Finite Group Databasebeta

← #16857505

Subgroups — #16857505

Order 3968.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#14521861C212yesmaximal, complemented
2#14521856C212yesmaximal, complemented
3#14521422C211yesmaximal, characteristic, complemented
4#14521313C212yesmaximal, complemented
5#14521312C212yesmaximal, complemented
6#14521233C212yesmaximal, complemented
7#14521218C212yesmaximal, complemented
8#14521167C211yesmaximal, characteristic, complemented
9C31×#443C211yesmaximal, characteristic, complemented
10#11758567C2212yes—
11#11758566C2212yescomplemented
12C31×#135C2211yescharacteristic
13C31×#131C2212yescomplemented
14#11758528C2212yescomplemented
15#11758526C2212yes—
16#11758495—22no—
17#11758493—22no—
18SD16×D31—22no—
19#11758488—22no—
20#11758486—22no—
21#11758486C2212yescomplemented
22#11758485—22no—
23#11758485C2212yes—
24#11758481—22no—
25#11758481C2211yescharacteristic
26C2×#92470—22no—
27C2×#92470C2212yescomplemented
28C2×#92470C2212yescomplemented
29#11758478C2212yescomplemented
30#11758451C2211yescharacteristic
31#11758446C2211yescharacteristic, complemented
32C31×#108C2211yescharacteristic, complemented
33C31×#104C2212yescomplemented
34C4×C8×C31C2211yescharacteristic, complemented
35#11758412C2212yescomplemented
36#11758411C2212yescomplemented
37#11758407C2211yescharacteristic, complemented
38#11758393C2212yescomplemented
39#41×C31C2312yes—
40#92499—22no—
41Q8×D31—22no—
42#92497—22no—
43#92497—42no—
44D4×D31—22no—
45D4×D31—42no—
46#92495—22no—
47#92495—22no—
48#92495C2312yes—
49C2×D124—22no—
50C2×D124—41no—
51C2×D124C2312yes—
52C2×Dic62—22no—
53C2×Dic62C2312yes—
54Q16×C31D411yescharacteristic, complemented
55SD16×C31D412yescomplemented
56D8×C31D411yescharacteristic, complemented
57M16×C31—22no—
58M16×C31C2312yes—
59C2×C8×C31—22no—
60C2×C8×C31C2311yescharacteristic
61C2×C8×C31C2311yescharacteristic
62C42×C31C2311yescharacteristic
63#92482—22no—
64#92481—22no—
65#92480—22no—
66#92479—22no—
67C4⋊Dic31—41no—
68#92474C2312yes—
69Dic124—22no—
70Dic124D411yescharacteristic, complemented
71D248—22no—
72D248D411yescharacteristic, complemented
73#92470—22no—
74#92470—22no—
75#92470—22no—
76#92470—22no—
77#92470—22no—
78#92470—22no—
79#92470D412yescomplemented
80#92469—22no—
81C8×D31—22no—
82C22×D31—22no—
83C22×D31—42no—
84Q8×C31C2×D412yes—
85D4×C31—22no—
86D4×C31C2×D412yes—
87C2×C4×C31—21no—
88C2×C4×C31—22no—
89C2×C4×C31C2411yescharacteristic
90C22⋊D31—22no—
91C22⋊D31—42no—
92C22⋊D31—42no—
93C2×Dic31—22no—
94C2×Dic31—42no—
95D124—22no—
96D124—22no—
97D124—42no—
98D124—82no—
99D124C2×D412yes—
100C4×D31—22no—
101C4×D31—42no—
102C4×D31—42no—
103Dic62—22no—
104Dic62—22no—
105Dic62—42no—
106Dic62C2×D412yes—
107C8×C31—22no—
108C8×C31C2×D411yescharacteristic
109C8×C31C2×D411yescharacteristic
110C8×C31C2×D411yescharacteristic
111C8×C31C2×D411yescharacteristic
112C31⋊C8—22no—
113#3291—311nomaximal, Sylow
114C22×C31—22no—
115C22×C31H(5,𝔽2)11yescharacteristic
116C2×D31—22no—
117C2×D31—42no—
118C2×D31—82no—
119C2×D31—162no—
120C4×C31—22no—
121C4×C31—22no—
122C4×C31C22×D411yescharacteristic
123C4×C31C22×D411yescharacteristic
124Dic31—22no—
125Dic31—42no—
126#577—312no—
127#577—312no—
128#492—311no—
129#471—312no—
130#471—312no—
131#456—312no—
132#453—312no—
133#443—311no—
134#443D3111yescharacteristic, complemented
135C2×C31—21no—
136C2×C31—42no—
137C2×C31D4211yescharacteristic
138D31—42no—
139D31—82no—
1402−1+4—312no—
141H(5,𝔽2)—312no—
142#137—312no—
143#137—312no—
144#137—622no—
145#137—622no—
146AGL(1,ℤ/8)—312no—
147AGL(1,ℤ/8)—312no—
148AGL(1,ℤ/8)—622no—
149AGL(1,ℤ/8)—622no—
150#135—311no—
151#135—622no—
152#135—622no—
153#135C2×D3111yescharacteristic
154C2×SD16—312no—
155C2×SD16—312no—
156C2×SD16—622no—
157C2×SD16—622no—
158#131—312no—
159#131C2×D3112yescomplemented
160C4⋊Q8—311no—
161#127—311no—
162#108—311no—
163#108C2×D3111yescharacteristic, complemented
164#104—312no—
165#104C2×D3112yescomplemented
166#101—312no—
167#100—312no—
168C4×C8C2×D3111yescharacteristic, complemented
169C31#329111yescharacteristic, complemented, Sylow
170#41—312no—
171#41—622no—
172#41—622no—
173#41—622no—
174#41—622no—
175#41—1242no—
176#41C22×D3112yes—
177C2×Q8—312no—
178C2×Q8—622no—
179C2×Q8—622no—
180C2×D4—312no—
181C2×D4—622no—
182C2×D4—622no—
183C2×D4—1241no—
184C2×D4—1242no—
185Q16—311no—
186Q16—622no—
187Q16—622no—
188Q16D12411yescharacteristic, complemented
189SD16—312no—
190SD16—622no—
191SD16—622no—
192SD16—622no—
193SD16—622no—
194SD16—622no—
195SD16—622no—
196SD16—622no—
197SD16—622no—
198SD16D12412yescomplemented
199D8—311no—
200D8—622no—
201D8—622no—
202D8D12411yescharacteristic, complemented
203M16—22no—
204M16—312no—
205M16—622no—
206M16C22×D3112yes—
207C2×C8—22no—
208C2×C8—622no—
209C2×C8C22×D3111yescharacteristic
210C2×C8C22×D3111yescharacteristic
211C4⋊C4—1241no—
212C42C22×D3111yescharacteristic
213C23—622no—
214C23—1242no—
215Q8—312no—
216Q8—622no—
217Q8—622no—
218Q8—1242no—
219Q8C2×D12412yes—
220D4—22no—
221D4—312no—
222D4—622no—
223D4—622no—
224D4—622no—
225D4—1242no—
226D4—1242no—
227D4—1242no—
228D4—2482no—
229D4C2×D12412yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—622no—
233C2×C4—622no—
234C2×C4—1242no—
235C2×C4—1242no—
236C2×C4—1242no—
237C2×C4C23×D3111yescharacteristic
238C8—22no—
239C8—622no—
240C8C2×D12411yescharacteristic
241C8C2×D12411yescharacteristic
242C8D4×D3111yescharacteristic
243C8D4×D3111yescharacteristic
244C22—22no—
245C22—622no—
246C22—1242no—
247C22—4962no—
248C22—2482no—
249C22#1175856611yescharacteristic
250C4—22no—
251C4—22no—
252C4—622no—
253C4—1242no—
254C4C22×D12411yescharacteristic
255C4C2×D4×D3111yescharacteristic
256C2—21no—
257C2—42no—
258C2—1242no—
259C2—2482no—
260C2D4×D12411yescharacteristic
subgroupG/H
centerC2D4×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#443C2
socleC2×C31D42
hypercenter#443D31
hypocenterC31#3291
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #14521861C2semidirect
2. #14521856C2semidirect
3. #14521422C2semidirect
4. #14521313C2semidirect
5. #14521312C2semidirect
6. #14521233C2semidirect
7. #14521218C2semidirect
8. #14521167C2semidirect
9. C31×#443C2semidirect
11. #11758566C22semidirect
13. C31×#131C22semidirect
14. #11758528C22semidirect
21. #11758486C22semidirect
27. C2×#92470C22semidirect
28. C2×#92470C22semidirect
29. #11758478C22semidirect
31. #11758446C22semidirect
32. C31×#108C22semidirect
33. C31×#104C22semidirect
34. C4×C8×C31C22semidirect
35. #11758412C22semidirect
36. #11758411C22semidirect
37. #11758407C22semidirect
38. #11758393C22semidirect
54. Q16×C31D4semidirect
55. SD16×C31D4semidirect
56. D8×C31D4semidirect
70. Dic124D4semidirect
72. D248D4semidirect
79. #92470D4semidirect
134. #443D31semidirect
159. #131C2×D31semidirect
163. #108C2×D31semidirect
165. #104C2×D31semidirect
168. C4×C8C2×D31semidirect
169. C31#3291semidirect
188. Q16D124semidirect
198. SD16D124semidirect
202. D8D124semidirect

Maximal subgroups

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

subgroupindex
#145218612
#145218562
#145214222
#145213132
#145213122
#145212332
#145212182
#145211672
C31×#4432
#329131