Finite Group Databasebeta

← C29×#19031 #20313931

Subgroups — C29×#19031 #20313931

Order 7424.

834 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3563C211yesmaximal, characteristic, complemented
2C29×#3235C211yesmaximal, characteristic, complemented
3C29×#3171C211yesmaximal, characteristic
4C29×#3142C211yesmaximal, characteristic, complemented
5C29×#1664C212yesmaximal, complemented
6C29×#1663C212yesmaximal, complemented
7C29×#1658C212yesmaximal, complemented
8C29×#1657C212yesmaximal, complemented
9C29×#1529C211yesmaximal, characteristic, complemented
10C29×#1528C211yesmaximal, characteristic, complemented
11C29×#1526C211yesmaximal, characteristic, complemented
12C29×#564C2212yes—
13C29×#563C2212yes—
14C29×#557—21no—
15C29×#554—21no—
16C29×#552—21no—
17C29×#552—22no—
18C29×#552—21no—
19C29×#544—21no—
20C29×#544—21no—
21C29×#541—21no—
22C29×#541—22no—
23C29×#539—21no—
24C29×#533C2211yescharacteristic
25C29×#532C2211yescharacteristic
26C29×#529C2211yescharacteristic
27C2×C29×#125C2211yescharacteristic
28C29×#501C2211yescharacteristic
29C29×#501C2212yes—
30C29×#496C2211yescharacteristic
31C29×#491C2212yes—
32C29×#490C2212yes—
33C29×#490C2212yes—
34C29×#490C2211yescharacteristic
35C29×#489C2211yescharacteristic
36C29×#488—22no—
37C29×#482—22no—
38C29×#476—21no—
39C29×#474—21no—
40C29×#469—21no—
41C29×#468—21no—
42C4×SD16×C29—21no—
43C4×D8×C29—21no—
44C29×#432C2211yescharacteristic
45C29×#417—21no—
46C29×#417—21no—
47C4×M16×C29C2211yescharacteristic
48C4×M16×C29C2211yescharacteristic
49C29×#330C2212yes—
50C29×#330C2212yes—
51C29×#330C2212yes—
52C29×#330C2212yes—
53C29×#330C2212yes—
54C29×#329C2212yes—
55C2×#41×C29—21no—
56C2×SD16×C29—21no—
57C2×D8×C29—21no—
58C2×M16×C29—21no—
59C2×M16×C29—21no—
60C29×C4⋊Q8—22no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—22no—
63C29×C4⋊Q8D411yescharacteristic
64C29×C4⋊Q8D411yescharacteristic
65C29×C4⋊Q8C2311yescharacteristic
66C29×#127C2311yescharacteristic
67C29×#126—22no—
68C29×#126—22no—
69C29×#126—22no—
70C29×#126—22no—
71C29×#126—21no—
72C29×#125—22no—
73C29×#125—22no—
74C29×#125—21no—
75C29×#125—22no—
76C29×#125—22no—
77C29×#125—22no—
78C29×#125—22no—
79C29×#125—22no—
80C29×#125—22no—
81C29×#125—21no—
82C29×#125—21no—
83C29×#125D412yes—
84C29×#125C2312yes—
85C29×#125C2311yescharacteristic
86C29×#125C2312yes—
87C29×#124—21no—
88C29×#124C2311yescharacteristic
89C29×#123—22no—
90C29×#123—22no—
91C29×#123—21no—
92C29×C22⋊Q8—22no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—21no—
95C29×C22⋊Q8—22no—
96C29×C22⋊Q8—21no—
97C29×C22⋊Q8—21no—
98C29×C22⋊Q8—22no—
99C29×C22⋊Q8—22no—
100C29×C22⋊Q8D411yescharacteristic
101C29×#121—21no—
102C29×#121—21no—
103C29×#121D411yescharacteristic
104C4×Q8×C29—21no—
105C4×Q8×C29—22no—
106C4×Q8×C29—21no—
107C4×Q8×C29—21no—
108C4×Q8×C29—21no—
109C4×Q8×C29D411yescharacteristic
110C4×D4×C29—22no—
111C4×D4×C29—21no—
112C4×D4×C29—21no—
113C4×D4×C29—21no—
114C4×D4×C29D411yescharacteristic
115C29×#117—22no—
116C29×#117—21no—
117C29×#117—22no—
118C29×#117—21no—
119C29×#117D412yes—
120C2×C4⋊C4×C29—21no—
121C2×C4⋊C4×C29—21no—
122C2×C4⋊C4×C29—21no—
123C2×C4⋊C4×C29D411yescharacteristic
124C2×C4⋊C4×C29D411yescharacteristic
125C2×C42×C29C2311yescharacteristic
126C29×#107—21no—
127C29×#107—22no—
128C29×#106—21no—
129C29×#106—22no—
130C29×C4⋊C8—21no—
131C29×#103—21no—
132C29×#103—22no—
133C29×#103—22no—
134C29×#102—21no—
135C29×#102—21no—
136C29×#102—21no—
137C29×#102—22no—
138C29×#102—22no—
139C29×#102—22no—
140C29×#102—22no—
141C29×C22⋊C8—21no—
142C29×#97C2312yes—
143C29×#97C2311yescharacteristic
144C29×#97C2312yes—
145C29×#97C2311yescharacteristic
146C4×C8×C29—21no—
147C4×C8×C29—21no—
148#41×C29—44no—
149C2×Q8×C29—22no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
153C2×Q8×C29C2×D411yescharacteristic
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—41no—
159C2×D4×C29C2×D411yescharacteristic
160C22×C4×C29—21no—
161C22×C4×C29—22no—
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—41no—
165C22×C4×C29C2×D411yescharacteristic
166C22×C4×C29C2×D411yescharacteristic
167C22×C4×C29C2×D411yescharacteristic
168SD16×C29—42no—
169D8×C29—42no—
170M16×C29—42no—
171M16×C29—42no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—22no—
175C2×C8×C29—22no—
176C4⋊C4×C29—22no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—22no—
180C4⋊C4×C29—22no—
181C4⋊C4×C29—22no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—22no—
193C4⋊C4×C29—22no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—22no—
197C4⋊C4×C29—22no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29C2×D412yes—
201C4⋊C4×C29C2×D412yes—
202C4⋊C4×C29C2×D412yes—
203C4⋊C4×C29C2×D412yes—
204C4⋊C4×C29C2×D411yescharacteristic
205C4⋊C4×C29C2×D411yescharacteristic
206C22⋊C4×C29—22no—
207C22⋊C4×C29—22no—
208C22⋊C4×C29—22no—
209C22⋊C4×C29—21no—
210C22⋊C4×C29—22no—
211C22⋊C4×C29—21no—
212C22⋊C4×C29—21no—
213C22⋊C4×C29—21no—
214C22⋊C4×C29—21no—
215C22⋊C4×C29—41no—
216C22⋊C4×C29—41no—
217C42×C29—22no—
218C42×C29—22no—
219C42×C29—22no—
220C42×C29—22no—
221C42×C29—21no—
222C42×C29C2×D411yescharacteristic
223C42×C29C2×D411yescharacteristic
224C42×C29C2×D411yescharacteristic
225C42×C29C2411yescharacteristic
226#19031C2911yesmaximal, characteristic, direct product factor, Sylow
227C23×C29—21no—
228C23×C29—41no—
229C23×C29#12011yescharacteristic
230Q8×C29—41no—
231Q8×C29—42no—
232Q8×C29—42no—
233Q8×C29—81no—
234Q8×C29—82no—
235D4×C29—41no—
236D4×C29—41no—
237D4×C29—41no—
238D4×C29—42no—
239D4×C29—42no—
240D4×C29—42no—
241D4×C29—82no—
242C2×C4×C29—22no—
243C2×C4×C29—22no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—22no—
248C2×C4×C29—22no—
249C2×C4×C29—22no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—42no—
253C2×C4×C29—42no—
254C2×C4×C29—41no—
255C2×C4×C29—81no—
256C2×C4×C29—82no—
257C2×C4×C29—82no—
258C2×C4×C29#12011yescharacteristic
259C2×C4×C29#12011yescharacteristic
260C2×C4×C29#12011yescharacteristic
261C2×C4×C29C22×D411yescharacteristic
262C2×C4×C29C22×D411yescharacteristic
263C2×C4×C29C22×D411yescharacteristic
264C8×C29—22no—
265C8×C29—42no—
266C8×C29—42no—
267C8×C29—41no—
268#3563C2×C2911yescharacteristic, complemented
269#3235C2×C2911yescharacteristic, complemented
270#3171C2×C2911yescharacteristic
271#3142C2×C2911yescharacteristic, complemented
272#1664C2×C2912yescomplemented
273#1663C2×C2912yescomplemented
274#1658C2×C2912yescomplemented
275#1657C2×C2912yescomplemented
276#1529C2×C2911yescharacteristic, complemented
277#1528C2×C2911yescharacteristic, complemented
278#1526C2×C2911yescharacteristic, complemented
279C22×C29—21no—
280C22×C29—21no—
281C22×C29—21no—
282C22×C29—41no—
283C22×C29—41no—
284C22×C29—41no—
285C22×C29—81no—
286C22×C29—81no—
287C22×C29—81no—
288C22×C29C2×#12011yescharacteristic
289C4×C29—21no—
290C4×C29—21no—
291C4×C29—21no—
292C4×C29—21no—
293C4×C29—21no—
294C4×C29—41no—
295C4×C29—42no—
296C4×C29—42no—
297C4×C29—42no—
298C4×C29—41no—
299C4×C29—42no—
300C4×C29—41no—
301C4×C29—81no—
302C4×C29#45412yes—
303#564C22×C2912yes—
304#563C22×C2912yes—
305#557—21no—
306#554—21no—
307#552—21no—
308#552—22no—
309#552—21no—
310#544—21no—
311#544—21no—
312#541—21no—
313#541—22no—
314#539—21no—
315#533C22×C2911yescharacteristic
316#532C22×C2911yescharacteristic
317#529C22×C2911yescharacteristic
318C2×#125C22×C2911yescharacteristic
319#501C22×C2911yescharacteristic
320#501C22×C2912yes—
321#496C22×C2911yescharacteristic
322#491C22×C2912yes—
323#490C22×C2912yes—
324#490C22×C2911yescharacteristic
325#490C22×C2912yes—
326#489C22×C2911yescharacteristic
327#488—22no—
328#482—22no—
329#476—21no—
330#474—21no—
331#469—21no—
332#468—21no—
333C4×SD16—21no—
334C4×D8—21no—
335#432C22×C2911yescharacteristic
336#417—21no—
337#417—21no—
338C4×M16C22×C2911yescharacteristic
339C4×M16C22×C2911yescharacteristic
340#330C22×C2912yes—
341#330C22×C2912yes—
342#330C22×C2912yes—
343#330C22×C2912yes—
344#330C22×C2912yes—
345#329C22×C2912yes—
346C2×C29—41no—
347C2×C29—81no—
348C2×C29—161no—
349C2×C29C2×#45411yescharacteristic
350C2×C29#301811yescharacteristic
351C2×C29#302011yescharacteristic
352C2×#41—21no—
353C2×SD16—21no—
354C2×D8—21no—
355C2×M16—21no—
356C2×M16—21no—
357C4⋊Q8—22no—
358C4⋊Q8—21no—
359C4⋊Q8—22no—
360C4⋊Q8D4×C2911yescharacteristic
361C4⋊Q8D4×C2911yescharacteristic
362C4⋊Q8C23×C2911yescharacteristic
363#127C23×C2911yescharacteristic
364#126—22no—
365#126—22no—
366#126—22no—
367#126—22no—
368#126—21no—
369#125—22no—
370#125—22no—
371#125—21no—
372#125—22no—
373#125—22no—
374#125—22no—
375#125—22no—
376#125—22no—
377#125—22no—
378#125—21no—
379#125—21no—
380#125D4×C2912yes—
381#125C23×C2912yes—
382#125C23×C2911yescharacteristic
383#125C23×C2912yes—
384#124—21no—
385#124C23×C2911yescharacteristic
386#123—22no—
387#123—22no—
388#123—21no—
389C22⋊Q8—22no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8D4×C2911yescharacteristic
398#121—21no—
399#121—21no—
400#121D4×C2911yescharacteristic
401C4×Q8—21no—
402C4×Q8—22no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8D4×C2911yescharacteristic
407C4×D4—22no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4D4×C2911yescharacteristic
412#117—22no—
413#117—21no—
414#117—22no—
415#117—21no—
416#117D4×C2912yes—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4D4×C2911yescharacteristic
421C2×C4⋊C4D4×C2911yescharacteristic
422C2×C42C23×C2911yescharacteristic
423#107—21no—
424#107—22no—
425#106—21no—
426#106—22no—
427C4⋊C8—21no—
428#103—21no—
429#103—22no—
430#103—22no—
431#102—21no—
432#102—22no—
433#102—22no—
434#102—21no—
435#102—21no—
436#102—22no—
437#102—22no—
438C22⋊C8—21no—
439#97C23×C2912yes—
440#97C23×C2912yes—
441#97C23×C2911yescharacteristic
442#97C23×C2911yescharacteristic
443C4×C8—21no—
444C4×C8—21no—
445C29#1903111yescharacteristic, direct product factor, Sylow
446#41—44no—
447C2×Q8—22no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×D4×C2911yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—41no—
457C2×D4C2×D4×C2911yescharacteristic
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4C2×D4×C2911yescharacteristic
464C22×C4C2×D4×C2911yescharacteristic
465C22×C4C2×D4×C2911yescharacteristic
466SD16—42no—
467D8—42no—
468M16—42no—
469M16—42no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—22no—
473C2×C8—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4C2×D4×C2912yes—
499C4⋊C4C2×D4×C2912yes—
500C4⋊C4C2×D4×C2912yes—
501C4⋊C4C2×D4×C2911yescharacteristic
502C4⋊C4C2×D4×C2912yes—
503C4⋊C4C2×D4×C2911yescharacteristic
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—22no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—22no—
516C42—22no—
517C42—22no—
518C42—22no—
519C42—21no—
520C42C2×D4×C2911yescharacteristic
521C42C2×D4×C2911yescharacteristic
522C42C2×D4×C2911yescharacteristic
523C42C24×C2911yescharacteristic
524C23—21no—
525C23—41no—
526C23C29×#12011yescharacteristic
527Q8—41no—
528Q8—42no—
529Q8—42no—
530Q8—81no—
531Q8—82no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—82no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—81no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4C29×#12011yescharacteristic
556C2×C4C29×#12011yescharacteristic
557C2×C4C29×#12011yescharacteristic
558C2×C4C22×D4×C2911yescharacteristic
559C2×C4C22×D4×C2911yescharacteristic
560C2×C4C22×D4×C2911yescharacteristic
561C8—22no—
562C8—42no—
563C8—41no—
564C8—42no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22C2×C29×#12011yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—41no—
581C4—42no—
582C4—42no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—81no—
588C4C29×#45412yes—
589C2—41no—
590C2—81no—
591C2—161no—
592C2C2×C29×#45411yescharacteristic
593C2C29×#301811yescharacteristic
594C2C29×#302011yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3171C2
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
1. C29×#3563C2semidirect
2. C29×#3235C2semidirect
4. C29×#3142C2semidirect
5. C29×#1664C2semidirect
6. C29×#1663C2semidirect
7. C29×#1658C2semidirect
8. C29×#1657C2semidirect
9. C29×#1529C2semidirect
10. C29×#1528C2semidirect
11. C29×#1526C2semidirect
226. #19031C29direct (N × H)
268. #3563C2×C29semidirect
269. #3235C2×C29semidirect
271. #3142C2×C29semidirect
272. #1664C2×C29semidirect
273. #1663C2×C29semidirect
274. #1658C2×C29semidirect
275. #1657C2×C29semidirect
276. #1529C2×C29semidirect
277. #1528C2×C29semidirect
278. #1526C2×C29semidirect
445. C29#19031direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35632
C29×#32352
C29×#31712
C29×#31422
C29×#16642
C29×#16632
C29×#16582
C29×#16572
C29×#15292
C29×#15282
C29×#15262
#1903129