Finite Group Databasebeta

← #14674758

Subgroups — #14674758

Order 2816.

194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 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#13070893C211yesmaximal, characteristic, complemented
2#13070864C211yesmaximal, characteristic
3#13066795C211yesmaximal, characteristic, complemented
4#13066794C211yesmaximal, characteristic, complemented
5#13066793C211yesmaximal, characteristic, complemented
6#13066749C211yesmaximal, characteristic, complemented
7C11×#1415C211yesmaximal, characteristic, complemented
8C2×C11×D16C2211yescharacteristic
9#10622764—21no—
10C2×#66890—21no—
11C2×D176C2211yescharacteristic
12#10622491—21no—
13C2×C11×C32C2211yescharacteristic
14C11×#366C2211yescharacteristic
15#10622142C2211yescharacteristic
16C16×Dic11C2211yescharacteristic
17C2×C11⋊C32C2211yescharacteristic
18#10622128—21no—
19C2×C11×D8—21no—
20#66993—41no—
21C2×#4323—41no—
22C2×D88—21no—
23#66943—41no—
24C11×D16—21no—
25C11×D16—21no—
26C2×C11×C16C2311yescharacteristic
27C11×#107—21no—
28#66890—42no—
29#66882—21no—
30C8×Dic11D411yescharacteristic
31C2×C11⋊C16D411yescharacteristic
32#66872—41no—
33D176—21no—
34D176—21no—
35C11×C32—21no—
36C11⋊C32—21no—
37#13723—111nomaximal, Sylow
38C2×D4×C11—41no—
39C2×C22⋊D11—81no—
40C2×C22⋊D11—81no—
41C2×D44—41no—
42C11×D8—41no—
43C11×D8—41no—
44C2×C8×C11C2×D411yescharacteristic
45C11×C4⋊C4—41no—
46#4323—82no—
47C4⋊Dic11—41no—
48C4⋊Dic11—81no—
49Dic11⋊C4—81no—
50C4×Dic11D811yescharacteristic
51C2×C11⋊C8D811yescharacteristic
52D88—41no—
53D88—41no—
54C11×C16#4111yescharacteristic
55C11×C16#4111yescharacteristic
56C11⋊C16SD1612yes—
57#2253—111no—
58#2246—111no—
59#1415—111no—
60#1415—111no—
61#1415—111no—
62#1415D1111yescharacteristic, complemented
63#1397—111no—
64C23×C11—81no—
65C22×D11—81no—
66D4×C11—81no—
67D4×C11—81no—
68C2×C4×C11—81no—
69C2×C4×C11C2×D811yescharacteristic
70C22⋊D11—162no—
71C22⋊D11—162no—
72C2×Dic11—81no—
73C2×Dic11D1611yescharacteristic
74C2×Dic11D1611yescharacteristic
75D44—81no—
76D44—81no—
77C8×C11#12411yescharacteristic
78C8×C11C2×SD1611yescharacteristic
79C11⋊C8SD3212yes—
80C2×D16—111no—
81C2×D16—221no—
82C2×D16C2×D1111yescharacteristic
83#499—221no—
84#493—221no—
85C2×C32—111no—
86C2×C32C2×D1111yescharacteristic
87#367—221no—
88#366—111no—
89#366C2×D1111yescharacteristic
90C4×C16—111no—
91C22×C11—161no—
92C22×C11—161no—
93C22×C11—161no—
94C22×C11C2×D1611yescharacteristic
95C2×D11—161no—
96C2×D11—161no—
97C2×D11—161no—
98C4×C11—161no—
99C4×C11#48611yescharacteristic
100C4×C11C2×SD3211yescharacteristic
101Dic11—21no—
102Dic11—21no—
103Dic11—161no—
104C2×D8—21no—
105C2×D8—221no—
106C2×D8—441no—
107#127—441no—
108#125—441no—
109D16—21no—
110D16—21no—
111D16—221no—
112D16—221no—
113D16—442no—
114C2×C16—111no—
115C2×C16C22×D1111yescharacteristic
116#107—21no—
117#107—221no—
118#106—441no—
119C4×C8—111no—
120C32—21no—
121C32—221no—
122C2×C11—321no—
123C2×C11#224011yescharacteristic
124C2×C11#226311yescharacteristic
125C2×C11#226311yescharacteristic
126D11—321no—
127C2×D4—41no—
128C2×D4—441no—
129C2×D4—881no—
130C2×D4—881no—
131D8—41no—
132D8—41no—
133D8—441no—
134D8—441no—
135D8—882no—
136C2×C8—111no—
137C2×C8D4×D1111yescharacteristic
138C4⋊C4—41no—
139C4⋊C4—441no—
140C4⋊C4—881no—
141C4⋊C4—881no—
142C42—111no—
143C16—112no—
144C16#433911yescharacteristic
145C16#434111yescharacteristic
146C11#1372311yescharacteristic, complemented, Sylow
147C23—81no—
148C23—881no—
149D4—81no—
150D4—81no—
151D4—881no—
152D4—881no—
153D4—1762no—
154D4—1762no—
155C2×C4—81no—
156C2×C4—111no—
157C2×C4—111no—
158C2×C4—881no—
159C2×C4D8×D1111yescharacteristic
160C8—112no—
161C8#6693811yescharacteristic
162C8SD16×D1111yescharacteristic
163C22—161no—
164C22—161no—
165C22—161no—
166C22—1761no—
167C22—1761no—
168C22—1761no—
169C22D11×D1611yescharacteristic
170C4—161no—
171C4—221no—
172C4—221no—
173C4—1761no—
174C4#1062237311yescharacteristic
175C4D11×SD3211yescharacteristic
176C2—321no—
177C2—3521no—
178C2#1307083811yescharacteristic
179C2#1307092711yescharacteristic
180C2#1307093011yescharacteristic
subgroupG/H
centerC22D11×D16
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×#1415C2
socleC22×C11C2×D16
prime radical#13070864C2
hypercenter#1415D11
hypocenterC11#13723
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. #13070893C2semidirect
3. #13066795C2semidirect
4. #13066794C2semidirect
5. #13066793C2semidirect
6. #13066749C2semidirect
7. C11×#1415C2semidirect
62. #1415D11semidirect
146. C11#13723semidirect

Maximal subgroups

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

subgroupindex
#130708932
#130708642
#130667952
#130667942
#130667932
#130667492
C11×#14152
#1372311