Finite Group Databasebeta

← C2×#14521047 #16854220

Subgroups — C2×#14521047 #16854220

Order 3968.

816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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×#92497C211yesmaximal, characteristic
2C22×#92469C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D31C211yesmaximal, characteristic, complemented
4#14521047C218yesmaximal, direct product factor
5C2×#11758404C211yesmaximal, characteristic, complemented
6C2×#11758398C211yesmaximal, characteristic, complemented
7C2×#11758420C211yesmaximal, characteristic, complemented
8C2×C31×#102C211yesmaximal, characteristic, complemented
9C22×D4×C31C2211yescharacteristic
10C22×C22⋊D31—21no—
11C23×Dic31—21no—
12C2×#92497—22no—
13C2×#92497—24no—
14C2×#92497C418yescomplemented
15C2×#92497C2214yes—
16C22×C4×D31—21no—
17C22×C4×D31C2211yescharacteristic
18C22×Dic62C2211yescharacteristic
19C22×C8×C31C2211yescharacteristic
20C2×C4⋊C4×C31C2211yescharacteristic
21C2×C4⋊Dic31C2211yescharacteristic
22C2×Dic31⋊C4—21no—
23C22×C31⋊C8C2211yescharacteristic
24C2×#92469—24no—
25C2×#92469C2214yescomplemented
26C4⋊C4×D31—22no—
27C4⋊C4×D31C2214yescomplemented
28C31×#102C2214yescomplemented
29#11758420C2214yescomplemented
30#11758404C2214yescomplemented
31#11758398C2214yescomplemented
32C24×C31—21no—
33C23×D31D411yescharacteristic
34C2×D4×C31—21no—
35C2×D4×C31—22no—
36C2×D4×C31C2×C414yescomplemented
37C2×D4×C31C2312yes—
38C22×C4×C31—21no—
39C22×C4×C31C2311yescharacteristic
40C2×C22⋊D31—28no—
41C2×C22⋊D31—24no—
42C22×Dic31—21no—
43C22×Dic31—28no—
44C22×Dic31—24no—
45C22×Dic31—21no—
46C22×Dic31D411yescharacteristic
47#92497—216no—
48#92497—28no—
49#92497C2×C4116yescomplemented
50C2×C4×D31—24no—
51C2×C4×D31—44no—
52C2×C4×D31C2×C414yes—
53C2×C4×D31D412yes—
54C2×C4×D31D414yes—
55C2×C4×D31C2312yes—
56C2×Dic62—21no—
57C2×Dic62—22no—
58C2×Dic62C2×C414yescomplemented
59C2×Dic62C2312yes—
60C2×C8×C31—22no—
61C2×C8×C31C2312yes—
62C4⋊C4×C31—21no—
63C4⋊C4×C31C2312yes—
64C4⋊Dic31—21no—
65C4⋊Dic31C2312yes—
66Dic31⋊C4—24no—
67C2×C31⋊C8—22no—
68C2×C31⋊C8C2312yes—
69#92469—28no—
70C23×C31—24no—
71C23×C31—22no—
72C23×C31—42no—
73C23×C31—42no—
74C23×C31C2×D411yescharacteristic
75C22×D31—22no—
76C22×D31—22no—
77C22×D31C22⋊C414yes—
78C22×D31C2×D412yes—
79D4×C31—24no—
80D4×C31—22no—
81D4×C31C22×C414yescomplemented
82C2×C4×C31—22no—
83C2×C4×C31—42no—
84C2×C4×C31C22×C412yes—
85C2×C4×C31C2×D411yescharacteristic
86C2×C4×C31C2×D412yes—
87C2×C4×C31C2411yescharacteristic
88C22⋊D31—216no—
89C2×Dic31—24no—
90C2×Dic31—22no—
91C2×Dic31—216no—
92C2×Dic31—22no—
93C2×Dic31—42no—
94C2×Dic31C22⋊C414yes—
95C2×Dic31C2×D412yes—
96C4×D31—48no—
97C4×D31C22⋊C418yes—
98C4×D31C22×C414yes—
99C4×D31C2×D414yes—
100Dic62—24no—
101Dic62—22no—
102Dic62C22×C414yescomplemented
103C8×C31—22no—
104C31⋊C8—22no—
105C2×#417—311nomaximal, Sylow
106C22×C31—24no—
107C22×C31—42no—
108C22×C31—42no—
109C22×C31—48no—
110C22×C31C2×C22⋊C412yes—
111C22×C31AGL(1,ℤ/8)12yes—
112C22×C31#13712yes—
113C22×C31C22×D411yescharacteristic
114C2×D31—22no—
115C2×D31—22no—
116C2×D31—28no—
117C2×D31C2×C22⋊C414yes—
118C4×C31—42no—
119C4×C31C2×C22⋊C412yes—
120C4×C31C23×C411yescharacteristic
121C4×C31C22×D411yescharacteristic
122Dic31—24no—
123Dic31—42no—
124Dic31C2×C22⋊C414yes—
125C22×#41—311no—
126C22×M16—311no—
127C22×C4⋊C4—311no—
128#417—318no—
129C2×#103—311no—
130C2×#103—311no—
131C2×#102—311no—
132C2×#102D3111yescharacteristic, complemented
133C2×C31—44no—
134C2×C31#41714yescomplemented
135C2×C31C22×C22⋊C411yescharacteristic
136C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C31C2×#13711yescharacteristic
138D31—24no—
139C2×#41—318no—
140C2×#41—314no—
141C2×#41—622no—
142C2×#41—624no—
143C22×Q8—311no—
144C22×D4—621no—
145C22×D4C2×D3111yescharacteristic
146C23×C4—311no—
147C23×C4—621no—
148C23×C4—621no—
149C2×M16—314no—
150C2×M16—624no—
151C22×C8—311no—
152C22×C8C2×D3111yescharacteristic
153C2×C4⋊C4—311no—
154C2×C4⋊C4—314no—
155C2×C4⋊C4—622no—
156C2×C4⋊C4—621no—
157C2×C4⋊C4C2×D3111yescharacteristic
158#103—314no—
159#103—314no—
160#102—314no—
161#102C2×D3114yescomplemented
162C31C2×#41711yescharacteristic, complemented, Sylow
163C24—21no—
164C24—311no—
165#41—3116no—
166#41—6216no—
167#41—628no—
168C2×Q8—314no—
169C2×Q8—312no—
170C2×Q8—622no—
171C2×Q8—621no—
172C2×D4—21no—
173C2×D4—22no—
174C2×D4—628no—
175C2×D4—624no—
176C2×D4C4×D3114yescomplemented
177C2×D4C22×D3112yes—
178C22×C4—21no—
179C22×C4—311no—
180C22×C4—314no—
181C22×C4—312no—
182C22×C4—314no—
183C22×C4—312no—
184C22×C4—624no—
185C22×C4—628no—
186C22×C4—624no—
187C22×C4—621no—
188C22×C4—621no—
189C22×C4—1244no—
190C22×C4C22×D3111yescharacteristic
191M16—628no—
192C2×C8—22no—
193C2×C8—312no—
194C2×C8—622no—
195C2×C8C22×D3112yes—
196C4⋊C4—21no—
197C4⋊C4—312no—
198C4⋊C4—624no—
199C4⋊C4—621no—
200C4⋊C4C22×D3112yes—
201C23—24no—
202C23—22no—
203C23—42no—
204C23—42no—
205C23—314no—
206C23—312no—
207C23—622no—
208C23—622no—
209C23D4×D3111yescharacteristic
210Q8—314no—
211Q8—624no—
212Q8—622no—
213D4—24no—
214D4—22no—
215D4—6216no—
216D4C2×C4×D3114yescomplemented
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—314no—
220C2×C4—312no—
221C2×C4—318no—
222C2×C4—314no—
223C2×C4—314no—
224C2×C4—6216no—
225C2×C4—624no—
226C2×C4—622no—
227C2×C4—622no—
228C2×C4—1248no—
229C2×C4—1242no—
230C2×C4C2×C4×D3112yes—
231C2×C4D4×D3111yescharacteristic
232C2×C4D4×D3112yes—
233C2×C4C23×D3111yescharacteristic
234C8—22no—
235C8—622no—
236C22—24no—
237C22—48no—
238C22—42no—
239C22—42no—
240C22—314no—
241C22—628no—
242C22—622no—
243C22—622no—
244C22C22⋊C4×D3112yes—
245C22#1175848812yes—
246C22#1175849212yes—
247C22C2×D4×D3111yescharacteristic
248C4—42no—
249C4—314no—
250C4—624no—
251C4—1242no—
252C4C22⋊C4×D3112yes—
253C4C22×C4×D3111yescharacteristic
254C4C2×D4×D3111yescharacteristic
255C2—44no—
256C2—624no—
257C2#1452104714yesdirect product factor
258C2C2×C22⋊C4×D3111yescharacteristic
259C2C2×#1175848811yescharacteristic
260C2C2×#1175849211yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC2×C31×#102C2
socleC23×C31C2×D4
prime radicalC22×#92497C2
cosocleC2×C4×C31C24
hypercenterC2×#102D31
hypocenterC31C2×#417
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×#92469C2semidirect
3. C2×C4⋊C4×D31C2semidirect
4. #14521047C2direct (N × H)
5. C2×#11758404C2semidirect
6. C2×#11758398C2semidirect
7. C2×#11758420C2semidirect
8. C2×C31×#102C2semidirect
14. C2×#92497C4semidirect
25. C2×#92469C22semidirect
27. C4⋊C4×D31C22semidirect
28. C31×#102C22semidirect
29. #11758420C22semidirect
30. #11758404C22semidirect
31. #11758398C22semidirect
36. C2×D4×C31C2×C4semidirect
49. #92497C2×C4semidirect
58. C2×Dic62C2×C4semidirect
81. D4×C31C22×C4semidirect
102. Dic62C22×C4semidirect
132. C2×#102D31semidirect
134. C2×C31#417semidirect
161. #102C2×D31semidirect
162. C31C2×#417semidirect
176. C2×D4C4×D31semidirect
216. D4C2×C4×D31semidirect
257. C2#14521047direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924972
C22×#924692
C2×C4⋊C4×D312
#145210472
C2×#117584042
C2×#117583982
C2×#117584202
C2×C31×#1022
C2×#41731