Finite Group Databasebeta

← #16829959

Subgroups — #16829959

Order 3712.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745304C211yesmaximal, characteristic, complemented
2C2×#11745270C211yesmaximal, characteristic, complemented
3C2×#11745311C211yesmaximal, characteristic, complemented
4#14271709C211yesmaximal, characteristic, complemented
5C2×#11745309C211yesmaximal, characteristic, complemented
6#14271556C212yesmaximal, complemented
7#14271549C212yesmaximal, complemented
8#14271548C212yesmaximal, complemented
9#14271544C212yesmaximal, complemented
10M16×Dic29C211yesmaximal, characteristic, complemented
11C2×C29×#137C211yesmaximal, characteristic, complemented
12C2×#41×C29C2211yescharacteristic
13C22×Q8×C29C2211yescharacteristic
14C2×#90805C2211yescharacteristic
15C22×D116C2211yescharacteristic
16C29×#137—24no—
17C2×Q16×C29C2212yescomplemented
18C2×SD16×C29C2212yescomplemented
19C2×M16×C29C2211yescharacteristic
20#11745311—24no—
21#11745309—22no—
22#11745309C2212yes—
23#11745309C2212yes—
24#11745309C2211yescharacteristic, complemented
25#11745306C2211yescharacteristic, complemented
26C2×#90785C2212yescomplemented
27#11745304—24no—
28C2×#90784C2212yes—
29C2×#90784C2212yescomplemented
30#11745302C2211yescharacteristic, complemented
31#11745301—22no—
32#11745298C2211yescharacteristic, complemented
33C2×#90782C2212yes—
34C4×C22⋊D29—22no—
35C2×#90781—22no—
36C2×C4×Dic29C2211yescharacteristic
37C2×#90777C2211yescharacteristic
38#11745270—24no—
39C2×D232C2212yes—
40C2×#90773C2212yes—
41#11745163C2212yescomplemented
42C8×Dic29C2212yescomplemented
43C23×D29—21no—
44#41×C29—22no—
45#41×C29—22no—
46C2×Q8×C29—21no—
47C2×Q8×C29—22no—
48C2×Q8×C29—22no—
49C2×Q8×C29C2311yescharacteristic
50C2×Q8×C29C2312yes—
51C2×D4×C29—21no—
52C2×D4×C29C2311yescharacteristic
53C22×C4×C29—21no—
54C22×C4×C29—21no—
55C22×C4×C29C2311yescharacteristic
56C2×C22⋊D29—21no—
57C2×C22⋊D29—22no—
58C22×Dic29D412yes—
59#90805—22no—
60#90805—22no—
61C2×D116—22no—
62C2×D116—22no—
63C2×D116—21no—
64C2×D116C2312yes—
65C2×D116C2311yescharacteristic
66C2×C4×D29—21no—
67C2×Dic58C2311yescharacteristic
68Q16×C29—24no—
69SD16×C29—24no—
70M16×C29D414yescomplemented
71C2×C8×C29C2312yes—
72C22⋊Dic29—22no—
73#90785—24no—
74#90784—24no—
75#90784—24no—
76#90782—24no—
77#90781—24no—
78#90781—24no—
79#90781—22no—
80#90779—22no—
81C4×Dic29D412yes—
82C4×Dic29C2311yescharacteristic
83C4×Dic29C2311yescharacteristic
84#90777D414yescomplemented
85C2×#6597C2312yes—
86D232—24no—
87#90773—24no—
88C23×C29—21no—
89C23×C29C2×D411yescharacteristic
90C22×D29—22no—
91C22×D29—21no—
92C22×D29—44no—
93C22×D29—42no—
94Q8×C29—21no—
95Q8×C29—22no—
96Q8×C29—22no—
97Q8×C29—21no—
98Q8×C29—42no—
99D4×C29—21no—
100D4×C29—21no—
101D4×C29—42no—
102C2×C4×C29—21no—
103C2×C4×C29—22no—
104C2×C4×C29—42no—
105C2×C4×C29—42no—
106C2×C4×C29C2×D411yescharacteristic
107C2×C4×C29C2×D412yes—
108C2×C4×C29C2×D412yes—
109C2×C4×C29C2411yescharacteristic
110C22⋊D29—44no—
111C22⋊D29—42no—
112C2×Dic29—21no—
113C2×Dic29—42no—
114C2×Dic29C2×D412yes—
115C2×Dic29C2×D412yes—
116D116—22no—
117D116—21no—
118D116—22no—
119D116—21no—
120D116—42no—
121C4×D29—42no—
122Dic58—21no—
123Dic58—21no—
124C8×C29C2×D414yes—
125#6597C2×D414yes—
126#3153—291nomaximal, Sylow
127C22×C29—22no—
128C22×C29—41no—
129C22×C29—42no—
130C22×C29#12712yes—
131C22×C29C22×D411yescharacteristic
132C2×D29—41no—
133C2×D29—42no—
134C2×D29—42no—
135C2×D29—44no—
136C2×D29—84no—
137C4×C29—41no—
138C4×C29—42no—
139C4×C29#12712yes—
140C4×C29C22×D411yescharacteristic
141C4×C29C22×D411yescharacteristic
142Dic29—22no—
143Dic29—22no—
144Dic29—41no—
145C2×#137—291no—
146C2×#137D2911yescharacteristic, complemented
147C2×AGL(1,ℤ/8)—291no—
148C2×AGL(1,ℤ/8)—291no—
149#532—291no—
150C2×#124—291no—
151#497—292no—
152#496—292no—
153#495—292no—
154#495—292no—
155C4×M16—291no—
156C2×C29—22no—
157C2×C29—81no—
158C2×C29C2×#12711yescharacteristic
159C2×C29#57512yes—
160D29—81no—
161D29—82no—
162C2×#41—291no—
163C2×#41C2×D2911yescharacteristic
164C22×Q8C2×D2911yescharacteristic
165C22×D4—291no—
166#137—24no—
167#137—584no—
168AGL(1,ℤ/8)—584no—
169AGL(1,ℤ/8)—584no—
170C2×Q16—292no—
171C2×Q16C2×D2912yescomplemented
172C2×SD16—292no—
173C2×SD16—292no—
174C2×SD16—292no—
175C2×SD16C2×D2912yescomplemented
176C2×D8—292no—
177C2×D8—292no—
178C2×M16—291no—
179C2×M16C2×D2911yescharacteristic
180C4⋊Q8—291no—
181#127—291no—
182#124—292no—
183#124—292no—
184#124—291no—
185#124—291no—
186#124—582no—
187#121—582no—
188C4×D4—582no—
189C2×C22⋊C4—582no—
190C2×C42—291no—
191#97—292no—
192C4×C8—292no—
193C29#315311yescharacteristic, complemented, Sylow
194C24—581no—
195#41—22no—
196#41—22no—
197#41—582no—
198#41—582no—
199C2×Q8—21no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—291no—
203C2×Q8C22×D2912yes—
204C2×Q8C22×D2911yescharacteristic
205C2×D4—21no—
206C2×D4—292no—
207C2×D4—291no—
208C2×D4—582no—
209C2×D4—581no—
210C2×D4—582no—
211C2×D4—581no—
212C2×D4—582no—
213C2×D4C22×D2911yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—292no—
217C22×C4—581no—
218C22×C4C22×D2911yescharacteristic
219Q16—24no—
220Q16—584no—
221SD16—24no—
222SD16—584no—
223SD16—584no—
224SD16—584no—
225D8—584no—
226D8—584no—
227M16—294no—
228M16C22⋊D2914yescomplemented
229C2×C8—292no—
230C2×C8C22×D2912yes—
231C4⋊C4—582no—
232C22⋊C4—584no—
233C22⋊C4—584no—
234C22⋊C4—582no—
235C22⋊C4—582no—
236C42—292no—
237C42—291no—
238C42—291no—
239C23—21no—
240C23—582no—
241C23—581no—
242C23—1164no—
243C23—1162no—
244C23D4×D2911yescharacteristic
245Q8—21no—
246Q8—22no—
247Q8—22no—
248Q8—21no—
249Q8—42no—
250Q8—581no—
251Q8—581no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—582no—
256D4—581no—
257D4—581no—
258D4—582no—
259D4—1164no—
260D4—1162no—
261D4—1162no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—292no—
267C2×C4—292no—
268C2×C4—581no—
269C2×C4—1162no—
270C2×C4—1162no—
271C2×C4D4×D2911yescharacteristic
272C2×C4D4×D2912yes—
273C2×C4C2×C22⋊D2912yes—
274C2×C4C23×D2911yescharacteristic
275C8—294no—
276C8C2×C22⋊D2914yes—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—1161no—
281C22—1162no—
282C22—1162no—
283C22—1164no—
284C22—2324no—
285C22#1174530212yes—
286C22C2×D4×D2911yescharacteristic
287C4—41no—
288C4—42no—
289C4—582no—
290C4—582no—
291C4—1161no—
292C4#1174530212yes—
293C4C2×D4×D2911yescharacteristic
294C4C22×C22⋊D2911yescharacteristic
295C2—22no—
296C2—81no—
297C2—2322no—
298C2—2321no—
299C2C2×#1174530211yescharacteristic
300C2#1427196212yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#137C2
socleC22×C29C22×D4
hypercenterC2×#137D29
hypocenterC29#3153
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#11745304C2semidirect
2. C2×#11745270C2semidirect
3. C2×#11745311C2semidirect
4. #14271709C2semidirect
5. C2×#11745309C2semidirect
6. #14271556C2semidirect
7. #14271549C2semidirect
8. #14271548C2semidirect
9. #14271544C2semidirect
10. M16×Dic29C2semidirect
11. C2×C29×#137C2semidirect
17. C2×Q16×C29C22semidirect
18. C2×SD16×C29C22semidirect
24. #11745309C22semidirect
25. #11745306C22semidirect
26. C2×#90785C22semidirect
29. C2×#90784C22semidirect
30. #11745302C22semidirect
32. #11745298C22semidirect
41. #11745163C22semidirect
42. C8×Dic29C22semidirect
70. M16×C29D4semidirect
84. #90777D4semidirect
146. C2×#137D29semidirect
171. C2×Q16C2×D29semidirect
175. C2×SD16C2×D29semidirect
193. C29#3153semidirect
228. M16C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117453042
C2×#117452702
C2×#117453112
#142717092
C2×#117453092
#142715562
#142715492
#142715482
#142715442
M16×Dic292
C2×C29×#1372
#315329