Finite Group Databasebeta

← #16854560

Subgroups — #16854560

Order 3968.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D31C211yesmaximal, characteristic
2#14521521C212yesmaximal, complemented
3#14521162C211yesmaximal, characteristic, complemented
4#14521161C211yesmaximal, characteristic, complemented
5#14521160C211yesmaximal, characteristic, complemented
6C4×#92479C212yesmaximal, complemented
7#14521129C212yesmaximal, complemented
8#14521084C211yesmaximal, characteristic, complemented
9#14521052C212yesmaximal, complemented
10#14521006C211yesmaximal, characteristic, complemented
11C31×#442C211yesmaximal, characteristic, complemented
12C2×D4×D31C2212yes—
13C2×D8×C31C2211yescharacteristic
14C4×D4×C31C2212yescomplemented
15D4×Dic31C2212yescomplemented
16C2×#92479C2212yes—
17C4×C22⋊D31—22no—
18C2×(C2×D31)⋊C4—22no—
19D8×D31C418yescomplemented
20C2×D248C2211yescharacteristic
21C2×#92469C2211yescharacteristic
22C2×C8×D31C2211yescharacteristic
23#11758470C2212yescomplemented
24#11758469C2212yes—
25(C22⋊D31)⋊C4—22no—
26C22⋊C4×D31—22no—
27C4×D124C2212yescomplemented
28#11758449C2211yescharacteristic
29C31×#106C2211yescharacteristic, complemented
30C31×#102C2212yescomplemented
31C31×#97C2211yescharacteristic, complemented
32#11758420C2212yescomplemented
33#11758409C2212yescomplemented
34#11758405C2211yescharacteristic, complemented
35#11758403C2211yescharacteristic, complemented
36C8×Dic31C2211yescharacteristic, complemented
37#11758397C2212yescomplemented
38#11758395C2212yescomplemented
39C4×C31⋊C8C2211yescharacteristic, complemented
40C23×D31—22no—
41C2×D4×C31C2312yes—
42C22×C4×C31—22no—
43C2×C22⋊D31—22no—
44C22×Dic31—22no—
45D4×D31—24no—
46D4×D31C2×C418yescomplemented
47C2×D124C2312yes—
48C2×C4×D31—22no—
49C2×C4×D31—22no—
50C2×C4×D31C2311yescharacteristic
51D8×C31C2×C414yescomplemented
52C2×C8×C31C2311yescharacteristic
53C2×C8×C31C2311yescharacteristic
54C4⋊C4×C31C2312yes—
55C22⋊C4×C31—22no—
56C42×C31C2311yescharacteristic
57C22⋊Dic31—22no—
58#92479C2×C418yescomplemented
59(C2×D31)⋊C4—22no—
60(C2×D31)⋊C4—22no—
61(C2×D31)⋊C4—22no—
62(C2×D31)⋊C4D412yes—
63C4⋊Dic31C2312yes—
64Dic31⋊C4D412yes—
65C4×Dic31—22no—
66C4×Dic31C2311yescharacteristic
67C2×C31⋊C8C2311yescharacteristic
68C2×C31⋊C8C2311yescharacteristic
69D248C2×C414yescomplemented
70#92469—22no—
71C8×D31C2×C414yescomplemented
72C23×C31—22no—
73C22×D31—22no—
74C22×D31—28no—
75C22×D31—82no—
76C22×D31—82no—
77C22×D31C2×D411yescharacteristic
78D4×C31—22no—
79D4×C31C22×C414yes—
80C2×C4×C31—22no—
81C2×C4×C31—82no—
82C2×C4×C31C2×D412yes—
83C2×C4×C31C2411yescharacteristic
84C22⋊D31—28no—
85C2×Dic31—22no—
86C2×Dic31—82no—
87C2×Dic31C2×D412yes—
88C2×Dic31C2×D411yescharacteristic
89D124—22no—
90D124C22×C414yes—
91C4×D31—82no—
92C4×D31—82no—
93C4×D31C22×C412yes—
94C4×D31#4112yes—
95C8×C31—21no—
96C8×C31C22×C412yes—
97C31⋊C8—21no—
98C31⋊C8C22×C412yes—
99#2948—311nomaximal, Sylow
100C22×C31—24no—
101C22×C31—42no—
102C22×C31—42no—
103C22×C31C22×D411yescharacteristic
104C2×D31—22no—
105C2×D31—24no—
106C2×D31—42no—
107C2×D31—42no—
108C2×D31—88no—
109C2×D31C4×D412yes—
110C4×C31—22no—
111C4×C31—42no—
112C4×C31C23×C411yescharacteristic
113C4×C31C2×#4111yescharacteristic
114Dic31—22no—
115Dic31—42no—
116Dic31C4×D412yes—
117C22×D8—311no—
118#518—312no—
119#442—311no—
120#442—311no—
121#442—311no—
122#442D3111yescharacteristic, complemented
123C4×D8—312no—
124C4×D8—312no—
125#427—311no—
126#418—312no—
127#405—311no—
128C2×C31—44no—
129C2×C31C2×C4×D411yescharacteristic
130C2×C31#57612yes—
131D31—22no—
132D31—44no—
133C22×D4—312no—
134C2×D8—312no—
135C2×D8—318no—
136C2×D8—311no—
137C2×D8C2×D3111yescharacteristic
138C2×M16—311no—
139C22×C8—311no—
140C4×D4—312no—
141C4×D4—312no—
142C4×D4—312no—
143C4×D4—622no—
144C4×D4—622no—
145C4×D4C2×D3112yescomplemented
146#117—311no—
147#117—312no—
148C2×C22⋊C4—622no—
149C2×C22⋊C4—622no—
150#107—312no—
151#106—311no—
152#106C2×D3111yescharacteristic, complemented
153#102—312no—
154#102—312no—
155#102—312no—
156#102C2×D3112yescomplemented
157#97—311no—
158#97C2×D3111yescharacteristic, complemented
159C4×C8—311no—
160C4×C8—311no—
161C31#294811yescharacteristic, complemented, Sylow
162C24—622no—
163C2×D4—318no—
164C2×D4—312no—
165C2×D4—624no—
166C2×D4—622no—
167C2×D4C22×D3112yes—
168C22×C4—22no—
169C22×C4—311no—
170C22×C4—622no—
171C22×C4—622no—
172C22×C4—622no—
173D8—318no—
174D8—314no—
175D8C4×D3114yescomplemented
176M16—622no—
177C2×C8—311no—
178C2×C8—314no—
179C2×C8—311no—
180C2×C8C22×D3111yescharacteristic
181C2×C8C22×D3111yescharacteristic
182C4⋊C4—312no—
183C4⋊C4—312no—
184C4⋊C4C22×D3112yes—
185C22⋊C4—22no—
186C22⋊C4—312no—
187C22⋊C4—622no—
188C22⋊C4—622no—
189C22⋊C4—622no—
190C22⋊C4—622no—
191C42—311no—
192C42—622no—
193C42C22×D3111yescharacteristic
194C23—22no—
195C23—311no—
196C23—628no—
197C23—622no—
198C23—2482no—
199C23—2482no—
200D4—22no—
201D4—314no—
202D4—628no—
203D4—622no—
204D4C2×C4×D3114yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—311no—
208C2×C4—312no—
209C2×C4—312no—
210C2×C4—312no—
211C2×C4—622no—
212C2×C4—2482no—
213C2×C4—2482no—
214C2×C4—2482no—
215C2×C4D4×D3112yes—
216C2×C4C23×D3111yescharacteristic
217C8—21no—
218C8—312no—
219C8—621no—
220C8C2×C4×D3112yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—312no—
225C22—622no—
226C22—624no—
227C22—1242no—
228C22—1242no—
229C22—2488no—
230C22C2×D4×D3111yescharacteristic
231C4—22no—
232C4—42no—
233C4—312no—
234C4—622no—
235C4—1242no—
236C4C22×C4×D3111yescharacteristic
237C4#41×D3111yescharacteristic
238C2—44no—
239C2—622no—
240C2—1244no—
241C2C4×D4×D3111yescharacteristic
242C2#1452185312yes—
subgroupG/H
centerC22C2×D4×D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC31×#442C2
socleC22×C31C22×D4
prime radicalC2×D8×D31C2
cosocleC2×C4×C31C24
hypercenter#442D31
hypocenterC31#2948
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #14521521C2semidirect
3. #14521162C2semidirect
4. #14521161C2semidirect
5. #14521160C2semidirect
6. C4×#92479C2semidirect
7. #14521129C2semidirect
8. #14521084C2semidirect
9. #14521052C2semidirect
10. #14521006C2semidirect
11. C31×#442C2semidirect
14. C4×D4×C31C22semidirect
15. D4×Dic31C22semidirect
19. D8×D31C4semidirect
23. #11758470C22semidirect
27. C4×D124C22semidirect
29. C31×#106C22semidirect
30. C31×#102C22semidirect
31. C31×#97C22semidirect
32. #11758420C22semidirect
33. #11758409C22semidirect
34. #11758405C22semidirect
35. #11758403C22semidirect
36. C8×Dic31C22semidirect
37. #11758397C22semidirect
38. #11758395C22semidirect
39. C4×C31⋊C8C22semidirect
46. D4×D31C2×C4semidirect
51. D8×C31C2×C4semidirect
58. #92479C2×C4semidirect
69. D248C2×C4semidirect
71. C8×D31C2×C4semidirect
122. #442D31semidirect
145. C4×D4C2×D31semidirect
152. #106C2×D31semidirect
156. #102C2×D31semidirect
158. #97C2×D31semidirect
161. C31#2948semidirect
175. D8C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D312
#145215212
#145211622
#145211612
#145211602
C4×#924792
#145211292
#145210842
#145210522
#145210062
C31×#4422
#294831