Finite Group Databasebeta

← D29×#464 #16828932

Subgroups — D29×#464 #16828932

Order 3712.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D29C211yesmaximal, characteristic, complemented
2C2×SD16×D29C211yesmaximal, characteristic
3#124×D29C211yesmaximal, characteristic
4C4×Q8×D29C211yesmaximal, characteristic, complemented
5#14271388C211yesmaximal, characteristic, complemented
6#14271387C211yesmaximal, characteristic, complemented
7#14271386C211yesmaximal, characteristic, complemented
8#14271385C211yesmaximal, characteristic, complemented
9#14271384C211yesmaximal, characteristic, complemented
10#14271383C211yesmaximal, characteristic, complemented
11#14271382C211yesmaximal, characteristic, complemented
12C4⋊C8×D29C211yesmaximal, characteristic, complemented
13#103×D29C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic
15C29×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D29C2211yescharacteristic
17C2×Q8×D29C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic
19C2×Q16×C29C2211yescharacteristic, complemented
20C2×SD16×C29C2211yescharacteristic
21C29×#124C2211yescharacteristic
22C4×Q8×C29C2211yescharacteristic, complemented
23#11745309C2211yescharacteristic
24Q8×Dic29C2211yescharacteristic, complemented
25C2×#90785C2211yescharacteristic, complemented
26C2×#90785C2211yescharacteristic, complemented
27C2×#90784C2211yescharacteristic
28#11745298C2211yescharacteristic
29C2×#90783C2211yescharacteristic
30Q16×D29—24no—
31SD16×D29—24no—
32C2×Dic116C2211yescharacteristic, complemented
33C2×#90773C2211yescharacteristic
34C2×C8×D29C2211yescharacteristic
35C2×C8×D29C2211yescharacteristic
36C4⋊C4×D29—21no—
37C4⋊C4×D29C2211yescharacteristic
38#11745249—21no—
39#11745249C2211yescharacteristic, complemented
40#11745247—21no—
41#11745247—21no—
42C22⋊C4×D29—21no—
43C22⋊C4×D29—21no—
44#11745237C2211yescharacteristic
45C42×D29—21no—
46C42×D29C2211yescharacteristic
47C4×Dic58—21no—
48C4×Dic58C2211yescharacteristic, complemented
49C29×C4⋊C8C2211yescharacteristic, complemented
50C29×#103C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic
52#11745183C2211yescharacteristic, complemented
53#11745180C2211yescharacteristic
54#11745169C2211yescharacteristic
55#11745164C2211yescharacteristic, complemented
56#11745162C2211yescharacteristic, complemented
57#11745162C2211yescharacteristic, complemented
58#11745158C2211yescharacteristic, complemented
59#11745157C2211yescharacteristic
60C4⋊#6597C2211yescharacteristic, complemented
61C23×D29—21no—
62C2×Q8×C29C2311yescharacteristic
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66Q8×D29—22no—
67Q8×D29—22no—
68Q8×D29—22no—
69Q8×D29D414yes—
70D4×D29—22no—
71D4×D29—22no—
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29D411yescharacteristic
77C2×C4×D29D411yescharacteristic
78C2×C4×D29C2311yescharacteristic
79C2×Dic58—21no—
80C2×Dic58—21no—
81C2×Dic58C2311yescharacteristic
82C2×Dic58C2311yescharacteristic
83Q16×C29—22no—
84SD16×C29—22no—
85C2×C8×C29C2311yescharacteristic
86C2×C8×C29C2311yescharacteristic
87C4⋊C4×C29—21no—
88C4⋊C4×C29C2311yescharacteristic
89C22⋊C4×C29—21no—
90C22⋊C4×C29—21no—
91C42×C29—21no—
92C42×C29C2311yescharacteristic
93C22⋊Dic29—21no—
94C22⋊Dic29—21no—
95#90785—22no—
96#90785—22no—
97#90784—22no—
98#90783—22no—
99#90781—21no—
100#90781—21no—
101#90781—21no—
102#90781—21no—
103C4⋊Dic29—21no—
104C4⋊Dic29C2311yescharacteristic
105#90779—21no—
106#90779—21no—
107#90779—21no—
108C4×Dic29—21no—
109C4×Dic29—21no—
110C4×Dic29—21no—
111C4×Dic29D411yescharacteristic
112C4×Dic29D411yescharacteristic
113C4×Dic29C2311yescharacteristic
114C2×#6597C2311yescharacteristic
115C2×#6597C2311yescharacteristic
116Dic116—22no—
117#90773—22no—
118C8×D29—22no—
119C8×D29—22no—
120C23×C29—21no—
121C22×D29—21no—
122C22×D29—42no—
123C22×D29—42no—
124C22×D29—42no—
125C22×D29C2×D411yescharacteristic
126Q8×C29—21no—
127Q8×C29—21no—
128Q8×C29—21no—
129Q8×C29C2×D412yes—
130D4×C29—21no—
131D4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2411yescharacteristic
138C22⋊D29—42no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141C2×Dic29—21no—
142C2×Dic29C2×D411yescharacteristic
143C2×Dic29C2×D411yescharacteristic
144C2×Dic29C2×D411yescharacteristic
145D116—21no—
146D116—21no—
147C4×D29—24no—
148C4×D29—22no—
149C4×D29—22no—
150C4×D29—42no—
151C4×D29—42no—
152C4×D29C2×D412yes—
153C4×D29#4112yes—
154Dic58—21no—
155Dic58—24no—
156Dic58—21no—
157Dic58—21no—
158Dic58—42no—
159Dic58C2×D412yes—
160C8×C29—21no—
161C8×C29—21no—
162#6597—21no—
163#6597—21no—
164C2×#464—291nomaximal, Sylow
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—41no—
168C22×C29C22×D411yescharacteristic
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—84no—
173C2×D29#12112yes—
174C2×D29#13512yes—
175C2×D29#13712yes—
176C4×C29—22no—
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—41no—
180C4×C29—41no—
181C4×C29C22×D411yescharacteristic
182C4×C29C2×#4111yescharacteristic
183Dic29—22no—
184Dic29—21no—
185Dic29—21no—
186Dic29—41no—
187Dic29—41no—
188Dic29#12112yes—
189C22×Q16—291no—
190C22×SD16—291no—
191C2×#124—291no—
192C2×C4×Q8—291no—
193#464—291no—
194#464—291no—
195#464—291no—
196#464—291no—
197#464—291no—
198#464—291no—
199#464—291no—
200#464D2911yescharacteristic, direct product factor
201C2×C4⋊C8—291no—
202C2×#103—291no—
203C2×#102—291no—
204C2×C29—81no—
205C2×C29C2×#12111yescharacteristic
206C2×C29C2×#13511yescharacteristic
207C2×C29C2×#13711yescharacteristic
208D29—81no—
209D29#46414yesdirect product factor
210C22×Q8—291no—
211C22×Q8—291no—
212C22×D4—291no—
213C2×Q16—291no—
214C2×Q16—291no—
215C2×Q16—291no—
216C2×Q16—584no—
217C2×Q16C2×D2911yescharacteristic, complemented
218C2×SD16—291no—
219C2×SD16—291no—
220C2×SD16—291no—
221C2×SD16—584no—
222C2×SD16C2×D2911yescharacteristic
223C22×C8—291no—
224C22×C8—291no—
225#124—291no—
226#124—291no—
227#124—291no—
228#124—581no—
229#124—581no—
230#124C2×D2911yescharacteristic
231C4×Q8—291no—
232C4×Q8—291no—
233C4×Q8—291no—
234C4×Q8—581no—
235C4×Q8—581no—
236C4×Q8C2×D2911yescharacteristic, complemented
237C2×C4⋊C4—291no—
238C2×C4⋊C4—581no—
239C2×C22⋊C4—581no—
240C2×C22⋊C4—581no—
241C2×C42—291no—
242C2×C42—581no—
243C4⋊C8—291no—
244C4⋊C8—291no—
245C4⋊C8—291no—
246C4⋊C8C2×D2911yescharacteristic, complemented
247#103—291no—
248#103—291no—
249#103—291no—
250#103C2×D2911yescharacteristic, complemented
251#102—291no—
252#102—291no—
253#102—291no—
254#102C2×D2911yescharacteristic
255C29C2×#46411yescharacteristic, complemented, Sylow
256C24—581no—
257C2×Q8—294no—
258C2×Q8—291no—
259C2×Q8—291no—
260C2×Q8—581no—
261C2×Q8—581no—
262C2×Q8—582no—
263C2×Q8—582no—
264C2×Q8—582no—
265C2×Q8C22×D2911yescharacteristic
266C2×Q8C22×D2911yescharacteristic
267C2×D4—291no—
268C2×D4—582no—
269C2×D4—582no—
270C2×D4—581no—
271C2×D4C22×D2911yescharacteristic
272C22×C4—291no—
273C22×C4—291no—
274C22×C4—291no—
275C22×C4—581no—
276C22×C4—581no—
277C22×C4—581no—
278Q16—22no—
279Q16—582no—
280Q16—582no—
281Q16—582no—
282SD16—22no—
283SD16—582no—
284SD16—582no—
285SD16—582no—
286C2×C8—291no—
287C2×C8—291no—
288C2×C8—582no—
289C2×C8—582no—
290C2×C8C22×D2911yescharacteristic
291C2×C8C22×D2911yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—291no—
294C4⋊C4—581no—
295C4⋊C4—581no—
296C4⋊C4—581no—
297C4⋊C4—581no—
298C4⋊C4C22×D2911yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4—581no—
305C22⋊C4—581no—
306C22⋊C4—581no—
307C42—21no—
308C42—291no—
309C42—291no—
310C42—291no—
311C42—581no—
312C42—581no—
313C42—581no—
314C42C22×D2911yescharacteristic
315C23—21no—
316C23—291no—
317C23—581no—
318C23—1162no—
319C23—1162no—
320C23—1162no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—292no—
325Q8—584no—
326Q8—581no—
327Q8—581no—
328Q8—581no—
329Q8—1162no—
330Q8D4×D2912yes—
331D4—21no—
332D4—21no—
333D4—581no—
334D4—581no—
335D4—1162no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—291no—
340C2×C4—292no—
341C2×C4—292no—
342C2×C4—291no—
343C2×C4—291no—
344C2×C4—582no—
345C2×C4—582no—
346C2×C4—584no—
347C2×C4—581no—
348C2×C4—581no—
349C2×C4—581no—
350C2×C4—1162no—
351C2×C4—1162no—
352C2×C4D4×D2911yescharacteristic
353C2×C4D4×D2911yescharacteristic
354C2×C4C23×D2911yescharacteristic
355C8—21no—
356C8—21no—
357C8—581no—
358C8—581no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—292no—
363C22—292no—
364C22—292no—
365C22—1161no—
366C22—1161no—
367C22—1161no—
368C22—2324no—
369C22C2×D4×D2911yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—292no—
376C4—582no—
377C4—581no—
378C4—581no—
379C4—1161no—
380C4—1161no—
381C4C2×D4×D2911yescharacteristic
382C4#41×D2911yescharacteristic
383C2—81no—
384C2—294no—
385C2—2321no—
386C2#121×D2911yescharacteristic
387C2#135×D2911yescharacteristic
388C2#137×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#464C2
socleC22×C29C22×D4
prime radicalC2×D4×D29C22
hypercenter#464D29
hypocenterC29C2×#464
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D29C2semidirect
4. C4×Q8×D29C2semidirect
5. #14271388C2semidirect
6. #14271387C2semidirect
7. #14271386C2semidirect
8. #14271385C2semidirect
9. #14271384C2semidirect
10. #14271383C2semidirect
11. #14271382C2semidirect
12. C4⋊C8×D29C2semidirect
13. #103×D29C2semidirect
15. C29×#464C2semidirect
19. C2×Q16×C29C22semidirect
22. C4×Q8×C29C22semidirect
24. Q8×Dic29C22semidirect
25. C2×#90785C22semidirect
26. C2×#90785C22semidirect
32. C2×Dic116C22semidirect
39. #11745249C22semidirect
48. C4×Dic58C22semidirect
49. C29×C4⋊C8C22semidirect
50. C29×#103C22semidirect
52. #11745183C22semidirect
55. #11745164C22semidirect
56. #11745162C22semidirect
57. #11745162C22semidirect
58. #11745158C22semidirect
60. C4⋊#6597C22semidirect
200. #464D29direct (N × H)
209. D29#464direct (N × H)
217. C2×Q16C2×D29semidirect
236. C4×Q8C2×D29semidirect
246. C4⋊C8C2×D29semidirect
250. #103C2×D29semidirect
255. C29C2×#464semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D292
C2×SD16×D292
#124×D292
C4×Q8×D292
#142713882
#142713872
#142713862
#142713852
#142713842
#142713832
#142713822
C4⋊C8×D292
#103×D292
#102×D292
C29×#4642
C2×#46429