Finite Group Databasebeta

← C29×#19947 #20314847

Subgroups — C29×#19947 #20314847

Order 7424.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3399C211yesmaximal, characteristic, complemented
2C29×#3394C211yesmaximal, characteristic, complemented
3C29×#3353C211yesmaximal, characteristic, complemented
4C29×#3284C211yesmaximal, characteristic, complemented
5C29×#1706C211yesmaximal, characteristic, complemented
6C29×#1694C211yesmaximal, characteristic, complemented
7C29×#1687C211yesmaximal, characteristic, complemented
8C29×#1666C211yesmaximal, characteristic, complemented
9C29×#1665C211yesmaximal, characteristic, complemented
10C29×#1641C211yesmaximal, characteristic, complemented
11C29×#1640C211yesmaximal, characteristic, complemented
12C29×#1628C211yesmaximal, characteristic, complemented
13C29×#1625C211yesmaximal, characteristic, complemented
14C29×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C29C211yesmaximal, characteristic, complemented
16C2×C29×#135—21no—
17C29×#559C2211yescharacteristic
18C29×#556C2211yescharacteristic
19C29×#550C2211yescharacteristic
20C29×#547C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#496—21no—
23C29×#495—21no—
24C29×#493C2211yescharacteristic
25C29×#492C2211yescharacteristic
26C29×#492C2211yescharacteristic
27C29×#486C2211yescharacteristic
28C29×#486C2211yescharacteristic
29C29×#484—21no—
30C29×#482—21no—
31C29×#475C2211yescharacteristic
32C29×#474C2211yescharacteristic
33C29×#468—21no—
34C29×#465—21no—
35C29×#464—21no—
36C29×#463—21no—
37C29×#463—21no—
38C29×#462C2211yescharacteristic
39C29×#462C2211yescharacteristic
40C29×#460C2211yescharacteristic
41C29×#459—21no—
42C29×#459C2211yescharacteristic
43C29×#459C2211yescharacteristic
44C29×#459C2211yescharacteristic
45C29×#452—21no—
46C29×#449—21no—
47C29×#446C2211yescharacteristic
48C8×Q8×C29C2211yescharacteristic
49C29×#442—21no—
50C4×SD16×C29—21no—
51C4×SD16×C29C2211yescharacteristic
52C4×SD16×C29C2211yescharacteristic
53C29×#436C2211yescharacteristic
54C8×D4×C29C2211yescharacteristic
55C29×#428—21no—
56C29×#334C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#332C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#331C2211yescharacteristic
61C29×#331C2211yescharacteristic
62C29×Q8⋊C8C2211yescharacteristic
63C29×Q8⋊C8C2211yescharacteristic
64C29×D4⋊C8C2211yescharacteristic
65C29×D4⋊C8C2211yescharacteristic
66C82×C29C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C29×#135—44no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×SD16×C29D411yescharacteristic
78C2×SD16×C29D411yescharacteristic
79C2×D8×C29—21no—
80C2×D8×C29—21no—
81C2×D8×C29—21no—
82C2×D8×C29—21no—
83C2×D8×C29—21no—
84C2×M16×C29—21no—
85C22×C8×C29—21no—
86C29×C4⋊Q8C2311yescharacteristic
87C29×C4⋊Q8C2311yescharacteristic
88C29×#127—21no—
89C29×#127C2311yescharacteristic
90C29×#127C2311yescharacteristic
91C29×#126—41no—
92C29×#124—21no—
93C29×#124—21no—
94C29×#124—21no—
95C29×#123—41no—
96C29×#123—41no—
97C29×C22⋊Q8—21no—
98C29×C22⋊Q8—21no—
99C29×#121—21no—
100C29×#121—21no—
101C29×#121—41no—
102C4×Q8×C29—21no—
103C4×Q8×C29C2311yescharacteristic
104C4×Q8×C29C2311yescharacteristic
105C4×D4×C29—21no—
106C4×D4×C29—21no—
107C4×D4×C29—21no—
108C4×D4×C29C2311yescharacteristic
109C4×D4×C29C2311yescharacteristic
110C29×#117—21no—
111C2×C4⋊C4×C29—21no—
112C29×#107—21no—
113C29×#107—21no—
114C29×#107—21no—
115C29×#106—21no—
116C29×#106D411yescharacteristic
117C29×#106D411yescharacteristic
118C29×C4⋊C8—21no—
119C29×C4⋊C8—21no—
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×C4⋊C8C2311yescharacteristic
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103D411yescharacteristic
128C29×#103D411yescharacteristic
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—41no—
135C29×#102—41no—
136C29×#102D411yescharacteristic
137C29×#102D411yescharacteristic
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—42no—
147#41×C29—81no—
148#41×C29—81no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×Q8×C29C2×D411yescharacteristic
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—41no—
160C2×D4×C29—41no—
161C2×D4×C29—41no—
162C2×D4×C29C2×D411yescharacteristic
163C2×D4×C29C2×D411yescharacteristic
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—41no—
167C22×C4×C29—41no—
168C22×C4×C29—41no—
169Q16×C29—42no—
170Q16×C29—81no—
171SD16×C29—22no—
172SD16×C29—22no—
173SD16×C29—42no—
174SD16×C29—42no—
175SD16×C29—81no—
176SD16×C29—81no—
177SD16×C29—81no—
178D8×C29—42no—
179D8×C29—42no—
180D8×C29—81no—
181D8×C29—81no—
182D8×C29—81no—
183M16×C29—42no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—42no—
190C2×C8×C29C2×D411yescharacteristic
191C2×C8×C29C2×D411yescharacteristic
192C2×C8×C29C2×D411yescharacteristic
193C2×C8×C29C2×D411yescharacteristic
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—41no—
201C4⋊C4×C29—41no—
202C4⋊C4×C29C2×D411yescharacteristic
203C4⋊C4×C29C2×D411yescharacteristic
204C4⋊C4×C29C2×D411yescharacteristic
205C4⋊C4×C29C2×D411yescharacteristic
206C22⋊C4×C29—21no—
207C22⋊C4×C29—21no—
208C22⋊C4×C29—41no—
209C22⋊C4×C29—41no—
210C22⋊C4×C29—41no—
211C22⋊C4×C29—41no—
212C22⋊C4×C29—41no—
213C22⋊C4×C29—41no—
214C22⋊C4×C29—41no—
215C42×C29—21no—
216C42×C29—21no—
217C42×C29—41no—
218C42×C29C2411yescharacteristic
219#19947C2911yesmaximal, characteristic, direct product factor, Sylow
220C23×C29—21no—
221C23×C29—21no—
222C23×C29—41no—
223C23×C29—41no—
224Q8×C29—21no—
225Q8×C29—21no—
226Q8×C29—21no—
227Q8×C29—21no—
228Q8×C29—41no—
229Q8×C29—41no—
230Q8×C29—41no—
231Q8×C29—41no—
232D4×C29—21no—
233D4×C29—21no—
234D4×C29—21no—
235D4×C29—21no—
236D4×C29—41no—
237D4×C29—41no—
238D4×C29—41no—
239D4×C29—41no—
240D4×C29—41no—
241D4×C29—41no—
242D4×C29—41no—
243D4×C29—41no—
244D4×C29—81no—
245D4×C29—81no—
246D4×C29—82no—
247D4×C29—82no—
248D4×C29—161no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—82no—
262C2×C4×C29—82no—
263C2×C4×C29—161no—
264C2×C4×C29C22×D411yescharacteristic
265C2×C4×C29C22×D411yescharacteristic
266C2×C4×C29H(5,𝔽2)11yescharacteristic
267C8×C29—21no—
268C8×C29—21no—
269C8×C29—41no—
270C8×C29—41no—
271C8×C29—41no—
272C8×C29—41no—
273C8×C29—41no—
274C8×C29#13512yescomplemented
275C8×C29AGL(1,ℤ/8)12yes—
276#3399C2×C2911yescharacteristic, complemented
277#3394C2×C2911yescharacteristic, complemented
278#3353C2×C2911yescharacteristic, complemented
279#3284C2×C2911yescharacteristic, complemented
280#1706C2×C2911yescharacteristic, complemented
281#1694C2×C2911yescharacteristic, complemented
282#1687C2×C2911yescharacteristic, complemented
283#1666C2×C2911yescharacteristic, complemented
284#1665C2×C2911yescharacteristic, complemented
285#1641C2×C2911yescharacteristic, complemented
286#1640C2×C2911yescharacteristic, complemented
287#1628C2×C2911yescharacteristic, complemented
288#1625C2×C2911yescharacteristic, complemented
289#1590C2×C2911yescharacteristic, complemented
290C8×SD16C2×C2911yescharacteristic, complemented
291C22×C29—41no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—81no—
298C22×C29—81no—
299C22×C29—81no—
300C22×C29—81no—
301C22×C29—81no—
302C22×C29—81no—
303C22×C29D4211yescharacteristic
304C4×C29—21no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—41no—
308C4×C29—41no—
309C4×C29—41no—
310C4×C29—41no—
311C4×C29—81no—
312C4×C29—81no—
313C4×C29C2×#13511yescharacteristic
314C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
315C4×C29#57611yescharacteristic
316C4×C29#57711yescharacteristic
317C2×#135—21no—
318#559C22×C2911yescharacteristic
319#556C22×C2911yescharacteristic
320#550C22×C2911yescharacteristic
321#547C22×C2911yescharacteristic
322#500C22×C2911yescharacteristic
323#496—21no—
324#495—21no—
325#493C22×C2911yescharacteristic
326#492C22×C2911yescharacteristic
327#492C22×C2911yescharacteristic
328#486C22×C2911yescharacteristic
329#486C22×C2911yescharacteristic
330#484—21no—
331#482—21no—
332#475C22×C2911yescharacteristic
333#474C22×C2911yescharacteristic
334#468—21no—
335#465—21no—
336#464—21no—
337#463—21no—
338#463—21no—
339#462C22×C2911yescharacteristic
340#462C22×C2911yescharacteristic
341#460C22×C2911yescharacteristic
342#459—21no—
343#459C22×C2911yescharacteristic
344#459C22×C2911yescharacteristic
345#459C22×C2911yescharacteristic
346#452—21no—
347#449—21no—
348#446C22×C2911yescharacteristic
349C8×Q8C22×C2911yescharacteristic
350#442—21no—
351C4×SD16—21no—
352C4×SD16C22×C2911yescharacteristic
353C4×SD16C22×C2911yescharacteristic
354#436C22×C2911yescharacteristic
355C8×D4C22×C2911yescharacteristic
356#428—21no—
357#334C22×C2911yescharacteristic
358#334C22×C2911yescharacteristic
359#332C22×C2911yescharacteristic
360#332C22×C2911yescharacteristic
361#331C22×C2911yescharacteristic
362#331C22×C2911yescharacteristic
363Q8⋊C8C22×C2911yescharacteristic
364Q8⋊C8C22×C2911yescharacteristic
365D4⋊C8C22×C2911yescharacteristic
366D4⋊C8C22×C2911yescharacteristic
367C82C22×C2911yescharacteristic
368C2×C29—81no—
369C2×C29—81no—
370C2×C29—161no—
371C2×C29—161no—
372C2×C29#327411yescharacteristic
373C2×C29#328411yescharacteristic
374C2×C29#329011yescharacteristic
375C2×#41—21no—
376C2×#41—21no—
377#135—44no—
378C2×Q16—21no—
379C2×Q16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16D4×C2911yescharacteristic
386C2×SD16D4×C2911yescharacteristic
387C2×D8—21no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×M16—21no—
393C22×C8—21no—
394C4⋊Q8C23×C2911yescharacteristic
395C4⋊Q8C23×C2911yescharacteristic
396#127—21no—
397#127C23×C2911yescharacteristic
398#127C23×C2911yescharacteristic
399#126—41no—
400#124—21no—
401#124—21no—
402#124—21no—
403#123—41no—
404#123—41no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407#121—21no—
408#121—21no—
409#121—41no—
410C4×Q8—21no—
411C4×Q8C23×C2911yescharacteristic
412C4×Q8C23×C2911yescharacteristic
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4C23×C2911yescharacteristic
417C4×D4C23×C2911yescharacteristic
418#117—21no—
419C2×C4⋊C4—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#106—21no—
424#106D4×C2911yescharacteristic
425#106D4×C2911yescharacteristic
426C4⋊C8—21no—
427C4⋊C8—21no—
428C4⋊C8C23×C2911yescharacteristic
429C4⋊C8C23×C2911yescharacteristic
430C4⋊C8C23×C2911yescharacteristic
431C4⋊C8C23×C2911yescharacteristic
432#103—21no—
433#103—21no—
434#103—21no—
435#103D4×C2911yescharacteristic
436#103D4×C2911yescharacteristic
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102—41no—
444#102D4×C2911yescharacteristic
445#102D4×C2911yescharacteristic
446C22⋊C8—21no—
447C22⋊C8—21no—
448#97—21no—
449C4×C8—21no—
450C4×C8C23×C2911yescharacteristic
451C4×C8C23×C2911yescharacteristic
452C4×C8C23×C2911yescharacteristic
453C29#1994711yescharacteristic, direct product factor, Sylow
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C2911yescharacteristic
461C2×Q8C2×D4×C2911yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C2×D4×C2911yescharacteristic
472C2×D4C2×D4×C2911yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478Q16—42no—
479Q16—81no—
480SD16—22no—
481SD16—22no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487D8—42no—
488D8—42no—
489D8—81no—
490D8—81no—
491D8—81no—
492M16—42no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—42no—
499C2×C8C2×D4×C2911yescharacteristic
500C2×C8C2×D4×C2911yescharacteristic
501C2×C8C2×D4×C2911yescharacteristic
502C2×C8C2×D4×C2911yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C2911yescharacteristic
512C4⋊C4C2×D4×C2911yescharacteristic
513C4⋊C4C2×D4×C2911yescharacteristic
514C4⋊C4C2×D4×C2911yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C42—21no—
525C42—21no—
526C42—41no—
527C42C24×C2911yescharacteristic
528C23—21no—
529C23—21no—
530C23—41no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—81no—
553D4—81no—
554D4—82no—
555D4—82no—
556D4—161no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—161no—
572C2×C4C22×D4×C2911yescharacteristic
573C2×C4C22×D4×C2911yescharacteristic
574C2×C4C29×H(5,𝔽2)11yescharacteristic
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8C29×#13512yescomplemented
583C8C29×AGL(1,ℤ/8)12yes—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C2911yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4C2×C29×#13511yescharacteristic
607C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
608C4C29×#57611yescharacteristic
609C4C29×#57711yescharacteristic
610C2—81no—
611C2—81no—
612C2—161no—
613C2—161no—
614C2C29×#327411yescharacteristic
615C2C29×#328411yescharacteristic
616C2C29×#329011yescharacteristic
subgroupG/H
center, socleC22×C29D42
commutator, Frattini, cosocleC42C24×C29
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×#3399C2semidirect
2. C29×#3394C2semidirect
3. C29×#3353C2semidirect
4. C29×#3284C2semidirect
5. C29×#1706C2semidirect
6. C29×#1694C2semidirect
7. C29×#1687C2semidirect
8. C29×#1666C2semidirect
9. C29×#1665C2semidirect
10. C29×#1641C2semidirect
11. C29×#1640C2semidirect
12. C29×#1628C2semidirect
13. C29×#1625C2semidirect
14. C29×#1590C2semidirect
15. C8×SD16×C29C2semidirect
219. #19947C29direct (N × H)
274. C8×C29#135semidirect
276. #3399C2×C29semidirect
277. #3394C2×C29semidirect
278. #3353C2×C29semidirect
279. #3284C2×C29semidirect
280. #1706C2×C29semidirect
281. #1694C2×C29semidirect
282. #1687C2×C29semidirect
283. #1666C2×C29semidirect
284. #1665C2×C29semidirect
285. #1641C2×C29semidirect
286. #1640C2×C29semidirect
287. #1628C2×C29semidirect
288. #1625C2×C29semidirect
289. #1590C2×C29semidirect
290. C8×SD16C2×C29semidirect
453. C29#19947direct (N × H)
582. C8C29×#135semidirect

Maximal subgroups

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

subgroupindex
C29×#33992
C29×#33942
C29×#33532
C29×#32842
C29×#17062
C29×#16942
C29×#16872
C29×#16662
C29×#16652
C29×#16412
C29×#16402
C29×#16282
C29×#16252
C29×#15902
C8×SD16×C292
#1994729