Finite Group Databasebeta

← #16857497

Subgroups — #16857497

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#14521857C212yesmaximal, complemented
2#14521851C211yesmaximal, characteristic, complemented
3#14521434C211yesmaximal, characteristic, complemented
4#14521321C211yesmaximal, characteristic, complemented
5#14521319C211yesmaximal, characteristic, complemented
6#14521314C212yesmaximal, complemented
7#14521225C212yesmaximal, complemented
8#14521222C212yesmaximal, complemented
9#14521166C211yesmaximal, characteristic, complemented
10#14521164C211yesmaximal, characteristic, complemented
11C31×#578C211yesmaximal, characteristic, complemented
12C31×2−1+4C2212yescomplemented
13#11758566C2212yes—
14C31×#137—22no—
15C31×#137C2212yescomplemented
16C31×#135—21no—
17C31×#135C2211yescharacteristic
18C2×Q16×C31—21no—
19C2×Q16×C31C2211yescharacteristic, complemented
20C31×#131C2211yescharacteristic, complemented
21#11758527—22no—
22#11758527C2211yescharacteristic
23#11758526—22no—
24#11758526C2212yes—
25#11758526C2212yescomplemented
26#11758525C2212yescomplemented
27#11758524C2212yescomplemented
28#11758519—22no—
29#11758519C2212yes—
30C2×#92481—22no—
31C2×#92481C2212yescomplemented
32#11758496—21no—
33#11758491—22no—
34D8×D31—21no—
35C2×D248C2211yescharacteristic
36#11758478C2211yescharacteristic
37#11758425C2211yescharacteristic, complemented
38#11758425C2212yescomplemented
39#11758424C2212yescomplemented
40#11758413C2211yescharacteristic
41#11758411C2212yescomplemented
42#11758410C2211yescharacteristic, complemented
43#11758407C2211yescharacteristic, complemented
44C8×Dic31C2211yescharacteristic, complemented
45#41×C31—22no—
46#41×C31—22no—
47#41×C31—42no—
48#41×C31C2312yes—
49#41×C31C2311yescharacteristic
50C2×Q8×C31—22no—
51C2×Q8×C31—22no—
52C2×Q8×C31C2312yes—
53#92499—22no—
54D4×D31—22no—
55D4×D31—42no—
56#92495—22no—
57#92495C2311yescharacteristic
58C2×D124—22no—
59C2×D124C2312yes—
60Q16×C31—22no—
61Q16×C31—21no—
62Q16×C31—21no—
63Q16×C31D411yescharacteristic
64SD16×C31—22no—
65SD16×C31D412yes—
66D8×C31D411yescharacteristic
67M16×C31—21no—
68M16×C31C2311yescharacteristic
69C2×C8×C31—21no—
70C2×C8×C31C2311yescharacteristic
71#92482—22no—
72#92482D411yescharacteristic
73#92481—22no—
74#92481—22no—
75#92481—22no—
76#92481—22no—
77#92481—22no—
78#92481D411yescharacteristic
79#92480D411yescharacteristic
80#92479—22no—
81#92479—22no—
82#92479D411yescharacteristic
83(C2×D31)⋊C4—42no—
84C4×Dic31C2311yescharacteristic
85#92474—22no—
86#92474C2312yes—
87#92474C2311yescharacteristic
88C2×C31⋊C8—22no—
89C2×C31⋊C8C2311yescharacteristic
90D248—21no—
91D248—21no—
92#92469—21no—
93C8×D31—21no—
94C22×D31—22no—
95C22×D31—42no—
96Q8×C31—22no—
97Q8×C31—22no—
98Q8×C31—42no—
99Q8×C31C2×D411yescharacteristic
100Q8×C31C2×D412yes—
101D4×C31—22no—
102D4×C31—21no—
103D4×C31—42no—
104D4×C31C2×D411yescharacteristic
105D4×C31C2×D412yes—
106C2×C4×C31—22no—
107C2×C4×C31—21no—
108C2×C4×C31—22no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31C2411yescharacteristic
112C22⋊D31—21no—
113C22⋊D31—42no—
114C2×Dic31—21no—
115D124—22no—
116D124—22no—
117D124—42no—
118D124C2×D411yescharacteristic
119C4×D31—21no—
120C4×D31—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×C31H(5,𝔽2)11yescharacteristic
133C2×D31—21no—
134C2×D31—42no—
135C2×D31—82no—
136C2×D31—162no—
137C4×C31—22no—
138C4×C31—21no—
139C4×C31—42no—
140C4×C31C22×D411yescharacteristic
141C4×C31C22×D411yescharacteristic
142Dic31—21no—
143Dic31—41no—
144#578D3111yescharacteristic, complemented
145#577—312no—
146#576—311no—
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×C31D4211yescharacteristic
159D31—41no—
160D31—82no—
1612−1+4C2×D3112yescomplemented
162H(5,𝔽2)—312no—
163#137—22no—
164#137—312no—
165#137—622no—
166#137C2×D3112yescomplemented
167AGL(1,ℤ/8)—312no—
168AGL(1,ℤ/8)—312no—
169AGL(1,ℤ/8)—622no—
170AGL(1,ℤ/8)—622no—
171#135—21no—
172#135—311no—
173#135—622no—
174#135—621no—
175#135C2×D3111yescharacteristic
176C2×Q16—21no—
177C2×Q16C2×D3111yescharacteristic, complemented
178C2×SD16—312no—
179C2×SD16—622no—
180C2×D8—311no—
181C2×D8—621no—
182#131—312no—
183#131—311no—
184#131C2×D3111yescharacteristic, complemented
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—42no—
198#41—311no—
199#41—622no—
200#41—622no—
201#41C22×D3111yescharacteristic
202#41C22×D3112yes—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8C22×D3112yes—
206C2×D4—312no—
207C2×D4—622no—
208C2×D4—622no—
209C2×D4—1242no—
210Q16—22no—
211Q16—21no—
212Q16—21no—
213Q16—311no—
214Q16—622no—
215Q16C22⋊D3111yescharacteristic
216SD16—22no—
217SD16—311no—
218SD16—311no—
219SD16—622no—
220SD16—622no—
221SD16—622no—
222SD16—622no—
223SD16—622no—
224SD16C22⋊D3112yes—
225D8—311no—
226D8—622no—
227D8—622no—
228D8—621no—
229D8—621no—
230D8C22⋊D3111yescharacteristic
231M16—21no—
232M16—312no—
233M16—311no—
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—622no—
245C23—1242no—
246Q8—22no—
247Q8—22no—
248Q8—42no—
249Q8—311no—
250Q8D4×D3111yescharacteristic
251Q8C2×C22⋊D3112yes—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—311no—
256D4—621no—
257D4—622no—
258D4—622no—
259D4—1242no—
260D4—1242no—
261D4D4×D3111yescharacteristic
262D4C2×C22⋊D3112yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—621no—
269C2×C4—621no—
270C2×C4—1242no—
271C2×C4C23×D3111yescharacteristic
272C8—21no—
273C8—311no—
274C8—311no—
275C8—622no—
276C8—621no—
277C8C2×C22⋊D3111yescharacteristic
278C8C2×C22⋊D3111yescharacteristic
279C22—21no—
280C22—22no—
281C22—621no—
282C22—1242no—
283C22—4962no—
284C22—2482no—
285C22#1175856111yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—621no—
290C4—1241no—
291C4C2×D4×D3111yescharacteristic
292C4C22×C22⋊D3111yescharacteristic
293C2—21no—
294C2—42no—
295C2—41no—
296C2—1241no—
297C2—2482no—
298C2D4×C22⋊D3111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#578C2
socleC2×C31D42
hypercenter#578D31
hypocenterC31#3290
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #14521857C2semidirect
2. #14521851C2semidirect
3. #14521434C2semidirect
4. #14521321C2semidirect
5. #14521319C2semidirect
6. #14521314C2semidirect
7. #14521225C2semidirect
8. #14521222C2semidirect
9. #14521166C2semidirect
10. #14521164C2semidirect
11. C31×#578C2semidirect
12. C31×2−1+4C22semidirect
15. C31×#137C22semidirect
19. C2×Q16×C31C22semidirect
20. C31×#131C22semidirect
25. #11758526C22semidirect
26. #11758525C22semidirect
27. #11758524C22semidirect
31. C2×#92481C22semidirect
37. #11758425C22semidirect
38. #11758425C22semidirect
39. #11758424C22semidirect
41. #11758411C22semidirect
42. #11758410C22semidirect
43. #11758407C22semidirect
44. C8×Dic31C22semidirect
144. #578D31semidirect
161. 2−1+4C2×D31semidirect
166. #137C2×D31semidirect
177. C2×Q16C2×D31semidirect
184. #131C2×D31semidirect
194. C31#3290semidirect

Maximal subgroups

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

subgroupindex
#145218572
#145218512
#145214342
#145213212
#145213192
#145213142
#145212252
#145212222
#145211662
#145211642
C31×#5782
#329031