Finite Group Databasebeta

← C29×#19963 #20314863

Subgroups — C29×#19963 #20314863

Order 7424.

608 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3399C211yesmaximal, characteristic
2C29×#3398C211yesmaximal, characteristic, complemented
3C29×#3365C211yesmaximal, characteristic, complemented
4C29×#3304C211yesmaximal, characteristic, complemented
5C29×#1709C211yesmaximal, characteristic, complemented
6C29×#1690C211yesmaximal, characteristic, complemented
7C29×#1688C211yesmaximal, characteristic, complemented
8C29×#1682C211yesmaximal, characteristic, complemented
9C29×#1681C211yesmaximal, characteristic, complemented
10C29×#1642C211yesmaximal, characteristic, complemented
11C29×#1640C211yesmaximal, characteristic, complemented
12C29×#1628C211yesmaximal, characteristic, complemented
13C29×#1626C211yesmaximal, characteristic, complemented
14C29×#1591C211yesmaximal, characteristic, complemented
15C8×SD16×C29C211yesmaximal, characteristic, complemented
16C29×#559C2211yescharacteristic
17C29×#557C2211yescharacteristic
18C29×#556C2211yescharacteristic
19C29×#550C2211yescharacteristic
20C29×#497—21no—
21C29×#496—21no—
22C29×#494C2211yescharacteristic
23C29×#493C2211yescharacteristic
24C29×#488—21no—
25C29×#486C2211yescharacteristic
26C29×#486C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#482—21no—
30C29×#478—21no—
31C29×#475C2211yescharacteristic
32C29×#475C2211yescharacteristic
33C29×#465—21no—
34C29×#464—21no—
35C29×#464—21no—
36C29×#463—21no—
37C29×#462—21no—
38C29×#462C2211yescharacteristic
39C29×#461C2211yescharacteristic
40C29×#460C2211yescharacteristic
41C29×#460C2211yescharacteristic
42C29×#460C2211yescharacteristic
43C29×#459—21no—
44C29×#459C2211yescharacteristic
45C29×#452—21no—
46C29×#446C2211yescharacteristic
47C29×#446C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#442—21no—
50C29×#441—21no—
51C4×Q16×C29C2211yescharacteristic
52C4×SD16×C29—21no—
53C4×SD16×C29C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C29×#416—21no—
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
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—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×Q16×C29D411yescharacteristic
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29D411yescharacteristic
77C2×D8×C29—21no—
78C2×D8×C29—21no—
79C2×D8×C29—21no—
80C22×C8×C29—21no—
81C29×C4⋊Q8—21no—
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×#127—21no—
85C29×#127C2311yescharacteristic
86C29×#127C2311yescharacteristic
87C29×#126—41no—
88C29×#125—21no—
89C29×#125—41no—
90C29×#124—21no—
91C29×#124—21no—
92C29×#124—21no—
93C29×#123—41no—
94C29×C22⋊Q8—21no—
95C29×#121—21no—
96C29×#121—41no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29—21no—
100C4×Q8×C29C2311yescharacteristic
101C4×Q8×C29C2311yescharacteristic
102C4×Q8×C29C2311yescharacteristic
103C4×D4×C29—21no—
104C4×D4×C29—21no—
105C4×D4×C29—21no—
106C4×D4×C29C2311yescharacteristic
107C29×#117—21no—
108C29×#107D411yescharacteristic
109C29×#106—21no—
110C29×#106—21no—
111C29×#106D411yescharacteristic
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—21no—
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103D411yescharacteristic
124C29×#103D411yescharacteristic
125C29×#103D411yescharacteristic
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—41no—
135C29×#102—41no—
136C29×#102D411yescharacteristic
137C29×C22⋊C8—21no—
138C29×#97—21no—
139C29×#97—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×C29C2×D411yescharacteristic
149C2×Q8×C29C2×D411yescharacteristic
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—41no—
158C2×D4×C29—41no—
159C2×D4×C29C2×D411yescharacteristic
160C22×C4×C29—21no—
161C22×C4×C29—41no—
162C22×C4×C29—41no—
163Q16×C29—41no—
164Q16×C29—42no—
165Q16×C29—81no—
166Q16×C29—81no—
167SD16×C29—22no—
168SD16×C29—42no—
169SD16×C29—81no—
170SD16×C29—81no—
171SD16×C29—81no—
172D8×C29—42no—
173D8×C29—81no—
174D8×C29—81no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—81no—
181C2×C8×C29C2×D411yescharacteristic
182C2×C8×C29C2×D411yescharacteristic
183C2×C8×C29C2×D411yescharacteristic
184C2×C8×C29C2×D411yescharacteristic
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29C2×D411yescharacteristic
197C4⋊C4×C29C2×D411yescharacteristic
198C4⋊C4×C29C2×D411yescharacteristic
199C4⋊C4×C29C2×D411yescharacteristic
200C22⋊C4×C29—21no—
201C22⋊C4×C29—41no—
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C42×C29—21no—
208C42×C29—21no—
209C42×C29—21no—
210C42×C29—41no—
211C42×C29—41no—
212C42×C29C2411yescharacteristic
213#19963C2911yesmaximal, characteristic, direct product factor, Sylow
214C23×C29—21no—
215C23×C29—41no—
216C23×C29—41no—
217Q8×C29—21no—
218Q8×C29—21no—
219Q8×C29—21no—
220Q8×C29—21no—
221Q8×C29—21no—
222Q8×C29—21no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227D4×C29—21no—
228D4×C29—21no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—41no—
236D4×C29—41no—
237D4×C29—81no—
238D4×C29—81no—
239D4×C29—82no—
240D4×C29—161no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—82no—
253C2×C4×C29—161no—
254C2×C4×C29C22×D411yescharacteristic
255C2×C4×C29C22×D411yescharacteristic
256C2×C4×C29H(5,𝔽2)11yescharacteristic
257C8×C29—21no—
258C8×C29—21no—
259C8×C29—21no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29—41no—
265C8×C29#13512yes—
266#3399C2×C2911yescharacteristic
267#3398C2×C2911yescharacteristic, complemented
268#3365C2×C2911yescharacteristic, complemented
269#3304C2×C2911yescharacteristic, complemented
270#1709C2×C2911yescharacteristic, complemented
271#1690C2×C2911yescharacteristic, complemented
272#1688C2×C2911yescharacteristic, complemented
273#1682C2×C2911yescharacteristic, complemented
274#1681C2×C2911yescharacteristic, complemented
275#1642C2×C2911yescharacteristic, complemented
276#1640C2×C2911yescharacteristic, complemented
277#1628C2×C2911yescharacteristic, complemented
278#1626C2×C2911yescharacteristic, complemented
279#1591C2×C2911yescharacteristic, complemented
280C8×SD16C2×C2911yescharacteristic, complemented
281C22×C29—41no—
282C22×C29—41no—
283C22×C29—41no—
284C22×C29—81no—
285C22×C29—81no—
286C22×C29—81no—
287C22×C29—81no—
288C22×C29—81no—
289C22×C29—81no—
290C22×C29D4211yescharacteristic
291C4×C29—21no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—41no—
296C4×C29—41no—
297C4×C29—41no—
298C4×C29—41no—
299C4×C29—81no—
300C4×C29—81no—
301C4×C29C2×#13511yescharacteristic
302C4×C29#57511yescharacteristic
303C4×C29#57611yescharacteristic
304C4×C29#57711yescharacteristic
305#559C22×C2911yescharacteristic
306#557C22×C2911yescharacteristic
307#556C22×C2911yescharacteristic
308#550C22×C2911yescharacteristic
309#497—21no—
310#496—21no—
311#494C22×C2911yescharacteristic
312#493C22×C2911yescharacteristic
313#488—21no—
314#486C22×C2911yescharacteristic
315#486C22×C2911yescharacteristic
316#486C22×C2911yescharacteristic
317#486C22×C2911yescharacteristic
318#482—21no—
319#478—21no—
320#475C22×C2911yescharacteristic
321#475C22×C2911yescharacteristic
322#465—21no—
323#464—21no—
324#464—21no—
325#463—21no—
326#462—21no—
327#462C22×C2911yescharacteristic
328#461C22×C2911yescharacteristic
329#460C22×C2911yescharacteristic
330#460C22×C2911yescharacteristic
331#460C22×C2911yescharacteristic
332#459—21no—
333#459C22×C2911yescharacteristic
334#452—21no—
335#446C22×C2911yescharacteristic
336#446C22×C2911yescharacteristic
337C8×Q8C22×C2911yescharacteristic
338#442—21no—
339#441—21no—
340C4×Q16C22×C2911yescharacteristic
341C4×SD16—21no—
342C4×SD16C22×C2911yescharacteristic
343C8×D4C22×C2911yescharacteristic
344#416—21no—
345#335C22×C2911yescharacteristic
346#334C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#332C22×C2911yescharacteristic
349#331C22×C2911yescharacteristic
350#331C22×C2911yescharacteristic
351Q8⋊C8C22×C2911yescharacteristic
352Q8⋊C8C22×C2911yescharacteristic
353Q8⋊C8C22×C2911yescharacteristic
354D4⋊C8C22×C2911yescharacteristic
355C82C22×C2911yescharacteristic
356C2×C29—81no—
357C2×C29—161no—
358C2×C29—161no—
359C2×C29#327511yescharacteristic
360C2×C29#328711yescharacteristic
361C2×C29#329011yescharacteristic
362C2×#41—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16D4×C2911yescharacteristic
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16D4×C2911yescharacteristic
372C2×D8—21no—
373C2×D8—21no—
374C2×D8—21no—
375C22×C8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C2911yescharacteristic
378C4⋊Q8C23×C2911yescharacteristic
379#127—21no—
380#127C23×C2911yescharacteristic
381#127C23×C2911yescharacteristic
382#126—41no—
383#125—21no—
384#125—41no—
385#124—21no—
386#124—21no—
387#124—21no—
388#123—41no—
389C22⋊Q8—21no—
390#121—21no—
391#121—41no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8C23×C2911yescharacteristic
396C4×Q8C23×C2911yescharacteristic
397C4×Q8C23×C2911yescharacteristic
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4C23×C2911yescharacteristic
402#117—21no—
403#107D4×C2911yescharacteristic
404#106—21no—
405#106—21no—
406#106D4×C2911yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C2911yescharacteristic
411C4⋊C8C23×C2911yescharacteristic
412C4⋊C8C23×C2911yescharacteristic
413C4⋊C8C23×C2911yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103D4×C2911yescharacteristic
419#103D4×C2911yescharacteristic
420#103D4×C2911yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—41no—
430#102—41no—
431#102D4×C2911yescharacteristic
432C22⋊C8—21no—
433#97—21no—
434#97—21no—
435C4×C8—21no—
436C4×C8C23×C2911yescharacteristic
437C4×C8C23×C2911yescharacteristic
438C4×C8C23×C2911yescharacteristic
439C29#1996311yescharacteristic, direct product factor, Sylow
440#41—42no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×D4×C2911yescharacteristic
445C2×Q8C2×D4×C2911yescharacteristic
446C2×Q8C2×D4×C2911yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4C2×D4×C2911yescharacteristic
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—41no—
460Q16—42no—
461Q16—81no—
462Q16—81no—
463SD16—22no—
464SD16—42no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468D8—42no—
469D8—81no—
470D8—81no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8C2×D4×C2911yescharacteristic
478C2×C8C2×D4×C2911yescharacteristic
479C2×C8C2×D4×C2911yescharacteristic
480C2×C8C2×D4×C2911yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C2911yescharacteristic
493C4⋊C4C2×D4×C2911yescharacteristic
494C4⋊C4C2×D4×C2911yescharacteristic
495C4⋊C4C2×D4×C2911yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42C24×C2911yescharacteristic
509C23—21no—
510C23—41no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—81no—
533D4—81no—
534D4—82no—
535D4—161no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—161no—
549C2×C4C22×D4×C2911yescharacteristic
550C2×C4C22×D4×C2911yescharacteristic
551C2×C4C29×H(5,𝔽2)11yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8C29×#13512yes—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C2911yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4C2×C29×#13511yescharacteristic
582C4C29×#57511yescharacteristic
583C4C29×#57611yescharacteristic
584C4C29×#57711yescharacteristic
585C2—81no—
586C2—161no—
587C2—161no—
588C2C29×#327511yescharacteristic
589C2C29×#328711yescharacteristic
590C2C29×#329011yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3399C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3398C2semidirect
3. C29×#3365C2semidirect
4. C29×#3304C2semidirect
5. C29×#1709C2semidirect
6. C29×#1690C2semidirect
7. C29×#1688C2semidirect
8. C29×#1682C2semidirect
9. C29×#1681C2semidirect
10. C29×#1642C2semidirect
11. C29×#1640C2semidirect
12. C29×#1628C2semidirect
13. C29×#1626C2semidirect
14. C29×#1591C2semidirect
15. C8×SD16×C29C2semidirect
213. #19963C29direct (N × H)
267. #3398C2×C29semidirect
268. #3365C2×C29semidirect
269. #3304C2×C29semidirect
270. #1709C2×C29semidirect
271. #1690C2×C29semidirect
272. #1688C2×C29semidirect
273. #1682C2×C29semidirect
274. #1681C2×C29semidirect
275. #1642C2×C29semidirect
276. #1640C2×C29semidirect
277. #1628C2×C29semidirect
278. #1626C2×C29semidirect
279. #1591C2×C29semidirect
280. C8×SD16C2×C29semidirect
439. C29#19963direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33992
C29×#33982
C29×#33652
C29×#33042
C29×#17092
C29×#16902
C29×#16882
C29×#16822
C29×#16812
C29×#16422
C29×#16402
C29×#16282
C29×#16262
C29×#15912
C8×SD16×C292
#1996329