Finite Group Databasebeta

← C29×#19925 #20314825

Subgroups — C29×#19925 #20314825

Order 7424.

608 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3375C211yesmaximal, characteristic, complemented
2C29×#3362C211yesmaximal, characteristic, complemented
3C29×#3361C211yesmaximal, characteristic, complemented
4C29×#3333C211yesmaximal, characteristic, complemented
5C29×#1709C211yesmaximal, characteristic, complemented
6C29×#1698C211yesmaximal, characteristic, complemented
7C29×#1697C211yesmaximal, characteristic, complemented
8C29×#1678C211yesmaximal, characteristic, complemented
9C29×#1678C211yesmaximal, characteristic, complemented
10C29×#1633C211yesmaximal, characteristic, complemented
11C29×#1632C211yesmaximal, characteristic, complemented
12C29×#1621C211yesmaximal, characteristic
13C29×#1620C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×Q16×C29C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17Q82×C29C2211yescharacteristic
18C29×#554C2211yescharacteristic
19C29×#550C2211yescharacteristic
20C29×#494C2211yescharacteristic
21C29×#493C2211yescharacteristic
22C29×#489—21no—
23C29×#488—21no—
24C29×#486—21no—
25C29×#486C2211yescharacteristic
26C29×#486C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#480—21no—
30C29×#478—21no—
31C29×#477C2211yescharacteristic
32C29×#477C2211yescharacteristic
33C29×#477C2211yescharacteristic
34C29×#476—21no—
35C29×#476C2211yescharacteristic
36C29×#474—21no—
37C29×#468—21no—
38C29×#464—21no—
39C29×#463—21no—
40C29×#460—21no—
41C29×#460C2211yescharacteristic
42C29×#460C2211yescharacteristic
43C29×#460C2211yescharacteristic
44C29×#459C2211yescharacteristic
45C29×#452—21no—
46C29×#446C2211yescharacteristic
47C8×Q8×C29C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#440—21no—
50C4×Q16×C29C2211yescharacteristic
51C4×SD16×C29—21no—
52C4×SD16×C29C2211yescharacteristic
53C4×D8×C29—21no—
54C29×#436C2211yescharacteristic
55C29×#417—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#333C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#331C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×Q8⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×#41×C29—21no—
68C2×Q16×C29—41no—
69C2×Q16×C29D411yescharacteristic
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29D411yescharacteristic
74C2×D8×C29—21no—
75C2×D8×C29—41no—
76C2×M16×C29—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8—41no—
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×#127—21no—
83C29×#127C2311yescharacteristic
84C29×#127C2311yescharacteristic
85C29×#125—21no—
86C29×#124—21no—
87C29×#124—21no—
88C29×#123—41no—
89C29×C22⋊Q8—21no—
90C29×C22⋊Q8—41no—
91C29×#121—21no—
92C29×#121—41no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29C2311yescharacteristic
96C4×Q8×C29C2311yescharacteristic
97C4×Q8×C29C2311yescharacteristic
98C4×D4×C29—21no—
99C4×D4×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29C2311yescharacteristic
103C2×C4⋊C4×C29—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107D411yescharacteristic
108C29×#106—21no—
109C29×#106D411yescharacteristic
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8C2311yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×#103—21no—
118C29×#103—21no—
119C29×#103—21no—
120C29×#103D411yescharacteristic
121C29×#103D411yescharacteristic
122C29×#103D411yescharacteristic
123C29×#102—21no—
124C29×#102—21no—
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—21no—
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×#97—21no—
139C4×C8×C29—21no—
140C4×C8×C29—21no—
141C4×C8×C29C2311yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—42no—
145#41×C29—81no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—41no—
149C2×Q8×C29C2×D411yescharacteristic
150C2×Q8×C29C2×D411yescharacteristic
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—41no—
159C2×D4×C29—41no—
160C2×D4×C29C2×D411yescharacteristic
161C22×C4×C29—21no—
162C22×C4×C29—41no—
163C22×C4×C29—41no—
164C22×C4×C29—41no—
165Q16×C29—22no—
166Q16×C29—82no—
167SD16×C29—41no—
168SD16×C29—42no—
169SD16×C29—42no—
170SD16×C29—81no—
171D8×C29—42no—
172D8×C29—82no—
173M16×C29—81no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29C2×D411yescharacteristic
180C2×C8×C29C2×D411yescharacteristic
181C2×C8×C29C2×D411yescharacteristic
182C2×C8×C29C2×D411yescharacteristic
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C4⋊C4×C29C2×D411yescharacteristic
197C4⋊C4×C29C2×D411yescharacteristic
198C22⋊C4×C29—21no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—21no—
207C42×C29—41no—
208C42×C29C2411yescharacteristic
209#19925C2911yesmaximal, characteristic, direct product factor, Sylow
210C23×C29—21no—
211C23×C29—41no—
212C23×C29—41no—
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—21no—
217Q8×C29—21no—
218Q8×C29—81no—
219Q8×C29—81no—
220Q8×C29—161no—
221Q8×C29#13512yes—
222D4×C29—21no—
223D4×C29—21no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—82no—
233D4×C29—81no—
234D4×C29—81no—
235D4×C29—161no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—82no—
248C2×C4×C29—161no—
249C2×C4×C29—161no—
250C2×C4×C29C22×D411yescharacteristic
251C2×C4×C29C22×D411yescharacteristic
252C2×C4×C29H(5,𝔽2)11yescharacteristic
253C8×C29—22no—
254C8×C29—21no—
255C8×C29—21no—
256C8×C29—21no—
257C8×C29—21no—
258C8×C29—41no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262#3375C2×C2911yescharacteristic, complemented
263#3362C2×C2911yescharacteristic, complemented
264#3361C2×C2911yescharacteristic, complemented
265#3333C2×C2911yescharacteristic, complemented
266#1709C2×C2911yescharacteristic, complemented
267#1698C2×C2911yescharacteristic, complemented
268#1697C2×C2911yescharacteristic, complemented
269#1678C2×C2911yescharacteristic, complemented
270#1678C2×C2911yescharacteristic, complemented
271#1633C2×C2911yescharacteristic, complemented
272#1632C2×C2911yescharacteristic, complemented
273#1621C2×C2911yescharacteristic
274#1620C2×C2911yescharacteristic, complemented
275#1590C2×C2911yescharacteristic, complemented
276C8×Q16C2×C2911yescharacteristic, complemented
277C22×C29—41no—
278C22×C29—41no—
279C22×C29—41no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29—81no—
283C22×C29—81no—
284C22×C29—81no—
285C22×C29—81no—
286C22×C29D4211yescharacteristic
287C4×C29—22no—
288C4×C29—21no—
289C4×C29—41no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—81no—
296C4×C29—81no—
297C4×C29C2×#13511yescharacteristic
298C4×C29#57511yescharacteristic
299C4×C29#57711yescharacteristic
300C4×C29#57811yescharacteristic
301#559C22×C2911yescharacteristic
302Q82C22×C2911yescharacteristic
303#554C22×C2911yescharacteristic
304#550C22×C2911yescharacteristic
305#494C22×C2911yescharacteristic
306#493C22×C2911yescharacteristic
307#489—21no—
308#488—21no—
309#486—21no—
310#486C22×C2911yescharacteristic
311#486C22×C2911yescharacteristic
312#486C22×C2911yescharacteristic
313#486C22×C2911yescharacteristic
314#480—21no—
315#478—21no—
316#477C22×C2911yescharacteristic
317#477C22×C2911yescharacteristic
318#477C22×C2911yescharacteristic
319#476—21no—
320#476C22×C2911yescharacteristic
321#474—21no—
322#468—21no—
323#464—21no—
324#463—21no—
325#460—21no—
326#460C22×C2911yescharacteristic
327#460C22×C2911yescharacteristic
328#460C22×C2911yescharacteristic
329#459C22×C2911yescharacteristic
330#452—21no—
331#446C22×C2911yescharacteristic
332C8×Q8C22×C2911yescharacteristic
333C8×Q8C22×C2911yescharacteristic
334#440—21no—
335C4×Q16C22×C2911yescharacteristic
336C4×SD16—21no—
337C4×SD16C22×C2911yescharacteristic
338C4×D8—21no—
339#436C22×C2911yescharacteristic
340#417—21no—
341#335C22×C2911yescharacteristic
342#334C22×C2911yescharacteristic
343#333C22×C2911yescharacteristic
344#333C22×C2911yescharacteristic
345#331C22×C2911yescharacteristic
346#331C22×C2911yescharacteristic
347Q8⋊C8C22×C2911yescharacteristic
348Q8⋊C8C22×C2911yescharacteristic
349Q8⋊C8C22×C2911yescharacteristic
350D4⋊C8C22×C2911yescharacteristic
351C82C22×C2911yescharacteristic
352C2×C29—81no—
353C2×C29—161no—
354C2×C29—161no—
355C2×C29#327711yescharacteristic
356C2×C29#328211yescharacteristic
357C2×C29#329211yescharacteristic
358C2×#41—21no—
359C2×Q16—41no—
360C2×Q16D4×C2911yescharacteristic
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16D4×C2911yescharacteristic
365C2×D8—21no—
366C2×D8—41no—
367C2×M16—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—41no—
371C4⋊Q8C23×C2911yescharacteristic
372C4⋊Q8C23×C2911yescharacteristic
373#127—21no—
374#127C23×C2911yescharacteristic
375#127C23×C2911yescharacteristic
376#125—21no—
377#124—21no—
378#124—21no—
379#123—41no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382#121—21no—
383#121—41no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8C23×C2911yescharacteristic
387C4×Q8C23×C2911yescharacteristic
388C4×Q8C23×C2911yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C23×C2911yescharacteristic
394C2×C4⋊C4—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107D4×C2911yescharacteristic
399#106—21no—
400#106D4×C2911yescharacteristic
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C2911yescharacteristic
405C4⋊C8C23×C2911yescharacteristic
406C4⋊C8C23×C2911yescharacteristic
407C4⋊C8C23×C2911yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103D4×C2911yescharacteristic
412#103D4×C2911yescharacteristic
413#103D4×C2911yescharacteristic
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102D4×C2911yescharacteristic
428C22⋊C8—21no—
429#97—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8C23×C2911yescharacteristic
433C4×C8C23×C2911yescharacteristic
434C4×C8C23×C2911yescharacteristic
435C29#1992511yescharacteristic, direct product factor, Sylow
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8C2×D4×C2911yescharacteristic
442C2×Q8C2×D4×C2911yescharacteristic
443C2×Q8C2×D4×C2911yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×D4×C2911yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457Q16—22no—
458Q16—82no—
459SD16—41no—
460SD16—42no—
461SD16—42no—
462SD16—81no—
463D8—42no—
464D8—82no—
465M16—81no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×D4×C2911yescharacteristic
472C2×C8C2×D4×C2911yescharacteristic
473C2×C8C2×D4×C2911yescharacteristic
474C2×C8C2×D4×C2911yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C2911yescharacteristic
487C4⋊C4C2×D4×C2911yescharacteristic
488C4⋊C4C2×D4×C2911yescharacteristic
489C4⋊C4C2×D4×C2911yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42C24×C2911yescharacteristic
501C23—21no—
502C23—41no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—81no—
510Q8—81no—
511Q8—161no—
512Q8C29×#13512yes—
513D4—21no—
514D4—21no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—82no—
524D4—81no—
525D4—81no—
526D4—161no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—161no—
540C2×C4—161no—
541C2×C4C22×D4×C2911yescharacteristic
542C2×C4C22×D4×C2911yescharacteristic
543C2×C4C29×H(5,𝔽2)11yescharacteristic
544C8—22no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22D42×C2911yescharacteristic
563C4—22no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4C2×C29×#13511yescharacteristic
574C4C29×#57511yescharacteristic
575C4C29×#57711yescharacteristic
576C4C29×#57811yescharacteristic
577C2—81no—
578C2—161no—
579C2—161no—
580C2C29×#327711yescharacteristic
581C2C29×#328211yescharacteristic
582C2C29×#329211yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#1621C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3375C2semidirect
2. C29×#3362C2semidirect
3. C29×#3361C2semidirect
4. C29×#3333C2semidirect
5. C29×#1709C2semidirect
6. C29×#1698C2semidirect
7. C29×#1697C2semidirect
8. C29×#1678C2semidirect
9. C29×#1678C2semidirect
10. C29×#1633C2semidirect
11. C29×#1632C2semidirect
13. C29×#1620C2semidirect
14. C29×#1590C2semidirect
15. C8×Q16×C29C2semidirect
209. #19925C29direct (N × H)
262. #3375C2×C29semidirect
263. #3362C2×C29semidirect
264. #3361C2×C29semidirect
265. #3333C2×C29semidirect
266. #1709C2×C29semidirect
267. #1698C2×C29semidirect
268. #1697C2×C29semidirect
269. #1678C2×C29semidirect
270. #1678C2×C29semidirect
271. #1633C2×C29semidirect
272. #1632C2×C29semidirect
274. #1620C2×C29semidirect
275. #1590C2×C29semidirect
276. C8×Q16C2×C29semidirect
435. C29#19925direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33752
C29×#33622
C29×#33612
C29×#33332
C29×#17092
C29×#16982
C29×#16972
C29×#16782
C29×#16332
C29×#16322
C29×#16212
C29×#16202
C29×#15902
C8×Q16×C292
#1992529