Finite Group Databasebeta

← #16829105

Subgroups — #16829105

Order 3712.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D29C211yesmaximal, characteristic, complemented
2#14271670C211yesmaximal, characteristic, complemented
3C2×#11745300C211yesmaximal, characteristic, complemented
4#14271413C212yesmaximal, complemented
5#14271406C212yesmaximal, complemented
6#14271396C212yesmaximal, complemented
7#14271389C212yesmaximal, complemented
8#14271205C211yesmaximal, characteristic, complemented
9#14271168C211yesmaximal, characteristic, complemented
10#14271164C211yesmaximal, characteristic, complemented
11C2×C29×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
12C2×#41×C29C2211yescharacteristic
13C22×D4×C29C2211yescharacteristic
14C22×C22⋊D29—21no—
15C22×C4×D29C2211yescharacteristic
16C29×AGL(1,ℤ/8)—24no—
17C2×SD16×C29C2212yescomplemented
18C2×D8×C29C2212yescomplemented
19C2×M16×C29C2211yescharacteristic
20C2×C22⋊Dic29—21no—
21#11745308C2211yescharacteristic, complemented
22#11745308C2211yescharacteristic, complemented
23#11745300—21no—
24#11745300—21no—
25#11745300C2212yes—
26#11745300C2212yes—
27#11745300C2211yescharacteristic, complemented
28#11745300C2211yescharacteristic, complemented
29#11745299—21no—
30#11745297—21no—
31C4×C22⋊D29—21no—
32C4×C22⋊D29—21no—
33#11745288C2211yescharacteristic
34C2×C4⋊Dic29C2211yescharacteristic
35C2×#90777C2211yescharacteristic
36M16×D29—24no—
37C2×#90772C2212yescomplemented
38C2×C8×D29C2212yescomplemented
39#11745183C2212yescomplemented
40#11745180C2212yescomplemented
41#11745180C2212yescomplemented
42#11745180C2212yescomplemented
43#11745166C2212yescomplemented
44#11745165C2212yescomplemented
45C24×C29—21no—
46C23×D29D411yescharacteristic
47#41×C29—22no—
48#41×C29—22no—
49C2×Q8×C29C2311yescharacteristic
50C2×D4×C29—21no—
51C2×D4×C29—22no—
52C2×D4×C29—21no—
53C2×D4×C29—22no—
54C2×D4×C29C2312yes—
55C2×D4×C29C2311yescharacteristic
56C22×C4×C29—21no—
57C22×C4×C29C2311yescharacteristic
58C2×C22⋊D29—21no—
59C2×C22⋊D29—21no—
60C2×C22⋊D29—22no—
61C2×C22⋊D29—22no—
62C2×C22⋊D29—44no—
63C22×Dic29—21no—
64C22×Dic29D411yescharacteristic
65C2×C4×D29—22no—
66C2×C4×D29—22no—
67C2×C4×D29D411yescharacteristic
68C2×C4×D29D411yescharacteristic
69C2×C4×D29C2311yescharacteristic
70C2×C4×D29C2311yescharacteristic
71SD16×C29—24no—
72D8×C29—24no—
73M16×C29D414yescomplemented
74C2×C8×C29C2312yes—
75C22⋊Dic29—21no—
76C22⋊Dic29—21no—
77C22⋊Dic29—21no—
78C22⋊Dic29—22no—
79C22⋊Dic29—22no—
80#90781—21no—
81#90781—21no—
82C4⋊Dic29—21no—
83C4⋊Dic29C2312yes—
84C4⋊Dic29C2311yescharacteristic
85C4⋊Dic29C2311yescharacteristic
86#90779—21no—
87#90779—21no—
88C4×Dic29—21no—
89#90777—22no—
90C2×#6597C2312yes—
91#90772—24no—
92C8×D29—24no—
93C23×C29—21no—
94C23×C29—22no—
95C23×C29—42no—
96C23×C29—42no—
97C23×C29—42no—
98C23×C29C2×D411yescharacteristic
99C22×D29—22no—
100C22×D29—22no—
101C22×D29—41no—
102C22×D29C2×D411yescharacteristic
103C22×D29C2×D411yescharacteristic
104Q8×C29—21no—
105Q8×C29—21no—
106D4×C29—21no—
107D4×C29—22no—
108D4×C29—22no—
109D4×C29—21no—
110D4×C29—42no—
111D4×C29—42no—
112C2×C4×C29—21no—
113C2×C4×C29—42no—
114C2×C4×C29C2×D411yescharacteristic
115C2×C4×C29C2×D412yes—
116C2×C4×C29#4112yes—
117C2×C4×C29C2411yescharacteristic
118C22⋊D29—42no—
119C22⋊D29—44no—
120C22⋊D29—42no—
121C22⋊D29—44no—
122C2×Dic29—22no—
123C2×Dic29—21no—
124C2×Dic29—21no—
125C2×Dic29—22no—
126C2×Dic29—42no—
127C2×Dic29C2×D411yescharacteristic
128C2×Dic29C2×D411yescharacteristic
129C4×D29—22no—
130C4×D29—22no—
131C4×D29—21no—
132C4×D29—21no—
133C4×D29—21no—
134C4×D29—21no—
135C8×C29C2×D414yescomplemented
136#6597—22no—
137#3055—291nomaximal, Sylow
138C22×C29—21no—
139C22×C29—21no—
140C22×C29—41no—
141C22×C29—42no—
142C22×C29—42no—
143C22×C29—41no—
144C22×C29—41no—
145C22×C29—42no—
146C22×C29—84no—
147C22×C29#12112yes—
148C22×C29C22×D411yescharacteristic
149C2×D29—21no—
150C2×D29—21no—
151C2×D29—21no—
152C2×D29—21no—
153C2×D29—21no—
154C2×D29—44no—
155C2×D29AGL(1,ℤ/8)12yescomplemented
156C4×C29—41no—
157C4×C29#12112yes—
158C4×C29C22×D411yescharacteristic
159C4×C29C2×#4111yescharacteristic
160Dic29—21no—
161Dic29—21no—
162Dic29—42no—
163Dic29—41no—
164Dic29—41no—
165C2×AGL(1,ℤ/8)D2911yescharacteristic, complemented
166C22×M16—291no—
167#525—291no—
168C2×#121—291no—
169#469—292no—
170#468—292no—
171#466—292no—
172#465—292no—
173#428—291no—
174#418—291no—
175#417—291no—
176C2×C29—22no—
177C2×C29—81no—
178C2×C29—82no—
179C2×C29C2×#12111yescharacteristic
180C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C29#57511yescharacteristic
182D29—22no—
183D29—41no—
184C2×#41C2×D2911yescharacteristic
185C22×D4—581no—
186C22×D4C2×D2911yescharacteristic
187C23×C4—291no—
188AGL(1,ℤ/8)—24no—
189C2×SD16C2×D2912yescomplemented
190C2×D8C2×D2912yescomplemented
191C2×M16—291no—
192C2×M16—292no—
193C2×M16—584no—
194C2×M16C2×D2911yescharacteristic
195C22×C8—292no—
196#123—581no—
197C22⋊Q8—291no—
198C22⋊Q8—291no—
199#121—292no—
200#121—292no—
201#121—291no—
202#121—291no—
203#121—581no—
204#121—581no—
205#120—581no—
206C4×D4—581no—
207C4×D4—581no—
208#117—291no—
209C2×C4⋊C4—291no—
210C2×C22⋊C4—581no—
211#107—292no—
212#106—292no—
213#103—292no—
214#102—292no—
215#102—292no—
216#102—292no—
217C29#305511yescharacteristic, complemented, Sylow
218C24—21no—
219C24—291no—
220#41—22no—
221#41—22no—
222C2×Q8C22×D2911yescharacteristic
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—581no—
228C2×D4—581no—
229C2×D4—582no—
230C2×D4—582no—
231C2×D4—1164no—
232C2×D4C22×D2911yescharacteristic
233C2×D4C22×D2912yes—
234C22×C4—21no—
235C22×C4—291no—
236C22×C4—291no—
237C22×C4—291no—
238C22×C4—291no—
239C22×C4—291no—
240C22×C4—582no—
241C22×C4—582no—
242C22×C4—581no—
243C22×C4C22×D2911yescharacteristic
244SD16—24no—
245D8—24no—
246M16—582no—
247M16—584no—
248M16C22⋊D2914yescomplemented
249C2×C8—292no—
250C2×C8—584no—
251C2×C8C22×D2912yes—
252C4⋊C4—291no—
253C4⋊C4—291no—
254C4⋊C4—292no—
255C4⋊C4—581no—
256C4⋊C4—581no—
257C4⋊C4—581no—
258C22⋊C4—581no—
259C22⋊C4—581no—
260C22⋊C4—582no—
261C22⋊C4—582no—
262C22⋊C4—581no—
263C22⋊C4—581no—
264C22⋊C4—581no—
265C42—581no—
266C23—21no—
267C23—22no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—291no—
272C23—291no—
273C23—582no—
274C23—582no—
275C23—1161no—
276C23D4×D2911yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—22no—
280D4—21no—
281D4—21no—
282D4—22no—
283D4—42no—
284D4—42no—
285D4—1164no—
286D4—1162no—
287D4—1164no—
288D4—1162no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—291no—
292C2×C4—291no—
293C2×C4—582no—
294C2×C4—582no—
295C2×C4—582no—
296C2×C4—581no—
297C2×C4—581no—
298C2×C4—581no—
299C2×C4—581no—
300C2×C4—581no—
301C2×C4—581no—
302C2×C4—582no—
303C2×C4—1162no—
304C2×C4D4×D2911yescharacteristic
305C2×C4#9080712yes—
306C2×C4C2×C22⋊D2912yes—
307C2×C4C23×D2911yescharacteristic
308C8—582no—
309C8C2×C22⋊D2914yescomplemented
310C22—21no—
311C22—21no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—42no—
318C22—84no—
319C22—292no—
320C22—581no—
321C22—581no—
322C22—581no—
323C22—581no—
324C22—581no—
325C22—1164no—
326C22#1174530012yes—
327C22C2×D4×D2911yescharacteristic
328C4—41no—
329C4—581no—
330C4—581no—
331C4—1162no—
332C4—1161no—
333C4—1161no—
334C4#1174530012yes—
335C4C2×#9080711yescharacteristic
336C4C22×C22⋊D2911yescharacteristic
337C2—22no—
338C2—82no—
339C2—81no—
340C2—582no—
341C2—1161no—
342C2C2×#1174530011yescharacteristic
343C2AGL(1,ℤ/8)×D2911yescharacteristic
344C2#1427195911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×AGL(1,ℤ/8)C2
socleC22×C29C22×D4
hypercenterC2×AGL(1,ℤ/8)D29
hypocenterC29#3055
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×M16×D29C2semidirect
2. #14271670C2semidirect
3. C2×#11745300C2semidirect
4. #14271413C2semidirect
5. #14271406C2semidirect
6. #14271396C2semidirect
7. #14271389C2semidirect
8. #14271205C2semidirect
9. #14271168C2semidirect
10. #14271164C2semidirect
11. C2×C29×AGL(1,ℤ/8)C2semidirect
17. C2×SD16×C29C22semidirect
18. C2×D8×C29C22semidirect
21. #11745308C22semidirect
22. #11745308C22semidirect
27. #11745300C22semidirect
28. #11745300C22semidirect
37. C2×#90772C22semidirect
38. C2×C8×D29C22semidirect
39. #11745183C22semidirect
40. #11745180C22semidirect
41. #11745180C22semidirect
42. #11745180C22semidirect
43. #11745166C22semidirect
44. #11745165C22semidirect
73. M16×C29D4semidirect
135. C8×C29C2×D4semidirect
155. C2×D29AGL(1,ℤ/8)semidirect
165. C2×AGL(1,ℤ/8)D29semidirect
189. C2×SD16C2×D29semidirect
190. C2×D8C2×D29semidirect
217. C29#3055semidirect
248. M16C22⋊D29semidirect
309. C8C2×C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D292
#142716702
C2×#117453002
#142714132
#142714062
#142713962
#142713892
#142712052
#142711682
#142711642
C2×C29×AGL(1,ℤ/8)2
#305529