Finite Group Databasebeta

← D29×#450 #16828671

Subgroups — D29×#450 #16828671

Order 3712.

996 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C22×D4×D29C211yesmaximal, characteristic
2C2×SD16×D29C212yesmaximal, complemented
3C22⋊Q8×D29C211yesmaximal, characteristic, complemented
4#14271316C211yesmaximal, characteristic, complemented
5#14271315C212yesmaximal, complemented
6#14271314C211yesmaximal, characteristic, complemented
7#14271313C211yesmaximal, characteristic, complemented
8#14271312C212yesmaximal, complemented
9#102×D29C212yesmaximal, complemented
10C22⋊C8×D29C211yesmaximal, characteristic, complemented
11C29×#450C211yesmaximal, characteristic, complemented
12C24×D29—21no—
13C22×D4×C29C2211yescharacteristic
14C22×C22⋊D29—21no—
15C2×Q8×D29C2211yescharacteristic, complemented
16C2×D4×D29—28no—
17C2×D4×D29—21no—
18C2×D4×D29—21no—
19C2×D4×D29C2212yes—
20C2×D4×D29C2212yes—
21C22×D116C2211yescharacteristic
22C22×C4×D29C2211yescharacteristic
23C2×SD16×C29C2212yescomplemented
24C29×C22⋊Q8C2211yescharacteristic, complemented
25#11745308C2211yescharacteristic, complemented
26C2×#90784C2212yescomplemented
27C2×#90783C2212yescomplemented
28#11745286C2211yescharacteristic, complemented
29SD16×D29—28no—
30C2×#90773C2212yescomplemented
31C2×C8×D29C2212yescomplemented
32#11745259C2211yescharacteristic, complemented
33#11745258—21no—
34C4⋊C4×D29—21no—
35C4⋊C4×D29C2211yescharacteristic, complemented
36C22⋊C4×D29—21no—
37#11745240—21no—
38C29×#102C2212yescomplemented
39C29×C22⋊C8C2211yescharacteristic, complemented
40#11745180C2212yescomplemented
41C22⋊#6597C2211yescharacteristic, complemented
42#11745169C2212yescomplemented
43#11745168C2212yescomplemented
44#11745157C2212yescomplemented
45C24×C29—21no—
46C23×D29—28no—
47C23×D29—21no—
48C23×D29—22no—
49C23×D29—22no—
50C23×D29—44no—
51C23×D29—44no—
52C23×D29D411yescharacteristic
53C2×Q8×C29C2311yescharacteristic, complemented
54C2×D4×C29—24no—
55C2×D4×C29—21no—
56C2×D4×C29C2312yes—
57C22×C4×C29C2311yescharacteristic
58C2×C22⋊D29—28no—
59C2×C22⋊D29—22no—
60C2×C22⋊D29—22no—
61C22×Dic29D411yescharacteristic
62Q8×D29—24no—
63D4×D29—28no—
64D4×D29—28no—
65D4×D29—24no—
66D4×D29—24no—
67D4×D29—24no—
68D4×D29D418yes—
69C2×D116—21no—
70C2×D116—24no—
71C2×D116C2312yes—
72C2×C4×D29—24no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29D411yescharacteristic
76C2×C4×D29D411yescharacteristic
77C2×C4×D29C2311yescharacteristic
78C2×C4×D29C2311yescharacteristic
79C2×Dic58—21no—
80C2×Dic58C2311yescharacteristic, complemented
81SD16×C29—24no—
82C2×C8×C29C2312yescomplemented
83C4⋊C4×C29—21no—
84C4⋊C4×C29C2311yescharacteristic, complemented
85C22⋊C4×C29—21no—
86C22⋊Dic29—21no—
87#90784—24no—
88#90783—24no—
89#90781—21no—
90#90781—21no—
91C4⋊Dic29—21no—
92C4⋊Dic29C2311yescharacteristic, complemented
93#90779—21no—
94#90779—21no—
95#90779—21no—
96C2×#6597C2312yescomplemented
97#90773—24no—
98C8×D29—24no—
99C23×C29—24no—
100C23×C29—22no—
101C23×C29—42no—
102C23×C29—42no—
103C23×C29C2×D411yescharacteristic
104C22×D29—22no—
105C22×D29—22no—
106C22×D29—24no—
107C22×D29—28no—
108C22×D29—22no—
109C22×D29—28no—
110C22×D29—44no—
111C22×D29—432no—
112C22×D29—42no—
113C22×D29—42no—
114C22×D29—44no—
115C22×D29—44no—
116C22×D29—44no—
117C22×D29SD1614yescomplemented
118C22×D29C2×D411yescharacteristic
119C22×D29C2×D411yescharacteristic
120Q8×C29—22no—
121D4×C29—24no—
122D4×C29—22no—
123D4×C29C2×D414yes—
124C2×C4×C29—22no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2411yescharacteristic
129C22⋊D29—28no—
130C22⋊D29—28no—
131C2×Dic29—22no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136D116—24no—
137D116—22no—
138D116C2×D414yes—
139C4×D29—22no—
140C4×D29—22no—
141C4×D29—22no—
142C4×D29—42no—
143C4×D29—42no—
144C4×D29C2×D414yes—
145Dic58—22no—
146Dic58—42no—
147C8×C29—22no—
148#6597—22no—
149C2×#450—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—24no—
153C22×C29—48no—
154C22×C29—42no—
155C22×C29—42no—
156C22×C29C2×SD1612yescomplemented
157C22×C29C22×D411yescharacteristic
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—28no—
161C2×D29—24no—
162C2×D29—416no—
163C2×D29—48no—
164C2×D29—42no—
165C2×D29—42no—
166C2×D29—416no—
167C2×D29#12012yes—
168C2×D29C2×SD1612yes—
169C2×D29C2×SD1612yescomplemented
170C2×D29AGL(1,ℤ/8)12yes—
171C4×C29—21no—
172C4×C29—41no—
173C4×C29—41no—
174C4×C29C22×D412yes—
175Dic29—21no—
176Dic29—41no—
177Dic29—41no—
178Dic29#12012yes—
179C23×D4—291no—
180C22×SD16—292no—
181C2×C22⋊Q8—291no—
182#450—291no—
183#450—292no—
184#450—291no—
185#450—292no—
186#450—291no—
187#450D2911yescharacteristic, direct product factor
188C2×#102—292no—
189C2×C22⋊C8—291no—
190C2×C29—22no—
191C2×C29—44no—
192C2×C29C2×#12011yescharacteristic
193C2×C29C22×SD1611yescharacteristic
194C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
195D29—22no—
196D29—44no—
197D29#45014yesdirect product factor
198C25—581no—
199C22×Q8—291no—
200C22×D4—292no—
201C22×D4—292no—
202C22×D4—291no—
203C22×D4—581no—
204C22×D4—581no—
205C22×D4—581no—
206C22×D4—588no—
207C22×D4C2×D2911yescharacteristic
208C23×C4—291no—
209C2×SD16—292no—
210C2×SD16—292no—
211C2×SD16—292no—
212C2×SD16—588no—
213C2×SD16C2×D2912yescomplemented
214C22×C8—292no—
215C22⋊Q8—291no—
216C22⋊Q8—291no—
217C22⋊Q8—291no—
218C22⋊Q8—581no—
219C22⋊Q8—581no—
220C22⋊Q8C2×D2911yescharacteristic, complemented
221C2×C4⋊C4—291no—
222C2×C4⋊C4—581no—
223C2×C22⋊C4—581no—
224#102—292no—
225#102—292no—
226#102—292no—
227#102C2×D2912yescomplemented
228C22⋊C8—291no—
229C22⋊C8—292no—
230C22⋊C8C2×D2911yescharacteristic, complemented
231C29C2×#45011yescharacteristic, complemented, Sylow
232C24—21no—
233C24—291no—
234C24—582no—
235C24—582no—
236C24—588no—
237C24—581no—
238C24—1164no—
239C24—1164no—
240C2×Q8—291no—
241C2×Q8—581no—
242C2×Q8—584no—
243C2×Q8C22×D2911yescharacteristic, complemented
244C2×D4—24no—
245C2×D4—21no—
246C2×D4—298no—
247C2×D4—292no—
248C2×D4—584no—
249C2×D4—584no—
250C2×D4—582no—
251C2×D4—582no—
252C2×D4—584no—
253C2×D4—588no—
254C2×D4—588no—
255C2×D4—588no—
256C2×D4—584no—
257C2×D4—581no—
258C2×D4C22×D2912yes—
259C22×C4—291no—
260C22×C4—291no—
261C22×C4—291no—
262C22×C4—291no—
263C22×C4—291no—
264C22×C4—584no—
265C22×C4—581no—
266C22×C4—581no—
267C22×C4C22×D2911yescharacteristic
268SD16—24no—
269SD16—584no—
270SD16—584no—
271SD16—584no—
272C2×C8—292no—
273C2×C8—584no—
274C2×C8C22×D2912yescomplemented
275C4⋊C4—21no—
276C4⋊C4—291no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4C22×D2911yescharacteristic, complemented
282C22⋊C4—21no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C23—24no—
287C23—22no—
288C23—42no—
289C23—42no—
290C23—291no—
291C23—291no—
292C23—294no—
293C23—582no—
294C23—582no—
295C23—588no—
296C23—584no—
297C23—588no—
298C23—582no—
299C23—1162no—
300C23—1164no—
301C23—1164no—
302C23—1164no—
303C23—11632no—
304C23—1164no—
305C23—1162no—
306C23D4×D2911yescharacteristic
307Q8—22no—
308Q8—582no—
309Q8—1162no—
310D4—24no—
311D4—22no—
312D4—294no—
313D4—584no—
314D4—588no—
315D4—588no—
316D4—582no—
317D4D4×D2914yes—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—291no—
322C2×C4—294no—
323C2×C4—291no—
324C2×C4—582no—
325C2×C4—582no—
326C2×C4—582no—
327C2×C4—582no—
328C2×C4—581no—
329C2×C4—581no—
330C2×C4—1162no—
331C2×C4—1162no—
332C2×C4D4×D2911yescharacteristic
333C2×C4C23×D2911yescharacteristic
334C8—22no—
335C8—582no—
336C22—21no—
337C22—21no—
338C22—24no—
339C22—48no—
340C22—42no—
341C22—42no—
342C22—292no—
343C22—292no—
344C22—292no—
345C22—292no—
346C22—588no—
347C22—581no—
348C22—581no—
349C22—584no—
350C22—1168no—
351C22—11616no—
352C22—11616no—
353C22—1162no—
354C22—1162no—
355C22SD16×D2912yescomplemented
356C22C2×D4×D2911yescharacteristic
357C4—21no—
358C4—41no—
359C4—41no—
360C4—292no—
361C4—581no—
362C4—1161no—
363C4—1161no—
364C4C2×D4×D2912yes—
365C2—22no—
366C2—44no—
367C2—294no—
368C2—582no—
369C2—1164no—
370C2#120×D2911yescharacteristic
371C2C2×SD16×D2911yescharacteristic
372C2AGL(1,ℤ/8)×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#450C2
socleC22×C29C22×D4
prime radicalC22×D4×D29C2
hypercenter#450D29
hypocenterC29C2×#450
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. C2×SD16×D29C2semidirect
3. C22⋊Q8×D29C2semidirect
4. #14271316C2semidirect
5. #14271315C2semidirect
6. #14271314C2semidirect
7. #14271313C2semidirect
8. #14271312C2semidirect
9. #102×D29C2semidirect
10. C22⋊C8×D29C2semidirect
11. C29×#450C2semidirect
15. C2×Q8×D29C22semidirect
23. C2×SD16×C29C22semidirect
24. C29×C22⋊Q8C22semidirect
25. #11745308C22semidirect
26. C2×#90784C22semidirect
27. C2×#90783C22semidirect
28. #11745286C22semidirect
30. C2×#90773C22semidirect
31. C2×C8×D29C22semidirect
32. #11745259C22semidirect
35. C4⋊C4×D29C22semidirect
38. C29×#102C22semidirect
39. C29×C22⋊C8C22semidirect
40. #11745180C22semidirect
41. C22⋊#6597C22semidirect
42. #11745169C22semidirect
43. #11745168C22semidirect
44. #11745157C22semidirect
53. C2×Q8×C29C23semidirect
80. C2×Dic58C23semidirect
82. C2×C8×C29C23semidirect
84. C4⋊C4×C29C23semidirect
92. C4⋊Dic29C23semidirect
96. C2×#6597C23semidirect
117. C22×D29SD16semidirect
156. C22×C29C2×SD16semidirect
169. C2×D29C2×SD16semidirect
187. #450D29direct (N × H)
197. D29#450direct (N × H)
213. C2×SD16C2×D29semidirect
220. C22⋊Q8C2×D29semidirect
227. #102C2×D29semidirect
230. C22⋊C8C2×D29semidirect
231. C29C2×#450semidirect
243. C2×Q8C22×D29semidirect
274. C2×C8C22×D29semidirect
281. C4⋊C4C22×D29semidirect
355. C22SD16×D29semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D292
C2×SD16×D292
C22⋊Q8×D292
#142713162
#142713152
#142713142
#142713132
#142713122
#102×D292
C22⋊C8×D292
C29×#4502
C2×#45029