Finite Group Databasebeta

← C29×#3311 #16817025

Subgroups — C29×#3311 #16817025

Order 3712.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#556C211yesmaximal, characteristic, complemented
2C29×#546C211yesmaximal, characteristic
3C29×#489C211yesmaximal, characteristic, complemented
4C29×#485C211yesmaximal, characteristic, complemented
5C29×#482C211yesmaximal, characteristic, complemented
6C29×#476C211yesmaximal, characteristic, complemented
7C29×#470C211yesmaximal, characteristic, complemented
8C29×#465C211yesmaximal, characteristic, complemented
9C29×#464C211yesmaximal, characteristic, complemented
10C29×#452C211yesmaximal, characteristic, complemented
11C29×#450C211yesmaximal, characteristic, complemented
12C29×#440C211yesmaximal, characteristic, complemented
13C29×#435C211yesmaximal, characteristic, complemented
14C29×#418C211yesmaximal, characteristic, complemented
15C29×#416C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×D4×C29C2211yescharacteristic
18C2×Q16×C29C2211yescharacteristic, complemented
19C2×SD16×C29C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic
21C2×M16×C29C2211yescharacteristic
22C22×C8×C29C2211yescharacteristic, complemented
23C29×C4⋊Q8C2211yescharacteristic, complemented
24C29×#126—21no—
25C29×#126—21no—
26C29×#124—21no—
27C29×#124C2211yescharacteristic
28C29×#123—21no—
29C29×C22⋊Q8C2211yescharacteristic
30C29×C22⋊Q8C2211yescharacteristic
31C29×C22⋊Q8C2211yescharacteristic, complemented
32C29×#121—21no—
33C29×#121C2211yescharacteristic
34C29×#120—21no—
35C4×Q8×C29—21no—
36C4×Q8×C29C2211yescharacteristic, complemented
37C4×D4×C29C2211yescharacteristic
38C4×D4×C29C2211yescharacteristic
39C29×#117C2211yescharacteristic
40C29×#117C2211yescharacteristic, complemented
41C2×C22⋊C4×C29—21no—
42C29×#107C2211yescharacteristic, complemented
43C29×#106C2211yescharacteristic, complemented
44C29×#106C2211yescharacteristic, complemented
45C29×C4⋊C8C2211yescharacteristic, complemented
46C29×#103C2211yescharacteristic, complemented
47C29×#103C2211yescharacteristic, complemented
48C29×#103C2211yescharacteristic, complemented
49C29×#103C2211yescharacteristic, complemented
50C29×#102C2211yescharacteristic
51C29×#102C2211yescharacteristic
52C29×#102C2211yescharacteristic
53C29×#102C2211yescharacteristic
54C29×#102C2211yescharacteristic
55C29×#102C2211yescharacteristic
56C29×C22⋊C8C2211yescharacteristic
57C29×C22⋊C8C2211yescharacteristic, complemented
58C29×#97C2211yescharacteristic, complemented
59C24×C29—21no—
60#41×C29—22no—
61#41×C29—41no—
62C2×Q8×C29—21no—
63C2×Q8×C29C2311yescharacteristic
64C2×Q8×C29C2311yescharacteristic
65C2×D4×C29—22no—
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29—21no—
69C2×D4×C29—41no—
70C2×D4×C29D411yescharacteristic
71C2×D4×C29C2311yescharacteristic
72C2×D4×C29C2311yescharacteristic
73C22×C4×C29—21no—
74C22×C4×C29—21no—
75C22×C4×C29C2311yescharacteristic
76C22×C4×C29C2311yescharacteristic
77Q16×C29—41no—
78SD16×C29—22no—
79SD16×C29—41no—
80M16×C29—41no—
81C2×C8×C29—41no—
82C2×C8×C29C2311yescharacteristic
83C2×C8×C29C2311yescharacteristic
84C2×C8×C29C2311yescharacteristic
85C2×C8×C29C2311yescharacteristic
86C4⋊C4×C29—21no—
87C4⋊C4×C29—21no—
88C4⋊C4×C29—21no—
89C4⋊C4×C29—21no—
90C4⋊C4×C29—21no—
91C4⋊C4×C29D411yescharacteristic
92C4⋊C4×C29C2311yescharacteristic
93C4⋊C4×C29C2311yescharacteristic
94C4⋊C4×C29C2311yescharacteristic
95C4⋊C4×C29C2311yescharacteristic
96C22⋊C4×C29—21no—
97C22⋊C4×C29—21no—
98C22⋊C4×C29—21no—
99C22⋊C4×C29—21no—
100C22⋊C4×C29—21no—
101C22⋊C4×C29—21no—
102C22⋊C4×C29—21no—
103C22⋊C4×C29—21no—
104C22⋊C4×C29—21no—
105C22⋊C4×C29D411yescharacteristic
106C22⋊C4×C29D411yescharacteristic
107C42×C29—21no—
108C42×C29—21no—
109C42×C29—21no—
110C42×C29C2311yescharacteristic
111C23×C29—21no—
112C23×C29—21no—
113C23×C29—42no—
114C23×C29—42no—
115C23×C29—81no—
116C23×C29C2×D411yescharacteristic
117C23×C29C2×D411yescharacteristic
118Q8×C29—21no—
119Q8×C29—21no—
120Q8×C29—21no—
121Q8×C29—21no—
122Q8×C29—42no—
123D4×C29—21no—
124D4×C29—21no—
125D4×C29—21no—
126D4×C29—41no—
127D4×C29—42no—
128D4×C29—42no—
129D4×C29—81no—
130D4×C29#4112yes—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—42no—
142C2×C4×C29—81no—
143C2×C4×C29C2×D411yescharacteristic
144C2×C4×C29C2×D411yescharacteristic
145C2×C4×C29C2×D411yescharacteristic
146C2×C4×C29C2×D411yescharacteristic
147C2×C4×C29C2411yescharacteristic
148C8×C29—21no—
149C8×C29—21no—
150C8×C29—21no—
151C8×C29—21no—
152#3311C2911yesmaximal, characteristic, direct product factor, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—22no—
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29—84no—
166C22×C29C22×D411yescharacteristic
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—41no—
172C4×C29—41no—
173C4×C29—41no—
174C4×C29—41no—
175C4×C29—41no—
176C4×C29—41no—
177C4×C29C2×#4111yescharacteristic
178C4×C29H(5,𝔽2)11yescharacteristic
179#556C2×C2911yescharacteristic, complemented
180#546C2×C2911yescharacteristic
181#489C2×C2911yescharacteristic, complemented
182#485C2×C2911yescharacteristic, complemented
183#482C2×C2911yescharacteristic, complemented
184#476C2×C2911yescharacteristic, complemented
185#470C2×C2911yescharacteristic, complemented
186#465C2×C2911yescharacteristic, complemented
187#464C2×C2911yescharacteristic, complemented
188#452C2×C2911yescharacteristic, complemented
189#450C2×C2911yescharacteristic, complemented
190#440C2×C2911yescharacteristic, complemented
191#435C2×C2911yescharacteristic, complemented
192#418C2×C2911yescharacteristic, complemented
193#416C2×C2911yescharacteristic, complemented
194C2×C29—41no—
195C2×C29—41no—
196C2×C29—42no—
197C2×C29—81no—
198C2×C29#54611yescharacteristic
199C2×C29#57511yescharacteristic
200C2×C29#57711yescharacteristic
201C2×#41C22×C2911yescharacteristic
202C22×D4C22×C2911yescharacteristic
203C2×Q16C22×C2911yescharacteristic, complemented
204C2×SD16C22×C2911yescharacteristic
205C2×SD16C22×C2911yescharacteristic
206C2×M16C22×C2911yescharacteristic
207C22×C8C22×C2911yescharacteristic, complemented
208C4⋊Q8C22×C2911yescharacteristic, complemented
209#126—21no—
210#126—21no—
211#124—21no—
212#124C22×C2911yescharacteristic
213#123—21no—
214C22⋊Q8C22×C2911yescharacteristic
215C22⋊Q8C22×C2911yescharacteristic
216C22⋊Q8C22×C2911yescharacteristic, complemented
217#121—21no—
218#121C22×C2911yescharacteristic
219#120—21no—
220C4×Q8—21no—
221C4×Q8C22×C2911yescharacteristic, complemented
222C4×D4C22×C2911yescharacteristic
223C4×D4C22×C2911yescharacteristic
224#117C22×C2911yescharacteristic
225#117C22×C2911yescharacteristic, complemented
226C2×C22⋊C4—21no—
227#107C22×C2911yescharacteristic, complemented
228#106C22×C2911yescharacteristic, complemented
229#106C22×C2911yescharacteristic, complemented
230C4⋊C8C22×C2911yescharacteristic, complemented
231#103C22×C2911yescharacteristic, complemented
232#103C22×C2911yescharacteristic, complemented
233#103C22×C2911yescharacteristic, complemented
234#103C22×C2911yescharacteristic, complemented
235#102C22×C2911yescharacteristic
236#102C22×C2911yescharacteristic
237#102C22×C2911yescharacteristic
238#102C22×C2911yescharacteristic
239#102C22×C2911yescharacteristic
240#102C22×C2911yescharacteristic
241C22⋊C8C22×C2911yescharacteristic
242C22⋊C8C22×C2911yescharacteristic, complemented
243#97C22×C2911yescharacteristic, complemented
244C29#331111yescharacteristic, direct product factor, Sylow
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—21no—
249C2×Q8C23×C2911yescharacteristic
250C2×Q8C23×C2911yescharacteristic
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4D4×C2911yescharacteristic
257C2×D4C23×C2911yescharacteristic
258C2×D4C23×C2911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C23×C2911yescharacteristic
262C22×C4C23×C2911yescharacteristic
263Q16—41no—
264SD16—22no—
265SD16—41no—
266M16—41no—
267C2×C8—41no—
268C2×C8C23×C2911yescharacteristic
269C2×C8C23×C2911yescharacteristic
270C2×C8C23×C2911yescharacteristic
271C2×C8C23×C2911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4D4×C2911yescharacteristic
278C4⋊C4C23×C2911yescharacteristic
279C4⋊C4C23×C2911yescharacteristic
280C4⋊C4C23×C2911yescharacteristic
281C4⋊C4C23×C2911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4D4×C2911yescharacteristic
292C22⋊C4D4×C2911yescharacteristic
293C42—21no—
294C42—21no—
295C42—21no—
296C42C23×C2911yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×D4×C2911yescharacteristic
303C23C2×D4×C2911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—42no—
314D4—42no—
315D4—81no—
316D4#41×C2912yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4C2×D4×C2911yescharacteristic
330C2×C4C2×D4×C2911yescharacteristic
331C2×C4C2×D4×C2911yescharacteristic
332C2×C4C2×D4×C2911yescharacteristic
333C2×C4C24×C2911yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×D4×C2911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4C2×#41×C2911yescharacteristic
363C4C29×H(5,𝔽2)11yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2C29×#54611yescharacteristic
369C2C29×#57511yescharacteristic
370C2C29×#57711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
prime radicalC29×#546C2
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×#556C2semidirect
3. C29×#489C2semidirect
4. C29×#485C2semidirect
5. C29×#482C2semidirect
6. C29×#476C2semidirect
7. C29×#470C2semidirect
8. C29×#465C2semidirect
9. C29×#464C2semidirect
10. C29×#452C2semidirect
11. C29×#450C2semidirect
12. C29×#440C2semidirect
13. C29×#435C2semidirect
14. C29×#418C2semidirect
15. C29×#416C2semidirect
18. C2×Q16×C29C22semidirect
22. C22×C8×C29C22semidirect
23. C29×C4⋊Q8C22semidirect
31. C29×C22⋊Q8C22semidirect
36. C4×Q8×C29C22semidirect
40. C29×#117C22semidirect
42. C29×#107C22semidirect
43. C29×#106C22semidirect
44. C29×#106C22semidirect
45. C29×C4⋊C8C22semidirect
46. C29×#103C22semidirect
47. C29×#103C22semidirect
48. C29×#103C22semidirect
49. C29×#103C22semidirect
57. C29×C22⋊C8C22semidirect
58. C29×#97C22semidirect
152. #3311C29direct (N × H)
179. #556C2×C29semidirect
181. #489C2×C29semidirect
182. #485C2×C29semidirect
183. #482C2×C29semidirect
184. #476C2×C29semidirect
185. #470C2×C29semidirect
186. #465C2×C29semidirect
187. #464C2×C29semidirect
188. #452C2×C29semidirect
189. #450C2×C29semidirect
190. #440C2×C29semidirect
191. #435C2×C29semidirect
192. #418C2×C29semidirect
193. #416C2×C29semidirect
203. C2×Q16C22×C29semidirect
207. C22×C8C22×C29semidirect
208. C4⋊Q8C22×C29semidirect
216. C22⋊Q8C22×C29semidirect
221. C4×Q8C22×C29semidirect
225. #117C22×C29semidirect
227. #107C22×C29semidirect
228. #106C22×C29semidirect
229. #106C22×C29semidirect
230. C4⋊C8C22×C29semidirect
231. #103C22×C29semidirect
232. #103C22×C29semidirect
233. #103C22×C29semidirect
234. #103C22×C29semidirect
242. C22⋊C8C22×C29semidirect
243. #97C22×C29semidirect
244. C29#3311direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5562
C29×#5462
C29×#4892
C29×#4852
C29×#4822
C29×#4762
C29×#4702
C29×#4652
C29×#4642
C29×#4522
C29×#4502
C29×#4402
C29×#4352
C29×#4182
C29×#4162
#331129