Finite Group Databasebeta

← #16857477

Subgroups — #16857477

Order 3968.

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

normal subgroups only

This group has 464 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#14521855C212yesmaximal, complemented
2#14521850C212yesmaximal, complemented
3#14521316C212yesmaximal, complemented
4#14521309C212yesmaximal, complemented
5#14521226C211yesmaximal, characteristic, complemented
6#14521221C211yesmaximal, characteristic, complemented
7#14521216C212yesmaximal, complemented
8#14521172C212yesmaximal, complemented
9C31×#496C211yesmaximal, characteristic, complemented
10#11758564C2211yescharacteristic, complemented
11#11758561C2211yescharacteristic
12#11758561C2212yescomplemented
13C2×SD16×C31C2212yescomplemented
14C2×D8×C31C2212yescomplemented
15C31×#127C2211yescharacteristic, complemented
16C31×#124C2211yescharacteristic, complemented
17#11758519C2212yescomplemented
18#11758509C2212yes—
19#11758509C2212yescomplemented
20#11758509C2212yescomplemented
21#11758493—22no—
22#11758492—22no—
23#11758491—22no—
24SD16×D31—22no—
25#11758489—22no—
26#11758488—22no—
27#11758488—22no—
28D8×D31—22no—
29#11758481C2212yes—
30#11758478C2212yescomplemented
31#11758478C2212yescomplemented
32C31×#97C2211yescharacteristic, complemented
33#11758424C2211yescharacteristic, complemented
34#11758421C2212yescomplemented
35#11758421C2211yescharacteristic, complemented
36#11758407C2212yescomplemented
37#11758393C2212yescomplemented
38#11758393C2212yescomplemented
39C2×Q8×C31C2311yescharacteristic
40C2×D4×C31—41no—
41C2×D4×C31C2312yes—
42C2×D4×C31C2311yescharacteristic
43C2×C22⋊D31—41no—
44C2×C22⋊D31—42no—
45#92499—22no—
46Q8×D31—22no—
47#92497—22no—
48#92497—22no—
49#92497—22no—
50D4×D31—22no—
51D4×D31—22no—
52D4×D31—22no—
53#92495—41no—
54#92495C2312yes—
55#92495C2312yes—
56SD16×C31—22no—
57SD16×C31—22no—
58D8×C31—22no—
59D8×C31—22no—
60C2×C8×C31C2312yes—
61C22⋊C4×C31—41no—
62C42×C31C2311yescharacteristic
63#92482—22no—
64#92481—22no—
65#92480—22no—
66#92480—22no—
67#92480—22no—
68#92479—22no—
69#92479—22no—
70#92479—22no—
71#92474C2312yes—
72#92474C2312yes—
73Dic124D412yescomplemented
74D248D412yescomplemented
75#92470D412yescomplemented
76#92470D412yescomplemented
77#92469—22no—
78#92469—22no—
79C8×D31—22no—
80C8×D31—22no—
81C23×C31—21no—
82C23×C31—22no—
83C22×D31—42no—
84C22×D31—41no—
85Q8×C31—22no—
86D4×C31—22no—
87D4×C31—22no—
88D4×C31—22no—
89D4×C31—82no—
90C2×C4×C31—21no—
91C2×C4×C31—21no—
92C2×C4×C31C2411yescharacteristic
93C22⋊D31—22no—
94C22⋊D31—22no—
95C22⋊D31—42no—
96C22⋊D31—42no—
97C22⋊D31—42no—
98C2×Dic31—42no—
99C2×Dic31—41no—
100D124—41no—
101D124C2×D412yes—
102D124C2×D412yes—
103C4×D31—22no—
104C4×D31—22no—
105C4×D31—42no—
106Dic62—41no—
107Dic62C2×D412yes—
108Dic62C2×D412yes—
109C8×C31C2×D412yes—
110C8×C31C2×D412yes—
111C31⋊C8—22no—
112C31⋊C8—22no—
113#3288—311nomaximal, Sylow
114C22×C31—41no—
115C22×C31—42no—
116C22×C31—82no—
117C22×C31—81no—
118C22×C31H(5,𝔽2)11yescharacteristic
119C2×D31—22no—
120C2×D31—22no—
121C2×D31—162no—
122C2×D31—161no—
123C4×C31—41no—
124C4×C31—41no—
125C4×C31C22×D412yes—
126Dic31—22no—
127Dic31—22no—
128#577—312no—
129#576—312no—
130#496D3111yescharacteristic, complemented
131#472—312no—
132#471—312no—
133#455—311no—
134#454—311no—
135#453—312no—
136#444—312no—
137C2×C31—21no—
138C2×C31—82no—
139C2×C31—81no—
140C2×C31D4211yescharacteristic
141D31—42no—
142D31—42no—
1432−1+4—311no—
144H(5,𝔽2)—311no—
145H(5,𝔽2)—312no—
146#137—312no—
147#137—622no—
148AGL(1,ℤ/8)—312no—
149AGL(1,ℤ/8)—312no—
150AGL(1,ℤ/8)—312no—
151AGL(1,ℤ/8)—622no—
152AGL(1,ℤ/8)—622no—
153AGL(1,ℤ/8)—622no—
154#135—312no—
155#135—622no—
156#135—622no—
157C2×SD16—622no—
158C2×SD16C2×D3112yescomplemented
159C2×D8—622no—
160C2×D8C2×D3112yescomplemented
161#131—312no—
162#131—312no—
163#127C2×D3111yescharacteristic, complemented
164#124C2×D3111yescharacteristic, complemented
165#108—312no—
166#104—312no—
167#104—312no—
168#101—311no—
169#100—312no—
170#100—311no—
171#97C2×D3111yescharacteristic, complemented
172C31#328811yescharacteristic, complemented, Sylow
173#41—312no—
174#41—312no—
175#41—622no—
176#41—622no—
177#41—622no—
178#41—622no—
179#41—1241no—
180C2×Q8—622no—
181C2×Q8C22×D3111yescharacteristic
182C2×D4—41no—
183C2×D4—622no—
184C2×D4—622no—
185C2×D4—622no—
186C2×D4—1241no—
187C2×D4—1242no—
188C2×D4C22×D3111yescharacteristic
189C2×D4C22×D3112yes—
190Q16—312no—
191Q16—622no—
192SD16—22no—
193SD16—22no—
194SD16—312no—
195SD16—312no—
196SD16—622no—
197SD16—622no—
198SD16—622no—
199SD16—622no—
200D8—22no—
201D8—22no—
202D8—312no—
203D8—622no—
204D8—622no—
205D8—622no—
206M16—312no—
207M16—312no—
208M16—622no—
209M16—622no—
210C2×C8—622no—
211C2×C8—622no—
212C2×C8C22×D3112yes—
213C22⋊C4—41no—
214C42C22×D3111yescharacteristic
215C23—21no—
216C23—22no—
217C23—1242no—
218C23—1241no—
219Q8—22no—
220Q8—312no—
221Q8—312no—
222Q8—1241no—
223D4—22no—
224D4—22no—
225D4—22no—
226D4—82no—
227D4—312no—
228D4—312no—
229D4—622no—
230D4—622no—
231D4—1241no—
232D4—1242no—
233D4—1242no—
234D4—1242no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—622no—
238C2×C4—622no—
239C2×C4—1242no—
240C2×C4—1241no—
241C2×C4—1242no—
242C2×C4C23×D3111yescharacteristic
243C8—622no—
244C8—622no—
245C8D4×D3112yes—
246C8D4×D3112yes—
247C22—41no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—622no—
252C22—622no—
253C22—4961no—
254C22—4962no—
255C22#1175856111yescharacteristic
256C4—41no—
257C4—41no—
258C4—622no—
259C4—622no—
260C4C2×D4×D3112yes—
261C2—21no—
262C2—82no—
263C2—81no—
264C2—1242no—
265C2—1242no—
266C2#1452168411yescharacteristic
subgroupG/H
centerC2#14521684
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#496C2
socleC2×C31D42
hypercenter#496D31
hypocenterC31#3288
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14521855C2semidirect
2. #14521850C2semidirect
3. #14521316C2semidirect
4. #14521309C2semidirect
5. #14521226C2semidirect
6. #14521221C2semidirect
7. #14521216C2semidirect
8. #14521172C2semidirect
9. C31×#496C2semidirect
10. #11758564C22semidirect
12. #11758561C22semidirect
13. C2×SD16×C31C22semidirect
14. C2×D8×C31C22semidirect
15. C31×#127C22semidirect
16. C31×#124C22semidirect
17. #11758519C22semidirect
19. #11758509C22semidirect
20. #11758509C22semidirect
30. #11758478C22semidirect
31. #11758478C22semidirect
32. C31×#97C22semidirect
33. #11758424C22semidirect
34. #11758421C22semidirect
35. #11758421C22semidirect
36. #11758407C22semidirect
37. #11758393C22semidirect
38. #11758393C22semidirect
73. Dic124D4semidirect
74. D248D4semidirect
75. #92470D4semidirect
76. #92470D4semidirect
130. #496D31semidirect
158. C2×SD16C2×D31semidirect
160. C2×D8C2×D31semidirect
163. #127C2×D31semidirect
164. #124C2×D31semidirect
171. #97C2×D31semidirect
172. C31#3288semidirect

Maximal subgroups

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

subgroupindex
#145218552
#145218502
#145213162
#145213092
#145212262
#145212212
#145212162
#145211722
C31×#4962
#328831