Finite Group Databasebeta

← #16831094

Subgroups — #16831094

Order 3712.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11745270C212yesmaximal, complemented
2#14271818C211yesmaximal, characteristic, complemented
3D4×D116C211yesmaximal, characteristic, complemented
4#14271536C211yesmaximal, characteristic, complemented
5#14271409C212yesmaximal, complemented
6#14271369C211yesmaximal, characteristic, complemented
7#14271359C211yesmaximal, characteristic, complemented
8#14271316C212yesmaximal, complemented
9#14271310C212yesmaximal, complemented
10C4×D232C211yesmaximal, characteristic, complemented
11C29×#436C211yesmaximal, characteristic, complemented
12C2×D4×D29—21no—
13C2×#90805C2212yescomplemented
14C22×D116C2212yes—
15C2×M16×C29C2212yescomplemented
16C4×D4×C29C2211yescharacteristic
17#11745300—21no—
18#11745292C2212yes—
19#11745286C2212yescomplemented
20#11745270—28no—
21C2×D232C2211yescharacteristic
22C2×D232C2212yescomplemented
23C2×#90773C2212yes—
24C2×#90773C2212yescomplemented
25C2×#90773C2212yescomplemented
26#11745257—21no—
27C4⋊C4×D29—21no—
28#11745245—22no—
29#11745244—22no—
30#11745236C2211yescharacteristic
31C4×D116C2211yescharacteristic
32C4×D116C2211yescharacteristic, complemented
33#11745231C2211yescharacteristic, complemented
34C29×C4⋊C8C2211yescharacteristic, complemented
35C29×C22⋊C8C2212yescomplemented
36C4×C8×C29C2211yescharacteristic, complemented
37#11745169C2211yescharacteristic
38#11745169C2211yescharacteristic, complemented
39#11745169C2212yescomplemented
40#11745166C2211yescharacteristic, complemented
41#11745164C2212yescomplemented
42C23×D29—22no—
43C2×D4×C29D411yescharacteristic
44C22×C4×C29C2312yes—
45C2×C22⋊D29—22no—
46C2×C22⋊D29—22no—
47D4×D29—44no—
48#90805—24no—
49#90805—42no—
50C2×D116—24no—
51C2×D116—22no—
52C2×D116—21no—
53C2×D116—21no—
54C2×D116—42no—
55C2×D116C2312yes—
56C2×D116C2311yescharacteristic
57C2×D116C2311yescharacteristic
58C2×C4×D29—21no—
59C2×C4×D29—22no—
60C2×C4×D29—21no—
61C2×Dic58C2312yes—
62M16×C29—24no—
63C2×C8×C29C2312yes—
64C2×C8×C29C2311yescharacteristic
65C2×C8×C29C2311yescharacteristic
66C4⋊C4×C29D411yescharacteristic
67C22⋊C4×C29D412yes—
68C42×C29C2311yescharacteristic
69C22⋊Dic29—22no—
70#90781—22no—
71#90781—21no—
72#90781—21no—
73C4⋊Dic29—21no—
74C4⋊Dic29—21no—
75C4⋊Dic29C2311yescharacteristic
76C4⋊Dic29C2311yescharacteristic
77#90779—22no—
78D232—24no—
79D232D414yescomplemented
80#90773—24no—
81#90773—24no—
82#90773—42no—
83C23×C29C2×D412yes—
84C22×D29—21no—
85C22×D29—21no—
86C22×D29—22no—
87C22×D29—44no—
88C22×D29—44no—
89C22×D29—82no—
90D4×C29—22no—
91C2×C4×C29—22no—
92C2×C4×C29—22no—
93C2×C4×C29C2×D412yes—
94C2×C4×C29C2×D411yescharacteristic
95C2×C4×C29C2×D411yescharacteristic
96C2×C4×C29C2411yescharacteristic
97C22⋊D29—44no—
98C22⋊D29—44no—
99C2×Dic29—21no—
100C2×Dic29—22no—
101C2×Dic29—21no—
102D116—22no—
103D116—21no—
104D116—21no—
105D116—22no—
106D116—44no—
107D116—42no—
108D116—81no—
109D116C2×D412yes—
110D116C2×D412yescomplemented
111C4×D29—44no—
112C4×D29—42no—
113C4×D29—42no—
114Dic58—22no—
115Dic58—22no—
116C8×C29—22no—
117C8×C29—21no—
118C8×C29C2×D412yescomplemented
119#3272—291nomaximal, Sylow
120C22×C29—22no—
121C22×C29—22no—
122C22×C29—22no—
123C22×C29C22×D411yescharacteristic
124C2×D29—22no—
125C2×D29—22no—
126C2×D29—41no—
127C2×D29—41no—
128C2×D29—41no—
129C2×D29—41no—
130C2×D29—42no—
131C2×D29—42no—
132C2×D29—42no—
133C2×D29—88no—
134C4×C29—22no—
135C4×C29—21no—
136C4×C29AGL(1,ℤ/8)12yescomplemented
137C4×C29C22×D411yescharacteristic
138C4×C29H(5,𝔽2)11yescharacteristic
139Dic29—42no—
140Dic29—41no—
141Dic29—41no—
142C2×AGL(1,ℤ/8)—292no—
143#547—291no—
144D42—291no—
145#492—291no—
146#468—292no—
147#461—291no—
148#459—291no—
149#450—292no—
150#449—292no—
151C4×D8—291no—
152#436D2911yescharacteristic, complemented
153C2×C29—42no—
154C2×C29D4211yescharacteristic
155C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C29#57711yescharacteristic
157D29—42no—
158D29—42no—
159D29—82no—
160C2×#41—292no—
161C22×D4—292no—
162C22×D4—581no—
163AGL(1,ℤ/8)—588no—
164C2×SD16—292no—
165C2×SD16—292no—
166C2×SD16—292no—
167C2×D8—291no—
168C2×D8—292no—
169C2×M16C2×D2912yescomplemented
170C4⋊Q8—291no—
171#127—291no—
172#123—582no—
173C22⋊Q8—292no—
174#121—292no—
175#121—581no—
176#121—581no—
177#120—582no—
178C4×D4—291no—
179C4×D4—291no—
180C4×D4C2×D2911yescharacteristic
181C2×C4⋊C4—581no—
182#107—291no—
183C4⋊C8C2×D2911yescharacteristic, complemented
184#103—292no—
185#102—291no—
186#102—291no—
187#102—292no—
188C22⋊C8C2×D2912yescomplemented
189C4×C8C2×D2911yescharacteristic, complemented
190C29#327211yescharacteristic, complemented, Sylow
191C24—582no—
192#41—584no—
193#41—1162no—
194C2×Q8—292no—
195C2×D4—291no—
196C2×D4—291no—
197C2×D4—292no—
198C2×D4—584no—
199C2×D4—582no—
200C2×D4—582no—
201C2×D4—582no—
202C2×D4—581no—
203C2×D4—581no—
204C2×D4—1162no—
205C2×D4—1164no—
206C2×D4D11611yescharacteristic
207C22×C4—581no—
208C22×C4—582no—
209C22×C4—581no—
210C22×C4C22×D2912yes—
211SD16—584no—
212SD16—584no—
213SD16—1162no—
214D8—294no—
215D8—584no—
216M16—24no—
217C2×C8C22×D2911yescharacteristic
218C2×C8C22×D2912yes—
219C2×C8C22×D2911yescharacteristic
220C4⋊C4—291no—
221C4⋊C4—291no—
222C4⋊C4—581no—
223C4⋊C4—582no—
224C4⋊C4—581no—
225C4⋊C4D11611yescharacteristic
226C22⋊C4—582no—
227C22⋊C4—581no—
228C22⋊C4—581no—
229C22⋊C4—582no—
230C22⋊C4D11612yes—
231C42C22×D2911yescharacteristic
232C23—581no—
233C23—581no—
234C23—582no—
235C23—1164no—
236C23—1164no—
237C23—2322no—
238C23C2×D11612yes—
239Q8—582no—
240Q8—582no—
241D4—22no—
242D4—292no—
243D4—292no—
244D4—582no—
245D4—581no—
246D4—581no—
247D4—582no—
248D4—1164no—
249D4—1164no—
250D4—1164no—
251D4—1162no—
252D4—2321no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—581no—
256C2×C4—581no—
257C2×C4—582no—
258C2×C4—1164no—
259C2×C4—1162no—
260C2×C4—1162no—
261C2×C4C2×D11611yescharacteristic
262C2×C4C2×D11612yes—
263C2×C4C2×D11611yescharacteristic
264C2×C4C23×D2911yescharacteristic
265C8—22no—
266C8—21no—
267C8D4×D2912yescomplemented
268C22—22no—
269C22—22no—
270C22—22no—
271C22—582no—
272C22—582no—
273C22—1161no—
274C22—1161no—
275C22—1161no—
276C22—1161no—
277C22—1162no—
278C22—1162no—
279C22—1162no—
280C22—2328no—
281C22C22×D11611yescharacteristic
282C4—22no—
283C4—21no—
284C4—1162no—
285C4—1161no—
286C4—1161no—
287C4#1174527012yescomplemented
288C4C2×D4×D2911yescharacteristic
289C4#1174536411yescharacteristic
290C2—42no—
291C2—1162no—
292C2—1162no—
293C2—2322no—
294C2D4×D11611yescharacteristic
295C2C2×#1174527011yescharacteristic
296C2#1427197511yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#436C2
socleC22×C29C22×D4
hypercenter#436D29
hypocenterC29#3272
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#11745270C2semidirect
2. #14271818C2semidirect
3. D4×D116C2semidirect
4. #14271536C2semidirect
5. #14271409C2semidirect
6. #14271369C2semidirect
7. #14271359C2semidirect
8. #14271316C2semidirect
9. #14271310C2semidirect
10. C4×D232C2semidirect
11. C29×#436C2semidirect
13. C2×#90805C22semidirect
15. C2×M16×C29C22semidirect
19. #11745286C22semidirect
22. C2×D232C22semidirect
24. C2×#90773C22semidirect
25. C2×#90773C22semidirect
32. C4×D116C22semidirect
33. #11745231C22semidirect
34. C29×C4⋊C8C22semidirect
35. C29×C22⋊C8C22semidirect
36. C4×C8×C29C22semidirect
38. #11745169C22semidirect
39. #11745169C22semidirect
40. #11745166C22semidirect
41. #11745164C22semidirect
79. D232D4semidirect
110. D116C2×D4semidirect
118. C8×C29C2×D4semidirect
136. C4×C29AGL(1,ℤ/8)semidirect
152. #436D29semidirect
169. C2×M16C2×D29semidirect
183. C4⋊C8C2×D29semidirect
188. C22⋊C8C2×D29semidirect
189. C4×C8C2×D29semidirect
190. C29#3272semidirect
267. C8D4×D29semidirect
287. C4#11745270semidirect

Maximal subgroups

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

subgroupindex
C2×#117452702
#142718182
D4×D1162
#142715362
#142714092
#142713692
#142713592
#142713162
#142713102
C4×D2322
C29×#4362
#327229