Finite Group Databasebeta

← C29×#19470 #20314370

Subgroups — C29×#19470 #20314370

Order 7424.

694 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3205C211yesmaximal, characteristic
2C29×#3112C211yesmaximal, characteristic, complemented
3C2×C29×#460C211yesmaximal, characteristic, complemented
4C29×#2984C211yesmaximal, characteristic, complemented
5C29×#1698C212yesmaximal, complemented
6C29×#1688C212yesmaximal, complemented
7C29×#1678C212yesmaximal, complemented
8C29×#1668C212yesmaximal, complemented
9C29×#1573C211yesmaximal, characteristic, complemented
10C29×#1555C211yesmaximal, characteristic, complemented
11C29×#1551C211yesmaximal, characteristic, complemented
12C22×SD16×C29—21no—
13C29×#532C2211yescharacteristic
14C2×C29×#127C2211yescharacteristic
15C2×C4×Q8×C29C2211yescharacteristic
16C29×#493C2212yes—
17C29×#486C2212yes—
18C29×#480—21no—
19C29×#477C2211yescharacteristic, complemented
20C29×#477C2211yescharacteristic, complemented
21C29×#460—21no—
22C29×#460—21no—
23C29×#460C2212yes—
24C29×#460C2212yes—
25C29×#460C2211yescharacteristic, complemented
26C29×#460C2211yescharacteristic, complemented
27C29×#459—22no—
28C29×#448—21no—
29C29×#447—21no—
30C29×#447—21no—
31C29×#446—22no—
32C29×#446C2212yescomplemented
33C8×Q8×C29C2212yescomplemented
34C29×#440—21no—
35C29×#440—21no—
36C29×#432—21no—
37C29×#432C2211yescharacteristic
38C29×#432C2211yescharacteristic
39C29×#431—21no—
40C29×#431C2211yescharacteristic
41C2×C29×C4⋊C8C2211yescharacteristic
42C2×C29×#102—21no—
43C29×#335C2212yescomplemented
44C29×#334C2212yescomplemented
45C29×#333C2212yescomplemented
46C29×#331C2212yes—
47C29×#331C2212yes—
48C29×#331C2212yescomplemented
49C2×#41×C29—21no—
50C22×Q8×C29D411yescharacteristic
51C22×D4×C29—21no—
52C22×D4×C29—21no—
53C22×D4×C29—21no—
54C2×SD16×C29—21no—
55C2×SD16×C29—21no—
56C2×SD16×C29—22no—
57C2×SD16×C29—22no—
58C2×SD16×C29—44no—
59C2×D8×C29—22no—
60C2×D8×C29—22no—
61C22×C8×C29—21no—
62C29×C4⋊Q8C2311yescharacteristic
63C29×#127—21no—
64C29×#127—21no—
65C29×#127—21no—
66C29×#127C2312yes—
67C29×#127C2311yescharacteristic
68C29×#124—21no—
69C29×#121—21no—
70C29×#121—21no—
71C4×Q8×C29—21no—
72C4×Q8×C29—21no—
73C4×Q8×C29D411yescharacteristic
74C4×Q8×C29D411yescharacteristic
75C4×Q8×C29C2311yescharacteristic
76C4×Q8×C29C2311yescharacteristic
77C4×D4×C29—21no—
78C4×D4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29D411yescharacteristic
81C2×C42×C29—21no—
82C2×C42×C29C2311yescharacteristic
83C29×#107—21no—
84C29×#107—21no—
85C29×C4⋊C8—22no—
86C29×C4⋊C8—22no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8D412yes—
89C29×C4⋊C8C2312yes—
90C29×C4⋊C8C2311yescharacteristic
91C29×C4⋊C8C2311yescharacteristic
92C29×C4⋊C8C2312yes—
93C29×#103—21no—
94C29×#103—21no—
95C29×#102—22no—
96C29×#102—22no—
97C29×#102—21no—
98C29×#102—21no—
99C29×#102—22no—
100C29×#102—22no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—21no—
103C29×C22⋊C8D411yescharacteristic
104C29×C22⋊C8D411yescharacteristic
105C29×#97—22no—
106C29×#97—21no—
107C29×#97—21no—
108C4×C8×C29—22no—
109C4×C8×C29C2312yes—
110C24×C29—41no—
111#41×C29—82no—
112C2×Q8×C29—21no—
113C2×Q8×C29—22no—
114C2×Q8×C29—21no—
115C2×Q8×C29—41no—
116C2×Q8×C29C2×D411yescharacteristic
117C2×Q8×C29C2×D411yescharacteristic
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—22no—
121C2×D4×C29—22no—
122C2×D4×C29—21no—
123C2×D4×C29—22no—
124C2×D4×C29—42no—
125C2×D4×C29—42no—
126C2×D4×C29—41no—
127C2×D4×C29—41no—
128C2×D4×C29—41no—
129C2×D4×C29—41no—
130C2×D4×C29—82no—
131C2×D4×C29—82no—
132C22×C4×C29—21no—
133C22×C4×C29—21no—
134C22×C4×C29—41no—
135C22×C4×C29C2×D411yescharacteristic
136C22×C4×C29C2×D411yescharacteristic
137C22×C4×C29#4111yescharacteristic
138SD16×C29—42no—
139SD16×C29—44no—
140SD16×C29—42no—
141SD16×C29—44no—
142D8×C29—82no—
143D8×C29—82no—
144C2×C8×C29—22no—
145C2×C8×C29—21no—
146C2×C8×C29—21no—
147C2×C8×C29—22no—
148C2×C8×C29—42no—
149C2×C8×C29C2×D412yes—
150C2×C8×C29C2×D412yes—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—21no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29C2×D411yescharacteristic
159C4⋊C4×C29C2×D411yescharacteristic
160C22⋊C4×C29—41no—
161C22⋊C4×C29—41no—
162C42×C29—21no—
163C42×C29—21no—
164C42×C29—21no—
165C42×C29—21no—
166C42×C29C2×D411yescharacteristic
167C42×C29C2×D411yescharacteristic
168C42×C29#4111yescharacteristic
169C42×C29C2411yescharacteristic
170#19470C2911yesmaximal, characteristic, direct product factor, Sylow
171C23×C29—41no—
172C23×C29—42no—
173C23×C29—82no—
174C23×C29—82no—
175C23×C29—82no—
176C23×C29#12111yescharacteristic
177Q8×C29—21no—
178Q8×C29—21no—
179Q8×C29—21no—
180Q8×C29—42no—
181Q8×C29—81no—
182Q8×C29AGL(1,ℤ/8)12yes—
183D4×C29—42no—
184D4×C29—41no—
185D4×C29—41no—
186D4×C29—42no—
187D4×C29—42no—
188D4×C29—42no—
189D4×C29—42no—
190D4×C29—82no—
191D4×C29—81no—
192D4×C29—82no—
193D4×C29—82no—
194D4×C29—82no—
195D4×C29—82no—
196C2×C4×C29—21no—
197C2×C4×C29—22no—
198C2×C4×C29—21no—
199C2×C4×C29—21no—
200C2×C4×C29—22no—
201C2×C4×C29—21no—
202C2×C4×C29—21no—
203C2×C4×C29—21no—
204C2×C4×C29—42no—
205C2×C4×C29—42no—
206C2×C4×C29—41no—
207C2×C4×C29—82no—
208C2×C4×C29#12111yescharacteristic
209C2×C4×C29#12111yescharacteristic
210C2×C4×C29#12111yescharacteristic
211C2×C4×C29C22×D411yescharacteristic
212C2×C4×C29C22×D411yescharacteristic
213C2×C4×C29C2×#4111yescharacteristic
214C8×C29—22no—
215C8×C29—22no—
216C8×C29—42no—
217C8×C29—41no—
218C8×C29—41no—
219C8×C29—42no—
220#3205C2×C2911yescharacteristic
221#3112C2×C2911yescharacteristic, complemented
222C2×#460C2×C2911yescharacteristic, complemented
223#2984C2×C2911yescharacteristic, complemented
224#1698C2×C2912yescomplemented
225#1688C2×C2912yescomplemented
226#1678C2×C2912yescomplemented
227#1668C2×C2912yescomplemented
228#1573C2×C2911yescharacteristic, complemented
229#1555C2×C2911yescharacteristic, complemented
230#1551C2×C2911yescharacteristic, complemented
231C22×C29—21no—
232C22×C29—21no—
233C22×C29—82no—
234C22×C29—81no—
235C22×C29—82no—
236C22×C29—81no—
237C22×C29—81no—
238C22×C29—82no—
239C22×C29—164no—
240C22×C29#47212yes—
241C22×C29C2×#12111yescharacteristic
242C4×C29—21no—
243C4×C29—21no—
244C4×C29—22no—
245C4×C29—21no—
246C4×C29—21no—
247C4×C29—41no—
248C4×C29—41no—
249C4×C29—41no—
250C4×C29—81no—
251C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C29#57511yescharacteristic
253C4×C29#57712yes—
254C22×SD16—21no—
255#532C22×C2911yescharacteristic
256C2×#127C22×C2911yescharacteristic
257C2×C4×Q8C22×C2911yescharacteristic
258#493C22×C2912yes—
259#486C22×C2912yes—
260#480—21no—
261#477C22×C2911yescharacteristic, complemented
262#477C22×C2911yescharacteristic, complemented
263#460—21no—
264#460—21no—
265#460C22×C2912yes—
266#460C22×C2912yes—
267#460C22×C2911yescharacteristic, complemented
268#460C22×C2911yescharacteristic, complemented
269#459—22no—
270#448—21no—
271#447—21no—
272#447—21no—
273#446—22no—
274#446C22×C2912yescomplemented
275C8×Q8C22×C2912yescomplemented
276#440—21no—
277#440—21no—
278#432—21no—
279#432C22×C2911yescharacteristic
280#432C22×C2911yescharacteristic
281#431—21no—
282#431C22×C2911yescharacteristic
283C2×C4⋊C8C22×C2911yescharacteristic
284C2×#102—21no—
285#335C22×C2912yescomplemented
286#334C22×C2912yescomplemented
287#333C22×C2912yescomplemented
288#331C22×C2912yes—
289#331C22×C2912yes—
290#331C22×C2912yescomplemented
291C2×C29—22no—
292C2×C29—161no—
293C2×C29—162no—
294C2×C29#304311yescharacteristic
295C2×C29#305511yescharacteristic
296C2×C29C2×#47211yescharacteristic
297C2×#41—21no—
298C22×Q8D4×C2911yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C2×SD16—22no—
303C2×SD16—22no—
304C2×SD16—21no—
305C2×SD16—21no—
306C2×SD16—44no—
307C2×D8—22no—
308C2×D8—22no—
309C22×C8—21no—
310C4⋊Q8C23×C2911yescharacteristic
311#127—21no—
312#127—21no—
313#127—21no—
314#127C23×C2912yes—
315#127C23×C2911yescharacteristic
316#124—21no—
317#121—21no—
318#121—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8D4×C2911yescharacteristic
322C4×Q8D4×C2911yescharacteristic
323C4×Q8C23×C2911yescharacteristic
324C4×Q8C23×C2911yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4D4×C2911yescharacteristic
329C2×C42—21no—
330C2×C42C23×C2911yescharacteristic
331#107—21no—
332#107—21no—
333C4⋊C8—22no—
334C4⋊C8—22no—
335C4⋊C8—21no—
336C4⋊C8D4×C2912yes—
337C4⋊C8C23×C2912yes—
338C4⋊C8C23×C2911yescharacteristic
339C4⋊C8C23×C2911yescharacteristic
340C4⋊C8C23×C2912yes—
341#103—21no—
342#103—21no—
343#102—22no—
344#102—22no—
345#102—22no—
346#102—22no—
347#102—21no—
348#102—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8D4×C2911yescharacteristic
352C22⋊C8D4×C2911yescharacteristic
353#97—22no—
354#97—21no—
355#97—21no—
356C4×C8—22no—
357C4×C8C23×C2912yes—
358C29#1947011yescharacteristic, direct product factor, Sylow
359C24—41no—
360#41—82no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—21no—
364C2×Q8—41no—
365C2×Q8C2×D4×C2911yescharacteristic
366C2×Q8C2×D4×C2911yescharacteristic
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—82no—
380C2×D4—82no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—41no—
384C22×C4C2×D4×C2911yescharacteristic
385C22×C4C2×D4×C2911yescharacteristic
386C22×C4#41×C2911yescharacteristic
387SD16—44no—
388SD16—42no—
389SD16—44no—
390SD16—42no—
391D8—82no—
392D8—82no—
393C2×C8—22no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—22no—
397C2×C8—42no—
398C2×C8C2×D4×C2912yes—
399C2×C8C2×D4×C2912yes—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4C2×D4×C2911yescharacteristic
408C4⋊C4C2×D4×C2911yescharacteristic
409C22⋊C4—41no—
410C22⋊C4—41no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42C2×D4×C2911yescharacteristic
416C42C2×D4×C2911yescharacteristic
417C42#41×C2911yescharacteristic
418C42C24×C2911yescharacteristic
419C23—41no—
420C23—42no—
421C23—82no—
422C23—82no—
423C23—82no—
424C23C29×#12111yescharacteristic
425Q8—21no—
426Q8—21no—
427Q8—21no—
428Q8—42no—
429Q8—81no—
430Q8C29×AGL(1,ℤ/8)12yes—
431D4—42no—
432D4—41no—
433D4—41no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—82no—
439D4—81no—
440D4—82no—
441D4—82no—
442D4—82no—
443D4—82no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—82no—
456C2×C4C29×#12111yescharacteristic
457C2×C4C29×#12111yescharacteristic
458C2×C4C29×#12111yescharacteristic
459C2×C4C22×D4×C2911yescharacteristic
460C2×C4C22×D4×C2911yescharacteristic
461C2×C4C2×#41×C2911yescharacteristic
462C8—22no—
463C8—22no—
464C8—42no—
465C8—41no—
466C8—41no—
467C8—42no—
468C22—21no—
469C22—21no—
470C22—82no—
471C22—81no—
472C22—82no—
473C22—81no—
474C22—81no—
475C22—82no—
476C22—164no—
477C22C29×#47212yes—
478C22C2×C29×#12111yescharacteristic
479C4—21no—
480C4—21no—
481C4—22no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—81no—
488C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
489C4C29×#57511yescharacteristic
490C4C29×#57712yes—
491C2—22no—
492C2—162no—
493C2—161no—
494C2C29×#304311yescharacteristic
495C2C29×#305511yescharacteristic
496C2C2×C29×#47211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3205C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3112C2semidirect
3. C2×C29×#460C2semidirect
4. C29×#2984C2semidirect
5. C29×#1698C2semidirect
6. C29×#1688C2semidirect
7. C29×#1678C2semidirect
8. C29×#1668C2semidirect
9. C29×#1573C2semidirect
10. C29×#1555C2semidirect
11. C29×#1551C2semidirect
19. C29×#477C22semidirect
20. C29×#477C22semidirect
25. C29×#460C22semidirect
26. C29×#460C22semidirect
32. C29×#446C22semidirect
33. C8×Q8×C29C22semidirect
43. C29×#335C22semidirect
44. C29×#334C22semidirect
45. C29×#333C22semidirect
48. C29×#331C22semidirect
170. #19470C29direct (N × H)
221. #3112C2×C29semidirect
222. C2×#460C2×C29semidirect
223. #2984C2×C29semidirect
224. #1698C2×C29semidirect
225. #1688C2×C29semidirect
226. #1678C2×C29semidirect
227. #1668C2×C29semidirect
228. #1573C2×C29semidirect
229. #1555C2×C29semidirect
230. #1551C2×C29semidirect
261. #477C22×C29semidirect
262. #477C22×C29semidirect
267. #460C22×C29semidirect
268. #460C22×C29semidirect
274. #446C22×C29semidirect
275. C8×Q8C22×C29semidirect
285. #335C22×C29semidirect
286. #334C22×C29semidirect
287. #333C22×C29semidirect
290. #331C22×C29semidirect
358. C29#19470direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32052
C29×#31122
C2×C29×#4602
C29×#29842
C29×#16982
C29×#16882
C29×#16782
C29×#16682
C29×#15732
C29×#15552
C29×#15512
#1947029