Finite Group Databasebeta

← C2×#14521234 #16855055

Subgroups — C2×#14521234 #16855055

Order 3968.

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

normal subgroups only

This group has 708 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
2C2×#11758486C212yesmaximal, complemented
3C2×#11758521C211yesmaximal, characteristic, complemented
4#14521234C218yesmaximal, direct product factor
5C2×#11758413C212yesmaximal, complemented
6C2×C31×#101C211yesmaximal, characteristic, complemented
7C22×Q8×C31C2211yescharacteristic
8#11758564—22no—
9#11758564—24no—
10#11758564C2214yes—
11C2×#92499—22no—
12C2×Q8×D31—22no—
13C2×#92495—22no—
14C2×#92495C2212yes—
15C22×Dic62C2211yescharacteristic
16C2×M16×C31C2212yes—
17#11758521—22no—
18#11758521C2214yescomplemented
19C2×Dic31⋊C4—22no—
20C2×C4×Dic31C2211yescharacteristic
21#11758486—24no—
22#11758486C2218yescomplemented
23C2×Dic124—22no—
24C2×#92470—22no—
25C31×#101C2214yescomplemented
26#11758413C2218yescomplemented
27C2×Q8×C31—22no—
28C2×Q8×C31—22no—
29C2×Q8×C31D412yes—
30C2×Q8×C31C2312yes—
31C22×C4×C31D412yes—
32C22×C4×C31C2311yescharacteristic
33C2×C22⋊D31—22no—
34C22×Dic31—21no—
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×D124D412yes—
48C2×C4×D31—24no—
49C2×C4×D31—22no—
50C2×Dic62—22no—
51C2×Dic62—22no—
52C2×Dic62—22no—
53C2×Dic62—21no—
54C2×Dic62D412yes—
55C2×Dic62C2312yes—
56M16×C31—22no—
57M16×C31C2314yes—
58C2×C8×C31—22no—
59Dic31⋊C4—28no—
60C4×Dic31—21no—
61C4×Dic31C2312yes—
62Dic124—28no—
63#92470—28no—
64C23×C31C2×D411yescharacteristic
65C22×D31—22no—
66Q8×C31—24no—
67Q8×C31—24no—
68C2×C4×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31C2×D414yes—
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31C2×D412yes—
73C2×C4×C31C2×D412yes—
74C2×C4×C31C2411yescharacteristic
75C22⋊D31—24no—
76C22⋊D31—24no—
77C2×Dic31—24no—
78C2×Dic31—22no—
79C2×Dic31—22no—
80C2×Dic31—22no—
81C2×Dic31—41no—
82C2×Dic31—41no—
83D124—28no—
84D124—22no—
85D124C2×D414yes—
86C4×D31—216no—
87C4×D31—24no—
88C4×D31—24no—
89Dic62—28no—
90Dic62—22no—
91Dic62—24no—
92Dic62—42no—
93Dic62C2×D414yes—
94C8×C31—24no—
95C2×#456—311nomaximal, Sylow
96C22×C31—22no—
97C22×C31#12011yescharacteristic
98C22×C31#12011yescharacteristic
99C22×C31C22×D411yescharacteristic
100C2×D31—24no—
101C2×D31—44no—
102C4×C31—24no—
103C4×C31#12012yes—
104C4×C31C22×D412yes—
105Dic31—24no—
106Dic31—24no—
107Dic31—42no—
108C2×2−1+4—311no—
109C2×#137—312no—
110C2×C4⋊Q8—311no—
111#456—318no—
112C2×#104—312no—
113C2×#101D3111yescharacteristic, complemented
114C2×C31—21no—
115C2×C31—21no—
116C2×C31#45612yescomplemented
117C2×C31C2×#12011yescharacteristic
118D31—44no—
1192−1+4—314no—
1202−1+4—624no—
1212−1+4—622no—
122C2×#41—312no—
123C2×#41—622no—
124C2×#41—622no—
125C22×Q8—311no—
126C22×Q8—622no—
127C22×Q8C2×D3111yescharacteristic
128#137—318no—
129#137—624no—
130C2×Q16—622no—
131C2×SD16—622no—
132C2×M16C2×D3112yes—
133C4⋊Q8—314no—
134C4⋊Q8—622no—
135C2×C4⋊C4—622no—
136C2×C42—311no—
137#104—318no—
138#101C2×D3114yescomplemented
139C31C2×#45611yescharacteristic, complemented, Sylow
140#41—314no—
141#41—314no—
142#41—628no—
143#41—628no—
144#41—628no—
145#41—622no—
146#41—628no—
147#41—622no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—312no—
151C2×Q8—312no—
152C2×Q8—622no—
153C2×Q8—628no—
154C2×Q8—628no—
155C2×Q8—621no—
156C2×Q8—622no—
157C2×Q8—622no—
158C2×Q8D12412yes—
159C2×Q8C22×D3112yes—
160C2×D4—312no—
161C2×D4—622no—
162C2×D4—622no—
163C22×C4—624no—
164C22×C4—621no—
165C22×C4—622no—
166C22×C4—621no—
167C22×C4D12412yes—
168C22×C4C22×D3111yescharacteristic
169Q16—628no—
170SD16—628no—
171M16—22no—
172M16C22×D3114yes—
173C2×C8—22no—
174C4⋊C4—628no—
175C42—312no—
176C42—621no—
177C23—622no—
178C23C2×D12411yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—314no—
182Q8—628no—
183Q8—622no—
184Q8—624no—
185Q8—1242no—
186D4—314no—
187D4—628no—
188D4—624no—
189D4—624no—
190D4—622no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—6216no—
194C2×C4—624no—
195C2×C4—622no—
196C2×C4—622no—
197C2×C4—624no—
198C2×C4—624no—
199C2×C4—622no—
200C2×C4—1241no—
201C2×C4—1241no—
202C2×C4C2×D12414yes—
203C2×C4C2×D12411yescharacteristic
204C2×C4D4×D3112yes—
205C2×C4D4×D3112yes—
206C2×C4C23×D3111yescharacteristic
207C8—24no—
208C22—22no—
209C22—624no—
210C22—1244no—
211C22#1175845911yescharacteristic
212C22#1175845911yescharacteristic
213C22C22×D12411yescharacteristic
214C4—24no—
215C4—624no—
216C4—624no—
217C4—1242no—
218C4#1175845912yes—
219C4C2×D4×D3112yes—
220C2—21no—
221C2—21no—
222C2—1244no—
223C2#1452123412yesdirect product factor
224C2C2×#1175845911yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#101C2
socleC22×C31#120
prime radicalC2×#11758564C2
hypercenterC2×#101D31
hypocenterC31C2×#456
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
2. C2×#11758486C2semidirect
3. C2×#11758521C2semidirect
4. #14521234C2direct (N × H)
5. C2×#11758413C2semidirect
6. C2×C31×#101C2semidirect
18. #11758521C22semidirect
22. #11758486C22semidirect
25. C31×#101C22semidirect
26. #11758413C22semidirect
113. C2×#101D31semidirect
116. C2×C31#456semidirect
138. #101C2×D31semidirect
139. C31C2×#456semidirect
223. C2#14521234direct (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×#117584862
C2×#117585212
#145212342
C2×#117584132
C2×C31×#1012
C2×#45631