Finite Group Databasebeta

← C29×#60238 #20355138

Subgroups — C29×#60238 #20355138

Order 7424.

2090 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3449C211yesmaximal, characteristic
2C29×#2978C214yesmaximal, complemented
3C29×#2977C214yesmaximal, complemented
4C29×#2976C218yesmaximal, complemented
5C29×#2935C214yesmaximal, complemented
6C29×#2932C212yesmaximal, complemented
7C29×#2931C212yesmaximal, complemented
8C29×#2921C211yesmaximal, characteristic, complemented
9C2×C29×#433C211yesmaximal, characteristic, complemented
10C29×#2880C214yesmaximal, complemented
11C22×#41×C29C2212yes—
12C2×C29×#131C2214yescomplemented
13C2×C29×#131C2214yescomplemented
14C29×#537C414yes—
15C29×#536C414yes—
16C29×#535C414yes—
17C29×#534C414yes—
18C29×#532C2212yes—
19C29×#532C2212yes—
20C29×#525C2214yes—
21C29×#525C2214yes—
22C2×C29×#117C2211yescharacteristic
23C29×#436C2214yescomplemented
24C29×#436C2214yescomplemented
25C29×#436C2218yescomplemented
26C29×#435C2218yescomplemented
27C29×#435C2218yescomplemented
28C29×#435C2218yescomplemented
29C29×#435C2218yescomplemented
30C8×D4×C29C2214yescomplemented
31C8×D4×C29C2214yescomplemented
32C8×D4×C29C2218yescomplemented
33C29×#433C2214yescomplemented
34C29×#433C2214yescomplemented
35C29×#433C2212yescomplemented
36C29×#433C2214yescomplemented
37C29×#433C2212yescomplemented
38C29×#423C2212yescomplemented
39C2×C29×C4⋊C8C2212yescomplemented
40C29×#408C2218yes—
41C29×#408C2218yes—
42C29×#408C2214yescomplemented
43C29×#408C2214yescomplemented
44C29×#407C2212yes—
45C29×#407C2218yescomplemented
46C2×C29×C22⋊C8C2212yes—
47C2×C29×C22⋊C8C2218yescomplemented
48C4×M16×C29C2212yescomplemented
49C2×C29×#97C2211yescharacteristic, complemented
50C2×C4×C8×C29C2211yescharacteristic, complemented
51C2×#41×C29—48no—
52C2×#41×C29C2×C414yes—
53C2×#41×C29C2×C414yes—
54C2×#41×C29C2314yes—
55C2×#41×C29C2314yes—
56C22×Q8×C29C2×C412yes—
57C22×D4×C29C2×C414yes—
58C22×D4×C29C2×C412yes—
59C23×C4×C29C2311yescharacteristic
60C23×C4×C29C2314yes—
61C29×#131—48no—
62C29×#131—48no—
63C2×M16×C29C2314yes—
64C2×M16×C29C2318yes—
65C2×M16×C29C2318yes—
66C22×C8×C29C2312yes—
67C22×C8×C29C2312yes—
68C22×C8×C29C2318yes—
69C22×C8×C29C2318yes—
70C29×C4⋊Q8C2×C412yes—
71C29×C4⋊Q8C2×C412yes—
72C29×#127C2×C412yes—
73C29×#127C2×C412yes—
74C29×#124C2×C414yes—
75C29×#124C2×C414yes—
76C29×#123C2×C418yes—
77C29×#123C2×C418yes—
78C29×C22⋊Q8C2×C418yes—
79C29×C22⋊Q8C2×C418yes—
80C29×#121C2×C418yes—
81C29×#121C2×C418yes—
82C29×#121C2×C414yes—
83C29×#121C2×C414yes—
84C29×#121C2×C418yes—
85C29×#120C2×C418yes—
86C29×#120C2×C418yes—
87C4×D4×C29C2314yes—
88C4×D4×C29C2314yes—
89C4×D4×C29C2318yes—
90C29×#117C2×C414yes—
91C29×#117C2312yes—
92C29×#117C2312yes—
93C2×C4⋊C4×C29C2×C412yes—
94C2×C22⋊C4×C29C2×C412yes—
95C2×C42×C29C2311yescharacteristic
96C2×C42×C29C2311yescharacteristic
97C29×C4⋊C8C2314yes—
98C29×C4⋊C8C2314yes—
99C29×C4⋊C8C2314yes—
100C29×C4⋊C8C2314yes—
101C29×C22⋊C8C2314yes—
102C29×C22⋊C8C2314yes—
103C29×C22⋊C8C2318yes—
104C29×C22⋊C8C2318yes—
105C29×C22⋊C8C2318yes—
106C29×C22⋊C8C2318yes—
107C29×C22⋊C8C2318yes—
108C29×#97C2312yes—
109C29×#97C2312yes—
110C29×#97C2314yes—
111C4×C8×C29C2311yescharacteristic
112C4×C8×C29C2312yes—
113C4×C8×C29C2314yes—
114C4×C8×C29C2311yescharacteristic
115C24×C29C22×C411yescharacteristic
116C24×C29C22×C414yes—
117#41×C29—28no—
118#41×C29—28no—
119#41×C29—48no—
120#41×C29—48no—
121#41×C29—48no—
122C2×Q8×C29—44no—
123C2×Q8×C29C22×C414yes—
124C2×Q8×C29C22×C414yes—
125C2×D4×C29—44no—
126C2×D4×C29—48no—
127C2×D4×C29C22×C418yes—
128C2×D4×C29C22×C414yes—
129C2×D4×C29C22×C414yes—
130C2×D4×C29C22×C414yes—
131C2×D4×C29C22×C418yes—
132C2×D4×C29C22×C418yes—
133C2×D4×C29C22×C414yes—
134C22×C4×C29—24no—
135C22×C4×C29—48no—
136C22×C4×C29C22×C411yescharacteristic
137C22×C4×C29C22×C412yes—
138C22×C4×C29C22×C412yes—
139C22×C4×C29C22×C412yes—
140C22×C4×C29C22×C418yes—
141C22×C4×C29C22×C414yes—
142C22×C4×C29C2412yes—
143C22×C4×C29C2418yes—
144C22×C4×C29C2411yescharacteristic
145M16×C29—28no—
146M16×C29—48no—
147M16×C29—48no—
148C2×C8×C29—24no—
149C2×C8×C29—24no—
150C2×C8×C29—48no—
151C2×C8×C29—48no—
152C2×C8×C29C2412yes—
153C2×C8×C29C2414yes—
154C2×C8×C29C2418yes—
155C2×C8×C29C2412yes—
156C4⋊C4×C29C22×C414yes—
157C4⋊C4×C29C22×C414yes—
158C4⋊C4×C29C22×C414yes—
159C4⋊C4×C29C22×C414yes—
160C4⋊C4×C29C22×C418yes—
161C22⋊C4×C29C22×C414yes—
162C22⋊C4×C29C22×C414yes—
163C22⋊C4×C29C22×C418yes—
164C22⋊C4×C29C22×C418yes—
165C22⋊C4×C29C22×C418yes—
166C22⋊C4×C29C22×C418yes—
167C42×C29C22×C412yes—
168C42×C29C22×C412yes—
169C42×C29C2411yescharacteristic
170C42×C29C2411yescharacteristic
171C42×C29C2412yes—
172#60238C2911yesmaximal, characteristic, direct product factor, Sylow
173C23×C29—22no—
174C23×C29—44no—
175C23×C29—42no—
176C23×C29—48no—
177C23×C29C23×C412yes—
178C23×C29C23×C418yes—
179C23×C29C23×C411yescharacteristic
180Q8×C29—28no—
181Q8×C29—44no—
182D4×C29—216no—
183D4×C29—28no—
184D4×C29—44no—
185D4×C29—48no—
186D4×C29—44no—
187D4×C29—44no—
188D4×C29—48no—
189C2×C4×C29—22no—
190C2×C4×C29—24no—
191C2×C4×C29—28no—
192C2×C4×C29—28no—
193C2×C4×C29—24no—
194C2×C4×C29—44no—
195C2×C4×C29—48no—
196C2×C4×C29—42no—
197C2×C4×C29—42no—
198C2×C4×C29C23×C412yes—
199C2×C4×C29C23×C412yes—
200C2×C4×C29C23×C414yes—
201C2×C4×C29C23×C418yes—
202C2×C4×C29C23×C412yes—
203C2×C4×C29C23×C411yescharacteristic
204C2×C4×C29H(5,𝔽2)14yes—
205C2×C4×C29C2511yescharacteristic
206C8×C29—22no—
207C8×C29—24no—
208C8×C29—22no—
209C8×C29—28no—
210#3449C2×C2911yescharacteristic
211#2978C2×C2914yescomplemented
212#2977C2×C2914yescomplemented
213#2976C2×C2918yescomplemented
214#2935C2×C2914yescomplemented
215#2932C2×C2912yescomplemented
216#2931C2×C2912yescomplemented
217#2921C2×C2911yescharacteristic, complemented
218C2×#433C2×C2911yescharacteristic, complemented
219#2880C2×C2914yescomplemented
220C22×C29—22no—
221C22×C29—22no—
222C22×C29—28no—
223C22×C29—28no—
224C22×C29—28no—
225C22×C29—24no—
226C22×C29—82no—
227C22×C29—88no—
228C22×C29#51812yes—
229C22×C29C24×C411yescharacteristic
230C4×C29—22no—
231C4×C29—28no—
232C4×C29—22no—
233C4×C29—22no—
234C4×C29—24no—
235C4×C29#51812yes—
236C4×C29C2×H(5,𝔽2)12yes—
237C22×#41C22×C2912yes—
238C2×#131C22×C2914yescomplemented
239C2×#131C22×C2914yescomplemented
240#537C4×C2914yes—
241#536C4×C2914yes—
242#535C4×C2914yes—
243#534C4×C2914yes—
244#532C22×C2912yes—
245#532C22×C2912yes—
246#525C22×C2914yes—
247#525C22×C2914yes—
248C2×#117C22×C2911yescharacteristic
249#436C22×C2914yescomplemented
250#436C22×C2914yescomplemented
251#436C22×C2918yescomplemented
252#435C22×C2918yescomplemented
253#435C22×C2918yescomplemented
254#435C22×C2918yescomplemented
255#435C22×C2918yescomplemented
256C8×D4C22×C2914yescomplemented
257C8×D4C22×C2914yescomplemented
258C8×D4C22×C2918yescomplemented
259#433C22×C2914yescomplemented
260#433C22×C2912yescomplemented
261#433C22×C2912yescomplemented
262#433C22×C2914yescomplemented
263#433C22×C2914yescomplemented
264#423C22×C2912yescomplemented
265C2×C4⋊C8C22×C2912yescomplemented
266#408C22×C2918yes—
267#408C22×C2918yes—
268#408C22×C2914yescomplemented
269#408C22×C2914yescomplemented
270#407C22×C2912yes—
271#407C22×C2918yescomplemented
272C2×C22⋊C8C22×C2912yes—
273C2×C22⋊C8C22×C2918yescomplemented
274C4×M16C22×C2912yescomplemented
275C2×#97C22×C2911yescharacteristic, complemented
276C2×C4×C8C22×C2911yescharacteristic, complemented
277C2×C29—22no—
278C2×C29—48no—
279C2×C29—42no—
280C2×C29C2×#51811yescharacteristic
281C2×C29#357312yes—
282C2×#41—48no—
283C2×#41C2×C4×C2914yes—
284C2×#41C2×C4×C2914yes—
285C2×#41C23×C2914yes—
286C2×#41C23×C2914yes—
287C22×Q8C2×C4×C2912yes—
288C22×D4C2×C4×C2914yes—
289C22×D4C2×C4×C2912yes—
290C23×C4C23×C2911yescharacteristic
291C23×C4C23×C2914yes—
292#131—48no—
293#131—48no—
294C2×M16C23×C2914yes—
295C2×M16C23×C2918yes—
296C2×M16C23×C2918yes—
297C22×C8C23×C2912yes—
298C22×C8C23×C2912yes—
299C22×C8C23×C2918yes—
300C22×C8C23×C2918yes—
301C4⋊Q8C2×C4×C2912yes—
302C4⋊Q8C2×C4×C2912yes—
303#127C2×C4×C2912yes—
304#127C2×C4×C2912yes—
305#124C2×C4×C2914yes—
306#124C2×C4×C2914yes—
307#123C2×C4×C2918yes—
308#123C2×C4×C2918yes—
309C22⋊Q8C2×C4×C2918yes—
310C22⋊Q8C2×C4×C2918yes—
311#121C2×C4×C2918yes—
312#121C2×C4×C2918yes—
313#121C2×C4×C2914yes—
314#121C2×C4×C2914yes—
315#121C2×C4×C2918yes—
316#120C2×C4×C2918yes—
317#120C2×C4×C2918yes—
318C4×D4C23×C2914yes—
319C4×D4C23×C2918yes—
320C4×D4C23×C2914yes—
321#117C2×C4×C2914yes—
322#117C23×C2912yes—
323#117C23×C2912yes—
324C2×C4⋊C4C2×C4×C2912yes—
325C2×C22⋊C4C2×C4×C2912yes—
326C2×C42C23×C2911yescharacteristic
327C2×C42C23×C2911yescharacteristic
328C4⋊C8C23×C2914yes—
329C4⋊C8C23×C2914yes—
330C4⋊C8C23×C2914yes—
331C4⋊C8C23×C2914yes—
332C22⋊C8C23×C2914yes—
333C22⋊C8C23×C2914yes—
334C22⋊C8C23×C2918yes—
335C22⋊C8C23×C2918yes—
336C22⋊C8C23×C2918yes—
337C22⋊C8C23×C2918yes—
338C22⋊C8C23×C2918yes—
339#97C23×C2912yes—
340#97C23×C2912yes—
341#97C23×C2914yes—
342C4×C8C23×C2911yescharacteristic
343C4×C8C23×C2912yes—
344C4×C8C23×C2911yescharacteristic
345C4×C8C23×C2914yes—
346C29#6023811yescharacteristic, direct product factor, Sylow
347C24C22×C4×C2911yescharacteristic
348C24C22×C4×C2914yes—
349#41—28no—
350#41—28no—
351#41—48no—
352#41—48no—
353#41—48no—
354C2×Q8—44no—
355C2×Q8C22×C4×C2914yes—
356C2×Q8C22×C4×C2914yes—
357C2×D4—44no—
358C2×D4—48no—
359C2×D4C22×C4×C2918yes—
360C2×D4C22×C4×C2914yes—
361C2×D4C22×C4×C2914yes—
362C2×D4C22×C4×C2918yes—
363C2×D4C22×C4×C2914yes—
364C2×D4C22×C4×C2918yes—
365C2×D4C22×C4×C2914yes—
366C22×C4—24no—
367C22×C4—48no—
368C22×C4C22×C4×C2911yescharacteristic
369C22×C4C22×C4×C2912yes—
370C22×C4C22×C4×C2912yes—
371C22×C4C22×C4×C2912yes—
372C22×C4C22×C4×C2918yes—
373C22×C4C22×C4×C2914yes—
374C22×C4C24×C2912yes—
375C22×C4C24×C2918yes—
376C22×C4C24×C2911yescharacteristic
377M16—28no—
378M16—48no—
379M16—48no—
380C2×C8—24no—
381C2×C8—24no—
382C2×C8—48no—
383C2×C8—48no—
384C2×C8C24×C2912yes—
385C2×C8C24×C2912yes—
386C2×C8C24×C2918yes—
387C2×C8C24×C2914yes—
388C4⋊C4C22×C4×C2914yes—
389C4⋊C4C22×C4×C2914yes—
390C4⋊C4C22×C4×C2914yes—
391C4⋊C4C22×C4×C2918yes—
392C4⋊C4C22×C4×C2914yes—
393C22⋊C4C22×C4×C2914yes—
394C22⋊C4C22×C4×C2914yes—
395C22⋊C4C22×C4×C2918yes—
396C22⋊C4C22×C4×C2918yes—
397C22⋊C4C22×C4×C2918yes—
398C22⋊C4C22×C4×C2918yes—
399C42C22×C4×C2912yes—
400C42C22×C4×C2912yes—
401C42C24×C2911yescharacteristic
402C42C24×C2911yescharacteristic
403C42C24×C2912yes—
404C23—22no—
405C23—44no—
406C23—42no—
407C23—48no—
408C23C23×C4×C2912yes—
409C23C23×C4×C2918yes—
410C23C23×C4×C2911yescharacteristic
411Q8—28no—
412Q8—44no—
413D4—216no—
414D4—28no—
415D4—44no—
416D4—48no—
417D4—44no—
418D4—48no—
419D4—44no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—28no—
423C2×C4—28no—
424C2×C4—24no—
425C2×C4—44no—
426C2×C4—48no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4C23×C4×C2912yes—
430C2×C4C23×C4×C2912yes—
431C2×C4C23×C4×C2914yes—
432C2×C4C23×C4×C2918yes—
433C2×C4C23×C4×C2912yes—
434C2×C4C23×C4×C2911yescharacteristic
435C2×C4C29×H(5,𝔽2)14yes—
436C2×C4C25×C2911yescharacteristic
437C8—22no—
438C8—24no—
439C8—22no—
440C8—28no—
441C22—22no—
442C22—28no—
443C22—28no—
444C22—24no—
445C22—22no—
446C22—28no—
447C22—82no—
448C22—88no—
449C22C29×#51812yes—
450C22C24×C4×C2911yescharacteristic
451C4—22no—
452C4—22no—
453C4—24no—
454C4—22no—
455C4—28no—
456C4C29×#51812yes—
457C4C2×C29×H(5,𝔽2)12yes—
458C2—22no—
459C2—42no—
460C2—48no—
461C2C2×C29×#51811yescharacteristic
462C2C29×#357312yes—
subgroupG/H
centerC2×C4×C29C25
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3449C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2978C2semidirect
3. C29×#2977C2semidirect
4. C29×#2976C2semidirect
5. C29×#2935C2semidirect
6. C29×#2932C2semidirect
7. C29×#2931C2semidirect
8. C29×#2921C2semidirect
9. C2×C29×#433C2semidirect
10. C29×#2880C2semidirect
12. C2×C29×#131C22semidirect
13. C2×C29×#131C22semidirect
23. C29×#436C22semidirect
24. C29×#436C22semidirect
25. C29×#436C22semidirect
26. C29×#435C22semidirect
27. C29×#435C22semidirect
28. C29×#435C22semidirect
29. C29×#435C22semidirect
30. C8×D4×C29C22semidirect
31. C8×D4×C29C22semidirect
32. C8×D4×C29C22semidirect
33. C29×#433C22semidirect
34. C29×#433C22semidirect
35. C29×#433C22semidirect
36. C29×#433C22semidirect
37. C29×#433C22semidirect
38. C29×#423C22semidirect
39. C2×C29×C4⋊C8C22semidirect
42. C29×#408C22semidirect
43. C29×#408C22semidirect
45. C29×#407C22semidirect
47. C2×C29×C22⋊C8C22semidirect
48. C4×M16×C29C22semidirect
49. C2×C29×#97C22semidirect
50. C2×C4×C8×C29C22semidirect
172. #60238C29direct (N × H)
211. #2978C2×C29semidirect
212. #2977C2×C29semidirect
213. #2976C2×C29semidirect
214. #2935C2×C29semidirect
215. #2932C2×C29semidirect
216. #2931C2×C29semidirect
217. #2921C2×C29semidirect
218. C2×#433C2×C29semidirect
219. #2880C2×C29semidirect
238. C2×#131C22×C29semidirect
239. C2×#131C22×C29semidirect
249. #436C22×C29semidirect
250. #436C22×C29semidirect
251. #436C22×C29semidirect
252. #435C22×C29semidirect
253. #435C22×C29semidirect
254. #435C22×C29semidirect
255. #435C22×C29semidirect
256. C8×D4C22×C29semidirect
257. C8×D4C22×C29semidirect
258. C8×D4C22×C29semidirect
259. #433C22×C29semidirect
260. #433C22×C29semidirect
261. #433C22×C29semidirect
262. #433C22×C29semidirect
263. #433C22×C29semidirect
264. #423C22×C29semidirect
265. C2×C4⋊C8C22×C29semidirect
268. #408C22×C29semidirect
269. #408C22×C29semidirect
271. #407C22×C29semidirect
273. C2×C22⋊C8C22×C29semidirect
274. C4×M16C22×C29semidirect
275. C2×#97C22×C29semidirect
276. C2×C4×C8C22×C29semidirect
346. C29#60238direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34492
C29×#29782
C29×#29772
C29×#29762
C29×#29352
C29×#29322
C29×#29312
C29×#29212
C2×C29×#4332
C29×#28802
#6023829