×D16D414yes—
28C2×C11×C16—22no—
29C2×C11×C16D411yescharacteristic
30C2×C11×C16C2311yescharacteristic
31#66882—21no—
32#66880—41no—
33Dic88—22no—
34C11⋊C32—22no—
35#13664—111nomaximal, Sylow
36C24×C11—81no—
37C2×D4×C11—44no—
38C2×D4×C11—42no—
39C2×D4×C11—82no—
40C2×D4×C11—81no—
41C22×C4×C11D811yescharacteristic
42C2×Dic22—41no—
43C11×D8—24no—
44C11×D8—44no—
45C11×D8—42no—
46C2×C8×C11—21no—
47C2×C8×C11—21no—
48C2×C8×C11D811yescharacteristic
49C2×C8×C11C2×D411yescharacteristic
50C22⋊Dic11—81no—
51C4⋊Dic11—41no—
52Dic11⋊C4—81no—
53Dic44—41no—
54Dic44—41no—
55C11×C16—21no—
56C11×C16C2×D412yes—
57C22×D16D1111yescharacteristic
58C2×SD64—112no—
59#2216—111no—
60#1415—112no—
61C22⋊C32—111no—
62C23×C11—84no—
63C23×C11—82no—
64C23×C11—162no—
65C23×C11—162no—
66C23×C11D1611yescharacteristic
67D4×C11—44no—
68D4×C11—84no—
69D4×C11—82no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11D1611yescharacteristic
73C2×C4×C11C2×D811yescharacteristic
74C2×Dic11—81no—
75C2×Dic11—81no—
76Dic22—81no—
77Dic22—81no—
78C8×C11—21no—
79C8×C11#12011yescharacteristic
80C8×C11AGL(1,ℤ/8)11yescharacteristic
81C22×D8—21no—
82C2×Q32—111no—
83C2×D16—24no—
84C2×D16—21no—
85C2×D16C2×D1112yes—
86C22×C16C2×D1111yescharacteristic
87#467—221no—
88SD64—224no—
89C2×C32—112no—
90#366—111no—
91#358—221no—
92C22×C11—21no—
93C22×C11—21no—
94C22×C11—84no—
95C22×C11—168no—
96C22×C11—162no—
97C22×C11—162no—
98C22×C11SD6412yescomplemented
99C22×C11C2×D1611yescharacteristic
100C4×C11—21no—
101C4×C11#44711yescharacteristic
102C4×C11#50911yescharacteristic
103Dic11—161no—
104Dic11—161no—
105C22×D4—41no—
106C2×Q16—221no—
107C2×D8—24no—
108C2×D8—22no—
109C2×D8—42no—
110C2×D8—41no—
111C22×C8C22⋊D1111yescharacteristic
112C22⋊Q8—441no—
113Q32—222no—
114D16—24no—
115D16—22no—
116D16C22⋊D1114yes—
117C2×C16—22no—
118C2×C16C22⋊D1111yescharacteristic
119C2×C16C22×D1111yescharacteristic
120#107—221no—
121#103—441no—
122C32—222no—
123C2×C11—22no—
124C2×C11—164no—
125C2×C11#218411yescharacteristic
126C2×C11C2×SD6411yescharacteristic
127C2×C11#226311yescharacteristic
128C24—81no—
129C2×Q8—441no—
130C2×D4—44no—
131C2×D4—42no—
132C2×D4—82no—
133C2×D4—81no—
134C22×C4#432311yescharacteristic
135Q16—441no—
136Q16—441no—
137D8—24no—
138D8—44no—
139D8—42no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8#432311yescharacteristic
143C2×C8C2×C22⋊D1111yescharacteristic
144C4⋊C4—441no—
145C4⋊C4—881no—
146C22⋊C4—881no—
147C16—21no—
148C16C2×C22⋊D1112yes—
149C11#1366411yescharacteristic, complemented, Sylow
150C23—84no—
151C23—82no—
152C23—162no—
153C23—162no—
154C23#6689011yescharacteristic
155Q8—881no—
156Q8—881no—
157D4—44no—
158D4—84no—
159D4—82no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—881no—
163C2×C4—881no—
164C2×C4#6689011yescharacteristic
165C2×C4C2×#432311yescharacteristic
166C8—21no—
167C8#6698511yescharacteristic
168C8#6700611yescharacteristic
169C22—21no—
170C22—21no—
171C22—84no—
172C22—168no—
173C22—162no—
174C22—162no—
175C22#1062215812yescomplemented
176C22C2×#6689011yescharacteristic
177C4—21no—
178C4—1761no—
179C4—1761no—
180C4#1062276011yescharacteristic
181C4#1062283011yescharacteristic
182C2—22no—
183C2—164no—
184C2#1307052811yescharacteristic
185C2C2×#1062215811yescharacteristic
186C2#1307092911yescharacteristic
subgroupG/H
centerC22C2×#66890
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
Fitting, prime radicalC22×C11×D16C2
socleC22×C11C2×D16
hypercenterC22×D16D11
hypocenterC11#13664
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C2×#10622158C2semidirect
2. #13070707C2semidirect
3. #13066794C2semidirect
4. C22⋊(C11⋊C32)C2semidirect
12. C2×Dic88C22semidirect
14. #10622142C22semidirect
16. C2×C11⋊C32C22semidirect
98. C22×C11SD64semidirect
149. C11#13664semidirect
175. C22#10622158semidirect

Maximal subgroups

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

subgroupindex
C2×#106221582
#130707072
#130667942
C22⋊(C11⋊C32)2
C22×C11×D162
#1366411