Finite Group Databasebeta

← #16857493

Subgroups — #16857493

Order 3968.

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

normal subgroups only

This group has 454 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#14521863C211yesmaximal, characteristic, complemented
2#14521860C212yesmaximal, complemented
3#14521432C211yesmaximal, characteristic, complemented
4#14521324C211yesmaximal, characteristic, complemented
5#14521316C211yesmaximal, characteristic, complemented
6#14521310C212yesmaximal, complemented
7#14521227C212yesmaximal, complemented
8#14521220C212yesmaximal, complemented
9#14521166C211yesmaximal, characteristic, complemented
10#14521164C211yesmaximal, characteristic, complemented
11C31×#576C211yesmaximal, characteristic, complemented
12C31×H(5,𝔽2)C2212yes—
13#11758567C2212yescomplemented
14C31×AGL(1,ℤ/8)—22no—
15C31×AGL(1,ℤ/8)C2212yes—
16C31×#135—21no—
17C31×#135C2211yescharacteristic
18C2×D8×C31—21no—
19C2×D8×C31C2211yescharacteristic
20C31×#131C2211yescharacteristic
21#11758528—22no—
22#11758528C2212yes—
23#11758528C2212yescomplemented
24#11758527—22no—
25#11758527C2211yescharacteristic
26#11758525C2212yescomplemented
27#11758513C2212yescomplemented
28C2×#92480—22no—
29C2×#92480C2212yescomplemented
30#11758509—22no—
31#11758509C2212yescomplemented
32Q16×D31—21no—
33#11758492—22no—
34#11758489—21no—
35C2×Dic124C2211yescharacteristic, complemented
36#11758478C2211yescharacteristic, complemented
37#11758425C2211yescharacteristic
38#11758425C2212yescomplemented
39#11758421C2212yescomplemented
40#11758413C2211yescharacteristic, complemented
41#11758412C2212yescomplemented
42#11758410C2211yescharacteristic, complemented
43#11758407C2211yescharacteristic, complemented
44C8×Dic31C2211yescharacteristic, complemented
45#41×C31—22no—
46#41×C31—22no—
47#41×C31C2311yescharacteristic
48#41×C31C2312yes—
49C2×D4×C31—22no—
50C2×D4×C31—22no—
51C2×D4×C31—42no—
52C2×D4×C31C2312yes—
53Q8×D31—22no—
54#92497—22no—
55#92497—42no—
56#92495—22no—
57#92495C2311yescharacteristic
58C2×Dic62—22no—
59C2×Dic62C2312yes—
60Q16×C31D411yescharacteristic
61SD16×C31—22no—
62SD16×C31D412yes—
63D8×C31—22no—
64D8×C31—21no—
65D8×C31—21no—
66D8×C31D411yescharacteristic
67M16×C31—21no—
68M16×C31C2311yescharacteristic
69C2×C8×C31—21no—
70C2×C8×C31C2311yescharacteristic
71C22⋊Dic31—42no—
72#92482—22no—
73#92482—22no—
74#92482D411yescharacteristic
75#92481D411yescharacteristic
76#92480—22no—
77#92480—22no—
78#92480—22no—
79#92480—22no—
80#92480—22no—
81#92480D411yescharacteristic
82#92479—22no—
83#92479D411yescharacteristic
84C4×Dic31C2311yescharacteristic
85#92474—22no—
86#92474C2312yes—
87#92474C2311yescharacteristic
88C2×C31⋊C8—22no—
89C2×C31⋊C8C2311yescharacteristic
90Dic124—21no—
91Dic124—21no—
92#92469—21no—
93C8×D31—21no—
94C23×C31—22no—
95C23×C31—42no—
96Q8×C31C2×D411yescharacteristic
97Q8×C31C2×D412yes—
98D4×C31—22no—
99D4×C31—21no—
100D4×C31—22no—
101D4×C31—22no—
102D4×C31—42no—
103D4×C31—42no—
104D4×C31C2×D411yescharacteristic
105D4×C31C2×D412yes—
106C2×C4×C31—22no—
107C2×C4×C31—21no—
108C2×C4×C31—42no—
109C2×C4×C31C2411yescharacteristic
110C22⋊D31—21no—
111C22⋊D31—42no—
112C2×Dic31—21no—
113C2×Dic31—22no—
114C2×Dic31—42no—
115D124C2×D411yescharacteristic
116C4×D31—21no—
117C4×D31—42no—
118Dic62—22no—
119Dic62—22no—
120Dic62—42no—
121Dic62C2×D411yescharacteristic
122C8×C31—21no—
123C8×C31C2×D411yescharacteristic
124C8×C31C2×D411yescharacteristic
125C31⋊C8—21no—
126C31⋊C8—22no—
127C31⋊C8C2×D411yescharacteristic
128C31⋊C8C2×D411yescharacteristic
129#3290—311nomaximal, Sylow
130C22×C31—22no—
131C22×C31—21no—
132C22×C31—42no—
133C22×C31—82no—
134C22×C31—162no—
135C22×C31H(5,𝔽2)11yescharacteristic
136C2×D31—21no—
137C4×C31—22no—
138C4×C31—21no—
139C4×C31C22×D411yescharacteristic
140C4×C31C22×D411yescharacteristic
141Dic31—21no—
142Dic31—41no—
143Dic31—42no—
144#578—311no—
145#577—312no—
146#576D3111yescharacteristic, complemented
147#495—311no—
148#473—311no—
149#472—311no—
150#471—312no—
151#455—312no—
152#454—312no—
153#443—311no—
154#443—311no—
155C2×C31—21no—
156C2×C31—42no—
157C2×C31—41no—
158C2×C31—82no—
159C2×C31D4211yescharacteristic
160D31—41no—
1612−1+4—312no—
162H(5,𝔽2)C2×D3112yes—
163#137—312no—
164#137—312no—
165#137—622no—
166#137—622no—
167AGL(1,ℤ/8)—22no—
168AGL(1,ℤ/8)—312no—
169AGL(1,ℤ/8)—622no—
170AGL(1,ℤ/8)C2×D3112yes—
171#135—21no—
172#135—311no—
173#135—622no—
174#135—621no—
175#135C2×D3111yescharacteristic
176C2×Q16—311no—
177C2×Q16—621no—
178C2×SD16—312no—
179C2×SD16—622no—
180C2×D8—21no—
181C2×D8C2×D3111yescharacteristic
182#131—312no—
183#131—311no—
184#131C2×D3111yescharacteristic
185#124—312no—
186#108—311no—
187#108—311no—
188#104—311no—
189#104—312no—
190#104—311no—
191#101—312no—
192#100—312no—
193C4×C8—311no—
194C31#329011yescharacteristic, complemented, Sylow
195#41—22no—
196#41—22no—
197#41—311no—
198#41—622no—
199#41—622no—
200#41—1242no—
201#41C22×D3111yescharacteristic
202#41C22×D3112yes—
203C2×Q8—312no—
204C2×Q8—622no—
205C2×Q8—622no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4C22×D3112yes—
210Q16—311no—
211Q16—622no—
212Q16—622no—
213Q16—621no—
214Q16—621no—
215Q16C22⋊D3111yescharacteristic
216SD16—22no—
217SD16—311no—
218SD16—311no—
219SD16—622no—
220SD16—622no—
221SD16—622no—
222SD16—622no—
223SD16—622no—
224SD16C22⋊D3112yes—
225D8—22no—
226D8—21no—
227D8—21no—
228D8—311no—
229D8—622no—
230D8C22⋊D3111yescharacteristic
231M16—21no—
232M16—311no—
233M16—312no—
234M16—622no—
235M16—621no—
236M16C22×D3111yescharacteristic
237C2×C8—21no—
238C2×C8—311no—
239C2×C8—622no—
240C2×C8—621no—
241C2×C8C22×D3111yescharacteristic
242C22⋊C4—1242no—
243C42—311no—
244C23—22no—
245C23—42no—
246Q8—311no—
247Q8—622no—
248Q8—622no—
249Q8—1242no—
250Q8D4×D3111yescharacteristic
251Q8C2×C22⋊D3112yes—
252D4—21no—
253D4—22no—
254D4—22no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—311no—
259D4—621no—
260D4—1242no—
261D4D4×D3111yescharacteristic
262D4C2×C22⋊D3112yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—621no—
267C2×C4—621no—
268C2×C4—622no—
269C2×C4—1242no—
270C2×C4—1242no—
271C2×C4C23×D3111yescharacteristic
272C8—21no—
273C8—311no—
274C8—311no—
275C8—622no—
276C8—621no—
277C8C2×C22⋊D3111yescharacteristic
278C8C2×C22⋊D3111yescharacteristic
279C22—22no—
280C22—21no—
281C22—42no—
282C22—82no—
283C22—162no—
284C22—621no—
285C22#1175856111yescharacteristic
286C4—21no—
287C4—22no—
288C4—621no—
289C4—1241no—
290C4—1242no—
291C4C2×D4×D3111yescharacteristic
292C4C22×C22⋊D3111yescharacteristic
293C2—21no—
294C2—41no—
295C2—42no—
296C2—82no—
297C2—1241no—
298C2D4×C22⋊D3111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#576C2
socleC2×C31D42
hypercenter#576D31
hypocenterC31#3290
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #14521863C2semidirect
2. #14521860C2semidirect
3. #14521432C2semidirect
4. #14521324C2semidirect
5. #14521316C2semidirect
6. #14521310C2semidirect
7. #14521227C2semidirect
8. #14521220C2semidirect
9. #14521166C2semidirect
10. #14521164C2semidirect
11. C31×#576C2semidirect
13. #11758567C22semidirect
23. #11758528C22semidirect
26. #11758525C22semidirect
27. #11758513C22semidirect
29. C2×#92480C22semidirect
31. #11758509C22semidirect
35. C2×Dic124C22semidirect
36. #11758478C22semidirect
38. #11758425C22semidirect
39. #11758421C22semidirect
40. #11758413C22semidirect
41. #11758412C22semidirect
42. #11758410C22semidirect
43. #11758407C22semidirect
44. C8×Dic31C22semidirect
146. #576D31semidirect
194. C31#3290semidirect

Maximal subgroups

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

subgroupindex
#145218632
#145218602
#145214322
#145213242
#145213162
#145213102
#145212272
#145212202
#145211662
#145211642
C31×#5762
#329031