Finite Group Databasebeta

← #16831277

Subgroups — #16831277

Order 3712.

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

normal subgroups only

This group has 454 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#14271976C211yesmaximal, characteristic, complemented
2#14271969C212yesmaximal, complemented
3#14271964C211yesmaximal, characteristic, complemented
4#14271435C211yesmaximal, characteristic, complemented
5#14271430C211yesmaximal, characteristic, complemented
6#14271423C212yesmaximal, complemented
7#14271340C212yesmaximal, complemented
8#14271335C212yesmaximal, complemented
9#14271281C211yesmaximal, characteristic, complemented
10#14271281C211yesmaximal, characteristic, complemented
11C29×#495C211yesmaximal, characteristic, complemented
12#11745362C2212yescomplemented
13#11745359C2212yes—
14C2×Q16×C29C2211yescharacteristic, complemented
15C2×SD16×C29C2212yescomplemented
16C2×D8×C29C2211yescharacteristic
17C29×#124C2212yescomplemented
18#11745304C2212yes—
19#11745304C2212yescomplemented
20#11745294C2212yes—
21#11745294C2212yescomplemented
22#11745281—21no—
23#11745280—22no—
24Q16×D29—21no—
25#11745278—22no—
26#11745277—22no—
27#11745276—22no—
28SD16×D29—22no—
29#11745274—21no—
30#11745273—22no—
31D8×D29—21no—
32#11745266C2211yescharacteristic
33#11745266C2211yescharacteristic
34#11745263C2211yescharacteristic
35#11745263C2212yescomplemented
36#11745263C2211yescharacteristic, complemented
37C4×C8×C29C2211yescharacteristic, complemented
38#11745184C2212yescomplemented
39#11745181C2212yescomplemented
40#11745167C2211yescharacteristic, complemented
41#11745167C2211yescharacteristic, complemented
42#11745153C2211yescharacteristic
43#11745153C2211yescharacteristic, complemented
44#11745153C2212yescomplemented
45C2×Q8×C29C2312yes—
46C2×D4×C29C2312yes—
47C2×C22⋊D29—42no—
48#90809—22no—
49#90809—22no—
50Q8×D29—22no—
51Q8×D29—22no—
52#90807—22no—
53#90807—22no—
54D4×D29—22no—
55D4×D29—22no—
56#90805—42no—
57#90805C2312yes—
58#90805C2311yescharacteristic
59#90805C2311yescharacteristic
60Q16×C29—21no—
61Q16×C29—21no—
62SD16×C29—22no—
63SD16×C29—22no—
64D8×C29—21no—
65D8×C29—21no—
66C2×C8×C29C2311yescharacteristic
67C2×C8×C29C2311yescharacteristic
68C22⋊C4×C29—42no—
69C42×C29C2311yescharacteristic
70#90785—22no—
71#90785—22no—
72#90784—22no—
73#90784—22no—
74#90783—22no—
75#90783—22no—
76#90782—22no—
77#90782—22no—
78#90777C2311yescharacteristic
79#90777C2312yes—
80#90777C2311yescharacteristic
81Dic116D411yescharacteristic
82Dic116D411yescharacteristic
83D232D411yescharacteristic
84D232D411yescharacteristic
85#90773D412yes—
86#90773D411yescharacteristic
87#90773D411yescharacteristic
88#90772—21no—
89#90772—21no—
90#90772—22no—
91C8×D29—21no—
92C8×D29—21no—
93C8×D29—22no—
94C23×C29—22no—
95C22×D29—42no—
96Q8×C29—22no—
97Q8×C29—22no—
98D4×C29—22no—
99D4×C29—22no—
100C2×C4×C29—21no—
101C2×C4×C29—22no—
102C2×C4×C29C2411yescharacteristic
103C22⋊D29—21no—
104C22⋊D29—22no—
105C22⋊D29—21no—
106C22⋊D29—42no—
107C22⋊D29—42no—
108C2×Dic29—42no—
109D116—42no—
110D116C2×D411yescharacteristic
111D116C2×D412yes—
112D116C2×D411yescharacteristic
113C4×D29—21no—
114C4×D29—22no—
115C4×D29—21no—
116C4×D29—42no—
117C4×D29—42no—
118Dic58—42no—
119Dic58C2×D411yescharacteristic
120Dic58C2×D412yes—
121Dic58C2×D411yescharacteristic
122C8×C29C2×D411yescharacteristic
123C8×C29C2×D411yescharacteristic
124C8×C29C2×D411yescharacteristic
125C8×C29C2×D411yescharacteristic
126#6597—21no—
127#6597—22no—
128#6597—21no—
129#3290—291nomaximal, Sylow
130C22×C29—42no—
131C22×C29—82no—
132C22×C29H(5,𝔽2)11yescharacteristic
133C2×D29—21no—
134C2×D29—22no—
135C2×D29—21no—
136C2×D29—162no—
137C4×C29—41no—
138C4×C29—42no—
139C4×C29C22×D411yescharacteristic
140C4×C29C22×D411yescharacteristic
141Dic29—21no—
142Dic29—22no—
143Dic29—21no—
144#578—291no—
145#577—292no—
146#576—291no—
147#495D2911yescharacteristic, complemented
148#473—291no—
149#472—291no—
150#471—292no—
151#455—292no—
152#454—292no—
153#443—291no—
154#443—291no—
155C2×C29—21no—
156C2×C29—82no—
157C2×C29D4211yescharacteristic
158D29—41no—
159D29—42no—
160D29—41no—
1612−1+4—292no—
162H(5,𝔽2)—292no—
163#137—292no—
164#137—292no—
165#137—582no—
166#137—582no—
167AGL(1,ℤ/8)—292no—
168AGL(1,ℤ/8)—292no—
169AGL(1,ℤ/8)—582no—
170AGL(1,ℤ/8)—582no—
171#135—291no—
172#135—291no—
173#135—581no—
174#135—581no—
175#135—582no—
176C2×Q16—581no—
177C2×Q16C2×D2911yescharacteristic, complemented
178C2×SD16—582no—
179C2×SD16C2×D2912yescomplemented
180C2×D8—581no—
181C2×D8C2×D2911yescharacteristic
182#131—291no—
183#131—292no—
184#131—291no—
185#124C2×D2912yescomplemented
186#108—291no—
187#108—291no—
188#104—291no—
189#104—291no—
190#104—292no—
191#101—292no—
192#100—292no—
193C4×C8C2×D2911yescharacteristic, complemented
194C29#329011yescharacteristic, complemented, Sylow
195#41—291no—
196#41—292no—
197#41—291no—
198#41—582no—
199#41—582no—
200#41—582no—
201#41—582no—
202#41—1162no—
203C2×Q8—582no—
204C2×Q8—582no—
205C2×Q8C22×D2912yes—
206C2×D4—582no—
207C2×D4—582no—
208C2×D4—1162no—
209C2×D4C22×D2912yes—
210Q16—21no—
211Q16—21no—
212Q16—291no—
213Q16—291no—
214Q16—582no—
215Q16—582no—
216SD16—22no—
217SD16—22no—
218SD16—291no—
219SD16—291no—
220SD16—292no—
221SD16—582no—
222SD16—582no—
223SD16—582no—
224SD16—582no—
225D8—21no—
226D8—21no—
227D8—291no—
228D8—291no—
229D8—582no—
230D8—582no—
231M16—291no—
232M16—292no—
233M16—291no—
234M16—581no—
235M16—582no—
236M16—581no—
237C2×C8—581no—
238C2×C8—582no—
239C2×C8—581no—
240C2×C8C22×D2911yescharacteristic
241C2×C8C22×D2911yescharacteristic
242C22⋊C4—42no—
243C42C22×D2911yescharacteristic
244C23—22no—
245C23—1162no—
246Q8—22no—
247Q8—22no—
248Q8—291no—
249Q8—292no—
250Q8—291no—
251Q8—1162no—
252D4—22no—
253D4—22no—
254D4—291no—
255D4—292no—
256D4—291no—
257D4—581no—
258D4—582no—
259D4—581no—
260D4—1162no—
261D4—1162no—
262D4—1162no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—581no—
266C2×C4—582no—
267C2×C4—581no—
268C2×C4—1162no—
269C2×C4—1162no—
270C2×C4—1162no—
271C2×C4C23×D2911yescharacteristic
272C8—581no—
273C8—582no—
274C8—581no—
275C8D4×D2911yescharacteristic
276C8D4×D2911yescharacteristic
277C8D4×D2911yescharacteristic
278C8D4×D2911yescharacteristic
279C22—42no—
280C22—82no—
281C22—581no—
282C22—582no—
283C22—581no—
284C22—4642no—
285C22#1174535911yescharacteristic
286C4—41no—
287C4—42no—
288C4—581no—
289C4—582no—
290C4—581no—
291C4C2×D4×D2911yescharacteristic
292C4C2×D4×D2911yescharacteristic
293C2—21no—
294C2—82no—
295C2—1161no—
296C2—1162no—
297C2—1161no—
298C2#1427179811yescharacteristic
subgroupG/H
centerC2#14271798
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#495C2
socleC2×C29D42
hypercenter#495D29
hypocenterC29#3290
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #14271976C2semidirect
2. #14271969C2semidirect
3. #14271964C2semidirect
4. #14271435C2semidirect
5. #14271430C2semidirect
6. #14271423C2semidirect
7. #14271340C2semidirect
8. #14271335C2semidirect
9. #14271281C2semidirect
10. #14271281C2semidirect
11. C29×#495C2semidirect
12. #11745362C22semidirect
14. C2×Q16×C29C22semidirect
15. C2×SD16×C29C22semidirect
17. C29×#124C22semidirect
19. #11745304C22semidirect
21. #11745294C22semidirect
35. #11745263C22semidirect
36. #11745263C22semidirect
37. C4×C8×C29C22semidirect
38. #11745184C22semidirect
39. #11745181C22semidirect
40. #11745167C22semidirect
41. #11745167C22semidirect
43. #11745153C22semidirect
44. #11745153C22semidirect
147. #495D29semidirect
177. C2×Q16C2×D29semidirect
179. C2×SD16C2×D29semidirect
185. #124C2×D29semidirect
193. C4×C8C2×D29semidirect
194. C29#3290semidirect

Maximal subgroups

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

subgroupindex
#142719762
#142719692
#142719642
#142714352
#142714302
#142714232
#142713402
#142713352
#142712812
C29×#4952
#329029