Finite Group Databasebeta

← C2×#14521237 #16855096

Subgroups — C2×#14521237 #16855096

Order 3968.

1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 1018 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×#11758561C211yesmaximal, characteristic, complemented
2C2×#11758459C212yesmaximal, complemented
3C2×#11758514C211yesmaximal, characteristic, complemented
4#14521237C218yesmaximal, direct product factor
5C2×#11758394C212yesmaximal, complemented
6C2×C31×#99C211yesmaximal, characteristic, complemented
7C24×D31C2211yescharacteristic, complemented
8C22×D4×C31C2211yescharacteristic
9C22×C22⋊D31—21no—
10C22×C22⋊D31—21no—
11C22×C22⋊D31C2212yes—
12#11758561—22no—
13#11758561—24no—
14#11758561C2214yescomplemented
15C2×#92497—22no—
16C2×D4×D31—22no—
17C2×#92495—21no—
18C22×D124—22no—
19C2×C22⋊C4×C31C2212yescomplemented
20C2×C22⋊Dic31C2211yescharacteristic, complemented
21#11758514—22no—
22#11758514C2214yescomplemented
23C2×(C2×D31)⋊C4—21no—
24C2×(C2×D31)⋊C4—22no—
25#11758459—24no—
26#11758459C2218yescomplemented
27C31×#99C2214yescomplemented
28#11758394C2218yescomplemented
29C24×C31D411yescharacteristic, complemented
30C24×C31C2311yescharacteristic
31C23×D31—22no—
32C23×D31—21no—
33C23×D31—21no—
34C23×D31—22no—
35C23×D31—21no—
36C23×D31—44no—
37C23×D31D412yescomplemented
38C23×D31C2312yescomplemented
39C2×D4×C31—22no—
40C2×D4×C31—22no—
41C2×D4×C31D412yescomplemented
42C2×D4×C31C2312yes—
43C22×C4×C31—22no—
44C22×C4×C31D411yescharacteristic, complemented
45C2×C22⋊D31—22no—
46C2×C22⋊D31—24no—
47C2×C22⋊D31—22no—
48C2×C22⋊D31—22no—
49C2×C22⋊D31—22no—
50C2×C22⋊D31—22no—
51C2×C22⋊D31—24no—
52C2×C22⋊D31—24no—
53C2×C22⋊D31—44no—
54C2×C22⋊D31D414yescomplemented
55C2×C22⋊D31C2314yes—
56C22×Dic31—21no—
57C22×Dic31—21no—
58C22×Dic31D412yescomplemented
59#92497—28no—
60#92497—28no—
61D4×D31—28no—
62D4×D31—28no—
63#92495—24no—
64#92495—24no—
65C2×D124—21no—
66C2×D124—28no—
67C2×D124—48no—
68C2×C4×D31—22no—
69C2×Dic62—21no—
70C22⋊C4×C31—22no—
71C22⋊C4×C31C2314yescomplemented
72C22⋊Dic31—21no—
73C22⋊Dic31C2312yescomplemented
74(C2×D31)⋊C4—24no—
75(C2×D31)⋊C4—28no—
76C23×C31—21no—
77C23×C31—21no—
78C23×C31—42no—
79C23×C31—42no—
80C23×C31C2×D411yescharacteristic
81C23×C31C2×D411yescharacteristic
82C23×C31C2×D412yes—
83C23×C31C2×D412yes—
84C23×C31C2×D412yescomplemented
85C23×C31C2411yescharacteristic
86C22×D31—28no—
87C22×D31—24no—
88C22×D31—22no—
89C22×D31—24no—
90C22×D31—22no—
91C22×D31—24no—
92C22×D31—22no—
93C22×D31—44no—
94C22×D31—48no—
95C22×D31—44no—
96C22×D31—42no—
97C22×D31—44no—
98C22×D31—42no—
99C22×D31—41no—
100C22×D31—41no—
101C22×D31—44no—
102C22×D31—82no—
103C22×D31C2×D414yescomplemented
104D4×C31—24no—
105D4×C31—24no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—24no—
109C2×C4×C31—44no—
110C2×C4×C31C2×D412yescomplemented
111C22⋊D31—28no—
112C22⋊D31—24no—
113C22⋊D31—24no—
114C22⋊D31—24no—
115C22⋊D31—24no—
116C22⋊D31—48no—
117C2×Dic31—24no—
118C2×Dic31—22no—
119C2×Dic31—22no—
120C2×Dic31—22no—
121C2×Dic31—42no—
122C2×Dic31C2×D414yescomplemented
123D124—24no—
124D124—416no—
125C4×D31—28no—
126Dic62—24no—
127C2×B(4,𝔽2)—311nomaximal, Sylow
128C22×C31—22no—
129C22×C31—24no—
130C22×C31—22no—
131C22×C31—41no—
132C22×C31—42no—
133C22×C31—41no—
134C22×C31—42no—
135C22×C31—42no—
136C22×C31—81no—
137C22×C31#12012yes—
138C22×C31#12011yescharacteristic
139C22×C31#12011yescharacteristic
140C22×C31C22×D411yescharacteristic
141C22×C31C22×D412yes—
142C2×D31—28no—
143C2×D31—24no—
144C2×D31—24no—
145C2×D31—42no—
146C2×D31—44no—
147C2×D31—48no—
148C2×D31—44no—
149C2×D31—42no—
150C2×D31—44no—
151C2×D31—44no—
152C2×D31—44no—
153C2×D31—82no—
154C2×D31—84no—
155C4×C31—22no—
156C4×C31—44no—
157Dic31—24no—
158Dic31—42no—
159C2×H(5,𝔽2)—311no—
160C2×#120—311no—
161C2×#120—312no—
162B(4,𝔽2)—318no—
163C2×#99—312no—
164C2×#99D3111yescharacteristic, complemented
165C2×C31—21no—
166C2×C31—22no—
167C2×C31—22no—
168C2×C31—21no—
169C2×C31—42no—
170C2×C31B(4,𝔽2)12yescomplemented
171C2×C31C2×#12011yescharacteristic
172D31—44no—
173D31—44no—
174C25—311no—
175H(5,𝔽2)—314no—
176H(5,𝔽2)—624no—
177H(5,𝔽2)—622no—
178C2×#41—622no—
179C2×#41—621no—
180C22×D4—312no—
181C22×D4—622no—
182C22×D4—622no—
183C22×D4—621no—
184C22×D4—621no—
185C22×D4C2×D3111yescharacteristic
186#120—314no—
187#120—318no—
188#120—624no—
189#120—622no—
190C2×C22⋊C4—311no—
191C2×C22⋊C4—622no—
192C2×C22⋊C4—621no—
193C2×C22⋊C4C2×D3112yescomplemented
194#99—318no—
195#99C2×D3114yescomplemented
196C31C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
197C24—312no—
198C24—312no—
199C24—621no—
200C24—621no—
201C24—622no—
202C24—621no—
203C24—622no—
204C24—1244no—
205C24D12411yescharacteristic, complemented
206C24C22×D3111yescharacteristic
207#41—624no—
208#41—628no—
209#41—628no—
210#41—624no—
211C2×Q8—621no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—314no—
215C2×D4—314no—
216C2×D4—621no—
217C2×D4—628no—
218C2×D4—628no—
219C2×D4—628no—
220C2×D4—622no—
221C2×D4—624no—
222C2×D4—622no—
223C2×D4—622no—
224C2×D4—624no—
225C2×D4—622no—
226C2×D4—622no—
227C2×D4—624no—
228C2×D4—1248no—
229C2×D4—1244no—
230C2×D4D12412yescomplemented
231C2×D4C22×D3112yes—
232C22×C4—22no—
233C22×C4—312no—
234C22×C4—622no—
235C22×C4—621no—
236C22×C4—621no—
237C22×C4D12411yescharacteristic, complemented
238C22⋊C4—22no—
239C22⋊C4—312no—
240C22⋊C4—628no—
241C22⋊C4—621no—
242C22⋊C4—624no—
243C22⋊C4C22×D3114yescomplemented
244C23—21no—
245C23—21no—
246C23—42no—
247C23—42no—
248C23—314no—
249C23—628no—
250C23—624no—
251C23—624no—
252C23—622no—
253C23—622no—
254C23—624no—
255C23—622no—
256C23—1244no—
257C23—1242no—
258C23—1244no—
259C23—1244no—
260C23—1244no—
261C23—1248no—
262C23—1241no—
263C23—1242no—
264C23—1241no—
265C23—2482no—
266C23C2×D12411yescharacteristic
267C23C2×D12411yescharacteristic
268C23C2×D12412yescomplemented
269C23D4×D3112yes—
270C23D4×D3112yes—
271C23C23×D3111yescharacteristic
272Q8—624no—
273D4—24no—
274D4—24no—
275D4—624no—
276D4—628no—
277D4—624no—
278D4—624no—
279D4—624no—
280D4—624no—
281D4—12416no—
282D4—1248no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—44no—
287C2×C4—314no—
288C2×C4—628no—
289C2×C4—624no—
290C2×C4—622no—
291C2×C4—622no—
292C2×C4—622no—
293C2×C4—1242no—
294C2×C4C2×D12412yescomplemented
295C22—24no—
296C22—22no—
297C22—22no—
298C22—41no—
299C22—42no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—628no—
305C22—624no—
306C22—624no—
307C22—1244no—
308C22—1244no—
309C22—1242no—
310C22—1244no—
311C22—1248no—
312C22—1244no—
313C22—1244no—
314C22—1242no—
315C22—2482no—
316C22—2484no—
317C22#1175845911yescharacteristic
318C22#1175845912yes—
319C22#1175845911yescharacteristic
320C22C22×D12411yescharacteristic
321C22C2×D4×D3112yes—
322C4—22no—
323C4—44no—
324C4—624no—
325C4—1242no—
326C2—22no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2—42no—
331C2—1244no—
332C2—1244no—
333C2#1452123712yesdirect product factor
334C2C2×#1175845911yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC23×C31C24
FrattiniC23C23×D31
FittingC2×C31×#99C2
socleC22×C31#120
hypercenterC2×#99D31
hypocenterC31C2×B(4,𝔽2)
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#11758561C2semidirect
2. C2×#11758459C2semidirect
3. C2×#11758514C2semidirect
4. #14521237C2direct (N × H)
5. C2×#11758394C2semidirect
6. C2×C31×#99C2semidirect
7. C24×D31C22semidirect
14. #11758561C22semidirect
19. C2×C22⋊C4×C31C22semidirect
20. C2×C22⋊Dic31C22semidirect
22. #11758514C22semidirect
26. #11758459C22semidirect
27. C31×#99C22semidirect
28. #11758394C22semidirect
29. C24×C31D4semidirect
37. C23×D31D4semidirect
38. C23×D31C23semidirect
41. C2×D4×C31D4semidirect
44. C22×C4×C31D4semidirect
54. C2×C22⋊D31D4semidirect
58. C22×Dic31D4semidirect
71. C22⋊C4×C31C23semidirect
73. C22⋊Dic31C23semidirect
84. C23×C31C2×D4semidirect
103. C22×D31C2×D4semidirect
110. C2×C4×C31C2×D4semidirect
122. C2×Dic31C2×D4semidirect
164. C2×#99D31semidirect
170. C2×C31B(4,𝔽2)semidirect
193. C2×C22⋊C4C2×D31semidirect
195. #99C2×D31semidirect
196. C31C2×B(4,𝔽2)semidirect
205. C24D124semidirect
230. C2×D4D124semidirect
237. C22×C4D124semidirect
243. C22⋊C4C22×D31semidirect
268. C23C2×D124semidirect
294. C2×C4C2×D124semidirect
333. C2#14521237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585612
C2×#117584592
C2×#117585142
#145212372
C2×#117583942
C2×C31×#992
C2×B(4,𝔽2)31