Finite Group Databasebeta

← D31×#483 #16855585

Subgroups — D31×#483 #16855585

Order 3968.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 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⋊Q8×D31C211yesmaximal, characteristic
2C2×C4⋊C4×D31C211yesmaximal, characteristic
3#14521381C212yesmaximal, complemented
4#14521380C211yesmaximal, characteristic, complemented
5#14521379C211yesmaximal, characteristic, complemented
6#14521378C212yesmaximal, complemented
7#14521377C211yesmaximal, characteristic, complemented
8#106×D31C212yesmaximal, complemented
9#103×D31C212yesmaximal, complemented
10C22⋊C8×D31C211yesmaximal, characteristic
11C31×#483C211yesmaximal, characteristic, complemented
12C2×Q8×D31C2211yescharacteristic
13C22×C4×D31—21no—
14C22×C4×D31C2211yescharacteristic
15C31×C22⋊Q8C2211yescharacteristic
16C2×C4⋊C4×C31C2211yescharacteristic
17#11758523C2211yescharacteristic
18C2×C4⋊Dic31C2211yescharacteristic
19#11758501C2211yescharacteristic
20C2×Dic31⋊C4—21no—
21C2×C8×D31C2212yes—
22#11758474C2211yescharacteristic
23#11758473—21no—
24C4⋊C4×D31—21no—
25C4⋊C4×D31—21no—
26C4⋊C4×D31—21no—
27C4⋊C4×D31C2212yes—
28C4⋊C4×D31C2212yes—
29C4⋊C4×D31C2211yescharacteristic
30C22⋊C4×D31—21no—
31#11758455—21no—
32C31×#106C2212yescomplemented
33C31×#103C2212yescomplemented
34C31×C22⋊C8C2211yescharacteristic
35#11758423C2212yescomplemented
36C22⋊(C31⋊C8)C2211yescharacteristic
37(C2×D31)⋊C8C2212yes—
38#11758405C2212yescomplemented
39#11758404C2212yescomplemented
40#11758398C2212yescomplemented
41#11758396C2212yescomplemented
42#11758396C2212yescomplemented
43C23×D31D411yescharacteristic
44C2×Q8×C31C2311yescharacteristic
45C22×C4×C31—21no—
46C22×C4×C31C2311yescharacteristic
47C22×Dic31—21no—
48C22×Dic31D411yescharacteristic
49Q8×D31—24no—
50C2×C4×D31—24no—
51C2×C4×D31—21no—
52C2×C4×D31—21no—
53C2×C4×D31—22no—
54C2×C4×D31—22no—
55C2×C4×D31—44no—
56C2×C4×D31D411yescharacteristic
57C2×C4×D31D411yescharacteristic
58C2×C4×D31C2311yescharacteristic
59C2×C4×D31C2311yescharacteristic
60C2×Dic62—21no—
61C2×Dic62C2311yescharacteristic
62C2×C8×C31C2312yes—
63C4⋊C4×C31—21no—
64C4⋊C4×C31—21no—
65C4⋊C4×C31C2311yescharacteristic
66C4⋊C4×C31C2312yes—
67C22⋊C4×C31—21no—
68C22⋊Dic31—21no—
69(C2×D31)⋊C4—21no—
70(C2×D31)⋊C4—21no—
71C4⋊Dic31—21no—
72C4⋊Dic31—21no—
73C4⋊Dic31C2311yescharacteristic
74C4⋊Dic31C2312yes—
75Dic31⋊C4—21no—
76Dic31⋊C4—21no—
77Dic31⋊C4—21no—
78Dic31⋊C4—22no—
79Dic31⋊C4—22no—
80C2×C31⋊C8C2312yes—
81C8×D31—24no—
82C23×C31C2×D411yescharacteristic
83C22×D31—22no—
84C22×D31—22no—
85C22×D31SD1614yes—
86C22×D31C2×D411yescharacteristic
87C22×D31C2×D411yescharacteristic
88Q8×C31—22no—
89C2×C4×C31—22no—
90C2×C4×C31—22no—
91C2×C4×C31—21no—
92C2×C4×C31—21no—
93C2×C4×C31—42no—
94C2×C4×C31C2×D411yescharacteristic
95C2×C4×C31C2411yescharacteristic
96C2×Dic31—22no—
97C2×Dic31—21no—
98C2×Dic31—22no—
99C2×Dic31—21no—
100C2×Dic31—42no—
101C2×Dic31C2×D411yescharacteristic
102C2×Dic31C2×D411yescharacteristic
103C4×D31—22no—
104C4×D31—22no—
105C4×D31—22no—
106C4×D31—42no—
107C4×D31—44no—
108C4×D31—44no—
109C4×D31—42no—
110C4×D31#4114yes—
111Dic62—22no—
112Dic62—42no—
113C8×C31—22no—
114C31⋊C8—22no—
115C2×#483—311nomaximal, Sylow
116C22×C31—21no—
117C22×C31—21no—
118C22×C31C2×SD1612yes—
119C22×C31C22×D411yescharacteristic
120C2×D31—21no—
121C2×D31—21no—
122C2×D31—28no—
123C2×D31#12312yes—
124C2×D31C2×SD1612yes—
125C2×D31C2×SD1612yes—
126C2×D31#13712yes—
127C4×C31—21no—
128C4×C31—41no—
129C4×C31—42no—
130C4×C31—41no—
131C4×C31C2×#4112yes—
132Dic31—21no—
133Dic31—41no—
134Dic31—42no—
135Dic31—41no—
136Dic31#12312yes—
137C2×C22⋊Q8—311no—
138C22×C4⋊C4—311no—
139#483—311no—
140#483—311no—
141#483—312no—
142#483—312no—
143#483—311no—
144#483D3111yescharacteristic, direct product factor
145C2×#106—312no—
146C2×#103—312no—
147C2×C22⋊C8—311no—
148C2×C31—22no—
149C2×C31C2×#12311yescharacteristic
150C2×C31C22×SD1611yescharacteristic
151C2×C31C2×#13711yescharacteristic
152D31—22no—
153D31#48314yesdirect product factor
154C22×Q8—311no—
155C23×C4—311no—
156C23×C4—621no—
157C22×C8—312no—
158C22⋊Q8—311no—
159C22⋊Q8—311no—
160C22⋊Q8—311no—
161C22⋊Q8—621no—
162C22⋊Q8—621no—
163C22⋊Q8C2×D3111yescharacteristic
164C2×C4⋊C4—311no—
165C2×C4⋊C4—312no—
166C2×C4⋊C4—312no—
167C2×C4⋊C4—311no—
168C2×C4⋊C4—621no—
169C2×C4⋊C4—621no—
170C2×C4⋊C4—621no—
171C2×C4⋊C4—621no—
172C2×C4⋊C4C2×D3111yescharacteristic
173C2×C22⋊C4—621no—
174#106—312no—
175#106—312no—
176#106—312no—
177#106C2×D3112yescomplemented
178#103—312no—
179#103—312no—
180#103—312no—
181#103C2×D3112yescomplemented
182C22⋊C8—311no—
183C22⋊C8—312no—
184C22⋊C8C2×D3111yescharacteristic
185C31C2×#48311yescharacteristic, complemented, Sylow
186C24—311no—
187C2×Q8—311no—
188C2×Q8—621no—
189C2×Q8—624no—
190C2×Q8C22×D3111yescharacteristic
191C22×C4—21no—
192C22×C4—311no—
193C22×C4—311no—
194C22×C4—311no—
195C22×C4—311no—
196C22×C4—311no—
197C22×C4—624no—
198C22×C4—621no—
199C22×C4—621no—
200C22×C4—622no—
201C22×C4—622no—
202C22×C4—621no—
203C22×C4—1244no—
204C22×C4C22×D3111yescharacteristic
205C2×C8—312no—
206C2×C8—624no—
207C2×C8C22×D3112yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—312no—
211C4⋊C4—311no—
212C4⋊C4—622no—
213C4⋊C4—622no—
214C4⋊C4—621no—
215C4⋊C4—621no—
216C4⋊C4—621no—
217C4⋊C4—621no—
218C4⋊C4—621no—
219C4⋊C4C22×D3112yes—
220C4⋊C4C22×D3111yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—621no—
223C22⋊C4—621no—
224C22⋊C4—621no—
225C23—311no—
226C23—314no—
227C23—311no—
228C23—622no—
229C23—622no—
230C23D4×D3111yescharacteristic
231Q8—22no—
232Q8—622no—
233Q8—1242no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—311no—
240C2×C4—314no—
241C2×C4—311no—
242C2×C4—622no—
243C2×C4—622no—
244C2×C4—622no—
245C2×C4—622no—
246C2×C4—621no—
247C2×C4—621no—
248C2×C4—622no—
249C2×C4—1242no—
250C2×C4—1244no—
251C2×C4—1244no—
252C2×C4—1242no—
253C2×C4—1242no—
254C2×C4D4×D3111yescharacteristic
255C2×C4C23×D3111yescharacteristic
256C8—22no—
257C8—622no—
258C22—21no—
259C22—21no—
260C22—312no—
261C22—312no—
262C22—312no—
263C22—312no—
264C22—628no—
265C22—621no—
266C22—621no—
267C22SD16×D3112yes—
268C22C2×D4×D3111yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—312no—
274C4—621no—
275C4—1241no—
276C4—1242no—
277C4—1241no—
278C4#41×D3112yes—
279C2—22no—
280C2—314no—
281C2—622no—
282C2#123×D3111yescharacteristic
283C2C2×SD16×D3111yescharacteristic
284C2#137×D3111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#483C2
socleC22×C31C22×D4
prime radicalC23×D31D4
hypercenter#483D31
hypocenterC31C2×#483
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #14521381C2semidirect
4. #14521380C2semidirect
5. #14521379C2semidirect
6. #14521378C2semidirect
7. #14521377C2semidirect
8. #106×D31C2semidirect
9. #103×D31C2semidirect
11. C31×#483C2semidirect
32. C31×#106C22semidirect
33. C31×#103C22semidirect
35. #11758423C22semidirect
38. #11758405C22semidirect
39. #11758404C22semidirect
40. #11758398C22semidirect
41. #11758396C22semidirect
42. #11758396C22semidirect
144. #483D31direct (N × H)
153. D31#483direct (N × H)
177. #106C2×D31semidirect
181. #103C2×D31semidirect
185. C31C2×#483semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D312
C2×C4⋊C4×D312
#145213812
#145213802
#145213792
#145213782
#145213772
#106×D312
#103×D312
C22⋊C8×D312
C31×#4832
C2×#48331