Finite Group Databasebeta

← #16831095

Subgroups — #16831095

Order 3712.

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

normal subgroups only

This group has 546 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
1C2×#11745276C212yesmaximal, complemented
2#14271816C211yesmaximal, characteristic, complemented
3D4×D116C211yesmaximal, characteristic, complemented
4#14271537C211yesmaximal, characteristic, complemented
5#14271412C212yesmaximal, complemented
6#14271359C211yesmaximal, characteristic, complemented
7#14271312C212yesmaximal, complemented
8#14271311C212yesmaximal, complemented
9C4×#90782C211yesmaximal, characteristic, complemented
10#14271240C211yesmaximal, characteristic, complemented
11C29×#461C211yesmaximal, characteristic, complemented
12C2×#90809C2212yescomplemented
13C2×D4×D29C2212yes—
14C22×D116—21no—
15C2×SD16×C29C2212yes—
16C29×C4⋊Q8C2211yescharacteristic, complemented
17C4×D4×C29C2211yescharacteristic
18#11745308C2212yescomplemented
19C2×#90784C2212yescomplemented
20C2×#90784C2212yescomplemented
21C2×#90782C2211yescharacteristic
22#11745292—21no—
23#11745276—28no—
24C2×D232C2212yescomplemented
25C2×#90772C2212yescomplemented
26#11745257—21no—
27#11745257C2212yes—
28#11745256—22no—
29C4⋊C4×D29—21no—
30#11745244—22no—
31#11745236C2211yescharacteristic
32C4×D116C2211yescharacteristic
33C4×D116C2211yescharacteristic, complemented
34C29×C4⋊C8C2211yescharacteristic, complemented
35C29×#103C2212yescomplemented
36#11745180C2211yescharacteristic
37#11745169C2212yescomplemented
38#11745168C2212yescomplemented
39#11745157C2211yescharacteristic, complemented
40#11745155C2211yescharacteristic, complemented
41C4×#6597C2211yescharacteristic, complemented
42C23×D29—22no—
43C2×Q8×C29C2312yes—
44C2×D4×C29C2311yescharacteristic
45C22×C4×C29—21no—
46C2×C22⋊D29—22no—
47#90809—24no—
48#90809—42no—
49D4×D29—24no—
50D4×D29—42no—
51C2×D116—22no—
52C2×D116—22no—
53C2×D116—21no—
54C2×D116—21no—
55C2×D116—44no—
56C2×D116D411yescharacteristic
57C2×D116C2312yes—
58C2×D116C2311yescharacteristic
59C2×C4×D29—21no—
60C2×C4×D29—22no—
61C2×C4×D29C2312yes—
62SD16×C29—24no—
63C2×C8×C29C2312yes—
64C4⋊C4×C29—21no—
65C4⋊C4×C29—21no—
66C4⋊C4×C29C2311yescharacteristic
67C22⋊C4×C29—21no—
68C42×C29C2311yescharacteristic
69#90784—24no—
70#90784—42no—
71#90782D414yescomplemented
72#90781—22no—
73#90781—21no—
74#90781—22no—
75#90781D412yes—
76C4⋊Dic29D411yescharacteristic
77C4⋊Dic29C2311yescharacteristic
78#90779—22no—
79C2×#6597C2311yescharacteristic
80C2×#6597C2311yescharacteristic
81D232—24no—
82#90772—24no—
83C23×C29—21no—
84C22×D29—21no—
85C22×D29—22no—
86C22×D29—44no—
87C22×D29—44no—
88C22×D29—82no—
89C22×D29C2×D412yes—
90Q8×C29—22no—
91Q8×C29—22no—
92D4×C29—21no—
93D4×C29C2×D412yes—
94C2×C4×C29—22no—
95C2×C4×C29—21no—
96C2×C4×C29—42no—
97C2×C4×C29C2×D411yescharacteristic
98C2×C4×C29C2×D411yescharacteristic
99C2×C4×C29C2411yescharacteristic
100C22⋊D29—44no—
101C2×Dic29—21no—
102C2×Dic29C2×D412yes—
103D116—22no—
104D116—22no—
105D116—21no—
106D116—22no—
107D116—44no—
108D116—44no—
109D116—42no—
110D116—81no—
111D116C2×D412yescomplemented
112C4×D29—22no—
113C4×D29—22no—
114C4×D29—44no—
115C4×D29—42no—
116C8×C29—22no—
117#6597—21no—
118#6597C2×D412yescomplemented
119#3272—291nomaximal, Sylow
120C22×C29—22no—
121C22×C29—41no—
122C22×C29—41no—
123C22×C29C22×D411yescharacteristic
124C2×D29—22no—
125C2×D29—22no—
126C2×D29—22no—
127C2×D29—22no—
128C2×D29—41no—
129C2×D29—41no—
130C2×D29—42no—
131C2×D29—42no—
132C2×D29—42no—
133C2×D29—88no—
134C4×C29—21no—
135C4×C29—42no—
136C4×C29—41no—
137C4×C29AGL(1,ℤ/8)12yescomplemented
138C4×C29C22×D411yescharacteristic
139C4×C29H(5,𝔽2)11yescharacteristic
140Dic29—22no—
141Dic29—41no—
142C2×AGL(1,ℤ/8)—292no—
143#547—291no—
144D42—291no—
145#492—291no—
146#468—292no—
147#461D2911yescharacteristic, complemented
148#459—291no—
149#450—292no—
150#449—292no—
151C4×D8—291no—
152#436—291no—
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×SD16C2×D2912yes—
167C2×D8—291no—
168C2×D8—292no—
169C2×M16—292no—
170C4⋊Q8C2×D2911yescharacteristic, complemented
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#103C2×D2912yescomplemented
185#102—291no—
186#102—292no—
187#102—291no—
188C22⋊C8—292no—
189C4×C8—291no—
190C29#327211yescharacteristic, complemented, Sylow
191C24—582no—
192#41—584no—
193#41—1162no—
194C2×Q8C22×D2912yes—
195C2×D4—291no—
196C2×D4—291no—
197C2×D4—292no—
198C2×D4—582no—
199C2×D4—582no—
200C2×D4—582no—
201C2×D4—584no—
202C2×D4—581no—
203C2×D4—581no—
204C2×D4—1164no—
205C2×D4—1162no—
206C2×D4C22×D2911yescharacteristic
207C22×C4—21no—
208C22×C4—292no—
209C22×C4—582no—
210C22×C4—581no—
211SD16—24no—
212SD16—584no—
213SD16—1162no—
214D8—294no—
215D8—584no—
216M16—584no—
217C2×C8—291no—
218C2×C8—291no—
219C2×C8C22×D2912yes—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—291no—
223C4⋊C4—291no—
224C4⋊C4—582no—
225C4⋊C4C22×D2911yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—292no—
228C22⋊C4—582no—
229C22⋊C4—582no—
230C22⋊C4—581no—
231C42C22×D2911yescharacteristic
232C23—21no—
233C23—292no—
234C23—581no—
235C23—582no—
236C23—1164no—
237C23—1164no—
238C23—2322no—
239Q8—22no—
240Q8—22no—
241D4—21no—
242D4—292no—
243D4—582no—
244D4—581no—
245D4—582no—
246D4—582no—
247D4—1164no—
248D4—1164no—
249D4—1164no—
250D4—1162no—
251D4—2321no—
252D4D4×D2912yes—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—292no—
257C2×C4—582no—
258C2×C4—582no—
259C2×C4—581no—
260C2×C4—1164no—
261C2×C4—1162no—
262C2×C4D4×D2911yescharacteristic
263C2×C4D4×D2911yescharacteristic
264C2×C4C23×D2911yescharacteristic
265C8—22no—
266C8—292no—
267C8—581no—
268C22—22no—
269C22—41no—
270C22—41no—
271C22—582no—
272C22—582no—
273C22—582no—
274C22—582no—
275C22—1161no—
276C22—1161no—
277C22—1162no—
278C22—1162no—
279C22—1162no—
280C22—2328no—
281C22C2×D4×D2911yescharacteristic
282C4—21no—
283C4—42no—
284C4—41no—
285C4—582no—
286C4—1161no—
287C4#1174527612yescomplemented
288C4C2×D4×D2911yescharacteristic
289C4#1174536411yescharacteristic
290C2—42no—
291C2—1162no—
292C2—1162no—
293C2—2322no—
294C2#1427179711yescharacteristic
295C2C2×#1174527611yescharacteristic
296C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#461C2
socleC22×C29C22×D4
hypercenter#461D29
hypocenterC29#3272
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#11745276C2semidirect
2. #14271816C2semidirect
3. D4×D116C2semidirect
4. #14271537C2semidirect
5. #14271412C2semidirect
6. #14271359C2semidirect
7. #14271312C2semidirect
8. #14271311C2semidirect
9. C4×#90782C2semidirect
10. #14271240C2semidirect
11. C29×#461C2semidirect
12. C2×#90809C22semidirect
16. C29×C4⋊Q8C22semidirect
18. #11745308C22semidirect
19. C2×#90784C22semidirect
20. C2×#90784C22semidirect
24. C2×D232C22semidirect
25. C2×#90772C22semidirect
33. C4×D116C22semidirect
34. C29×C4⋊C8C22semidirect
35. C29×#103C22semidirect
37. #11745169C22semidirect
38. #11745168C22semidirect
39. #11745157C22semidirect
40. #11745155C22semidirect
41. C4×#6597C22semidirect
71. #90782D4semidirect
111. D116C2×D4semidirect
118. #6597C2×D4semidirect
137. C4×C29AGL(1,ℤ/8)semidirect
147. #461D29semidirect
170. C4⋊Q8C2×D29semidirect
183. C4⋊C8C2×D29semidirect
184. #103C2×D29semidirect
190. C29#3272semidirect
287. C4#11745276semidirect

Maximal subgroups

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

subgroupindex
C2×#117452762
#142718162
D4×D1162
#142715372
#142714122
#142713592
#142713122
#142713112
C4×#907822
#142712402
C29×#4612
#327229