Finite Group Databasebeta

← C29×#60317 #20355217

Subgroups — C29×#60317 #20355217

Order 7424.

1892 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3481C211yesmaximal, characteristic
2C29×#2993C214yesmaximal, complemented
3C29×#2991C212yesmaximal, complemented
4C29×#2979C211yesmaximal, characteristic, complemented
5C29×#2978C214yesmaximal, complemented
6C29×#2975C214yesmaximal, complemented
7C29×#2969C214yesmaximal, complemented
8C29×#2965C212yesmaximal, complemented
9D4×M16×C29C214yesmaximal, complemented
10C29×#2931C211yesmaximal, characteristic, complemented
11C29×#2930C214yesmaximal, complemented
12C2×C29×#131C2212yescomplemented
13C22×M16×C29C2214yescomplemented
14C29×#559C411yescharacteristic
15C29×#554C412yes—
16C29×#553C414yes—
17C29×#551C414yes—
18C29×#546C414yes—
19D42×C29C411yescharacteristic
20C29×#532C2211yescharacteristic
21C29×#529C2214yes—
22C29×#525C2214yes—
23C4×#41×C29C2212yes—
24C2×C4×D4×C29C2214yes—
25C29×#446C2212yescomplemented
26C29×#446C2212yescomplemented
27C8×Q8×C29C2214yescomplemented
28C29×#436C2212yes—
29C29×#436C2214yes—
30C29×#436C2212yes—
31C29×#436C2218yescomplemented
32C29×#436C2218yescomplemented
33C29×#436C2214yescomplemented
34C29×#436C2218yescomplemented
35C29×#436C2214yescomplemented
36C29×#435C2214yescomplemented
37C29×#435C2218yescomplemented
38C29×#435C2218yescomplemented
39C29×#435C2214yescomplemented
40C8×D4×C29C2214yescomplemented
41C8×D4×C29C2214yescomplemented
42C29×#433C2218yescomplemented
43C29×#431C2214yescomplemented
44C29×#431C2212yescomplemented
45C29×#431C2214yescomplemented
46C29×#424C2214yescomplemented
47C29×#423C2211yescharacteristic, complemented
48C29×#423C2214yescomplemented
49C29×#408C2214yescomplemented
50C29×#408C2212yescomplemented
51C29×#407C2214yescomplemented
52C29×#407C2218yescomplemented
53C29×#405C2214yescomplemented
54C4×M16×C29C2214yescomplemented
55C2×C4×C8×C29C2211yescharacteristic, complemented
56C2×#41×C29C2×C412yes—
57C2×#41×C29C2312yes—
58C22×D4×C29C2×C414yes—
59C23×C4×C29C2314yes—
60C29×#131—44no—
61C2×M16×C29—48no—
62C2×M16×C29C2314yes—
63C2×M16×C29C2318yes—
64C2×M16×C29C2314yes—
65C2×M16×C29C2314yes—
66C2×M16×C29C2312yes—
67C2×M16×C29C2314yes—
68C22×C8×C29C2314yes—
69C22×C8×C29C2311yescharacteristic
70C22×C8×C29C2314yes—
71C22×C8×C29C2311yescharacteristic
72C29×C4⋊Q8C2×C411yescharacteristic
73C29×#127C2×C411yescharacteristic
74C29×#126C2×C418yes—
75C29×#125C2×C414yes—
76C29×#124C2×C414yes—
77C29×#124C2×C412yes—
78C29×#123C2×C414yes—
79C29×#123C2×C414yes—
80C29×#123C2×C418yes—
81C29×C22⋊Q8C2×C418yes—
82C29×C22⋊Q8C2×C414yes—
83C29×#121C2×C418yes—
84C29×#121C2×C414yes—
85C29×#121C2×C414yes—
86C29×#120C2×C414yes—
87C29×#120C2×C414yes—
88C4×Q8×C29C2×C412yes—
89C4×Q8×C29C2312yes—
90C4×D4×C29C2×C414yes—
91C4×D4×C29C2×C418yes—
92C4×D4×C29C2×C414yes—
93C4×D4×C29C2×C412yes—
94C4×D4×C29C2×C414yes—
95C4×D4×C29C2314yes—
96C4×D4×C29C2318yes—
97C4×D4×C29C2314yes—
98C4×D4×C29C2312yes—
99C29×#117C2×C414yes—
100C29×#117C2×C412yes—
101C29×#117C2314yes—
102C2×C4⋊C4×C29C2×C414yes—
103C2×C22⋊C4×C29C2×C418yes—
104C2×C42×C29C2314yes—
105C2×C42×C29C2311yescharacteristic
106C29×C4⋊C8C2312yes—
107C29×C4⋊C8C2314yes—
108C29×C4⋊C8C2312yes—
109C29×C4⋊C8C2314yes—
110C29×C4⋊C8C2314yes—
111C29×C4⋊C8C2318yes—
112C29×C22⋊C8C2314yes—
113C29×C22⋊C8C2314yes—
114C29×C22⋊C8C2314yes—
115C29×C22⋊C8C2318yes—
116C29×C22⋊C8C2318yes—
117C29×C22⋊C8C2318yes—
118C29×#97C2314yes—
119C29×#97C2314yes—
120C4×C8×C29C2314yes—
121C4×C8×C29C2312yes—
122C4×C8×C29C2318yes—
123C4×C8×C29C2312yes—
124C24×C29C22×C414yes—
125#41×C29—42no—
126#41×C29—42no—
127#41×C29—44no—
128C2×Q8×C29C22×C412yes—
129C2×Q8×C29C22×C412yes—
130C2×D4×C29—48no—
131C2×D4×C29C22×C412yes—
132C2×D4×C29C22×C414yes—
133C2×D4×C29C22×C414yes—
134C2×D4×C29C22×C418yes—
135C2×D4×C29C22×C412yes—
136C2×D4×C29C22×C414yes—
137C22×C4×C29—44no—
138C22×C4×C29—44no—
139C22×C4×C29C22×C414yes—
140C22×C4×C29C22×C412yes—
141C22×C4×C29C22×C414yes—
142C22×C4×C29C22×C418yes—
143C22×C4×C29C22×C414yes—
144C22×C4×C29C2411yescharacteristic
145C22×C4×C29C2414yes—
146C22×C4×C29C2414yes—
147M16×C29—28no—
148M16×C29—48no—
149M16×C29—44no—
150M16×C29—44no—
151M16×C29—44no—
152M16×C29—42no—
153C2×C8×C29—28no—
154C2×C8×C29—22no—
155C2×C8×C29—41no—
156C2×C8×C29—44no—
157C2×C8×C29C2414yes—
158C2×C8×C29C2414yes—
159C2×C8×C29C2411yescharacteristic
160C2×C8×C29C2412yes—
161C2×C8×C29C2414yes—
162C2×C8×C29C2411yescharacteristic
163C4⋊C4×C29C22×C412yes—
164C4⋊C4×C29C22×C414yes—
165C4⋊C4×C29C22×C418yes—
166C4⋊C4×C29C22×C412yes—
167C4⋊C4×C29C22×C414yes—
168C4⋊C4×C29C22×C414yes—
169C4⋊C4×C29C22×C418yes—
170C22⋊C4×C29C22×C414yes—
171C22⋊C4×C29C22×C418yes—
172C22⋊C4×C29C22×C418yes—
173C22⋊C4×C29C22×C418yes—
174C22⋊C4×C29C22×C414yes—
175C22⋊C4×C29C22×C414yes—
176C22⋊C4×C29C22×C414yes—
177C22⋊C4×C29C22×C414yes—
178C42×C29C22×C411yescharacteristic
179C42×C29C22×C414yes—
180C42×C29C22×C414yes—
181C42×C29C22×C411yescharacteristic
182C42×C29C2412yes—
183C42×C29C2414yes—
184#60317C2911yesmaximal, characteristic, direct product factor, Sylow
185C23×C29—44no—
186C23×C29—48no—
187C23×C29C23×C414yes—
188C23×C29C23×C414yes—
189C23×C29C23×C411yescharacteristic
190Q8×C29—24no—
191Q8×C29—42no—
192D4×C29—24no—
193D4×C29—28no—
194D4×C29—48no—
195D4×C29—44no—
196D4×C29—42no—
197D4×C29—44no—
198C2×C4×C29—28no—
199C2×C4×C29—24no—
200C2×C4×C29—24no—
201C2×C4×C29—21no—
202C2×C4×C29—24no—
203C2×C4×C29—21no—
204C2×C4×C29—24no—
205C2×C4×C29—24no—
206C2×C4×C29—44no—
207C2×C4×C29—48no—
208C2×C4×C29—44no—
209C2×C4×C29C23×C412yes—
210C2×C4×C29C23×C414yes—
211C2×C4×C29C23×C411yescharacteristic
212C2×C4×C29C23×C414yes—
213C2×C4×C29C23×C414yes—
214C2×C4×C29C23×C414yes—
215C2×C4×C29C23×C412yes—
216C2×C4×C29C2511yescharacteristic
217C8×C29—24no—
218C8×C29—21no—
219C8×C29—24no—
220C8×C29—22no—
221C8×C29—24no—
222C8×C29H(5,𝔽2)12yes—
223#3481C2×C2911yescharacteristic
224#2993C2×C2914yescomplemented
225#2991C2×C2912yescomplemented
226#2979C2×C2911yescharacteristic, complemented
227#2978C2×C2914yescomplemented
228#2975C2×C2914yescomplemented
229#2969C2×C2914yescomplemented
230#2965C2×C2912yescomplemented
231D4×M16C2×C2914yescomplemented
232#2931C2×C2911yescharacteristic, complemented
233#2930C2×C2914yescomplemented
234C22×C29—24no—
235C22×C29—24no—
236C22×C29—21no—
237C22×C29—22no—
238C22×C29—24no—
239C22×C29—24no—
240C22×C29—28no—
241C22×C29—88no—
242C22×C29C24×C411yescharacteristic
243C4×C29—24no—
244C4×C29—24no—
245C4×C29—21no—
246C4×C29—22no—
247C4×C29—24no—
248C4×C29—24no—
249C4×C29#56814yes—
250C4×C29C2×H(5,𝔽2)11yescharacteristic
251C4×C29#58511yescharacteristic
252C2×#131C22×C2912yescomplemented
253C22×M16C22×C2914yescomplemented
254#559C4×C2911yescharacteristic
255#554C4×C2912yes—
256#553C4×C2914yes—
257#551C4×C2914yes—
258#546C4×C2914yes—
259D42C4×C2911yescharacteristic
260#532C22×C2911yescharacteristic
261#529C22×C2914yes—
262#525C22×C2914yes—
263C4×#41C22×C2912yes—
264C2×C4×D4C22×C2914yes—
265#446C22×C2912yescomplemented
266#446C22×C2912yescomplemented
267C8×Q8C22×C2914yescomplemented
268#436C22×C2912yes—
269#436C22×C2914yes—
270#436C22×C2912yes—
271#436C22×C2918yescomplemented
272#436C22×C2918yescomplemented
273#436C22×C2914yescomplemented
274#436C22×C2918yescomplemented
275#436C22×C2914yescomplemented
276#435C22×C2914yescomplemented
277#435C22×C2918yescomplemented
278#435C22×C2918yescomplemented
279#435C22×C2914yescomplemented
280C8×D4C22×C2914yescomplemented
281C8×D4C22×C2914yescomplemented
282#433C22×C2918yescomplemented
283#431C22×C2914yescomplemented
284#431C22×C2912yescomplemented
285#431C22×C2914yescomplemented
286#424C22×C2914yescomplemented
287#423C22×C2911yescharacteristic, complemented
288#423C22×C2914yescomplemented
289#408C22×C2914yescomplemented
290#408C22×C2912yescomplemented
291#407C22×C2914yescomplemented
292#407C22×C2918yescomplemented
293#405C22×C2914yescomplemented
294C4×M16C22×C2914yescomplemented
295C2×C4×C8C22×C2911yescharacteristic, complemented
296C2×C29—41no—
297C2×C29—44no—
298C2×C29—44no—
299C2×C29C4×H(5,𝔽2)11yescharacteristic
300C2×C29C2×#56812yes—
301C2×#41C2×C4×C2912yes—
302C2×#41C23×C2912yes—
303C22×D4C2×C4×C2914yes—
304C23×C4C23×C2914yes—
305#131—44no—
306C2×M16—48no—
307C2×M16C23×C2914yes—
308C2×M16C23×C2918yes—
309C2×M16C23×C2914yes—
310C2×M16C23×C2912yes—
311C2×M16C23×C2914yes—
312C2×M16C23×C2914yes—
313C22×C8C23×C2914yes—
314C22×C8C23×C2911yescharacteristic
315C22×C8C23×C2914yes—
316C22×C8C23×C2911yescharacteristic
317C4⋊Q8C2×C4×C2911yescharacteristic
318#127C2×C4×C2911yescharacteristic
319#126C2×C4×C2918yes—
320#125C2×C4×C2914yes—
321#124C2×C4×C2914yes—
322#124C2×C4×C2912yes—
323#123C2×C4×C2914yes—
324#123C2×C4×C2914yes—
325#123C2×C4×C2918yes—
326C22⋊Q8C2×C4×C2918yes—
327C22⋊Q8C2×C4×C2914yes—
328#121C2×C4×C2918yes—
329#121C2×C4×C2914yes—
330#121C2×C4×C2914yes—
331#120C2×C4×C2914yes—
332#120C2×C4×C2914yes—
333C4×Q8C2×C4×C2912yes—
334C4×Q8C23×C2912yes—
335C4×D4C2×C4×C2914yes—
336C4×D4C2×C4×C2918yes—
337C4×D4C2×C4×C2914yes—
338C4×D4C2×C4×C2912yes—
339C4×D4C2×C4×C2914yes—
340C4×D4C23×C2912yes—
341C4×D4C23×C2918yes—
342C4×D4C23×C2914yes—
343C4×D4C23×C2914yes—
344#117C2×C4×C2914yes—
345#117C2×C4×C2912yes—
346#117C23×C2914yes—
347C2×C4⋊C4C2×C4×C2914yes—
348C2×C22⋊C4C2×C4×C2918yes—
349C2×C42C23×C2914yes—
350C2×C42C23×C2911yescharacteristic
351C4⋊C8C23×C2912yes—
352C4⋊C8C23×C2914yes—
353C4⋊C8C23×C2918yes—
354C4⋊C8C23×C2914yes—
355C4⋊C8C23×C2912yes—
356C4⋊C8C23×C2914yes—
357C22⋊C8C23×C2914yes—
358C22⋊C8C23×C2914yes—
359C22⋊C8C23×C2918yes—
360C22⋊C8C23×C2918yes—
361C22⋊C8C23×C2918yes—
362C22⋊C8C23×C2914yes—
363#97C23×C2914yes—
364#97C23×C2914yes—
365C4×C8C23×C2912yes—
366C4×C8C23×C2912yes—
367C4×C8C23×C2914yes—
368C4×C8C23×C2918yes—
369C29#6031711yescharacteristic, direct product factor, Sylow
370C24C22×C4×C2914yes—
371#41—42no—
372#41—42no—
373#41—44no—
374C2×Q8C22×C4×C2912yes—
375C2×Q8C22×C4×C2912yes—
376C2×D4—48no—
377C2×D4C22×C4×C2912yes—
378C2×D4C22×C4×C2914yes—
379C2×D4C22×C4×C2914yes—
380C2×D4C22×C4×C2918yes—
381C2×D4C22×C4×C2912yes—
382C2×D4C22×C4×C2914yes—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4C22×C4×C2914yes—
386C22×C4C22×C4×C2912yes—
387C22×C4C22×C4×C2914yes—
388C22×C4C22×C4×C2918yes—
389C22×C4C22×C4×C2914yes—
390C22×C4C24×C2911yescharacteristic
391C22×C4C24×C2914yes—
392C22×C4C24×C2914yes—
393M16—28no—
394M16—48no—
395M16—44no—
396M16—42no—
397M16—44no—
398M16—44no—
399C2×C8—28no—
400C2×C8—22no—
401C2×C8—44no—
402C2×C8—41no—
403C2×C8C24×C2914yes—
404C2×C8C24×C2912yes—
405C2×C8C24×C2911yescharacteristic
406C2×C8C24×C2914yes—
407C2×C8C24×C2914yes—
408C2×C8C24×C2911yescharacteristic
409C4⋊C4C22×C4×C2912yes—
410C4⋊C4C22×C4×C2914yes—
411C4⋊C4C22×C4×C2918yes—
412C4⋊C4C22×C4×C2912yes—
413C4⋊C4C22×C4×C2914yes—
414C4⋊C4C22×C4×C2914yes—
415C4⋊C4C22×C4×C2918yes—
416C22⋊C4C22×C4×C2914yes—
417C22⋊C4C22×C4×C2918yes—
418C22⋊C4C22×C4×C2918yes—
419C22⋊C4C22×C4×C2918yes—
420C22⋊C4C22×C4×C2914yes—
421C22⋊C4C22×C4×C2914yes—
422C22⋊C4C22×C4×C2914yes—
423C22⋊C4C22×C4×C2914yes—
424C42C22×C4×C2911yescharacteristic
425C42C22×C4×C2914yes—
426C42C22×C4×C2914yes—
427C42C22×C4×C2911yescharacteristic
428C42C24×C2912yes—
429C42C24×C2914yes—
430C23—44no—
431C23—48no—
432C23C23×C4×C2914yes—
433C23C23×C4×C2914yes—
434C23C23×C4×C2911yescharacteristic
435Q8—24no—
436Q8—42no—
437D4—24no—
438D4—28no—
439D4—48no—
440D4—44no—
441D4—44no—
442D4—42no—
443C2×C4—28no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—44no—
452C2×C4—48no—
453C2×C4—44no—
454C2×C4C23×C4×C2912yes—
455C2×C4C23×C4×C2914yes—
456C2×C4C23×C4×C2911yescharacteristic
457C2×C4C23×C4×C2914yes—
458C2×C4C23×C4×C2914yes—
459C2×C4C23×C4×C2914yes—
460C2×C4C23×C4×C2912yes—
461C2×C4C25×C2911yescharacteristic
462C8—24no—
463C8—21no—
464C8—24no—
465C8—22no—
466C8—24no—
467C8C29×H(5,𝔽2)12yes—
468C22—22no—
469C22—24no—
470C22—24no—
471C22—28no—
472C22—24no—
473C22—24no—
474C22—21no—
475C22—88no—
476C22C24×C4×C2911yescharacteristic
477C4—22no—
478C4—24no—
479C4—24no—
480C4—24no—
481C4—24no—
482C4—21no—
483C4C29×#56814yes—
484C4C2×C29×H(5,𝔽2)11yescharacteristic
485C4C29×#58511yescharacteristic
486C2—44no—
487C2—44no—
488C2—41no—
489C2C4×C29×H(5,𝔽2)11yescharacteristic
490C2C2×C29×#56812yes—
subgroupG/H
centerC2×C4×C29C25
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3481C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2993C2semidirect
3. C29×#2991C2semidirect
4. C29×#2979C2semidirect
5. C29×#2978C2semidirect
6. C29×#2975C2semidirect
7. C29×#2969C2semidirect
8. C29×#2965C2semidirect
9. D4×M16×C29C2semidirect
10. C29×#2931C2semidirect
11. C29×#2930C2semidirect
12. C2×C29×#131C22semidirect
13. C22×M16×C29C22semidirect
25. C29×#446C22semidirect
26. C29×#446C22semidirect
27. C8×Q8×C29C22semidirect
31. C29×#436C22semidirect
32. C29×#436C22semidirect
33. C29×#436C22semidirect
34. C29×#436C22semidirect
35. C29×#436C22semidirect
36. C29×#435C22semidirect
37. C29×#435C22semidirect
38. C29×#435C22semidirect
39. C29×#435C22semidirect
40. C8×D4×C29C22semidirect
41. C8×D4×C29C22semidirect
42. C29×#433C22semidirect
43. C29×#431C22semidirect
44. C29×#431C22semidirect
45. C29×#431C22semidirect
46. C29×#424C22semidirect
47. C29×#423C22semidirect
48. C29×#423C22semidirect
49. C29×#408C22semidirect
50. C29×#408C22semidirect
51. C29×#407C22semidirect
52. C29×#407C22semidirect
53. C29×#405C22semidirect
54. C4×M16×C29C22semidirect
55. C2×C4×C8×C29C22semidirect
184. #60317C29direct (N × H)
224. #2993C2×C29semidirect
225. #2991C2×C29semidirect
226. #2979C2×C29semidirect
227. #2978C2×C29semidirect
228. #2975C2×C29semidirect
229. #2969C2×C29semidirect
230. #2965C2×C29semidirect
231. D4×M16C2×C29semidirect
232. #2931C2×C29semidirect
233. #2930C2×C29semidirect
252. C2×#131C22×C29semidirect
253. C22×M16C22×C29semidirect
265. #446C22×C29semidirect
266. #446C22×C29semidirect
267. C8×Q8C22×C29semidirect
271. #436C22×C29semidirect
272. #436C22×C29semidirect
273. #436C22×C29semidirect
274. #436C22×C29semidirect
275. #436C22×C29semidirect
276. #435C22×C29semidirect
277. #435C22×C29semidirect
278. #435C22×C29semidirect
279. #435C22×C29semidirect
280. C8×D4C22×C29semidirect
281. C8×D4C22×C29semidirect
282. #433C22×C29semidirect
283. #431C22×C29semidirect
284. #431C22×C29semidirect
285. #431C22×C29semidirect
286. #424C22×C29semidirect
287. #423C22×C29semidirect
288. #423C22×C29semidirect
289. #408C22×C29semidirect
290. #408C22×C29semidirect
291. #407C22×C29semidirect
292. #407C22×C29semidirect
293. #405C22×C29semidirect
294. C4×M16C22×C29semidirect
295. C2×C4×C8C22×C29semidirect
369. C29#60317direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34812
C29×#29932
C29×#29912
C29×#29792
C29×#29782
C29×#29752
C29×#29692
C29×#29652
D4×M16×C292
C29×#29312
C29×#29302
#6031729