Finite Group Databasebeta

← #16857507

Subgroups — #16857507

Order 3968.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#14521853C212yesmaximal, complemented
2#14521852C212yesmaximal, complemented
3#14521425C211yesmaximal, characteristic, complemented
4#14521318C212yesmaximal, complemented
5#14521317C212yesmaximal, complemented
6#14521218C212yesmaximal, complemented
7#14521216C211yesmaximal, characteristic, complemented
8#14521163C212yesmaximal, complemented
9C31×#453C211yesmaximal, characteristic, complemented
10C31×H(5,𝔽2)C2211yescharacteristic, complemented
11#11758566C2212yescomplemented
12#11758561C2211yescharacteristic, complemented
13C31×AGL(1,ℤ/8)C2212yescomplemented
14C31×#127C2211yescharacteristic, complemented
15#11758527—22no—
16#11758527C2212yes—
17#11758526—22no—
18#11758526C2212yescomplemented
19#11758525C2212yescomplemented
20#11758509—22no—
21#11758509C2212yescomplemented
22C2×#92479—22no—
23C2×#92479C2212yescomplemented
24C2×#92479C2212yescomplemented
25#11758493—22no—
26#11758491—22no—
27#11758488—22no—
28D8×D31—22no—
29#11758485C2212yescomplemented
30#11758484C2212yescomplemented
31#11758451C2211yescharacteristic, complemented
32C31×#104C2212yescomplemented
33C31×#100C2211yescharacteristic, complemented
34#11758421C2211yescharacteristic, complemented
35#11758411C2212yescomplemented
36#11758410C2212yescomplemented
37#11758393C2212yescomplemented
38C4×C31⋊C8C2211yescharacteristic, complemented
39#41×C31—22no—
40#41×C31C2312yes—
41C2×D4×C31—22no—
42C2×D4×C31—41no—
43C2×D4×C31—41no—
44C2×D4×C31C2311yescharacteristic
45C2×D4×C31C2311yescharacteristic
46C2×C22⋊D31—41no—
47#92499—22no—
48#92497—22no—
49D4×D31—22no—
50D4×D31—22no—
51D4×D31—42no—
52#92495—22no—
53#92495C2312yes—
54C2×D124—22no—
55C2×D124—41no—
56C2×D124C2312yes—
57SD16×C31—22no—
58D8×C31—22no—
59M16×C31C2312yes—
60C42×C31C2311yescharacteristic
61#92482D412yescomplemented
62#92481—22no—
63#92481D412yescomplemented
64#92480—22no—
65#92480D412yescomplemented
66#92479—22no—
67#92479—22no—
68#92479—22no—
69#92479—22no—
70#92479—22no—
71#92479—22no—
72#92479D412yescomplemented
73#92474—22no—
74#92474C2312yes—
75C2×C31⋊C8—22no—
76C2×C31⋊C8C2312yes—
77D248—22no—
78#92470—22no—
79#92469—22no—
80C8×D31—22no—
81C23×C31—21no—
82C23×C31—21no—
83C23×C31—41no—
84C22×D31—22no—
85C22×D31—41no—
86C22×D31—42no—
87Q8×C31C2×D412yes—
88D4×C31—22no—
89D4×C31—22no—
90D4×C31—22no—
91D4×C31—42no—
92D4×C31—82no—
93D4×C31C2×D412yes—
94C2×C4×C31—21no—
95C2×C4×C31—22no—
96C2×C4×C31—41no—
97C2×C4×C31C2411yescharacteristic
98C22⋊D31—22no—
99C22⋊D31—42no—
100C22⋊D31—42no—
101C2×Dic31—41no—
102D124—22no—
103D124—22no—
104D124—42no—
105D124—82no—
106D124C2×D412yes—
107C4×D31—22no—
108C4×D31—42no—
109Dic62C2×D412yes—
110C8×C31—22no—
111C31⋊C8—22no—
112C31⋊C8C2×D412yes—
113C31⋊C8C2×D412yes—
114#3292—311nomaximal, Sylow
115C22×C31—22no—
116C22×C31—41no—
117C22×C31—41no—
118C22×C31—81no—
119C22×C31—81no—
120C22×C31—161no—
121C22×C31H(5,𝔽2)11yescharacteristic
122C2×D31—22no—
123C2×D31—42no—
124C2×D31—82no—
125C2×D31—161no—
126C2×D31—162no—
127C4×C31—22no—
128C4×C31—22no—
129C4×C31C22×D412yes—
130Dic31—22no—
131#576—312no—
132#576—312no—
133#493—311no—
134#472—312no—
135#472—312no—
136#453—311no—
137#453—312no—
138#453D3111yescharacteristic, complemented
139#443—312no—
140C2×C31—21no—
141C2×C31—42no—
142C2×C31—81no—
143C2×C31—81no—
144C2×C31D4211yescharacteristic
145D31—42no—
146D31—82no—
147H(5,𝔽2)—312no—
148H(5,𝔽2)—311no—
149H(5,𝔽2)C2×D3111yescharacteristic, complemented
150AGL(1,ℤ/8)—312no—
151AGL(1,ℤ/8)—312no—
152AGL(1,ℤ/8)—312no—
153AGL(1,ℤ/8)—622no—
154AGL(1,ℤ/8)—622no—
155AGL(1,ℤ/8)—622no—
156AGL(1,ℤ/8)—622no—
157AGL(1,ℤ/8)C2×D3112yescomplemented
158#135—312no—
159#135—622no—
160#135—622no—
161C2×D8—312no—
162C2×D8—312no—
163C2×D8—622no—
164C2×D8—622no—
165#131—312no—
166#131—312no—
167#127—311no—
168#127C2×D3111yescharacteristic, complemented
169#108—312no—
170#104—312no—
171#104C2×D3112yescomplemented
172#100—311no—
173#100—312no—
174#100C2×D3111yescharacteristic, complemented
175C4×C8—311no—
176C31#329211yescharacteristic, complemented, Sylow
177#41—22no—
178#41—312no—
179#41—622no—
180#41—622no—
181#41—622no—
182#41C22×D3112yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—312no—
187C2×D4—622no—
188C2×D4—622no—
189C2×D4—622no—
190C2×D4—1241no—
191C2×D4—1242no—
192C2×D4—1241no—
193C2×D4C22×D3111yescharacteristic
194C2×D4C22×D3111yescharacteristic
195Q16—312no—
196SD16—22no—
197SD16—312no—
198SD16—312no—
199SD16—622no—
200SD16—622no—
201SD16—622no—
202D8—22no—
203D8—312no—
204D8—622no—
205D8—622no—
206D8—622no—
207D8—622no—
208D8—622no—
209D8—622no—
210D8—622no—
211M16—312no—
212M16—622no—
213M16—622no—
214M16C22×D3112yes—
215C2×C8—312no—
216C2×C8—622no—
217C2×C8—622no—
218C42C22×D3111yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—622no—
223C23—1242no—
224C23—1241no—
225Q8—312no—
226Q8D4×D3112yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—312no—
233D4—622no—
234D4—622no—
235D4—622no—
236D4—1242no—
237D4—1242no—
238D4—1242no—
239D4—2482no—
240D4D4×D3112yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—622no—
245C2×C4—1242no—
246C2×C4—1241no—
247C2×C4C23×D3111yescharacteristic
248C8—22no—
249C8—312no—
250C8—312no—
251C8—622no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—622no—
259C22—1242no—
260C22—4962no—
261C22—4961no—
262C22—2482no—
263C22#1175856111yescharacteristic
264C4—22no—
265C4—22no—
266C4—622no—
267C4C2×D4×D3112yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—1242no—
273C2—2482no—
274C2#1452168111yescharacteristic
subgroupG/H
centerC2#14521681
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#453C2
socleC2×C31D42
hypercenter#453D31
hypocenterC31#3292
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14521853C2semidirect
2. #14521852C2semidirect
3. #14521425C2semidirect
4. #14521318C2semidirect
5. #14521317C2semidirect
6. #14521218C2semidirect
7. #14521216C2semidirect
8. #14521163C2semidirect
9. C31×#453C2semidirect
10. C31×H(5,𝔽2)C22semidirect
11. #11758566C22semidirect
12. #11758561C22semidirect
13. C31×AGL(1,ℤ/8)C22semidirect
14. C31×#127C22semidirect
18. #11758526C22semidirect
19. #11758525C22semidirect
21. #11758509C22semidirect
23. C2×#92479C22semidirect
24. C2×#92479C22semidirect
29. #11758485C22semidirect
30. #11758484C22semidirect
31. #11758451C22semidirect
32. C31×#104C22semidirect
33. C31×#100C22semidirect
34. #11758421C22semidirect
35. #11758411C22semidirect
36. #11758410C22semidirect
37. #11758393C22semidirect
38. C4×C31⋊C8C22semidirect
61. #92482D4semidirect
63. #92481D4semidirect
65. #92480D4semidirect
72. #92479D4semidirect
138. #453D31semidirect
149. H(5,𝔽2)C2×D31semidirect
157. AGL(1,ℤ/8)C2×D31semidirect
168. #127C2×D31semidirect
171. #104C2×D31semidirect
174. #100C2×D31semidirect
176. C31#3292semidirect

Maximal subgroups

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

subgroupindex
#145218532
#145218522
#145214252
#145213182
#145213172
#145212182
#145212162
#145211632
C31×#4532
#329231