Finite Group Databasebeta

← #14658552

Subgroups — #14658552

Order 2816.

310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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#13069448C211yesmaximal, characteristic
2#13067266C212yesmaximal
3#13066513C212yesmaximal, complemented
4#13066445C211yesmaximal, characteristic, complemented
5C11×#1832C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7C2×C11×C4⋊C8C2212yes—
8C11×#376C2211yescharacteristic
9C2×#66869—22no—
10#10622538C2212yes—
11#10622537C2211yescharacteristic
12C11×#336—22no—
13#10622123—22no—
14#10622120—22no—
15C2×#4339—21no—
16C22×C8×C11—22no—
17C2×C42×C11D412yes—
18C2×C42×C11C2311yescharacteristic
19#66983—22no—
20C2×#4318—21no—
21#66928—21no—
22#66927D411yescharacteristic
23C4×D44—22no—
24#66922D411yescharacteristic
25C11×C4⋊C8—22no—
26C11×C4⋊C8—22no—
27C11×#95—22no—
28C22⋊(C11⋊C8)—22no—
29#66869—44no—
30C4⋊(C11⋊C8)—22no—
31C4⋊(C11⋊C8)—22no—
32C4×C11⋊C8—22no—
33#10629—111nomaximal, Sylow
34C22×C4×C11—22no—
35C22×C4×C11C2×D411yescharacteristic
36C22×C4×C11#4112yes—
37C2×C22⋊D11—41no—
38#4339—42no—
39#4339—42no—
40C2×D44—21no—
41C2×D44—22no—
42C2×C4×D11—41no—
43C2×Dic22—21no—
44C2×C8×C11—42no—
45C2×C8×C11—42no—
46C2×C8×C11—42no—
47C42×C11—22no—
48C42×C11—22no—
49C42×C11C2×D411yescharacteristic
50C42×C11#4111yescharacteristic
51C42×C11#4112yes—
52(C2×D11)⋊C4—42no—
53C4⋊Dic11—22no—
54#4318—42no—
55C2×C11⋊C8—42no—
56C2×C11⋊C8—41no—
57#1963—111no—
58#1832D1111yescharacteristic, complemented
59#1540—112no—
60#1301—112no—
61#1274—111no—
62C23×C11#12311yescharacteristic
63C22×D11—41no—
64C2×C4×C11—42no—
65C2×C4×C11—44no—
66C2×C4×C11—42no—
67C2×C4×C11#12111yescharacteristic
68C2×C4×C11#12312yes—
69C2×C4×C11#12411yescharacteristic
70C2×C4×C11#12612yes—
71C2×C4×C11#13512yes—
72C2×C4×C11AGL(1,ℤ/8)12yes—
73C22⋊D11—82no—
74C2×Dic11—41no—
75D44—42no—
76D44—82no—
77C4×D11—81no—
78C4×D11—81no—
79Dic22—42no—
80C8×C11—82no—
81C11⋊C8—82no—
82C11⋊C8—81no—
83#532—111no—
84#431—112no—
85#423—111no—
86C2×C4⋊C8C2×D1112yes—
87C2×#104—222no—
88#376C2×D1111yescharacteristic
89#336—22no—
90#332—222no—
91#331—222no—
92C22×C11—22no—
93C22×C11#39711yescharacteristic
94C22×C11#48212yes—
95C2×D11—81no—
96C2×D11—82no—
97C4×C11—22no—
98C4×C11—22no—
99C4×C11—82no—
100C4×C11#46312yes—
101C4×C11#48811yescharacteristic
102C4×C11#49011yescharacteristic
103Dic11—81no—
104C2×#41—221no—
105C2×M16—221no—
106C22×C8—22no—
107C4⋊Q8—111no—
108#127—111no—
109#124—221no—
110#121—222no—
111C4×D4—222no—
112C2×C42C22⋊D1112yes—
113C2×C42C22×D1111yescharacteristic
114C4⋊C8—22no—
115C4⋊C8—22no—
116C4⋊C8—222no—
117C4⋊C8—222no—
118#104—444no—
119C22⋊C8—222no—
120C4×C8—222no—
121#95—22no—
122C2×C11—22no—
123C2×C11#207311yescharacteristic
124C2×C11#208012yes—
125D11—161no—
126#41—442no—
127#41—442no—
128C2×Q8—221no—
129C2×D4—222no—
130C2×D4—221no—
131C2×D4—441no—
132C22×C4—22no—
133C22×C4—441no—
134C22×C4#433912yes—
135C22×C4C2×C22⋊D1111yescharacteristic
136M16—442no—
137C2×C8—42no—
138C2×C8—42no—
139C2×C8—42no—
140C2×C8—442no—
141C2×C8—441no—
142C4⋊C4—222no—
143C22⋊C4—442no—
144C42—22no—
145C42—22no—
146C42D4×D1111yescharacteristic
147C42#434111yescharacteristic
148C42#434312yes—
149C11#1062911yescharacteristic, complemented, Sylow
150C23—441no—
151C23#6698211yescharacteristic
152Q8—442no—
153D4—442no—
154D4—882no—
155D4—882no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—42no—
159C2×C4—441no—
160C2×C4—881no—
161C2×C4—881no—
162C2×C4#6694712yes—
163C2×C4#6695112yes—
164C2×C4#6699111yescharacteristic
165C2×C4#6700011yescharacteristic
166C2×C4#6700212yes—
167C2×C4#6700312yes—
168C8—82no—
169C8—882no—
170C8—881no—
171C22—22no—
172C22—881no—
173C22—882no—
174C22#1062260611yescharacteristic
175C22#1062261612yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—881no—
180C4#1062267012yes—
181C4#1062268011yescharacteristic
182C4#1062268111yescharacteristic
183C2—22no—
184C2—1761no—
185C2#1307003011yescharacteristic
186C2#1307006712yes—
subgroupG/H
centerC2×C4#67000
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1832C2
socleC22×C11#397
prime radical#10623008C22
hypercenter#1832D11
hypocenterC11#10629
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
3. #13066513C2semidirect
4. #13066445C2semidirect
5. C11×#1832C2semidirect
58. #1832D11semidirect
149. C11#10629semidirect

Maximal subgroups

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

subgroupindex
#130694482
#130672662
#130665132
#130664452
C11×#18322
#1062911