Finite Group Databasebeta

← C29×#3310 #16817024

Subgroups — C29×#3310 #16817024

Order 3712.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#552C211yesmaximal, characteristic, complemented
2D42×C29C211yesmaximal, characteristic
3C29×#490C211yesmaximal, characteristic, complemented
4C29×#482C211yesmaximal, characteristic, complemented
5C29×#480C211yesmaximal, characteristic, complemented
6C29×#478C211yesmaximal, characteristic, complemented
7C29×#468C211yesmaximal, characteristic, complemented
8C29×#465C211yesmaximal, characteristic, complemented
9C29×#460C211yesmaximal, characteristic, complemented
10C29×#450C211yesmaximal, characteristic, complemented
11C29×#450C211yesmaximal, characteristic, complemented
12C29×#440C211yesmaximal, characteristic, complemented
13C29×#435C211yesmaximal, characteristic, complemented
14C29×#418C211yesmaximal, characteristic, complemented
15C2×C29×#102C211yesmaximal, characteristic, complemented
16C22×D4×C29—21no—
17C22×D4×C29C2211yescharacteristic
18C22×D4×C29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic, complemented
21C2×SD16×C29C2211yescharacteristic, complemented
22C2×M16×C29C2211yescharacteristic, complemented
23C22×C8×C29C2211yescharacteristic, complemented
24C29×#127C2211yescharacteristic
25C29×#126—21no—
26C29×#125—21no—
27C29×#125C2211yescharacteristic, complemented
28C29×#123—21no—
29C29×C22⋊Q8C2211yescharacteristic, complemented
30C29×C22⋊Q8C2211yescharacteristic, complemented
31C29×#121—21no—
32C29×#121C2211yescharacteristic
33C29×#121C2211yescharacteristic
34C29×#120—21no—
35C29×#120—21no—
36C4×Q8×C29C2211yescharacteristic, complemented
37C4×D4×C29C2211yescharacteristic
38C4×D4×C29C2211yescharacteristic
39C29×#117—21no—
40C29×#117C2211yescharacteristic, complemented
41C2×C4⋊C4×C29C2211yescharacteristic, complemented
42C29×#107C2211yescharacteristic, complemented
43C29×#107C2211yescharacteristic, complemented
44C29×#106C2211yescharacteristic, complemented
45C29×C4⋊C8C2211yescharacteristic, complemented
46C29×#103C2211yescharacteristic, complemented
47C29×#102C2211yescharacteristic
48C29×#102C2211yescharacteristic
49C29×#102C2211yescharacteristic
50C29×#102C2211yescharacteristic, complemented
51C29×#102C2211yescharacteristic, complemented
52C29×#102C2211yescharacteristic, complemented
53C29×#102C2211yescharacteristic, complemented
54C29×#102C2211yescharacteristic, complemented
55C29×#102C2211yescharacteristic, complemented
56C29×C22⋊C8C2211yescharacteristic, complemented
57C29×C22⋊C8C2211yescharacteristic, complemented
58C29×#97C2211yescharacteristic, complemented
59C24×C29—21no—
60C24×C29—21no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29—22no—
63C2×D4×C29—22no—
64C2×D4×C29—21no—
65C2×D4×C29—21no—
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29—21no—
69C2×D4×C29—21no—
70C2×D4×C29—41no—
71C2×D4×C29—41no—
72C2×D4×C29—44no—
73C2×D4×C29D411yescharacteristic
74C2×D4×C29C2311yescharacteristic
75C2×D4×C29C2311yescharacteristic
76C2×D4×C29C2311yescharacteristic
77C22×C4×C29—21no—
78C22×C4×C29—21no—
79C22×C4×C29C2311yescharacteristic
80C22×C4×C29C2311yescharacteristic
81SD16×C29—22no—
82SD16×C29—41no—
83SD16×C29—41no—
84M16×C29—41no—
85C2×C8×C29—41no—
86C2×C8×C29C2311yescharacteristic
87C2×C8×C29C2311yescharacteristic
88C2×C8×C29C2311yescharacteristic
89C2×C8×C29C2311yescharacteristic
90C4⋊C4×C29—21no—
91C4⋊C4×C29—21no—
92C4⋊C4×C29—21no—
93C4⋊C4×C29—21no—
94C4⋊C4×C29—21no—
95C4⋊C4×C29—21no—
96C4⋊C4×C29D411yescharacteristic
97C4⋊C4×C29C2311yescharacteristic
98C4⋊C4×C29C2311yescharacteristic
99C4⋊C4×C29C2311yescharacteristic
100C4⋊C4×C29C2311yescharacteristic
101C22⋊C4×C29—21no—
102C22⋊C4×C29—21no—
103C22⋊C4×C29—21no—
104C22⋊C4×C29—21no—
105C22⋊C4×C29—21no—
106C22⋊C4×C29—21no—
107C22⋊C4×C29D411yescharacteristic
108C22⋊C4×C29D411yescharacteristic
109C42×C29—21no—
110C42×C29—21no—
111C42×C29C2311yescharacteristic
112C23×C29—21no—
113C23×C29—21no—
114C23×C29—21no—
115C23×C29—42no—
116C23×C29—42no—
117C23×C29—42no—
118C23×C29—42no—
119C23×C29—81no—
120C23×C29—81no—
121C23×C29C2×D411yescharacteristic
122C23×C29C2×D411yescharacteristic
123Q8×C29—21no—
124Q8×C29—21no—
125D4×C29—22no—
126D4×C29—21no—
127D4×C29—21no—
128D4×C29—21no—
129D4×C29—21no—
130D4×C29—21no—
131D4×C29—42no—
132D4×C29—42no—
133D4×C29—42no—
134D4×C29—42no—
135D4×C29—42no—
136D4×C29—81no—
137D4×C29#4112yes—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—42no—
148C2×C4×C29—42no—
149C2×C4×C29C2×D411yescharacteristic
150C2×C4×C29C2×D411yescharacteristic
151C2×C4×C29C2×D411yescharacteristic
152C2×C4×C29C2×D411yescharacteristic
153C2×C4×C29C2411yescharacteristic
154C8×C29—21no—
155C8×C29—21no—
156C8×C29—21no—
157C8×C29—21no—
158#3310C2911yesmaximal, characteristic, direct product factor, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—22no—
163C22×C29—21no—
164C22×C29—21no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—41no—
168C22×C29—41no—
169C22×C29—41no—
170C22×C29—41no—
171C22×C29—41no—
172C22×C29—41no—
173C22×C29—84no—
174C22×C29—84no—
175C22×C29AGL(1,ℤ/8)12yes—
176C22×C29C22×D411yescharacteristic
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—21no—
181C4×C29—41no—
182C4×C29—41no—
183C4×C29—41no—
184C4×C29—41no—
185C4×C29—41no—
186C4×C29C2×#4111yescharacteristic
187C4×C29H(5,𝔽2)11yescharacteristic
188#552C2×C2911yescharacteristic, complemented
189D42C2×C2911yescharacteristic
190#490C2×C2911yescharacteristic, complemented
191#482C2×C2911yescharacteristic, complemented
192#480C2×C2911yescharacteristic, complemented
193#478C2×C2911yescharacteristic, complemented
194#468C2×C2911yescharacteristic, complemented
195#465C2×C2911yescharacteristic, complemented
196#460C2×C2911yescharacteristic, complemented
197#450C2×C2911yescharacteristic, complemented
198#450C2×C2911yescharacteristic, complemented
199#440C2×C2911yescharacteristic, complemented
200#435C2×C2911yescharacteristic, complemented
201#418C2×C2911yescharacteristic, complemented
202C2×#102C2×C2911yescharacteristic, complemented
203C2×C29—22no—
204C2×C29—41no—
205C2×C29—42no—
206C2×C29—81no—
207C2×C29—81no—
208C2×C29#54611yescharacteristic
209C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
210C2×C29#57711yescharacteristic
211C22×D4—21no—
212C22×D4C22×C2911yescharacteristic
213C22×D4C22×C2911yescharacteristic
214C2×SD16C22×C2911yescharacteristic
215C2×SD16C22×C2911yescharacteristic, complemented
216C2×SD16C22×C2911yescharacteristic, complemented
217C2×M16C22×C2911yescharacteristic, complemented
218C22×C8C22×C2911yescharacteristic, complemented
219#127C22×C2911yescharacteristic
220#126—21no—
221#125—21no—
222#125C22×C2911yescharacteristic, complemented
223#123—21no—
224C22⋊Q8C22×C2911yescharacteristic, complemented
225C22⋊Q8C22×C2911yescharacteristic, complemented
226#121—21no—
227#121C22×C2911yescharacteristic
228#121C22×C2911yescharacteristic
229#120—21no—
230#120—21no—
231C4×Q8C22×C2911yescharacteristic, complemented
232C4×D4C22×C2911yescharacteristic
233C4×D4C22×C2911yescharacteristic
234#117—21no—
235#117C22×C2911yescharacteristic, complemented
236C2×C4⋊C4C22×C2911yescharacteristic, complemented
237#107C22×C2911yescharacteristic, complemented
238#107C22×C2911yescharacteristic, complemented
239#106C22×C2911yescharacteristic, complemented
240C4⋊C8C22×C2911yescharacteristic, complemented
241#103C22×C2911yescharacteristic, complemented
242#102C22×C2911yescharacteristic
243#102C22×C2911yescharacteristic
244#102C22×C2911yescharacteristic
245#102C22×C2911yescharacteristic, complemented
246#102C22×C2911yescharacteristic, complemented
247#102C22×C2911yescharacteristic, complemented
248#102C22×C2911yescharacteristic, complemented
249#102C22×C2911yescharacteristic, complemented
250#102C22×C2911yescharacteristic, complemented
251C22⋊C8C22×C2911yescharacteristic, complemented
252C22⋊C8C22×C2911yescharacteristic, complemented
253#97C22×C2911yescharacteristic, complemented
254C29#331011yescharacteristic, direct product factor, Sylow
255C24—21no—
256C24—21no—
257C2×Q8C23×C2911yescharacteristic
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4D4×C2911yescharacteristic
270C2×D4C23×C2911yescharacteristic
271C2×D4C23×C2911yescharacteristic
272C2×D4C23×C2911yescharacteristic
273C22×C4—21no—
274C22×C4—21no—
275C22×C4C23×C2911yescharacteristic
276C22×C4C23×C2911yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—41no—
280M16—41no—
281C2×C8—41no—
282C2×C8C23×C2911yescharacteristic
283C2×C8C23×C2911yescharacteristic
284C2×C8C23×C2911yescharacteristic
285C2×C8C23×C2911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4D4×C2911yescharacteristic
293C4⋊C4C23×C2911yescharacteristic
294C4⋊C4C23×C2911yescharacteristic
295C4⋊C4C23×C2911yescharacteristic
296C4⋊C4C23×C2911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4D4×C2911yescharacteristic
304C22⋊C4D4×C2911yescharacteristic
305C42—21no—
306C42—21no—
307C42C23×C2911yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×D4×C2911yescharacteristic
318C23C2×D4×C2911yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#41×C2912yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4C2×D4×C2911yescharacteristic
346C2×C4C2×D4×C2911yescharacteristic
347C2×C4C2×D4×C2911yescharacteristic
348C2×C4C2×D4×C2911yescharacteristic
349C2×C4C24×C2911yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22C29×AGL(1,ℤ/8)12yes—
371C22C22×D4×C2911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4C2×#41×C2911yescharacteristic
382C4C29×H(5,𝔽2)11yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2C29×#54611yescharacteristic
389C2C2×C29×AGL(1,ℤ/8)11yescharacteristic
390C2C29×#57711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
prime radicalD42×C29C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#552C2semidirect
3. C29×#490C2semidirect
4. C29×#482C2semidirect
5. C29×#480C2semidirect
6. C29×#478C2semidirect
7. C29×#468C2semidirect
8. C29×#465C2semidirect
9. C29×#460C2semidirect
10. C29×#450C2semidirect
11. C29×#450C2semidirect
12. C29×#440C2semidirect
13. C29×#435C2semidirect
14. C29×#418C2semidirect
15. C2×C29×#102C2semidirect
20. C2×SD16×C29C22semidirect
21. C2×SD16×C29C22semidirect
22. C2×M16×C29C22semidirect
23. C22×C8×C29C22semidirect
27. C29×#125C22semidirect
29. C29×C22⋊Q8C22semidirect
30. C29×C22⋊Q8C22semidirect
36. C4×Q8×C29C22semidirect
40. C29×#117C22semidirect
41. C2×C4⋊C4×C29C22semidirect
42. C29×#107C22semidirect
43. C29×#107C22semidirect
44. C29×#106C22semidirect
45. C29×C4⋊C8C22semidirect
46. C29×#103C22semidirect
50. C29×#102C22semidirect
51. C29×#102C22semidirect
52. C29×#102C22semidirect
53. C29×#102C22semidirect
54. C29×#102C22semidirect
55. C29×#102C22semidirect
56. C29×C22⋊C8C22semidirect
57. C29×C22⋊C8C22semidirect
58. C29×#97C22semidirect
158. #3310C29direct (N × H)
188. #552C2×C29semidirect
190. #490C2×C29semidirect
191. #482C2×C29semidirect
192. #480C2×C29semidirect
193. #478C2×C29semidirect
194. #468C2×C29semidirect
195. #465C2×C29semidirect
196. #460C2×C29semidirect
197. #450C2×C29semidirect
198. #450C2×C29semidirect
199. #440C2×C29semidirect
200. #435C2×C29semidirect
201. #418C2×C29semidirect
202. C2×#102C2×C29semidirect
215. C2×SD16C22×C29semidirect
216. C2×SD16C22×C29semidirect
217. C2×M16C22×C29semidirect
218. C22×C8C22×C29semidirect
222. #125C22×C29semidirect
224. C22⋊Q8C22×C29semidirect
225. C22⋊Q8C22×C29semidirect
231. C4×Q8C22×C29semidirect
235. #117C22×C29semidirect
236. C2×C4⋊C4C22×C29semidirect
237. #107C22×C29semidirect
238. #107C22×C29semidirect
239. #106C22×C29semidirect
240. C4⋊C8C22×C29semidirect
241. #103C22×C29semidirect
245. #102C22×C29semidirect
246. #102C22×C29semidirect
247. #102C22×C29semidirect
248. #102C22×C29semidirect
249. #102C22×C29semidirect
250. #102C22×C29semidirect
251. C22⋊C8C22×C29semidirect
252. C22⋊C8C22×C29semidirect
253. #97C22×C29semidirect
254. C29#3310direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5522
D42×C292
C29×#4902
C29×#4822
C29×#4802
C29×#4782
C29×#4682
C29×#4652
C29×#4602
C29×#4502
C29×#4402
C29×#4352
C29×#4182
C2×C29×#1022
#331029