Finite Group Databasebeta

← #16831091

Subgroups — #16831091

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
3#14271798C211yesmaximal, characteristic, complemented
4#14271406C212yesmaximal, complemented
5#14271365C211yesmaximal, characteristic, complemented
6#14271355C211yesmaximal, characteristic, complemented
7#14271312C212yesmaximal, complemented
8#14271307C212yesmaximal, complemented
9C4×D232C211yesmaximal, characteristic, complemented
10#14271242C211yesmaximal, characteristic, complemented
11C29×#492C211yesmaximal, characteristic, complemented
12C2×#90809C2212yescomplemented
13C2×D4×D29—21no—
14C2×D4×D29C2212yes—
15C2×SD16×C29C2212yescomplemented
16C2×SD16×C29C2212yescomplemented
17C29×C4⋊Q8C2211yescharacteristic, complemented
18C29×#127C2211yescharacteristic
19#11745308C2212yescomplemented
20C2×#90784C2212yes—
21#11745300—21no—
22#11745300C2212yes—
23#11745299—22no—
24C2×#90782C2212yescomplemented
25#11745276—28no—
26C2×D232C2211yescharacteristic
27C2×#90772C2212yescomplemented
28#11745257—21no—
29#11745256—22no—
30C4⋊C4×D29—21no—
31C4×D116C2211yescharacteristic
32C4×D116C2211yescharacteristic
33C4×D116C2211yescharacteristic, complemented
34C4×C8×C29C2211yescharacteristic, complemented
35#11745183C2212yescomplemented
36#11745180C2212yescomplemented
37#11745169C2211yescharacteristic
38#11745169C2211yescharacteristic, complemented
39#11745168C2212yescomplemented
40#11745166C2211yescharacteristic, complemented
41C4⋊#6597C2211yescharacteristic, complemented
42C23×D29—22no—
43C2×Q8×C29C2312yes—
44C2×D4×C29—21no—
45C2×D4×C29—21no—
46C2×D4×C29C2312yes—
47C2×C22⋊D29—22no—
48C2×C22⋊D29—22no—
49#90809—24no—
50#90809—42no—
51D4×D29—24no—
52D4×D29—42no—
53D4×D29—44no—
54C2×D116—22no—
55C2×D116D411yescharacteristic
56C2×D116C2311yescharacteristic
57C2×D116C2311yescharacteristic
58C2×C4×D29—21no—
59C2×C4×D29—21no—
60C2×C4×D29—22no—
61C2×C4×D29C2312yes—
62SD16×C29—24no—
63SD16×C29—42no—
64C2×C8×C29C2311yescharacteristic
65C2×C8×C29C2311yescharacteristic
66C4⋊C4×C29—21no—
67C4⋊C4×C29—21no—
68C42×C29C2311yescharacteristic
69C22⋊Dic29—22no—
70#90784—24no—
71#90782—24no—
72#90781—22no—
73#90781—21no—
74#90781—21no—
75#90781D412yes—
76C4⋊Dic29D411yescharacteristic
77C4⋊Dic29C2311yescharacteristic
78C4⋊Dic29C2311yescharacteristic
79#90779—22no—
80C2×#6597C2312yes—
81D232D414yescomplemented
82#90772—24no—
83C23×C29—22no—
84C22×D29—21no—
85C22×D29—21no—
86C22×D29—44no—
87C22×D29—44no—
88C22×D29—82no—
89C22×D29C2×D412yes—
90Q8×C29—22no—
91Q8×C29—22no—
92D4×C29—22no—
93D4×C29—22no—
94D4×C29—42no—
95D4×C29—81no—
96C2×C4×C29—22no—
97C2×C4×C29C2×D411yescharacteristic
98C2×C4×C29C2×D411yescharacteristic
99C2×C4×C29C2411yescharacteristic
100C22⋊D29—44no—
101C22⋊D29—44no—
102C2×Dic29—21no—
103C2×Dic29—21no—
104C2×Dic29C2×D412yes—
105D116—22no—
106D116—21no—
107D116—21no—
108D116—44no—
109D116C2×D412yes—
110D116C2×D412yescomplemented
111C4×D29—22no—
112C4×D29—22no—
113C4×D29—44no—
114C4×D29—42no—
115C4×D29—42no—
116C8×C29—21no—
117C8×C29C2×D412yescomplemented
118#6597—22no—
119#3272—291nomaximal, Sylow
120C22×C29—42no—
121C22×C29—42no—
122C22×C29—42no—
123C22×C29C22×D411yescharacteristic
124C2×D29—22no—
125C2×D29—22no—
126C2×D29—22no—
127C2×D29—22no—
128C2×D29—22no—
129C2×D29—41no—
130C2×D29—41no—
131C2×D29—41no—
132C2×D29—41no—
133C2×D29—88no—
134C4×C29—21no—
135C4×C29—42no—
136C4×C29AGL(1,ℤ/8)12yescomplemented
137C4×C29C22×D411yescharacteristic
138C4×C29H(5,𝔽2)11yescharacteristic
139Dic29—22no—
140Dic29—41no—
141Dic29—41no—
142C2×AGL(1,ℤ/8)—292no—
143#547—291no—
144D42—291no—
145#492D2911yescharacteristic, complemented
146#468—292no—
147#461—291no—
148#459—291no—
149#450—292no—
150#449—292no—
151C4×D8—291no—
152#436—291no—
153C2×C29—82no—
154C2×C29D4211yescharacteristic
155C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C29#57711yescharacteristic
157D29—42no—
158D29—42no—
159D29—42no—
160C2×#41—292no—
161C22×D4—292no—
162C22×D4—581no—
163AGL(1,ℤ/8)—588no—
164C2×SD16—292no—
165C2×SD16C2×D2912yescomplemented
166C2×SD16C2×D2912yescomplemented
167C2×D8—292no—
168C2×D8—291no—
169C2×M16—292no—
170C4⋊Q8C2×D2911yescharacteristic, complemented
171#127C2×D2911yescharacteristic
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×D4—291no—
181C2×C4⋊C4—581no—
182#107—291no—
183C4⋊C8—291no—
184#103—292no—
185#102—292no—
186#102—291no—
187#102—291no—
188C22⋊C8—292no—
189C4×C8C2×D2911yescharacteristic, complemented
190C29#327211yescharacteristic, complemented, Sylow
191C24—582no—
192#41—584no—
193#41—1162no—
194C2×Q8C22×D2912yes—
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—291no—
198C2×D4—291no—
199C2×D4—291no—
200C2×D4—582no—
201C2×D4—582no—
202C2×D4—584no—
203C2×D4—582no—
204C2×D4—1162no—
205C2×D4—1164no—
206C2×D4C22×D2912yes—
207C22×C4—292no—
208C22×C4—582no—
209C22×C4—581no—
210C22×C4—581no—
211SD16—24no—
212SD16—42no—
213SD16—584no—
214D8—294no—
215D8—584no—
216M16—584no—
217C2×C8—292no—
218C2×C8C22×D2911yescharacteristic
219C2×C8C22×D2911yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—291no—
223C4⋊C4—291no—
224C4⋊C4—291no—
225C4⋊C4—582no—
226C22⋊C4—292no—
227C22⋊C4—582no—
228C22⋊C4—582no—
229C22⋊C4—581no—
230C22⋊C4—581no—
231C42C22×D2911yescharacteristic
232C23—22no—
233C23—292no—
234C23—581no—
235C23—581no—
236C23—1164no—
237C23—1164no—
238C23—2322no—
239Q8—22no—
240Q8—22no—
241D4—22no—
242D4—22no—
243D4—42no—
244D4—81no—
245D4—292no—
246D4—292no—
247D4—581no—
248D4—581no—
249D4—582no—
250D4—1164no—
251D4—1164no—
252D4—1164no—
253C2×C4—22no—
254C2×C4—292no—
255C2×C4—582no—
256C2×C4—582no—
257C2×C4—581no—
258C2×C4—581no—
259C2×C4—1164no—
260C2×C4—1162no—
261C2×C4—1162no—
262C2×C4D4×D2911yescharacteristic
263C2×C4D4×D2911yescharacteristic
264C2×C4C23×D2911yescharacteristic
265C8—21no—
266C8—582no—
267C8D4×D2912yescomplemented
268C22—42no—
269C22—42no—
270C22—42no—
271C22—582no—
272C22—582no—
273C22—582no—
274C22—582no—
275C22—582no—
276C22—1161no—
277C22—1161no—
278C22—1161no—
279C22—1161no—
280C22—2328no—
281C22C2×D4×D2911yescharacteristic
282C4—21no—
283C4—42no—
284C4—582no—
285C4—1161no—
286C4—1161no—
287C4#1174527612yescomplemented
288C4C2×D4×D2911yescharacteristic
289C4#1174535911yescharacteristic
290C2—82no—
291C2—1162no—
292C2—1162no—
293C2—1162no—
294C2#1427179811yescharacteristic
295C2C2×#1174527611yescharacteristic
296C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#492C2
socleC22×C29C22×D4
hypercenter#492D29
hypocenterC29#3272
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#11745276C2semidirect
2. #14271816C2semidirect
3. #14271798C2semidirect
4. #14271406C2semidirect
5. #14271365C2semidirect
6. #14271355C2semidirect
7. #14271312C2semidirect
8. #14271307C2semidirect
9. C4×D232C2semidirect
10. #14271242C2semidirect
11. C29×#492C2semidirect
12. C2×#90809C22semidirect
15. C2×SD16×C29C22semidirect
16. C2×SD16×C29C22semidirect
17. C29×C4⋊Q8C22semidirect
19. #11745308C22semidirect
24. C2×#90782C22semidirect
27. C2×#90772C22semidirect
33. C4×D116C22semidirect
34. C4×C8×C29C22semidirect
35. #11745183C22semidirect
36. #11745180C22semidirect
38. #11745169C22semidirect
39. #11745168C22semidirect
40. #11745166C22semidirect
41. C4⋊#6597C22semidirect
81. D232D4semidirect
110. D116C2×D4semidirect
117. C8×C29C2×D4semidirect
136. C4×C29AGL(1,ℤ/8)semidirect
145. #492D29semidirect
165. C2×SD16C2×D29semidirect
166. C2×SD16C2×D29semidirect
170. C4⋊Q8C2×D29semidirect
189. C4×C8C2×D29semidirect
190. C29#3272semidirect
267. C8D4×D29semidirect
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
#142717982
#142714062
#142713652
#142713552
#142713122
#142713072
C4×D2322
#142712422
C29×#4922
#327229