Finite Group Databasebeta

← #14674649

Subgroups — #14674649

Order 2816.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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×#10622087C211yesmaximal, characteristic, complemented
2#13070909C211yesmaximal, characteristic, complemented
3#13070742C211yesmaximal, characteristic, complemented
4#13070737C211yesmaximal, characteristic
5#13066808C211yesmaximal, characteristic, complemented
6#13066805C211yesmaximal, characteristic, complemented
7C11×#1425C211yesmaximal, characteristic, complemented
8C2×Dic88C2211yescharacteristic
9C2×D176C2211yescharacteristic
10#10622514C2211yescharacteristic
11#10622510—21no—
12#10622509—21no—
13C2×C11×C32C2211yescharacteristic
14C11×#368C2211yescharacteristic
15C11×#368C2211yescharacteristic
16#10622137C2211yescharacteristic
17#10622134—21no—
18#10622133—21no—
19#10622087—21no—
20#10622087—21no—
21#10622085—21no—
22D11×C32—21no—
23#66962—41no—
24#66961—41no—
25C2×Dic44—21no—
26C2×D88—21no—
27#66954D411yescharacteristic
28C2×C11×C16C2311yescharacteristic
29C11×#108—21no—
30C11×#108—21no—
31#66888—41no—
32#66887—41no—
33#66876D411yescharacteristic
34Dic88—21no—
35Dic88—21no—
36D176—21no—
37D176—21no—
38#66862—21no—
39C16×D11—21no—
40C11×C32D411yescharacteristic
41C11×C32D411yescharacteristic
42C11⋊C32—21no—
43#13702—111nomaximal, Sylow
44#4339D811yescharacteristic
45C2×D44—41no—
46C2×Dic22—41no—
47C11×M16—41no—
48C11×M16—41no—
49C2×C8×C11C2×D411yescharacteristic
50#4318D811yescharacteristic
51Dic44—41no—
52Dic44—41no—
53Dic44—81no—
54D88—41no—
55D88—41no—
56D88—81no—
57#4314—81no—
58#4314—81no—
59#4313—21no—
60C8×D11—21no—
61C11×C16C2×D411yescharacteristic
62C11×C16#4111yescharacteristic
63C11⋊C16—21no—
64C2×SD64—111no—
65#2258—111no—
66#2222—111no—
67#2221—111no—
68#1425D1111yescharacteristic, complemented
69#1420—111no—
70#1419—111no—
71C22×D11—81no—
72C2×C4×C11C2×D811yescharacteristic
73C22⋊D11—21no—
74C2×Dic11—81no—
75D44—81no—
76D44—81no—
77D44D1611yescharacteristic
78C4×D11—21no—
79Dic22—81no—
80Dic22—81no—
81Dic22D1611yescharacteristic
82C8×C11—81no—
83C8×C11—81no—
84C8×C11#12111yescharacteristic
85C8×C11#13511yescharacteristic
86C11⋊C8—21no—
87C2×Q32—111no—
88C2×D16—111no—
89#504—111no—
90#473—221no—
91#472—221no—
92SD64—221no—
93SD64—221no—
94M64—111no—
95M64—221no—
96C2×C32—221no—
97C2×C32C2×D1111yescharacteristic
98#368C2×D1111yescharacteristic
99#368C2×D1111yescharacteristic
100#362—221no—
101#361—221no—
102C22×C11#50811yescharacteristic
103C2×D11—21no—
104C2×D11—161no—
105C2×D11—321no—
106C4×C11#46611yescharacteristic
107C4×C11C2×D1611yescharacteristic
108Dic11—21no—
109Dic11—161no—
110#137—441no—
111AGL(1,ℤ/8)—441no—
112C2×Q16—221no—
113C2×D8—221no—
114#131—111no—
115Q32—221no—
116Q32—221no—
117D16—221no—
118D16—221no—
119M32—111no—
120M32—221no—
121C2×C16—221no—
122C2×C16C22×D1111yescharacteristic
123#108—21no—
124#108—21no—
125#101—441no—
126#100—441no—
127C32—221no—
128C32D4411yescharacteristic
129C32D4411yescharacteristic
130C2×C11—21no—
131C2×C11#221511yescharacteristic
132D11—41no—
133D11—321no—
134#41—111no—
135C2×Q8—441no—
136C2×D4—441no—
137Q16—441no—
138Q16—441no—
139Q16—881no—
140SD16—881no—
141SD16—881no—
142D8—441no—
143D8—441no—
144D8—881no—
145M16—41no—
146M16—41no—
147M16—111no—
148M16—221no—
149C2×C8—221no—
150C2×C8D4×D1111yescharacteristic
151C16—221no—
152C16C2×D4411yescharacteristic
153C16#434311yescharacteristic
154C11#1370211yescharacteristic, complemented, Sylow
155C23—881no—
156Q8—111no—
157Q8—881no—
158Q8—881no—
159D4—111no—
160D4—221no—
161D4—881no—
162D4—881no—
163C2×C4—221no—
164C2×C4—881no—
165C2×C4D8×D1111yescharacteristic
166C8—81no—
167C8—81no—
168C8—221no—
169C8#6694811yescharacteristic
170C8#6697211yescharacteristic
171C22—221no—
172C22—3521no—
173C22—1761no—
174C22#1062253211yescharacteristic
175C4—221no—
176C4—1761no—
177C4#1062249611yescharacteristic
178C4D11×D1611yescharacteristic
179C2—21no—
180C2—441no—
181C2—3521no—
182C2#1307070311yescharacteristic
subgroupG/H
centerC2#13070703
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×#1425C2
socleC2×C11#2215
prime radical#13070737C2
hypercenter#1425D11
hypocenterC11#13702
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1425

Complements

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

NH ≅ G/Ntype
1. C2×#10622087C2semidirect
2. #13070909C2semidirect
3. #13070742C2semidirect
5. #13066808C2semidirect
6. #13066805C2semidirect
7. C11×#1425C2semidirect
68. #1425D11semidirect
154. C11#13702semidirect

Maximal subgroups

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

subgroupindex
C2×#106220872
#130709092
#130707422
#130707372
#130668082
#130668052
C11×#14252
#1370211