Finite Group Databasebeta

← C2×#14521224 #16855049

Subgroups — C2×#14521224 #16855049

Order 3968.

728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758564C211yesmaximal, characteristic, complemented
2C2×#11758485C212yesmaximal, complemented
3C2×#11758524C211yesmaximal, characteristic, complemented
4#14521224C218yesmaximal, direct product factor
5C2×#11758413C212yesmaximal, complemented
6C2×C31×#101C211yesmaximal, characteristic, complemented
7C22×Q8×C31C2211yescharacteristic
8#11758564—22no—
9#11758564—24no—
10#11758564C2214yescomplemented
11C2×#92499—22no—
12C2×Q8×D31—22no—
13C2×#92495—22no—
14C2×#92495C2212yes—
15C22×D124C2211yescharacteristic
16C2×M16×C31C2212yes—
17#11758524—22no—
18#11758524C2214yescomplemented
19C2×(C2×D31)⋊C4—22no—
20C2×C4×Dic31C2211yescharacteristic
21#11758485—24no—
22#11758485C2218yescomplemented
23C2×D248—22no—
24C2×#92470—22no—
25C31×#101C2214yescomplemented
26#11758413C2218yescomplemented
27C23×D31—21no—
28C2×Q8×C31—22no—
29C2×Q8×C31—22no—
30C2×Q8×C31D412yes—
31C2×Q8×C31C2312yes—
32C22×C4×C31D412yes—
33C22×C4×C31C2311yescharacteristic
34C2×C22⋊D31—22no—
35C22×Dic31—21no—
36#92499—28no—
37#92499—28no—
38Q8×D31—28no—
39Q8×D31—28no—
40#92495—28no—
41#92495—28no—
42#92495—22no—
43#92495—22no—
44#92495D414yes—
45#92495C2314yes—
46C2×D124—22no—
47C2×D124—22no—
48C2×D124—22no—
49C2×D124—21no—
50C2×D124D412yes—
51C2×D124C2312yes—
52C2×C4×D31—24no—
53C2×C4×D31—22no—
54C2×Dic62—22no—
55C2×Dic62D412yes—
56M16×C31—22no—
57M16×C31C2314yes—
58C2×C8×C31—22no—
59(C2×D31)⋊C4—28no—
60C4×Dic31—21no—
61C4×Dic31C2312yes—
62D248—28no—
63#92470—28no—
64C23×C31C2×D411yescharacteristic
65C22×D31—22no—
66C22×D31—22no—
67C22×D31—44no—
68C22×D31—41no—
69C22×D31—41no—
70Q8×C31—24no—
71Q8×C31—24no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31C2×D414yes—
75C2×C4×C31C2×D411yescharacteristic
76C2×C4×C31C2×D412yes—
77C2×C4×C31C2×D412yes—
78C2×C4×C31C2411yescharacteristic
79C22⋊D31—24no—
80C22⋊D31—24no—
81C2×Dic31—22no—
82C2×Dic31—22no—
83C2×Dic31—42no—
84D124—28no—
85D124—22no—
86D124—24no—
87D124—42no—
88D124C2×D414yes—
89C4×D31—216no—
90C4×D31—24no—
91C4×D31—24no—
92Dic62—28no—
93Dic62—22no—
94Dic62C2×D414yes—
95C8×C31—24no—
96C2×#454—311nomaximal, Sylow
97C22×C31—22no—
98C22×C31#12011yescharacteristic
99C22×C31#12011yescharacteristic
100C22×C31C22×D411yescharacteristic
101C2×D31—24no—
102C2×D31—44no—
103C2×D31—44no—
104C2×D31—42no—
105C2×D31—82no—
106C2×D31—82no—
107C4×C31—24no—
108C4×C31#12012yes—
109C4×C31C22×D412yes—
110Dic31—24no—
111Dic31—42no—
112C2×2−1+4—311no—
113C2×AGL(1,ℤ/8)—312no—
114C2×#124—311no—
115#454—318no—
116C2×#104—312no—
117C2×#101D3111yescharacteristic, complemented
118C2×C31—21no—
119C2×C31—21no—
120C2×C31#45412yescomplemented
121C2×C31C2×#12011yescharacteristic
122D31—44no—
123D31—82no—
1242−1+4—314no—
1252−1+4—624no—
1262−1+4—622no—
127C2×#41—312no—
128C2×#41—622no—
129C2×#41—622no—
130C22×Q8—622no—
131C22×Q8C2×D3111yescharacteristic
132C22×D4—311no—
133AGL(1,ℤ/8)—318no—
134AGL(1,ℤ/8)—624no—
135C2×SD16—622no—
136C2×D8—622no—
137C2×M16C2×D3112yes—
138#124—314no—
139#124—622no—
140C2×C22⋊C4—622no—
141C2×C42—311no—
142#104—318no—
143#101C2×D3114yescomplemented
144C31C2×#45411yescharacteristic, complemented, Sylow
145C24—621no—
146#41—314no—
147#41—314no—
148#41—628no—
149#41—628no—
150#41—628no—
151#41—622no—
152#41—628no—
153#41—622no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—312no—
157C2×Q8—622no—
158C2×Q8—628no—
159C2×Q8—628no—
160C2×Q8D12412yes—
161C2×Q8C22×D3112yes—
162C2×D4—312no—
163C2×D4—312no—
164C2×D4—622no—
165C2×D4—622no—
166C2×D4—621no—
167C2×D4—622no—
168C2×D4—622no—
169C22×C4—624no—
170C22×C4—622no—
171C22×C4—621no—
172C22×C4D12412yes—
173C22×C4C22×D3111yescharacteristic
174SD16—628no—
175D8—628no—
176M16—22no—
177M16C22×D3114yes—
178C2×C8—22no—
179C22⋊C4—628no—
180C42—312no—
181C42—621no—
182C23—622no—
183C23—622no—
184C23—1244no—
185C23—1241no—
186C23—1241no—
187C23C2×D12411yescharacteristic
188Q8—24no—
189Q8—24no—
190Q8—314no—
191Q8—628no—
192Q8—622no—
193D4—314no—
194D4—628no—
195D4—624no—
196D4—624no—
197D4—622no—
198D4—624no—
199D4—1242no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—6216no—
203C2×C4—622no—
204C2×C4—624no—
205C2×C4—624no—
206C2×C4—622no—
207C2×C4—1242no—
208C2×C4C2×D12414yes—
209C2×C4C2×D12411yescharacteristic
210C2×C4D4×D3112yes—
211C2×C4D4×D3112yes—
212C2×C4C23×D3111yescharacteristic
213C8—24no—
214C22—22no—
215C22—624no—
216C22—1244no—
217C22—1244no—
218C22—1242no—
219C22—2482no—
220C22—2482no—
221C22#1175845911yescharacteristic
222C22#1175845911yescharacteristic
223C22C22×D12411yescharacteristic
224C4—24no—
225C4—624no—
226C4—1242no—
227C4#1175845912yes—
228C4C2×D4×D3112yes—
229C2—21no—
230C2—21no—
231C2—1244no—
232C2—2482no—
233C2#1452122412yesdirect product factor
234C2C2×#1175845911yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#101C2
socleC22×C31#120
hypercenterC2×#101D31
hypocenterC31C2×#454
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#11758564C2semidirect
2. C2×#11758485C2semidirect
3. C2×#11758524C2semidirect
4. #14521224C2direct (N × H)
5. C2×#11758413C2semidirect
6. C2×C31×#101C2semidirect
10. #11758564C22semidirect
18. #11758524C22semidirect
22. #11758485C22semidirect
25. C31×#101C22semidirect
26. #11758413C22semidirect
117. C2×#101D31semidirect
120. C2×C31#454semidirect
143. #101C2×D31semidirect
144. C31C2×#454semidirect
233. C2#14521224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585642
C2×#117584852
C2×#117585242
#145212242
C2×#117584132
C2×C31×#1012
C2×#45431