Finite Group Databasebeta

← #14656882

Subgroups — #14656882

Order 2816.

402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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#13077003C211yesmaximal, characteristic, complemented
2#13069444C211yesmaximal, characteristic
3#13067177C212yesmaximal
4#13066475C212yesmaximal, complemented
5C11×#1276C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7C11×#431C2212yes—
8C43×C11C2211yescharacteristic
9#10622549C2212yes—
10#10622546—24no—
11#10622541—22no—
12C2×#66869—22no—
13#10622537C2211yescharacteristic
14#10622108—24no—
15C2×#4339—21no—
16C2×C42×C11—22no—
17C2×C42×C11D412yes—
18C2×C42×C11C2311yescharacteristic
19#66983—22no—
20C2×C4⋊Dic11—22no—
21C2×Dic11⋊C4—24no—
22C2×#4318—21no—
23#66928—21no—
24#66927Q811yescharacteristic
25C4×D44—22no—
26#66922Q811yescharacteristic
27C11×C4⋊C8—22no—
28C11×C22⋊C8—22no—
29C4×C8×C11—22no—
30C11⋊#95—24no—
31C11⋊#95—22no—
32C11⋊#95D414yes—
33#66869—44no—
34C4⋊(C11⋊C8)—22no—
35#10366—111nomaximal, Sylow
36C22×C4×C11—22no—
37C22×C4×C11C2×D412yes—
38C22×C4×C11C2×D411yescharacteristic
39C2×C22⋊D11—41no—
40C22×Dic11—24no—
41#4339—42no—
42#4339—42no—
43C2×D44—21no—
44C2×D44—22no—
45C2×C4×D11—41no—
46C2×Dic22—21no—
47C2×C8×C11—42no—
48C42×C11—22no—
49C42×C11—22no—
50C42×C11—44no—
51C42×C11C2×Q811yescharacteristic
52C42×C11#4112yes—
53C42×C11#4111yescharacteristic
54(C2×D11)⋊C4—42no—
55C4⋊Dic11—22no—
56C4⋊Dic11—42no—
57C4⋊Dic11—42no—
58Dic11⋊C4—48no—
59#4318—42no—
60C2×C11⋊C8—41no—
61#2864—111no—
62#1962—111no—
63#1517—112no—
64#1286—112no—
65#1276D1111yescharacteristic, complemented
66C23×C11#12011yescharacteristic
67C22×D11—41no—
68C2×C4×C11—24no—
69C2×C4×C11—42no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11C22⋊Q812yes—
73C2×C4×C11C22⋊Q811yescharacteristic
74C2×C4×C11#12411yescharacteristic
75C2×C4×C11#12412yes—
76C2×C4×C11#13512yes—
77C2×C4×C11AGL(1,ℤ/8)12yes—
78C22⋊D11—82no—
79C2×Dic11—48no—
80C2×Dic11—41no—
81C2×Dic11—44no—
82D44—42no—
83D44—82no—
84C4×D11—81no—
85C4×D11—81no—
86Dic22—42no—
87C8×C11—82no—
88C11⋊C8—81no—
89#532—111no—
90#431C2×D1112yes—
91#423—111no—
92C2×#104—222no—
93#389—222no—
94#387—224no—
95#382—112no—
96C43C2×D1111yescharacteristic
97#327—224no—
98C22×C11—22no—
99C22×C11#39311yescharacteristic
100C22×C11#44912yes—
101C2×D11—81no—
102C2×D11—82no—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11—44no—
106C4×C11#47812yes—
107C4×C11#48811yescharacteristic
108C4×C11#49011yescharacteristic
109Dic11—84no—
110Dic11—81no—
111C2×#41—221no—
112C2×M16—221no—
113C4⋊Q8—111no—
114#127—111no—
115#124—221no—
116#121—222no—
117C4×D4—222no—
118C2×C4⋊C4—224no—
119C2×C4⋊C4—222no—
120C2×C42—22no—
121C2×C42D4412yes—
122C2×C42C22×D1111yescharacteristic
123C4⋊C8—22no—
124C4⋊C8—222no—
125#104—444no—
126C22⋊C8—22no—
127C4×C8—22no—
128#95—114no—
129#95—224no—
130#95—222no—
131C2×C11—22no—
132C2×C11#202511yescharacteristic
133C2×C11#203112yes—
134D11—161no—
135#41—442no—
136#41—442no—
137C2×Q8—221no—
138C2×D4—222no—
139C2×D4—221no—
140C2×D4—441no—
141C22×C4—22no—
142C22×C4—224no—
143C22×C4—441no—
144C22×C4C2×D4411yescharacteristic
145C22×C4D4×D1112yes—
146M16—442no—
147C2×C8—42no—
148C2×C8—441no—
149C4⋊C4—222no—
150C4⋊C4—448no—
151C4⋊C4—442no—
152C4⋊C4—442no—
153C22⋊C4—442no—
154C42—22no—
155C42—22no—
156C42—44no—
157C42#433912yes—
158C42#434111yescharacteristic
159C42Q8×D1111yescharacteristic
160C11#1036611yescharacteristic, complemented, Sylow
161C23—441no—
162C23#6693511yescharacteristic
163Q8—442no—
164D4—442no—
165D4—882no—
166D4—882no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—448no—
172C2×C4—441no—
173C2×C4—444no—
174C2×C4—881no—
175C2×C4—881no—
176C2×C4#6692811yescharacteristic
177C2×C4#6693812yes—
178C2×C4#6694912yes—
179C2×C4#6695011yescharacteristic
180C2×C4#6695712yes—
181C2×C4#6696112yes—
182C8—82no—
183C8—881no—
184C22—22no—
185C22—881no—
186C22—882no—
187C22#1062228611yescharacteristic
188C22#1062234712yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—884no—
193C4—881no—
194C4#1062231011yescharacteristic
195C4#1062232611yescharacteristic
196C4#1062246012yes—
197C2—22no—
198C2—1761no—
199C2#1306976311yescharacteristic
200C2#1306978912yes—
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#1276D11
hypocenterC11#10366
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #13077003C2semidirect
4. #13066475C2semidirect
5. C11×#1276C2semidirect
65. #1276D11semidirect
160. C11#10366semidirect

Maximal subgroups

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

subgroupindex
#130770032
#130694442
#130671772
#130664752
C11×#12762
#1036611