Finite Group Databasebeta

← D29×#447 #16828665

Subgroups — D29×#447 #16828665

Order 3712.

1048 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 1048 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, complemented
2C2×D8×D29C212yesmaximal, complemented
3#121×D29C211yesmaximal, characteristic, complemented
4#14271299C211yesmaximal, characteristic, complemented
5#14271298C212yesmaximal, complemented
6#14271297C211yesmaximal, characteristic, complemented
7#14271296C211yesmaximal, characteristic, complemented
8#14271295C212yesmaximal, complemented
9#102×D29C212yesmaximal, complemented
10C22⋊C8×D29C211yesmaximal, characteristic, complemented
11C29×#447C211yesmaximal, characteristic, complemented
12C24×D29—21no—
13C22×D4×C29C2211yescharacteristic, complemented
14C22×C22⋊D29—21no—
15C2×D4×D29—28no—
16C2×D4×D29—21no—
17C2×D4×D29—21no—
18C2×D4×D29—21no—
19C2×D4×D29C2212yes—
20C2×D4×D29C2212yescomplemented
21C2×D4×D29C2211yescharacteristic, complemented
22C22×D116C2211yescharacteristic, complemented
23C22×C4×D29C2211yescharacteristic
24C2×D8×C29C2212yescomplemented
25C29×#121C2211yescharacteristic, complemented
26#11745301—21no—
27#11745300C2211yescharacteristic, complemented
28C2×#90782C2212yescomplemented
29C2×#90782C2212yescomplemented
30#11745292C2211yescharacteristic, complemented
31D8×D29—28no—
32C2×D232C2212yescomplemented
33C2×C8×D29C2212yescomplemented
34#11745257C2211yescharacteristic, complemented
35C4⋊C4×D29C2211yescharacteristic, complemented
36#11745246—21no—
37C22⋊C4×D29—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—21no—
51C23×D29—44no—
52C23×D29—44no—
53C23×D29D411yescharacteristic
54C2×D4×C29—24no—
55C2×D4×C29—21no—
56C2×D4×C29—21no—
57C2×D4×C29C2312yes—
58C2×D4×C29C2311yescharacteristic, complemented
59C22×C4×C29C2311yescharacteristic
60C2×C22⋊D29—28no—
61C2×C22⋊D29—21no—
62C2×C22⋊D29—21no—
63C2×C22⋊D29—22no—
64C2×C22⋊D29—22no—
65C2×C22⋊D29—21no—
66C22×Dic29D411yescharacteristic
67D4×D29—28no—
68D4×D29—28no—
69D4×D29—24no—
70D4×D29—24no—
71D4×D29—24no—
72D4×D29—24no—
73D4×D29—44no—
74D4×D29D418yescomplemented
75C2×D116—21no—
76C2×D116—24no—
77C2×D116—21no—
78C2×D116C2312yes—
79C2×D116C2311yescharacteristic, complemented
80C2×C4×D29—24no—
81C2×C4×D29—21no—
82C2×C4×D29D411yescharacteristic
83C2×C4×D29D411yescharacteristic
84C2×C4×D29C2311yescharacteristic
85C2×C4×D29C2311yescharacteristic
86D8×C29—24no—
87C2×C8×C29C2312yescomplemented
88C4⋊C4×C29C2311yescharacteristic, complemented
89C22⋊C4×C29—21no—
90C22⋊Dic29—21no—
91#90782—24no—
92#90782—24no—
93#90781—21no—
94#90781—21no—
95C4⋊Dic29C2311yescharacteristic, complemented
96#90779—21no—
97C2×#6597C2312yescomplemented
98D232—24no—
99C8×D29—24no—
100C23×C29—24no—
101C23×C29—22no—
102C23×C29—21no—
103C23×C29—42no—
104C23×C29—42no—
105C23×C29C2×D411yescharacteristic
106C22×D29—22no—
107C22×D29—22no—
108C22×D29—24no—
109C22×D29—28no—
110C22×D29—22no—
111C22×D29—28no—
112C22×D29—21no—
113C22×D29—44no—
114C22×D29—432no—
115C22×D29—42no—
116C22×D29—42no—
117C22×D29—44no—
118C22×D29—44no—
119C22×D29—44no—
120C22×D29—42no—
121C22×D29—42no—
122C22×D29—42no—
123C22×D29D814yescomplemented
124C22×D29C2×D411yescharacteristic
125C22×D29C2×D411yescharacteristic
126D4×C29—24no—
127D4×C29—22no—
128D4×C29—22no—
129D4×C29—42no—
130D4×C29C2×D414yescomplemented
131C2×C4×C29—22no—
132C2×C4×C29—21no—
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2411yescharacteristic
135C22⋊D29—28no—
136C22⋊D29—28no—
137C22⋊D29—42no—
138C22⋊D29—42no—
139C22⋊D29—42no—
140C2×Dic29—22no—
141C2×Dic29—21no—
142C2×Dic29C2×D411yescharacteristic
143C2×Dic29C2×D411yescharacteristic
144D116—24no—
145D116—22no—
146D116—22no—
147D116—42no—
148D116C2×D414yescomplemented
149C4×D29—22no—
150C4×D29—22no—
151C4×D29—22no—
152C4×D29—42no—
153C4×D29C2×D414yes—
154C8×C29—22no—
155#6597—22no—
156C2×#447—291nomaximal, Sylow
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—24no—
160C22×C29—48no—
161C22×C29—42no—
162C22×C29—42no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29C2×D812yescomplemented
167C22×C29C22×D411yescharacteristic
168C2×D29—21no—
169C2×D29—21no—
170C2×D29—28no—
171C2×D29—24no—
172C2×D29—416no—
173C2×D29—48no—
174C2×D29—42no—
175C2×D29—42no—
176C2×D29—416no—
177C2×D29—41no—
178C2×D29—41no—
179C2×D29—41no—
180C2×D29—84no—
181C2×D29#12012yes—
182C2×D29C2×D812yes—
183C2×D29C2×D812yescomplemented
184C2×D29AGL(1,ℤ/8)12yes—
185C4×C29—21no—
186C4×C29—41no—
187C4×C29C22×D412yes—
188Dic29—21no—
189Dic29—41no—
190Dic29#12012yes—
191C23×D4—291no—
192C22×D8—292no—
193C2×#121—291no—
194#447—291no—
195#447—292no—
196#447—291no—
197#447—292no—
198#447—291no—
199#447D2911yescharacteristic, direct product factor
200C2×#102—292no—
201C2×C22⋊C8—291no—
202C2×C29—22no—
203C2×C29—44no—
204C2×C29—81no—
205C2×C29C2×#12011yescharacteristic
206C2×C29C22×D811yescharacteristic
207C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
208D29—22no—
209D29—44no—
210D29—81no—
211D29#44714yesdirect product factor
212C25—581no—
213C22×D4—292no—
214C22×D4—292no—
215C22×D4—291no—
216C22×D4—291no—
217C22×D4—581no—
218C22×D4—581no—
219C22×D4—581no—
220C22×D4—588no—
221C22×D4—581no—
222C22×D4C2×D2911yescharacteristic, complemented
223C23×C4—291no—
224C2×D8—292no—
225C2×D8—292no—
226C2×D8—292no—
227C2×D8—588no—
228C2×D8C2×D2912yescomplemented
229C22×C8—292no—
230#121—291no—
231#121—291no—
232#121—291no—
233#121—581no—
234#121—581no—
235#121C2×D2911yescharacteristic, complemented
236C2×C4⋊C4—291no—
237C2×C22⋊C4—581no—
238#102—292no—
239#102—292no—
240#102—292no—
241#102C2×D2912yescomplemented
242C22⋊C8—291no—
243C22⋊C8—292no—
244C22⋊C8C2×D2911yescharacteristic, complemented
245C29C2×#44711yescharacteristic, complemented, Sylow
246C24—21no—
247C24—291no—
248C24—582no—
249C24—582no—
250C24—581no—
251C24—588no—
252C24—581no—
253C24—1164no—
254C24—1164no—
255C2×D4—24no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—298no—
259C2×D4—292no—
260C2×D4—291no—
261C2×D4—584no—
262C2×D4—581no—
263C2×D4—584no—
264C2×D4—584no—
265C2×D4—582no—
266C2×D4—582no—
267C2×D4—581no—
268C2×D4—584no—
269C2×D4—588no—
270C2×D4—588no—
271C2×D4—588no—
272C2×D4—584no—
273C2×D4—581no—
274C2×D4—581no—
275C2×D4—581no—
276C2×D4—1164no—
277C2×D4C22×D2912yes—
278C2×D4C22×D2911yescharacteristic, complemented
279C22×C4—291no—
280C22×C4—291no—
281C22×C4—291no—
282C22×C4—291no—
283C22×C4—291no—
284C22×C4—584no—
285C22×C4—581no—
286C22×C4C22×D2911yescharacteristic
287D8—24no—
288D8—584no—
289D8—584no—
290D8—584no—
291C2×C8—292no—
292C2×C8—584no—
293C2×C8C22×D2912yescomplemented
294C4⋊C4—291no—
295C4⋊C4—581no—
296C4⋊C4C22×D2911yescharacteristic, complemented
297C22⋊C4—21no—
298C22⋊C4—581no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C23—24no—
302C23—22no—
303C23—21no—
304C23—42no—
305C23—42no—
306C23—291no—
307C23—291no—
308C23—294no—
309C23—582no—
310C23—582no—
311C23—588no—
312C23—584no—
313C23—588no—
314C23—582no—
315C23—581no—
316C23—1162no—
317C23—1164no—
318C23—1164no—
319C23—1164no—
320C23—1162no—
321C23—1162no—
322C23—1162no—
323C23—11632no—
324C23—1164no—
325C23—1162no—
326C23D4×D2911yescharacteristic
327D4—24no—
328D4—22no—
329D4—22no—
330D4—42no—
331D4—294no—
332D4—584no—
333D4—588no—
334D4—588no—
335D4—582no—
336D4—582no—
337D4—1162no—
338D4—1162no—
339D4—1162no—
340D4—1162no—
341D4D4×D2914yescomplemented
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—291no—
345C2×C4—294no—
346C2×C4—291no—
347C2×C4—582no—
348C2×C4—582no—
349C2×C4—582no—
350C2×C4—582no—
351C2×C4—581no—
352C2×C4—1162no—
353C2×C4D4×D2911yescharacteristic
354C2×C4C23×D2911yescharacteristic
355C8—22no—
356C8—582no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—48no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—292no—
367C22—292no—
368C22—292no—
369C22—292no—
370C22—588no—
371C22—581no—
372C22—581no—
373C22—584no—
374C22—1168no—
375C22—11616no—
376C22—11616no—
377C22—1162no—
378C22—1162no—
379C22—1161no—
380C22—1161no—
381C22—1161no—
382C22—2324no—
383C22D8×D2912yescomplemented
384C22C2×D4×D2911yescharacteristic
385C4—21no—
386C4—41no—
387C4—292no—
388C4—581no—
389C4—1161no—
390C4C2×D4×D2912yes—
391C2—22no—
392C2—44no—
393C2—81no—
394C2—294no—
395C2—582no—
396C2—1164no—
397C2—2321no—
398C2#120×D2911yescharacteristic
399C2C2×D8×D2911yescharacteristic
400C2AGL(1,ℤ/8)×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#447C2
socleC22×C29C22×D4
hypercenter#447D29
hypocenterC29C2×#447
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×D4×D29C2semidirect
2. C2×D8×D29C2semidirect
3. #121×D29C2semidirect
4. #14271299C2semidirect
5. #14271298C2semidirect
6. #14271297C2semidirect
7. #14271296C2semidirect
8. #14271295C2semidirect
9. #102×D29C2semidirect
10. C22⋊C8×D29C2semidirect
11. C29×#447C2semidirect
13. C22×D4×C29C22semidirect
20. C2×D4×D29C22semidirect
21. C2×D4×D29C22semidirect
22. C22×D116C22semidirect
24. C2×D8×C29C22semidirect
25. C29×#121C22semidirect
27. #11745300C22semidirect
28. C2×#90782C22semidirect
29. C2×#90782C22semidirect
30. #11745292C22semidirect
32. C2×D232C22semidirect
33. C2×C8×D29C22semidirect
34. #11745257C22semidirect
35. C4⋊C4×D29C22semidirect
38. C29×#102C22semidirect
39. C29×C22⋊C8C22semidirect
40. #11745180C22semidirect
41. C22⋊#6597C22semidirect
42. #11745169C22semidirect
43. #11745168C22semidirect
44. #11745157C22semidirect
58. C2×D4×C29C23semidirect
74. D4×D29D4semidirect
79. C2×D116C23semidirect
87. C2×C8×C29C23semidirect
88. C4⋊C4×C29C23semidirect
95. C4⋊Dic29C23semidirect
97. C2×#6597C23semidirect
123. C22×D29D8semidirect
130. D4×C29C2×D4semidirect
148. D116C2×D4semidirect
166. C22×C29C2×D8semidirect
183. C2×D29C2×D8semidirect
199. #447D29direct (N × H)
211. D29#447direct (N × H)
222. C22×D4C2×D29semidirect
228. C2×D8C2×D29semidirect
235. #121C2×D29semidirect
241. #102C2×D29semidirect
244. C22⋊C8C2×D29semidirect
245. C29C2×#447semidirect
278. C2×D4C22×D29semidirect
293. C2×C8C22×D29semidirect
296. C4⋊C4C22×D29semidirect
341. D4D4×D29semidirect
383. C22D8×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×D8×D292
#121×D292
#142712992
#142712982
#142712972
#142712962
#142712952
#102×D292
C22⋊C8×D292
C29×#4472
C2×#44729