Finite Group Databasebeta

← C2×#14521198 #16854891

Subgroups — C2×#14521198 #16854891

Order 3968.

996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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×D4×D31C211yesmaximal, characteristic
2C22×#92481C211yesmaximal, characteristic, complemented
3C2×#11758523C211yesmaximal, characteristic, complemented
4#14521198C218yesmaximal, direct product factor
5C2×#11758409C211yesmaximal, characteristic, complemented
6C2×#11758420C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C31C211yesmaximal, characteristic, complemented
9C24×D31—21no—
10C22×Q8×C31C2211yescharacteristic, complemented
11C22×D4×C31C2211yescharacteristic
12C22×C22⋊D31—21no—
13C2×D4×D31—24no—
14C2×D4×D31—24no—
15C2×D4×D31—22no—
16C2×D4×D31C2214yes—
17C22×D124C2211yescharacteristic
18C22×C4×D31C2211yescharacteristic
19C2×SD16×C31—24no—
20C2×SD16×C31C2214yescomplemented
21C22×C8×C31C2211yescharacteristic, complemented
22#11758523—22no—
23#11758523C2214yescomplemented
24C2×#92481—24no—
25C2×#92481C2214yescomplemented
26C2×(C2×D31)⋊C4—21no—
27C2×C4⋊Dic31C2211yescharacteristic, complemented
28C2×Dic31⋊C4—21no—
29C22×C31⋊C8C2211yescharacteristic, complemented
30#11758420C2214yescomplemented
31#11758409C2214yescomplemented
32(C2×D31)⋊C8C2214yescomplemented
33C24×C31—21no—
34C23×D31—28no—
35C23×D31—21no—
36C23×D31—24no—
37C23×D31—44no—
38C23×D31—44no—
39C23×D31D411yescharacteristic
40C2×Q8×C31—21no—
41C2×Q8×C31—22no—
42C2×Q8×C31—22no—
43C2×Q8×C31C2312yescomplemented
44C2×D4×C31—21no—
45C2×D4×C31—22no—
46C2×D4×C31D414yes—
47C2×D4×C31C2312yes—
48C22×C4×C31—21no—
49C22×C4×C31C2311yescharacteristic
50C2×C22⋊D31—28no—
51C2×C22⋊D31—24no—
52C22×Dic31—21no—
53C22×Dic31D411yescharacteristic
54D4×D31—216no—
55D4×D31—28no—
56D4×D31—28no—
57C2×D124—21no—
58C2×D124—22no—
59C2×D124D414yes—
60C2×D124C2312yes—
61C2×C4×D31—22no—
62C2×C4×D31—22no—
63C2×C4×D31D412yes—
64C2×C4×D31C2312yes—
65SD16×C31—28no—
66C2×C8×C31—22no—
67C2×C8×C31C2312yescomplemented
68#92481—28no—
69(C2×D31)⋊C4—24no—
70C4⋊Dic31—21no—
71C4⋊Dic31C2312yescomplemented
72Dic31⋊C4—24no—
73C2×C31⋊C8—22no—
74C2×C31⋊C8C2312yescomplemented
75C23×C31—24no—
76C23×C31—22no—
77C23×C31—42no—
78C23×C31—42no—
79C23×C31C2×D411yescharacteristic
80C22×D31—22no—
81C22×D31—22no—
82C22×D31—216no—
83C22×D31—24no—
84C22×D31—22no—
85C22×D31—48no—
86C22×D31—432no—
87C22×D31—42no—
88C22×D31—42no—
89C22×D31—48no—
90C22×D31SD1614yescomplemented
91C22×D31C2×D412yes—
92Q8×C31—22no—
93Q8×C31—22no—
94Q8×C31—42no—
95D4×C31—24no—
96D4×C31—22no—
97D4×C31C2×D414yes—
98C2×C4×C31—22no—
99C2×C4×C31—42no—
100C2×C4×C31C2×D411yescharacteristic
101C2×C4×C31C2×D412yes—
102C2×C4×C31C2×D412yes—
103C2×C4×C31C2411yescharacteristic
104C22⋊D31—216no—
105C2×Dic31—22no—
106C2×Dic31—22no—
107C2×Dic31—42no—
108C2×Dic31C2×D412yes—
109D124—24no—
110D124—22no—
111D124C2×D414yes—
112C4×D31—24no—
113C4×D31—22no—
114C4×D31—22no—
115C8×C31—22no—
116C31⋊C8—22no—
117C2×#450—311nomaximal, Sylow
118C22×C31—24no—
119C22×C31—42no—
120C22×C31—42no—
121C22×C31—48no—
122C22×C31#12012yes—
123C22×C31C2×SD1612yes—
124C22×C31AGL(1,ℤ/8)12yes—
125C22×C31C22×D411yescharacteristic
126C2×D31—22no—
127C2×D31—22no—
128C2×D31—28no—
129C2×D31—24no—
130C2×D31—432no—
131C2×D31—42no—
132C2×D31—42no—
133C2×D31—48no—
134C2×D31C2×SD1614yescomplemented
135C4×C31—42no—
136C4×C31#12012yes—
137C4×C31C22×D411yescharacteristic
138C4×C31C22×D411yescharacteristic
139Dic31—22no—
140Dic31—42no—
141C23×D4—311no—
142C22×SD16—311no—
143C22×SD16D3111yescharacteristic, complemented
144C2×C22⋊Q8—311no—
145#450—318no—
146C2×#102—311no—
147C2×#102—311no—
148C2×C22⋊C8—311no—
149C2×C31—44no—
150C2×C31#45014yescomplemented
151C2×C31C2×#12011yescharacteristic
152C2×C31C22×SD1611yescharacteristic
153C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
154D31—24no—
155D31—44no—
156C25—621no—
157C22×Q8C2×D3111yescharacteristic, complemented
158C22×D4—314no—
159C22×D4—311no—
160C22×D4—622no—
161C22×D4—621no—
162C22×D4—624no—
163C22×D4—624no—
164C22×D4C2×D3111yescharacteristic
165C23×C4—311no—
166C2×SD16—24no—
167C2×SD16—314no—
168C2×SD16—624no—
169C2×SD16C2×D3114yescomplemented
170C22×C8—311no—
171C22×C8C2×D3111yescharacteristic, complemented
172C22⋊Q8—314no—
173C22⋊Q8—622no—
174C2×C4⋊C4—311no—
175C2×C4⋊C4—621no—
176C2×C22⋊C4—621no—
177#102—314no—
178#102—314no—
179C22⋊C8—314no—
180C31C2×#45011yescharacteristic, complemented, Sylow
181C24—21no—
182C24—311no—
183C24—624no—
184C24—628no—
185C24—621no—
186C24—1244no—
187C24—1244no—
188C2×Q8—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8C22×D3112yescomplemented
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—314no—
195C2×D4—312no—
196C2×D4—624no—
197C2×D4—628no—
198C2×D4—6216no—
199C2×D4—628no—
200C2×D4—628no—
201C2×D4—621no—
202C2×D4—622no—
203C2×D4C22⋊D3114yes—
204C2×D4C22×D3112yes—
205C22×C4—21no—
206C22×C4—311no—
207C22×C4—312no—
208C22×C4—312no—
209C22×C4—622no—
210C22×C4—622no—
211C22×C4—621no—
212C22×C4C22×D3111yescharacteristic
213SD16—28no—
214SD16—628no—
215C2×C8—22no—
216C2×C8—312no—
217C2×C8—622no—
218C2×C8C22×D3112yescomplemented
219C4⋊C4—312no—
220C4⋊C4—624no—
221C4⋊C4—621no—
222C22⋊C4—624no—
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—314no—
228C23—312no—
229C23—6216no—
230C23—622no—
231C23—622no—
232C23—624no—
233C23—622no—
234C23—1248no—
235C23—12432no—
236C23—1248no—
237C23—1242no—
238C23—1242no—
239C23D4×D3111yescharacteristic
240Q8—22no—
241Q8—22no—
242Q8—42no—
243D4—24no—
244D4—22no—
245D4—314no—
246D4—6216no—
247D4—624no—
248D4—622no—
249D4C2×C22⋊D3114yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—312no—
253C2×C4—622no—
254C2×C4—624no—
255C2×C4—622no—
256C2×C4—622no—
257C2×C4—622no—
258C2×C4—1242no—
259C2×C4D4×D3111yescharacteristic
260C2×C4D4×D3112yes—
261C2×C4C2×C22⋊D3112yes—
262C2×C4C23×D3111yescharacteristic
263C8—22no—
264C8—622no—
265C22—24no—
266C22—48no—
267C22—42no—
268C22—42no—
269C22—314no—
270C22—628no—
271C22—622no—
272C22—622no—
273C22—624no—
274C22—12432no—
275C22—1248no—
276C22—1242no—
277C22—1242no—
278C22SD16×D3112yes—
279C22#1175849112yes—
280C22#1175851412yes—
281C22C2×D4×D3111yescharacteristic
282C4—42no—
283C4—622no—
284C4—1242no—
285C4#1175851412yes—
286C4C2×D4×D3111yescharacteristic
287C4C22×C22⋊D3111yescharacteristic
288C2—44no—
289C2—624no—
290C2—1244no—
291C2#1452119814yesdirect product factor
292C2C2×#1175851411yescharacteristic
293C2C2×SD16×D3111yescharacteristic
294C2C2×#1175849111yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC22×SD16×C31C2
socleC23×C31C2×D4
prime radicalC22×D4×D31C2
hypercenterC22×SD16D31
hypocenterC31C2×#450
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C22×#92481C2semidirect
3. C2×#11758523C2semidirect
4. #14521198C2direct (N × H)
5. C2×#11758409C2semidirect
6. C2×#11758420C2semidirect
7. C2×(C2×D31)⋊C8C2semidirect
8. C22×SD16×C31C2semidirect
10. C22×Q8×C31C22semidirect
20. C2×SD16×C31C22semidirect
21. C22×C8×C31C22semidirect
23. #11758523C22semidirect
25. C2×#92481C22semidirect
27. C2×C4⋊Dic31C22semidirect
29. C22×C31⋊C8C22semidirect
30. #11758420C22semidirect
31. #11758409C22semidirect
32. (C2×D31)⋊C8C22semidirect
43. C2×Q8×C31C23semidirect
67. C2×C8×C31C23semidirect
71. C4⋊Dic31C23semidirect
74. C2×C31⋊C8C23semidirect
90. C22×D31SD16semidirect
134. C2×D31C2×SD16semidirect
143. C22×SD16D31semidirect
150. C2×C31#450semidirect
157. C22×Q8C2×D31semidirect
169. C2×SD16C2×D31semidirect
171. C22×C8C2×D31semidirect
180. C31C2×#450semidirect
191. C2×Q8C22×D31semidirect
218. C2×C8C22×D31semidirect
291. C2#14521198direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D312
C22×#924812
C2×#117585232
#145211982
C2×#117584092
C2×#117584202
C2×(C2×D31)⋊C82
C22×SD16×C312
C2×#45031