Finite Group Databasebeta

← C2×#14521299 #16855304

Subgroups — C2×#14521299 #16855304

Order 3968.

596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×#92469C211yesmaximal, characteristic, complemented
2C2×#11758515C212yesmaximal, complemented
3#14521299C218yesmaximal, direct product factor
4C2×#11758405C211yesmaximal, characteristic, complemented
5C2×#11758420C212yesmaximal, complemented
6C22×D8×C31C211yesmaximal, characteristic, complemented
7C22×D4×C31C2212yes—
8C22×C22⋊D31—22no—
9C22×C4×D31C2211yescharacteristic
10C2×D8×C31—24no—
11C2×D8×C31C2214yescomplemented
12C22×C8×C31C2211yescharacteristic
13C2×C22⋊Dic31—22no—
14#11758515—24no—
15#11758515C2218yescomplemented
16C2×C4⋊Dic31C2212yes—
17C22×C31⋊C8C2211yescharacteristic
18C2×#92469—24no—
19C2×#92469C2214yescomplemented
20#11758420C2218yescomplemented
21#11758405C2214yescomplemented
22C24×C31—22no—
23C23×D31D411yescharacteristic
24C2×D4×C31—24no—
25C2×D4×C31—22no—
26C2×D4×C31—24no—
27C2×D4×C31C2314yes—
28C22×C4×C31C2311yescharacteristic
29C2×C22⋊D31—28no—
30C2×C22⋊D31—48no—
31C22×Dic31—22no—
32C22×Dic31D411yescharacteristic
33C2×C4×D31—22no—
34C2×C4×D31—22no—
35C2×C4×D31D412yes—
36C2×C4×D31C2312yes—
37D8×C31—28no—
38C2×C8×C31D414yescomplemented
39C2×C8×C31C2312yes—
40C22⋊Dic31—28no—
41C4⋊Dic31—22no—
42C4⋊Dic31C2314yes—
43C2×C31⋊C8—22no—
44C2×C31⋊C8C2312yes—
45#92469—28no—
46C23×C31—24no—
47C23×C31—44no—
48C23×C31—44no—
49C23×C31—44no—
50C23×C31C2×D411yescharacteristic
51C22×D31—22no—
52C22×D31—24no—
53C22×D31C2×D412yes—
54D4×C31—24no—
55D4×C31—24no—
56D4×C31—44no—
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D412yes—
59C2×C4×C31#4112yes—
60C2×C4×C31C2411yescharacteristic
61C22⋊D31—416no—
62C2×Dic31—22no—
63C2×Dic31—24no—
64C2×Dic31—44no—
65C2×Dic31C2×D412yes—
66C4×D31—24no—
67C4×D31—22no—
68C4×D31—22no—
69C8×C31C2×D414yescomplemented
70C31⋊C8—22no—
71C2×#469—311nomaximal, Sylow
72C22×C31—44no—
73C22×C31—44no—
74C22×C31—44no—
75C22×C31—88no—
76C22×C31#12112yes—
77C22×C31AGL(1,ℤ/8)14yes—
78C22×C31C22×D411yescharacteristic
79C2×D31—22no—
80C2×D31—24no—
81C2×D31—44no—
82C4×C31#12112yes—
83C4×C31C22×D411yescharacteristic
84C4×C31C2×#4111yescharacteristic
85Dic31—22no—
86Dic31—44no—
87C22×D8D3111yescharacteristic, complemented
88C22×M16—311no—
89C2×#121—312no—
90#469—318no—
91C2×#106—311no—
92C2×#102—312no—
93C2×C31—84no—
94C2×C31#46914yescomplemented
95C2×C31C2×#12111yescharacteristic
96C2×C31C2×AGL(1,ℤ/8)12yes—
97D31—42no—
98C22×D4—622no—
99C22×D4C2×D3112yes—
100C23×C4—311no—
101C2×D8—24no—
102C2×D8C2×D3114yescomplemented
103C2×M16—314no—
104C2×M16—624no—
105C22×C8—311no—
106C22×C8C2×D3111yescharacteristic
107#121—318no—
108#121—624no—
109C2×C4⋊C4—312no—
110C2×C22⋊C4—622no—
111#106—314no—
112#102—318no—
113C31C2×#46911yescharacteristic, complemented, Sylow
114C24—22no—
115C24—311no—
116C2×D4—22no—
117C2×D4—24no—
118C2×D4—24no—
119C2×D4—628no—
120C2×D4—1248no—
121C2×D4C22×D3114yes—
122C22×C4—311no—
123C22×C4—312no—
124C22×C4—312no—
125C22×C4—622no—
126C22×C4—622no—
127C22×C4—622no—
128C22×C4C22×D3111yescharacteristic
129D8—28no—
130M16—628no—
131C2×C8—312no—
132C2×C8—622no—
133C2×C8C22⋊D3114yescomplemented
134C2×C8C22×D3112yes—
135C4⋊C4—314no—
136C4⋊C4—622no—
137C22⋊C4—628no—
138C23—24no—
139C23—44no—
140C23—44no—
141C23—44no—
142C23—312no—
143C23—624no—
144C23—622no—
145C23D4×D3111yescharacteristic
146D4—24no—
147D4—24no—
148D4—44no—
149D4—12416no—
150C2×C4—312no—
151C2×C4—622no—
152C2×C4—624no—
153C2×C4—622no—
154C2×C4—622no—
155C2×C4—624no—
156C2×C4—1244no—
157C2×C4D4×D3111yescharacteristic
158C2×C4#9249712yes—
159C2×C4C2×C22⋊D3112yes—
160C2×C4C23×D3111yescharacteristic
161C8—622no—
162C8C2×C22⋊D3114yescomplemented
163C22—44no—
164C22—44no—
165C22—44no—
166C22—88no—
167C22—622no—
168C22—624no—
169C22—1244no—
170C22#1175848814yes—
171C22#1175851512yes—
172C22C2×D4×D3111yescharacteristic
173C4—622no—
174C4—1244no—
175C4#1175851512yes—
176C4C2×#9249711yescharacteristic
177C4C22×C22⋊D3111yescharacteristic
178C2—84no—
179C2—1242no—
180C2#1452129914yesdirect product factor
181C2C2×#1175851511yescharacteristic
182C2C2×#1175848812yes—
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC22×D8×C31C2
socleC23×C31C2×D4
hypercenterC22×D8D31
hypocenterC31C2×#469
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#92469C2semidirect
2. C2×#11758515C2semidirect
3. #14521299C2direct (N × H)
4. C2×#11758405C2semidirect
5. C2×#11758420C2semidirect
6. C22×D8×C31C2semidirect
11. C2×D8×C31C22semidirect
15. #11758515C22semidirect
19. C2×#92469C22semidirect
20. #11758420C22semidirect
21. #11758405C22semidirect
38. C2×C8×C31D4semidirect
69. C8×C31C2×D4semidirect
87. C22×D8D31semidirect
94. C2×C31#469semidirect
102. C2×D8C2×D31semidirect
113. C31C2×#469semidirect
133. C2×C8C22⋊D31semidirect
162. C8C2×C22⋊D31semidirect
180. C2#14521299direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924692
C2×#117585152
#145212992
C2×#117584052
C2×#117584202
C22×D8×C312
C2×#46931