Finite Group Databasebeta

← C22×#1057⋊C8 #16792565

Subgroups — C22×#1057⋊C8 #16792565

Order 3328.

1182 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#1057C211yesmaximal, characteristic
2C22×C4×#1057C211yesmaximal, characteristic
3C2×#1057⋊C8C2112yesmaximal, direct product factor
4C22×C8×Dic13C211yesmaximal, characteristic
5C23×#1057C412yes—
6C23×#1057C412yes—
7C23×C8×C13C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C23×#1055C411yescharacteristic
10C2×C4×#1057C416yes—
11C2×C4×#1057C416yes—
12C2×C4×#1057C2216yes—
13C2×C4×#1057C2216yes—
14C2×C8×Dic13C416yes—
15C2×C8×Dic13C2216yes—
16#1057⋊C8C22116yesdirect product factor
17C23×C4×C13C2×C411yescharacteristic
18C23×Dic13C2×C411yescharacteristic
19C23×Dic13C2×C411yescharacteristic
20C22×#1057—28no—
21C22×#1057C8116yescomplemented
22C22×#1057C2×C4112yes—
23C22×#1057C2×C4112yes—
24C22×C8×C13—24no—
25C22×C8×C13C2×C416yes—
26C2×C4×Dic13C2×C413yes—
27C2×C4×Dic13C2×C413yes—
28C2×C4×Dic13C2×C413yes—
29C2×C4×Dic13C2313yes—
30C22×#1055—24no—
31C22×#1055C2×C416yes—
32C4×#1057C2×C4112yes—
33C4×#1057C2×C4112yes—
34C4×#1057C2314yes—
35C4×#1057C2314yes—
36C8×Dic13C2×C4112yes—
37C8×Dic13C2314yes—
38C22×#322—131nomaximal, Sylow
39C24×C13C4211yescharacteristic
40C22×C4×C13C4213yes—
41C22×C4×C13M1614yes—
42C22×C4×C13M1614yes—
43C22×C4×C13C22×C413yes—
44C22×Dic13C4213yes—
45C22×Dic13C4213yes—
46C22×Dic13C2×C818yes—
47C22×Dic13M1618yes—
48C22×Dic13C22×C413yes—
49C22×Dic13C22×C413yes—
50C2×#1057—224no—
51C2×#1057C2×C8148yescomplemented
52C2×#1057C22×C418yes—
53C2×#1057C22×C418yes—
54C2×C8×C13—212no—
55C2×C8×C13C22×C414yes—
56C4×Dic13C4216yes—
57C4×Dic13C22×C413yes—
58C4×Dic13C22×C413yes—
59C4×Dic13C22×C413yes—
60C4×Dic13C2411yescharacteristic
61C2×#1055—212no—
62C2×#1055C22×C414yes—
63C22×C4×C8—131no—
64C22×C4×C8—131no—
65C22×C4×C8—131no—
66C2×#322—1312no—
67C23×C13C4×C814yes—
68C23×C13#9714yes—
69C23×C13#9714yes—
70C23×C13C2×C4213yes—
71C2×C4×C13#97112yes—
72C2×C4×C13C2×C4213yes—
73C2×C4×C13C2×M1616yes—
74C2×C4×C13C2×M1616yes—
75C2×C4×C13C23×C411yescharacteristic
76C2×Dic13C4×C8112yes—
77C2×Dic13#97112yes—
78C2×Dic13C2×C4213yes—
79C2×Dic13C2×C4213yes—
80C2×Dic13C22×C8112yes—
81C2×Dic13C2×M16112yes—
82C2×Dic13C23×C411yescharacteristic
83C2×Dic13C23×C411yescharacteristic
84#1057—28no—
85#1057C22×C8116yescomplemented
86C8×C13—24no—
87#1055—24no—
88C23×C8—132no—
89C23×C8—132no—
90C23×C8—131no—
91C23×C8#26111yescharacteristic
92C22×C42—131no—
93C2×C4×C8—136no—
94C2×C4×C8—136no—
95C2×C4×C8—136no—
96C2×C4×C8—136no—
97C2×C4×C8—136no—
98C2×C4×C8—136no—
99#322—1316no—
100C22×C13#322116yescomplemented
101C22×C13C2×C4×C816yes—
102C22×C13C2×#9716yes—
103C22×C13C2×#9716yes—
104C22×C13C22×C4211yescharacteristic
105C4×C13C2×#9716yes—
106C4×C13C22×M1611yescharacteristic
107C4×C13C22×M1611yescharacteristic
108Dic13C2×C4×C816yes—
109Dic13C2×#9716yes—
110Dic13C23×C812yes—
111Dic13C22×M1612yes—
112C23×C4—131no—
113C23×C4—131no—
114C23×C4C2×#26111yescharacteristic
115C22×C8—24no—
116C22×C8—1312no—
117C22×C8—1316no—
118C22×C8—1312no—
119C22×C8—136no—
120C22×C8—268no—
121C22×C8—264no—
122C22×C8C2×#26116yes—
123C2×C42—133no—
124C2×C42—133no—
125C2×C42—133no—
126C2×C42—133no—
127C4×C8—1312no—
128C4×C8—1312no—
129C4×C8—134no—
130C4×C8—134no—
131C4×C8—134no—
132C4×C8—1312no—
133C2×C13C2×#322112yescomplemented
134C2×C13C22×C4×C811yescharacteristic
135C2×C13C22×#9711yescharacteristic
136C2×C13C22×#9711yescharacteristic
137C24C4×#26111yescharacteristic
138C22×C4—138no—
139C22×C4—138no—
140C22×C4—133no—
141C22×C4—133no—
142C22×C4—133no—
143C22×C4—133no—
144C22×C4#611814yes—
145C22×C4C4×#26113yes—
146C22×C4#612214yes—
147C22×C4C22×#26113yes—
148C2×C8—212no—
149C2×C8—138no—
150C2×C8—1348no—
151C2×C8—138no—
152C2×C8—134no—
153C2×C8—2624no—
154C2×C8—2612no—
155C2×C8C22×#26114yes—
156C42—133no—
157C42—133no—
158C42—136no—
159C42—131no—
160C42—133no—
161C13C22×#32211yescharacteristic, complemented, Sylow
162C23C8×#26114yes—
163C23#8810014yes—
164C23#8811014yes—
165C23C2×C4×#26113yes—
166C2×C4—1312no—
167C2×C4—1312no—
168C2×C4—1312no—
169C2×C4—1312no—
170C2×C4—131no—
171C2×C4—131no—
172C2×C4—133no—
173C2×C4—133no—
174C2×C4#88110112yes—
175C2×C4C2×#611816yes—
176C2×C4C2×C4×#26113yes—
177C2×C4C2×#612216yes—
178C2×C4C23×#26111yescharacteristic
179C8—24no—
180C8—1316no—
181C8—268no—
182C8—264no—
183C22#1057⋊C8116yesdirect product factor
184C22C2×C8×#26116yes—
185C22C2×#8810016yes—
186C22C2×#8811016yes—
187C22C22×C4×#26111yescharacteristic
188C4—132no—
189C4—136no—
190C4—132no—
191C4—136no—
192C4C2×#8811016yes—
193C4C22×#611811yescharacteristic
194C4C22×#612211yescharacteristic
195C2C2×#1057⋊C8112yesdirect product factor
196C2C22×C8×#26111yescharacteristic
197C2C22×#8810011yescharacteristic
198C2C22×#8811011yescharacteristic
subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC23×C8×C13C4
socle, prime radicalC24×C13C42
cosocleC4×Dic13C24
hypercenterC23×C8#261
hypocenterC13C22×#322
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
3. C2×#1057⋊C8C2direct (N × H)
16. #1057⋊C8C22direct (N × H)
21. C22×#1057C8semidirect
51. C2×#1057C2×C8semidirect
85. #1057C22×C8semidirect
100. C22×C13#322semidirect
133. C2×C13C2×#322semidirect
161. C13C22×#322semidirect
183. C22#1057⋊C8direct (N × H)
195. C2C2×#1057⋊C8direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#10572
C2×#1057⋊C82
C22×C8×Dic132
C22×#32213