Finite Group Databasebeta

← D29×#448 #16828677

Subgroups — D29×#448 #16828677

Order 3712.

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

normal subgroups only

This group has 792 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×Q8×D29C211yesmaximal, characteristic, complemented
2C2×SD16×D29C212yesmaximal, complemented
3#121×D29C211yesmaximal, characteristic
4#14271304C211yesmaximal, characteristic, complemented
5#14271303C212yesmaximal, complemented
6#14271302C211yesmaximal, characteristic, complemented
7#14271301C211yesmaximal, characteristic, complemented
8#14271300C212yesmaximal, complemented
9#103×D29C212yesmaximal, complemented
10C22⋊C8×D29C211yesmaximal, characteristic, complemented
11C29×#448C211yesmaximal, characteristic, complemented
12C22×Q8×C29C2211yescharacteristic, complemented
13C2×Q8×D29—28no—
14C2×Q8×D29—21no—
15C2×Q8×D29—21no—
16C2×Q8×D29C2212yes—
17C2×Q8×D29C2212yescomplemented
18C2×D4×D29—21no—
19C2×D4×D29C2211yescharacteristic
20C22×C4×D29—21no—
21C22×C4×D29C2211yescharacteristic
22C22×Dic58—21no—
23C22×Dic58C2211yescharacteristic, complemented
24C2×SD16×C29C2212yescomplemented
25C29×#121C2211yescharacteristic
26C2×#90784C2212yescomplemented
27#11745301—21no—
28#11745300C2211yescharacteristic
29C2×#90783C2212yescomplemented
30#11745292C2211yescharacteristic
31SD16×D29—28no—
32C2×#90773C2212yescomplemented
33C2×C8×D29C2212yes—
34#11745257C2211yescharacteristic
35C4⋊C4×D29C2211yescharacteristic
36#11745246—21no—
37C22⋊C4×D29—21no—
38C29×#103C2212yescomplemented
39C29×C22⋊C8C2211yescharacteristic, complemented
40#11745183C2212yescomplemented
41C22⋊#6597C2211yescharacteristic, complemented
42#11745168C2212yescomplemented
43#11745164C2212yescomplemented
44#11745158C2212yescomplemented
45C23×D29—21no—
46C23×D29D411yescharacteristic
47C2×Q8×C29—24no—
48C2×Q8×C29—21no—
49C2×Q8×C29C2312yes—
50C2×D4×C29—21no—
51C2×D4×C29C2311yescharacteristic
52C22×C4×C29—21no—
53C22×C4×C29C2311yescharacteristic
54C2×C22⋊D29—21no—
55C2×C22⋊D29—21no—
56C2×C22⋊D29—21no—
57C22×Dic29—21no—
58C22×Dic29D411yescharacteristic
59Q8×D29—28no—
60Q8×D29—28no—
61Q8×D29—24no—
62Q8×D29—24no—
63Q8×D29—24no—
64Q8×D29D418yescomplemented
65D4×D29—24no—
66D4×D29—44no—
67C2×D116—21no—
68C2×D116C2311yescharacteristic
69C2×C4×D29—28no—
70C2×C4×D29—22no—
71C2×C4×D29—22no—
72C2×C4×D29—24no—
73C2×C4×D29—21no—
74C2×C4×D29D411yescharacteristic
75C2×C4×D29D411yescharacteristic
76C2×C4×D29C2311yescharacteristic
77C2×C4×D29C2311yescharacteristic
78C2×Dic58—28no—
79C2×Dic58—21no—
80C2×Dic58—22no—
81C2×Dic58—22no—
82C2×Dic58—24no—
83C2×Dic58C2312yes—
84SD16×C29—24no—
85C2×C8×C29C2312yes—
86C4⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29—21no—
88C22⋊Dic29—21no—
89#90784—24no—
90#90783—24no—
91#90781—21no—
92#90781—21no—
93C4⋊Dic29C2311yescharacteristic
94#90779—21no—
95C2×#6597C2312yes—
96#90773—24no—
97C8×D29—24no—
98C23×C29—21no—
99C23×C29C2×D411yescharacteristic
100C22×D29—22no—
101C22×D29—22no—
102C22×D29—21no—
103C22×D29—42no—
104C22×D29—42no—
105C22×D29—42no—
106C22×D29SD1614yescomplemented
107C22×D29C2×D411yescharacteristic
108C22×D29C2×D411yescharacteristic
109Q8×C29—24no—
110Q8×C29—22no—
111Q8×C29C2×D414yescomplemented
112D4×C29—22no—
113D4×C29—42no—
114C2×C4×C29—24no—
115C2×C4×C29—22no—
116C2×C4×C29—22no—
117C2×C4×C29—21no—
118C2×C4×C29C2×D411yescharacteristic
119C2×C4×C29C2411yescharacteristic
120C22⋊D29—42no—
121C22⋊D29—42no—
122C22⋊D29—42no—
123C2×Dic29—24no—
124C2×Dic29—22no—
125C2×Dic29—22no—
126C2×Dic29—21no—
127C2×Dic29C2×D411yescharacteristic
128C2×Dic29C2×D411yescharacteristic
129D116—22no—
130D116—42no—
131C4×D29—28no—
132C4×D29—28no—
133C4×D29—22no—
134C4×D29—22no—
135C4×D29—22no—
136C4×D29—42no—
137C4×D29C2×D414yes—
138Dic58—28no—
139Dic58—24no—
140Dic58—22no—
141Dic58—28no—
142Dic58C2×D414yescomplemented
143C8×C29—22no—
144#6597—22no—
145C2×#448—291nomaximal, Sylow
146C22×C29—21no—
147C22×C29—21no—
148C22×C29—41no—
149C22×C29—41no—
150C22×C29—41no—
151C22×C29C2×SD1612yescomplemented
152C22×C29C22×D411yescharacteristic
153C2×D29—21no—
154C2×D29—21no—
155C2×D29—28no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—84no—
160C2×D29#12012yes—
161C2×D29C2×SD1612yes—
162C2×D29C2×SD1612yescomplemented
163C2×D29#13712yes—
164C4×C29—24no—
165C4×C29—21no—
166C4×C29—41no—
167C4×C29C22×D412yes—
168Dic29—21no—
169Dic29—24no—
170Dic29—41no—
171Dic29#12012yes—
172C23×Q8—291no—
173C22×SD16—292no—
174C2×#121—291no—
175#448—291no—
176#448—292no—
177#448—291no—
178#448—292no—
179#448—291no—
180#448D2911yescharacteristic, direct product factor
181C2×#103—292no—
182C2×C22⋊C8—291no—
183C2×C29—22no—
184C2×C29—81no—
185C2×C29C2×#12011yescharacteristic
186C2×C29C22×SD1611yescharacteristic
187C2×C29C2×#13711yescharacteristic
188D29—22no—
189D29—81no—
190D29#44814yesdirect product factor
191C22×Q8—292no—
192C22×Q8—292no—
193C22×Q8—291no—
194C22×Q8—581no—
195C22×Q8—581no—
196C22×Q8—581no—
197C22×Q8—588no—
198C22×Q8C2×D2911yescharacteristic, complemented
199C22×D4—291no—
200C22×D4—581no—
201C23×C4—291no—
202C23×C4—581no—
203C2×SD16—292no—
204C2×SD16—292no—
205C2×SD16—292no—
206C2×SD16—588no—
207C2×SD16C2×D2912yescomplemented
208C22×C8—292no—
209#121—291no—
210#121—291no—
211#121—291no—
212#121—581no—
213#121—581no—
214#121C2×D2911yescharacteristic
215C2×C4⋊C4—291no—
216C2×C22⋊C4—581no—
217#103—292no—
218#103—292no—
219#103—292no—
220#103C2×D2912yescomplemented
221C22⋊C8—291no—
222C22⋊C8—292no—
223C22⋊C8C2×D2911yescharacteristic, complemented
224C29C2×#44811yescharacteristic, complemented, Sylow
225C24—291no—
226C24—581no—
227C2×Q8—24no—
228C2×Q8—21no—
229C2×Q8—298no—
230C2×Q8—292no—
231C2×Q8—582no—
232C2×Q8—582no—
233C2×Q8—584no—
234C2×Q8—588no—
235C2×Q8—584no—
236C2×Q8—584no—
237C2×Q8—588no—
238C2×Q8—588no—
239C2×Q8—584no—
240C2×Q8—581no—
241C2×Q8C22×D2912yes—
242C2×D4—21no—
243C2×D4—291no—
244C2×D4—581no—
245C2×D4—584no—
246C2×D4—581no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4—1164no—
250C2×D4C22×D2911yescharacteristic
251C22×C4—21no—
252C22×C4—291no—
253C22×C4—291no—
254C22×C4—291no—
255C22×C4—291no—
256C22×C4—291no—
257C22×C4—584no—
258C22×C4—582no—
259C22×C4—582no—
260C22×C4—588no—
261C22×C4—581no—
262C22×C4—581no—
263C22×C4C22×D2911yescharacteristic
264SD16—24no—
265SD16—584no—
266SD16—584no—
267SD16—584no—
268C2×C8—292no—
269C2×C8—584no—
270C2×C8C22×D2912yes—
271C4⋊C4—291no—
272C4⋊C4—581no—
273C4⋊C4C22×D2911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C23—21no—
279C23—291no—
280C23—291no—
281C23—294no—
282C23—582no—
283C23—582no—
284C23—581no—
285C23—1162no—
286C23—1162no—
287C23—1162no—
288C23D4×D2911yescharacteristic
289Q8—24no—
290Q8—22no—
291Q8—294no—
292Q8—588no—
293Q8—588no—
294Q8—584no—
295Q8—582no—
296Q8D4×D2914yescomplemented
297D4—22no—
298D4—42no—
299D4—582no—
300D4—1162no—
301D4—1162no—
302D4—1162no—
303D4—1162no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—291no—
309C2×C4—294no—
310C2×C4—291no—
311C2×C4—582no—
312C2×C4—582no—
313C2×C4—588no—
314C2×C4—588no—
315C2×C4—582no—
316C2×C4—584no—
317C2×C4—582no—
318C2×C4—582no—
319C2×C4—581no—
320C2×C4—1162no—
321C2×C4D4×D2911yescharacteristic
322C2×C4C23×D2911yescharacteristic
323C8—22no—
324C8—582no—
325C22—21no—
326C22—21no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—292no—
331C22—292no—
332C22—292no—
333C22—292no—
334C22—588no—
335C22—581no—
336C22—581no—
337C22—1161no—
338C22—1161no—
339C22—1161no—
340C22—2324no—
341C22SD16×D2912yescomplemented
342C22C2×D4×D2911yescharacteristic
343C4—24no—
344C4—21no—
345C4—41no—
346C4—292no—
347C4—581no—
348C4—584no—
349C4—1161no—
350C4C2×D4×D2912yes—
351C2—22no—
352C2—81no—
353C2—294no—
354C2—582no—
355C2—2321no—
356C2#120×D2911yescharacteristic
357C2C2×SD16×D2911yescharacteristic
358C2#137×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#448C2
socleC22×C29C22×D4
prime radical#121×D29C2
hypercenter#448D29
hypocenterC29C2×#448
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D29C2semidirect
2. C2×SD16×D29C2semidirect
4. #14271304C2semidirect
5. #14271303C2semidirect
6. #14271302C2semidirect
7. #14271301C2semidirect
8. #14271300C2semidirect
9. #103×D29C2semidirect
10. C22⋊C8×D29C2semidirect
11. C29×#448C2semidirect
12. C22×Q8×C29C22semidirect
17. C2×Q8×D29C22semidirect
23. C22×Dic58C22semidirect
24. C2×SD16×C29C22semidirect
26. C2×#90784C22semidirect
29. C2×#90783C22semidirect
32. C2×#90773C22semidirect
38. C29×#103C22semidirect
39. C29×C22⋊C8C22semidirect
40. #11745183C22semidirect
41. C22⋊#6597C22semidirect
42. #11745168C22semidirect
43. #11745164C22semidirect
44. #11745158C22semidirect
64. Q8×D29D4semidirect
106. C22×D29SD16semidirect
111. Q8×C29C2×D4semidirect
142. Dic58C2×D4semidirect
151. C22×C29C2×SD16semidirect
162. C2×D29C2×SD16semidirect
180. #448D29direct (N × H)
190. D29#448direct (N × H)
198. C22×Q8C2×D29semidirect
207. C2×SD16C2×D29semidirect
220. #103C2×D29semidirect
223. C22⋊C8C2×D29semidirect
224. C29C2×#448semidirect
296. Q8D4×D29semidirect
341. C22SD16×D29semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D292
C2×SD16×D292
#121×D292
#142713042
#142713032
#142713022
#142713012
#142713002
#103×D292
C22⋊C8×D292
C29×#4482
C2×#44829