Finite Group Databasebeta

← #16855105

Subgroups — #16855105

Order 3968.

766 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 145 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#14521885C211yesmaximal, characteristic, complemented
2#14521561C212yesmaximal, complemented
3#14521556C211yesmaximal, characteristic, complemented
4#14521240C214yesmaximal, complemented
5#14521237C214yesmaximal, complemented
6#14521022C212yesmaximal, complemented
7C31×#410C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9#11758567—22no—
10#11758566—22no—
11#41×D31—24no—
12#11758564—21no—
13#11758561—21no—
14#11758561C2214yes—
15C2×#92495—22no—
16C2×#92495C2212yes—
17C22×C4×D31C2211yescharacteristic, complemented
18C31×#117C2212yescomplemented
19#11758523—21no—
20#11758515—21no—
21#11758514C2212yescomplemented
22#11758512C2212yescomplemented
23C4×C22⋊D31—22no—
24#11758503C2211yescharacteristic, complemented
25#11758474—22no—
26#11758472—22no—
27#11758463C2214yescomplemented
28#11758459C2214yescomplemented
29C4×D124—24no—
30C31×#99C2214yescomplemented
31#11758394C2218yescomplemented
32C23×D31C2311yescharacteristic
33#41×C31—22no—
34#41×C31—22no—
35C2×Q8×C31D411yescharacteristic, complemented
36C2×D4×C31D411yescharacteristic, complemented
37C2×D4×C31C2312yes—
38C22×C4×C31D412yescomplemented
39C22×C4×C31C2311yescharacteristic
40C2×C22⋊D31—24no—
41C2×C22⋊D31—22no—
42C2×C22⋊D31C2314yes—
43C22×Dic31C2311yescharacteristic
44#92499—24no—
45Q8×D31—24no—
46#92497—24no—
47#92497—28no—
48D4×D31—24no—
49D4×D31—28no—
50#92495—24no—
51#92495—24no—
52#92495—22no—
53#92495—24no—
54#92495—22no—
55#92495—22no—
56#92495—22no—
57C2×D124—22no—
58C2×D124—24no—
59C2×D124D412yescomplemented
60C2×C4×D31—24no—
61C2×C4×D31—22no—
62C2×C4×D31—22no—
63C2×C4×D31—21no—
64C2×C4×D31—21no—
65C2×C4×D31D414yescomplemented
66C2×Dic62—22no—
67C2×Dic62D412yescomplemented
68C4⋊C4×C31—22no—
69C22⋊C4×C31C2314yes—
70C42×C31—22no—
71C22⋊Dic31—22no—
72C22⋊Dic31C2312yes—
73(C2×D31)⋊C4—24no—
74(C2×D31)⋊C4—22no—
75(C2×D31)⋊C4—24no—
76C4⋊Dic31—21no—
77C4⋊Dic31—24no—
78Dic31⋊C4—22no—
79C4×Dic31—21no—
80C23×C31C2×D412yes—
81C23×C31C2411yescharacteristic
82C22×D31—22no—
83C22×D31—21no—
84C22×D31—24no—
85C22×D31—42no—
86C22×D31C2×D414yes—
87Q8×C31—22no—
88D4×C31—24no—
89D4×C31—22no—
90C2×C4×C31—22no—
91C2×C4×C31—22no—
92C2×C4×C31—24no—
93C2×C4×C31C2×D412yes—
94C2×C4×C31C2×D411yescharacteristic
95C2×C4×C31C2×D411yescharacteristic
96C2×C4×C31C2×D412yes—
97C2×C4×C31C2×D412yes—
98C22⋊D31—28no—
99C22⋊D31—24no—
100C22⋊D31—24no—
101C22⋊D31—44no—
102C2×Dic31—24no—
103C2×Dic31—22no—
104C2×Dic31—21no—
105C2×Dic31—22no—
106C2×Dic31C2×D414yes—
107D124—24no—
108D124—22no—
109D124—22no—
110D124—48no—
111C4×D31—28no—
112C4×D31—24no—
113C4×D31—24no—
114C4×D31—41no—
115C4×D31—42no—
116C4×D31—41no—
117Dic62—24no—
118Dic62—22no—
119Dic62—22no—
120#3025—311nomaximal, Sylow
121C22×C31—22no—
122C22×C31—41no—
123C22×C31—42no—
124C22×C31C22×D411yescharacteristic
125C22×C31C22×D412yes—
126C2×D31—24no—
127C2×D31—22no—
128C2×D31—24no—
129C2×D31—41no—
130C2×D31—42no—
131C2×D31—41no—
132C2×D31—44no—
133C2×D31—84no—
134C4×C31—22no—
135C4×C31—44no—
136C4×C31#12011yescharacteristic
137C4×C31#12012yes—
138C4×C31#12011yescharacteristic
139Dic31—24no—
140Dic31—42no—
141Dic31—41no—
142#585—311no—
143#525—311no—
144#525—312no—
145#458—314no—
146B(4,𝔽2)—314no—
147#410—312no—
148#410D3111yescharacteristic, complemented
149C2×C31—21no—
150C2×C31—22no—
151C2×C31—42no—
152C2×C31C2×#12011yescharacteristic
153D31—42no—
154D31—44no—
1552−1+4—622no—
1562−1+4—621no—
157H(5,𝔽2)—314no—
158H(5,𝔽2)—622no—
159H(5,𝔽2)—621no—
160C2×#41—312no—
161C2×#41—624no—
162C2×#41—622no—
163C2×#41C2×D3111yescharacteristic
164C23×C4—311no—
165#123—312no—
166#123—314no—
167C22⋊Q8—622no—
168C22⋊Q8—621no—
169#121—622no—
170#121—621no—
171#120—312no—
172#120—314no—
173C4×D4—624no—
174C4×D4—622no—
175#117—311no—
176#117C2×D3112yescomplemented
177#99—318no—
178#99C2×D3114yescomplemented
179C31#302511yescharacteristic, complemented, Sylow
180C24—311no—
181#41—22no—
182#41—22no—
183#41—624no—
184#41—624no—
185#41—628no—
186#41—624no—
187#41—624no—
188#41—622no—
189#41—622no—
190#41—624no—
191#41—622no—
192#41—622no—
193C2×Q8—312no—
194C2×Q8—622no—
195C2×Q8—624no—
196C2×Q8D12411yescharacteristic, complemented
197C2×D4—314no—
198C2×D4—312no—
199C2×D4—622no—
200C2×D4—624no—
201C2×D4—628no—
202C2×D4—624no—
203C2×D4—624no—
204C2×D4—622no—
205C2×D4D12411yescharacteristic, complemented
206C2×D4C22×D3112yes—
207C22×C4—314no—
208C22×C4—311no—
209C22×C4—624no—
210C22×C4—621no—
211C22×C4—621no—
212C22×C4—622no—
213C22×C4—622no—
214C22×C4D12412yescomplemented
215C22×C4C22×D3111yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—624no—
218C4⋊C4—622no—
219C4⋊C4—621no—
220C22⋊C4—312no—
221C22⋊C4—624no—
222C22⋊C4—624no—
223C22⋊C4—622no—
224C22⋊C4—622no—
225C22⋊C4C22×D3114yes—
226C42—22no—
227C42—621no—
228C23—314no—
229C23—624no—
230C23—621no—
231C23—622no—
232C23—1242no—
233C23C2×D12412yes—
234C23C23×D3111yescharacteristic
235Q8—22no—
236Q8—624no—
237Q8—622no—
238Q8—622no—
239D4—24no—
240D4—22no—
241D4—624no—
242D4—628no—
243D4—624no—
244D4—624no—
245D4—622no—
246D4—622no—
247D4—1248no—
248D4—1244no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—314no—
253C2×C4—628no—
254C2×C4—624no—
255C2×C4—624no—
256C2×C4—624no—
257C2×C4—622no—
258C2×C4—621no—
259C2×C4—622no—
260C2×C4—1241no—
261C2×C4—1242no—
262C2×C4—1241no—
263C2×C4C2×D12412yes—
264C2×C4C2×D12411yescharacteristic
265C2×C4C2×D12411yescharacteristic
266C2×C4D4×D3112yes—
267C2×C4D4×D3112yes—
268C22—22no—
269C22—41no—
270C22—42no—
271C22—624no—
272C22—622no—
273C22—624no—
274C22—1244no—
275C22—1242no—
276C22—1241no—
277C22—1241no—
278C22—2484no—
279C22C22×D12411yescharacteristic
280C22C2×D4×D3112yes—
281C4—22no—
282C4—44no—
283C4—624no—
284C4—1242no—
285C4—1241no—
286C4#1175845911yescharacteristic
287C4#1175845912yes—
288C4#1175845911yescharacteristic
289C2—22no—
290C2—21no—
291C2—42no—
292C2—1242no—
293C2—1244no—
294C2C2×#1175845911yescharacteristic
subgroupG/H
centerC4#11758459
commutator, cosocleC23×C31C24
FrattiniC23C23×D31
FittingC31×#410C2
socleC2×C31C2×#120
hypercenter#410D31
hypocenterC31#3025
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14521885C2semidirect
2. #14521561C2semidirect
3. #14521556C2semidirect
4. #14521240C2semidirect
5. #14521237C2semidirect
6. #14521022C2semidirect
7. C31×#410C2semidirect
17. C22×C4×D31C22semidirect
18. C31×#117C22semidirect
21. #11758514C22semidirect
22. #11758512C22semidirect
24. #11758503C22semidirect
27. #11758463C22semidirect
28. #11758459C22semidirect
30. C31×#99C22semidirect
31. #11758394C22semidirect
35. C2×Q8×C31D4semidirect
36. C2×D4×C31D4semidirect
38. C22×C4×C31D4semidirect
59. C2×D124D4semidirect
65. C2×C4×D31D4semidirect
67. C2×Dic62D4semidirect
148. #410D31semidirect
176. #117C2×D31semidirect
178. #99C2×D31semidirect
179. C31#3025semidirect
196. C2×Q8D124semidirect
205. C2×D4D124semidirect
214. C22×C4D124semidirect

Maximal subgroups

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

subgroupindex
#145218852
#145215612
#145215562
#145212402
#145212372
#145210222
C31×#4102
#302531